diff --git a/research/complex-t16-evacuation-increment/CANDIDATE.json b/research/complex-t16-evacuation-increment/CANDIDATE.json
new file mode 100644
index 0000000000..d33c7388a4
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/CANDIDATE.json
@@ -0,0 +1,59 @@
+{
+  "claim_type": "conditional T16 owner-packing improvement",
+  "word_and_suppliers": "Fixed selected PR1094 word, gauge44 complex supplier, and unchanged PR589 bit supplier.",
+  "predecessor_kappa": "0.001673614205725695",
+  "expected_updates": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "complex_lower": "838212092705151621517/500000000000000000000000",
+    "conservative_complex_lower": "167642418254791971833/100000000000000000000000",
+    "kappa": "209202311361877/125000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 144
+    },
+    "mutations_rejected": 15,
+    "hosted_residuals": 69120,
+    "rank_mass": 1041408,
+    "actual_73column_sigmas": 10008,
+    "cross_replica_helper_roles": 57417,
+    "idle_remainders": 7394,
+    "idle_remainder_profile": {
+      "1": 2392,
+      "2": 8,
+      "3": 110,
+      "7": 2,
+      "16": 2,
+      "48": 4880
+    },
+    "global_profile": {
+      "1": 349720,
+      "2": 60200,
+      "3": 62318,
+      "4": 20448,
+      "5": 11808,
+      "7": 2,
+      "8": 1152,
+      "16": 2,
+      "48": 4880
+    },
+    "live": 14336,
+    "physical": 14826,
+    "conservative_kappa_decimal": "0.001673618488042206",
+    "kappa_decimal": "0.001673618490895016"
+  },
+  "changed_rows_vs_predecessor": 163,
+  "relocated_rows_vs_predecessor": 142,
+  "offset_only_rows_vs_predecessor": 21,
+  "search_status": "finite CP-SAT search best; no optimality claim",
+  "word_ceiling": {
+    "a_hi": "0.001690054109089",
+    "implied_kappa_ceiling": "0.0016872026453254019737168092357730518079784723022911",
+    "fraction_realized": "0.99194871198902958766575607143578602999758455859606",
+    "fraction_of_selected_to_ceiling_gap_closed": "0.0658963196377817987102974155083040295071362586"
+  },
+  "packing_ceiling": {
+    "max_empty_cap48_bins": 4887,
+    "surrogate_E_max": 908139.013,
+    "not_a_kappa_bound": true
+  }
+}
diff --git a/research/complex-t16-evacuation-increment/DIFF-vs-predecessor.json b/research/complex-t16-evacuation-increment/DIFF-vs-predecessor.json
new file mode 100644
index 0000000000..deef1cbefa
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/DIFF-vs-predecessor.json
@@ -0,0 +1,4729 @@
+[
+ {
+  "index": 60,
+  "before": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 60,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 0,
+   "stage": 0,
+   "time": 0,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 186,
+   "family": 1306,
+   "helper": 60,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 74,
+   "replica": 0,
+   "stage": 0,
+   "time": 0,
+   "width": 9
+  }
+ },
+ {
+  "index": 283,
+  "before": {
+   "child": 0,
+   "copy": 135,
+   "family": 1143,
+   "helper": 283,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 23,
+   "replica": 0,
+   "stage": 0,
+   "time": 0,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 286,
+   "family": 2190,
+   "helper": 283,
+   "offset": 4,
+   "owner_replica": 2,
+   "port": 62,
+   "replica": 0,
+   "stage": 0,
+   "time": 0,
+   "width": 9
+  }
+ },
+ {
+  "index": 523,
+  "before": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 43,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 330,
+   "family": 2122,
+   "helper": 43,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 106,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 9
+  }
+ },
+ {
+  "index": 650,
+  "before": {
+   "child": 2,
+   "copy": 15,
+   "family": 351,
+   "helper": 170,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 15,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 254,
+   "family": 2158,
+   "helper": 170,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 30,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  }
+ },
+ {
+  "index": 788,
+  "before": {
+   "child": 0,
+   "copy": 135,
+   "family": 1143,
+   "helper": 308,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 23,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 7
+  },
+  "after": {
+   "child": 2,
+   "copy": 905,
+   "family": 7513,
+   "helper": 308,
+   "offset": 0,
+   "owner_replica": 8,
+   "port": 9,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 7
+  }
+ },
+ {
+  "index": 826,
+  "before": {
+   "child": 0,
+   "copy": 112,
+   "family": 1120,
+   "helper": 346,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 0,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 283,
+   "family": 2075,
+   "helper": 346,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 59,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 9
+  }
+ },
+ {
+  "index": 861,
+  "before": {
+   "child": 2,
+   "copy": 13,
+   "family": 349,
+   "helper": 381,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 13,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 195,
+   "family": 1315,
+   "helper": 381,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 83,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  }
+ },
+ {
+  "index": 869,
+  "before": {
+   "child": 2,
+   "copy": 9,
+   "family": 345,
+   "helper": 389,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 9,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 193,
+   "family": 1313,
+   "helper": 389,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 81,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 4
+  }
+ },
+ {
+  "index": 939,
+  "before": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 459,
+   "offset": 0,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 5
+  },
+  "after": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 459,
+   "offset": 18,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 5
+  }
+ },
+ {
+  "index": 952,
+  "before": {
+   "child": 2,
+   "copy": 905,
+   "family": 7513,
+   "helper": 472,
+   "offset": 0,
+   "owner_replica": 8,
+   "port": 9,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 112,
+   "family": 1120,
+   "helper": 472,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 0,
+   "replica": 8,
+   "stage": 0,
+   "time": 1,
+   "width": 8
+  }
+ },
+ {
+  "index": 1081,
+  "before": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 121,
+   "offset": 5,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 1730,
+   "family": 13714,
+   "helper": 121,
+   "offset": 0,
+   "owner_replica": 15,
+   "port": 50,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  }
+ },
+ {
+  "index": 1194,
+  "before": {
+   "child": 0,
+   "copy": 88,
+   "family": 312,
+   "helper": 234,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 88,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 1292,
+   "family": 10140,
+   "helper": 234,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 60,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  }
+ },
+ {
+  "index": 1218,
+  "before": {
+   "child": 0,
+   "copy": 70,
+   "family": 294,
+   "helper": 258,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 70,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 254,
+   "family": 2158,
+   "helper": 258,
+   "offset": 4,
+   "owner_replica": 2,
+   "port": 30,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  }
+ },
+ {
+  "index": 1227,
+  "before": {
+   "child": 0,
+   "copy": 67,
+   "family": 291,
+   "helper": 267,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 67,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 15,
+   "family": 351,
+   "helper": 267,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 15,
+   "replica": 1,
+   "stage": 0,
+   "time": 2,
+   "width": 9
+  }
+ },
+ {
+  "index": 1453,
+  "before": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 13,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 13,
+   "family": 349,
+   "helper": 13,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 13,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  }
+ },
+ {
+  "index": 1524,
+  "before": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 84,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 9,
+   "family": 345,
+   "helper": 84,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 9,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  }
+ },
+ {
+  "index": 1595,
+  "before": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 155,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 88,
+   "family": 312,
+   "helper": 155,
+   "offset": 4,
+   "owner_replica": 0,
+   "port": 88,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 9
+  }
+ },
+ {
+  "index": 1796,
+  "before": {
+   "child": 2,
+   "copy": 905,
+   "family": 7513,
+   "helper": 356,
+   "offset": 8,
+   "owner_replica": 8,
+   "port": 9,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 264,
+   "family": 2056,
+   "helper": 356,
+   "offset": 4,
+   "owner_replica": 2,
+   "port": 40,
+   "replica": 9,
+   "stage": 0,
+   "time": 3,
+   "width": 8
+  }
+ },
+ {
+  "index": 1973,
+  "before": {
+   "child": 0,
+   "copy": 283,
+   "family": 2075,
+   "helper": 53,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 59,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 15,
+   "family": 351,
+   "helper": 53,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 15,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  }
+ },
+ {
+  "index": 2067,
+  "before": {
+   "child": 0,
+   "copy": 88,
+   "family": 312,
+   "helper": 147,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 88,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 88,
+   "family": 312,
+   "helper": 147,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 88,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  }
+ },
+ {
+  "index": 2091,
+  "before": {
+   "child": 0,
+   "copy": 264,
+   "family": 2056,
+   "helper": 171,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 40,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 171,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2121,
+  "before": {
+   "child": 0,
+   "copy": 234,
+   "family": 2026,
+   "helper": 201,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 10,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 201,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2127,
+  "before": {
+   "child": 0,
+   "copy": 228,
+   "family": 2020,
+   "helper": 207,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 4,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 207,
+   "offset": 9,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2189,
+  "before": {
+   "child": 2,
+   "copy": 15,
+   "family": 351,
+   "helper": 269,
+   "offset": 4,
+   "owner_replica": 0,
+   "port": 15,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 905,
+   "family": 7513,
+   "helper": 269,
+   "offset": 7,
+   "owner_replica": 8,
+   "port": 9,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2191,
+  "before": {
+   "child": 2,
+   "copy": 13,
+   "family": 349,
+   "helper": 271,
+   "offset": 4,
+   "owner_replica": 0,
+   "port": 13,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 135,
+   "family": 1143,
+   "helper": 271,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 23,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2200,
+  "before": {
+   "child": 2,
+   "copy": 9,
+   "family": 345,
+   "helper": 280,
+   "offset": 4,
+   "owner_replica": 0,
+   "port": 9,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 70,
+   "family": 294,
+   "helper": 280,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 70,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 9
+  }
+ },
+ {
+  "index": 2319,
+  "before": {
+   "child": 0,
+   "copy": 70,
+   "family": 294,
+   "helper": 399,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 70,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 13,
+   "family": 349,
+   "helper": 399,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 13,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  }
+ },
+ {
+  "index": 2326,
+  "before": {
+   "child": 0,
+   "copy": 67,
+   "family": 291,
+   "helper": 406,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 67,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 9,
+   "family": 345,
+   "helper": 406,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 9,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 4
+  }
+ },
+ {
+  "index": 2342,
+  "before": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 422,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 422,
+   "offset": 0,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 0,
+   "stage": 1,
+   "time": 4,
+   "width": 5
+  }
+ },
+ {
+  "index": 2488,
+  "before": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 88,
+   "offset": 0,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 88,
+   "offset": 5,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 9
+  }
+ },
+ {
+  "index": 2805,
+  "before": {
+   "child": 2,
+   "copy": 193,
+   "family": 1313,
+   "helper": 405,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 81,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 222,
+   "family": 1342,
+   "helper": 405,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 110,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 4
+  }
+ },
+ {
+  "index": 2830,
+  "before": {
+   "child": 2,
+   "copy": 184,
+   "family": 1304,
+   "helper": 430,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 72,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 135,
+   "family": 1143,
+   "helper": 430,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 23,
+   "replica": 8,
+   "stage": 1,
+   "time": 5,
+   "width": 4
+  }
+ },
+ {
+  "index": 2929,
+  "before": {
+   "child": 2,
+   "copy": 193,
+   "family": 1313,
+   "helper": 49,
+   "offset": 8,
+   "owner_replica": 1,
+   "port": 81,
+   "replica": 2,
+   "stage": 0,
+   "time": 6,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 186,
+   "family": 1306,
+   "helper": 49,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 74,
+   "replica": 2,
+   "stage": 0,
+   "time": 6,
+   "width": 4
+  }
+ },
+ {
+  "index": 3343,
+  "before": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 463,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 2,
+   "stage": 0,
+   "time": 6,
+   "width": 5
+  },
+  "after": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 463,
+   "offset": 18,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 2,
+   "stage": 0,
+   "time": 6,
+   "width": 5
+  }
+ },
+ {
+  "index": 3569,
+  "before": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 209,
+   "offset": 14,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 10,
+   "stage": 0,
+   "time": 7,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 184,
+   "family": 1304,
+   "helper": 209,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 72,
+   "replica": 10,
+   "stage": 0,
+   "time": 7,
+   "width": 9
+  }
+ },
+ {
+  "index": 3583,
+  "before": {
+   "child": 2,
+   "copy": 786,
+   "family": 6610,
+   "helper": 223,
+   "offset": 0,
+   "owner_replica": 7,
+   "port": 2,
+   "replica": 10,
+   "stage": 0,
+   "time": 7,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 223,
+   "offset": 14,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 10,
+   "stage": 0,
+   "time": 7,
+   "width": 9
+  }
+ },
+ {
+  "index": 3925,
+  "before": {
+   "child": 2,
+   "copy": 193,
+   "family": 1313,
+   "helper": 85,
+   "offset": 4,
+   "owner_replica": 1,
+   "port": 81,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 184,
+   "family": 1304,
+   "helper": 85,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 72,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 4
+  }
+ },
+ {
+  "index": 3979,
+  "before": {
+   "child": 2,
+   "copy": 254,
+   "family": 2158,
+   "helper": 139,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 30,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 139,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  }
+ },
+ {
+  "index": 4023,
+  "before": {
+   "child": 0,
+   "copy": 330,
+   "family": 2122,
+   "helper": 183,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 106,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 183,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  }
+ },
+ {
+  "index": 4078,
+  "before": {
+   "child": 0,
+   "copy": 283,
+   "family": 2075,
+   "helper": 238,
+   "offset": 4,
+   "owner_replica": 2,
+   "port": 59,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 234,
+   "family": 2026,
+   "helper": 238,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 10,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  }
+ },
+ {
+  "index": 4174,
+  "before": {
+   "child": 2,
+   "copy": 186,
+   "family": 1306,
+   "helper": 334,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 74,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 228,
+   "family": 2020,
+   "helper": 334,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 4,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  }
+ },
+ {
+  "index": 4184,
+  "before": {
+   "child": 2,
+   "copy": 184,
+   "family": 1304,
+   "helper": 344,
+   "offset": 4,
+   "owner_replica": 1,
+   "port": 72,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  },
+  "after": {
+   "child": 2,
+   "copy": 193,
+   "family": 1313,
+   "helper": 344,
+   "offset": 4,
+   "owner_replica": 1,
+   "port": 81,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 9
+  }
+ },
+ {
+  "index": 4306,
+  "before": {
+   "child": 1,
+   "copy": 8,
+   "family": 232,
+   "helper": 466,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 8,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 112,
+   "family": 1120,
+   "helper": 466,
+   "offset": 8,
+   "owner_replica": 1,
+   "port": 0,
+   "replica": 1,
+   "stage": 1,
+   "time": 8,
+   "width": 8
+  }
+ },
+ {
+  "index": 4420,
+  "before": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 100,
+   "offset": 14,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 100,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 9
+  }
+ },
+ {
+  "index": 4526,
+  "before": {
+   "child": 2,
+   "copy": 1232,
+   "family": 10192,
+   "helper": 206,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 0,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 206,
+   "offset": 0,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 9
+  }
+ },
+ {
+  "index": 4711,
+  "before": {
+   "child": 0,
+   "copy": 234,
+   "family": 2026,
+   "helper": 391,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 10,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 326,
+   "family": 2118,
+   "helper": 391,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 102,
+   "replica": 9,
+   "stage": 1,
+   "time": 9,
+   "width": 4
+  }
+ },
+ {
+  "index": 5000,
+  "before": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 200,
+   "offset": 23,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 200,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 9
+  }
+ },
+ {
+  "index": 5064,
+  "before": {
+   "child": 0,
+   "copy": 1231,
+   "family": 9295,
+   "helper": 264,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 111,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 8
+  },
+  "after": {
+   "child": 1,
+   "copy": 8,
+   "family": 232,
+   "helper": 264,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 8,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 8
+  }
+ },
+ {
+  "index": 5187,
+  "before": {
+   "child": 0,
+   "copy": 264,
+   "family": 2056,
+   "helper": 387,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 40,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 264,
+   "family": 2056,
+   "helper": 387,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 40,
+   "replica": 0,
+   "stage": 2,
+   "time": 10,
+   "width": 4
+  }
+ },
+ {
+  "index": 5984,
+  "before": {
+   "child": 0,
+   "copy": 228,
+   "family": 2020,
+   "helper": 224,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 4,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 7
+  },
+  "after": {
+   "child": 0,
+   "copy": 234,
+   "family": 2026,
+   "helper": 224,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 10,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 7
+  }
+ },
+ {
+  "index": 6037,
+  "before": {
+   "child": 2,
+   "copy": 286,
+   "family": 2190,
+   "helper": 277,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 62,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 1231,
+   "family": 9295,
+   "helper": 277,
+   "offset": 8,
+   "owner_replica": 10,
+   "port": 111,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 8
+  }
+ },
+ {
+  "index": 6155,
+  "before": {
+   "child": 0,
+   "copy": 330,
+   "family": 2122,
+   "helper": 395,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 106,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 283,
+   "family": 2075,
+   "helper": 395,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 59,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 4
+  }
+ },
+ {
+  "index": 6163,
+  "before": {
+   "child": 0,
+   "copy": 326,
+   "family": 2118,
+   "helper": 403,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 102,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 228,
+   "family": 2020,
+   "helper": 403,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 4,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 4
+  }
+ },
+ {
+  "index": 6221,
+  "before": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 461,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 461,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 3,
+   "stage": 0,
+   "time": 12,
+   "width": 5
+  }
+ },
+ {
+  "index": 6629,
+  "before": {
+   "child": 2,
+   "copy": 254,
+   "family": 2158,
+   "helper": 389,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 30,
+   "replica": 11,
+   "stage": 0,
+   "time": 13,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 330,
+   "family": 2122,
+   "helper": 389,
+   "offset": 9,
+   "owner_replica": 2,
+   "port": 106,
+   "replica": 11,
+   "stage": 0,
+   "time": 13,
+   "width": 4
+  }
+ },
+ {
+  "index": 6638,
+  "before": {
+   "child": 2,
+   "copy": 286,
+   "family": 2190,
+   "helper": 398,
+   "offset": 12,
+   "owner_replica": 2,
+   "port": 62,
+   "replica": 11,
+   "stage": 0,
+   "time": 13,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 286,
+   "family": 2190,
+   "helper": 398,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 62,
+   "replica": 11,
+   "stage": 0,
+   "time": 13,
+   "width": 4
+  }
+ },
+ {
+  "index": 6806,
+  "before": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 86,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 2,
+   "stage": 1,
+   "time": 14,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 86,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 2,
+   "stage": 1,
+   "time": 14,
+   "width": 9
+  }
+ },
+ {
+  "index": 7150,
+  "before": {
+   "child": 2,
+   "copy": 286,
+   "family": 2190,
+   "helper": 430,
+   "offset": 8,
+   "owner_replica": 2,
+   "port": 62,
+   "replica": 2,
+   "stage": 1,
+   "time": 14,
+   "width": 4
+  },
+  "after": {
+   "child": 0,
+   "copy": 264,
+   "family": 2056,
+   "helper": 430,
+   "offset": 12,
+   "owner_replica": 2,
+   "port": 40,
+   "replica": 2,
+   "stage": 1,
+   "time": 14,
+   "width": 4
+  }
+ },
+ {
+  "index": 7254,
+  "before": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 54,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 54,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 9
+  }
+ },
+ {
+  "index": 7266,
+  "before": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 66,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 66,
+   "offset": 14,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 9
+  }
+ },
+ {
+  "index": 7539,
+  "before": {
+   "child": 0,
+   "copy": 393,
+   "family": 2969,
+   "helper": 339,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 57,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 1243,
+   "family": 10203,
+   "helper": 339,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 11,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 8
+  }
+ },
+ {
+  "index": 7618,
+  "before": {
+   "child": 0,
+   "copy": 1231,
+   "family": 9295,
+   "helper": 418,
+   "offset": 8,
+   "owner_replica": 10,
+   "port": 111,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 1231,
+   "family": 9295,
+   "helper": 418,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 111,
+   "replica": 10,
+   "stage": 1,
+   "time": 15,
+   "width": 8
+  }
+ },
+ {
+  "index": 7849,
+  "before": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 169,
+   "offset": 14,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 169,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  }
+ },
+ {
+  "index": 7901,
+  "before": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 221,
+   "offset": 14,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 221,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  }
+ },
+ {
+  "index": 7946,
+  "before": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 266,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 266,
+   "offset": 0,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 1,
+   "stage": 2,
+   "time": 16,
+   "width": 9
+  }
+ },
+ {
+  "index": 8493,
+  "before": {
+   "child": 2,
+   "copy": 1232,
+   "family": 10192,
+   "helper": 333,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 0,
+   "replica": 9,
+   "stage": 2,
+   "time": 17,
+   "width": 7
+  },
+  "after": {
+   "child": 2,
+   "copy": 1314,
+   "family": 10274,
+   "helper": 333,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 82,
+   "replica": 9,
+   "stage": 2,
+   "time": 17,
+   "width": 7
+  }
+ },
+ {
+  "index": 8670,
+  "before": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 30,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 27,
+   "family": 475,
+   "helper": 30,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 27,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  }
+ },
+ {
+  "index": 8742,
+  "before": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 102,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 82,
+   "family": 642,
+   "helper": 102,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 82,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  }
+ },
+ {
+  "index": 8811,
+  "before": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 171,
+   "offset": 23,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 31,
+   "family": 591,
+   "helper": 171,
+   "offset": 9,
+   "owner_replica": 0,
+   "port": 31,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 9
+  }
+ },
+ {
+  "index": 8903,
+  "before": {
+   "child": 2,
+   "copy": 1243,
+   "family": 10203,
+   "helper": 263,
+   "offset": 8,
+   "owner_replica": 11,
+   "port": 11,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 1232,
+   "family": 10192,
+   "helper": 263,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 0,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 8
+  }
+ },
+ {
+  "index": 9028,
+  "before": {
+   "child": 0,
+   "copy": 393,
+   "family": 2969,
+   "helper": 388,
+   "offset": 8,
+   "owner_replica": 3,
+   "port": 57,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 432,
+   "family": 3120,
+   "helper": 388,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 96,
+   "replica": 0,
+   "stage": 3,
+   "time": 18,
+   "width": 8
+  }
+ },
+ {
+  "index": 9177,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 57,
+   "offset": 0,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 938,
+   "family": 7658,
+   "helper": 57,
+   "offset": 23,
+   "owner_replica": 8,
+   "port": 42,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 9
+  }
+ },
+ {
+  "index": 9385,
+  "before": {
+   "child": 0,
+   "copy": 1292,
+   "family": 10140,
+   "helper": 265,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 60,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 432,
+   "family": 3120,
+   "helper": 265,
+   "offset": 8,
+   "owner_replica": 3,
+   "port": 96,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 8
+  }
+ },
+ {
+  "index": 9416,
+  "before": {
+   "child": 2,
+   "copy": 1243,
+   "family": 10203,
+   "helper": 296,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 11,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 1232,
+   "family": 10192,
+   "helper": 296,
+   "offset": 8,
+   "owner_replica": 11,
+   "port": 0,
+   "replica": 8,
+   "stage": 3,
+   "time": 19,
+   "width": 8
+  }
+ },
+ {
+  "index": 9658,
+  "before": {
+   "child": 0,
+   "copy": 1292,
+   "family": 10140,
+   "helper": 58,
+   "offset": 12,
+   "owner_replica": 11,
+   "port": 60,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 1243,
+   "family": 10203,
+   "helper": 58,
+   "offset": 8,
+   "owner_replica": 11,
+   "port": 11,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 4
+  }
+ },
+ {
+  "index": 9673,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 73,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 73,
+   "offset": 5,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 9
+  }
+ },
+ {
+  "index": 9788,
+  "before": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 188,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 188,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 4,
+   "stage": 0,
+   "time": 20,
+   "width": 9
+  }
+ },
+ {
+  "index": 10087,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 7,
+   "offset": 4,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 12,
+   "stage": 0,
+   "time": 21,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 7,
+   "offset": 14,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 12,
+   "stage": 0,
+   "time": 21,
+   "width": 9
+  }
+ },
+ {
+  "index": 10322,
+  "before": {
+   "child": 2,
+   "copy": 432,
+   "family": 3120,
+   "helper": 242,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 96,
+   "replica": 12,
+   "stage": 0,
+   "time": 21,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 393,
+   "family": 2969,
+   "helper": 242,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 57,
+   "replica": 12,
+   "stage": 0,
+   "time": 21,
+   "width": 9
+  }
+ },
+ {
+  "index": 10701,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 141,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 141,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 9
+  }
+ },
+ {
+  "index": 10787,
+  "before": {
+   "child": 2,
+   "copy": 432,
+   "family": 3120,
+   "helper": 227,
+   "offset": 9,
+   "owner_replica": 3,
+   "port": 96,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 7
+  },
+  "after": {
+   "child": 0,
+   "copy": 393,
+   "family": 2969,
+   "helper": 227,
+   "offset": 9,
+   "owner_replica": 3,
+   "port": 57,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 7
+  }
+ },
+ {
+  "index": 10999,
+  "before": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 439,
+   "offset": 9,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 439,
+   "offset": 18,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 3,
+   "stage": 1,
+   "time": 22,
+   "width": 5
+  }
+ },
+ {
+  "index": 11091,
+  "before": {
+   "child": 0,
+   "copy": 1292,
+   "family": 10140,
+   "helper": 51,
+   "offset": 8,
+   "owner_replica": 11,
+   "port": 60,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 4
+  },
+  "after": {
+   "child": 2,
+   "copy": 1243,
+   "family": 10203,
+   "helper": 51,
+   "offset": 12,
+   "owner_replica": 11,
+   "port": 11,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 4
+  }
+ },
+ {
+  "index": 11163,
+  "before": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 123,
+   "offset": 18,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 123,
+   "offset": 9,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 9
+  }
+ },
+ {
+  "index": 11404,
+  "before": {
+   "child": 2,
+   "copy": 1314,
+   "family": 10274,
+   "helper": 364,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 82,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 7
+  },
+  "after": {
+   "child": 0,
+   "copy": 1292,
+   "family": 10140,
+   "helper": 364,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 60,
+   "replica": 11,
+   "stage": 1,
+   "time": 23,
+   "width": 7
+  }
+ },
+ {
+  "index": 11796,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 276,
+   "offset": 18,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 2,
+   "stage": 2,
+   "time": 24,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 1678,
+   "family": 12878,
+   "helper": 276,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 110,
+   "replica": 2,
+   "stage": 2,
+   "time": 24,
+   "width": 8
+  }
+ },
+ {
+  "index": 11895,
+  "before": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 375,
+   "offset": 27,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 2,
+   "stage": 2,
+   "time": 24,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 375,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 2,
+   "stage": 2,
+   "time": 24,
+   "width": 5
+  }
+ },
+ {
+  "index": 12558,
+  "before": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 78,
+   "offset": 0,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 1,
+   "stage": 3,
+   "time": 26,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 140,
+   "family": 1372,
+   "helper": 78,
+   "offset": 23,
+   "owner_replica": 1,
+   "port": 28,
+   "replica": 1,
+   "stage": 3,
+   "time": 26,
+   "width": 9
+  }
+ },
+ {
+  "index": 12961,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 1,
+   "offset": 9,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 9,
+   "stage": 3,
+   "time": 27,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 1,
+   "offset": 14,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 9,
+   "stage": 3,
+   "time": 27,
+   "width": 9
+  }
+ },
+ {
+  "index": 13020,
+  "before": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 60,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 9,
+   "stage": 3,
+   "time": 27,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 60,
+   "offset": 9,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 9,
+   "stage": 3,
+   "time": 27,
+   "width": 9
+  }
+ },
+ {
+  "index": 13495,
+  "before": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 55,
+   "offset": 14,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 0,
+   "stage": 4,
+   "time": 28,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 55,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 0,
+   "stage": 4,
+   "time": 28,
+   "width": 9
+  }
+ },
+ {
+  "index": 13895,
+  "before": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 455,
+   "offset": 18,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 0,
+   "stage": 4,
+   "time": 28,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 455,
+   "offset": 9,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 0,
+   "stage": 4,
+   "time": 28,
+   "width": 5
+  }
+ },
+ {
+  "index": 14365,
+  "before": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 445,
+   "offset": 9,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 8,
+   "stage": 4,
+   "time": 29,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 445,
+   "offset": 9,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 8,
+   "stage": 4,
+   "time": 29,
+   "width": 5
+  }
+ },
+ {
+  "index": 14383,
+  "before": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 463,
+   "offset": 9,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 8,
+   "stage": 4,
+   "time": 29,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 463,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 8,
+   "stage": 4,
+   "time": 29,
+   "width": 5
+  }
+ },
+ {
+  "index": 14695,
+  "before": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 295,
+   "offset": 14,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 5,
+   "stage": 0,
+   "time": 30,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 295,
+   "offset": 14,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 5,
+   "stage": 0,
+   "time": 30,
+   "width": 9
+  }
+ },
+ {
+  "index": 14746,
+  "before": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 346,
+   "offset": 14,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 5,
+   "stage": 0,
+   "time": 30,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 346,
+   "offset": 9,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 5,
+   "stage": 0,
+   "time": 30,
+   "width": 9
+  }
+ },
+ {
+  "index": 14938,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 58,
+   "offset": 18,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 13,
+   "stage": 0,
+   "time": 31,
+   "width": 4
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 58,
+   "offset": 0,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 13,
+   "stage": 0,
+   "time": 31,
+   "width": 4
+  }
+ },
+ {
+  "index": 15125,
+  "before": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 245,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 13,
+   "stage": 0,
+   "time": 31,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 245,
+   "offset": 23,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 13,
+   "stage": 0,
+   "time": 31,
+   "width": 9
+  }
+ },
+ {
+  "index": 15967,
+  "before": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 127,
+   "offset": 9,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 127,
+   "offset": 0,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  }
+ },
+ {
+  "index": 16037,
+  "before": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 197,
+   "offset": 23,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 197,
+   "offset": 0,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  }
+ },
+ {
+  "index": 16047,
+  "before": {
+   "child": 4,
+   "copy": 1186,
+   "family": 9474,
+   "helper": 207,
+   "offset": 23,
+   "owner_replica": 10,
+   "port": 66,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 207,
+   "offset": 18,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 12,
+   "stage": 1,
+   "time": 33,
+   "width": 9
+  }
+ },
+ {
+  "index": 16758,
+  "before": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 438,
+   "offset": 0,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 3,
+   "stage": 2,
+   "time": 34,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 438,
+   "offset": 27,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 3,
+   "stage": 2,
+   "time": 34,
+   "width": 5
+  }
+ },
+ {
+  "index": 17237,
+  "before": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 437,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 11,
+   "stage": 2,
+   "time": 35,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 437,
+   "offset": 18,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 11,
+   "stage": 2,
+   "time": 35,
+   "width": 5
+  }
+ },
+ {
+  "index": 17339,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 59,
+   "offset": 22,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 2,
+   "stage": 3,
+   "time": 36,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1196,
+   "family": 9484,
+   "helper": 59,
+   "offset": 23,
+   "owner_replica": 10,
+   "port": 76,
+   "replica": 2,
+   "stage": 3,
+   "time": 36,
+   "width": 9
+  }
+ },
+ {
+  "index": 18336,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 96,
+   "offset": 31,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 1,
+   "stage": 4,
+   "time": 38,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 96,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 1,
+   "stage": 4,
+   "time": 38,
+   "width": 9
+  }
+ },
+ {
+  "index": 19489,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 289,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 0,
+   "stage": 5,
+   "time": 40,
+   "width": 8
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 289,
+   "offset": 0,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 0,
+   "stage": 5,
+   "time": 40,
+   "width": 8
+  }
+ },
+ {
+  "index": 19607,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 407,
+   "offset": 26,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 0,
+   "stage": 5,
+   "time": 40,
+   "width": 4
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 407,
+   "offset": 18,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 0,
+   "stage": 5,
+   "time": 40,
+   "width": 4
+  }
+ },
+ {
+  "index": 19891,
+  "before": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 211,
+   "offset": 9,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 8,
+   "stage": 5,
+   "time": 41,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 211,
+   "offset": 8,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 8,
+   "stage": 5,
+   "time": 41,
+   "width": 9
+  }
+ },
+ {
+  "index": 20019,
+  "before": {
+   "child": 8,
+   "copy": 1006,
+   "family": 7950,
+   "helper": 339,
+   "offset": 40,
+   "owner_replica": 8,
+   "port": 110,
+   "replica": 8,
+   "stage": 5,
+   "time": 41,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 786,
+   "family": 6610,
+   "helper": 339,
+   "offset": 0,
+   "owner_replica": 7,
+   "port": 2,
+   "replica": 8,
+   "stage": 5,
+   "time": 41,
+   "width": 8
+  }
+ },
+ {
+  "index": 20630,
+  "before": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 470,
+   "offset": 18,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 6,
+   "stage": 0,
+   "time": 42,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 470,
+   "offset": 9,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 6,
+   "stage": 0,
+   "time": 42,
+   "width": 5
+  }
+ },
+ {
+  "index": 21117,
+  "before": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 477,
+   "offset": 18,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 14,
+   "stage": 0,
+   "time": 43,
+   "width": 5
+  },
+  "after": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 477,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 14,
+   "stage": 0,
+   "time": 43,
+   "width": 5
+  }
+ },
+ {
+  "index": 21259,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 139,
+   "offset": 8,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 5,
+   "stage": 1,
+   "time": 44,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 139,
+   "offset": 14,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 5,
+   "stage": 1,
+   "time": 44,
+   "width": 9
+  }
+ },
+ {
+  "index": 21293,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 173,
+   "offset": 30,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 5,
+   "stage": 1,
+   "time": 44,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 173,
+   "offset": 17,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 5,
+   "stage": 1,
+   "time": 44,
+   "width": 9
+  }
+ },
+ {
+  "index": 22697,
+  "before": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 137,
+   "offset": 23,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 12,
+   "stage": 2,
+   "time": 47,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 137,
+   "offset": 4,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 12,
+   "stage": 2,
+   "time": 47,
+   "width": 9
+  }
+ },
+ {
+  "index": 22774,
+  "before": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 214,
+   "offset": 23,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 12,
+   "stage": 2,
+   "time": 47,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 214,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 12,
+   "stage": 2,
+   "time": 47,
+   "width": 9
+  }
+ },
+ {
+  "index": 23260,
+  "before": {
+   "child": 4,
+   "copy": 441,
+   "family": 3241,
+   "helper": 220,
+   "offset": 23,
+   "owner_replica": 3,
+   "port": 105,
+   "replica": 3,
+   "stage": 3,
+   "time": 48,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1247,
+   "family": 10319,
+   "helper": 220,
+   "offset": 23,
+   "owner_replica": 11,
+   "port": 15,
+   "replica": 3,
+   "stage": 3,
+   "time": 48,
+   "width": 9
+  }
+ },
+ {
+  "index": 23523,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 3,
+   "offset": 13,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 3,
+   "offset": 13,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  }
+ },
+ {
+  "index": 23624,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 104,
+   "offset": 17,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 104,
+   "offset": 26,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  }
+ },
+ {
+  "index": 23795,
+  "before": {
+   "child": 0,
+   "copy": 1678,
+   "family": 12878,
+   "helper": 275,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 110,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1315,
+   "family": 10387,
+   "helper": 275,
+   "offset": 23,
+   "owner_replica": 11,
+   "port": 83,
+   "replica": 11,
+   "stage": 3,
+   "time": 49,
+   "width": 9
+  }
+ },
+ {
+  "index": 24154,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 154,
+   "offset": 0,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 2,
+   "stage": 4,
+   "time": 50,
+   "width": 4
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 154,
+   "offset": 35,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 2,
+   "stage": 4,
+   "time": 50,
+   "width": 4
+  }
+ },
+ {
+  "index": 24254,
+  "before": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 254,
+   "offset": 18,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 2,
+   "stage": 4,
+   "time": 50,
+   "width": 9
+  },
+  "after": {
+   "child": 0,
+   "copy": 1601,
+   "family": 12801,
+   "helper": 254,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 33,
+   "replica": 2,
+   "stage": 4,
+   "time": 50,
+   "width": 9
+  }
+ },
+ {
+  "index": 24788,
+  "before": {
+   "child": 0,
+   "copy": 1678,
+   "family": 12878,
+   "helper": 308,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 110,
+   "replica": 10,
+   "stage": 4,
+   "time": 51,
+   "width": 7
+  },
+  "after": {
+   "child": 0,
+   "copy": 1730,
+   "family": 13714,
+   "helper": 308,
+   "offset": 9,
+   "owner_replica": 15,
+   "port": 50,
+   "replica": 10,
+   "stage": 4,
+   "time": 51,
+   "width": 7
+  }
+ },
+ {
+  "index": 24979,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 19,
+   "offset": 0,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 1,
+   "stage": 5,
+   "time": 52,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 19,
+   "offset": 23,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 1,
+   "stage": 5,
+   "time": 52,
+   "width": 9
+  }
+ },
+ {
+  "index": 25182,
+  "before": {
+   "child": 8,
+   "copy": 199,
+   "family": 1655,
+   "helper": 222,
+   "offset": 39,
+   "owner_replica": 1,
+   "port": 87,
+   "replica": 1,
+   "stage": 5,
+   "time": 52,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 144,
+   "family": 1712,
+   "helper": 222,
+   "offset": 39,
+   "owner_replica": 1,
+   "port": 32,
+   "replica": 1,
+   "stage": 5,
+   "time": 52,
+   "width": 9
+  }
+ },
+ {
+  "index": 25909,
+  "before": {
+   "child": 4,
+   "copy": 1364,
+   "family": 11220,
+   "helper": 469,
+   "offset": 27,
+   "owner_replica": 12,
+   "port": 20,
+   "replica": 9,
+   "stage": 5,
+   "time": 53,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 469,
+   "offset": 9,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 9,
+   "stage": 5,
+   "time": 53,
+   "width": 5
+  }
+ },
+ {
+  "index": 27082,
+  "before": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 202,
+   "offset": 5,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 0,
+   "stage": 6,
+   "time": 56,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 202,
+   "offset": 14,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 0,
+   "stage": 6,
+   "time": 56,
+   "width": 9
+  }
+ },
+ {
+  "index": 27109,
+  "before": {
+   "child": 2,
+   "copy": 786,
+   "family": 6610,
+   "helper": 229,
+   "offset": 9,
+   "owner_replica": 7,
+   "port": 2,
+   "replica": 0,
+   "stage": 6,
+   "time": 56,
+   "width": 7
+  },
+  "after": {
+   "child": 0,
+   "copy": 1601,
+   "family": 12801,
+   "helper": 229,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 33,
+   "replica": 0,
+   "stage": 6,
+   "time": 56,
+   "width": 7
+  }
+ },
+ {
+  "index": 27446,
+  "before": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 86,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 86,
+   "offset": 0,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  }
+ },
+ {
+  "index": 27458,
+  "before": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 98,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 98,
+   "offset": 13,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  }
+ },
+ {
+  "index": 27483,
+  "before": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 123,
+   "offset": 5,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 123,
+   "offset": 22,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 9
+  }
+ },
+ {
+  "index": 27625,
+  "before": {
+   "child": 0,
+   "copy": 1601,
+   "family": 12801,
+   "helper": 265,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 33,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 8
+  },
+  "after": {
+   "child": 2,
+   "copy": 786,
+   "family": 6610,
+   "helper": 265,
+   "offset": 8,
+   "owner_replica": 7,
+   "port": 2,
+   "replica": 8,
+   "stage": 6,
+   "time": 57,
+   "width": 8
+  }
+ },
+ {
+  "index": 28614,
+  "before": {
+   "child": 0,
+   "copy": 1601,
+   "family": 12801,
+   "helper": 294,
+   "offset": 8,
+   "owner_replica": 14,
+   "port": 33,
+   "replica": 14,
+   "stage": 1,
+   "time": 59,
+   "width": 8
+  },
+  "after": {
+   "child": 0,
+   "copy": 1678,
+   "family": 12878,
+   "helper": 294,
+   "offset": 8,
+   "owner_replica": 14,
+   "port": 110,
+   "replica": 14,
+   "stage": 1,
+   "time": 59,
+   "width": 8
+  }
+ },
+ {
+  "index": 28823,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 23,
+   "offset": 31,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 5,
+   "stage": 2,
+   "time": 60,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 23,
+   "offset": 14,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 5,
+   "stage": 2,
+   "time": 60,
+   "width": 9
+  }
+ },
+ {
+  "index": 28872,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 72,
+   "offset": 26,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 5,
+   "stage": 2,
+   "time": 60,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 72,
+   "offset": 31,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 5,
+   "stage": 2,
+   "time": 60,
+   "width": 9
+  }
+ },
+ {
+  "index": 29437,
+  "before": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 157,
+   "offset": 23,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 13,
+   "stage": 2,
+   "time": 61,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 157,
+   "offset": 0,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 13,
+   "stage": 2,
+   "time": 61,
+   "width": 9
+  }
+ },
+ {
+  "index": 29584,
+  "before": {
+   "child": 0,
+   "copy": 1730,
+   "family": 13714,
+   "helper": 304,
+   "offset": 0,
+   "owner_replica": 15,
+   "port": 50,
+   "replica": 13,
+   "stage": 2,
+   "time": 61,
+   "width": 8
+  },
+  "after": {
+   "child": 8,
+   "copy": 327,
+   "family": 2567,
+   "helper": 304,
+   "offset": 40,
+   "owner_replica": 2,
+   "port": 103,
+   "replica": 13,
+   "stage": 2,
+   "time": 61,
+   "width": 8
+  }
+ },
+ {
+  "index": 30365,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 125,
+   "offset": 22,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 12,
+   "stage": 3,
+   "time": 63,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 1475,
+   "family": 12115,
+   "helper": 125,
+   "offset": 23,
+   "owner_replica": 13,
+   "port": 19,
+   "replica": 12,
+   "stage": 3,
+   "time": 63,
+   "width": 9
+  }
+ },
+ {
+  "index": 30995,
+  "before": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 275,
+   "offset": 14,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 3,
+   "stage": 4,
+   "time": 64,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 275,
+   "offset": 0,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 3,
+   "stage": 4,
+   "time": 64,
+   "width": 9
+  }
+ },
+ {
+  "index": 31157,
+  "before": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 437,
+   "offset": 0,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 3,
+   "stage": 4,
+   "time": 64,
+   "width": 5
+  },
+  "after": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 437,
+   "offset": 27,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 3,
+   "stage": 4,
+   "time": 64,
+   "width": 5
+  }
+ },
+ {
+  "index": 31506,
+  "before": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 306,
+   "offset": 23,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 11,
+   "stage": 4,
+   "time": 65,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 306,
+   "offset": 22,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 11,
+   "stage": 4,
+   "time": 65,
+   "width": 9
+  }
+ },
+ {
+  "index": 32877,
+  "before": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 237,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 1,
+   "stage": 6,
+   "time": 68,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 237,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 1,
+   "stage": 6,
+   "time": 68,
+   "width": 9
+  }
+ },
+ {
+  "index": 33397,
+  "before": {
+   "child": 0,
+   "copy": 1730,
+   "family": 13714,
+   "helper": 277,
+   "offset": 8,
+   "owner_replica": 15,
+   "port": 50,
+   "replica": 9,
+   "stage": 6,
+   "time": 69,
+   "width": 8
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 277,
+   "offset": 31,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 9,
+   "stage": 6,
+   "time": 69,
+   "width": 8
+  }
+ },
+ {
+  "index": 34539,
+  "before": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 459,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 15,
+   "stage": 1,
+   "time": 71,
+   "width": 5
+  },
+  "after": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 459,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 15,
+   "stage": 1,
+   "time": 71,
+   "width": 5
+  }
+ },
+ {
+  "index": 34740,
+  "before": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 180,
+   "offset": 5,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 0,
+   "stage": 7,
+   "time": 72,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 180,
+   "offset": 14,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 0,
+   "stage": 7,
+   "time": 72,
+   "width": 9
+  }
+ },
+ {
+  "index": 36667,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 187,
+   "offset": 35,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 187,
+   "offset": 0,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  }
+ },
+ {
+  "index": 36697,
+  "before": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 217,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 581,
+   "family": 4949,
+   "helper": 217,
+   "offset": 23,
+   "owner_replica": 5,
+   "port": 21,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  }
+ },
+ {
+  "index": 36722,
+  "before": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 242,
+   "offset": 14,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 242,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 5,
+   "stage": 3,
+   "time": 76,
+   "width": 9
+  }
+ },
+ {
+  "index": 37215,
+  "before": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 255,
+   "offset": 9,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 13,
+   "stage": 3,
+   "time": 77,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 255,
+   "offset": 9,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 13,
+   "stage": 3,
+   "time": 77,
+   "width": 9
+  }
+ },
+ {
+  "index": 37757,
+  "before": {
+   "child": 8,
+   "copy": 1338,
+   "family": 10634,
+   "helper": 317,
+   "offset": 40,
+   "owner_replica": 11,
+   "port": 106,
+   "replica": 4,
+   "stage": 4,
+   "time": 78,
+   "width": 8
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 317,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 4,
+   "stage": 4,
+   "time": 78,
+   "width": 8
+  }
+ },
+ {
+  "index": 37827,
+  "before": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 387,
+   "offset": 44,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 4,
+   "stage": 4,
+   "time": 78,
+   "width": 4
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 387,
+   "offset": 9,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 4,
+   "stage": 4,
+   "time": 78,
+   "width": 4
+  }
+ },
+ {
+  "index": 38440,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 40,
+   "offset": 9,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 3,
+   "stage": 5,
+   "time": 80,
+   "width": 9
+  },
+  "after": {
+   "child": 8,
+   "copy": 357,
+   "family": 3381,
+   "helper": 40,
+   "offset": 39,
+   "owner_replica": 3,
+   "port": 21,
+   "replica": 3,
+   "stage": 5,
+   "time": 80,
+   "width": 9
+  }
+ },
+ {
+  "index": 39090,
+  "before": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 210,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 11,
+   "stage": 5,
+   "time": 81,
+   "width": 9
+  },
+  "after": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 210,
+   "offset": 18,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 11,
+   "stage": 5,
+   "time": 81,
+   "width": 9
+  }
+ },
+ {
+  "index": 40054,
+  "before": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 214,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 10,
+   "stage": 6,
+   "time": 83,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 214,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 10,
+   "stage": 6,
+   "time": 83,
+   "width": 9
+  }
+ },
+ {
+  "index": 40767,
+  "before": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 447,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 1,
+   "stage": 7,
+   "time": 84,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 1661,
+   "family": 13085,
+   "helper": 447,
+   "offset": 27,
+   "owner_replica": 14,
+   "port": 93,
+   "replica": 1,
+   "stage": 7,
+   "time": 84,
+   "width": 5
+  }
+ },
+ {
+  "index": 40787,
+  "before": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 467,
+   "offset": 18,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 1,
+   "stage": 7,
+   "time": 84,
+   "width": 5
+  },
+  "after": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 467,
+   "offset": 27,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 1,
+   "stage": 7,
+   "time": 84,
+   "width": 5
+  }
+ },
+ {
+  "index": 41020,
+  "before": {
+   "child": 6,
+   "copy": 1642,
+   "family": 13178,
+   "helper": 220,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 74,
+   "replica": 9,
+   "stage": 7,
+   "time": 85,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 220,
+   "offset": 26,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 9,
+   "stage": 7,
+   "time": 85,
+   "width": 9
+  }
+ },
+ {
+  "index": 41037,
+  "before": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 237,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 9,
+   "stage": 7,
+   "time": 85,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1633,
+   "family": 13169,
+   "helper": 237,
+   "offset": 0,
+   "owner_replica": 14,
+   "port": 65,
+   "replica": 9,
+   "stage": 7,
+   "time": 85,
+   "width": 9
+  }
+ },
+ {
+  "index": 42532,
+  "before": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 292,
+   "offset": 14,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 0,
+   "stage": 8,
+   "time": 88,
+   "width": 9
+  },
+  "after": {
+   "child": 6,
+   "copy": 1616,
+   "family": 13152,
+   "helper": 292,
+   "offset": 23,
+   "owner_replica": 14,
+   "port": 48,
+   "replica": 0,
+   "stage": 8,
+   "time": 88,
+   "width": 9
+  }
+ },
+ {
+  "index": 47255,
+  "before": {
+   "child": 4,
+   "copy": 892,
+   "family": 6828,
+   "helper": 215,
+   "offset": 23,
+   "owner_replica": 7,
+   "port": 108,
+   "replica": 2,
+   "stage": 7,
+   "time": 98,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 215,
+   "offset": 35,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 2,
+   "stage": 7,
+   "time": 98,
+   "width": 9
+  }
+ },
+ {
+  "index": 51050,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 170,
+   "offset": 18,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 5,
+   "stage": 5,
+   "time": 106,
+   "width": 4
+  },
+  "after": {
+   "child": 10,
+   "copy": 1649,
+   "family": 13409,
+   "helper": 170,
+   "offset": 44,
+   "owner_replica": 14,
+   "port": 81,
+   "replica": 5,
+   "stage": 5,
+   "time": 106,
+   "width": 4
+  }
+ },
+ {
+  "index": 55810,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 130,
+   "offset": 22,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 6,
+   "stage": 5,
+   "time": 116,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 130,
+   "offset": 22,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 6,
+   "stage": 5,
+   "time": 116,
+   "width": 9
+  }
+ },
+ {
+  "index": 56929,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 289,
+   "offset": 31,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 5,
+   "stage": 6,
+   "time": 118,
+   "width": 8
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 289,
+   "offset": 31,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 5,
+   "stage": 6,
+   "time": 118,
+   "width": 8
+  }
+ },
+ {
+  "index": 57707,
+  "before": {
+   "child": 8,
+   "copy": 840,
+   "family": 7000,
+   "helper": 107,
+   "offset": 39,
+   "owner_replica": 7,
+   "port": 56,
+   "replica": 4,
+   "stage": 7,
+   "time": 120,
+   "width": 9
+  },
+  "after": {
+   "child": 10,
+   "copy": 1728,
+   "family": 14272,
+   "helper": 107,
+   "offset": 39,
+   "owner_replica": 15,
+   "port": 48,
+   "replica": 4,
+   "stage": 7,
+   "time": 120,
+   "width": 9
+  }
+ }
+]
diff --git a/research/complex-t16-evacuation-increment/README.md b/research/complex-t16-evacuation-increment/README.md
new file mode 100644
index 0000000000..8e9889dd33
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/README.md
@@ -0,0 +1,79 @@
+# T16 owner-packing improvement from an OR-Tools evacuation neighbourhood
+
+This package records a **conditional packing gain**, not a new word, supplier,
+mechanism, or multiplication theorem. On the same selected PR1094 T16 word and
+both unchanged suppliers, a finite OR-Tools CP-SAT large-neighbourhood search
+found an owner map with exact **κ = 0.001673618490895016**. The immediately
+preceding map had κ = 0.001673614205725695, so the increase is
+**4.285169321 × 10⁻⁹** (0.0002560428% relative). The map changes 163 rows of its
+predecessor: 142 helper relocations and 21 offset-only edits.
+
+The exact selected-word ceiling from `complex-local-word-ceiling/ceiling.py` is
+`a_hi = 0.001690054109089`, giving `κ < a_hi/(1+a_hi) =
+0.001687202645325402…`. This candidate realizes **99.194871%** of that κ
+ceiling. The gain closes 6.589632% of the κ gap from the selected PR1094 map to
+this ceiling. These are ceilings for the fixed word, template,
+coverage law, and halving guard. They do not bound other words or changed
+mechanisms.
+
+The inherited exact packing certificate still proves at most 4,887 empty
+capacity-48 bins and `Σ f ln(f) ≤ 908,139.013`; this candidate has 4,880 such
+bins and `Σ f ln(f) = 907,279.723`. That surrogate certificate is not a κ
+optimality proof. The CP-SAT run ended `FEASIBLE` with objective 10,463,952 and
+solver bound 10,540,812. Exact κ and legality came from independent replay and
+pricing, not from the solver objective. Later evacuation, relocation-cost,
+single-call, and time-window neighbourhood rounds did not improve the exact κ.
+The finite search does not establish an optimum.
+
+## Verification
+
+The verifier reconstructs the candidate from the predecessor's compressed
+owner rows plus `DIFF-vs-predecessor.json`, regenerates `OWNERS`, `PLAN`, and
+`SPEC` through the existing builder, then runs the unchanged strict T16 replay.
+It also runs the independent seed67 owner audit, prices both suppliers with the
+pinned engines and PR1069 sweep, calls the exact word-ceiling routine, and runs
+the exact-integer packing-ceiling checker. The strict replay recomputes the
+73-column chart count as 10,008.
+
+From the repository root, run:
+
+```sh
+python3.12 scripts/research_package.py --package research/complex-t16-evacuation-increment --check-only
+python3.12 scripts/research_package.py --package research/complex-t16-evacuation-increment
+```
+
+The search used OR-Tools 9.11.4210 with Python 3.10.12. Reproducing the search
+itself requires the pinned research environment described in `SEARCH.json`;
+the registered verifier deliberately replays and audits the candidate without
+running an optimizer.
+
+## Search overlap
+
+The live overlap refresh on 2026-10-17 at 21:23 UTC returned 350 open PRs and
+321 discussion records. It found no matching open T16 owner-packing PR. The
+nearest scoped results are a census of single whole-helper relocations
+(Discussion #1332 / closed PR #1343), which explicitly excluded multi-row
+repacking, and a rank-48 idle-only repartition ceiling (Discussion #1265 /
+closed PR #1276) below this candidate's κ. An idle-axis overlay (Discussion
+#1339 / PR #1387) did not pass actual stream composition. These checks support
+the stated scoped distinction, not a claim of global novelty. The returned
+inventory and details are recorded in `evidence/OVERLAP.json` and `SEARCH.json`.
+
+## Open next questions
+
+The structured questions are in `TASK.json`. Three bounded probes of a rounded
+exact-moment objective did not improve the candidate, so that
+objective/neighbourhood combination is not the next search to repeat. A more
+promising question is whether exact supplier prices can drive a decomposed
+master problem with pricing cuts instead of a single rounded surrogate. This
+candidate improved exact κ even though its `Σ f ln(f)` surrogate is higher than
+its predecessor's, so the surrogate can mis-rank nearby maps. A proof-quality
+bound on the remaining κ gap is also open.
+
+## Credit
+
+The predecessor packing, builder, exact checkers, strict replay, and proof
+retain their original authorship and notices. This incremental map and search
+record were prepared by OpenAI Codex at the user's direction with substantial
+AI assistance. No independent human review is claimed. New package material is
+Apache-2.0.
diff --git a/research/complex-t16-evacuation-increment/SEARCH.json b/research/complex-t16-evacuation-increment/SEARCH.json
new file mode 100644
index 0000000000..8a4afc1ef7
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/SEARCH.json
@@ -0,0 +1,134 @@
+{
+  "scope": "Finite OR-Tools CP-SAT large-neighbourhood search for an improved legal owner map on the fixed selected PR1094 T16 supplier and word.",
+  "claim_type": "Conditional packing improvement only. This is a search best, not an optimum or complete multiplication theorem.",
+  "result": {
+    "predecessor_kappa": "0.001673614205725695",
+    "candidate_kappa": "0.001673618490895016",
+    "absolute_delta": "4.285169321E-9",
+    "relative_delta": "0.00000256042838686464777095642507160470540321556562816905590345767",
+    "changed_rows_vs_predecessor": 163,
+    "relocated_rows": 142,
+    "offset_only_rows": 21,
+    "idle_profile": {
+      "1": 2392,
+      "2": 8,
+      "3": 110,
+      "7": 2,
+      "16": 2,
+      "48": 4880
+    },
+    "surrogate_E": 907279.723,
+    "empty_cap48_bins": 4880,
+    "proven_max_empty_cap48_bins": 4887,
+    "packing_surrogate_ceiling": 908139.013,
+    "actual_73column_charts": 10008
+  },
+  "best_run": {
+    "command": "env OMP_NUM_THREADS=1 NW=2 DIV=0 TL2=30 NB=60 python3.10 research/complex-t16-two-stage-cycles/search/lns2.py research/complex-t16-two-stage-cycles/search research/complex-t16-two-stage-cycles/data/OWNERS.json.gz /tmp/t16-evac-small 1 20261019 300 evac 2",
+    "solver": "OR-Tools 9.11.4210 CP-SAT",
+    "python": "3.10.12",
+    "numpy": "2.2.6",
+    "scipy": "1.15.3",
+    "neighborhood": {
+      "bins": 65,
+      "helpers": 173,
+      "variables": 3508,
+      "time_limit_seconds": 300
+    },
+    "status": "FEASIBLE",
+    "objective": 10463952,
+    "best_bound": 10540812,
+    "wall_seconds": 330.3,
+    "note": "The integer surrogate objective was not the acceptance criterion; only exact replay and exact pricing accepted a map."
+  },
+  "other_searches": [
+    {
+      "route": "Aggregate full-map winlp target, 66,140 variables",
+      "outcome": "FEASIBLE surrogate 908133.1032 vs solver bound 908155.8984; downstream guided realization exhausted memory at 27,699 bins; no candidate."
+    },
+    {
+      "route": "Guide / single-class LNS",
+      "outcome": "Local guide UNKNOWN; single-class rounds UNKNOWN or optimal without exact-kappa gain."
+    },
+    {
+      "route": "Post-winner evacuation neighbourhoods, 90 and 65 bins",
+      "outcome": "FEASIBLE candidates, no exact-kappa improvement."
+    },
+    {
+      "route": "Plateau neighbourhood families: evacuation (6 rounds), rc (3), call 0 (3), randomized time windows (12)",
+      "outcome": "No exact-kappa improvement; legal alternative maps existed."
+    }
+  ],
+  "overlap": {
+    "method": "Complete paginated GitHub REST inventory of open pull requests and repository discussions; title/body search plus inspection of nearest prior T16 results.",
+    "checked_utc": "2026-10-17 21:23:20 UTC",
+    "snapshot": "evidence/OVERLAP.json; 350 open PRs and 321 discussion records returned by the API.",
+    "finding": "No open PR for this T16 multi-role owner-packing improvement. Nearest work is distinct: Discussion #1332 / closed PR #1343 exactly censused single whole-helper moves and found no legal strictly improving one-role relocation, explicitly excluding multi-role repacking; this contribution changes multiple owner rows jointly and passes full replay. Discussion #1265 / closed PR #1276 bounded within-group repartitions of the selected map\u2019s unhosted idle rank-48 children (kappa ceiling 0.001673151843213755, no admitted gain); this full owner repack reaches 0.001673618490895016 by changing hosted-helper placements and the aggregate idle profile. Discussion #1339 / PR #1387 priced a structural idle-axis optimum but its overlay failed the actual stream-composition check. Open PR #1807 certifies selected owner-row bindings in Lean, and #3209 changes T16 audit parsing; neither changes the packing.",
+    "added_value": "An exact-replayed, multi-row legal owner-map improvement beyond the single-relocation census and idle-only repartition domains, with exact pricing and independent controls.",
+    "limits": "A matching title or nearby scoped result is not proof of global novelty; this claim is restricted to the fixed selected word and supplier."
+  },
+  "interpretation": {
+    "word_ceiling": "ceiling.ceiling() gives a_hi = 0.001690054109089; under kappa < a/(1+a), the kappa ceiling is about 0.001687202645325402.",
+    "fraction_of_kappa_ceiling": "0.99194871198902958766575607143578602999758455859606",
+    "proved_packing_ceiling": "The unchanged exact checker proves E <= 908139.013 and at most 4,887 empty cap-48 bins; neither statement is a kappa optimality bound.",
+    "fraction_of_selected_to_ceiling_gap_closed": "0.0658963196377817987102974155083040295071362586"
+  },
+  "moment_cost_probe": {
+    "status": "Exploratory local-only negative result; no later OR-Tools search justified by these runs.",
+    "idea": "On a copy of lns2.py, minimize the separable complex moment contribution f*(73/f)^a per bin at the incumbent endpoint a=0.001676424185410303243034, rounded to integer coefficients; exact supplier pricing decides acceptance.",
+    "reproducibility": "The copied experimental edit was not retained in the package. These probes are not required to reproduce the shipped map or its verification.",
+    "runs": [
+      {
+        "mode": "evac",
+        "seed": 20261020,
+        "bins": 135,
+        "helpers": 410,
+        "variables": 11441,
+        "coefficient_scale": 1000000000,
+        "status": "FEASIBLE",
+        "objective": 134698962470,
+        "incumbent_objective": 134698962470,
+        "best_bound": 134677813389,
+        "seconds": 298.9,
+        "exact_kappa": "0.001673618490895016",
+        "outcome": "No strict objective improvement; no candidate accepted."
+      },
+      {
+        "mode": "rc",
+        "seed": 20261021,
+        "bins": 224,
+        "helpers": 556,
+        "variables": 5521,
+        "coefficient_scale": 1000000000,
+        "status": "FEASIBLE",
+        "objective": 220861301787,
+        "incumbent_objective": 220722797217,
+        "best_bound": 220566749151,
+        "seconds": 135.4,
+        "candidate_kappa": "0.001673573431572098",
+        "outcome": "The candidate had lower exact kappa and was rejected."
+      },
+      {
+        "mode": "evac",
+        "seed": 20261022,
+        "bins": 50,
+        "helpers": 124,
+        "variables": 1674,
+        "coefficient_scale": 1000000000000,
+        "status": "FEASIBLE",
+        "objective": 320577984465754,
+        "incumbent_objective": 320577984465754,
+        "best_bound": 320577984465753,
+        "seconds": 330.3,
+        "exact_kappa": "0.001673618490895016",
+        "outcome": "Plateau map had the same exact kappa."
+      }
+    ],
+    "conclusion": "This small sample does not establish local optimality. It shows no utility for spending more search budget on this objective/neighbourhood combination now."
+  },
+  "upstream_refresh": {
+    "command": "git fetch --no-tags origin main",
+    "result": "PASS; origin/main resolved to the package base commit 463113d675af7410ac91d53a4fed51ec6494eb9a before submission.",
+    "guidance": "No newer main changes were present at the refresh; the package source bindings remain on the refreshed base."
+  }
+}
diff --git a/research/complex-t16-evacuation-increment/SOURCES.json b/research/complex-t16-evacuation-increment/SOURCES.json
new file mode 100644
index 0000000000..c6dc323d01
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/SOURCES.json
@@ -0,0 +1,276 @@
+{
+  "schema_version": 1,
+  "base_commit": "463113d675af7410ac91d53a4fed51ec6494eb9a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "input",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    },
+    {
+      "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "c24daf067f9c543421d89ca2eeaa4eb78a57fb6f",
+      "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "a2e5a1ffd454a353bd2d2100bc26259ff5b57af7",
+      "sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json",
+      "usage": "input",
+      "git_blob": "526192f5056e4d7abd7c6ecd26d73319bc25d08e",
+      "sha256": "534ace870cabe515987e00f50f71550030965006ea18978e0924590ac6944345"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json",
+      "usage": "input",
+      "git_blob": "d6670b5c1555eff7695811e60f75d1285af16ad2",
+      "sha256": "ee9b86428278392d2c933f76d60e51f5af90d4ab67e4d3937ed2fa416e7755ab"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json",
+      "usage": "input",
+      "git_blob": "c2e057a3ab4e18ad9711bcd24071780918f81c40",
+      "sha256": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json",
+      "usage": "input",
+      "git_blob": "c2e057a3ab4e18ad9711bcd24071780918f81c40",
+      "sha256": "ad3f2b941127688f98ce6872d00f110644f1c2b156f8adad1b6700e838ed0e26"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json",
+      "usage": "input",
+      "git_blob": "ba436009d75f548e6345b7e32a21e343263bc5d4",
+      "sha256": "5c14538134dfffbc58fa4b4d2f26b270ec5f56d17d4bf23752c82964f45171db"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json",
+      "usage": "input",
+      "git_blob": "2b019f86cd37f3112ee051241f93b7ab3ec6261c",
+      "sha256": "79177449e404403964ce1b2f4a9a8bd49e1916daba3123d7fd7f5cfd1f1ac0ea"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz",
+      "usage": "input",
+      "git_blob": "3b2aa5db6747008c9f9c06a572cdc21e14eb8d27",
+      "sha256": "99a18eede965accf65943e490b8d2b2ffb9f1c9bc6babdb825413a80cbea2cde"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json",
+      "usage": "input",
+      "git_blob": "2a81814dca80e70ae99a2f9ca403de07573c36bd",
+      "sha256": "baafef737acc16dafbe1150896feb16744f3d669fa123bb2bff19ecc4e71b275"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json",
+      "usage": "input",
+      "git_blob": "089f202be813ab0221f52b8ac7072d478c3f7497",
+      "sha256": "73b3601a6239502475a272ea0c46945fd42034486aaf43e66a212eb4f012ca44"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json",
+      "usage": "input",
+      "git_blob": "5efe2efe55e1ef33eb3da11642034ad6085c21c1",
+      "sha256": "9a09146e686c4f535b04fdef3753fe01dad8f5e8881a69408a91394acb5b48f5"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json",
+      "usage": "input",
+      "git_blob": "d9a4f84211182ca200c081ea061d724c8a2cfb70",
+      "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz",
+      "usage": "input",
+      "git_blob": "3b0a475178f4e4ad107e3595992c872e47e83c63",
+      "sha256": "de2be0f4b6d24ace368fd5b834b7a00f9625d0a1824c4ff969f2db5f115db667"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+      "usage": "input",
+      "git_blob": "2fed13f432df4d76ce72185dd79fac63d96aee96",
+      "sha256": "322d29d43dbee8130cde15d4bf05396698b5e3dfe3735813899db91cc0ba7955"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py",
+      "usage": "input",
+      "git_blob": "14a90fa0e788217856f070382c9e61bd7c603c61",
+      "sha256": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py",
+      "usage": "input",
+      "git_blob": "7d697cb45203fe72d97037403d6da41f71f3b7fd",
+      "sha256": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py",
+      "usage": "input",
+      "git_blob": "43007488ad2c43187c77cc6798beff8b1cd76ad2",
+      "sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json",
+      "usage": "input",
+      "git_blob": "b61d859826246e0c3dabbe096e57ad7015eadfd5",
+      "sha256": "06eccee9f6b77e140833df83407e7996dc948c17d49b0779ab171fbe463fd28d"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py",
+      "usage": "input",
+      "git_blob": "650fc9fd77fd61930ab3a352cd8d0fb5b7f0f03b",
+      "sha256": "f5eae94aca965d0008bc07cff8245ccb7509042ccad457d3bcb7d51c1e9409f0"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json",
+      "usage": "input",
+      "git_blob": "a16bf40bccc81278a443e0d5f09b44495035de81",
+      "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478"
+    },
+    {
+      "path": "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz",
+      "usage": "input",
+      "git_blob": "3e28a9b59f8fde608e59ebd5fbdbc22ca54558d4",
+      "sha256": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    },
+    {
+      "path": "research/complex-t16-rare-pattern-exchanges/data/OWNERS.json.gz",
+      "usage": "input",
+      "git_blob": "d3ba33d7e703a3229d9fb8a360f69d2f318bbb70",
+      "sha256": "87902c528dfab7d503dcf8a784260e3ab6fb7424c418a1820f7261f25be7b6bc"
+    },
+    {
+      "path": "research/complex-t16-rare-pattern-exchanges/data/PLAN.json",
+      "usage": "input",
+      "git_blob": "f1bec76e8e9b7a1f09c1e05cb6cce973b6e59f1b",
+      "sha256": "7bd786ba8e66408f02aa9ef446eaf20c1bfe981ea2e4dd1e5a929f0aa7767bc0"
+    },
+    {
+      "path": "research/complex-t16-rare-pattern-exchanges/data/SPEC.json",
+      "usage": "input",
+      "git_blob": "af013ccc2975d9d575d116f8a463cc947f220c8d",
+      "sha256": "8cb51f25a5da4a29d3783853025b73ff1f452429d4fdb30c599e598bcab0e71d"
+    },
+    {
+      "path": "research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz",
+      "usage": "input",
+      "git_blob": "2970ef79b0441e937449bed30f68f2e0558186ba",
+      "sha256": "d4acf04daef85d4514f80ec5fcd2492d0c60e5d6c49fa71b3e6523f8db2dea86"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/LOCAL-PINS.json",
+      "usage": "input",
+      "git_blob": "e0f4d3152145ff103105c6e0ff0df9771e4de545",
+      "sha256": "c9e7ad3818f2a841ea0d224089ca2f975caff2d04cc12b55f072fca88df53140"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/ceiling_bound.py",
+      "usage": "input",
+      "git_blob": "dafb8c087c1ed45e6851e03bb8bc8f4a527e4597",
+      "sha256": "b8e22ba9ae03677b814de8d145f5a86eee21bc0d1d89642cbb41f9dabd15791b"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/check.py",
+      "usage": "input",
+      "git_blob": "4651e0f89f2c6fe0a59161b15a88bb3e2ee65ce6",
+      "sha256": "a7f7b3274109879ca10c7eda275bc247aae09bff1eb0a56151ae698c35bf4639"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/data/OWNERS.json.gz",
+      "usage": "input",
+      "git_blob": "aa664b8e35816e1b09b3a4cd8c3cf40e329cc073",
+      "sha256": "551fd1b3a75fa5fd67cfd8c00a6c77c2f893a5120cb0c0dd8a7699f25e9bddba"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/data/PLAN.json",
+      "usage": "input",
+      "git_blob": "99a48b1c72f02629fbbac00d74d01559eb6e7292",
+      "sha256": "67173cd2e38296699e596714deb8b98e199bcb3390b49c2218887011a07f23da"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/data/SPEC.json",
+      "usage": "input",
+      "git_blob": "fb46407cc69d658f15429908d773c10c0e81ae29",
+      "sha256": "e81f2dabf16bc4d56d427bf5bc4a06f05ce27fc6c539c3de4029cb5304ed9701"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/search/buildcand.py",
+      "usage": "input",
+      "git_blob": "28bd3641523d656cd26c1533a6e0eeb695b3c99a",
+      "sha256": "d9929e5ecfc9e9fcde3e73aa1cfe9ceba4e5032e80b808685014b1b340fa5669"
+    },
+    {
+      "path": "research/complex-t16-two-stage-cycles/search/lib.py",
+      "usage": "input",
+      "git_blob": "0e4de9240bc1a4c5d773bc18846f2ec882903313",
+      "sha256": "bd76fda0a3fe47005f898b41c563bb8ba8296a7214a0540bdcf06b22a135ff24"
+    },
+    {
+      "path": "research/frontier1094-idle-star-ceiling/analyze.py",
+      "usage": "input",
+      "git_blob": "c0521d10ddfc92e089e01e6b025ed8bd4b8d177f",
+      "sha256": "d9768cff06d5e19e75b2ccc4d03ff5bc2d93098f3192c167d3f208c802877bbc"
+    },
+    {
+      "path": "research/pending-claims-independent-pricing/SNAPSHOT.json",
+      "usage": "input",
+      "git_blob": "cab5ae8e67e646b38429548fab1cc53b25e7617f",
+      "sha256": "9f1a69818b64abacd96bde1809e750349ce7c79d45b77490ddcd3e213ac08613"
+    },
+    {
+      "path": "research/pending-claims-independent-pricing/arith.py",
+      "usage": "input",
+      "git_blob": "b9e30144438b375ee999e53c5fe7051e381e4c6f",
+      "sha256": "1b4766610223bbf5e346d7cebc036eaeaedfa2f7200c075136bd750ab26ece88"
+    },
+    {
+      "path": "research/pending-claims-independent-pricing/sweep.py",
+      "usage": "input",
+      "git_blob": "dc60fab01d7e72b3cbfa536a925c78fdd9ff8f78",
+      "sha256": "aeafc6a5e39817a893fa8392f4f7e767b23437e3317067075bb9d5552e3df23f"
+    },
+    {
+      "path": "research/t16-owner-audit-seed67/SOURCES.json",
+      "usage": "input",
+      "git_blob": "92b80c5f45c16a43f56a8ce51147cb5bd14c5e6a",
+      "sha256": "d3d71303dcd25fe84a3e026c4ad53535607ba6b288fd144736ad2a5376390396"
+    },
+    {
+      "path": "research/t16-owner-audit-seed67/inputs/k8-seven-slot-word.json.gz",
+      "usage": "input",
+      "git_blob": "723decbca8995e916d6f4b783aa3e1ddd4eb47fe",
+      "sha256": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289"
+    },
+    {
+      "path": "research/t16-owner-audit-seed67/verify.py",
+      "usage": "input",
+      "git_blob": "3ff276c3040ec4a52db932e0bcdd31df5a3cf0a4",
+      "sha256": "f6e27f76c9ccb87b3ce6c5e673588338a09847d22771da7b3f28579661c9404b"
+    }
+  ]
+}
diff --git a/research/complex-t16-evacuation-increment/TASK.json b/research/complex-t16-evacuation-increment/TASK.json
new file mode 100644
index 0000000000..eef5e5e56b
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/TASK.json
@@ -0,0 +1,78 @@
+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 6,
+  "base_commit": "463113d675af7410ac91d53a4fed51ec6494eb9a",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md",
+      "research/complex-local-word-ceiling/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ],
+    "existing_checks": [
+      {
+        "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.",
+        "evidence": "docs/research/community-efficient1000-review.md",
+        "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.",
+        "status": "reviewed",
+        "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "unchanged",
+  "actual_scope": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+  "scope_change_reason": null,
+  "bottleneck_link": "A better owner packing changes the idle residual profile of the fixed complex supplier and therefore improves its exactly priced endpoint, while staying below the same word-level ceiling. The bit supplier, local word, coverage law, template, and outer guard remain fixed.",
+  "budget_minutes": 540,
+  "stop_rule": "Keep the best exact-kappa map, then stop this bounded session after strict and independent replay and 24 subsequent evacuation/relocation/call/time-window neighbourhood rounds fail to improve exact kappa. This is a search stop, not an optimality criterion.",
+  "outcome": "completed",
+  "evidence": "SEARCH.json and evidence/: an OR-Tools CP-SAT evacuation neighbourhood produced a strict-replayed candidate at exact kappa 0.001673618490895016, up 4.285169321e-9 (0.0002560428% relative) over the immediately preceding map. The independent seed67 audit, exact pricing of both suppliers, PR1069 sweep, and unchanged 11-stage strict replay pass with controls 69/12/6/15. ceiling.ceiling() gives a_hi=0.001690054109089 and implied kappa ceiling 0.001687202645325402; the candidate realizes 99.194871% of that ceiling. The exact packing certificate remains E<=908139.013 and at most 4,887 empty cap-48 bins (candidate: 4,880); it is not a kappa bound. No optimum is claimed. The live 2026-10-17 21:23 UTC overlap refresh returned 350 open PRs and 321 discussion records, with no matching open T16 owner-packing PR; nearest scoped results are recorded in SEARCH.json and evidence/OVERLAP.json.",
+  "author": "OpenAI Codex (user-directed; donor name not recorded)",
+  "ai_assistance": "Substantial OpenAI Codex assistance: OR-Tools search orchestration, candidate packaging, documentation, and verifier integration. OR-Tools 9.11.4210 supplied the CP-SAT solver; exact replay, independent pricing, and ceiling checks supplied the acceptance evidence. No independent human review is claimed.",
+  "open_questions": [
+    {
+      "question": "Can exact supplier costs drive a decomposed master problem with pricing cuts more effectively than a rounded separable moment objective?",
+      "why_it_matters": "Three bounded rounded-moment CP-SAT probes produced no strict kappa gain, and the accepted map has higher surrogate E than its predecessor despite higher exact kappa. The residual profile is coupled through the exact supplier pricing function, so a master/pricing loop may preserve more of the true objective structure.",
+      "first_step": "Use the pinned exact engines to price a bounded set of residual-profile moves, derive valid discrete marginal cuts for a small master problem, then reconstruct and strict-replay every proposed owner map.",
+      "blocked_by": "No exact or safely useful discrete cut description for the nonlinear aggregate pricing function has been derived; the three local moment probes are exploratory and do not establish a local optimum."
+    },
+    {
+      "question": "Can the fixed-word kappa ceiling be tightened to a certificate on the remaining gap, or can a concrete packing approach it further?",
+      "why_it_matters": "The current candidate realizes 99.194871% of the word ceiling, but the ceiling is an endpoint relaxation rather than a packing optimum, and seven more empty cap-48 bins remain possible under the coarse packing certificate.",
+      "first_step": "Price the exact bound-attaining and near-bound idle profiles, then formulate a small residual-class CP-SAT model with exact post-pricing of its realized maps.",
+      "blocked_by": "The current E and empty-bin bounds do not imply a kappa bound or a realizable owner map."
+    }
+  ]
+}
diff --git a/research/complex-t16-evacuation-increment/VERIFY.json b/research/complex-t16-evacuation-increment/VERIFY.json
new file mode 100644
index 0000000000..f876d0368a
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/VERIFY.json
@@ -0,0 +1,62 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/community-frontier1094-audit/ASSEMBLY.json",
+    "research/community-frontier1094-audit/selected-replay.tar.gz",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-RECIPES.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CLIFFORD-REVIEW.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-LOCAL-REPLAY.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INDEPENDENT-REPLAY.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/INTEGRATION.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-CHECKS.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/LOCAL-PROGRAMS.json.gz",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/RESIDUAL-ADAPTERS.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/SCALAR-FRAME-AUDIT.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/WRAPPER-CHECKS.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json",
+    "research/community-k492-audit/pr622/replay/baseline558/complex-global/controller-input/split-centres/CANONICAL-WORD.json.gz",
+    "research/complex-k492-owner-repair/vendor/multicold/code/run_portable.py",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py",
+    "research/complex-k492-owner-repair/vendor/multicold/inputs/PR543-EXPECTED.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/code/prepare_supplier_base.py",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz",
+    "research/complex-local-word-ceiling/ceiling.py",
+    "research/complex-t16-rare-pattern-exchanges/data/OWNERS.json.gz",
+    "research/complex-t16-rare-pattern-exchanges/data/PLAN.json",
+    "research/complex-t16-rare-pattern-exchanges/data/SPEC.json",
+    "research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz",
+    "research/complex-t16-two-stage-cycles/LOCAL-PINS.json",
+    "research/complex-t16-two-stage-cycles/ceiling_bound.py",
+    "research/complex-t16-two-stage-cycles/check.py",
+    "research/complex-t16-two-stage-cycles/data/OWNERS.json.gz",
+    "research/complex-t16-two-stage-cycles/data/PLAN.json",
+    "research/complex-t16-two-stage-cycles/data/SPEC.json",
+    "research/complex-t16-two-stage-cycles/search/buildcand.py",
+    "research/complex-t16-two-stage-cycles/search/lib.py",
+    "research/frontier1094-idle-star-ceiling/analyze.py",
+    "research/pending-claims-independent-pricing/SNAPSHOT.json",
+    "research/pending-claims-independent-pricing/arith.py",
+    "research/pending-claims-independent-pricing/sweep.py",
+    "research/t16-owner-audit-seed67/SOURCES.json",
+    "research/t16-owner-audit-seed67/inputs/k8-seven-slot-word.json.gz",
+    "research/t16-owner-audit-seed67/verify.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Reconstruct the 163-row delta and semantically regenerate OWNER/PLAN/SPEC while authenticating byte hashes; run unchanged strict T16 replay with controls; independently audit and price both suppliers plus PR1069 sweep; run ceiling.ceiling() and exact packing-ceiling checker. No optimizer or optimality claim."
+    }
+  ]
+}
diff --git a/research/complex-t16-evacuation-increment/data/OWNERS.json.gz b/research/complex-t16-evacuation-increment/data/OWNERS.json.gz
new file mode 100644
index 0000000000..333908e718
Binary files /dev/null and b/research/complex-t16-evacuation-increment/data/OWNERS.json.gz differ
diff --git a/research/complex-t16-evacuation-increment/data/PLAN.json b/research/complex-t16-evacuation-increment/data/PLAN.json
new file mode 100644
index 0000000000..cb802762de
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/data/PLAN.json
@@ -0,0 +1,85661 @@
+{
+  "status": "FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION",
+  "mode": "gauge44-all144-t16-idle-concentration",
+  "K": 4,
+  "T": 16,
+  "M": 73,
+  "L": 9,
+  "live": 14336,
+  "deficit": 5120,
+  "profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62318,
+    "4": 20448,
+    "5": 11808,
+    "7": 2,
+    "8": 1152,
+    "16": 2,
+    "48": 4880
+  },
+  "order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      8
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      0,
+      9
+    ],
+    [
+      1,
+      0
+    ],
+    [
+      1,
+      8
+    ],
+    [
+      0,
+      2
+    ],
+    [
+      0,
+      10
+    ],
+    [
+      1,
+      1
+    ],
+    [
+      1,
+      9
+    ],
+    [
+      2,
+      0
+    ],
+    [
+      2,
+      8
+    ],
+    [
+      0,
+      3
+    ],
+    [
+      0,
+      11
+    ],
+    [
+      1,
+      2
+    ],
+    [
+      1,
+      10
+    ],
+    [
+      2,
+      1
+    ],
+    [
+      2,
+      9
+    ],
+    [
+      3,
+      0
+    ],
+    [
+      3,
+      8
+    ],
+    [
+      0,
+      4
+    ],
+    [
+      0,
+      12
+    ],
+    [
+      1,
+      3
+    ],
+    [
+      1,
+      11
+    ],
+    [
+      2,
+      2
+    ],
+    [
+      2,
+      10
+    ],
+    [
+      3,
+      1
+    ],
+    [
+      3,
+      9
+    ],
+    [
+      4,
+      0
+    ],
+    [
+      4,
+      8
+    ],
+    [
+      0,
+      5
+    ],
+    [
+      0,
+      13
+    ],
+    [
+      1,
+      4
+    ],
+    [
+      1,
+      12
+    ],
+    [
+      2,
+      3
+    ],
+    [
+      2,
+      11
+    ],
+    [
+      3,
+      2
+    ],
+    [
+      3,
+      10
+    ],
+    [
+      4,
+      1
+    ],
+    [
+      4,
+      9
+    ],
+    [
+      5,
+      0
+    ],
+    [
+      5,
+      8
+    ],
+    [
+      0,
+      6
+    ],
+    [
+      0,
+      14
+    ],
+    [
+      1,
+      5
+    ],
+    [
+      1,
+      13
+    ],
+    [
+      2,
+      4
+    ],
+    [
+      2,
+      12
+    ],
+    [
+      3,
+      3
+    ],
+    [
+      3,
+      11
+    ],
+    [
+      4,
+      2
+    ],
+    [
+      4,
+      10
+    ],
+    [
+      5,
+      1
+    ],
+    [
+      5,
+      9
+    ],
+    [
+      0,
+      7
+    ],
+    [
+      0,
+      15
+    ],
+    [
+      6,
+      0
+    ],
+    [
+      6,
+      8
+    ],
+    [
+      1,
+      6
+    ],
+    [
+      1,
+      14
+    ],
+    [
+      2,
+      5
+    ],
+    [
+      2,
+      13
+    ],
+    [
+      3,
+      4
+    ],
+    [
+      3,
+      12
+    ],
+    [
+      4,
+      3
+    ],
+    [
+      4,
+      11
+    ],
+    [
+      5,
+      2
+    ],
+    [
+      5,
+      10
+    ],
+    [
+      6,
+      1
+    ],
+    [
+      6,
+      9
+    ],
+    [
+      1,
+      7
+    ],
+    [
+      1,
+      15
+    ],
+    [
+      7,
+      0
+    ],
+    [
+      7,
+      8
+    ],
+    [
+      2,
+      6
+    ],
+    [
+      2,
+      14
+    ],
+    [
+      3,
+      5
+    ],
+    [
+      3,
+      13
+    ],
+    [
+      4,
+      4
+    ],
+    [
+      4,
+      12
+    ],
+    [
+      5,
+      3
+    ],
+    [
+      5,
+      11
+    ],
+    [
+      6,
+      2
+    ],
+    [
+      6,
+      10
+    ],
+    [
+      7,
+      1
+    ],
+    [
+      7,
+      9
+    ],
+    [
+      2,
+      7
+    ],
+    [
+      2,
+      15
+    ],
+    [
+      8,
+      0
+    ],
+    [
+      8,
+      8
+    ],
+    [
+      3,
+      6
+    ],
+    [
+      3,
+      14
+    ],
+    [
+      4,
+      5
+    ],
+    [
+      4,
+      13
+    ],
+    [
+      5,
+      4
+    ],
+    [
+      5,
+      12
+    ],
+    [
+      6,
+      3
+    ],
+    [
+      6,
+      11
+    ],
+    [
+      7,
+      2
+    ],
+    [
+      7,
+      10
+    ],
+    [
+      8,
+      1
+    ],
+    [
+      8,
+      9
+    ],
+    [
+      3,
+      7
+    ],
+    [
+      3,
+      15
+    ],
+    [
+      4,
+      6
+    ],
+    [
+      4,
+      14
+    ],
+    [
+      5,
+      5
+    ],
+    [
+      5,
+      13
+    ],
+    [
+      6,
+      4
+    ],
+    [
+      6,
+      12
+    ],
+    [
+      7,
+      3
+    ],
+    [
+      7,
+      11
+    ],
+    [
+      8,
+      2
+    ],
+    [
+      8,
+      10
+    ],
+    [
+      4,
+      7
+    ],
+    [
+      4,
+      15
+    ],
+    [
+      5,
+      6
+    ],
+    [
+      5,
+      14
+    ],
+    [
+      6,
+      5
+    ],
+    [
+      6,
+      13
+    ],
+    [
+      7,
+      4
+    ],
+    [
+      7,
+      12
+    ],
+    [
+      8,
+      3
+    ],
+    [
+      8,
+      11
+    ],
+    [
+      5,
+      7
+    ],
+    [
+      5,
+      15
+    ],
+    [
+      6,
+      6
+    ],
+    [
+      6,
+      14
+    ],
+    [
+      7,
+      5
+    ],
+    [
+      7,
+      13
+    ],
+    [
+      8,
+      4
+    ],
+    [
+      8,
+      12
+    ],
+    [
+      6,
+      7
+    ],
+    [
+      6,
+      15
+    ],
+    [
+      7,
+      6
+    ],
+    [
+      7,
+      14
+    ],
+    [
+      8,
+      5
+    ],
+    [
+      8,
+      13
+    ],
+    [
+      7,
+      7
+    ],
+    [
+      7,
+      15
+    ],
+    [
+      8,
+      6
+    ],
+    [
+      8,
+      14
+    ],
+    [
+      8,
+      7
+    ],
+    [
+      8,
+      15
+    ]
+  ],
+  "windows": {
+    "0,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4
+      ]
+    ],
+    "0,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4
+      ]
+    ],
+    "8,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5
+      ]
+    ],
+    "8,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5
+      ]
+    ],
+    "1,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8
+      ]
+    ],
+    "1,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8
+      ]
+    ],
+    "9,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9
+      ]
+    ],
+    "9,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9
+      ]
+    ],
+    "0,1": [
+      8,
+      [
+        5,
+        6,
+        7,
+        8,
+        9,
+        10
+      ]
+    ],
+    "0,3": [
+      8,
+      [
+        5,
+        6,
+        7,
+        8,
+        9,
+        10
+      ]
+    ],
+    "8,1": [
+      8,
+      [
+        6,
+        7,
+        8,
+        9,
+        10,
+        11
+      ]
+    ],
+    "8,3": [
+      8,
+      [
+        6,
+        7,
+        8,
+        9,
+        10,
+        11
+      ]
+    ],
+    "2,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    ],
+    "2,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14
+      ]
+    ],
+    "10,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15
+      ]
+    ],
+    "10,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15
+      ]
+    ],
+    "1,1": [
+      8,
+      [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16
+      ]
+    ],
+    "1,3": [
+      8,
+      [
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16
+      ]
+    ],
+    "9,1": [
+      8,
+      [
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17
+      ]
+    ],
+    "9,3": [
+      8,
+      [
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17
+      ]
+    ],
+    "0,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18
+      ]
+    ],
+    "0,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18
+      ]
+    ],
+    "8,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19
+      ]
+    ],
+    "8,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19
+      ]
+    ],
+    "3,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22
+      ]
+    ],
+    "3,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22
+      ]
+    ],
+    "11,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23
+      ]
+    ],
+    "11,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23
+      ]
+    ],
+    "2,1": [
+      8,
+      [
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24
+      ]
+    ],
+    "2,3": [
+      8,
+      [
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24
+      ]
+    ],
+    "10,1": [
+      8,
+      [
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25
+      ]
+    ],
+    "10,3": [
+      8,
+      [
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25
+      ]
+    ],
+    "1,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26
+      ]
+    ],
+    "1,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26
+      ]
+    ],
+    "9,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27
+      ]
+    ],
+    "9,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27
+      ]
+    ],
+    "0,5": [
+      8,
+      [
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28
+      ]
+    ],
+    "0,7": [
+      8,
+      [
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28
+      ]
+    ],
+    "8,5": [
+      8,
+      [
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29
+      ]
+    ],
+    "8,7": [
+      8,
+      [
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29
+      ]
+    ],
+    "4,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32
+      ]
+    ],
+    "4,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32
+      ]
+    ],
+    "12,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33
+      ]
+    ],
+    "12,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33
+      ]
+    ],
+    "3,1": [
+      8,
+      [
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34
+      ]
+    ],
+    "3,3": [
+      8,
+      [
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34
+      ]
+    ],
+    "11,1": [
+      8,
+      [
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35
+      ]
+    ],
+    "11,3": [
+      8,
+      [
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35
+      ]
+    ],
+    "2,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36
+      ]
+    ],
+    "2,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36
+      ]
+    ],
+    "10,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37
+      ]
+    ],
+    "10,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37
+      ]
+    ],
+    "1,5": [
+      8,
+      [
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38
+      ]
+    ],
+    "1,7": [
+      8,
+      [
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38
+      ]
+    ],
+    "9,5": [
+      8,
+      [
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39
+      ]
+    ],
+    "9,7": [
+      8,
+      [
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39
+      ]
+    ],
+    "0,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40
+      ]
+    ],
+    "0,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40
+      ]
+    ],
+    "8,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41
+      ]
+    ],
+    "8,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41
+      ]
+    ],
+    "5,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44
+      ]
+    ],
+    "5,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44
+      ]
+    ],
+    "13,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45
+      ]
+    ],
+    "13,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45
+      ]
+    ],
+    "4,1": [
+      8,
+      [
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46
+      ]
+    ],
+    "4,3": [
+      8,
+      [
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46
+      ]
+    ],
+    "12,1": [
+      8,
+      [
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47
+      ]
+    ],
+    "12,3": [
+      8,
+      [
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47
+      ]
+    ],
+    "3,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48
+      ]
+    ],
+    "3,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48
+      ]
+    ],
+    "11,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49
+      ]
+    ],
+    "11,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49
+      ]
+    ],
+    "2,5": [
+      8,
+      [
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50
+      ]
+    ],
+    "2,7": [
+      8,
+      [
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50
+      ]
+    ],
+    "10,5": [
+      8,
+      [
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51
+      ]
+    ],
+    "10,7": [
+      8,
+      [
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51
+      ]
+    ],
+    "1,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52
+      ]
+    ],
+    "1,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52
+      ]
+    ],
+    "9,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53
+      ]
+    ],
+    "9,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53
+      ]
+    ],
+    "0,9": [
+      8,
+      [
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56
+      ]
+    ],
+    "0,11": [
+      8,
+      [
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56
+      ]
+    ],
+    "8,9": [
+      8,
+      [
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57
+      ]
+    ],
+    "8,11": [
+      8,
+      [
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57
+      ]
+    ],
+    "6,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58
+      ]
+    ],
+    "6,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58
+      ]
+    ],
+    "14,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59
+      ]
+    ],
+    "14,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59
+      ]
+    ],
+    "5,1": [
+      8,
+      [
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60
+      ]
+    ],
+    "5,3": [
+      8,
+      [
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60
+      ]
+    ],
+    "13,1": [
+      8,
+      [
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61
+      ]
+    ],
+    "13,3": [
+      8,
+      [
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61
+      ]
+    ],
+    "4,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62
+      ]
+    ],
+    "4,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62
+      ]
+    ],
+    "12,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63
+      ]
+    ],
+    "12,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63
+      ]
+    ],
+    "3,5": [
+      8,
+      [
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64
+      ]
+    ],
+    "3,7": [
+      8,
+      [
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64
+      ]
+    ],
+    "11,5": [
+      8,
+      [
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65
+      ]
+    ],
+    "11,7": [
+      8,
+      [
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65
+      ]
+    ],
+    "2,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66
+      ]
+    ],
+    "2,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66
+      ]
+    ],
+    "10,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67
+      ]
+    ],
+    "10,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67
+      ]
+    ],
+    "1,9": [
+      8,
+      [
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68
+      ]
+    ],
+    "1,11": [
+      8,
+      [
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68
+      ]
+    ],
+    "9,9": [
+      8,
+      [
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69
+      ]
+    ],
+    "9,11": [
+      8,
+      [
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69
+      ]
+    ],
+    "7,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70
+      ]
+    ],
+    "7,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70
+      ]
+    ],
+    "15,0": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71
+      ]
+    ],
+    "15,2": [
+      16,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71
+      ]
+    ],
+    "6,1": [
+      8,
+      [
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74
+      ]
+    ],
+    "6,3": [
+      8,
+      [
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74
+      ]
+    ],
+    "14,1": [
+      8,
+      [
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75
+      ]
+    ],
+    "14,3": [
+      8,
+      [
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75
+      ]
+    ],
+    "5,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76
+      ]
+    ],
+    "5,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76
+      ]
+    ],
+    "13,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77
+      ]
+    ],
+    "13,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77
+      ]
+    ],
+    "4,5": [
+      8,
+      [
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78
+      ]
+    ],
+    "4,7": [
+      8,
+      [
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78
+      ]
+    ],
+    "12,5": [
+      8,
+      [
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79
+      ]
+    ],
+    "12,7": [
+      8,
+      [
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79
+      ]
+    ],
+    "3,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80
+      ]
+    ],
+    "3,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80
+      ]
+    ],
+    "11,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81
+      ]
+    ],
+    "11,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81
+      ]
+    ],
+    "2,9": [
+      8,
+      [
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82
+      ]
+    ],
+    "2,11": [
+      8,
+      [
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82
+      ]
+    ],
+    "10,9": [
+      8,
+      [
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83
+      ]
+    ],
+    "10,11": [
+      8,
+      [
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83
+      ]
+    ],
+    "7,1": [
+      8,
+      [
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86
+      ]
+    ],
+    "7,3": [
+      8,
+      [
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86
+      ]
+    ],
+    "15,1": [
+      8,
+      [
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87
+      ]
+    ],
+    "15,3": [
+      8,
+      [
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87
+      ]
+    ],
+    "0,12": [
+      48,
+      [
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "0,13": [
+      48,
+      [
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "0,14": [
+      32,
+      [
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "0,15": [
+      32,
+      [
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "0,16": [
+      16,
+      [
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "0,17": [
+      16,
+      [
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88
+      ]
+    ],
+    "8,12": [
+      48,
+      [
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "8,13": [
+      48,
+      [
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "8,14": [
+      32,
+      [
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "8,15": [
+      32,
+      [
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "8,16": [
+      16,
+      [
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "8,17": [
+      16,
+      [
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89
+      ]
+    ],
+    "6,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90
+      ]
+    ],
+    "6,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90
+      ]
+    ],
+    "14,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91
+      ]
+    ],
+    "14,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91
+      ]
+    ],
+    "5,5": [
+      8,
+      [
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92
+      ]
+    ],
+    "5,7": [
+      8,
+      [
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92
+      ]
+    ],
+    "13,5": [
+      8,
+      [
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93
+      ]
+    ],
+    "13,7": [
+      8,
+      [
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93
+      ]
+    ],
+    "4,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94
+      ]
+    ],
+    "4,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94
+      ]
+    ],
+    "12,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95
+      ]
+    ],
+    "12,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95
+      ]
+    ],
+    "3,9": [
+      8,
+      [
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96
+      ]
+    ],
+    "3,11": [
+      8,
+      [
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96
+      ]
+    ],
+    "11,9": [
+      8,
+      [
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97
+      ]
+    ],
+    "11,11": [
+      8,
+      [
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97
+      ]
+    ],
+    "1,12": [
+      48,
+      [
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "1,13": [
+      48,
+      [
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "1,14": [
+      32,
+      [
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "1,15": [
+      32,
+      [
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "1,16": [
+      16,
+      [
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "1,17": [
+      16,
+      [
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100
+      ]
+    ],
+    "9,12": [
+      48,
+      [
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "9,13": [
+      48,
+      [
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "9,14": [
+      32,
+      [
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "9,15": [
+      32,
+      [
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "9,16": [
+      16,
+      [
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "9,17": [
+      16,
+      [
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101
+      ]
+    ],
+    "7,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102
+      ]
+    ],
+    "7,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102
+      ]
+    ],
+    "15,4": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103
+      ]
+    ],
+    "15,6": [
+      32,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103
+      ]
+    ],
+    "6,5": [
+      8,
+      [
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104
+      ]
+    ],
+    "6,7": [
+      8,
+      [
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104
+      ]
+    ],
+    "14,5": [
+      8,
+      [
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105
+      ]
+    ],
+    "14,7": [
+      8,
+      [
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105
+      ]
+    ],
+    "5,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106
+      ]
+    ],
+    "5,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106
+      ]
+    ],
+    "13,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107
+      ]
+    ],
+    "13,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107
+      ]
+    ],
+    "4,9": [
+      8,
+      [
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108
+      ]
+    ],
+    "4,11": [
+      8,
+      [
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108
+      ]
+    ],
+    "12,9": [
+      8,
+      [
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109
+      ]
+    ],
+    "12,11": [
+      8,
+      [
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109
+      ]
+    ],
+    "2,12": [
+      48,
+      [
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "2,13": [
+      48,
+      [
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "2,14": [
+      32,
+      [
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "2,15": [
+      32,
+      [
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "2,16": [
+      16,
+      [
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "2,17": [
+      16,
+      [
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112
+      ]
+    ],
+    "10,12": [
+      48,
+      [
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "10,13": [
+      48,
+      [
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "10,14": [
+      32,
+      [
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "10,15": [
+      32,
+      [
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "10,16": [
+      16,
+      [
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "10,17": [
+      16,
+      [
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113
+      ]
+    ],
+    "7,5": [
+      8,
+      [
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114
+      ]
+    ],
+    "7,7": [
+      8,
+      [
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114
+      ]
+    ],
+    "15,5": [
+      8,
+      [
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115
+      ]
+    ],
+    "15,7": [
+      8,
+      [
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115
+      ]
+    ],
+    "6,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116
+      ]
+    ],
+    "6,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116
+      ]
+    ],
+    "14,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117
+      ]
+    ],
+    "14,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117
+      ]
+    ],
+    "5,9": [
+      8,
+      [
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118
+      ]
+    ],
+    "5,11": [
+      8,
+      [
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118
+      ]
+    ],
+    "13,9": [
+      8,
+      [
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119
+      ]
+    ],
+    "13,11": [
+      8,
+      [
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119
+      ]
+    ],
+    "3,12": [
+      48,
+      [
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "3,13": [
+      48,
+      [
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "3,14": [
+      32,
+      [
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "3,15": [
+      32,
+      [
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "3,16": [
+      16,
+      [
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "3,17": [
+      16,
+      [
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122
+      ]
+    ],
+    "11,12": [
+      48,
+      [
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "11,13": [
+      48,
+      [
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "11,14": [
+      32,
+      [
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "11,15": [
+      32,
+      [
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "11,16": [
+      16,
+      [
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "11,17": [
+      16,
+      [
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123
+      ]
+    ],
+    "7,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124
+      ]
+    ],
+    "7,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124
+      ]
+    ],
+    "15,8": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125
+      ]
+    ],
+    "15,10": [
+      48,
+      [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8,
+        9,
+        10,
+        11,
+        12,
+        13,
+        14,
+        15,
+        16,
+        17,
+        18,
+        19,
+        20,
+        21,
+        22,
+        23,
+        24,
+        25,
+        26,
+        27,
+        28,
+        29,
+        30,
+        31,
+        32,
+        33,
+        34,
+        35,
+        36,
+        37,
+        38,
+        39,
+        40,
+        41,
+        42,
+        43,
+        44,
+        45,
+        46,
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125
+      ]
+    ],
+    "6,9": [
+      8,
+      [
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126
+      ]
+    ],
+    "6,11": [
+      8,
+      [
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126
+      ]
+    ],
+    "14,9": [
+      8,
+      [
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127
+      ]
+    ],
+    "14,11": [
+      8,
+      [
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127
+      ]
+    ],
+    "4,12": [
+      48,
+      [
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "4,13": [
+      48,
+      [
+        47,
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "4,14": [
+      32,
+      [
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "4,15": [
+      32,
+      [
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "4,16": [
+      16,
+      [
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "4,17": [
+      16,
+      [
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130
+      ]
+    ],
+    "12,12": [
+      48,
+      [
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "12,13": [
+      48,
+      [
+        48,
+        49,
+        50,
+        51,
+        52,
+        53,
+        54,
+        55,
+        56,
+        57,
+        58,
+        59,
+        60,
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "12,14": [
+      32,
+      [
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "12,15": [
+      32,
+      [
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "12,16": [
+      16,
+      [
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "12,17": [
+      16,
+      [
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131
+      ]
+    ],
+    "7,9": [
+      8,
+      [
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132
+      ]
+    ],
+    "7,11": [
+      8,
+      [
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132
+      ]
+    ],
+    "15,9": [
+      8,
+      [
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133
+      ]
+    ],
+    "15,11": [
+      8,
+      [
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133
+      ]
+    ],
+    "5,12": [
+      48,
+      [
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "5,13": [
+      48,
+      [
+        61,
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "5,14": [
+      32,
+      [
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "5,15": [
+      32,
+      [
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "5,16": [
+      16,
+      [
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "5,17": [
+      16,
+      [
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136
+      ]
+    ],
+    "13,12": [
+      48,
+      [
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "13,13": [
+      48,
+      [
+        62,
+        63,
+        64,
+        65,
+        66,
+        67,
+        68,
+        69,
+        70,
+        71,
+        72,
+        73,
+        74,
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "13,14": [
+      32,
+      [
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "13,15": [
+      32,
+      [
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "13,16": [
+      16,
+      [
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "13,17": [
+      16,
+      [
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137
+      ]
+    ],
+    "6,12": [
+      48,
+      [
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "6,13": [
+      48,
+      [
+        75,
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "6,14": [
+      32,
+      [
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "6,15": [
+      32,
+      [
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "6,16": [
+      16,
+      [
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "6,17": [
+      16,
+      [
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140
+      ]
+    ],
+    "14,12": [
+      48,
+      [
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "14,13": [
+      48,
+      [
+        76,
+        77,
+        78,
+        79,
+        80,
+        81,
+        82,
+        83,
+        84,
+        85,
+        86,
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "14,14": [
+      32,
+      [
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "14,15": [
+      32,
+      [
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "14,16": [
+      16,
+      [
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "14,17": [
+      16,
+      [
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141
+      ]
+    ],
+    "7,12": [
+      48,
+      [
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "7,13": [
+      48,
+      [
+        87,
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "7,14": [
+      32,
+      [
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "7,15": [
+      32,
+      [
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "7,16": [
+      16,
+      [
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "7,17": [
+      16,
+      [
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142
+      ]
+    ],
+    "15,12": [
+      48,
+      [
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ],
+    "15,13": [
+      48,
+      [
+        88,
+        89,
+        90,
+        91,
+        92,
+        93,
+        94,
+        95,
+        96,
+        97,
+        98,
+        99,
+        100,
+        101,
+        102,
+        103,
+        104,
+        105,
+        106,
+        107,
+        108,
+        109,
+        110,
+        111,
+        112,
+        113,
+        114,
+        115,
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ],
+    "15,14": [
+      32,
+      [
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ],
+    "15,15": [
+      32,
+      [
+        116,
+        117,
+        118,
+        119,
+        120,
+        121,
+        122,
+        123,
+        124,
+        125,
+        126,
+        127,
+        128,
+        129,
+        130,
+        131,
+        132,
+        133,
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ],
+    "15,16": [
+      16,
+      [
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ],
+    "15,17": [
+      16,
+      [
+        134,
+        135,
+        136,
+        137,
+        138,
+        139,
+        140,
+        141,
+        142,
+        143
+      ]
+    ]
+  },
+  "sides": {
+    "0": 0,
+    "2": 1,
+    "1": 0,
+    "3": 1,
+    "4": 0,
+    "6": 1,
+    "5": 0,
+    "7": 1,
+    "8": 0,
+    "10": 1,
+    "9": 0,
+    "11": 1,
+    "12": 0,
+    "13": 1,
+    "14": 0,
+    "15": 1,
+    "16": 0,
+    "17": 1
+  },
+  "pairs": {
+    "0": 1,
+    "2": 1,
+    "1": 1,
+    "3": 1,
+    "4": 2,
+    "6": 2,
+    "5": 2,
+    "7": 2,
+    "8": 3,
+    "10": 3,
+    "9": 3,
+    "11": 3,
+    "12": 0,
+    "13": 0,
+    "14": 1,
+    "15": 1,
+    "16": 2,
+    "17": 2
+  },
+  "solver_status": "exact pattern-flow LNS on the T16 actual-window geometry",
+  "gap": null,
+  "provider_calls": [
+    {
+      "time": 0,
+      "stage": 0,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 1,
+      "stage": 0,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 2,
+      "stage": 0,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 3,
+      "stage": 0,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 4,
+      "stage": 1,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 5,
+      "stage": 1,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 6,
+      "stage": 0,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 7,
+      "stage": 0,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 8,
+      "stage": 1,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 9,
+      "stage": 1,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 10,
+      "stage": 2,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 11,
+      "stage": 2,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 12,
+      "stage": 0,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 13,
+      "stage": 0,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 14,
+      "stage": 1,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 15,
+      "stage": 1,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 16,
+      "stage": 2,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 17,
+      "stage": 2,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 18,
+      "stage": 3,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 19,
+      "stage": 3,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 20,
+      "stage": 0,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 21,
+      "stage": 0,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 22,
+      "stage": 1,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 23,
+      "stage": 1,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 24,
+      "stage": 2,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 25,
+      "stage": 2,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 26,
+      "stage": 3,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 27,
+      "stage": 3,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 28,
+      "stage": 4,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 29,
+      "stage": 4,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 30,
+      "stage": 0,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 31,
+      "stage": 0,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 32,
+      "stage": 1,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 33,
+      "stage": 1,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 34,
+      "stage": 2,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 35,
+      "stage": 2,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 36,
+      "stage": 3,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 37,
+      "stage": 3,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 38,
+      "stage": 4,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 39,
+      "stage": 4,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 40,
+      "stage": 5,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 41,
+      "stage": 5,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 42,
+      "stage": 0,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 43,
+      "stage": 0,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 44,
+      "stage": 1,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 45,
+      "stage": 1,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 46,
+      "stage": 2,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 47,
+      "stage": 2,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 48,
+      "stage": 3,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 49,
+      "stage": 3,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 50,
+      "stage": 4,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 51,
+      "stage": 4,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 52,
+      "stage": 5,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 53,
+      "stage": 5,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 54,
+      "stage": 0,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 55,
+      "stage": 0,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 56,
+      "stage": 6,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 57,
+      "stage": 6,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 58,
+      "stage": 1,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 59,
+      "stage": 1,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 60,
+      "stage": 2,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 61,
+      "stage": 2,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 62,
+      "stage": 3,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 63,
+      "stage": 3,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 64,
+      "stage": 4,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 65,
+      "stage": 4,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 66,
+      "stage": 5,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 67,
+      "stage": 5,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 68,
+      "stage": 6,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 69,
+      "stage": 6,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 70,
+      "stage": 1,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 71,
+      "stage": 1,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 72,
+      "stage": 7,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 73,
+      "stage": 7,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 74,
+      "stage": 2,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 75,
+      "stage": 2,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 76,
+      "stage": 3,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 77,
+      "stage": 3,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 78,
+      "stage": 4,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 79,
+      "stage": 4,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 80,
+      "stage": 5,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 81,
+      "stage": 5,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 82,
+      "stage": 6,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 83,
+      "stage": 6,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 84,
+      "stage": 7,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 85,
+      "stage": 7,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 86,
+      "stage": 2,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 87,
+      "stage": 2,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 88,
+      "stage": 8,
+      "replica": 0,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 89,
+      "stage": 8,
+      "replica": 8,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 90,
+      "stage": 3,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 91,
+      "stage": 3,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 92,
+      "stage": 4,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 93,
+      "stage": 4,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 94,
+      "stage": 5,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 95,
+      "stage": 5,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 96,
+      "stage": 6,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 97,
+      "stage": 6,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 98,
+      "stage": 7,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 99,
+      "stage": 7,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 100,
+      "stage": 8,
+      "replica": 1,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 101,
+      "stage": 8,
+      "replica": 9,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 102,
+      "stage": 3,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 103,
+      "stage": 3,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 104,
+      "stage": 4,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 105,
+      "stage": 4,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 106,
+      "stage": 5,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 107,
+      "stage": 5,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 108,
+      "stage": 6,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 109,
+      "stage": 6,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 110,
+      "stage": 7,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 111,
+      "stage": 7,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 112,
+      "stage": 8,
+      "replica": 2,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 113,
+      "stage": 8,
+      "replica": 10,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 114,
+      "stage": 4,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 115,
+      "stage": 4,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 116,
+      "stage": 5,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 117,
+      "stage": 5,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 118,
+      "stage": 6,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 119,
+      "stage": 6,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 120,
+      "stage": 7,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 121,
+      "stage": 7,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 122,
+      "stage": 8,
+      "replica": 3,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 123,
+      "stage": 8,
+      "replica": 11,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 124,
+      "stage": 5,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 125,
+      "stage": 5,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 126,
+      "stage": 6,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 127,
+      "stage": 6,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 128,
+      "stage": 7,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 129,
+      "stage": 7,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 130,
+      "stage": 8,
+      "replica": 4,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 131,
+      "stage": 8,
+      "replica": 12,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 132,
+      "stage": 6,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 133,
+      "stage": 6,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 134,
+      "stage": 7,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 135,
+      "stage": 7,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 136,
+      "stage": 8,
+      "replica": 5,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 137,
+      "stage": 8,
+      "replica": 13,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 138,
+      "stage": 7,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 139,
+      "stage": 7,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "backward",
+      "local_program_sha256": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+    },
+    {
+      "time": 140,
+      "stage": 8,
+      "replica": 6,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 141,
+      "stage": 8,
+      "replica": 14,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 142,
+      "stage": 8,
+      "replica": 7,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    },
+    {
+      "time": 143,
+      "stage": 8,
+      "replica": 15,
+      "provider": "gauge44",
+      "orientation": "forward",
+      "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+    }
+  ],
+  "per_call_widths": [
+    {
+      "stage": 0,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 0,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 1,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 2,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 0,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 8,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 1,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 9,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 3,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 2,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 10,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 4,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 3,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 11,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 5,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 4,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 12,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 6,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 5,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 13,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 7,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 6,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 14,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 7,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    },
+    {
+      "stage": 8,
+      "replica": 15,
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ]
+    }
+  ],
+  "provider_registry": {
+    "gauge44": {
+      "directory": "providers/gauge44",
+      "artifact_sha256": {
+        "CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+        "LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+        "LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+        "INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "CLIFFORD-REVIEW.json": "59e1f8d7215c79081f70b953f85fcbaac2a32a75b8b12448f667b17271405f9e",
+        "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c"
+      },
+      "ports": [
+        11,
+        19,
+        35,
+        67,
+        131,
+        259,
+        13,
+        21,
+        37,
+        69,
+        133,
+        261,
+        41,
+        73,
+        137,
+        265,
+        49,
+        81,
+        145,
+        273,
+        161,
+        289,
+        193,
+        321,
+        385,
+        14,
+        22,
+        38,
+        70,
+        134,
+        262,
+        26,
+        74,
+        138,
+        266,
+        50,
+        146,
+        274,
+        98,
+        162,
+        290,
+        194,
+        322,
+        386,
+        28,
+        44,
+        140,
+        268,
+        84,
+        148,
+        276,
+        100,
+        164,
+        292,
+        196,
+        324,
+        388,
+        56,
+        88,
+        152,
+        280,
+        104,
+        168,
+        296,
+        200,
+        328,
+        392,
+        112,
+        176,
+        304,
+        208,
+        336,
+        400,
+        224,
+        352,
+        416,
+        448,
+        508,
+        506,
+        502,
+        494,
+        478,
+        446,
+        382,
+        254,
+        505,
+        501,
+        493,
+        477,
+        445,
+        381,
+        253,
+        499,
+        491,
+        475,
+        443,
+        379,
+        251,
+        487,
+        471,
+        439,
+        375,
+        247,
+        463,
+        431,
+        367,
+        239,
+        415,
+        351,
+        223,
+        319,
+        191
+      ],
+      "centers": [
+        92,
+        57,
+        81,
+        224,
+        11,
+        240,
+        9,
+        256
+      ],
+      "widths": [
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        8,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        4,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        4,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        7,
+        7,
+        8,
+        9,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        9,
+        7,
+        8,
+        8,
+        9,
+        9,
+        9,
+        9,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        9,
+        8,
+        9,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        8,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ],
+      "actual_paid_profile": {
+        "1": 2412,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82,
+        "8": 8
+      },
+      "orientation_program_sha256": {
+        "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+        "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23"
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+        "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+        "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+        "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+        "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+      }
+    }
+  },
+  "source_plan_sha256": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08",
+  "assignment_sha256": "0875c29c3da8ea23a20d4d261f7f6bcdb4b1eab750547eff8a7fc12e4dfc463b",
+  "source_owners_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a",
+  "assignment_content_sha256": "bb9438a7995d0d25689cfa079df9851064ff1eafd72e6a9549f480ea28dfd348",
+  "replica_lift": {
+    "groups": 2,
+    "source_replicas": 8,
+    "replicas": 16,
+    "parent_template_content_sha256": "8904bbbf46dfbf1c6df0e43479a23913fc59a410e879188112e88f16c850ede8",
+    "owners_file_sha256": "0875c29c3da8ea23a20d4d261f7f6bcdb4b1eab750547eff8a7fc12e4dfc463b",
+    "window_semantics": "strict physical source-event touch intervals, including bridges",
+    "schedule_content_sha256": "ef9b70f30251e90ca15f54e7802cedf9b2d23bdc150e8f2bc18c916d0f2f2312"
+  }
+}
diff --git a/research/complex-t16-evacuation-increment/data/SPEC.json b/research/complex-t16-evacuation-increment/data/SPEC.json
new file mode 100644
index 0000000000..7bc6168205
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/data/SPEC.json
@@ -0,0 +1,1975 @@
+{
+  "schema": "witness-spec/1",
+  "name": "gauge44-t16-two-bank",
+  "data": {
+    "owners_sha256": "0875c29c3da8ea23a20d4d261f7f6bcdb4b1eab750547eff8a7fc12e4dfc463b",
+    "plan_sha256": "7360bb466117ebae4ddeb551de25f857bac97a7abe8a2bf5ff0cc35498aff851"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      9,
+      "gauge44"
+    ],
+    [
+      1,
+      0,
+      "gauge44"
+    ],
+    [
+      1,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      10,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      1,
+      9,
+      "gauge44"
+    ],
+    [
+      2,
+      0,
+      "gauge44"
+    ],
+    [
+      2,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      3,
+      "gauge44"
+    ],
+    [
+      0,
+      11,
+      "gauge44"
+    ],
+    [
+      1,
+      2,
+      "gauge44"
+    ],
+    [
+      1,
+      10,
+      "gauge44"
+    ],
+    [
+      2,
+      1,
+      "gauge44"
+    ],
+    [
+      2,
+      9,
+      "gauge44"
+    ],
+    [
+      3,
+      0,
+      "gauge44"
+    ],
+    [
+      3,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      4,
+      "gauge44"
+    ],
+    [
+      0,
+      12,
+      "gauge44"
+    ],
+    [
+      1,
+      3,
+      "gauge44"
+    ],
+    [
+      1,
+      11,
+      "gauge44"
+    ],
+    [
+      2,
+      2,
+      "gauge44"
+    ],
+    [
+      2,
+      10,
+      "gauge44"
+    ],
+    [
+      3,
+      1,
+      "gauge44"
+    ],
+    [
+      3,
+      9,
+      "gauge44"
+    ],
+    [
+      4,
+      0,
+      "gauge44"
+    ],
+    [
+      4,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      5,
+      "gauge44"
+    ],
+    [
+      0,
+      13,
+      "gauge44"
+    ],
+    [
+      1,
+      4,
+      "gauge44"
+    ],
+    [
+      1,
+      12,
+      "gauge44"
+    ],
+    [
+      2,
+      3,
+      "gauge44"
+    ],
+    [
+      2,
+      11,
+      "gauge44"
+    ],
+    [
+      3,
+      2,
+      "gauge44"
+    ],
+    [
+      3,
+      10,
+      "gauge44"
+    ],
+    [
+      4,
+      1,
+      "gauge44"
+    ],
+    [
+      4,
+      9,
+      "gauge44"
+    ],
+    [
+      5,
+      0,
+      "gauge44"
+    ],
+    [
+      5,
+      8,
+      "gauge44"
+    ],
+    [
+      0,
+      6,
+      "gauge44"
+    ],
+    [
+      0,
+      14,
+      "gauge44"
+    ],
+    [
+      1,
+      5,
+      "gauge44"
+    ],
+    [
+      1,
+      13,
+      "gauge44"
+    ],
+    [
+      2,
+      4,
+      "gauge44"
+    ],
+    [
+      2,
+      12,
+      "gauge44"
+    ],
+    [
+      3,
+      3,
+      "gauge44"
+    ],
+    [
+      3,
+      11,
+      "gauge44"
+    ],
+    [
+      4,
+      2,
+      "gauge44"
+    ],
+    [
+      4,
+      10,
+      "gauge44"
+    ],
+    [
+      5,
+      1,
+      "gauge44"
+    ],
+    [
+      5,
+      9,
+      "gauge44"
+    ],
+    [
+      0,
+      7,
+      "gauge44"
+    ],
+    [
+      0,
+      15,
+      "gauge44"
+    ],
+    [
+      6,
+      0,
+      "gauge44"
+    ],
+    [
+      6,
+      8,
+      "gauge44"
+    ],
+    [
+      1,
+      6,
+      "gauge44"
+    ],
+    [
+      1,
+      14,
+      "gauge44"
+    ],
+    [
+      2,
+      5,
+      "gauge44"
+    ],
+    [
+      2,
+      13,
+      "gauge44"
+    ],
+    [
+      3,
+      4,
+      "gauge44"
+    ],
+    [
+      3,
+      12,
+      "gauge44"
+    ],
+    [
+      4,
+      3,
+      "gauge44"
+    ],
+    [
+      4,
+      11,
+      "gauge44"
+    ],
+    [
+      5,
+      2,
+      "gauge44"
+    ],
+    [
+      5,
+      10,
+      "gauge44"
+    ],
+    [
+      6,
+      1,
+      "gauge44"
+    ],
+    [
+      6,
+      9,
+      "gauge44"
+    ],
+    [
+      1,
+      7,
+      "gauge44"
+    ],
+    [
+      1,
+      15,
+      "gauge44"
+    ],
+    [
+      7,
+      0,
+      "gauge44"
+    ],
+    [
+      7,
+      8,
+      "gauge44"
+    ],
+    [
+      2,
+      6,
+      "gauge44"
+    ],
+    [
+      2,
+      14,
+      "gauge44"
+    ],
+    [
+      3,
+      5,
+      "gauge44"
+    ],
+    [
+      3,
+      13,
+      "gauge44"
+    ],
+    [
+      4,
+      4,
+      "gauge44"
+    ],
+    [
+      4,
+      12,
+      "gauge44"
+    ],
+    [
+      5,
+      3,
+      "gauge44"
+    ],
+    [
+      5,
+      11,
+      "gauge44"
+    ],
+    [
+      6,
+      2,
+      "gauge44"
+    ],
+    [
+      6,
+      10,
+      "gauge44"
+    ],
+    [
+      7,
+      1,
+      "gauge44"
+    ],
+    [
+      7,
+      9,
+      "gauge44"
+    ],
+    [
+      2,
+      7,
+      "gauge44"
+    ],
+    [
+      2,
+      15,
+      "gauge44"
+    ],
+    [
+      8,
+      0,
+      "gauge44"
+    ],
+    [
+      8,
+      8,
+      "gauge44"
+    ],
+    [
+      3,
+      6,
+      "gauge44"
+    ],
+    [
+      3,
+      14,
+      "gauge44"
+    ],
+    [
+      4,
+      5,
+      "gauge44"
+    ],
+    [
+      4,
+      13,
+      "gauge44"
+    ],
+    [
+      5,
+      4,
+      "gauge44"
+    ],
+    [
+      5,
+      12,
+      "gauge44"
+    ],
+    [
+      6,
+      3,
+      "gauge44"
+    ],
+    [
+      6,
+      11,
+      "gauge44"
+    ],
+    [
+      7,
+      2,
+      "gauge44"
+    ],
+    [
+      7,
+      10,
+      "gauge44"
+    ],
+    [
+      8,
+      1,
+      "gauge44"
+    ],
+    [
+      8,
+      9,
+      "gauge44"
+    ],
+    [
+      3,
+      7,
+      "gauge44"
+    ],
+    [
+      3,
+      15,
+      "gauge44"
+    ],
+    [
+      4,
+      6,
+      "gauge44"
+    ],
+    [
+      4,
+      14,
+      "gauge44"
+    ],
+    [
+      5,
+      5,
+      "gauge44"
+    ],
+    [
+      5,
+      13,
+      "gauge44"
+    ],
+    [
+      6,
+      4,
+      "gauge44"
+    ],
+    [
+      6,
+      12,
+      "gauge44"
+    ],
+    [
+      7,
+      3,
+      "gauge44"
+    ],
+    [
+      7,
+      11,
+      "gauge44"
+    ],
+    [
+      8,
+      2,
+      "gauge44"
+    ],
+    [
+      8,
+      10,
+      "gauge44"
+    ],
+    [
+      4,
+      7,
+      "gauge44"
+    ],
+    [
+      4,
+      15,
+      "gauge44"
+    ],
+    [
+      5,
+      6,
+      "gauge44"
+    ],
+    [
+      5,
+      14,
+      "gauge44"
+    ],
+    [
+      6,
+      5,
+      "gauge44"
+    ],
+    [
+      6,
+      13,
+      "gauge44"
+    ],
+    [
+      7,
+      4,
+      "gauge44"
+    ],
+    [
+      7,
+      12,
+      "gauge44"
+    ],
+    [
+      8,
+      3,
+      "gauge44"
+    ],
+    [
+      8,
+      11,
+      "gauge44"
+    ],
+    [
+      5,
+      7,
+      "gauge44"
+    ],
+    [
+      5,
+      15,
+      "gauge44"
+    ],
+    [
+      6,
+      6,
+      "gauge44"
+    ],
+    [
+      6,
+      14,
+      "gauge44"
+    ],
+    [
+      7,
+      5,
+      "gauge44"
+    ],
+    [
+      7,
+      13,
+      "gauge44"
+    ],
+    [
+      8,
+      4,
+      "gauge44"
+    ],
+    [
+      8,
+      12,
+      "gauge44"
+    ],
+    [
+      6,
+      7,
+      "gauge44"
+    ],
+    [
+      6,
+      15,
+      "gauge44"
+    ],
+    [
+      7,
+      6,
+      "gauge44"
+    ],
+    [
+      7,
+      14,
+      "gauge44"
+    ],
+    [
+      8,
+      5,
+      "gauge44"
+    ],
+    [
+      8,
+      13,
+      "gauge44"
+    ],
+    [
+      7,
+      7,
+      "gauge44"
+    ],
+    [
+      7,
+      15,
+      "gauge44"
+    ],
+    [
+      8,
+      6,
+      "gauge44"
+    ],
+    [
+      8,
+      14,
+      "gauge44"
+    ],
+    [
+      8,
+      7,
+      "gauge44"
+    ],
+    [
+      8,
+      15,
+      "gauge44"
+    ]
+  ],
+  "call_order": [
+    [
+      0,
+      0
+    ],
+    [
+      0,
+      8
+    ],
+    [
+      0,
+      1
+    ],
+    [
+      0,
+      9
+    ],
+    [
+      1,
+      0
+    ],
+    [
+      1,
+      8
+    ],
+    [
+      0,
+      2
+    ],
+    [
+      0,
+      10
+    ],
+    [
+      1,
+      1
+    ],
+    [
+      1,
+      9
+    ],
+    [
+      2,
+      0
+    ],
+    [
+      2,
+      8
+    ],
+    [
+      0,
+      3
+    ],
+    [
+      0,
+      11
+    ],
+    [
+      1,
+      2
+    ],
+    [
+      1,
+      10
+    ],
+    [
+      2,
+      1
+    ],
+    [
+      2,
+      9
+    ],
+    [
+      3,
+      0
+    ],
+    [
+      3,
+      8
+    ],
+    [
+      0,
+      4
+    ],
+    [
+      0,
+      12
+    ],
+    [
+      1,
+      3
+    ],
+    [
+      1,
+      11
+    ],
+    [
+      2,
+      2
+    ],
+    [
+      2,
+      10
+    ],
+    [
+      3,
+      1
+    ],
+    [
+      3,
+      9
+    ],
+    [
+      4,
+      0
+    ],
+    [
+      4,
+      8
+    ],
+    [
+      0,
+      5
+    ],
+    [
+      0,
+      13
+    ],
+    [
+      1,
+      4
+    ],
+    [
+      1,
+      12
+    ],
+    [
+      2,
+      3
+    ],
+    [
+      2,
+      11
+    ],
+    [
+      3,
+      2
+    ],
+    [
+      3,
+      10
+    ],
+    [
+      4,
+      1
+    ],
+    [
+      4,
+      9
+    ],
+    [
+      5,
+      0
+    ],
+    [
+      5,
+      8
+    ],
+    [
+      0,
+      6
+    ],
+    [
+      0,
+      14
+    ],
+    [
+      1,
+      5
+    ],
+    [
+      1,
+      13
+    ],
+    [
+      2,
+      4
+    ],
+    [
+      2,
+      12
+    ],
+    [
+      3,
+      3
+    ],
+    [
+      3,
+      11
+    ],
+    [
+      4,
+      2
+    ],
+    [
+      4,
+      10
+    ],
+    [
+      5,
+      1
+    ],
+    [
+      5,
+      9
+    ],
+    [
+      0,
+      7
+    ],
+    [
+      0,
+      15
+    ],
+    [
+      6,
+      0
+    ],
+    [
+      6,
+      8
+    ],
+    [
+      1,
+      6
+    ],
+    [
+      1,
+      14
+    ],
+    [
+      2,
+      5
+    ],
+    [
+      2,
+      13
+    ],
+    [
+      3,
+      4
+    ],
+    [
+      3,
+      12
+    ],
+    [
+      4,
+      3
+    ],
+    [
+      4,
+      11
+    ],
+    [
+      5,
+      2
+    ],
+    [
+      5,
+      10
+    ],
+    [
+      6,
+      1
+    ],
+    [
+      6,
+      9
+    ],
+    [
+      1,
+      7
+    ],
+    [
+      1,
+      15
+    ],
+    [
+      7,
+      0
+    ],
+    [
+      7,
+      8
+    ],
+    [
+      2,
+      6
+    ],
+    [
+      2,
+      14
+    ],
+    [
+      3,
+      5
+    ],
+    [
+      3,
+      13
+    ],
+    [
+      4,
+      4
+    ],
+    [
+      4,
+      12
+    ],
+    [
+      5,
+      3
+    ],
+    [
+      5,
+      11
+    ],
+    [
+      6,
+      2
+    ],
+    [
+      6,
+      10
+    ],
+    [
+      7,
+      1
+    ],
+    [
+      7,
+      9
+    ],
+    [
+      2,
+      7
+    ],
+    [
+      2,
+      15
+    ],
+    [
+      8,
+      0
+    ],
+    [
+      8,
+      8
+    ],
+    [
+      3,
+      6
+    ],
+    [
+      3,
+      14
+    ],
+    [
+      4,
+      5
+    ],
+    [
+      4,
+      13
+    ],
+    [
+      5,
+      4
+    ],
+    [
+      5,
+      12
+    ],
+    [
+      6,
+      3
+    ],
+    [
+      6,
+      11
+    ],
+    [
+      7,
+      2
+    ],
+    [
+      7,
+      10
+    ],
+    [
+      8,
+      1
+    ],
+    [
+      8,
+      9
+    ],
+    [
+      3,
+      7
+    ],
+    [
+      3,
+      15
+    ],
+    [
+      4,
+      6
+    ],
+    [
+      4,
+      14
+    ],
+    [
+      5,
+      5
+    ],
+    [
+      5,
+      13
+    ],
+    [
+      6,
+      4
+    ],
+    [
+      6,
+      12
+    ],
+    [
+      7,
+      3
+    ],
+    [
+      7,
+      11
+    ],
+    [
+      8,
+      2
+    ],
+    [
+      8,
+      10
+    ],
+    [
+      4,
+      7
+    ],
+    [
+      4,
+      15
+    ],
+    [
+      5,
+      6
+    ],
+    [
+      5,
+      14
+    ],
+    [
+      6,
+      5
+    ],
+    [
+      6,
+      13
+    ],
+    [
+      7,
+      4
+    ],
+    [
+      7,
+      12
+    ],
+    [
+      8,
+      3
+    ],
+    [
+      8,
+      11
+    ],
+    [
+      5,
+      7
+    ],
+    [
+      5,
+      15
+    ],
+    [
+      6,
+      6
+    ],
+    [
+      6,
+      14
+    ],
+    [
+      7,
+      5
+    ],
+    [
+      7,
+      13
+    ],
+    [
+      8,
+      4
+    ],
+    [
+      8,
+      12
+    ],
+    [
+      6,
+      7
+    ],
+    [
+      6,
+      15
+    ],
+    [
+      7,
+      6
+    ],
+    [
+      7,
+      14
+    ],
+    [
+      8,
+      5
+    ],
+    [
+      8,
+      13
+    ],
+    [
+      7,
+      7
+    ],
+    [
+      7,
+      15
+    ],
+    [
+      8,
+      6
+    ],
+    [
+      8,
+      14
+    ],
+    [
+      8,
+      7
+    ],
+    [
+      8,
+      15
+    ]
+  ],
+  "width_spot_helpers": [
+    258,
+    270,
+    282,
+    294
+  ],
+  "providers": {
+    "gauge44": {
+      "artifacts": {
+        "LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c"
+      },
+      "expected_local": {
+        "forward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198766,
+          "prefix_l1": "2765345294379392599/1024",
+          "coefficient_work_primitive_count": 98333
+        },
+        "backward": {
+          "events": 24767,
+          "macros": 19693,
+          "real_component_primitives": 198814,
+          "prefix_l1": "14824960514781440791821/64",
+          "coefficient_work_primitive_count": 98365
+        }
+      },
+      "inventory": {
+        "4": 56,
+        "5": 32,
+        "7": 30,
+        "8": 122,
+        "9": 240
+      },
+      "native_negative_controls": 25,
+      "phase_edges": 2896,
+      "expected_profile": {
+        "1": 2412,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82,
+        "8": 8
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+        "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+        "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+        "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+        "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+        "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+        "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+      },
+      "entering": 192,
+      "entrance": 384,
+      "width_digest": "ca0b972f2ee81a50449ce6489ddf9a94be914f84351136c2a9e3f81b37a0e387",
+      "program_hashes": {
+        "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23",
+        "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+      },
+      "complete_contract": {
+        "local": {
+          "backward": {
+            "events": 24767,
+            "macros": 19693,
+            "real_component_primitives": 198814,
+            "prefix_l1": "14824960514781440791821/64",
+            "prefix_bits": 68,
+            "coefficient_work_primitive_count": 98365,
+            "all_exact_columns": 704,
+            "dirty_helper_columns": 480,
+            "all_dirty_helper_columns_restored": true,
+            "private_centres_and_coefficient_work_cleared": true,
+            "pre_wrappers": 240,
+            "post_wrappers": 240,
+            "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+          },
+          "forward": {
+            "events": 24767,
+            "macros": 19693,
+            "real_component_primitives": 198766,
+            "prefix_l1": "2765345294379392599/1024",
+            "prefix_bits": 52,
+            "coefficient_work_primitive_count": 98333,
+            "all_exact_columns": 704,
+            "dirty_helper_columns": 480,
+            "all_dirty_helper_columns_restored": true,
+            "private_centres_and_coefficient_work_cleared": true,
+            "pre_wrappers": 240,
+            "post_wrappers": 240,
+            "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"
+          }
+        },
+        "helpers": 480,
+        "centres": 8,
+        "v": 112,
+        "h": 9,
+        "n": 704,
+        "entering_helpers": 192,
+        "entrance_rank": 384,
+        "terminal_codimension": 206,
+        "hyperplane_ended_helpers": 78,
+        "cold_hyperplane_ended_helpers": 48,
+        "width_inventory": {
+          "4": 56,
+          "5": 32,
+          "7": 30,
+          "8": 122,
+          "9": 240
+        },
+        "widths": [
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          8,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          8,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          4,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          4,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          7,
+          7,
+          8,
+          8,
+          8,
+          8,
+          9,
+          9,
+          9,
+          9,
+          9,
+          9,
+          8,
+          8,
+          8,
+          9,
+          8,
+          8,
+          9,
+          9,
+          9,
+          9,
+          8,
+          9,
+          7,
+          7,
+          8,
+          9,
+          8,
+          8,
+          9,
+          9,
+          9,
+          9,
+          8,
+          9,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          9,
+          7,
+          7,
+          7,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          9,
+          7,
+          8,
+          8,
+          9,
+          9,
+          9,
+          9,
+          8,
+          8,
+          8,
+          8,
+          7,
+          7,
+          7,
+          7,
+          9,
+          8,
+          9,
+          8,
+          8,
+          8,
+          8,
+          8,
+          7,
+          7,
+          9,
+          8,
+          9,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          8,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          7,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          4,
+          8,
+          4,
+          4,
+          4,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5,
+          8,
+          8,
+          8,
+          5,
+          8,
+          5,
+          5,
+          5
+        ],
+        "local_adapters": 387056,
+        "local_primitive_bound": 10038040553630,
+        "compiler": 25934336,
+        "children": 3494,
+        "paid_profile": {
+          "1": 2412,
+          "2": 418,
+          "3": 432,
+          "4": 142,
+          "5": 82,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23",
+          "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+          "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+          "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd",
+          "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8",
+          "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+          "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+          "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f"
+        }
+      },
+      "semantic_phase_sha256": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007",
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001636241501576388",
+    "complex_lower": "838212092705151621517/500000000000000000000000",
+    "conservative_complex_lower": "167642418254791971833/100000000000000000000000",
+    "kappa": "209202311361877/125000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 144
+    },
+    "mutations_rejected": 15,
+    "hosted_residuals": 69120,
+    "rank_mass": 1041408,
+    "actual_73column_sigmas": 10008,
+    "cross_replica_helper_roles": 57417,
+    "idle_remainders": 7394,
+    "idle_remainder_profile": {
+      "1": 2392,
+      "2": 8,
+      "3": 110,
+      "7": 2,
+      "16": 2,
+      "48": 4880
+    },
+    "global_profile": {
+      "1": 349720,
+      "2": 60200,
+      "3": 62318,
+      "4": 20448,
+      "5": 11808,
+      "7": 2,
+      "8": 1152,
+      "16": 2,
+      "48": 4880
+    },
+    "live": 14336,
+    "physical": 14826,
+    "conservative_kappa_decimal": "0.001673618488042206",
+    "kappa_decimal": "0.001673618490895016"
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/complex-t16-evacuation-increment/evidence/CEILING.json b/research/complex-t16-evacuation-increment/evidence/CEILING.json
new file mode 100644
index 0000000000..a92c6d0d6f
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/evidence/CEILING.json
@@ -0,0 +1,281 @@
+{
+ "bins": {
+  "8": 10752,
+  "16": 7168,
+  "32": 7168,
+  "48": 7168
+ },
+ "helpers": {
+  "4": 8064,
+  "5": 4608,
+  "7": 4320,
+  "8": 17568,
+  "9": 34560
+ },
+ "idle_total": 237024,
+ "patterns": 1163,
+ "theorem1": {
+  "a": {
+   "4": 3,
+   "5": 3,
+   "7": 5,
+   "8": 6,
+   "9": 7
+  },
+  "A": {
+   "8": 6,
+   "16": 12,
+   "32": 24,
+   "48": 37
+  },
+  "bin_weight": 587776,
+  "helper_weight": 406944,
+  "slack_total": 180832,
+  "max_empty_cap48": 4887
+ },
+ "theorem2": {
+  "lambda_over_ln48": "36/37",
+  "bound_over_ln48": "8679936/37",
+  "bound_decimal": "908156.136",
+  "tight_patterns": [
+   [
+    8,
+    [
+     0,
+     0,
+     0,
+     1,
+     0
+    ],
+    0
+   ],
+   [
+    8,
+    [
+     2,
+     0,
+     0,
+     0,
+     0
+    ],
+    0
+   ],
+   [
+    16,
+    [
+     0,
+     0,
+     0,
+     2,
+     0
+    ],
+    0
+   ],
+   [
+    16,
+    [
+     0,
+     0,
+     1,
+     0,
+     1
+    ],
+    0
+   ],
+   [
+    16,
+    [
+     2,
+     0,
+     0,
+     1,
+     0
+    ],
+    0
+   ],
+   [
+    16,
+    [
+     4,
+     0,
+     0,
+     0,
+     0
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     0,
+     0,
+     0,
+     4,
+     0
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     0,
+     0,
+     1,
+     2,
+     1
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     0,
+     0,
+     2,
+     0,
+     2
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     0,
+     1,
+     0,
+     0,
+     3
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     1,
+     0,
+     0,
+     0,
+     3
+    ],
+    1
+   ],
+   [
+    32,
+    [
+     2,
+     0,
+     0,
+     3,
+     0
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     2,
+     0,
+     1,
+     1,
+     1
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     4,
+     0,
+     0,
+     2,
+     0
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     4,
+     0,
+     1,
+     0,
+     1
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     6,
+     0,
+     0,
+     1,
+     0
+    ],
+    0
+   ],
+   [
+    32,
+    [
+     8,
+     0,
+     0,
+     0,
+     0
+    ],
+    0
+   ],
+   [
+    48,
+    [
+     0,
+     0,
+     0,
+     0,
+     0
+    ],
+    48
+   ],
+   [
+    48,
+    [
+     1,
+     0,
+     0,
+     1,
+     4
+    ],
+    0
+   ],
+   [
+    48,
+    [
+     3,
+     0,
+     0,
+     0,
+     4
+    ],
+    0
+   ]
+  ]
+ },
+ "theorem3": {
+  "rho_item": {
+   "slack": 34,
+   "free": 44
+  },
+  "bound": "4887 g(48) + g(17)",
+  "bound_decimal": "908139.013",
+  "float_full_knapsack": 908139.013
+ },
+ "this_map": {
+  "empty_cap48": 4880,
+  "E": 907279.723,
+  "surrogate_gap": 859.29,
+  "one_free_bins_by_cap_and_slack": {
+   "32,0": 2390,
+   "48,1": 2
+  }
+ }
+}
diff --git a/research/complex-t16-evacuation-increment/evidence/CHECK.json b/research/complex-t16-evacuation-increment/evidence/CHECK.json
new file mode 100644
index 0000000000..11cc57cb1e
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/evidence/CHECK.json
@@ -0,0 +1,2408 @@
+{
+ "spec_idle": {
+  "1": 2392,
+  "2": 8,
+  "3": 110,
+  "7": 2,
+  "16": 2,
+  "48": 4880
+ },
+ "selected": {
+  "idle": {
+   "1": 2276,
+   "3": 377,
+   "7": 7,
+   "48": 4866
+  },
+  "profile": {
+   "1": 349604,
+   "2": 60192,
+   "3": 62585,
+   "4": 20448,
+   "5": 11808,
+   "7": 7,
+   "8": 1152,
+   "48": 4866
+  },
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "controls": 11,
+  "cross_replica_roles": 57480
+ },
+ "candidate": {
+  "idle": {
+   "1": 2392,
+   "2": 8,
+   "3": 110,
+   "7": 2,
+   "16": 2,
+   "48": 4880
+  },
+  "profile": {
+   "1": 349720,
+   "2": 60200,
+   "3": 62318,
+   "4": 20448,
+   "5": 11808,
+   "7": 2,
+   "8": 1152,
+   "16": 2,
+   "48": 4880
+  },
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "controls": 11,
+  "cross_replica_roles": 57417
+ },
+ "changed_rows": 2683,
+ "relocated_rows": [
+  49,
+  51,
+  53,
+  58,
+  60,
+  65,
+  67,
+  69,
+  224,
+  225,
+  226,
+  227,
+  228,
+  229,
+  230,
+  283,
+  472,
+  473,
+  523,
+  529,
+  579,
+  595,
+  611,
+  639,
+  641,
+  650,
+  788,
+  826,
+  861,
+  869,
+  879,
+  885,
+  891,
+  893,
+  909,
+  911,
+  939,
+  952,
+  1018,
+  1081,
+  1184,
+  1191,
+  1194,
+  1218,
+  1227,
+  1374,
+  1453,
+  1489,
+  1524,
+  1527,
+  1595,
+  1645,
+  1648,
+  1649,
+  1653,
+  1662,
+  1664,
+  1665,
+  1666,
+  1667,
+  1668,
+  1669,
+  1670,
+  1671,
+  1672,
+  1673,
+  1676,
+  1677,
+  1678,
+  1679,
+  1681,
+  1685,
+  1694,
+  1695,
+  1696,
+  1697,
+  1698,
+  1700,
+  1701,
+  1706,
+  1711,
+  1724,
+  1725,
+  1727,
+  1747,
+  1796,
+  1811,
+  1813,
+  1814,
+  1815,
+  1859,
+  1861,
+  1862,
+  1863,
+  1867,
+  1873,
+  1874,
+  1884,
+  1888,
+  1969,
+  1971,
+  1973,
+  1978,
+  1985,
+  2001,
+  2007,
+  2017,
+  2021,
+  2023,
+  2026,
+  2035,
+  2042,
+  2051,
+  2053,
+  2058,
+  2065,
+  2071,
+  2081,
+  2082,
+  2089,
+  2090,
+  2091,
+  2097,
+  2099,
+  2102,
+  2106,
+  2109,
+  2110,
+  2112,
+  2113,
+  2116,
+  2117,
+  2119,
+  2121,
+  2123,
+  2127,
+  2128,
+  2129,
+  2131,
+  2152,
+  2156,
+  2160,
+  2162,
+  2164,
+  2168,
+  2169,
+  2170,
+  2171,
+  2176,
+  2188,
+  2189,
+  2190,
+  2191,
+  2198,
+  2200,
+  2211,
+  2226,
+  2244,
+  2245,
+  2303,
+  2310,
+  2318,
+  2319,
+  2323,
+  2326,
+  2331,
+  2333,
+  2334,
+  2342,
+  2347,
+  2350,
+  2388,
+  2396,
+  2449,
+  2451,
+  2488,
+  2656,
+  2667,
+  2668,
+  2669,
+  2725,
+  2744,
+  2799,
+  2805,
+  2827,
+  2830,
+  2876,
+  2929,
+  2931,
+  2933,
+  2938,
+  2945,
+  2947,
+  2997,
+  3013,
+  3262,
+  3267,
+  3269,
+  3275,
+  3277,
+  3278,
+  3283,
+  3285,
+  3287,
+  3343,
+  3447,
+  3463,
+  3569,
+  3583,
+  3608,
+  3609,
+  3610,
+  3611,
+  3612,
+  3613,
+  3699,
+  3790,
+  3889,
+  3891,
+  3893,
+  3898,
+  3905,
+  3907,
+  3909,
+  3914,
+  3921,
+  3923,
+  3925,
+  3930,
+  3936,
+  3937,
+  3939,
+  3940,
+  3941,
+  3946,
+  3947,
+  3953,
+  3954,
+  3955,
+  3956,
+  3957,
+  3959,
+  3960,
+  3962,
+  3963,
+  3964,
+  3968,
+  3972,
+  3974,
+  3979,
+  4023,
+  4059,
+  4062,
+  4078,
+  4083,
+  4087,
+  4094,
+  4097,
+  4099,
+  4107,
+  4108,
+  4109,
+  4120,
+  4121,
+  4135,
+  4146,
+  4174,
+  4184,
+  4186,
+  4269,
+  4306,
+  4420,
+  4483,
+  4526,
+  4537,
+  4538,
+  4540,
+  4542,
+  4552,
+  4553,
+  4554,
+  4562,
+  4574,
+  4576,
+  4578,
+  4579,
+  4586,
+  4589,
+  4590,
+  4598,
+  4601,
+  4603,
+  4607,
+  4613,
+  4699,
+  4701,
+  4707,
+  4710,
+  4711,
+  4715,
+  4718,
+  4719,
+  4723,
+  4725,
+  4731,
+  4874,
+  4938,
+  4945,
+  4947,
+  4949,
+  4954,
+  4961,
+  4970,
+  5000,
+  5024,
+  5025,
+  5026,
+  5027,
+  5028,
+  5029,
+  5030,
+  5031,
+  5060,
+  5061,
+  5064,
+  5084,
+  5179,
+  5181,
+  5182,
+  5189,
+  5190,
+  5191,
+  5195,
+  5197,
+  5199,
+  5205,
+  5206,
+  5211,
+  5213,
+  5227,
+  5229,
+  5354,
+  5367,
+  5427,
+  5429,
+  5434,
+  5441,
+  5443,
+  5445,
+  5450,
+  5476,
+  5477,
+  5478,
+  5479,
+  5480,
+  5481,
+  5482,
+  5483,
+  5484,
+  5485,
+  5486,
+  5487,
+  5488,
+  5489,
+  5491,
+  5492,
+  5493,
+  5494,
+  5495,
+  5496,
+  5497,
+  5498,
+  5499,
+  5500,
+  5501,
+  5502,
+  5503,
+  5504,
+  5505,
+  5506,
+  5507,
+  5508,
+  5509,
+  5510,
+  5511,
+  5512,
+  5513,
+  5514,
+  5515,
+  5516,
+  5517,
+  5518,
+  5519,
+  5520,
+  5521,
+  5522,
+  5523,
+  5524,
+  5525,
+  5526,
+  5527,
+  5534,
+  5535,
+  5536,
+  5537,
+  5538,
+  5539,
+  5540,
+  5541,
+  5546,
+  5547,
+  5548,
+  5549,
+  5550,
+  5551,
+  5555,
+  5558,
+  5559,
+  5560,
+  5561,
+  5563,
+  5564,
+  5565,
+  5567,
+  5570,
+  5571,
+  5572,
+  5573,
+  5575,
+  5586,
+  5587,
+  5588,
+  5589,
+  5598,
+  5599,
+  5602,
+  5603,
+  5604,
+  5605,
+  5610,
+  5611,
+  5612,
+  5614,
+  5616,
+  5624,
+  5626,
+  5659,
+  5661,
+  5662,
+  5663,
+  5667,
+  5669,
+  5670,
+  5671,
+  5675,
+  5677,
+  5678,
+  5679,
+  5683,
+  5686,
+  5687,
+  5693,
+  5694,
+  5695,
+  5707,
+  5709,
+  5710,
+  5809,
+  5845,
+  5847,
+  5863,
+  5893,
+  5898,
+  5905,
+  5909,
+  5914,
+  5921,
+  5923,
+  5925,
+  5930,
+  5984,
+  5985,
+  5986,
+  5987,
+  5988,
+  5989,
+  5990,
+  5991,
+  6008,
+  6009,
+  6010,
+  6011,
+  6012,
+  6013,
+  6020,
+  6021,
+  6022,
+  6023,
+  6024,
+  6025,
+  6032,
+  6033,
+  6034,
+  6036,
+  6037,
+  6042,
+  6044,
+  6045,
+  6046,
+  6048,
+  6049,
+  6054,
+  6056,
+  6057,
+  6058,
+  6059,
+  6060,
+  6061,
+  6062,
+  6063,
+  6064,
+  6065,
+  6067,
+  6068,
+  6069,
+  6070,
+  6071,
+  6072,
+  6073,
+  6074,
+  6075,
+  6076,
+  6077,
+  6079,
+  6080,
+  6081,
+  6086,
+  6087,
+  6088,
+  6089,
+  6090,
+  6091,
+  6092,
+  6093,
+  6095,
+  6097,
+  6098,
+  6099,
+  6100,
+  6101,
+  6102,
+  6103,
+  6105,
+  6107,
+  6108,
+  6109,
+  6120,
+  6121,
+  6122,
+  6123,
+  6124,
+  6125,
+  6126,
+  6127,
+  6139,
+  6141,
+  6142,
+  6143,
+  6149,
+  6150,
+  6155,
+  6158,
+  6163,
+  6165,
+  6166,
+  6167,
+  6174,
+  6175,
+  6187,
+  6191,
+  6221,
+  6240,
+  6327,
+  6343,
+  6464,
+  6465,
+  6466,
+  6467,
+  6468,
+  6469,
+  6470,
+  6471,
+  6488,
+  6489,
+  6490,
+  6500,
+  6501,
+  6522,
+  6524,
+  6525,
+  6547,
+  6548,
+  6549,
+  6559,
+  6570,
+  6571,
+  6572,
+  6573,
+  6579,
+  6582,
+  6583,
+  6622,
+  6623,
+  6629,
+  6631,
+  6638,
+  6639,
+  6643,
+  6646,
+  6647,
+  6651,
+  6653,
+  6654,
+  6669,
+  6670,
+  6769,
+  6771,
+  6773,
+  6778,
+  6806,
+  6807,
+  6823,
+  6842,
+  6944,
+  6945,
+  6946,
+  6950,
+  6951,
+  6968,
+  6969,
+  6970,
+  6971,
+  6980,
+  6981,
+  7004,
+  7005,
+  7027,
+  7028,
+  7029,
+  7035,
+  7037,
+  7040,
+  7041,
+  7047,
+  7048,
+  7049,
+  7050,
+  7051,
+  7052,
+  7058,
+  7059,
+  7060,
+  7061,
+  7063,
+  7068,
+  7072,
+  7075,
+  7076,
+  7078,
+  7079,
+  7081,
+  7083,
+  7085,
+  7087,
+  7088,
+  7089,
+  7150,
+  7254,
+  7266,
+  7287,
+  7361,
+  7363,
+  7424,
+  7425,
+  7426,
+  7427,
+  7428,
+  7429,
+  7430,
+  7431,
+  7460,
+  7461,
+  7485,
+  7507,
+  7508,
+  7509,
+  7519,
+  7530,
+  7531,
+  7533,
+  7539,
+  7542,
+  7543,
+  7546,
+  7560,
+  7561,
+  7562,
+  7563,
+  7564,
+  7565,
+  7566,
+  7567,
+  7630,
+  7683,
+  7707,
+  7708,
+  7731,
+  7733,
+  7738,
+  7745,
+  7747,
+  7767,
+  7783,
+  7928,
+  7929,
+  7930,
+  7931,
+  7932,
+  7933,
+  7942,
+  7943,
+  7944,
+  8077,
+  8078,
+  8079,
+  8083,
+  8234,
+  8247,
+  8263,
+  8384,
+  8385,
+  8386,
+  8387,
+  8388,
+  8389,
+  8390,
+  8391,
+  8408,
+  8409,
+  8410,
+  8411,
+  8412,
+  8413,
+  8420,
+  8421,
+  8493,
+  8670,
+  8689,
+  8691,
+  8693,
+  8698,
+  8705,
+  8707,
+  8709,
+  8714,
+  8721,
+  8723,
+  8725,
+  8727,
+  8730,
+  8743,
+  8866,
+  8867,
+  8869,
+  8870,
+  8888,
+  8889,
+  8890,
+  8891,
+  8892,
+  8893,
+  8901,
+  8902,
+  8903,
+  8904,
+  8905,
+  8912,
+  8913,
+  8914,
+  8916,
+  8917,
+  8922,
+  8926,
+  8928,
+  8929,
+  8934,
+  8936,
+  8937,
+  8938,
+  8939,
+  8940,
+  8941,
+  8942,
+  8943,
+  8948,
+  8970,
+  9028,
+  9169,
+  9177,
+  9207,
+  9223,
+  9368,
+  9369,
+  9370,
+  9371,
+  9372,
+  9373,
+  9382,
+  9383,
+  9384,
+  9385,
+  9392,
+  9393,
+  9394,
+  9396,
+  9397,
+  9398,
+  9399,
+  9400,
+  9401,
+  9402,
+  9403,
+  9406,
+  9407,
+  9408,
+  9409,
+  9410,
+  9411,
+  9412,
+  9413,
+  9414,
+  9415,
+  9416,
+  9417,
+  9418,
+  9419,
+  9420,
+  9421,
+  9422,
+  9423,
+  9424,
+  9425,
+  9426,
+  9430,
+  9431,
+  9432,
+  9433,
+  9434,
+  9435,
+  9436,
+  9437,
+  9438,
+  9440,
+  9441,
+  9442,
+  9443,
+  9444,
+  9445,
+  9446,
+  9447,
+  9448,
+  9449,
+  9454,
+  9456,
+  9464,
+  9625,
+  9651,
+  9653,
+  9658,
+  9665,
+  9669,
+  9673,
+  9674,
+  9685,
+  9687,
+  9690,
+  9697,
+  9699,
+  9701,
+  9703,
+  9706,
+  9713,
+  9715,
+  9717,
+  9722,
+  9729,
+  9731,
+  9733,
+  9738,
+  9745,
+  9824,
+  9848,
+  9849,
+  9850,
+  9851,
+  9852,
+  9853,
+  9862,
+  9863,
+  9864,
+  9865,
+  9872,
+  9873,
+  9874,
+  9876,
+  9877,
+  9882,
+  9886,
+  9888,
+  9889,
+  9894,
+  9896,
+  9897,
+  9898,
+  9899,
+  9900,
+  9901,
+  9902,
+  9903,
+  9904,
+  9905,
+  9910,
+  9911,
+  9912,
+  9913,
+  9914,
+  9915,
+  9916,
+  9917,
+  9920,
+  9921,
+  9926,
+  9927,
+  9930,
+  9932,
+  9934,
+  9936,
+  9944,
+  9946,
+  9960,
+  9997,
+  9998,
+  10087,
+  10131,
+  10133,
+  10167,
+  10183,
+  10286,
+  10287,
+  10289,
+  10290,
+  10291,
+  10292,
+  10293,
+  10294,
+  10295,
+  10297,
+  10299,
+  10301,
+  10302,
+  10303,
+  10304,
+  10312,
+  10313,
+  10315,
+  10316,
+  10317,
+  10318,
+  10322,
+  10328,
+  10329,
+  10330,
+  10331,
+  10332,
+  10333,
+  10342,
+  10343,
+  10344,
+  10345,
+  10352,
+  10353,
+  10354,
+  10356,
+  10357,
+  10362,
+  10366,
+  10368,
+  10369,
+  10374,
+  10376,
+  10377,
+  10378,
+  10379,
+  10380,
+  10381,
+  10382,
+  10383,
+  10384,
+  10385,
+  10390,
+  10391,
+  10392,
+  10393,
+  10394,
+  10395,
+  10396,
+  10397,
+  10400,
+  10401,
+  10406,
+  10407,
+  10421,
+  10458,
+  10465,
+  10468,
+  10507,
+  10529,
+  10538,
+  10546,
+  10556,
+  10598,
+  10625,
+  10689,
+  10701,
+  10787,
+  10999,
+  11089,
+  11091,
+  11093,
+  11098,
+  11105,
+  11107,
+  11109,
+  11114,
+  11121,
+  11123,
+  11125,
+  11130,
+  11137,
+  11139,
+  11141,
+  11146,
+  11153,
+  11157,
+  11162,
+  11171,
+  11210,
+  11265,
+  11267,
+  11268,
+  11269,
+  11270,
+  11288,
+  11301,
+  11325,
+  11341,
+  11359,
+  11371,
+  11372,
+  11383,
+  11398,
+  11401,
+  11402,
+  11404,
+  11471,
+  11506,
+  11532,
+  11533,
+  11534,
+  11535,
+  11537,
+  11538,
+  11540,
+  11541,
+  11542,
+  11744,
+  11745,
+  11746,
+  11747,
+  11748,
+  11749,
+  11750,
+  11751,
+  11780,
+  11781,
+  11796,
+  11804,
+  11805,
+  11827,
+  11828,
+  11829,
+  11839,
+  11850,
+  11851,
+  11852,
+  11853,
+  11856,
+  11860,
+  11862,
+  11863,
+  11880,
+  11881,
+  11882,
+  11883,
+  11884,
+  11885,
+  11886,
+  11887,
+  11895,
+  12049,
+  12058,
+  12087,
+  12103,
+  12224,
+  12225,
+  12226,
+  12227,
+  12228,
+  12229,
+  12230,
+  12231,
+  12248,
+  12249,
+  12250,
+  12251,
+  12252,
+  12253,
+  12260,
+  12261,
+  12262,
+  12263,
+  12264,
+  12265,
+  12272,
+  12284,
+  12285,
+  12307,
+  12308,
+  12309,
+  12315,
+  12319,
+  12330,
+  12331,
+  12332,
+  12333,
+  12342,
+  12480,
+  12529,
+  12558,
+  12657,
+  12961,
+  13020,
+  13358,
+  13493,
+  13495,
+  13527,
+  13543,
+  13664,
+  13665,
+  13666,
+  13667,
+  13668,
+  13669,
+  13688,
+  13689,
+  13690,
+  13795,
+  13802,
+  13825,
+  13836,
+  13856,
+  13858,
+  13895,
+  13969,
+  13971,
+  13973,
+  14007,
+  14144,
+  14145,
+  14146,
+  14147,
+  14148,
+  14149,
+  14169,
+  14173,
+  14183,
+  14192,
+  14194,
+  14196,
+  14197,
+  14202,
+  14365,
+  14503,
+  14629,
+  14630,
+  14648,
+  14649,
+  14650,
+  14651,
+  14652,
+  14653,
+  14684,
+  14695,
+  14707,
+  14708,
+  14709,
+  14719,
+  14731,
+  14733,
+  14743,
+  14746,
+  14760,
+  14762,
+  14763,
+  14765,
+  14929,
+  14938,
+  14967,
+  14983,
+  15104,
+  15105,
+  15125,
+  15128,
+  15129,
+  15130,
+  15131,
+  15132,
+  15133,
+  15142,
+  15143,
+  15144,
+  15145,
+  15152,
+  15153,
+  15154,
+  15156,
+  15157,
+  15162,
+  15221,
+  15309,
+  15375,
+  15376,
+  15377,
+  15378,
+  15379,
+  15380,
+  15383,
+  15586,
+  15588,
+  15591,
+  15620,
+  15621,
+  15668,
+  15669,
+  15692,
+  15693,
+  15724,
+  15727,
+  16047,
+  16271,
+  16486,
+  16623,
+  16758,
+  17024,
+  17025,
+  17049,
+  17050,
+  17051,
+  17052,
+  17053,
+  17062,
+  17237,
+  17320,
+  17321,
+  17322,
+  17323,
+  17339,
+  17504,
+  17505,
+  17506,
+  17507,
+  17508,
+  17509,
+  17510,
+  17511,
+  17533,
+  17540,
+  17541,
+  17542,
+  17543,
+  17544,
+  17545,
+  17552,
+  17553,
+  17554,
+  17562,
+  17564,
+  17565,
+  17566,
+  17569,
+  17577,
+  17578,
+  17579,
+  17580,
+  17581,
+  17582,
+  17583,
+  17584,
+  17585,
+  17587,
+  17588,
+  17589,
+  17590,
+  17599,
+  17984,
+  17985,
+  17986,
+  17987,
+  17988,
+  17989,
+  17990,
+  17991,
+  18008,
+  18009,
+  18012,
+  18013,
+  18020,
+  18021,
+  18022,
+  18025,
+  18032,
+  18036,
+  18044,
+  18045,
+  18048,
+  18049,
+  18056,
+  18057,
+  18058,
+  18059,
+  18060,
+  18061,
+  18067,
+  18068,
+  18069,
+  18079,
+  18090,
+  18277,
+  18308,
+  18336,
+  18405,
+  18459,
+  18464,
+  18558,
+  18627,
+  18631,
+  18671,
+  18778,
+  18885,
+  18890,
+  18944,
+  19099,
+  19265,
+  19489,
+  19519,
+  19600,
+  19607,
+  19687,
+  19735,
+  19749,
+  19767,
+  19783,
+  19891,
+  20019,
+  20048,
+  20189,
+  20630,
+  20705,
+  20905,
+  20912,
+  20913,
+  20914,
+  20916,
+  20917,
+  21117,
+  21205,
+  21226,
+  21259,
+  21260,
+  21293,
+  21344,
+  21345,
+  21346,
+  21347,
+  21348,
+  21349,
+  21350,
+  21351,
+  21380,
+  21487,
+  21550,
+  21824,
+  21825,
+  21826,
+  21827,
+  21828,
+  21829,
+  21830,
+  21831,
+  21860,
+  21861,
+  21884,
+  22188,
+  22191,
+  22218,
+  22304,
+  22305,
+  22343,
+  22369,
+  22382,
+  22383,
+  22385,
+  22390,
+  22391,
+  22393,
+  22394,
+  22395,
+  22396,
+  22400,
+  22401,
+  22406,
+  22659,
+  22697,
+  22858,
+  22859,
+  22860,
+  22877,
+  23071,
+  23072,
+  23073,
+  23074,
+  23076,
+  23077,
+  23079,
+  23080,
+  23081,
+  23096,
+  23098,
+  23105,
+  23260,
+  23264,
+  23265,
+  23381,
+  23385,
+  23523,
+  23571,
+  23576,
+  23624,
+  23664,
+  23690,
+  23744,
+  23795,
+  24053,
+  24097,
+  24103,
+  24106,
+  24149,
+  24154,
+  24159,
+  24160,
+  24161,
+  24254,
+  24504,
+  24515,
+  24531,
+  24560,
+  24788,
+  24829,
+  24979,
+  25011,
+  25090,
+  25121,
+  25124,
+  25126,
+  25128,
+  25129,
+  25131,
+  25133,
+  25134,
+  25136,
+  25139,
+  25142,
+  25146,
+  25147,
+  25148,
+  25150,
+  25151,
+  25153,
+  25154,
+  25157,
+  25182,
+  25184,
+  25185,
+  25186,
+  25187,
+  25188,
+  25189,
+  25190,
+  25191,
+  25220,
+  25221,
+  25234,
+  25236,
+  25237,
+  25242,
+  25244,
+  25245,
+  25267,
+  25268,
+  25269,
+  25279,
+  25290,
+  25291,
+  25292,
+  25293,
+  25302,
+  25505,
+  25507,
+  25664,
+  25665,
+  25666,
+  25667,
+  25668,
+  25669,
+  25670,
+  25671,
+  25700,
+  25701,
+  25724,
+  25725,
+  25747,
+  25748,
+  25749,
+  25759,
+  25770,
+  25771,
+  25772,
+  25773,
+  25782,
+  25847,
+  25909,
+  26429,
+  26632,
+  26633,
+  26787,
+  27031,
+  27040,
+  27042,
+  27044,
+  27076,
+  27082,
+  27105,
+  27108,
+  27109,
+  27110,
+  27140,
+  27165,
+  27166,
+  27168,
+  27187,
+  27188,
+  27189,
+  27213,
+  27222,
+  27223,
+  27242,
+  27243,
+  27244,
+  27278,
+  27360,
+  27446,
+  27458,
+  27483,
+  27586,
+  27588,
+  27625,
+  27667,
+  27703,
+  27725,
+  27726,
+  27727,
+  27913,
+  28128,
+  28129,
+  28134,
+  28136,
+  28137,
+  28157,
+  28187,
+  28229,
+  28567,
+  28572,
+  28573,
+  28582,
+  28583,
+  28584,
+  28592,
+  28593,
+  28594,
+  28596,
+  28597,
+  28614,
+  28823,
+  28831,
+  28872,
+  28876,
+  28877,
+  28963,
+  29024,
+  29025,
+  29026,
+  29027,
+  29028,
+  29029,
+  29030,
+  29031,
+  29060,
+  29061,
+  29084,
+  29085,
+  29093,
+  29097,
+  29099,
+  29100,
+  29104,
+  29107,
+  29108,
+  29109,
+  29119,
+  29130,
+  29131,
+  29132,
+  29133,
+  29142,
+  29143,
+  29160,
+  29161,
+  29162,
+  29163,
+  29164,
+  29189,
+  29215,
+  29332,
+  29504,
+  29505,
+  29568,
+  29569,
+  29577,
+  29578,
+  29579,
+  29580,
+  29582,
+  29583,
+  29584,
+  29984,
+  29985,
+  30070,
+  30073,
+  30294,
+  30365,
+  30464,
+  30465,
+  30489,
+  30725,
+  30758,
+  30858,
+  30944,
+  30945,
+  30946,
+  30947,
+  30948,
+  30949,
+  30950,
+  30951,
+  30980,
+  30981,
+  30982,
+  31004,
+  31005,
+  31027,
+  31028,
+  31029,
+  31039,
+  31050,
+  31051,
+  31052,
+  31157,
+  31248,
+  31252,
+  31254,
+  31255,
+  31424,
+  31452,
+  31506,
+  31730,
+  31788,
+  31791,
+  31793,
+  31798,
+  31904,
+  31905,
+  31906,
+  31907,
+  31908,
+  31909,
+  31910,
+  31911,
+  31928,
+  31929,
+  31940,
+  31950,
+  31951,
+  32191,
+  32193,
+  32231,
+  32232,
+  32233,
+  32263,
+  32384,
+  32385,
+  32386,
+  32387,
+  32388,
+  32389,
+  32390,
+  32391,
+  32408,
+  32420,
+  32421,
+  32444,
+  32445,
+  32467,
+  32468,
+  32469,
+  32679,
+  32710,
+  32864,
+  32865,
+  32866,
+  32867,
+  32868,
+  32869,
+  32870,
+  32871,
+  32877,
+  32900,
+  32901,
+  32914,
+  32924,
+  32943,
+  32945,
+  32950,
+  32952,
+  32960,
+  33171,
+  33397,
+  33402,
+  33408,
+  33434,
+  33440,
+  33447,
+  33448,
+  33717,
+  33722,
+  33729,
+  33761,
+  33824,
+  33825,
+  33826,
+  33827,
+  33828,
+  33873,
+  33971,
+  33973,
+  33981,
+  33982,
+  33983,
+  33987,
+  34093,
+  34304,
+  34305,
+  34306,
+  34307,
+  34308,
+  34309,
+  34310,
+  34311,
+  34340,
+  34341,
+  34362,
+  34364,
+  34365,
+  34387,
+  34388,
+  34389,
+  34399,
+  34410,
+  34411,
+  34412,
+  34413,
+  34422,
+  34423,
+  34440,
+  34441,
+  34485,
+  34487,
+  34539,
+  34740,
+  34865,
+  35089,
+  35091,
+  35264,
+  35265,
+  35266,
+  35351,
+  35766,
+  35923,
+  35927,
+  36387,
+  36626,
+  36697,
+  36960,
+  37209,
+  37211,
+  37215,
+  37547,
+  37664,
+  37665,
+  37666,
+  37667,
+  37668,
+  37670,
+  37671,
+  37700,
+  37701,
+  37757,
+  37829,
+  37830,
+  37854,
+  38144,
+  38145,
+  38146,
+  38147,
+  38148,
+  38149,
+  38150,
+  38151,
+  38180,
+  38247,
+  38248,
+  38249,
+  38255,
+  38440,
+  38462,
+  38624,
+  38625,
+  38626,
+  38627,
+  38628,
+  38629,
+  38630,
+  38631,
+  38660,
+  38661,
+  38684,
+  38685,
+  38707,
+  38709,
+  38738,
+  38965,
+  38970,
+  38977,
+  38997,
+  39002,
+  39090,
+  39104,
+  39105,
+  39106,
+  39107,
+  39108,
+  39109,
+  39110,
+  39111,
+  39140,
+  39141,
+  39164,
+  39165,
+  39187,
+  39189,
+  39210,
+  39434,
+  39577,
+  39578,
+  39697,
+  39709,
+  39851,
+  39897,
+  39908,
+  40054,
+  40175,
+  40179,
+  40180,
+  40187,
+  40188,
+  40403,
+  40410,
+  40417,
+  40419,
+  40421,
+  40426,
+  40433,
+  40435,
+  40437,
+  40442,
+  40453,
+  40475,
+  40545,
+  40767,
+  40787,
+  40812,
+  40821,
+  40828,
+  40831,
+  40832,
+  40833,
+  40836,
+  40837,
+  40844,
+  40856,
+  40861,
+  40862,
+  40963,
+  40965,
+  40970,
+  41020,
+  41024,
+  41025,
+  41073,
+  41074,
+  41077,
+  41134,
+  41179,
+  41181,
+  41183,
+  41187,
+  41190,
+  41198,
+  41205,
+  41206,
+  41207,
+  41211,
+  41213,
+  41214,
+  41215,
+  41386,
+  41504,
+  41505,
+  41506,
+  41507,
+  41543,
+  41612,
+  41841,
+  41892,
+  41984,
+  41985,
+  41986,
+  41987,
+  42022,
+  42024,
+  42061,
+  42321,
+  42389,
+  42464,
+  42532,
+  42539,
+  42586,
+  42925,
+  42944,
+  42991,
+  43349,
+  43429,
+  43502,
+  43503,
+  43504,
+  43505,
+  43510,
+  43511,
+  43512,
+  43904,
+  43906,
+  43908,
+  43909,
+  43980,
+  44234,
+  44330,
+  44367,
+  44368,
+  44385,
+  44386,
+  44445,
+  44463,
+  44464,
+  44465,
+  44467,
+  44468,
+  44469,
+  44539,
+  44549,
+  44741,
+  44746,
+  44755,
+  44757,
+  44769,
+  44785,
+  44787,
+  44925,
+  44942,
+  44943,
+  44944,
+  44945,
+  44947,
+  44948,
+  44950,
+  44951,
+  45019,
+  45035,
+  45344,
+  45393,
+  45722,
+  45873,
+  45874,
+  45876,
+  46202,
+  46254,
+  46308,
+  46309,
+  46311,
+  46340,
+  46693,
+  46698,
+  46705,
+  46707,
+  46721,
+  46723,
+  46787,
+  46788,
+  46789,
+  46790,
+  46791,
+  46820,
+  46827,
+  46829,
+  46931,
+  46933,
+  46999,
+  47015,
+  47125,
+  47142,
+  47225,
+  47237,
+  47255,
+  47257,
+  47264,
+  47269,
+  47272,
+  47273,
+  47298,
+  47306,
+  47309,
+  47343,
+  47345,
+  47350,
+  47351,
+  47352,
+  47353,
+  47354,
+  47355,
+  47356,
+  47438,
+  47439,
+  47443,
+  47445,
+  47563,
+  47626,
+  47640,
+  47747,
+  47750,
+  47944,
+  47945,
+  48129,
+  48224,
+  48227,
+  48228,
+  48229,
+  48419,
+  48421,
+  48446,
+  48820,
+  48821,
+  48829,
+  49066,
+  49077,
+  49105,
+  49107,
+  49259,
+  49260,
+  49261,
+  49262,
+  49591,
+  49595,
+  49600,
+  49602,
+  49612,
+  49614,
+  49616,
+  49620,
+  49622,
+  49627,
+  49629,
+  49630,
+  49634,
+  49635,
+  49636,
+  49638,
+  49641,
+  49642,
+  49643,
+  49649,
+  49652,
+  49653,
+  49656,
+  49659,
+  49660,
+  49661,
+  49662,
+  49668,
+  49669,
+  49673,
+  49676,
+  49680,
+  49681,
+  49683,
+  49684,
+  49695,
+  49696,
+  49697,
+  49698,
+  49705,
+  49707,
+  49709,
+  49711,
+  49712,
+  49714,
+  49715,
+  50428,
+  51050,
+  51106,
+  51286,
+  51483,
+  51585,
+  51773,
+  52065,
+  52066,
+  52183,
+  52324,
+  52326,
+  52327,
+  52328,
+  52329,
+  52330,
+  52332,
+  52333,
+  52334,
+  52335,
+  52336,
+  52337,
+  52338,
+  52394,
+  52547,
+  52809,
+  52830,
+  53026,
+  53336,
+  53338,
+  53770,
+  53807,
+  53831,
+  54050,
+  54311,
+  54373,
+  54378,
+  54387,
+  54493,
+  54845,
+  54944,
+  54945,
+  54993,
+  55002,
+  55251,
+  55258,
+  55265,
+  55417,
+  55477,
+  55482,
+  55486,
+  55488,
+  55489,
+  55494,
+  55497,
+  55498,
+  55499,
+  55500,
+  55810,
+  56176,
+  56929,
+  56937,
+  57132,
+  57660,
+  57661,
+  57663,
+  57664,
+  57665,
+  57707,
+  58098,
+  58352,
+  58353,
+  58354,
+  58357,
+  58366,
+  58368,
+  58369,
+  58374,
+  58376,
+  58377,
+  58622,
+  58974,
+  59118,
+  59130,
+  59139,
+  59141,
+  59146,
+  59155,
+  59157,
+  59271,
+  59290,
+  59291,
+  59292,
+  59293,
+  59300,
+  59301,
+  59302,
+  59303,
+  59312,
+  59313,
+  59327,
+  59429,
+  59689,
+  59888,
+  60126,
+  60133,
+  60783,
+  60784,
+  61521,
+  62301,
+  62515,
+  62548,
+  62558,
+  62711,
+  62715,
+  62717,
+  63759,
+  64006,
+  64065,
+  64461,
+  65088,
+  65096,
+  65409,
+  65411,
+  65508,
+  67499,
+  67983
+ ],
+ "offset_only_rows": 382,
+ "all_strictly_inside": true,
+ "helper_once_per_call": true,
+ "majorization": {
+  "residual_total": 237024,
+  "bins": 32256,
+  "candidate_majorizes_selected": true,
+  "strict": true
+ },
+ "price_selected": {
+  "endpoint": "67018507072324140917/40000000000000000000000",
+  "endpoint_decimal": "0.001675462676808103522925",
+  "kappa": "836330098538459/500000000000000000",
+  "kappa_decimal": "0.001672660197076918"
+ },
+ "price_new": {
+  "endpoint": "838212092705151621517/500000000000000000000000",
+  "endpoint_decimal": "0.001676424185410303243034",
+  "kappa": "209202311361877/125000000000000000",
+  "kappa_decimal": "0.001673618490895016"
+ },
+ "price_new_conservative": {
+  "endpoint": "167642418254791971833/100000000000000000000000",
+  "endpoint_decimal": "0.001676424182547919718330",
+  "kappa": "836809244021103/500000000000000000",
+  "kappa_decimal": "0.001673618488042206"
+ },
+ "rel_gain": "479146909049/836330098538459",
+ "indicative_ceiling_price": {
+  "idle": {
+   "1": 2431,
+   "17": 1,
+   "48": 4887
+  },
+  "kappa_decimal": "0.001674088611862992",
+  "complex_lower": "1676895884165954931459/1000000000000000000000000"
+ },
+ "sweep": {
+  "endpoint_certified": true,
+  "deficit_equals_W_minus_64N": true,
+  "halving": true,
+  "record_bit_is_pr589": true,
+  "kappa_equals_record": true,
+  "kappa_equals_title": true,
+  "kappa_exact_decimal": "0.001673618490895016",
+  "binding": "complex"
+ }
+}
diff --git a/research/complex-t16-evacuation-increment/evidence/OVERLAP.json b/research/complex-t16-evacuation-increment/evidence/OVERLAP.json
new file mode 100644
index 0000000000..a1712e38d7
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/evidence/OVERLAP.json
@@ -0,0 +1,963 @@
+{
+  "checked_utc": "2026-10-17 21:23:20 UTC",
+  "open_pr_count": 350,
+  "pr_error": null,
+  "pr_matches": [
+    {
+      "number": 3291,
+      "title": "Repair centre block proof with a sharp fifteen-owner graph floor",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3291",
+      "updated_at": "2026-10-17T20:49:47Z",
+      "state": "open"
+    },
+    {
+      "number": 3285,
+      "title": "Research: independently re-solve PR #2979's fixed-capacity stage caps and price each stage-one group alone (no new \u03ba)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3285",
+      "updated_at": "2026-10-17T20:47:03Z",
+      "state": "open"
+    },
+    {
+      "number": 3237,
+      "title": "Research: certify PR #2979's V45 final-word controls fail the complete packing budget",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3237",
+      "updated_at": "2026-10-17T18:50:09Z",
+      "state": "open"
+    },
+    {
+      "number": 3218,
+      "title": "Tooling: accelerate exact R2 Clifford comparisons with signed Pauli actions",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3218",
+      "updated_at": "2026-10-17T18:15:15Z",
+      "state": "open"
+    },
+    {
+      "number": 3209,
+      "title": "Reuse JSON parses in the complete T16 boundary audit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3209",
+      "updated_at": "2026-10-17T17:57:53Z",
+      "state": "open"
+    },
+    {
+      "number": 3190,
+      "title": "Conditional \u03ba = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3190",
+      "updated_at": "2026-10-17T17:13:48Z",
+      "state": "open"
+    },
+    {
+      "number": 3184,
+      "title": "Conditional \u03ba = 0.001730189061233850760095: idle rank-48 star exchanges on #3148's T740 fill (+0.0238%)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3184",
+      "updated_at": "2026-10-17T17:13:57Z",
+      "state": "open"
+    },
+    {
+      "number": 3181,
+      "title": "research: QQ16 52-bit interior dynamic-range collapse, backward adjoint ledger, and dyadic grid exactness",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3181",
+      "updated_at": "2026-10-17T15:16:09Z",
+      "state": "open"
+    },
+    {
+      "number": 3147,
+      "title": "research: centre sink duality, dependent-triple braid sparsity (|B| <= 12), and circle-cancellation sharing ceilings",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3147",
+      "updated_at": "2026-10-17T09:38:04Z",
+      "state": "open"
+    },
+    {
+      "number": 3120,
+      "title": "Copied-information floor of the selected centre path",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3120",
+      "updated_at": "2026-10-17T03:27:58Z",
+      "state": "open"
+    },
+    {
+      "number": 2818,
+      "title": "Conditional \u03ba = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2818",
+      "updated_at": "2026-10-15T23:36:53Z",
+      "state": "open"
+    },
+    {
+      "number": 2767,
+      "title": "Conditional \u03ba = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2767",
+      "updated_at": "2026-10-16T02:17:37Z",
+      "state": "open"
+    },
+    {
+      "number": 2762,
+      "title": "Census round 2: screening results for the 16 uncovered open complex claims (no new kappa)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2762",
+      "updated_at": "2026-10-15T20:48:03Z",
+      "state": "open"
+    },
+    {
+      "number": 2745,
+      "title": "Conditional \u03ba = 0.001716140425997441: #2696's lender assignment with #2679's pre-life hosting and a window-optimal fill",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2745",
+      "updated_at": "2026-10-15T19:43:14Z",
+      "state": "open"
+    },
+    {
+      "number": 2733,
+      "title": "Improve conditional kappa to 0.00171625567823018 with composition and a frame refit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2733",
+      "updated_at": "2026-10-15T20:17:41Z",
+      "state": "open"
+    },
+    {
+      "number": 2679,
+      "title": "Conditional \u03ba = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2679",
+      "updated_at": "2026-10-15T17:01:34Z",
+      "state": "open"
+    },
+    {
+      "number": 2673,
+      "title": "Conditional \u03ba = 0.001714600409398252: priority-ordered window-optimal owner fill on #2588's words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2673",
+      "updated_at": "2026-10-15T16:58:17Z",
+      "state": "open"
+    },
+    {
+      "number": 2588,
+      "title": "Conditional \u03ba = 0.001714252039260245: swapped helper labels for lenders 80 and 88 on #2530's source-partner words, with an evacuated owner fill",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2588",
+      "updated_at": "2026-10-15T15:32:24Z",
+      "state": "open"
+    },
+    {
+      "number": 2575,
+      "title": "Conditional \u03ba = 0.001713879320009017: owner evacuation on #2530's source-partner words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2575",
+      "updated_at": "2026-10-15T15:03:49Z",
+      "state": "open"
+    },
+    {
+      "number": 2559,
+      "title": "Conditional \u03ba = 0.0017044322370702051: owner-fill evacuation and two more retired-lender aliases on the #2526 T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2559",
+      "updated_at": "2026-10-15T17:01:37Z",
+      "state": "open"
+    },
+    {
+      "number": 2526,
+      "title": "Conditional \u03ba = 0.001703713039257905: a sixth #2436-type alias (helper 656 borrows lender 88) on the entrance-raised T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2526",
+      "updated_at": "2026-10-15T13:46:04Z",
+      "state": "open"
+    },
+    {
+      "number": 2474,
+      "title": "Conditional \u03ba = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2474",
+      "updated_at": "2026-10-15T13:10:26Z",
+      "state": "open"
+    },
+    {
+      "number": 2462,
+      "title": "Conditional \u03ba = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2462",
+      "updated_at": "2026-10-15T11:34:55Z",
+      "state": "open"
+    },
+    {
+      "number": 2447,
+      "title": "Conditional \u03ba = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2447",
+      "updated_at": "2026-10-15T12:58:16Z",
+      "state": "open"
+    },
+    {
+      "number": 2439,
+      "title": "[Lean] Execute paid exponent widening and half-source addition",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2439",
+      "updated_at": "2026-10-15T09:56:17Z",
+      "state": "open"
+    },
+    {
+      "number": 2438,
+      "title": "[Lean] Return reusable dyadic output with paid copy and sign split",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2438",
+      "updated_at": "2026-10-15T09:49:39Z",
+      "state": "open"
+    },
+    {
+      "number": 2436,
+      "title": "Conditional bound: four aliases + 24 entrance raises give \u03ba = 0.001699160892139825",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2436",
+      "updated_at": "2026-10-15T11:03:00Z",
+      "state": "open"
+    },
+    {
+      "number": 2435,
+      "title": "Conditional \u03ba = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2435",
+      "updated_at": "2026-10-15T12:58:20Z",
+      "state": "open"
+    },
+    {
+      "number": 2426,
+      "title": "[Lean] Execute encoded exponent alignment and dyadic addition",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2426",
+      "updated_at": "2026-10-15T09:07:29Z",
+      "state": "open"
+    },
+    {
+      "number": 2418,
+      "title": "[Lean] Pay positioned paired-track acquisition and global return",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2418",
+      "updated_at": "2026-10-15T08:41:46Z",
+      "state": "open"
+    },
+    {
+      "number": 2409,
+      "title": "Tooling: 2.49\u00d7 faster production HPE audit via integer rows with identical receipts",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2409",
+      "updated_at": "2026-10-15T23:07:18Z",
+      "state": "open"
+    },
+    {
+      "number": 2403,
+      "title": "[Lean] Restore saved exponents and refine ambient metadata XOR",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2403",
+      "updated_at": "2026-10-15T07:42:51Z",
+      "state": "open"
+    },
+    {
+      "number": 2374,
+      "title": "Conditional \u03ba = 0.001697194950901770: exact owner fill on #2322's handoff construction",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2374",
+      "updated_at": "2026-10-15T12:58:51Z",
+      "state": "open"
+    },
+    {
+      "number": 2371,
+      "title": "[Lean] Bind exact L450 fragment bytes to checked chart payload",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2371",
+      "updated_at": "2026-10-15T06:48:32Z",
+      "state": "open"
+    },
+    {
+      "number": 2357,
+      "title": "Tooling: 2.26\u00d7 faster production emitted-local audit via integer rows with identical receipts",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2357",
+      "updated_at": "2026-10-15T20:57:54Z",
+      "state": "open"
+    },
+    {
+      "number": 2349,
+      "title": "Conditional \u03ba = 0.001697065994108880: owner relocations on #2322's handoff construction",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2349",
+      "updated_at": "2026-10-15T06:07:34Z",
+      "state": "open"
+    },
+    {
+      "number": 2216,
+      "title": "QQ16: add an F0-B1 selected-state shear",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2216",
+      "updated_at": "2026-10-15T18:23:53Z",
+      "state": "open"
+    },
+    {
+      "number": 2180,
+      "title": "Conditional \u03ba = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263...: fixed-grid ceiling over PR2161",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2180",
+      "updated_at": "2026-10-14T22:24:17Z",
+      "state": "open"
+    },
+    {
+      "number": 2025,
+      "title": "[Lean] Connect reference SCALE traversal to exact dyadic arithmetic",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2025",
+      "updated_at": "2026-10-14T17:30:54Z",
+      "state": "open"
+    },
+    {
+      "number": 2016,
+      "title": "[Lean] Discover and check compact dictionary keys from original bytes",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2016",
+      "updated_at": "2026-10-14T17:14:32Z",
+      "state": "open"
+    },
+    {
+      "number": 1993,
+      "title": "[Lean] Recover compact dictionary values from original bytes and keys",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1993",
+      "updated_at": "2026-10-14T16:28:27Z",
+      "state": "open"
+    },
+    {
+      "number": 1978,
+      "title": "[Lean] Bind checked byte slices to named artifact columns",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1978",
+      "updated_at": "2026-10-14T15:49:03Z",
+      "state": "open"
+    },
+    {
+      "number": 1961,
+      "title": "[Lean] Validate compact column fragments and their byte representation",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1961",
+      "updated_at": "2026-10-14T15:14:12Z",
+      "state": "open"
+    },
+    {
+      "number": 1950,
+      "title": "[Lean] Recover binary certificates from named JSON and original bytes",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1950",
+      "updated_at": "2026-10-14T14:48:43Z",
+      "state": "open"
+    },
+    {
+      "number": 1927,
+      "title": "[Lean] Connect actual JSON fields to checked tables and binary charts",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1927",
+      "updated_at": "2026-10-14T14:02:51Z",
+      "state": "open"
+    },
+    {
+      "number": 1831,
+      "title": "[Lean] Bind all 144 selected parsed route tables to certified owners",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1831",
+      "updated_at": "2026-10-14T11:32:16Z",
+      "state": "open"
+    },
+    {
+      "number": 1813,
+      "title": "[Lean] Certify the complete historical PR926 Boolean D word",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1813",
+      "updated_at": "2026-10-14T10:34:28Z",
+      "state": "open"
+    },
+    {
+      "number": 1809,
+      "title": "[Lean] Derive the selected normalized-cost bound from explicit physical suppliers",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1809",
+      "updated_at": "2026-10-14T10:30:25Z",
+      "state": "open"
+    },
+    {
+      "number": 1807,
+      "title": "[Lean] Certify all 144 selected helper-owner rows and per-call injections",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1807",
+      "updated_at": "2026-10-14T10:29:35Z",
+      "state": "open"
+    },
+    {
+      "number": 1802,
+      "title": "[Lean] Add conditional current1094 private-centre hosting adapter",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1802",
+      "updated_at": "2026-10-14T10:32:17Z",
+      "state": "open"
+    },
+    {
+      "number": 1789,
+      "title": "Conditional \u03ba = 0.001677992607205282520732...: 105-digit slack refinement on PR1725 rectangular boundary batching + radix union outer with 600-digit T74 p566+k554 supplier",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1789",
+      "updated_at": "2026-10-14T16:46:20Z",
+      "state": "open"
+    },
+    {
+      "number": 1764,
+      "title": "Research: rank-two interface candidate for paired frame transitions",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1764",
+      "updated_at": "2026-10-14T09:12:58Z",
+      "state": "open"
+    },
+    {
+      "number": 1724,
+      "title": "Conditional \u03ba = 0.0016769381110224387711...: stacked pivot 566 + 554 kernels with 600-digit grid and 600-digit endpoints over PR1692",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1724",
+      "updated_at": "2026-10-14T15:59:32Z",
+      "state": "open"
+    },
+    {
+      "number": 1692,
+      "title": "Conditional \u03ba = 0.0016769381110224387711...: stacked pivot 566 + 554 kernels with 470-digit grid and 450-digit endpoints over PR1672",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1692",
+      "updated_at": "2026-10-14T15:58:23Z",
+      "state": "open"
+    },
+    {
+      "number": 1364,
+      "title": "Conditional \u03ba = 0.001675129371412064: T37 owners on PR1148's original three-demotion word (outdated, for completeness)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1364",
+      "updated_at": "2026-10-15T16:34:02Z",
+      "state": "open"
+    },
+    {
+      "number": 1204,
+      "title": "Conditional \u03ba = 0.001675608585476885: X54 slot on #1148's joint-entrance k8 word with exact T37 owners (independent; equals #1196)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1204",
+      "updated_at": "2026-10-15T16:33:59Z",
+      "state": "open"
+    },
+    {
+      "number": 1193,
+      "title": "Conditional \u03ba = 0.001675809683500501: mixed T37 allocation with X54 and fusions",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1193",
+      "updated_at": "2026-10-14T05:36:22Z",
+      "state": "open"
+    },
+    {
+      "number": 885,
+      "title": "[Lean] Prove the selected PR799 native Real moment bound",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/885",
+      "updated_at": "2026-10-13T10:01:44Z",
+      "state": "open"
+    },
+    {
+      "number": 878,
+      "title": "[Lean] Verify selected PR589 B boundaries and XOR interfaces",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/878",
+      "updated_at": "2026-10-13T09:25:59Z",
+      "state": "open"
+    },
+    {
+      "number": 501,
+      "title": "Conditional \u03ba = 0.001343518018117309: retimed pooled whole-owner complex supply",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/501",
+      "updated_at": "2026-10-11T21:40:05Z",
+      "state": "open"
+    },
+    {
+      "number": 473,
+      "title": "Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/473",
+      "updated_at": "2026-10-12T00:54:12Z",
+      "state": "open"
+    },
+    {
+      "number": 122,
+      "title": "Terminal accumulator elimination with exact majorization audit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/122",
+      "updated_at": "2026-10-13T21:50:21Z",
+      "state": "open"
+    }
+  ],
+  "discussion_count": 321,
+  "discussion_error": null,
+  "discussion_matches": [
+    {
+      "number": 1237,
+      "title": "Selected PR1094 residual charts: same projector versus exact phase",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1237",
+      "updated_at": "2026-10-13T21:12:25Z",
+      "state": "open"
+    },
+    {
+      "number": 1251,
+      "title": "CLAIM: fusion/repair sweep on the final X54 mixed-T37 words (#1193/#1218), Wronskode, expires 23:30Z",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1251",
+      "updated_at": "2026-10-13T21:46:23Z",
+      "state": "open"
+    },
+    {
+      "number": 1258,
+      "title": "CLAIM: simultaneous k8 helper dyadic gauges beyond two coordinates (seed 29)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1258",
+      "updated_at": "2026-10-13T22:23:05Z",
+      "state": "open"
+    },
+    {
+      "number": 1260,
+      "title": "Selected PR1094 precision: signed cancellation through unitary frames",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1260",
+      "updated_at": "2026-10-13T21:44:02Z",
+      "state": "open"
+    },
+    {
+      "number": 1265,
+      "title": "CLAIM: exact ceiling for within-group repartitions of #1094 idle rank-48 children (#1252 multi-child follow-up), expires 23:30Z",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1265",
+      "updated_at": "2026-10-13T21:35:51Z",
+      "state": "open"
+    },
+    {
+      "number": 1267,
+      "title": "DONE: nine-root obstruction for a fixed P112 co-star decoder",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1267",
+      "updated_at": "2026-10-15T08:21:32Z",
+      "state": "open"
+    },
+    {
+      "number": 1289,
+      "title": "CLAIM: selected PR589 bit hosting, ambient-axis disjointness across idle children",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1289",
+      "updated_at": "2026-10-15T16:45:01Z",
+      "state": "open"
+    },
+    {
+      "number": 1291,
+      "title": "Lean prefix norm corollary on the existing Lemma G stream interface",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1291",
+      "updated_at": "2026-10-13T22:21:39Z",
+      "state": "open"
+    },
+    {
+      "number": 1314,
+      "title": "DONE: helper-donor kernel census on the #1297/#1305 words (#1337); pivot-566 follow-up (#1625)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1314",
+      "updated_at": "2026-10-14T23:18:12Z",
+      "state": "open"
+    },
+    {
+      "number": 1315,
+      "title": "CLAIM: X2 acceptance boundary for the selected owner map (Navinor, expires 2026-10-14 00:40Z)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1315",
+      "updated_at": "2026-10-13T22:33:06Z",
+      "state": "open"
+    },
+    {
+      "number": 1328,
+      "title": "CLAIM: coverage-law relief thresholds for the selected complex local word (Navinor, expires 2026-10-14T00:50Z)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1328",
+      "updated_at": "2026-10-13T23:21:26Z",
+      "state": "open"
+    },
+    {
+      "number": 1332,
+      "title": "Selected PR1094: exact single whole-helper relocation census",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1332",
+      "updated_at": "2026-10-14T21:01:20Z",
+      "state": "open"
+    },
+    {
+      "number": 1335,
+      "title": "DONE: selected k8 singleton B-frame cap (seed 29; PR #1358)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1335",
+      "updated_at": "2026-10-13T23:23:42Z",
+      "state": "open"
+    },
+    {
+      "number": 1339,
+      "title": "Selected PR1094: exact simultaneous idle-axis reassignment domain",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1339",
+      "updated_at": "2026-10-13T23:57:11Z",
+      "state": "open"
+    },
+    {
+      "number": 1356,
+      "title": "CLAIM: fixed-tape recursive parking, exact call-boundary composition and ancestor locality",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1356",
+      "updated_at": "2026-10-13T23:48:52Z",
+      "state": "open"
+    },
+    {
+      "number": 1378,
+      "title": "DONE: selected k8 helper endpoint rigidity and admission audit (PR #1583)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1378",
+      "updated_at": "2026-10-14T03:27:00Z",
+      "state": "open"
+    },
+    {
+      "number": 1467,
+      "title": "DONE: faithful S3 vector output transport, 524 to 404 primitives (PR1488)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1467",
+      "updated_at": "2026-10-14T01:39:44Z",
+      "state": "open"
+    },
+    {
+      "number": 1489,
+      "title": "DONE: paid complex connector reader-change repair, 41 to 33 ADDs (PR1506)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1489",
+      "updated_at": "2026-10-14T01:55:33Z",
+      "state": "open"
+    },
+    {
+      "number": 1492,
+      "title": "DONE: cross-block mixing retains the fixed complex late-interface floor (PR1517)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1492",
+      "updated_at": "2026-10-14T02:09:40Z",
+      "state": "open"
+    },
+    {
+      "number": 1493,
+      "title": "DONE: distinct dyadic BIT outputs share a restored source tour (PR1522)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1493",
+      "updated_at": "2026-10-14T02:15:12Z",
+      "state": "open"
+    },
+    {
+      "number": 1501,
+      "title": "DONE: reader-observable connector repair, 72 to 61 XORs (PR1523)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1501",
+      "updated_at": "2026-10-14T02:14:31Z",
+      "state": "open"
+    },
+    {
+      "number": 1505,
+      "title": "DONE: mutable-source borrowing lowers fixed-cap echo work (PR1538)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1505",
+      "updated_at": "2026-10-14T02:29:06Z",
+      "state": "open"
+    },
+    {
+      "number": 1507,
+      "title": "DONE: exact J3 gate/positive-envelope frontier (PR1520)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1507",
+      "updated_at": "2026-10-14T02:11:49Z",
+      "state": "open"
+    },
+    {
+      "number": 1516,
+      "title": "CLAIM: can the centre path be hosted on idle coordinates like helper residuals? (ctoth, expires 05:00Z)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1516",
+      "updated_at": "2026-10-14T13:08:49Z",
+      "state": "open"
+    },
+    {
+      "number": 1539,
+      "title": "DONE: sixth-root phases retain the 14-call connector minimum (PR1551)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1539",
+      "updated_at": "2026-10-14T02:50:37Z",
+      "state": "open"
+    },
+    {
+      "number": 1547,
+      "title": "DONE: full-payload PR589 gzip rebuild comparisons (PR1559)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1547",
+      "updated_at": "2026-10-14T02:59:36Z",
+      "state": "open"
+    },
+    {
+      "number": 1587,
+      "title": "CLAIM: where does the one unpaid coordinate per live family come from, and is it forced? (ctoth, expires 07:30Z)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1587",
+      "updated_at": "2026-10-17T20:40:06Z",
+      "state": "open"
+    },
+    {
+      "number": 1596,
+      "title": "Selected complex rank-one block delivery: sharp integer budget and overhead tax",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1596",
+      "updated_at": "2026-10-17T01:41:13Z",
+      "state": "open"
+    },
+    {
+      "number": 1606,
+      "title": "CLAIM: port-count / puncture-depth lever priced with the exact packing ceiling (p = 0..24)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1606",
+      "updated_at": "2026-10-14T04:10:54Z",
+      "state": "open"
+    },
+    {
+      "number": 1618,
+      "title": "Selected R480 word: test read-free terminal/entrance fusion across complete-call boundaries",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1618",
+      "updated_at": "2026-10-14T05:32:41Z",
+      "state": "open"
+    },
+    {
+      "number": 1620,
+      "title": "DONE: independent integer-root audit of nine frozen packing ceilings (PR1632)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1620",
+      "updated_at": "2026-10-14T04:28:41Z",
+      "state": "open"
+    },
+    {
+      "number": 1630,
+      "title": "Closed fixed-weight conic slice: eleven calls cannot realize four full targets",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1630",
+      "updated_at": "2026-10-14T07:08:02Z",
+      "state": "open"
+    },
+    {
+      "number": 1636,
+      "title": "Centre-free E8 side shear: simultaneous spectral closure at 1 and -13",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1636",
+      "updated_at": "2026-10-14T09:54:49Z",
+      "state": "open"
+    },
+    {
+      "number": 1645,
+      "title": "DONE: one extra mixed total at the selected k8 cut fails the cost screen",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1645",
+      "updated_at": "2026-10-14T06:12:10Z",
+      "state": "open"
+    },
+    {
+      "number": 1659,
+      "title": "DONE: exact complete selected k8 frame ceiling (PR #1671)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1659",
+      "updated_at": "2026-10-14T06:24:23Z",
+      "state": "open"
+    },
+    {
+      "number": 1667,
+      "title": "Spinor paired-Walsh centres: exact 6272 COPY rank and phases, full supplier open",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1667",
+      "updated_at": "2026-10-14T12:22:29Z",
+      "state": "open"
+    },
+    {
+      "number": 1693,
+      "title": "CLAIM: one-touch rank-one climb retiming into rank-two children (seed 73506)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1693",
+      "updated_at": "2026-10-14T20:17:35Z",
+      "state": "open"
+    },
+    {
+      "number": 1723,
+      "title": "DONE: mandatory late blocks require eight interface changes before the target screen opens",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1723",
+      "updated_at": "2026-10-14T08:05:05Z",
+      "state": "open"
+    },
+    {
+      "number": 1730,
+      "title": "CLAIM: selected #1094 certificate-to-replay binding and invoice/outer recheck",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1730",
+      "updated_at": "2026-10-14T08:13:53Z",
+      "state": "open"
+    },
+    {
+      "number": 1737,
+      "title": "DONE: sharp COPY power floor for row-masked P112 basis switches",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1737",
+      "updated_at": "2026-10-14T08:33:55Z",
+      "state": "open"
+    },
+    {
+      "number": 1765,
+      "title": "HANDOFF: Joint rank-two child interface candidate (seed 0d762194)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1765",
+      "updated_at": "2026-10-14T09:12:31Z",
+      "state": "open"
+    },
+    {
+      "number": 1776,
+      "title": "DONE: exact mutable connector cost with sequential delivery cuts (PR1780)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1776",
+      "updated_at": "2026-10-16T21:29:58Z",
+      "state": "open"
+    },
+    {
+      "number": 1885,
+      "title": "DONE: independent R480 packing audit through a=1/2 (PR1914)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1885",
+      "updated_at": "2026-10-14T13:45:39Z",
+      "state": "open"
+    },
+    {
+      "number": 1952,
+      "title": "CLAIM: cyclic masked rank-three child profile (seed 380b8276)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1952",
+      "updated_at": "2026-10-14T15:06:26Z",
+      "state": "open"
+    },
+    {
+      "number": 1963,
+      "title": "CLAIM: nonadjacent centre-path sharing with role permutation (seed 146930b1)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1963",
+      "updated_at": "2026-10-14T15:39:14Z",
+      "state": "open"
+    },
+    {
+      "number": 1976,
+      "title": "Swapped-chart source-code order and growth on the selected 112-port query",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1976",
+      "updated_at": "2026-10-14T16:02:53Z",
+      "state": "open"
+    },
+    {
+      "number": 1980,
+      "title": "CLAIM: second universal support-axis invariant (seed 0654b173)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1980",
+      "updated_at": "2026-10-14T17:04:16Z",
+      "state": "open"
+    },
+    {
+      "number": 2000,
+      "title": "DONE: arbitrary selected k8 helper terminal frames retain the ceiling (PR #2013)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2000",
+      "updated_at": "2026-10-14T17:08:34Z",
+      "state": "open"
+    },
+    {
+      "number": 2024,
+      "title": "CLAIM: three-dimensional port decoder for selected P112 (Cycle 14)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2024",
+      "updated_at": "2026-10-14T18:02:02Z",
+      "state": "open"
+    },
+    {
+      "number": 2036,
+      "title": "CLAIM: three-source clean cache across two output lines (Cycle 17)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2036",
+      "updated_at": "2026-10-14T18:04:57Z",
+      "state": "open"
+    },
+    {
+      "number": 2051,
+      "title": "DONE: selected T16 invoice input boundary audit (#2081)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2051",
+      "updated_at": "2026-10-17T18:31:13Z",
+      "state": "open"
+    },
+    {
+      "number": 2058,
+      "title": "CLAIM: nonadjacent selected centre-source fanout window (seed 2803b7f3)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2058",
+      "updated_at": "2026-10-14T18:45:14Z",
+      "state": "open"
+    },
+    {
+      "number": 2080,
+      "title": "RELEASED \u2014 P104 terminal correction overlaps #1167",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2080",
+      "updated_at": "2026-10-14T19:07:23Z",
+      "state": "open"
+    },
+    {
+      "number": 2119,
+      "title": "FINDING: Phase B has only 12 mixed rank-six candidates",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2119",
+      "updated_at": "2026-10-15T01:16:13Z",
+      "state": "open"
+    },
+    {
+      "number": 2121,
+      "title": "FINDING / HANDOFF: delayed-query P104 side word and its cost limit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2121",
+      "updated_at": "2026-10-14T21:34:58Z",
+      "state": "open"
+    },
+    {
+      "number": 2211,
+      "title": "DONE: selected CI navigation and regression check, preserving #626 history",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2211",
+      "updated_at": "2026-10-15T00:09:27Z",
+      "state": "open"
+    },
+    {
+      "number": 2238,
+      "title": "FINDING / HANDOFF: selected complex compact adapters with sequential repair",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2238",
+      "updated_at": "2026-10-17T17:53:43Z",
+      "state": "open"
+    },
+    {
+      "number": 2253,
+      "title": "FINDING / HANDOFF: selected complex layer and recursive precision closure",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2253",
+      "updated_at": "2026-10-15T07:19:59Z",
+      "state": "open"
+    },
+    {
+      "number": 2299,
+      "title": "DONE: P104 private reuse composes with coalesced frames; owner invoice still loses",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2299",
+      "updated_at": "2026-10-15T04:30:05Z",
+      "state": "open"
+    },
+    {
+      "number": 2319,
+      "title": "Selected BIT first-node caller and recursive-return handoff",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2319",
+      "updated_at": "2026-10-17T20:51:37Z",
+      "state": "open"
+    },
+    {
+      "number": 2333,
+      "title": "DONE: Windows selected PR1094 successor replay (PR2336)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2333",
+      "updated_at": "2026-10-15T16:05:44Z",
+      "state": "open"
+    },
+    {
+      "number": 2347,
+      "title": "DONE: opt-in owner-bound selected replay successor (PR2355)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2347",
+      "updated_at": "2026-10-15T06:21:12Z",
+      "state": "open"
+    },
+    {
+      "number": 2352,
+      "title": "DONE: fixed-code polar E8 gluing excluded over 120 transvections",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2352",
+      "updated_at": "2026-10-15T06:38:42Z",
+      "state": "open"
+    },
+    {
+      "number": 2424,
+      "title": "DONE: QQ16 all-axis read criterion and sharp 88-port threshold",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2424",
+      "updated_at": "2026-10-15T12:05:21Z",
+      "state": "open"
+    },
+    {
+      "number": 2463,
+      "title": "DONE: T74 raised-entrance wrappers independently bound and checked (#2472)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2463",
+      "updated_at": "2026-10-15T11:58:20Z",
+      "state": "open"
+    },
+    {
+      "number": 2606,
+      "title": "CLAIM: PR2530 source-partner handoff cuts, independent dirty-lender audit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2606",
+      "updated_at": "2026-10-15T22:27:14Z",
+      "state": "open"
+    },
+    {
+      "number": 2612,
+      "title": "Cost-aware source-partner helper assignments above PR2588",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2612",
+      "updated_at": "2026-10-17T21:07:41Z",
+      "state": "open"
+    },
+    {
+      "number": 2616,
+      "title": "CLAIM: T74 PR2575 owner evacuation, exact allocation and all-exponent cost audit",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2616",
+      "updated_at": "2026-10-15T16:50:04Z",
+      "state": "open"
+    },
+    {
+      "number": 2648,
+      "title": "Independent QQ16 completed-defect audit and feedback guard refinement",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2648",
+      "updated_at": "2026-10-15T16:57:25Z",
+      "state": "open"
+    },
+    {
+      "number": 2650,
+      "title": "DONE: zero-early-retention QQ16 comparison with higher native cost",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2650",
+      "updated_at": "2026-10-15T19:02:31Z",
+      "state": "open"
+    },
+    {
+      "number": 2791,
+      "title": "CLAIM: exact terminal X/Y readouts of the selected centre-error response",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2791",
+      "updated_at": "2026-10-15T22:41:36Z",
+      "state": "open"
+    },
+    {
+      "number": 2887,
+      "title": "DONE: current-status review navigation through efficient1800",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2887",
+      "updated_at": "2026-10-16T07:44:22Z",
+      "state": "open"
+    },
+    {
+      "number": 2976,
+      "title": "DONE: selected scatter parity versus record-export membership",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2976",
+      "updated_at": "2026-10-17T18:21:00Z",
+      "state": "open"
+    },
+    {
+      "number": 3145,
+      "title": "HANDOFF: T740 allocation for the rank-7 coupled inventory",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/3145",
+      "updated_at": "2026-10-17T18:18:46Z",
+      "state": "open"
+    }
+  ]
+}
diff --git a/research/complex-t16-evacuation-increment/evidence/REPLAY.json b/research/complex-t16-evacuation-increment/evidence/REPLAY.json
new file mode 100644
index 0000000000..63c5c60add
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/evidence/REPLAY.json
@@ -0,0 +1,111 @@
+{
+  "status": "PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY",
+  "kappa": "209202311361877/125000000000000000",
+  "kappa_decimal": "0.001673618490895016",
+  "conservative_kappa_decimal": "0.001673618488042206",
+  "complex_lower": "838212092705151621517/500000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "complex_profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62318,
+    "4": 20448,
+    "5": 11808,
+    "7": 2,
+    "8": 1152,
+    "16": 2,
+    "48": 4880
+  },
+  "idle_remainder_profile": {
+    "1": 2392,
+    "2": 8,
+    "3": 110,
+    "7": 2,
+    "16": 2,
+    "48": 4880
+  },
+  "complete_invocations": 144,
+  "roles": 69120,
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16469,
+  "retained_row_coefficient": 20161,
+  "actual_73_axis_charts": 10008,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15
+  },
+  "t8_kappa": "167166528321877/100000000000000000",
+  "spec_sha256": "91d3a23fc5ee84fcbcb9f8cc60352615c4e9e785b7ef891b6273b3f8903e0d58",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.495,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.404,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "lift16",
+      "seconds": 3.445,
+      "exit_code": 0,
+      "log_sha256": "91d6bdbfc122b2145cd759c76bd32b2e2ab3546565ea10ffa6fe87736c525bec"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.437,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 7.463,
+      "exit_code": 0,
+      "log_sha256": "042a915c7b3cc2148744341b795e2a4046774c5672d9577b924d670f9c69167b"
+    },
+    {
+      "name": "audit",
+      "seconds": 26.153,
+      "exit_code": 0,
+      "log_sha256": "dee46c03036c599dfad33bc846e8d770433788b67b4a78422412720b4523ff5f"
+    },
+    {
+      "name": "invoice",
+      "seconds": 1.272,
+      "exit_code": 0,
+      "log_sha256": "8f7074e3f78a103318ded6362c8e9bc8fc0e8c1ea3b510e63b9b84b181452cb3"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.491,
+      "exit_code": 0,
+      "log_sha256": "dfde084f684c5a5934d23576d90ff8f76fdbdd04136c26ce9f055632c057bc5f"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.641,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.958,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent-t16",
+      "seconds": 1.302,
+      "exit_code": 0,
+      "log_sha256": "9a822ed55b91969189acb1bb1bbdcebafc800855952fbd5e91c5d977c29cbbf9"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/complex-t16-evacuation-increment/verify.py b/research/complex-t16-evacuation-increment/verify.py
new file mode 100644
index 0000000000..5ddeb7e9bc
--- /dev/null
+++ b/research/complex-t16-evacuation-increment/verify.py
@@ -0,0 +1,223 @@
+#!/usr/bin/env python3
+"""Rebuild and independently verify one finite T16 CP-SAT packing improvement."""
+from collections import Counter
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+import os
+import shutil
+import subprocess
+import sys
+import tarfile
+import tempfile
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+P = Path(__file__).resolve().parent
+OLD_KAPPA = Q('0.001673614205725695')
+CEILING_A_HI = Q(1690054109089, 10**15)
+CONTROLS = dict(admission=69, bit_supplier=12, independent_t16=6, controller_mutations=15)
+
+
+def read_json(path):
+    return json.loads(Path(path).read_text())
+
+
+def load_module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+def digest(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def clean_env():
+    env = {k: os.environ[k] for k in ('PATH', 'SYSTEMROOT', 'WINDIR', 'TMPDIR', 'TEMP', 'TMP') if k in os.environ}
+    env.update(PYTHONNOUSERSITE='1', PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0')
+    return env
+
+
+def reconstruct(main, work):
+    pins = read_json(P/'SOURCES.json')
+    for item in pins['files']:
+        if item['usage'] == 'input':
+            assert digest(main/item['path']) == item['sha256'], 'Changed pinned input: '+item['path']
+
+    # Apply the compact row delta to the immediately preceding owner map.
+    prev = main/'research/complex-t16-two-stage-cycles/data/OWNERS.json.gz'
+    rows = json.loads(gzip.decompress(prev.read_bytes()))
+    diff = read_json(P/'DIFF-vs-predecessor.json')
+    assert len(diff) == 163 and [r['index'] for r in diff] == sorted(r['index'] for r in diff)
+    moved = 0
+    for item in diff:
+        i = item['index']
+        assert 0 <= i < len(rows) and rows[i] == item['before'], ('delta base mismatch', i)
+        before, after = item['before'], item['after']
+        assert all(before[k] == after[k] for k in ('stage', 'replica', 'time', 'helper', 'width'))
+        moved += any(before[k] != after[k] for k in ('owner_replica', 'child', 'port'))
+        rows[i] = after
+    assert moved == 142 and len(diff)-moved == 21
+    owners = json.loads(gzip.decompress((P/'data/OWNERS.json.gz').read_bytes()))
+    assert rows == owners, 'predecessor + delta does not reconstruct the candidate'
+
+    # The existing builder derives all three shipped data files, including the actual chart count.
+    rebuilt = work/'rebuilt'
+    subprocess.run([sys.executable, '-B', str(main/'research/complex-t16-two-stage-cycles/search/buildcand.py'),
+                    str(main/'research/complex-t16-two-stage-cycles/search'), str(P/'data/OWNERS.json.gz'),
+                    str(rebuilt), '10008'], cwd=main, env=clean_env(), check=True)
+    rebuilt_rows = json.loads(gzip.decompress((rebuilt/'OWNERS.json.gz').read_bytes()))
+    assert rebuilt_rows == owners, 'builder changed owner rows'
+    # zlib may emit different gzip bytes across Python versions. Compare the
+    # complete JSON objects after removing only hashes of those compressed bytes.
+    rebuilt_plan, plan = read_json(rebuilt/'PLAN.json'), read_json(P/'data/PLAN.json')
+    assert digest(P/'data/OWNERS.json.gz') == plan['assignment_sha256']
+    assert digest(P/'data/OWNERS.json.gz') == plan['replica_lift']['owners_file_sha256']
+    assert digest(P/'data/PLAN.json') == read_json(P/'data/SPEC.json')['data']['plan_sha256']
+    assert digest(P/'data/OWNERS.json.gz') == read_json(P/'data/SPEC.json')['data']['owners_sha256']
+    for obj in (rebuilt_plan, plan):
+        obj.pop('assignment_sha256')
+        obj['replica_lift'].pop('owners_file_sha256')
+    assert rebuilt_plan == plan, 'builder mismatch in semantic PLAN fields'
+    rebuilt_spec, candidate_spec = read_json(rebuilt/'SPEC.json'), read_json(P/'data/SPEC.json')
+    rebuilt_spec['data'] = {'owners_sha256': 'compressed-bytes-vary', 'plan_sha256': 'compressed-bytes-vary'}
+    candidate_spec['data'] = {'owners_sha256': 'compressed-bytes-vary', 'plan_sha256': 'compressed-bytes-vary'}
+    assert rebuilt_spec == candidate_spec, 'builder mismatch in semantic SPEC fields'
+
+
+def strict_replay(main, work):
+    source = work/'source'
+    source.mkdir()
+    archive = main/'research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz'
+    with tarfile.open(archive) as tar:
+        for member in tar.getmembers():
+            assert member.isfile() and (source/member.name).resolve().is_relative_to(source.resolve())
+        tar.extractall(source, filter='data')
+    manifest = read_json(source/'MANIFEST.json')
+    actual = {f.relative_to(source).as_posix(): digest(f) for f in source.rglob('*')
+              if f.is_file() and f != source/'MANIFEST.json'}
+    assert actual == manifest, 'frozen PR1087 source manifest mismatch'
+    for name in ('OWNERS.json.gz', 'PLAN.json', 'SPEC.json'):
+        shutil.copyfile(P/'data'/name, source/'data'/name)
+
+    local = work/'local'
+    local.mkdir()
+    local_pins = read_json(main/'research/complex-t16-two-stage-cycles/LOCAL-PINS.json')
+    provider_archive = main/'research/community-frontier1094-audit/selected-replay.tar.gz'
+    prefix = 'candidate/strict/global/base/providers/gauge44/'
+    with tarfile.open(provider_archive) as tar:
+        for name, expected in local_pins.items():
+            member = tar.getmember(prefix+name)
+            assert member.isfile()
+            content = tar.extractfile(member).read()
+            assert hashlib.sha256(content).hexdigest() == expected, 'provider pin mismatch: '+name
+            (local/name).write_bytes(content)
+
+    replay_dir = work/'strict'
+    env = clean_env()
+    subprocess.run([sys.executable, '-E', '-S', '-B', str(source/'verify_t16.py'),
+                    '--main', str(main), '--local', str(local), '--work', str(replay_dir)],
+                   env=env, check=True)
+    result = read_json(replay_dir/'REPLAY.json')
+    expected = read_json(P/'data/SPEC.json')['expected']
+    assert result['status'] == 'PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY'
+    assert result['kappa'] == expected['kappa']
+    assert Decimal(result['kappa_decimal']) == Decimal(expected['kappa_decimal'])
+    assert Decimal(result['conservative_kappa_decimal']) == Decimal(expected['conservative_kappa_decimal'])
+    assert result['complex_profile'] == expected['global_profile']
+    assert result['idle_remainder_profile'] == expected['idle_remainder_profile']
+    assert result['actual_73_axis_charts'] == expected['actual_73column_sigmas'] == 10008
+    assert result['controls'] == CONTROLS
+    pinned = read_json(P/'evidence/REPLAY.json')
+    for key in ('status', 'kappa', 'kappa_decimal', 'conservative_kappa_decimal', 'actual_73_axis_charts', 'controls'):
+        assert result[key] == pinned[key], 'strict receipt differs from packaged evidence: '+key
+    return replay_dir, result
+
+
+def independent_audit(main, replay_dir, work):
+    check = load_module('t16_predecessor_independent_check', main/'research/complex-t16-two-stage-cycles/check.py')
+    check.P = P
+    out_path = work/'CHECK.json'
+    check.run(main, replay_dir, out_path)
+    result = read_json(out_path)
+    evidence = read_json(P/'evidence/CHECK.json')
+    for key in ('candidate', 'price_new', 'price_new_conservative', 'majorization', 'sweep',
+                'changed_rows', 'offset_only_rows', 'all_strictly_inside', 'helper_once_per_call'):
+        assert result[key] == evidence[key], 'independent receipt mismatch: '+key
+    assert result['relocated_rows'] == evidence['relocated_rows']
+    assert Decimal(result['price_new']['kappa_decimal']) == Decimal('0.001673618490895016')
+    assert result['majorization']['candidate_majorizes_selected'] is True
+    assert result['sweep']['binding'] == 'complex'
+    return result
+
+
+def check_word_ceiling(main, expected):
+    word_path = main/'research/t16-owner-audit-seed67/inputs/k8-seven-slot-word.json.gz'
+    word = json.loads(gzip.decompress(word_path.read_bytes()))
+    local = {int(k): int(v) for k, v in word['report']['local_profile'].items()}
+    mod = load_module('t16_word_ceiling', main/'research/complex-local-word-ceiling/ceiling.py')
+    a_lo, a_hi = mod.ceiling(local, 73, 896, 9, 64)
+    assert a_hi == CEILING_A_HI, (a_lo, a_hi)
+    kappa_cap = a_hi/(1+a_hi)
+    candidate_kappa = Q(expected['kappa'])
+    selected_kappa = Q('0.001672660197076918')
+    assert candidate_kappa < kappa_cap and candidate_kappa > OLD_KAPPA > selected_kappa
+    realized = candidate_kappa/kappa_cap
+    selected_gap_realized = (candidate_kappa-selected_kappa)/(kappa_cap-selected_kappa)
+    with localcontext() as ctx:
+        ctx.prec = 50
+        realized_decimal = Decimal(realized.numerator)/Decimal(realized.denominator)
+        gap_decimal = Decimal(selected_gap_realized.numerator)/Decimal(selected_gap_realized.denominator)
+        cap_decimal = Decimal(kappa_cap.numerator)/Decimal(kappa_cap.denominator)
+    return dict(a_hi=str(Decimal(a_hi.numerator)/Decimal(a_hi.denominator)),
+                kappa_ceiling=str(cap_decimal), fraction_of_kappa_ceiling_realized=str(realized_decimal),
+                fraction_of_selected_to_ceiling_gap_realized=str(gap_decimal))
+
+
+def packing_ceiling(main, work):
+    out_path = work/'CEILING.json'
+    subprocess.run([sys.executable, '-I', '-B', str(main/'research/complex-t16-two-stage-cycles/ceiling_bound.py'),
+                    '--data', str(P/'data'), '--out', str(out_path)], env=clean_env(), check=True)
+    result = read_json(out_path)
+    evidence = read_json(P/'evidence/CEILING.json')
+    assert result == evidence
+    assert result['theorem1']['max_empty_cap48'] == 4887
+    assert result['theorem3']['bound_decimal'] == '908139.013'
+    assert result['this_map']['empty_cap48'] == 4880
+    return result
+
+
+def run(main, work):
+    reconstruct(main, work)
+    replay_dir, replay = strict_replay(main, work)
+    audit = independent_audit(main, replay_dir, work)
+    spec = read_json(P/'data/SPEC.json')['expected']
+    old_delta = Q(spec['kappa'])-OLD_KAPPA
+    assert old_delta == Q(4285169321, 10**18)
+    cap = check_word_ceiling(main, spec)
+    packing = packing_ceiling(main, work)
+    print('PASS_T16_EVACUATION_INCREMENT', replay['kappa_decimal'],
+          'delta_vs_predecessor', Decimal(old_delta.numerator)/Decimal(old_delta.denominator),
+          'fraction_of_word_kappa_ceiling', cap['fraction_of_kappa_ceiling_realized'],
+          'changed/relocated', audit['changed_rows'], len(audit['relocated_rows']),
+          'packing ceiling E<=', packing['theorem3']['bound_decimal'])
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--main', type=Path, default=P.parents[1])
+    parser.add_argument('--work', type=Path)
+    args = parser.parse_args()
+    if args.work:
+        args.work.mkdir(parents=True, exist_ok=False)
+        run(args.main.resolve(), args.work.resolve())
+    else:
+        with tempfile.TemporaryDirectory(prefix='t16-evacuation-increment-') as tmp:
+            run(args.main.resolve(), Path(tmp))