diff --git a/research/arbitrary-pivot-schur-minimum/FIXTURES.json b/research/arbitrary-pivot-schur-minimum/FIXTURES.json
new file mode 100644
index 0000000000..2231f5bfc0
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/FIXTURES.json
@@ -0,0 +1,583 @@
+{
+  "d": 2,
+  "field": 2,
+  "schema_version": 1,
+  "fixtures": [
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,0,1,0],[1,1,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[0,1,1,0,0,0,0,1],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[0,1,1,0,0,0,0,1],[1,0,0,1,1,0,0,0],[1,1,1,0,0,1,0,1],[1,1,0,1,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1],[1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0],[1,1,0,1,1,0,0,1],[1,1,0,1,0,0,1,0],[1,1,0,0,1,1,0,1],[1,1,0,1,1,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,1,1,1,0],[1,1,0,0,0,0,0,1,1,0],[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,1,0,1,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[0,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[1,1,0,0,1,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[0,1,0,1,0,0,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,1],[1,0,0,0,1,1,0,0,1,0],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,1],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,1],[1,1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1,0],[1,1,1,0,1,0,0,1,1,1,0],[1,1,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,1,1,0,0],[1,1,0,0,1,0,0,0,0,1,1]],"Q":[[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1],[1,1,1,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[0,1,0,1,1,0,0,0],[1,0,1,1,1,1,0,1],[1,1,0,1,1,1,0,1],[0,1,0,1,1,0,0,0],[1,0,1,1,1,1,0,1],[1,1,0,1,1,1,0,0],[1,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,1,0,0],[1,0,0,1,0,0,0,1],[1,0,0,1,0,0,0,1],[1,1,0,0,1,1,0,0],[1,1,0,1,1,0,0,1],[1,1,0,1,1,0,0,0],[1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[0,1,0,1,1,1,0,0],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[0,1,0,1,1,1,0,0],[1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0],[1,1,0,1,1,1,1,0],[1,1,0,1,1,0,0,1]],"Q":[[0,1,0,1,1,1,1,0],[1,0,0,1,1,0,0,1],[1,0,0,1,1,0,0,1],[1,1,0,0,1,1,1,0],[1,1,0,1,0,0,0,1],[0,0,0,0,0,1,0,0],[1,1,0,1,1,1,0,0],[1,1,0,1,1,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[0,1,0,0,1,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[0,1,0,1,1,0,0],[1,0,1,0,0,1,1],[1,1,0,0,0,1,1],[0,1,0,1,1,0,0],[1,0,1,0,0,1,1],[1,1,0,1,1,1,0],[1,1,1,0,0,1,0]],"Q":[[0,1,0,1,1,1,0],[1,0,0,0,1,1,1],[1,0,0,0,1,1,1],[1,1,0,0,1,1,0],[1,1,0,0,0,1,1],[1,1,0,1,1,0,0],[1,1,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,1,0,0,1],[1,1,1,1,0,0,0,0,0,1],[0,1,1,0,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,1,1,0,1],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[0,1,1,1,1,1,0],[1,0,0,1,1,0,0],[1,1,1,1,1,0,0],[0,1,1,1,1,1,0],[1,0,0,1,1,0,0],[1,1,1,1,1,0,0],[1,1,0,1,1,0,1]],"Q":[[0,1,0,1,0,1,1],[1,0,0,1,1,0,1],[1,0,0,1,1,0,1],[1,1,0,0,0,1,1],[1,1,0,1,0,0,1],[1,1,0,1,0,0,1],[1,1,0,1,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0],[1,1,0,0,0,0,0,0,1,1],[1,1,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,1,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,1,1,1],[1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,0],[0,1,1,0,0,0,1,1,1],[1,0,0,1,0,0,1,1,0],[1,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,1],[1,0,0,0,0,1,1,1,0],[0,1,0,0,1,0,1,1,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,0],[1,1,0,0,1,0,0,1,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[0,1,1,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[0,1,1,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,0],[1,1,1,0,0,1,0,1,0],[1,1,0,1,1,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,0,0,0,0,1],[1,0,1,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[1,0,1,1,0,0,0,1,0],[1,1,0,1,0,0,1,0,1],[1,1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,1,0,0],[0,1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[1,1,1,1,1,0,0,0,0,0,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,0,0,0,1,1,0,0,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,0,1],[1,1,0,1,0,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[1,1,0,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,0,1,0,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,1,0,0,0,0,0,1],[1,0,0,1,0,0,1,1,0,1],[1,1,1,1,0,0,0,0,0,1],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[1,0,0,1,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,1],[1,1,0,1,0,0,1,1,0,0]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,1,0,0,0],[1,0,1,1,0,0,0,0],[0,1,1,1,1,0,0,0],[1,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0],[1,1,1,1,1,1,0,0],[1,1,1,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,1,1,1,1,0,0],[1,1,1,1,0,0,0,1],[1,1,0,1,1,1,0,0],[1,0,1,0,0,0,0,1],[0,0,0,0,1,0,0,0],[1,1,1,1,1,0,0,0],[1,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[0,1,0,0,1,1,0,0],[1,0,0,1,1,1,1,1],[1,1,1,1,1,1,1,1],[0,0,0,1,0,0,0,0],[0,1,0,0,1,1,0,0],[1,0,0,1,1,1,1,1],[1,1,0,0,1,1,1,0],[1,1,0,1,1,1,1,0]],"Q":[[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0],[1,0,0,0,1,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,0,1,0,0,1,0,0],[1,1,1,1,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,1,1,0,0,0],[1,0,0,1,0,0,1,0,0],[1,1,0,0,1,1,1,0,0],[1,1,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[0,1,0,1,1,0,0,0],[1,0,1,0,0,0,1,1],[1,1,0,0,0,0,1,1],[0,1,0,1,1,0,0,0],[1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0],[1,1,0,1,1,0,1,0],[1,1,1,0,0,0,1,0]],"Q":[[0,1,0,1,1,0,1,0],[1,1,0,0,0,1,1,1],[1,1,0,0,0,1,1,1],[1,1,0,0,1,0,1,0],[1,0,0,0,1,1,1,1],[0,0,0,0,0,1,0,0],[1,1,0,1,1,0,0,0],[1,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[0,1,0,1,1,1,1,1,1],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,1,1,1,1,1],[1,0,0,0,1,1,0,0,0],[1,1,0,1,1,1,0,1,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,0,1,1],[1,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1],[0,1,1,0,0,0,1,1],[1,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,1],[1,1,1,0,0,1,1,0]],"Q":[[0,1,0,1,0,1,1,1],[1,1,0,1,0,0,0,1],[0,1,0,1,0,1,1,1],[1,1,0,0,0,1,1,1],[1,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0],[1,1,0,1,0,1,0,1],[1,0,0,1,0,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,1,1],[1,0,0,0,1,0,0,1,0],[1,1,0,0,0,0,0,1,1],[1,1,0,1,1,0,0,1,0],[0,0,0,0,1,0,0,0,0],[0,1,1,0,0,0,0,1,1],[1,0,0,0,1,0,0,1,0],[1,1,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,0,1],[1,1,1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[1,1,0,1,1,1,0,0,0],[0,1,0,1,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[1,1,0,1,0,0,1,0,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,1,1,1,0],[1,1,0,0,0,0,0,1,1,0],[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,1,0,1,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,1,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[0,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,0,1,1,1,0,0],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,1,0,0,0,0],[1,0,1,1,0,0,0,0,1,0],[1,1,1,0,1,1,0,0,0,0],[1,1,1,0,0,0,0,0,1,0],[0,1,0,0,1,1,0,0,0,0],[1,0,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0,0],[1,1,1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,1,0,0],[1,1,0,1,1,1,0,0,0],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,1,0],[1,1,0,0,1,1,0,0,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,1,0,0],[1,0,0,1,0,0,1,1],[1,1,1,0,1,1,0,0],[1,1,0,0,0,0,1,1],[0,1,0,0,1,1,0,0],[1,0,0,1,0,0,1,1],[1,1,0,0,1,1,1,0],[1,1,0,1,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,0,0,1,1,0,1],[1,0,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,1,0,1],[1,1,1,0,0,0,0,0,0,1],[0,1,1,1,0,0,1,1,0,1],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,1,1,1,1],[1,1,1,1,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,0,1,0,1],[1,0,0,0,1,1,0,0,0,0],[1,1,0,1,0,0,0,1,0,1],[1,1,0,1,1,1,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,0,1,0],[1,0,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[1,1,0,0,0,0,0,1,1],[0,1,1,1,0,0,0,1,0],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0],[1,1,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,1,0,0,1],[1,1,1,1,0,0,0,0,0,1],[0,1,1,0,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,1,1,0,1],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[0,1,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,0]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,1,1],[1,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,1],[1,1,0,1,1,1,0,0],[0,1,1,0,0,0,1,1],[1,0,0,0,1,1,0,0],[1,1,1,0,0,0,0,1],[1,1,0,0,1,1,0,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,1,1,1],[1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,0],[0,1,1,0,0,0,1,1,1],[1,0,0,1,0,0,1,1,0],[1,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[0,1,1,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[0,1,1,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,0],[1,1,1,0,0,1,0,1,0],[1,1,0,1,1,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,1,0,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[0,1,1,0,0,0,0,0,1],[1,0,1,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1],[0,1,1,0,0,0,0,0,1],[1,0,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,1,0,1],[1,1,1,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,1,0,0,1],[1,1,0,1,0,0,0,1,0],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,1,0,0,1],[1,0,0,1,1,0,0,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,1,1,0,1],[1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,0,0,0,0,1],[1,0,0,0,1,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,1,1,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[1,0,0,0,1,0,0,1,0,0],[1,1,0,1,0,0,0,1,0,1],[1,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[1,1,1,1,1,0,0,0,0,0,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,1,1,1,0,0,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,1,0,0,0],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,1,1,0,0],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,1,1,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,1,1,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,1,1,1,1,1,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,1,1,0,0,0,1,0],[1,1,1,0,1,1,0,0,0],[1,1,1,0,0,0,0,1,0],[0,1,0,0,1,1,0,0,0],[1,0,1,1,0,0,0,1,0],[1,1,0,0,1,1,1,0,0],[1,1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,1,0,1,1],[1,0,0,0,1,1,0,1,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,1,0],[1,1,1,0,0,1,1,0,0],[1,1,0,1,1,0,0,1,0],[0,0,0,0,1,0,0,0,0],[0,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,1,0],[1,1,0,0,0,1,1,1,0],[1,1,0,0,1,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1,0],[1,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,1,1,1,1],[1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,0,1,0,0,0,1,1],[1,1,1,0,1,1,0,0,0],[1,1,0,0,0,0,0,1,1],[0,1,0,0,1,1,0,0,0],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0],[1,1,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,1,1],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,1,0,1,0,1],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[0,1,1,1,1,0,1,0,1],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,1,0,1,1,0,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,1,0,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[1,0,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,0,0,1,1,1,1],[1,0,1,0,0,0,0,1,1],[1,1,0,0,0,0,0,1,1],[0,1,1,0,0,1,1,1,1],[1,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,1,1,0,1],[1,1,1,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[0,1,0,1,1,1,1,1,1],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,1,1,1,1,1],[1,0,0,0,1,1,0,0,0],[1,1,0,1,1,1,0,1,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,1,1,1,1,0],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,0,1,1],[1,0,1,1,0,0,0,1],[1,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,1],[0,1,1,0,0,0,1,1],[1,0,1,1,0,0,0,1],[1,1,1,0,0,0,0,1],[1,1,1,1,0,0,0,0]],"Q":[[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[0,0,0,0,1,1,1,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[0,1,0,1,0,0,1,1,0],[1,0,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,1,1,0],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,1,0,0],[1,1,0,1,0,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,1,0,1],[1,0,0,0,0,1,0,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,1,1,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,1,0,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,0,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,1,1,1,0,0,0],[1,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,1,1,1,0,1,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,1,0,0,0,0],[1,0,1,1,1,0,0,1,1],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,0,0,0,0],[1,0,1,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,1,0,0],[1,1,1,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,0,1],[0,1,0,0,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,0,1,0,0,0,1],[0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,0,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,1,1,0,0,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,1,0,0,0],[0,1,0,1,1,1,0,0,0],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,1,1,0,0],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,1,0,0,1],[0,1,0,1,1,0,1,0,0],[1,1,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,0,1],[0,0,0,1,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,1,1,0,1],[0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,0,1,1,1,1,1,1],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,1,1,0,0,0],[1,0,0,1,1,1,1,1,1],[1,1,0,0,1,1,1,0,0],[1,1,0,1,1,1,1,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,1,1,0],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,0,0],[1,1,1,0,1,0,0,0,1],[1,1,0,1,0,1,1,0,0],[0,0,0,0,1,0,0,0,0],[0,1,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,0,0],[1,1,0,0,1,0,0,1,1],[1,1,0,0,0,1,1,0,1]],"Q":[[1,1,0,0,0,1,0,0,1],[0,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,1],[0,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,1,0],[0,1,0,0,0,1,0,1,1],[0,0,0,0,0,1,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,1,0,0,0,0,1],[1,0,0,1,0,0,1,0,1],[1,1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,0,0,1],[1,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1],[1,1,0,1,0,0,1,0,0]],"Q":[[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,1,1],[1,1,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,1],[0,1,1,0,0,1,0,0,1],[1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,1,1,0,1],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[0,1,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,0,0],[0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,1,0,1],[1,0,0,0,1,1,0,0,0],[1,1,0,1,0,0,1,0,1],[1,1,0,1,1,1,0,0,0],[0,1,1,1,0,0,1,0,1],[1,0,0,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,1,0],[1,0,0,1,0,0,1,1],[1,1,0,1,0,0,1,0],[1,1,0,0,0,0,1,1],[0,1,1,1,0,0,1,0],[1,0,0,1,0,0,1,1],[1,1,1,1,0,0,0,0],[1,1,0,1,0,0,1,0]],"Q":[[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,1,0,0,0,1,0,0],[0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,0,0,1,1],[1,0,1,0,0,1,1,1,1],[1,1,0,0,0,0,0,1,1],[0,1,1,0,0,0,0,1,1],[1,0,1,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,1,1,0,0,1,1,1,0]],"Q":[[1,1,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,1,0,0,0,1,0,1,1],[0,1,0,1,0,1,0,1,1],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[1,1,0,0,0,0,0,1,1],[1,1,0,1,1,1,0,0,0],[0,1,1,0,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,1,0,0,1,1,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1],[0,1,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,1],[0,1,0,0,1,1,0,1,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,0,1,1,0],[0,1,0,0,1,0,1,1,1,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,1,0,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,0,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,1,1,1,0,0,0],[1,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,1,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[0,1,1,1,1,0,0,0],[1,0,1,1,0,0,0,0],[0,1,1,1,1,0,0,0],[1,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0],[1,1,1,1,1,1,0,0],[1,1,1,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,1,1,1,0,0,1],[1,0,1,1,0,0,1,0],[0,1,0,1,1,0,0,1],[1,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0],[0,1,1,1,1,1,0,1],[1,1,1,1,0,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[0,1,0,0,1,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,0,0,1,1,1,1,1,1],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,1,1,0,0,0],[1,0,0,1,1,1,1,1,1],[1,1,0,0,1,1,1,0,0],[1,1,0,1,1,1,1,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,0,0,1,0,0,1,0,1,0],[1,1,1,1,0,0,1,0,1,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[1,0,0,1,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[1,1,0,1,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[0,1,0,1,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[1,1,0,1,0,0,1,1,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,1],[1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,0,1],[1,1,0,1,0,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[1,1,0,0,0,1,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,0,0,1],[1,0,0,1,0,0,0,1,1],[1,1,1,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[0,1,0,0,1,0,0,0,1],[1,0,0,1,0,0,0,1,1],[1,1,0,0,1,0,0,1,1],[1,1,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[1,1,1,1,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,0],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[0,1,0,1,1,1,1,1],[1,0,0,0,1,1,0,0],[1,1,1,0,1,1,0,0],[0,0,0,1,0,0,0,0],[0,1,0,1,1,1,1,1],[1,0,0,0,1,1,0,0],[1,1,0,1,1,1,0,1],[1,1,0,0,1,1,0,1]],"Q":[[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,0,1,0,0],[1,1,0,0,1,1,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[0,1,1,0,0,1,1,1],[1,0,1,0,0,0,1,1],[1,1,0,0,0,0,1,1],[0,1,1,0,0,1,1,1],[1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0],[1,1,1,0,0,1,0,1],[1,1,1,0,0,0,1,0]],"Q":[[1,1,0,0,1,1,1,0],[1,0,0,0,1,0,1,1],[1,0,0,0,1,0,1,1],[0,1,0,1,1,1,1,0],[1,1,0,0,0,0,1,1],[0,0,0,0,0,1,0,0],[0,1,0,0,1,1,0,0],[1,1,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[0,1,1,1,1,0,1,0],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[0,1,1,1,1,0,1,0],[1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0],[1,1,0,1,1,0,0,1]],"Q":[[1,1,0,0,0,1,1,1],[1,0,0,1,1,0,0,1],[1,0,0,1,1,0,0,1],[0,1,0,1,0,1,1,1],[1,1,0,1,0,0,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,1],[1,1,0,1,1,0,0,0]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,1,1,1,0],[1,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,1,1,0,0],[1,1,0,1,0,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,1,1,0,0,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,1,1,0],[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,1,1,0],[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[0,1,1,0,0,0,0,1,0],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,1,0],[1,1,0,1,0,0,0,0,0],[1,1,1,0,0,1,0,1,0],[1,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,1],[1,0,1,1,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[1,1,0,1,0,0,1,0,1],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,1,1,1,0,0],[1,1,0,1,0,0,0,1,0,0],[1,1,1,1,0,1,1,1,0,0],[1,0,0,0,0,0,0,1,0,0],[0,1,0,1,0,1,1,1,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,1,1,0,0,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,1,0,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,1,0,0,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[1,0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,1,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[1,0,0,1,0,0,0,0,0,1,1]],"Q":[[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,1,0,0,0,1,1],[1,1,1,0,1,0,1,1,1,1],[1,0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,1,0,1],[1,0,0,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,1,0,1,1,1,0,0],[1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,1,0,0],[1,0,0,1,0,0,0,1],[1,0,0,1,0,0,0,1],[1,1,0,0,1,1,0,0],[1,1,0,1,1,0,0,1],[1,1,0,1,1,0,0,0],[1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[0,1,0,1,1,1,0,0],[1,1,1,1,1,1,1,1],[1,0,0,1,1,1,1,1],[0,1,0,1,1,1,0,0],[1,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0],[1,1,0,1,1,1,1,0],[1,0,1,1,1,1,1,0]],"Q":[[0,1,0,1,1,1,1,0],[1,0,0,1,1,0,0,1],[1,0,0,1,1,0,0,1],[1,1,0,0,1,1,1,0],[1,1,0,1,0,0,0,1],[0,0,0,0,0,1,0,0],[1,1,0,1,1,1,0,0],[1,1,0,1,1,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[0,1,0,1,1,0,0,0,0],[1,1,1,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0],[0,1,0,1,1,0,0,0,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,1,0,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,0,1,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[1,1,0,0,1,0,1,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[0,1,0,0,1,1,0,0],[1,1,0,1,0,0,1,1],[1,0,1,1,0,0,1,1],[0,0,0,1,0,0,0,0],[0,1,0,0,1,1,0,0],[1,1,0,1,0,0,1,1],[1,1,0,0,1,1,1,0],[1,0,0,1,0,0,1,0]],"Q":[[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,1,0,0,1,1,0,0],[1,1,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[0,1,1,1,0,0,1,1,1],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[0,1,1,1,0,0,1,1,1],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,1,1],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,1,1,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,1,0,1,0,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,1,0,1],[1,1,1,0,0,0,0,1],[1,1,0,0,0,1,0,1],[1,0,1,1,0,0,0,1],[0,1,1,0,0,1,0,1],[1,1,1,0,0,0,0,1],[1,1,1,0,0,1,1,1],[1,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,1,1,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1,1,0],[1,1,1,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,1,0],[1,0,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,0],[1,1,1,0,0,1,0,1],[1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1],[1,1,0,1,0,0,1,0],[1,1,0,1,0,0,1,0],[1,1,0,1,1,0,0,1],[1,0,0,1,1,0,1,0],[1,1,0,0,1,1,0,1],[1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0,0],[1,1,1,1,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,1,0,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[1,1,1,1,0,1,1,1,1,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,1,1,0,1,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,1,0,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,1],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,1,0,0,0,0,1],[1,1,0,1,0,1,1,0,1],[1,1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,0,0,1],[1,1,0,1,0,1,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1],[1,0,0,1,0,1,1,0,0]],"Q":[[0,1,0,0,0,0,1,0,1],[1,1,0,0,0,1,0,1,0],[0,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,1],[1,0,0,0,0,1,0,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,0,0,1,1],[1,1,1,0,1,0,0,0,0,0,0,1],[1,0,0,1,0,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,0,1,1],[1,0,0,0,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,0,0,1,1,1],[0,1,0,0,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,0,1,0,0,1],[1,0,0,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[0,1,0,0,1,1,1,0,0,0],[1,1,0,1,1,1,1,1,0,1],[1,0,1,1,1,1,1,1,0,1],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0,0],[1,1,0,1,1,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,1,0,0],[1,0,0,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,0,0,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,0,0],[1,1,1,0,0,0],[0,1,1,1,0,0],[1,1,1,0,0,0],[1,1,1,1,1,0],[1,0,1,0,0,1]],"Q":[[0,1,1,1,1,0],[1,1,1,0,0,1],[1,1,0,1,1,0],[1,0,1,1,0,1],[1,1,1,1,0,0],[1,0,1,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[0,1,0,1,1,0,0,0],[1,1,1,0,0,1,0,0],[1,0,0,0,0,1,0,0],[0,1,0,1,1,0,0,0],[1,1,1,0,0,1,0,0],[1,1,0,1,1,1,0,0],[1,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,1,0,1],[1,1,0,0,1,1,0,0],[1,1,0,0,1,1,0,0],[1,1,0,0,1,1,0,1],[1,0,0,0,0,1,0,0],[1,1,0,1,1,0,0,1],[1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,1,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,1,1],[0,0,0,1,0,0,0,0,0],[0,1,0,0,1,1,0,0,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0],[1,0,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0],[1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,0],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,1,1,0],[1,1,1,0,1,1,1,0],[1,1,0,0,0,1,1,0],[0,1,1,0,0,1,1,0],[1,1,1,0,1,1,1,0],[1,1,1,0,0,0,1,0],[1,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,1,1,0],[1,1,0,1,1,0,0,1],[0,1,0,1,0,1,1,0],[1,1,0,0,0,1,1,0],[1,0,0,1,0,0,0,1],[1,1,0,1,0,0,1,0],[1,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[0,1,0,1,1,0,0,1,0],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,1,0,0,1,0],[1,1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,0],[1,0,0,0,1,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,0,0,0,1],[1,1,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,1,0,1],[1,0,0,0,1,0,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0],[1,1,0,0,0,0,1,1],[1,0,0,0,0,0,1,0],[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0],[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1]],"Q":[[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,0,0,0,0,0,1,0],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,0,0,1,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,1,0],[1,0,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,0,1],[1,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,0,1,1,0,0],[1,1,0,1,0,0,1,0,0],[1,1,1,1,0,1,1,0,0],[1,0,0,0,0,0,1,0,0],[0,1,0,1,0,1,1,0,0],[1,1,0,1,0,0,1,0,0],[1,1,0,1,0,1,0,0,0],[1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[1,1,1,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,1],[0,1,0,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[1,1,0,0,1,1,1,0,0],[1,0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,1,0,0,0,0],[1,1,1,0,0,0,0,0,1,0],[1,1,1,0,1,1,0,0,0,0],[1,0,1,1,0,0,0,0,1,0],[0,1,0,0,1,1,0,0,0,0],[1,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0,0],[1,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,1,1,0,0],[1,1,0,1,0,0,0,1,0],[1,1,1,0,1,1,1,0,0],[1,0,0,0,0,0,0,1,0],[0,1,0,0,1,1,1,0,0],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,1,0],[1,0,0,1,0,0,0,1,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,1,0,0],[1,1,0,0,1,0,0,0],[1,1,1,0,1,1,0,0],[1,0,0,1,1,0,0,0],[0,1,0,0,1,1,0,0],[1,1,0,0,1,0,0,0],[1,1,0,0,1,1,1,0],[1,0,0,0,1,0,0,1]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,0,1,1,0,0,1],[1,1,1,1,0,0,0,0,0,1],[1,1,0,1,0,1,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[0,1,1,1,0,1,1,0,0,1],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,1,1,1,0,1],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,1,0,0],[1,1,0,1,0,0,0,1,0,1],[1,0,0,0,0,0,0,1,0,0],[0,1,1,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,0],[1,1,0,1,0,0,0,1,0],[1,0,0,1,1,0,0,0,0],[0,1,1,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,0,1,1,0,1],[1,1,1,0,0,0,0,0,1],[1,1,0,0,0,1,1,0,1],[1,0,1,1,0,0,0,0,1],[0,1,1,0,0,1,1,0,1],[1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,1,1,1,1],[1,0,1,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0],[1,1,0,0,0,0,1,1],[1,0,0,0,0,0,1,0],[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0],[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,0],[1,1,0,0,0,0,1,1,1],[1,0,0,1,1,0,0,0,0],[0,1,1,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,0],[1,1,1,0,0,0,0,1,1],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[0,1,1,0,0,0,0,1,0],[1,1,1,0,1,0,0,1,0],[1,0,0,0,1,0,0,1,0],[0,1,1,0,0,0,0,1,0],[1,1,1,0,1,0,0,1,0],[1,1,1,0,0,1,0,1,0],[1,0,1,0,1,0,1,1,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,1,0,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[0,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,1,0,1],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,1,0,0,1],[1,1,0,1,0,0,0,1,0],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,1,0,0,1],[1,0,0,1,1,0,0,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,1,1,0,1],[1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[1,1,1,1,1,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[1,1,0,1,1,0,0,1,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,1,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,0,1,1,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,1,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,1,0,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,1,1,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,1,0,1,1,1,0,0],[1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,1,0,1,1],[1,1,0,1,0,0,1,0],[1,1,0,1,0,0,1,0],[0,0,0,0,1,0,1,1],[1,0,0,1,1,0,1,0],[0,0,0,1,1,1,1,1],[1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,1,0,0],[1,1,0,1,0,0,1,0],[1,1,1,0,1,1,0,0],[1,0,0,0,0,0,1,0],[0,1,0,0,1,1,0,0],[1,1,0,1,0,0,1,0],[1,1,0,0,1,1,1,0],[1,0,0,1,0,0,1,1]],"Q":[[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0],[0,0,0,0,1,1,1,1],[1,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,0,1,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,1,1,0,0,1,1,0,0,0],[1,0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,0,1,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,1,0],[1,0,0,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,0,0,1,1],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[0,1,1,1,0,0,1,1],[1,1,0,1,0,0,0,0],[0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,1],[1,0,0,1,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0],[1,1,0,1,0,0,0,1],[1,1,0,1,0,0,0,1],[0,0,0,1,0,1,1,0],[1,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0],[1,0,0,1,0,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,0,1,1,1,0,0],[1,1,1,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0],[0,1,1,0,1,1,1,0,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,1,1,0,0,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0,1],[1,1,0,0,1,0,1,0,0],[1,1,0,0,1,0,1,0,0],[0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,1],[0,1,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[0,0,0,0,1,1,1,1,0],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[0,1,0,1,1,0,1,0],[1,1,0,0,1,0,0,0],[1,0,1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,1,1,0,1,0],[1,1,0,0,1,0,0,0],[1,1,0,1,1,0,0,0],[1,0,0,0,1,0,0,1]],"Q":[[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0],[0,0,0,0,1,1,1,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,0,1,0],[1,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,0,1,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,1,0,1],[1,0,0,0,0,1,0,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[1,0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,1,1,0,1,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,1,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[0,1,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,1,1],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,1,1],[1,1,0,1,1,1,0,0,0],[1,0,1,1,1,0,1,1,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,1,1,1,0,1,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,1,0,0,0,0],[1,1,1,0,0,0,0,1,0],[1,1,1,1,1,0,0,0,0],[0,1,0,1,1,0,0,0,0],[1,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,0,1,0,0],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,0,1],[0,1,0,0,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,0,1,0,0,0,1],[0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,0,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[0,1,0,0,1,1,1,0,0,0],[1,1,0,1,1,1,1,1,0,1],[1,1,1,0,1,1,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0,0],[1,1,0,1,1,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,1,0,0],[1,0,0,1,1,1,1,1,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,1,0,0],[1,1,0,0,1,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,1,1,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,1,1,1,1,0,0,0],[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,0,0],[1,1,0,1,1,1,0,0],[1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1],[0,1,0,1,0,1,1,0],[1,1,0,1,1,0,0,1],[0,1,0,0,1,0,0,1],[0,0,0,1,1,1,1,0],[0,1,0,1,1,1,0,1],[0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[0,1,0,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,1,1,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[0,1,0,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[1,0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[0,1,0,1,0,0,0,1],[1,1,0,1,0,1,0,1],[1,1,1,1,0,0,0,1],[0,0,0,1,0,0,0,0],[0,1,0,1,0,0,0,1],[1,1,0,1,0,1,0,1],[1,1,0,1,0,0,1,1],[1,0,0,1,0,1,0,0]],"Q":[[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1],[0,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,0,0,0],[1,1,1,0,1,0,0,0,0,1],[1,0,0,1,0,1,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,1,0,1],[0,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,1,0,1,0,1],[0,1,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[0,1,1,1,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[0,1,1,0,1,1,0,1],[1,1,1,0,0,0,0,1],[1,1,0,0,1,1,0,1],[0,1,1,0,1,1,0,1],[1,1,1,0,0,0,0,1],[0,0,0,0,0,0,0,0],[1,1,1,0,1,1,1,1],[1,0,1,0,0,0,0,0]],"Q":[[1,1,0,0,1,0,1,0],[0,1,0,0,0,1,0,1],[1,1,0,0,1,0,1,0],[0,1,0,1,1,0,1,0],[0,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[0,1,1,1,0,0,1,0,1],[1,1,0,1,0,0,1,0,0],[1,1,0,1,0,0,1,0,1],[1,0,0,0,0,0,1,0,0],[0,1,1,1,0,0,1,0,1],[1,1,0,1,0,0,1,0,0],[1,1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,1,0],[1,1,0,0,1,0,0,0],[1,1,0,1,0,0,1,0],[1,0,0,1,1,0,0,0],[0,1,1,1,0,0,1,0],[1,1,0,0,1,0,0,0],[1,1,1,1,0,0,0,0],[1,0,0,0,1,0,0,1]],"Q":[[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,1,0,0,0,1,0,0],[0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[0,1,1,0,0,0,1,1,0],[1,1,1,0,1,1,1,1,0],[1,1,0,0,0,0,1,1,0],[0,1,1,0,0,0,1,1,0],[1,1,1,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,1,0],[1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,1,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,0],[0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,1,1],[0,0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,1,1,1],[0,1,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,1],[0,1,0,0,1,1,0,1,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[0,1,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,0,1,1,0],[0,1,0,0,1,0,1,1,1,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[0,1,1,1,0,0,0,0],[1,1,1,0,0,0,0,0],[0,1,1,1,0,0,0,0],[1,1,1,0,0,0,0,0],[1,1,1,1,1,0,0,0],[1,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,1,1,0,0,1,0],[1,0,1,0,0,0,0,1],[0,1,0,1,0,0,1,0],[1,1,1,1,0,0,0,1],[0,1,1,1,1,0,1,0],[1,1,1,0,0,1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[0,1,0,1,1,1,0,0,0],[1,1,1,0,0,0,0,1,0],[1,1,1,1,1,1,0,0,0],[0,1,0,1,1,1,0,0,0],[1,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,1,1,1,1,0,0],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,1,0,0,1],[1,0,0,1,1,0,0,1,0],[1,1,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,0,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,1,1,0,1],[1,1,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[0,1,0,0,1,1,0,0,0,0],[1,1,0,1,1,1,0,1,0,1],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,0,1,1,0,0,0,0],[1,1,0,1,1,1,0,1,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,1,0,0],[1,0,0,1,1,1,0,1,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[0,1,0,0,1,1,0,0,0],[1,1,0,1,0,0,1,1,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,0,1,1,0,0,0],[1,1,0,1,0,0,1,1,0],[1,1,0,0,1,1,1,0,0],[1,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[0,1,0,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[0,1,0,1,0,0,0,1,1],[1,1,0,1,0,1,0,1,1],[1,0,1,1,0,1,0,1,1],[0,0,0,1,0,0,0,0,0],[0,1,0,1,0,0,0,1,1],[1,1,0,1,0,1,0,1,1],[1,1,0,1,0,0,1,1,1],[1,0,0,1,0,1,0,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,1],[1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[0,1,0,0,1,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0],[1,1,1,0,1,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,1,0,0,0,0,1,1]],"Q":[[1,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,0,1,1],[1,1,1,0,1,0,0,0,0,1],[1,0,0,1,0,1,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,0,1,1],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,0,0,1,0]],"Q":[[1,1,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,1,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[0,1,0,1,1,0,1,0,1],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,1,0,1,1,0,1,0,1],[1,1,0,0,1,0,0,0,0],[1,1,0,1,1,0,0,0,1],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[0,1,1,1,0,0,1,0],[1,1,1,0,0,0,0,1],[1,1,0,1,0,0,1,0],[1,0,1,1,0,0,0,1],[0,1,1,1,0,0,1,0],[1,1,1,0,0,0,0,1],[1,1,1,1,0,0,0,0],[1,0,1,0,0,0,0,0]],"Q":[[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,0,1,0,0],[1,1,0,0,1,1,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[0,1,1,0,1,1,1,0,0],[1,1,1,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0],[0,1,1,0,1,1,1,0,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,0,1,1,0,0,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[0,1,0,1,1,0,1,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[0,1,1,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0],[1,0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,1,0],[1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,0,1,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[0,1,1,1,0,0,1,1,1],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[0,1,1,1,0,0,1,1,1],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[1,1,1,1,0,0,0,1,1],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[0,1,0,1,0,1,1,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[0,1,1,0,1,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,1,1,0,1,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,1],[1,0,1,0,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,1,1,0,0,0]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[0,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0],[1,1,0,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,0,1,0],[0,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[0,1],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[1,0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,0,0],[0,1,0,1,0,1,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,1,0,1,1,0,1,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,1,1,0],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,0,1,0],[1,1,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1,0],[0,0,1,0,0,0,0,1,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[1,1,0,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,1,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,0,1,0,0,1,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,1,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,1,1,1,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,1,1,0],[0,0,1,1,0,0,0,1,1,0],[1,0,1,0,0,0,1,1,1,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,1,0,1,0],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[0,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[1,1,0,0,1,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1,0],[0,0,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,1],[1,0,0,0,1,1,0,0,1,0],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,1],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,1],[1,1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[1,1,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,0,0,0,0,1,0,0],[0,1,1,0,0,1,1,0],[0,0,0,0,0,1,1,0],[1,0,0,0,0,1,0,0],[0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,1,0,0,1,1,1]],"Q":[[0,1,0,0,0,1,0,1],[1,0,0,0,1,0,1,1],[1,0,0,0,1,0,1,1],[1,1,0,1,0,1,0,1],[1,1,0,0,0,0,1,1],[0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1],[1,1,0,0,1,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[0,1,0,0,0,1,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,1,0,0,0],[1,1,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,1,0,1],[0,1,0,0,1,0,0,0,0,1],[0,0,1,0,1,0,0,1,0,1],[0,0,0,1,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0,1],[0,1,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,1,1,1],[0,0,0,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,0,0,1,0,0,0,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,0,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,0,1,0,1,0,0,1,0],[0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,0,0,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,1],[1,0,0,1,0,0,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,0,1],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,0,1,1],[0,1,0,0,1,0,0,0,1],[0,0,1,1,0,0,0,1,1],[0,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,1],[0,1,0,0,1,0,0,0,1],[0,0,0,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0]],"Q":[[0,1,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,1],[0,1,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1],[1,1,0,0,0,1,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,0,1,0,0,0,1,1],[0,1,0,0,0,1,0,0],[0,0,1,0,0,1,0,0],[1,0,1,0,0,0,1,1],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,1]],"Q":[[0,1,0,1,0,0,1,1],[1,0,0,0,0,1,1,0],[1,0,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,1,0,0,1,1,1,0],[0,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,1],[1,1,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1,0],[0,0,1,1,0,0,1,1,1],[0,0,1,1,0,0,1,1,0],[1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,1],[1,0,0,0,0,1,1,1,0],[0,1,0,0,1,0,1,1,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,0],[1,1,0,0,1,0,0,1,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1,0],[0,0,1,0,0,0,0,1,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,0,1],[1,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,1,0,1],[0,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,0,0,1],[1,1,0,0,1,0,1,0,0],[0,1,0,0,1,1,0,0,1],[1,1,0,1,1,1,0,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,0,1],[1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[1,0,0,1,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[1,1,0,1,0,1,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1,0],[0,0,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,1],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[1,0,0,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,1],[0,0,1,1,0,0,1,1,1],[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[0,0,0,1,0,0,1,1,0]],"Q":[[0,1,0,0,0,0,1,0,1],[1,1,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,1],[1,0,0,0,0,1,0,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[1,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[1,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,1,0,0,1],[1,1,0,0,0,1,1,1],[1,1,1,0,1,0,0,1],[1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[1,1,0,0,1,0,1,1],[1,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,1,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,0,0],[0,0,1,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,0,0,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,1,0,1,0,0,0,1,0],[0,0,0,1,0,1,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0]],"Q":[[0,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,0,0,1],[0,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,1,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,0,1,0,1,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,1,0,1],[1,1,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,1,1,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0,1],[1,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0],[1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,0],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,1,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,1,1,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,0],[1,1,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,1,1,0],[1,1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,0,0,1,0],[1,0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,1,0,1],[0,1,0,1,0,0,0,0,1],[0,0,1,1,0,0,1,0,1],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,0,1],[0,1,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,1],[0,0,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,0,0,0,1],[0,1,0,0,1,0,1,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,1,0,1],[1,0,0,0,1,0,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,0,0,1,1],[0,1,1,1,0,0,1,0],[0,0,1,1,0,0,1,1],[0,0,1,0,0,0,1,0],[1,0,0,1,0,0,1,1],[0,1,1,1,0,0,1,0],[0,0,0,1,0,0,0,1],[0,0,1,1,0,0,1,1]],"Q":[[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,0,0,0,0,0,1,0],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[1,0,1,0,0,0,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,0,1,0,0,0,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,0,1,1,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,0,0,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[0,0,1,0,0,0,1,0,1],[0,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,1,1,1,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,1,1,0],[0,0,1,1,0,0,0,1,1,0],[1,0,1,0,0,0,1,1,1,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,1,0,1,0],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,1,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[1,0,1,1,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,0,1,1,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,1,0,0,1,0,0,0],[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,1,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,0,0,1,1,0],[0,1,1,1,0,0,0,1,0],[0,0,0,1,0,0,1,1,0],[0,0,1,0,0,0,0,1,0],[1,0,1,1,0,0,1,1,0],[0,1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,1,0,0],[0,0,1,1,0,0,0,1,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,1],[0,1,1,0,0,0,1,1],[0,0,0,1,0,0,0,1],[0,0,1,1,0,0,1,1],[1,0,1,1,0,0,0,1],[0,1,1,0,0,0,1,1],[0,0,1,1,0,0,1,1],[0,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,1,1,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,0,0,1,0,0],[0,1,1,0,0,0,0,1,1],[0,0,1,0,0,0,1,0,0],[0,0,1,1,0,0,0,1,1],[1,0,0,0,0,0,1,0,0],[0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[0,0,1,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,0,0,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,1],[1,0,0,1,0,0,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,0,1],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,0],[0,0,1,1,0,0,0,1,1],[0,0,0,1,0,0,1,0,0],[1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,0,0,1,1],[0,1,1,1,0,0,1,0],[0,0,1,1,0,0,1,1],[0,0,1,0,0,0,1,0],[1,0,0,1,0,0,1,1],[0,1,1,1,0,0,1,0],[0,0,0,1,0,0,0,1],[0,0,1,1,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1,0],[0,0,1,1,0,0,1,1,1],[0,0,1,1,0,0,1,1,0],[1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[1,0,0,1,0,0,1,0,1,0],[0,1,0,1,0,0,0,0,1,0],[0,0,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,1,0,1,0],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,1,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[1,1,0,0,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[1,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[0,0,1,0,0,0,1,0,1],[0,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,1,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[1,0,0,1,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,0,0,1,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,1,0,0,1,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,1,1,0,1],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,1,1,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,1,1,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,1,1,1,1,1,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,1,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0,1,1],[1,1,0,0,0,1,0,0,1,0],[1,0,0,0,0,1,1,0,1,1],[1,1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,1,1,1],[1,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,1,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,0,0,1,1,0,0,0,1],[0,0,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0],[1,0,1,1,1,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,0,1,1,1,0,0,1,1],[0,0,1,1,0,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1,0],[1,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,1,1,1,1],[1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,0,0,1,1,0],[0,1,0,0,0,1,0,0],[0,0,1,0,0,1,0,0],[1,0,1,0,0,1,1,0],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,0,1,0,0,1,0,0],[0,0,0,0,0,1,0,1]],"Q":[[1,0,0,1,1,0,0,1],[1,1,0,0,0,1,1,1],[1,1,0,0,0,1,1,1],[0,0,0,0,1,0,0,1],[1,0,0,0,1,1,1,1],[0,0,0,0,0,1,0,0],[0,0,0,1,1,0,1,1],[1,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,1,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,1,0,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,1,1,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,1,0,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,1,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,1,1,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,0,1,0],[1,0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,0,1,1],[0,1,0,0,1,0,0,0,1],[0,0,1,1,0,0,0,1,1],[0,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,1],[0,1,0,0,1,0,0,0,1],[0,0,0,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[1,0,1,0,0,0,1,1],[0,1,1,0,0,1,1,1],[0,0,0,0,0,1,1,1],[1,0,1,0,0,0,1,1],[0,1,1,0,0,1,1,1],[0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1],[0,0,1,0,0,1,1,0]],"Q":[[1,0,0,0,1,1,1,1],[1,1,0,0,1,0,1,0],[1,1,0,0,1,0,1,0],[0,0,0,1,1,1,1,1],[1,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,1],[1,0,0,0,1,0,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[1,0,1,0,0,0,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,0,1,0,0,0,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[0,0,0,1,1,0,1,1,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,1,1,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,1,0,0,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,1,0,1],[0,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,1,0,0,1],[0,1,0,1,1,0,1,0,0],[1,1,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,0,1],[0,0,0,1,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,1,1,0,1],[0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,0,1,0,1,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,1,1,0],[1,1,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,1,1,0,1],[0,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,1,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[1,0,1,1,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,0,1,1,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,0,1],[0,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,1,0,0,1,0,0,0],[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,1,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,1,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,0,0,1,1,0,0,0,1],[0,0,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0],[1,0,1,1,1,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,0,1,1,1,0,0,1,1],[0,0,1,1,0,0,0,1,1]],"Q":[[1,1,0,0,0,1,0,0,1],[0,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,1],[0,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,1,0],[0,1,0,0,0,1,0,1,1],[0,0,0,0,0,1,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1],[0,0,0,0,0,1,1,1],[1,0,1,0,0,1,1,1],[0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0],[0,0,1,0,0,1,0,1],[0,0,1,0,0,0,1,0]],"Q":[[1,1,0,1,0,1,0,1],[0,1,0,1,0,0,1,1],[1,1,0,1,0,1,0,1],[0,1,0,0,0,1,0,1],[0,0,0,1,1,0,1,1],[0,0,0,0,0,1,0,0],[0,1,0,1,0,1,1,1],[0,0,0,1,0,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,1,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,0,0],[0,0,1,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,1,0,1,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,0],[0,0,1,0,1,0,0,0,1,0],[0,0,0,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,1,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,0,1,0,1,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,0,1],[0,1,0,0,0,1,1,1,0,0],[1,1,0,0,0,0,1,1,0,1],[0,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,1],[0,0,0,0,0,1,0,1,0,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,0,1,0,1,0,0,1,0],[0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[0,0,1,0,0,0,0,1,0]],"Q":[[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0],[0,0,0,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1,1],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,1,0,0,0,1,0,1,1],[0,1,0,1,0,1,0,1,1],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,0,0,1,0,0],[0,1,1,0,0,1,0,1],[0,0,1,0,0,1,0,0],[1,0,0,0,0,1,0,0],[0,1,1,0,0,1,0,1],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[0,0,1,0,0,1,0,0]],"Q":[[1,1,0,0,0,1,1,1],[0,1,0,1,1,0,1,0],[1,1,0,0,0,1,1,1],[0,1,0,1,0,1,1,1],[0,0,0,1,0,0,1,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,1],[0,0,0,1,1,0,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,1],[0,1,0,1,0,0,1,1,0],[1,1,0,0,0,1,1,1,1],[0,1,0,1,0,1,1,1,1],[0,0,0,1,1,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,1],[0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,1,1,1,0,1,0],[1,1,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,0,0,1,0,0,1,0,1,0],[0,1,0,1,0,0,0,0,1,0],[0,0,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,1,0,1,0],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,1,1,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,1,1,0,0,1,0],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,1,1,0,1],[1,1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,1,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,0,1,0,0,1,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,1,0,1,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,0,1,0,1,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,0],[0,1,0,0,0,1,1,1,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,0,1,0,0,1,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,0,1,0,0,1,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,1,1,0,1],[0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,0,1,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,1,0,1,1,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,1,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,1,1,0,1,0],[1,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,0,0,1,0,0,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,1],[0,1,1,0,0,0,1,1],[0,0,0,1,0,0,0,1],[0,0,1,1,0,0,1,1],[1,0,1,1,0,0,0,1],[0,1,1,0,0,0,1,1],[0,0,1,1,0,0,1,1],[0,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[0,1,0,0,0,0,0,1],[1,1,0,0,0,0,1,1],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,1],[0,1,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,1,0,1,0,0,0,1,0],[0,0,0,1,0,1,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0]],"Q":[[1,1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,0,0,1],[0,1,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,0,0,1,0,0,0,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,0,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,0,0,1,0,0,0,1,0],[0,1,0,1,0,0,1,1,0],[0,0,1,1,0,0,1,1,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,0,1,0],[0,1,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,1,0,0,1,1,1]],"Q":[[1,1,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,1,0],[1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,1,0,0],[1,1,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1,1],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[0,0,0,1,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,0,0,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,1],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,1],[1,1,0,0,1,1,0,0,0]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[1,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,1,0,1,1],[1,0,0,0,0,1,1,0],[0,1,1,0,1,0,1,1],[1,1,0,1,0,1,1,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,1],[1,1,0,0,0,1,1,1]]},
+    {"A":[[1,0],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,1],[1,0,0,0,1,0,1,1,0],[1,1,0,0,0,1,1,1,1],[0,1,0,1,0,1,1,1,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[1,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,0],[0,0,1,1,0,1,0,1,1],[1,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,1,0,0,1,0],[1,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,1,0],[1,0,1,1,0,0,0,1,0],[1,0,1,0,1,0,0,1,0],[1,1,1,0,0,0,0,1,0],[0,0,1,0,1,0,1,1,0],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,1,0,0,0,0,1,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,1,0,0,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[1,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,0,1,0,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,1,0,0,1],[1,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[1,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,0,0,1,1,0,0,1,0],[1,0,0,1,1,0,0,1,0],[1,1,0,1,0,1,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,1],[1,1,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0],[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[1,0,1,0,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[1,1,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,0,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,1,1],[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[1,0,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,0,0,1,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,1,0,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0]],"Q":[[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,1,0,1,0,0,0,1,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,1],[0,0,1,0,1,1,0,1,1],[1,0,0,1,1,0,0,1,1],[0,0,0,0,1,0,0,0,0],[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,1],[0,0,0,0,1,1,0,0,1],[1,0,0,0,1,0,0,1,0]],"Q":[[0,1,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,0,1,0,0,0,1,1,0],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[1,0,1,0,0,0,1,1,0],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,1,1,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,1,0,1,0,1,0],[1,1,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,1,1],[1,1,1,0,0,0,0,1],[0,0,1,1,0,0,1,1],[1,0,1,1,0,0,0,1],[1,0,0,1,0,0,1,1],[1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,1],[1,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,1,0,1,1,0],[1,1,0,1,0,0,0,1,0],[0,0,1,1,1,0,1,1,0],[1,0,0,0,0,0,0,1,0],[1,0,0,1,1,0,1,1,0],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,1,0,0],[1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,0,0,0,1,1,1],[1,1,0,0,1,0,0,1,1,0],[0,0,1,1,0,0,0,1,1,1],[1,0,0,1,1,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,0,1,1,1],[1,1,0,0,1,0,0,1,1,0],[0,0,0,1,0,0,0,0,1,1],[1,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,1,0,0,1,0,1,0],[1,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[1,0,0,1,1,0,0,1,1],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,1,0,0,1,1],[1,1,0,0,1,0,0,0,0],[0,0,0,1,1,0,1,1,1],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,1,0,0],[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,1,0,0],[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,1,0,1,1],[1,0,1,1,0,0,1,0,1,1],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[1,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0],[1,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,1,0,0],[1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1],[1,1,1,0,0,0,1,0],[1,1,1,0,1,0,1,1],[1,0,1,1,0,0,1,0],[0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,1],[1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[1,0,0,0,0,1,0,0],[1,1,1,0,0,0,1,0],[1,0,0,0,0,0,1,0],[1,0,0,0,0,1,0,0],[1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[1,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,1],[1,1,0,0,1,0,1,0],[1,1,0,0,1,0,1,0],[1,1,0,1,0,1,0,1],[1,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1],[1,0,0,0,1,0,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1,1],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1,0],[1,0,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,1,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,1,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1,0,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,0,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,0],[1,0,1,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,1]],"Q":[[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0],[1,0,0,0,1,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,1,0,0,1,0,1],[1,1,0,1,1,0,1,0,1],[0,0,1,1,0,0,1,0,1],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,0,1],[1,1,0,1,1,0,1,0,1],[0,0,0,1,0,0,0,0,1],[1,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,1,0,1,0,0,0,0,1,0],[1,0,0,1,0,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[0,1,0,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,0,1,0],[1,0,0,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,0,0,0],[1,0,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[0,0,1,1,0,0,1,1,0],[1,0,1,0,0,0,0,0,1],[1,0,0,1,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[0,0,0,1,0,0,0,1,0],[1,0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[1,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[1,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,1]],"Q":[[0,1,0,1,0,1,1,1],[1,1,0,1,0,0,0,1],[1,1,0,1,0,0,0,1],[1,1,0,0,0,1,1,1],[1,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0],[1,1,0,1,0,1,0,1],[1,0,0,1,0,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,1,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,1,1,1,0,0,1,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0],[1,0,0,1,1,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,1,1,0,0,0,1],[1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,1,0,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,1,1,1,0,1,1,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,1,0,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,1,0,1,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[1,0,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,1,0,1,0,1,0],[1,1,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,1,0,1,0],[1,0,1,1,0,0,0,0,1,0],[1,0,1,0,1,0,1,0,1,0],[1,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,1,0,1,1,1,0],[1,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[0,0,1,0,0,0,1,0,1],[1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,1,1,0,0,0,1],[1,1,1,1,0,0,0,0,1],[0,0,0,1,1,0,0,0,1],[1,0,1,0,0,0,0,0,1],[1,0,1,1,1,0,0,0,1],[1,1,1,1,0,0,0,0,1],[0,0,1,1,1,0,1,0,1],[1,0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,1,1,1],[1,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,1],[1,0,0,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,1,1],[1,0,0,1,0,0,0,1,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,1],[1,1,0,0,1,0,0,0],[0,0,0,1,0,0,0,1],[1,0,0,1,1,0,0,0],[1,0,1,1,0,0,0,1],[1,1,0,0,1,0,0,0],[0,0,1,1,0,0,1,1],[1,0,0,0,1,0,0,1]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0,0],[1,0,1,1,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1,0],[1,0,1,0,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[0,0,1,0,0,0,1,0,0],[1,0,0,1,1,0,0,0,0],[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,1,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[0,0,1,1,0,0,0,1,1],[1,0,1,1,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,1],[1,0,1,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0],[0,0,1,1,1,0,1,0],[1,0,0,0,0,0,1,0],[1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0],[0,0,0,1,1,0,0,0],[1,0,0,1,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,0,0,1,1,1],[1,1,0,0,1,0,0,0,0],[0,0,1,1,0,0,1,1,1],[1,0,0,1,1,0,0,0,0],[1,0,0,1,0,0,1,1,1],[1,1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,1,1],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[1,0,1,0,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,1,0],[1,0,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[1,0,0,1,1,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,1,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,0,1,1,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[1,1,0,0,1,0,0,0,1,0],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[1,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[0,0,1,0,0,0,1,0,1],[1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,1,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[1,0,0,1,1,0,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[1,0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,1,0,1,1,1,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,1,0,1,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,1,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,1,1,1,0,0,0,1,1,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,1,1,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,1],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[1,0,1,1,0,0,0,1],[1,1,0,1,0,0,0,0],[0,0,1,1,0,1,0,1],[1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,1,0,1,1],[1,1,0,1,0,0,1,0],[1,1,0,1,0,0,1,0],[0,0,0,0,1,0,1,1],[1,0,0,1,1,0,1,0],[0,0,0,1,1,1,1,1],[1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,0,1,0],[1,1,1,0,0,1,0],[1,0,0,0,0,1,0],[1,0,1,1,0,1,0],[1,1,1,0,0,1,0],[0,0,1,1,0,0,0],[1,0,1,0,0,1,1]],"Q":[[1,0,0,1,1,0,1],[1,1,0,0,1,1,0],[1,1,0,0,1,1,0],[0,0,0,0,1,0,1],[1,0,0,0,0,1,0],[0,0,0,1,1,1,1],[1,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1],[0,0,0,1,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[1,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[1,0,0,1,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0],[1,1,0,1,0,0,0,1],[1,1,0,1,0,0,0,1],[0,0,0,1,0,1,1,0],[1,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0],[1,0,0,1,0,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[0,0,1,0,0,0,0,1,0,0,0],[1,0,0,1,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[1,0,1,0,0,1,1,0],[1,1,1,1,0,1,1,0],[1,0,0,1,0,1,1,0],[1,0,1,0,0,1,1,0],[1,1,1,1,0,1,1,0],[0,0,1,0,0,0,1,0],[1,0,1,1,0,1,0,0],[0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,1,0],[1,1,0,1,1,0,0,1],[1,1,0,1,1,0,0,1],[0,0,0,1,1,1,1,0],[1,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,0],[1,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[1,0,1,0,0,1,1],[1,1,0,1,0,0,0],[1,0,1,1,0,0,0],[1,0,1,0,0,1,1],[1,1,0,1,0,0,0],[0,0,1,0,0,0,1],[1,0,0,1,0,0,1]],"Q":[[1,0,0,0,1,1,1],[1,1,0,1,0,0,1],[1,1,0,1,0,0,1],[0,0,0,1,1,1,1],[1,0,0,1,1,0,1],[0,0,0,0,1,0,1],[1,0,0,1,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0],[0,0,1,1,1,0,0,0,1,1],[1,0,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,0,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1]],"Q":[[1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,0,1,0,1,0],[1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,1,1],[1,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,1,1,0,0,0,0,1,1,1],[1,0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,1,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0],[1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,1,0,0,1,0,1,0],[1,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,1,1,1,0,1,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,1,0,0,0,1,0,1],[1,0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,1,0,0],[1,1,0,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,1,0,0],[0,1,0,0,0,1,1,0,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,1,1,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[1,0,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1],[1,0,0,1,1,0,0,0,0],[1,0,1,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,0,1,0,0,0,1,0,1],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[1,0,1,1,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,1,1,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,1,1,1,0,0,1,1,0],[1,0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,1,0,1,0],[1,1,1,0,0,0,0,1,0],[0,0,0,1,0,1,0,1,0],[1,0,1,1,0,1,0,1,0],[1,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,1,1,0,1,1,1,0],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,1,0,1,0],[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,1],[0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,0,0,0,1],[1,1,0,1,0,0,1,0],[0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,0],[1,0,1,1,0,0,0,1],[1,1,0,1,0,0,1,0],[0,0,1,1,0,0,1,1],[1,0,0,1,0,0,1,1]],"Q":[[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[0,1,0,0,0,0,0,1],[0,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,1],[1,0,0,1,1,0,0,0,0],[1,0,1,1,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,1,1,0,0,0,1,1],[1,0,0,0,1,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,1,1],[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[1,0,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,1,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[1,0,0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,1,0,1,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[1,0,1,0,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[1,0,0,1,0,0,1,0,1],[1,1,0,1,1,0,1,0,1],[0,0,1,1,0,0,1,0,1],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,0,1],[1,1,0,1,1,0,1,0,1],[0,0,0,1,0,0,0,0,1],[1,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,1],[0,1,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,0,0,1,0],[1,1,0,0,0,1,0,0,0],[0,0,1,0,1,0,0,1,0],[1,0,0,1,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[1,0,0,0,1,0,0,1,0],[1,1,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,0,0],[1,0,0,0,0,1,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0],[0,0,0,0,0,1,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,1,1,1,1],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[1,0,1,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,1,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,0],[0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,1],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0],[1,0,1,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,1,0,0,0,1,0,1,1],[0,1,0,1,0,1,0,1,1],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[1,0,0,0,0,0,1,0,0],[1,1,0,1,0,0,1,0,1],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,0,0,0,1,0,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0],[1,0,0,1,0,0,1,0,0]],"Q":[[1,1,0,0,0,0,1,1,1],[0,1,0,0,1,1,0,1,0],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[1,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,0],[0,0,1,0,0,1,0,0,0],[1,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,1],[0,1,0,1,0,0,1,1,0],[1,1,0,0,0,1,1,1,1],[0,1,0,1,0,1,1,1,1],[0,0,0,1,1,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,1],[0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,0],[1,0,1,1,0,0,0,0,0],[1,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,0,0],[0,0,1,1,0,1,0,1,1],[1,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,1,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,1,0,1,0,0,0,1,0,1],[1,0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[1,1,0,0,0,1,1,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,1,1,0,1],[1,1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,1,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,0,0,1,1,0,1,1,0],[1,1,0,1,0,0,1,1,0],[1,0,1,1,0,0,1,1,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,1,0,1,1,0],[1,1,0,1,0,0,1,1,0],[0,0,0,1,1,0,0,1,0],[1,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,0,0,1,1,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[1,0,1,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,1,1,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,1,1,0,0,1,1,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,0,1,1,0,0,0,1,1],[1,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,1,0],[1,0,1,1,0,0,0,1,1],[1,1,1,0,0,0,0,1,0],[0,0,1,1,0,0,1,1,1],[1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,1,0,0,1,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,0,1,1,0,1,1,0],[1,1,1,0,0,0,1,0],[1,0,0,0,0,0,1,0],[1,0,1,1,0,1,1,0],[1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,0],[0,0,1,1,0,1,0,0],[1,0,1,0,0,0,1,1]],"Q":[[1,1,0,1,0,0,0,1],[1,0,0,0,0,1,1,0],[1,0,0,0,0,1,1,0],[0,1,0,0,0,0,0,1],[1,1,0,0,1,1,1,0],[0,0,0,0,0,1,0,0],[0,1,0,1,0,0,1,1],[1,1,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,0,1,1,0,0,0,0,1],[1,1,0,0,1,0,0,1,1],[0,0,0,1,0,0,0,0,1],[1,0,0,1,1,0,0,1,1],[0,0,0,0,1,0,0,0,0],[1,0,1,1,0,0,0,0,1],[1,1,0,0,1,0,0,1,1],[0,0,1,1,0,0,0,1,1],[1,0,0,0,1,0,0,1,0]],"Q":[[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,0,0,1,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,1,0,0,1,0,0],[1,1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,0,0,1,0,0,1,0],[1,1,0,1,1,0,1,0],[1,0,1,1,1,0,1,0],[0,0,0,1,0,0,0,0],[1,0,0,1,0,0,1,0],[1,1,0,1,1,0,1,0],[0,0,0,1,0,0,0,0],[1,0,0,1,1,0,1,1]],"Q":[[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,0,1,0,0],[1,1,0,0,1,1,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,0,0,0,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,1,0,1,0,0,0,1,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,0,0,0,1,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,1,0,1,0,0,0,0,1,0],[1,0,0,1,0,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[1,0,0,0,1,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,1,1,0],[1,1,0,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,0,0,1,0,1,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0],[1,0,0,0,1,0,0,0],[1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,1,1,0,0],[1,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0],[1,0,1,0,0,0,0,1],[0,1,1,0,1,1,1,0],[1,1,1,1,0,0,0,1],[0,0,0,0,1,0,0,0],[0,1,0,0,1,0,1,0],[1,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,0,0,0,0,1,0,0],[1,1,1,0,0,0,0,1],[0,0,1,0,0,1,0,0],[1,0,0,0,0,1,0,0],[1,1,1,0,0,0,0,1],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0],[1,0,1,0,0,0,0,0]],"Q":[[1,1,0,0,0,1,1,1],[1,0,0,1,1,0,0,1],[1,1,0,0,0,1,1,1],[0,1,0,1,0,1,1,1],[1,1,0,1,0,0,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,1],[1,1,0,1,1,0,0,0]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,1,0,0,1],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1,0],[1,0,0,1,0,0,1,0,0,0]],"Q":[[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,0],[1,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,0,0,0,0,0,1,0,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,1,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,1,1,0],[1,1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,1,0,0,1,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,1,0,0,1,1,0,0,0],[0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,1,0],[0,1,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,1,0,0,1,0,0,0,0],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,0],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,1,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,1,0,0,1,1,0,0,0],[0,1,1,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,1],[1,1,0,0,1,1,0,0,0],[0,1,1,0,1,1,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[0,0,1,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,0,0,1],[1,0,0,0,1,0,1,1,0],[1,0,0,0,1,0,1,1,0],[1,1,0,1,1,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,0,1],[1,1,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0,1,1],[0,0,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,1,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[1,1,1,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[1,1,0,1,0,1,0,0,1],[1,1,0,0,1,0,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,1,1,1,1],[0,1,1,0,0,0,0,1,1],[0,1,0,0,0,1,1,1,1],[0,0,1,1,0,0,0,1,1],[1,1,1,0,0,1,1,1,1],[0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,1,1,0,1],[0,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[1,1,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,0,1,0,0,1],[0,1,0,1,0,0,0,0,1],[0,1,1,1,0,1,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,0,1,0,1,0,0,1],[0,1,0,1,0,0,0,0,1],[0,1,0,1,0,1,1,0,1],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,1,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0],[0,0,0,1,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,1,0,0,0,1,1,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,1,1,0,0,0,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,1,1,0,0,0,1,0,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,0,1,0,1],[1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,1,0,0],[1,1,0,0,1,0,1,0,1],[1,1,0,0,1,1,1,0,0],[0,0,0,0,0,1,0,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,0,0,1,0],[0,1,1,0,0,0,1,1],[0,1,1,1,0,0,1,0],[0,0,1,1,0,0,1,1],[1,1,0,1,0,0,1,0],[0,1,1,0,0,0,1,1],[0,1,0,1,0,0,0,0],[0,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[1,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,1,0,0,1,1,0,0],[1,1,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,0,1],[0,1,1,0,1,0,1,0,1],[0,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,0,0,0],[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,0,1],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,0,0]],"Q":[[0,1,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,1],[0,1,0,0,0,1,0,1,1],[1,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1],[1,1,0,0,0,1,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,1,0,0],[1,1,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,0,1,1,0],[0,1,1,0,1,0,0,1,1,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,1,1,1],[0,1,1,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,0,1,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[1,1,0,0,1,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,1,0,0,1,1,0,0,0],[0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,1,0],[0,1,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,1,1,1,0,1],[0,0,1,1,0,1,1,1,0,1],[0,0,0,1,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[0,0,0,1,0,1,1,1,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,1,0,0],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[1,1,0,1,0,0,0,0],[0,1,0,0,1,0,0,0],[1,1,0,1,0,0,0,0],[0,1,0,0,1,0,0,0],[0,0,0,0,0,0,0,0],[0,1,0,1,0,1,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,0,0,1],[1,1,0,0,1,1,1,0],[1,1,1,1,0,0,0,1],[1,0,0,1,1,1,1,0],[0,0,0,0,1,0,0,0],[1,1,0,1,0,1,0,1],[1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0,1,1],[0,0,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,1],[0,1,1,0,1,1,0,1],[0,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,1],[0,1,1,0,1,1,0,1],[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,1,1],[0,0,1,0,1,1,0,0]],"Q":[[0,1,0,0,0,1,0,1],[1,1,0,0,1,0,1,0],[0,1,0,0,0,1,0,1],[1,1,0,1,0,1,0,1],[1,0,0,0,0,0,1,0],[0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,1],[1,0,0,0,1,0,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[1,1,0,1,0,0,0,1,1,0],[0,1,0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,1]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,0,1],[0,1,1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,1,1,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,1,0,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,0,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,1,0,1],[0,1,0,1,0,0,0,1],[0,1,1,1,0,1,0,1],[0,0,0,1,0,0,0,0],[1,1,0,1,0,1,0,1],[0,1,0,1,0,0,0,1],[0,1,0,1,0,1,1,1],[0,0,0,1,0,0,0,0]],"Q":[[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0],[1,0,0,0,1,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,1,0,1],[0,1,1,1,0,0,1,0,0],[0,1,1,1,0,0,1,0,1],[0,0,1,0,0,0,1,0,0],[1,1,0,1,0,0,1,0,1],[0,1,1,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,1],[0,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[1,1,1,0,0,0,1,0],[0,1,0,0,0,1,0,0],[0,0,1,0,0,1,0,0],[1,1,1,0,0,0,1,0],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0],[0,0,0,0,0,1,0,1]],"Q":[[0,1,0,1,1,0,1,0],[1,1,0,0,0,1,1,1],[1,1,0,0,0,1,1,1],[1,1,0,0,1,0,1,0],[1,0,0,0,1,1,1,1],[0,0,0,0,0,1,0,0],[1,1,0,1,1,0,0,0],[1,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,1,0,0,1,1,0],[0,1,0,1,0,1,1,1,0],[0,1,1,1,0,0,1,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,1,1,0],[0,1,0,1,0,1,1,1,0],[0,1,0,1,0,0,0,1,0],[0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,1,0,0,0,0,1],[0,1,1,0,1,0,0,0,0,1,1],[0,0,0,1,0,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0,0,0]],"Q":[[0,1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,0,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,0,0,1,1],[0,1,1,1,0,0,0,1,0],[0,1,1,0,1,0,0,1,1],[0,0,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0],[1,1,0,0,1,0,0,1,1],[0,1,1,1,0,0,0,1,0],[0,1,0,0,1,0,0,0,1],[0,0,1,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,1,0],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,1,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,1,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,0,1,1,0,0],[0,1,1,1,0,0,1,0,0],[0,1,0,1,0,1,1,0,0],[0,0,1,0,0,0,1,0,0],[1,1,1,1,0,1,1,0,0],[0,1,1,1,0,0,1,0,0],[0,1,1,1,0,1,0,0,0],[0,0,1,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0,1,1],[0,0,0,1,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,1,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1],[0,0,1,1,0,0,0,1,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,1,1,1],[0,1,1,0,0,0,1,1],[0,1,0,0,0,1,1,1],[0,0,1,1,0,0,1,1],[1,1,1,0,0,1,1,1],[0,1,1,0,0,0,1,1],[0,1,1,0,0,1,0,1],[0,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,0,1,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,1,1,1,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,1],[1,1,0,1,0,1,1,0,0,1],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,1,1,1,0,1],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,0],[0,1,1,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,1,0,0],[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,1,1,1,0,0,0,1,0,1],[0,0,1,0,0,0,0,1,0,0],[1,1,0,1,0,0,0,1,0,1],[0,1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,0,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,1,1,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,1],[1,1,0,1,0,0,0,1,0],[0,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,1,1,0,0,1,0,0,0],[0,0,0,1,0,0,1,0,0],[1,1,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,0,1,0,0],[0,1,1,1,0,0,1,0],[0,1,1,0,0,1,0,0],[0,0,1,0,0,0,1,0],[1,1,0,0,0,1,0,0],[0,1,1,1,0,0,1,0],[0,1,0,0,0,1,1,0],[0,0,1,1,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,1,1,0,0,1,0,0,0],[0,0,1,1,0,0,1,1,0],[1,1,0,0,0,1,0,0,0],[0,1,1,0,0,0,1,1,0],[0,1,0,0,0,1,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,0,1],[0,1,1,0,1,1,0,0,1],[0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,1,0,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[1,0,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,1,0,0,0,0,1],[0,1,1,1,0,0,0,1,0,0],[0,1,0,1,1,0,0,0,0,1],[0,0,1,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,1],[0,1,1,1,0,0,0,1,0,0],[0,1,1,1,1,0,0,1,0,1],[0,0,1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,0,0,1,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,1,1,0,0,1,1,1,1],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,1,0,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,1,1,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[1,1,0,1,0,1,0,1,0],[0,1,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,1,0,1,0],[0,1,0,1,0,0,0,1,0],[0,1,0,1,0,1,1,1,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1],[1,0,0,0,1,1,0,1,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,1],[0,1,1,1,0,0,1,0],[0,1,0,0,0,0,0,1],[0,0,1,0,0,0,1,0],[1,1,1,0,0,0,0,1],[0,1,1,1,0,0,1,0],[0,1,1,0,0,0,1,1],[0,0,1,1,0,0,1,1]],"Q":[[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0],[0,0,0,0,1,1,1,1],[1,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[1,1,0,1,0,0,1,1,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,1,1,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,1,1],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,0,1],[0,1,1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,0,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,1,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0],[0,0,0,1,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0],[0,1,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0],[1,0,0,0,0,1,0,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[1,1,1,0,0,0,1,0,1],[0,1,1,0,1,1,1,0,1],[0,0,0,0,1,1,1,0,1],[1,1,1,0,0,0,1,0,1],[0,1,1,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1],[0,0,1,0,1,1,1,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0,1],[1,1,0,0,1,0,1,0,0],[1,1,0,0,1,0,1,0,0],[0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1],[1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[1,1,1,0,0,0,0,1,0],[0,1,0,0,0,0,1,0,0],[0,0,1,0,0,0,1,0,0],[1,1,1,0,0,0,0,1,0],[0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0,1]],"Q":[[1,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,0,1,1,1],[0,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1],[0,1,1,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,1],[0,1,0,0,0,1,1,0,0],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[0,0,0,0,1,1,1,1,0],[1,0,0,0,1,0,0,0,1],[0,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0,1],[0,1,1,0,0,0,1,0,0],[0,0,0,1,1,0,0,0,1],[0,0,0,0,1,0,0,0,0],[1,1,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0,1],[0,1,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,0,1,1,0,0],[0,1,1,1,0,0,0,1,0],[0,1,1,0,0,1,1,0,0],[0,0,1,0,0,0,0,1,0],[1,1,0,0,0,1,1,0,0],[0,1,1,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0],[0,0,1,1,0,0,0,1,1]],"Q":[[1,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,0,1,0],[1,0,0,0,0,1,1,1,1],[1,1,0,0,0,1,0,1,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,1,0,1],[1,0,0,0,0,1,0,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,1,0,0,0,0],[0,1,0,0,0,1,0,0,0],[0,0,1,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,0],[0,1,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,0],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[0,0,0,1,1,0,1,1,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,1,0],[0,0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,1,1,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,1,0,0,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0,0],[0,1,0,1,1,0,0,0,0,0,1],[0,0,1,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0,1],[0,0,1,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0,0,1],[0,1,0,0,0,1,1,0,1,0,0],[1,1,0,0,0,1,1,1,0,0,1],[0,1,0,0,0,1,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,1,1,0,1],[0,0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,0,1,1,1,0],[0,1,1,0,0,1,1,0],[0,1,0,0,1,1,1,0],[1,1,1,0,1,1,1,0],[0,1,1,0,0,1,1,0],[0,1,1,0,1,0,1,0],[0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1],[0,1,0,1,0,1,1,0],[1,1,0,1,1,0,0,1],[0,1,0,0,1,0,0,1],[0,0,0,1,1,1,1,0],[0,1,0,1,1,1,0,1],[0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,0,1,0,0,1],[0,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0,1,1],[0,0,0,1,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,1,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,1],[0,1,1,0,1,0,1],[0,1,0,0,0,0,1],[1,1,1,0,0,0,1],[0,1,1,0,1,0,1],[0,1,1,0,0,1,1],[0,0,1,0,1,0,0]],"Q":[[1,1,0,1,0,0,1],[0,1,0,1,1,1,0],[1,1,0,1,0,0,1],[0,1,0,0,0,0,1],[0,0,0,1,0,1,0],[0,1,0,1,0,1,1],[0,0,0,1,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,1],[0,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,1,1],[0,0,1,0,0,0,0,0,1,0]],"Q":[[1,1,0,0,0,1,0,1,0,1],[0,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,1,0,1,0,1],[0,1,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,1,1,1,0,1],[0,1,1,0,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0],[0,1,0,1,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[0,0,0,1,0,1,1,1,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[0,1,1,0,1,0,0,0],[1,1,0,0,1,0,0,0],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0],[0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,1,0,1,0],[0,1,0,0,0,1,0,1],[1,1,0,0,1,0,1,0],[0,1,0,1,1,0,1,0],[0,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,0,1,0,0,0],[0,1,1,0,1,0,0,1],[0,1,1,0,1,0,0,0],[1,1,0,0,1,0,0,0],[0,1,1,0,1,0,0,1],[0,1,0,0,1,1,0,0],[0,0,1,0,1,0,1,1],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,1],[0,1,0,1,1,1,0,0],[1,1,0,0,1,1,0,1],[0,1,0,1,1,1,0,1],[0,0,0,1,0,1,0,0],[0,1,0,0,1,0,0,1],[0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,0,1,0,0],[0,1,1,0,0,1,1],[0,1,1,0,1,0,0],[1,1,0,0,1,0,0],[0,1,1,0,0,1,1],[0,1,0,0,1,1,0],[0,0,1,0,0,1,0]],"Q":[[1,1,0,0,1,1,0],[0,1,0,1,0,1,1],[1,1,0,0,1,1,0],[0,1,0,1,1,1,0],[0,0,0,1,1,1,1],[0,1,0,0,1,0,0],[0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,1,0,0,0,1,1,0],[0,1,0,1,0,1,1,1,1,0],[0,1,1,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[0,1,0,1,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[0,0,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,0,0,0,1,0,0],[0,1,1,0,1,0,0,0,0,1,1],[0,0,0,1,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,1,1],[0,0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,0,0,0,1,1],[0,1,1,1,0,0,0,0,1,0],[0,1,1,0,1,0,0,0,1,1],[0,0,1,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[0,1,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[0,0,1,1,0,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,1,0,0,0,1,1,1],[0,1,1,0,0,0,0,0,1,1,0],[0,1,1,0,1,0,0,0,1,1,1],[0,0,1,1,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[0,1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[0,0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,1],[0,1,0,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,0,1,1,1,1],[0,1,0,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,1],[0,0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,1],[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,0,1],[0,1,1,0,1,1,0,0,1],[0,0,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[0,1,0,0,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[0,1,0,1,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[1,1,0,0,0,1,1,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,1,1,0,1],[1,1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,1,0,1,0,0,1,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,1,0,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,1,1,0,1],[0,1,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,0,0,0,1],[0,1,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,1],[0,0,1,1,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[0,1,1,0,0,0,1,1,0],[0,1,1,1,0,0,1,0,1],[0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,1,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,0],[0,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,1,0,1,0,1,0,1,0],[0,1,0,1,0,0,0,1,0],[0,0,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,1,0,1,0],[0,1,0,1,0,0,0,1,0],[0,1,0,1,0,1,1,1,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,0,0,1,1],[1,0,0,0,1,1,0,1,0],[1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,1,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,1,1,1],[0,1,0,0,0,1,0,0],[0,0,1,0,0,1,0,0],[1,1,1,0,0,1,1,1],[0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0],[0,1,1,0,0,1,0,1],[0,0,0,0,0,1,0,1]],"Q":[[1,1,0,1,0,0,0,1],[1,0,0,0,0,1,1,0],[1,0,0,0,0,1,1,0],[0,1,0,0,0,0,0,1],[1,1,0,0,1,1,1,0],[0,0,0,0,0,1,0,0],[0,1,0,1,0,0,1,1],[1,1,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,1,1],[0,1,0,0,1,0,0,0,1],[0,0,1,1,0,0,0,1,1],[0,0,0,0,1,0,0,0,0],[1,1,1,0,1,0,0,0,1],[0,1,1,0,0,0,0,1,1],[0,1,1,0,1,0,0,1,1],[0,0,1,0,0,0,0,1,0]],"Q":[[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[0,1,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,1,1,0,1],[0,1,1,0,0,1,0,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,0,0,1,0,0,0],[0,1,0,1,0,1,1,0,1],[0,1,0,0,0,1,1,0,0],[0,0,0,1,0,1,1,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,1],[0,1,1,0,0,1,0,0],[0,0,0,1,0,0,0,0],[1,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,1],[0,1,0,0,0,1,1,0],[0,0,0,1,0,0,0,0]],"Q":[[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,0,1,0,0],[1,1,0,0,1,1,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,0,0],[0,1,0,0,1,0,0,0],[1,1,0,1,0,0,0,0],[0,1,0,0,1,0,0,0],[0,0,0,0,0,0,0,0],[0,1,0,1,0,1,0,0],[0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,0,1,0,1],[1,0,0,0,1,1,0,0],[0,1,1,1,0,1,0,1],[1,1,0,1,1,1,0,0],[0,0,0,0,1,0,0,0],[0,1,0,1,0,0,0,1],[1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,1,0,0,1,1,0,0],[0,1,1,0,0,0,1,1],[0,1,1,0,1,1,0,0],[1,1,0,0,1,1,0,0],[0,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0],[0,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,1,1,1,0],[1,0,0,0,1,0,1,1],[1,1,0,0,1,1,1,0],[0,1,0,1,1,1,1,0],[1,1,0,0,0,0,1,1],[0,0,0,0,0,1,0,0],[0,1,0,0,1,1,0,0],[1,1,0,0,1,0,1,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[0,0,0,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,1,0,0,0,0,1],[0,1,1,0,1,0,0,0,0,1,1],[0,0,0,1,0,1,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,1,0,0,0]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,1,0,1,0,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,1],[0,1,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,1]],"Q":[[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,1,1],[1,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[0,1]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,1,0,1,0,0,0,1,1,1],[0,1,0,1,0,1,1,1,1,1],[0,0,1,1,0,1,1,1,1,1],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[0,1,0,1,0,1,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[0,0,0,1,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[1,0,0,0,0,1,0,1,1,0],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,1,1],[1,1,0,0,1,0,0,1,1],[1,1,0,0,1,0,0,0,0],[1,0,1,0,1,0,0,1,1],[0,1,0,0,1,1,0,0,0],[1,1,1,0,1,0,1,1,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,0],[1,0,0,1,0,0,0,0,1],[1,0,0,1,0,0,0,0,1],[1,1,0,1,1,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,1,0],[1,1,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[0,1,0,0,1,1,0,0],[1,1,0,1,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1],[1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0],[1,1,0,1,1,0,0,1],[1,1,0,1,0,0,1,0],[1,1,0,0,1,1,0,1],[1,1,0,1,1,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1,0],[1,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,0,0,1],[1,0,0,0,1,0,1,1,0],[1,0,0,0,1,0,1,1,0],[1,1,0,1,1,1,0,0,1],[1,1,0,0,0,0,1,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,1,1,0,1],[1,1,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,1,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,1,0,0,1],[1,1,1,1,0,0,0,0,0,1],[1,1,1,0,1,0,1,0,0,1],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,1,0,1,1,0,1],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,1,1,1,1,0,0,0,1],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,1],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,1,1,0,1,0,1],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,0,0,1,1,0,0,1,0],[1,0,0,1,1,0,0,1,0],[1,1,0,1,0,1,0,1,1],[1,1,0,1,0,0,0,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,1],[1,1,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,0,0,1,1]],"Q":[[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,1,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[1,1,0,0,1,0,1,0,1],[1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,1,1],[1,1,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,0],[1,1,1,1,0,0,0,0,1],[1,1,0,1,0,0,1,0,0],[1,0,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,0,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,0],[1,1,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,1,1,0,0,0,1,0],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[1,1,1,0,0,0,1,0],[1,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0],[1,1,0,1,1,0,0,1]],"Q":[[0,1,0,1,1,1,1,0],[1,0,0,1,1,0,0,1],[1,0,0,1,1,0,0,1],[1,1,0,0,1,1,1,0],[1,1,0,1,0,0,0,1],[0,0,0,0,0,1,0,0],[1,1,0,1,1,1,0,0],[1,1,0,1,1,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,1,1,1,0,0,0,0,1,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,1,0,1,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,0,1,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,1,0,1,1],[1,0,0,1,0,0,1,1],[0,1,1,1,1,0,1,1],[1,1,0,0,0,0,1,1],[1,1,0,1,1,0,1,1],[1,0,0,1,0,0,1,1],[0,1,0,1,1,0,0,1],[1,1,0,1,0,0,1,0]],"Q":[[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[1,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1],[1,1,0,0,1,1,0,0],[1,1,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,0,1,0,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,1,0,1,0,0,1,1],[1,0,0,0,1,1,0,0],[1,1,1,0,1,1,0,0],[0,0,0,1,0,0,0,0],[1,1,0,1,0,0,1,1],[1,0,0,0,1,1,0,0],[0,1,0,1,0,0,0,1],[1,1,0,0,1,1,0,1]],"Q":[[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,0,0,1],[1,1,0,0,1,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,1,0,1,1,0],[1,0,0,0,1,0,0,0,1,0],[0,1,1,0,1,1,0,1,1,0],[1,1,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,1,0,1,1,0],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,1,0,0],[1,1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,0,1,1,0],[0,1,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,1,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,1,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,1,1,0,1,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,1,1,1],[1,0,0,1,0,0,0,1,1,0],[0,1,0,0,1,0,0,0,1,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,1,0,1,1,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[0,0]],"P":[[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[1,1,0,1,0,0,0,0],[1,0,1,1,0,0,0,0],[0,1,0,1,1,0,0,0],[1,1,1,1,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,0,0,1,0],[1,1,1,1,0,0,0,1],[1,1,1,1,0,0,1,0],[1,0,1,0,0,0,0,1],[1,1,0,1,1,0,1,0],[1,0,1,1,0,1,0,1],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[0,1]],"P":[[1,1,0,0,0,1,0,0,0],[1,0,0,1,0,1,0,1,1],[1,1,1,1,0,1,0,1,1],[0,0,0,1,0,0,0,0,0],[1,1,0,0,0,1,0,0,0],[1,0,0,1,0,1,0,1,1],[0,1,0,0,0,1,1,0,0],[1,1,0,1,0,1,0,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,0,1],[1,1,0,0,1,0,0,1,0],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,1,1,0,1,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[1,0]],"P":[[1,1,0,0,0,1,1,0,0,0],[1,0,0,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,1,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,0,1,0,1,0,0],[1,1,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,0,1],[1,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,0],[1,1]],"P":[[1,1,0,0,1,0,0,0,0],[1,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1,0],[1,1,0,0,1,0,0,0,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,0,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[1,1,0,1,1,0,0,0,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,1,0,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[0,0]],"P":[[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,1,0,1,1,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,1,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,1,0,1,1],[0,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,1,1,1],[1,1,1,1,0,1,0,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,0,1,0,1,1],[1,1,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,1,1],[1,1,0,1,0,1,0,1,1],[1,0,0,1,1,0,0,1,0],[0,0,0,0,0,1,0,0,0],[1,1,0,0,0,1,1,1,1],[1,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1],[1,1,0,0,1,0,0,0,1,1]],"Q":[[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,1,0,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1],[0,1,0,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1],[1,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,1,1,1],[1,1,0,0,1,0,1,0,0,1],[1,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[0,0]],"P":[[1,1,1,0,0,0,1,0,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[1,1,1,0,0,0,1,0,0],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,1,1,1,1,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[1,1,0,1,1,1,0,0,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0,1,0],[1,0,1,1,0,0,0,1],[0,1,1,1,0,0,1,0],[1,1,1,0,0,0,0,1],[1,1,0,1,0,0,1,0],[1,0,1,1,0,0,0,1],[0,1,0,1,0,0,0,0],[1,1,1,1,0,0,0,0]],"Q":[[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[1,1,0,0,0,1,1,0],[1,0,0,0,1,1,0,1],[1,1,0,0,1,1,0,0],[1,0,0,0,1,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,1,0,1,0,0],[1,0,0,1,0,0,1,0,0],[0,1,1,1,1,0,1,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,1,0,1,0,0],[1,0,0,1,0,0,1,0,0],[0,1,0,1,1,0,0,0,0],[1,1,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,1,1,0,1],[1,1,0,0,0,1,1,0,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,0],[1,1,0,0,1,1,0,0,1],[1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,1,0,0,0,1,0],[1,0,0,1,0,0,0,0,1,1],[0,1,1,1,1,0,0,0,1,0],[1,1,0,0,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0],[1,1,0,1,1,0,0,0,1,0],[1,0,0,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0]],"Q":[[0,1,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,0,1,0],[1,0,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,1,0,0,0],[1,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,1,0,0,1,1,0],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,1,1,0],[1,0,0,0,1,1,0,0,0],[0,1,0,1,0,0,0,1,0],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[1,1,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,1,1,0],[1,0,0,0,1,0,0,0,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,1,1,1,0,0,0,0,0,0]],"Q":[[0,1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,0,0,0,1],[0,1,0,0,0,1,0,1,1,1],[1,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,1,0,0],[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,1,0,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,0,0,1,0],[0,1,1,0,1,0,0,0,1,1],[1,1,0,1,0,1,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,0,0,1,0],[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,0,1,1]],"Q":[[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,1,1,0],[0,1,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,0,1,1],[1,0,0,0,0,0,0,0,1,0],[1,1,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[0,1],[1,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,1,0,0,0,1,1,1],[1,0,0,1,1,0,1,1,1,1],[0,1,1,1,0,0,0,1,1,1],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[1,0,0,1,1,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[1,1,0,1,1,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[0,1,0,0,1,0,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0],[1,1,0,0,0,0,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,1,0,0,0,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,1,0,1,0,1,0],[1,0,1,1,0,0,0,0,1,0],[0,1,0,1,1,0,1,0,1,0],[1,1,1,0,0,0,0,0,1,0],[1,1,1,1,1,0,1,0,1,0],[1,0,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,1,0,1,1,1,0],[1,1,1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[0,1,0,1,0,0,0,0,1],[1,1,0,1,1,1,0,0,0],[1,1,1,1,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[0,1,1,1,0,0,1,0,1],[1,1,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[1,0,0,0,1,0,0,0,1],[0,1,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1,0],[0,1,0,1,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[1,0,0,0,1,0,1,0,0,1],[0,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,1,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1],[1,1,1,1,0,0,0,0,1],[1,1,1,0,1,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,1,0,1,0,1,0,1],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[1,0,0,0,1,1,0,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1,0],[0,1,0,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1,1],[1,1,1,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[1,0,0,0,1,1,0,0,1,1],[0,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,0,1,1,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,1,1,1,0,0,0],[1,1,1,0,0,0,0,0,1],[1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1],[1,1,0,0,1,1,0,0,1]],"Q":[[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[1,0,0,0,1,1,1,0,1],[0,1,0,0,1,1,0,1,0],[0,0,0,0,0,1,1,0,1],[0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1],[0,1,0,0,0,0,0,1],[1,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1],[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[1,0,0,0,1,1,0,1],[0,1,0,0,1,0,1,1],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,1,0,0,0,1,0,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,1,0,0,0,1,0,0],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,1,1,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1],[1,1,0,1,0,0,0,0,1,0],[1,0,1,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0]],"Q":[[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0,1,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,1,0,1,0,1,0],[0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,0,1,0,1],[1,0,0,0,1,1,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[1,1,0,1,1,1,0,0,0,0],[1,1,0,1,0,0,0,1,0,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[1,0,0,0,0,0,1,1,0,1],[0,1,0,0,1,1,0,1,0,0],[0,0,0,0,1,0,1,1,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,1,0,1,1,1],[1,0,0,1,0,0,0,1,1],[0,1,1,1,1,0,1,1,1],[1,1,0,0,0,0,0,1,1],[1,1,0,1,1,0,1,1,1],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,1,0,1],[1,1,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0],[0,1,0,0,1,0,0,1,1],[0,0,0,0,1,0,1,1,0],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,0,0,1,1,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,1,0,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0,0],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[1,0,0,0,0,1,1,1,1,0],[0,1,0,0,0,1,0,0,0,1],[0,0,0,0,1,1,1,1,1,0],[0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,0,1,0,0,0],[1,0,1,1,0,0,0,0,1],[0,1,1,0,0,1,0,0,0],[1,1,1,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,0],[1,0,1,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0],[1,1,1,1,0,0,0,0,0]],"Q":[[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[1,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,1,1,0,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,0,1,0,0],[1,0,0,0,1,1,0,0],[0,1,1,0,0,1,0,0],[1,1,0,1,1,1,0,0],[1,1,0,0,0,1,0,0],[1,0,0,0,1,1,0,0],[0,1,0,0,0,1,1,0],[1,1,0,0,1,1,0,1]],"Q":[[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[1,0,0,0,0,1,1,1],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[0,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,0,1,0,0,0],[1,0,0,1,0,0,1,1,0],[0,1,1,0,0,1,0,0,0],[1,1,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0],[1,0,0,1,0,0,1,1,0],[0,1,0,0,0,1,1,0,0],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,1,1,0],[0,0,0,0,1,1,1,1,1],[0,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,1,0,0,1,1],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[1,1,1,1,1,0,0,1,1],[1,0,0,1,1,0,0,0,0],[0,1,1,1,1,1,0,1,1],[1,1,0,1,1,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,1,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,1],[0,0,0,1,0,1,0,1,0],[1,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,1,0,1,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0,1],[1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[1,0,0,0,0,1,0,1,0,0,1],[1,1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,0,0,0,0,0,1],[1,0,0,0,1,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,1],[1,1,0,1,1,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,0,0,0,1,0,0,1,0,0],[0,1,1,1,0,0,0,1,0,1],[1,1,0,0,1,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,1,1,1,0],[1,0,1,0,0,0,1,1,0],[1,1,0,0,0,0,1,1,0],[1,1,1,1,0,1,1,1,0],[1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,1,1,0,1,0,1,0],[1,1,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1],[1,0,0,0,1,1,1,1,0],[0,0,0,0,0,1,0,0,0],[0,0,0,1,0,0,1,0,1],[1,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[0,0]],"P":[[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,1,0,1,1,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,1,0,1,0],[1,1,0,0,1,1,0,0,0,1],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,1,1,1,1,1,0],[1,0,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,1,0],[0,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,1,0],[0,1,1,0,0,0,1,1,1],[1,1,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,0],[1,0,0,0,1,1,0,1,1],[1,1,0,0,1,0,0,1,0],[0,0,0,0,0,1,0,1,1],[1,0,0,0,1,1,0,1,0],[0,0,0,0,1,1,1,1,1],[1,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[1,0]],"P":[[1,1,0,1,1,0,1,0],[1,0,0,1,0,0,1,0],[1,1,1,1,0,0,1,0],[0,0,0,1,0,0,0,0],[1,1,0,1,1,0,1,0],[1,0,0,1,0,0,1,0],[0,1,0,1,1,0,0,0],[1,1,0,1,0,0,1,1]],"Q":[[1,0,0,0,1,1,0,1],[1,1,0,0,0,1,1,0],[1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1],[1,0,0,0,0,0,1,0],[0,0,0,0,1,1,1,1],[1,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0]],"Q":[[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[1,1,0,0,0,0,1,1,1],[0,0,0,0,0,1,0,0,1],[1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,1,0,0],[0,0,0,0,1,1,0,1,1],[1,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[0,0]],"P":[[1,1,1,0,0,0,1,0,0],[1,0,0,1,1,0,0,0,0],[1,1,1,1,1,0,0,0,0],[1,1,1,0,0,0,1,0,0],[1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0,0],[1,1,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,1,0,0],[1,1,0,1,1,0,0,0,1],[1,1,0,1,1,0,0,0,1],[0,0,0,1,0,1,1,0,0],[1,0,0,1,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,0],[1,0,0,1,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[0,1]],"P":[[1,1,1,0,0,0,1,0],[1,0,1,1,0,1,1,0],[1,1,0,1,0,1,1,0],[1,1,1,0,0,0,1,0],[1,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,0],[1,1,1,1,0,1,1,1]],"Q":[[1,0,0,0,0,1,1,0],[1,1,0,1,0,0,0,1],[1,1,0,1,0,0,0,1],[0,0,0,1,0,1,1,0],[1,0,0,1,1,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,1,0,0],[1,0,0,1,0,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,1,1,1,0,0,0,0,1,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[1,0,0,0,0,0,0,1,1,0,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,1,0,1],[1,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,1,1,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,0,1,1],[0,1,1,1,1,0,0,0,0,1,0],[1,1,0,0,0,0,0,0,0,1,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,0,0,0,0,1,0],[1,0,0,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,0,0,1,0]],"Q":[[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[1,0,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,0,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,0,1,0,1,1,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[1,0,0,0,0,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[0,1,0,0,1,1,0,0],[1,1,0,1,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,1,1,1,0],[1,1,0,1,1,0,0,1],[1,1,0,1,1,0,0,1],[0,0,0,1,1,1,1,0],[1,0,0,1,0,0,0,1],[0,0,0,0,1,0,1,0],[1,0,0,1,1,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,0,1,0,0],[1,0,1,1,0,0,0,1],[0,1,1,0,0,1,0,0],[1,1,1,0,0,0,0,1],[1,1,0,0,0,1,0,0],[1,0,1,1,0,0,0,1],[0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0]],"Q":[[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[0,0,0,0,1,1,1,1],[1,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,1],[1,0,0,0,1,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1,0],[0,1,1,0,0,0,1,1,0,0],[1,1,0,1,1,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,0,0,1,1,0,0],[1,0,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,1,1,0],[1,1,0,0,1,0,0,0,1,1]],"Q":[[1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,0,1,0,1,0],[1,0,0,0,0,0,1,1,1,1],[1,1,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,1,1,1,1],[1,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,1,0,1],[1,0,0,0,0,0,1,0,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,0],[1,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,1,0],[0,1,1,0,0,1,0,0,0,0],[1,1,0,0,0,0,0,1,1,0],[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,0],[1,1,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,1,1,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,1,1,0,1,1,1],[1,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0,1,1],[1,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,0,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1],[1,1,1,1,0,0,0,0,1],[1,0,1,0,0,0,0,0,1],[0,1,1,1,0,1,0,0,1],[1,1,1,0,0,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,0,1],[1,1,0,1,1,0,0,1,0],[0,1,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,0,1],[0,1,0,1,1,1,0,1,0],[0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[0,1]],"P":[[1,1,1,1,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,1,0,1,1,0,0,0,0,0,1],[1,1,1,0,0,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,1,0,0,0,0,0,1],[1,0,1,1,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,1,0,0,0,1,0,1],[1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,0,1,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,0,0,0,0,0,1],[1,0,0,0,1,1,0,0,0,0],[0,1,0,1,0,0,0,0,0,1],[1,1,0,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0,0,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,1,0,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,1,0,0],[1,1,0,0,1,1,1,0,0,1],[0,1,0,0,1,1,0,1,0,0],[0,1,0,0,0,1,1,0,0,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,1,1,0,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1,0],[0,1,0,1,0,0,0,0,1],[1,1,0,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1,0],[0,1,1,1,0,0,1,0,1],[1,1,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[1,1,0,0,1,1,0,0,1],[0,1,0,0,1,0,1,1,0],[0,1,0,0,0,1,0,0,1],[0,0,0,0,1,1,1,1,0],[0,1,0,0,1,1,1,0,1],[0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0],[1,1,1,0,1,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,1,1,0],[1,1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[1,1,0,0,0,1,0,0,1,0],[0,1,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[0,1,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,1,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[0,1]],"P":[[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,1,0,1,1],[0,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,1,1],[1,0,1,1,0,1,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,1,1,1],[1,1,1,1,0,1,0,0,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,1,0,1,0],[1,1,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,1,1],[0,0,0,0,1,1,0,1,0],[0,0,0,0,0,1,0,0,0],[0,1,0,1,0,0,1,1,1],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[1,0]],"P":[[1,1,1,0,0,0,0,1],[1,0,0,0,1,1,0,0],[0,1,0,0,0,0,0,1],[1,1,0,1,1,1,0,0],[1,1,1,0,0,0,0,1],[1,0,0,0,1,1,0,0],[0,1,1,0,0,0,1,1],[1,1,0,0,1,1,0,1]],"Q":[[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[1,1,0,0,1,0,0,1],[0,1,0,0,1,1,1,0],[0,1,0,0,0,0,0,1],[0,0,0,0,1,0,1,0],[0,1,0,0,1,0,1,1],[0,0,0,0,1,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,1],[1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0],[0,1,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,1,0]],"Q":[[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,1,1],[1,1,0,0,1,0,1,0,1],[0,1,0,0,1,0,0,1,1],[0,1,0,0,0,0,1,0,1],[0,0,0,0,1,1,0,1,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,1,1,1],[0,0,0,0,1,0,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[0,0]],"P":[[1,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,1],[0,1,1,0,1,1,0,0,0],[1,1,0,0,1,1,0,0,0],[1,0,1,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0,0],[1,1,1,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0],[0,1,0,0,1,0,0,0,1],[1,1,0,0,1,1,1,0,0],[0,1,0,1,1,1,1,0,0],[0,0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,0,0,0],[0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[0,1]],"P":[[1,1,0,0,1,0,0,0],[1,0,1,0,1,0,1,1],[0,1,1,0,1,0,0,0],[1,1,0,0,1,0,0,0],[1,0,1,0,1,0,1,1],[0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,0],[1,1,1,0,1,0,1,0]],"Q":[[1,1,0,0,1,0,1,0],[0,1,0,0,0,1,0,1],[1,1,0,0,1,0,1,0],[0,1,0,1,1,0,1,0],[0,0,0,0,1,1,0,1],[0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,0],[0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[1,0]],"P":[[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[0,1,1,0,1,0,0,0],[1,1,0,0,1,0,0,0],[1,0,0,1,1,0,0,0],[0,1,0,0,1,1,0,0],[1,1,0,1,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,1],[0,1,0,1,1,1,0,0],[1,1,0,0,1,1,0,1],[0,1,0,1,1,1,0,1],[0,0,0,1,0,1,0,0],[0,1,0,0,1,0,0,1],[0,0,0,1,1,1,1,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,0],[1,1]],"P":[[1,1,0,0,0,1,0,0],[1,0,0,1,0,1,0,1],[0,1,1,0,0,1,0,0],[0,0,0,1,0,0,0,0],[1,1,0,0,0,1,0,0],[1,0,0,1,0,1,0,1],[0,1,0,0,0,1,1,0],[1,1,0,1,0,1,0,0]],"Q":[[1,1,0,0,0,1,1,0],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,0],[0,0,0,0,1,1,1,1],[0,1,0,0,0,1,0,0],[0,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[0,0]],"P":[[1,1,0,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,1,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,1,0,0,0,0,1,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,0],[0,0,0,0,0,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[0,1]],"P":[[1,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,0,1],[0,1,1,0,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,1,1],[1,0,1,1,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,0,0,0]],"Q":[[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[1,1,0,0,0,0,0,1,0,1,1],[0,1,0,0,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,1,1],[0,0,0,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,0,1],[0,0,0,0,0,0,0,0,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,1,0,0,0],[0,1,1,0,1,0,0,0,1,1],[1,1,0,1,0,1,1,0,0,0],[0,0,0,0,1,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1],[1,0,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,1,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,0,1,0],[1,1,0,0,0,0,0,1,1,1],[0,1,0,0,0,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1],[0,0,0,0,0,1,0,0,1,0],[0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,1,0,1],[0,0,0,0,0,1,1,0,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[0,1]],"H":[[1,1],[1,1]],"P":[[1,1,0,1,0,0,0,1,1,1],[1,0,0,1,1,0,1,1,1,1],[0,1,1,1,0,0,0,1,1,1],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,1],[1,0,0,1,1,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,1],[1,1,0,1,1,0,1,1,0,1],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,1],[0,1,0,0,1,0,0,1,1,0],[1,1,0,0,0,0,1,1,1,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,1],[0,0,0,0,1,1,0,1,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,1],[0,0,0,0,1,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[0,0]],"P":[[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,1],[1,1,1,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,1],[0,1,1,1,0,0,1,0,1,0],[1,1,1,0,0,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,0,1,0],[1,0,0,0,1,0,0,0,0,1],[0,1,0,0,0,1,0,0,1,0],[1,1,0,0,1,1,0,0,0,1],[0,1,0,0,1,1,1,0,1,0],[1,1,0,0,1,0,0,1,0,1],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[0,1]],"P":[[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[1,1,1,0,1,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,1,1,0,0,1,1],[1,0,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,1,1,0,1,1,1],[1,1,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,1,0,0,1],[1,0,0,0,1,1,0,0,1,0],[1,0,0,0,1,1,0,0,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,0,0,1],[1,1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,1,1,1,1,0,1],[1,1,0,0,1,1,0,0,0,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[1,0]],"P":[[1,1,1,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,1,0,1,0,0,0,0,0,0,1],[1,1,0,1,1,0,0,0,1,0,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,1,0,0,0,0,0,0,1],[1,0,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,1,0,0,0,0,1,0,1],[1,1,0,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,1,0,0,0,1],[1,0,0,0,0,0,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,1,0,1,0,1],[1,1,0,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,0],[1,1]],"P":[[1,1,1,1,0,1,1,0],[1,0,1,0,0,1,1,0],[1,1,0,0,0,1,1,0],[1,1,1,1,0,1,1,0],[1,0,1,0,0,1,1,0],[0,1,1,1,0,0,1,0],[1,1,1,0,0,1,0,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,1,0,0,1],[1,0,0,0,1,1,1,0],[1,0,0,0,1,1,1,0],[0,1,0,0,1,0,0,1],[1,1,0,0,0,1,1,0],[0,1,0,1,1,1,0,1],[1,1,0,0,1,1,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[0,0]],"P":[[1,1,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,1,0,0,1,0,0,0,0,1,0],[1,1,1,1,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0,0,0,0],[1,1,1,0,1,0,0,0,0,1,0],[1,0,1,0,0,0,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,1,0,1,0,0,0,1,1,0],[1,1,1,0,0,0,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[1,1,0,0,0,1,0,1,0,1,0],[1,0,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,1,0,1,0],[1,1,0,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,1,1,1,0],[1,1,0,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[0,1]],"P":[[1,1,1,1,1,0,0,1],[1,0,0,1,1,0,0,0],[1,1,1,1,1,0,0,0],[1,1,1,1,1,0,0,1],[1,0,0,1,1,0,0,0],[0,1,1,1,1,1,0,1],[1,1,0,1,1,0,1,0],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,1,0,0,1,1],[1,0,0,1,1,0,1,0],[1,0,0,1,1,0,1,0],[0,1,0,0,0,0,1,1],[1,1,0,1,0,0,1,0],[0,1,0,1,0,1,1,1],[1,1,0,1,1,0,0,0],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[1,0]],"P":[[1,1,0,1,1,0,1,1,0],[1,0,0,1,0,0,0,1,0],[1,1,1,1,0,0,0,1,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,1,0,1,1,0],[1,0,0,1,0,0,0,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,1,1,0,1,0,0],[1,1,0,1,0,0,0,1,1]],"Q":[[1,1,0,0,1,0,0,0,1],[1,0,0,0,0,0,1,1,0],[1,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,1,0,0],[0,1,0,0,1,0,0,1,1],[1,1,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[0,1],[1,1]],"P":[[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1],[0,1,0,0,0,0,0,1],[1,1,0,0,0,0,1,1],[1,1,1,0,0,0,0,1],[1,0,0,1,0,0,1,1],[0,1,1,0,0,0,1,1],[1,1,0,1,0,0,1,0]],"Q":[[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[1,1,0,0,1,0,0,1],[1,0,0,0,0,1,1,1],[0,1,0,0,0,0,0,1],[1,1,0,0,0,0,1,1],[0,1,0,0,1,0,1,1],[1,1,0,0,0,1,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[0,0]],"P":[[1,1,0,0,1,0,0,0],[1,0,1,0,0,0,0,1],[0,1,1,0,1,0,0,0],[1,1,0,0,1,0,0,0],[1,0,1,0,0,0,0,1],[0,1,0,0,1,1,0,0],[1,1,1,0,0,0,1,1],[0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,1,1,0,0],[1,0,0,1,0,0,0,1],[1,1,0,0,1,1,0,0],[0,1,0,1,1,1,0,0],[1,1,0,1,1,0,0,1],[0,1,0,0,1,0,0,0],[1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[0,1]],"P":[[1,1,0,1,0,0],[1,0,1,1,0,0],[1,1,0,1,0,0],[1,0,1,1,0,0],[0,1,0,1,1,0],[1,1,1,1,0,1]],"Q":[[1,1,0,1,1,0],[1,0,1,1,0,1],[0,1,1,1,1,0],[1,1,1,0,0,1],[0,1,0,1,0,0],[1,1,1,1,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[1,0]],"P":[[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,1,1,0,0,1,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,0,0,1,0,0,0,0],[1,0,0,1,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,0,0],[1,1,0,1,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,1,0,1,0,1],[1,0,0,0,0,0,1,1,0,0],[1,1,0,0,0,1,0,1,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,0,1,0,1],[1,1,0,0,0,1,1,1,0,0],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,1,0,0,0,1],[1,1,0,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,0],[1,1]],"P":[[1,1,0,0,0,1,1,0,0],[1,0,0,1,0,1,1,0,1],[0,1,1,0,0,1,1,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,0,0,1,1,0,0],[1,0,0,1,0,1,1,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,1,1,0],[1,1,0,1,0,1,1,0,0]],"Q":[[1,1,0,0,0,1,1,1,0],[1,0,0,0,0,1,0,1,1],[1,1,0,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,1,1,1,0],[1,1,0,0,0,0,0,1,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,1,1,0,0],[1,1,0,0,0,1,0,1,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[0,0]],"P":[[1,1,0,1,0,0,0,1,1,0],[1,0,0,1,1,0,1,1,1,0],[1,1,1,1,1,0,1,1,1,0],[0,0,0,1,0,0,0,0,0,0],[1,1,0,1,0,0,0,1,1,0],[1,0,0,1,1,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1,0],[1,1,0,1,1,0,1,1,0,0],[0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1,0],[1,0,0,0,1,0,0,0,0,1],[1,0,0,0,1,0,0,0,0,1],[0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1,0],[1,1,0,0,1,1,0,0,0,1],[0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,1,0,1,0],[1,1,0,0,1,0,0,0,1,1],[0,0,0,0,0,0,0,0,0,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[0,1]],"P":[[1,1,0,1,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[1,1,1,0,1,1,0,0,0],[0,0,0,1,0,0,0,0,0],[1,1,0,1,0,0,0,1,1],[1,0,0,0,1,1,0,0,0],[0,0,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,1],[1,1,0,0,1,1,0,0,1]],"Q":[[1,1,0,0,0,0,1,1,1],[1,0,0,0,1,1,0,0,1],[1,0,0,0,1,1,0,0,1],[0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,1,1,1],[1,1,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,1,0,1],[1,1,0,0,1,1,0,0,0]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[1,0]],"P":[[1,1,0,0,1,0,0,0,0,0,1,1],[1,0,0,0,0,1,0,0,0,0,1,0],[0,1,1,0,1,0,0,0,0,0,1,1],[1,1,0,1,0,1,0,0,0,0,1,0],[0,0,0,0,1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,0,0,1,1],[1,0,0,0,0,1,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,0,0,1],[1,1,0,0,0,1,0,0,0,0,1,1]],"Q":[[1,1,0,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,0,0,1,1,0],[1,1,0,0,0,0,0,0,1,0,1,1],[1,0,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,1,0,1,0,1,1],[1,1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0,1,0,0,1],[1,1,0,0,0,0,0,0,0,1,1,1]]},
+    {"A":[[1,1],[1,0]],"B":[[1,1],[1,0]],"H":[[1,1],[1,1]],"P":[[1,1,0,0,1,0,0,0,1,1,1],[1,0,0,1,0,0,0,0,1,1,0],[0,1,1,0,1,0,0,0,1,1,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,1,0,0,0,0,0,0],[1,1,0,0,1,0,0,0,1,1,1],[1,0,0,1,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,1,0,0,0,0,1,1],[1,1,0,1,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]],"Q":[[1,1,0,0,0,0,0,1,1,1,1],[1,0,0,0,0,0,1,0,1,1,0],[1,1,0,0,0,0,0,1,1,1,1],[1,0,0,0,0,0,1,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,1,0,1,1,1,1],[1,1,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,1,0,1,1],[1,1,0,0,0,0,1,0,1,0,0],[0,0,0,0,0,0,0,0,0,0,1]]}
+  ]
+}
diff --git a/research/arbitrary-pivot-schur-minimum/PROOF.md b/research/arbitrary-pivot-schur-minimum/PROOF.md
new file mode 100644
index 0000000000..c7d58883b4
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/PROOF.md
@@ -0,0 +1,222 @@
+# Prescribed arbitrary pivots: the exact Schur dimension
+
+Krzysztof Wojt, with substantial OpenAI Codex assistance. Apache-2.0.
+
+This is a scoped all-field algebraic proof. The ordered Schur factorization
+is Nick Petalas's #4597. The joint-sector and split-factor methods come from
+ssafwann #4657/#4671 and Nick Petalas #4746/#4771/#4774/#4785. The new step is
+the six-map criterion for arbitrary invertible, possibly noncommuting block
+pivots, and its exact prescribed-boundary minimum. No historical priority
+is claimed for the underlying linear algebra.
+
+## 1. Statement
+
+Let K be any field, d >= 1, and let A,B in GL_d(K) and H in M_d(K) be
+prescribed. There is no commutation assumption on A,B,H. Among all commuting
+idempotents P,Q in M_n(K) satisfying
+
+```
+P11=A, Q11=B, (PQ)11=H,
+S=P22-P21 A^-1 P12, Z=Q22-Q21 B^-1 Q12,
+rank(SZ-ZS)=2d,
+```
+
+the exact least dimension is
+
+```
+n_min = 3d + rank(I-A-B+H)
+           + nullity(A-H) + nullity(B-H) + nullity(H).       (1)
+```
+
+For the simultaneous eigenspaces indexed by 00,10,01,11, every such pair
+satisfies the componentwise bounds
+
+```
+r00 >= rank(I-A-B+H),
+r10 >= d+nullity(A-H),
+r01 >= d+nullity(B-H),
+r11 >= d+nullity(H).                                      (2)
+```
+
+All four equalities are attained together. The same construction attains
+both least input ranks
+
+```
+rank P = 2d+nullity(A-H)+nullity(H),
+rank Q = 2d+nullity(B-H)+nullity(H).                        (3)
+```
+
+Consequently it also minimizes both residual ranks, obtained by subtracting d.
+One may add any number of unused 00-sector dimensions, so every n >= n_min
+is feasible. Formula (1), not the finite verification, is the universal claim.
+
+## 2. Ordered ambient factors
+
+Let U=K^d, V=K^n, i:U -> V be inclusion of the first d coordinates and
+pi:V -> U the corresponding projection. Thus pi i=I and
+pi P i=A, pi Q i=B, pi PQ i=H. Define maps L:U^2 -> V and R:V -> U^2 by
+
+```
+L = [PQ i-Q i B^-1 H,  P i A^-1-Q i B^-1],
+R = [A^-1 pi P-B^-1 pi Q;
+     -pi PQ+H B^-1 pi Q].                                (4)
+```
+
+The order of all factors is part of (4). Direct substitution gives
+pi L=0 and R i=0. The operators
+
+```
+Ptilde=P-P i A^-1 pi P, Qtilde=Q-Q i B^-1 pi Q
+```
+
+have block forms diag(0,S), diag(0,Z). Multiplying (4) and cancelling the
+two identical terms Q i B^-1 H B^-1 pi Q gives
+
+```
+L R = Ptilde Qtilde-Qtilde Ptilde = diag(0,SZ-ZS).          (5)
+```
+
+This is the ambient form of #4597's ordered identity. It neither moves H
+past B^-1 nor moves any pivot past another block. In particular
+rank(SZ-ZS)<=2d. Equality holds exactly when L is injective and R is
+surjective: a surjection onto U^2 followed by an injection from U^2 has
+rank 2d, and rank 2d of the product forces both conditions.
+
+## 3. The six-map criterion without scalar pivots
+
+Commuting idempotents split V as the direct sum of their four simultaneous
+eigenspaces, in every characteristic. Write
+
+```
+E00=(I-P)(I-Q), E10=P(I-Q), E01=(I-P)Q, E11=PQ,
+Yj=Ej i:U -> Vj, Xj=pi|Vj:Vj -> U.
+```
+
+Their compressed products are
+
+```
+X00 Y00=I-A-B+H, X10 Y10=A-H,
+X01 Y01=B-H,     X11 Y11=H.                              (6)
+```
+
+In these coordinates the left factor is
+
+```
+L(x,y) = (0,
+          Y10 A^-1 y,
+         -Y01 B^-1(Hx+y),
+          Y11((I-B^-1 H)x+(A^-1-B^-1)y)).                (7)
+```
+
+**Criterion.** rank(SZ-ZS)=2d if and only if each of Y10,Y01,Y11 is
+injective and each of X10,X01,X11 is surjective.
+
+First prove that L is injective exactly when all three active Y maps are
+injective. For necessity:
+
+* If 0!=z is in ker Y10, then (A-H)z=0 by (6). The nonzero pair
+  (x,y)=(-z,Az) is killed by (7): its first active component is Y10 z,
+  its second uses -Hz+Az=0, and its last argument is
+  -z+B^-1 Hz+z-B^-1 Az=0.
+* If 0!=z is in ker Y01, then Hz=Bz. The pair (z,0) is killed by (7),
+  since B^-1 Hz=z and (I-B^-1 H)z=0.
+* If 0!=z is in ker Y11, then Hz=0. Again (z,0) is killed by (7).
+
+Conversely, if all three Y maps are injective and L(x,y)=0, its 10 component
+first gives y=0 because A is invertible. Its 01 component then gives Hx=0
+because B is invertible. Its 11 component finally gives x=0.
+
+Necessity of surjectivity of the X maps follows by applying this argument to
+P^t,Q^t. Their leading blocks are A^t,B^t, their product block is H^t
+(because PQ=QP), and their Schur commutator is -(SZ-ZS)^t. For each sector,
+rank(Ej^t i)=rank(pi Ej)=rank Xj. Hence equality of commutator rank forces
+all three X maps onto. This argument uses ranks, not an assumption that
+the given coordinate splitting is orthogonal to the joint eigenspaces.
+
+For sufficiency, the preceding argument gives injectivity of L. If a pair
+of row covectors (u,v) annihilates R, its restrictions to sectors 10,01,11
+are respectively
+
+```
+u A^-1 X10,
+(-u+vH) B^-1 X01,
+(u(A^-1-B^-1)-v+vH B^-1) X11.                           (8)
+```
+
+Surjectivity of X10 implies u=0. Surjectivity of X01 then implies vH=0.
+The 11 expression reduces to -v X11, so v=0. Thus R is onto, proving the
+criterion by (5). This also shows explicitly why noncommutation of A,B,H
+does not obstruct the argument.
+
+## 4. Lower bound and simultaneous attainment
+
+If X:K^r -> K^d is onto and Y:K^d -> K^r is injective, the rank inequality
+rank(XY)>=rank X+rank Y-r gives r>=d+nullity(XY). Apply it in each active
+sector of (6). The 00 sector needs only r00>=rank(X00Y00). These are (2),
+whose sum is (1). Adding the active sector dimensions of P and Q gives (3).
+
+Here is an explicit construction attaining them for every prescribed A,B,H.
+For any T in M_d(K), choose a matrix N_T whose columns complement im T
+in K^d and put
+
+```
+X_T=[T N_T], Y_T=[I;0].
+```
+
+The middle space has dimension d+nullity(T); X_T is onto, Y_T is injective,
+and X_T Y_T=T. Use these factors for T=A-H, B-H, H in sectors 10,01,11.
+For T00=I-A-B+H choose an ordinary rank factorization X00Y00=T00 through
+dimension rank T00. A zero-dimensional 00 sector is allowed.
+
+Let i be the vertical concatenation of the four Y maps and pi the horizontal
+concatenation of the four X maps. By (6), pi i=I. On the sector direct sum,
+define
+
+```
+P0=diag(0,I,0,I), Q0=diag(0,0,I,I).
+```
+
+They commute and are idempotent. Compression gives pi P0 i=A,
+pi Q0 i=B, pi P0 Q0 i=H. Choose a basis N of ker pi. Since pi i=I,
+M=[i N] is invertible. Set
+
+```
+P=M^-1 P0 M, Q=M^-1 Q0 M.
+```
+
+In the resulting coordinates, i is the first-block inclusion and pi its
+projection. Thus P,Q have exactly the prescribed three leading blocks.
+All six active maps have full rank, so their Schur commutator has rank 2d.
+Their sector dimensions and input ranks attain (2) and (3) simultaneously.
+This completes the proof; no diagonalization of H or compatibility condition
+between A,B,H is needed.
+
+## 5. Specializations and a noncommuting sharp example
+
+If A=B=lambda I, (1) is precisely the common scalar-block formula of #4785.
+If d=1 and A=p, B=q are distinct nonzero scalars, the three nullities sum
+to [h in {0,p,q}], recovering #4774. A=B=I specializes to #4746/#4671.
+These are consistency comparisons, not new results or predecessor audits.
+
+Over Q take
+
+```
+A=[[2,1],[0,2]], B=[[2,0],[1,2]], H=[[3,1],[1,3]].
+```
+
+All three pairwise commutators of A,B,H are nonzero. Yet H=A+B-I, and
+H, A-H=I-B, B-H=I-A are invertible. Formula (1) therefore gives n_min=6,
+with sectors (0,2,2,2), rank P=rank Q=4 and Schur-commutator rank 4.
+The same matrices reduced modulo three still give these ranks. These
+examples lie outside the scalar-block predecessors. The verifier constructs
+their complete matrices and checks their literal Schur products exactly.
+
+## 6. Boundary of the conclusion
+
+The theorem assumes both pivots invertible and P,Q commuting idempotents.
+It concerns one common deletion over a field. It does not classify arbitrary
+nonidempotent commuting inputs, singular-pivot generalized complements,
+coefficient rings, nonmaximal commutator ranks or complete-header frequencies.
+The attaining algebraic representation does not construct or price a physical
+header producer/consumer, arbitrary dirty-owner restoration, precision, stock,
+fixed tapes, recursive compilation or outer transfer. No new kappa follows.
diff --git a/research/arbitrary-pivot-schur-minimum/README.md b/research/arbitrary-pivot-schur-minimum/README.md
new file mode 100644
index 0000000000..ef76c6716c
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/README.md
@@ -0,0 +1,130 @@
+# Exact Schur dimension for arbitrary invertible block pivots
+
+Krzysztof Wojt, with substantial OpenAI Codex assistance and a bounded Luna
+subagent for the separate binary checker. New work: Apache-2.0.
+
+For any field K, any d >= 1, arbitrary invertible d-by-d matrices A,B and
+arbitrary H, the least dimension of commuting idempotents P,Q with
+`P11=A`, `Q11=B`, `(PQ)11=H` whose Schur complements have commutator rank
+`2d` is exactly
+
+```
+n_min = 3d + rank(I-A-B+H)
+           + nullity(A-H) + nullity(B-H) + nullity(H).
+```
+
+The matrices A,B,H need not commute. [PROOF.md](PROOF.md) proves the lower
+bound and constructs a pair attaining it over every field. It also gives
+the simultaneous minimum input ranks
+
+```
+rank P = 2d + nullity(A-H) + nullity(H),
+rank Q = 2d + nullity(B-H) + nullity(H).
+```
+
+The new step is extending the six-map criterion from scalar pivots to
+arbitrary invertible pivots, with the matrix order retained throughout.
+This resolves Open next question 1 of both
+[#4774](https://github.com/CrocSwap/integer-mult-bounds/pull/4774) and
+[#4785](https://github.com/CrocSwap/integer-mult-bounds/pull/4785), and goes
+beyond their unequal-scalar-block question. The ordered Schur factorization
+itself is the existing result of
+[#4597](https://github.com/CrocSwap/integer-mult-bounds/pull/4597).
+This package is a new theorem and construction, not a replication of those
+predecessors. [Claim and coordination: #5121](https://github.com/CrocSwap/integer-mult-bounds/discussions/5121).
+
+## Scope and evidence
+
+The proof is universal; the computations are finite corroboration. The
+standard-library exact constructor [verify.py](verify.py) checks:
+
+* All 576 ordered triples `A,B in GL_2(F_2), H in M_2(F_2)`.
+* 648 ternary triples: eight explicitly enumerated noncommuting pivot pairs,
+  each with all 81 choices of H.
+* 162 further structured cases over F_2, F_3, F_5, F_7 and Q, in dimensions
+  d=2,3,4. These include noncommuting pivots and singular compressed products.
+* The idempotence and commutation of the full matrices, all three prescribed
+  blocks, literal Schur complements, the ordered factor identity, sector
+  dimensions, input and residual ranks, and the exact minimum formula.
+* Six controls with one active X or Y map deficient, two singular-pivot
+  rejections, and factor-order mutations. Swapping the H and B-inverse
+  factors in either ordered factor is detected on 1,017 cases.
+
+This is 1,386 constructed cases, plus two explicit noncommuting rational and
+ternary examples and the deficient-map controls. The rational example uses
+
+```
+A=[[2,1],[0,2]], B=[[2,0],[1,2]], H=[[3,1],[1,3]],
+```
+
+and attains n=6, input ranks 4 and Schur-commutator rank 4. All three pairwise
+commutators of A,B,H are nonzero. The same example works modulo three.
+
+[binary_check.py](binary_check.py) independently implements raw matrix
+arithmetic with bitsets. It imports no primary-verifier code and reads the
+576 complete matrix fixtures in [FIXTURES.json](FIXTURES.json). It verifies
+exact coverage, the defining equations and all claimed ranks, including
+288 inputs with noncommuting A,B and 180 with pairwise noncommuting A,B,H.
+Its seven rejection controls cover matrix corruption, a false dimension,
+altered H, singular A, and missing or duplicate coverage. [RESULT.json](RESULT.json)
+records the primary counts, full rational/ternary examples and fixture digest.
+
+No independent human proof acceptance or formal proof-kernel check is claimed.
+The finite domains are not an exhaustive
+search for all full matrices or all dimensions; minimality follows from
+the sector argument in PROOF.md. No physical header, dirty-owner restoration,
+precision, stock, fixed-tape, recursive-compilation or outer-transfer claim
+is made. The selected frontier and kappa are unchanged.
+
+## Reproduce
+
+Python 3.12, standard library only. Each command is read-only; `-O` replay
+also checks that verification does not rely on Python assertions.
+
+```sh
+python3.12 -I -W error -B research/arbitrary-pivot-schur-minimum/verify.py
+python3.12 -I -O -W error -B research/arbitrary-pivot-schur-minimum/verify.py
+python3.12 -I -W error -B research/arbitrary-pivot-schur-minimum/binary_check.py
+python3.12 -I -O -W error -B research/arbitrary-pivot-schur-minimum/binary_check.py
+python3.12 -B scripts/check_research_commit.py --package research/arbitrary-pivot-schur-minimum --check-source-history
+```
+
+The first four commands can also be run by absolute path from a read-only,
+Git-free export with an empty PATH. `VERIFY.json` registers them. Explicit
+`verify.py --write` regenerates only FIXTURES.json and RESULT.json; normal
+verification regenerates in memory and requires byte-for-byte agreement.
+All external source files in SOURCES.json are provenance, not replay inputs.
+
+## Open next questions
+
+1. For the same prescribed A,B,H, which smaller Schur-commutator ranks are
+   feasible at each ambient dimension? The six-map equivalence here treats
+   only the maximal rank 2d. A bounded first step is to classify rank-two
+   residual commutators for d=2 over F_2 with fixed noncommuting A,B,H,
+   before attempting a general theorem. No such classification is claimed.
+2. Can the explicit n=6 ternary witness be realized by an admitted complete
+   header with fully priced producer and consumer? First identify an actual
+   caller and its interface requirements. Algebraic attainment alone gives
+   neither a physical construction nor a multiplication improvement.
+
+## Credit and provenance
+
+Nick Petalas's #4774 and #4785 state the open unequal-block-pivot questions;
+#4771 and #4746 supply the scalar and all-field identity-pivot predecessors.
+ssafwann's #4657/#4671 supply the sector and split-factor method. Nick
+Petalas's #4597/#4278 supply the ordered block and scalar factorizations.
+Ryanson Jonathan's #4609/#4617 and lee-phys's #4634 supply earlier sharpness
+constructions. Nick Petalas's #4259/#4228 retain the laminar-header and
+single-request context. Cinna Davis supplies the BIT request setting;
+source527, commdata2338 and Jose Manuel retain the normalizer lineage credit.
+No historical priority is claimed for the underlying linear algebra.
+
+The checkout starts at canonical main
+`81e9bd69e4a5b00ba9c713a1620e36d576d5522e`. TASK.json preserves the original
+priority-revision-7 card and explicitly changes its scope to this algebraic
+side result. SOURCES.json pins the predecessor documents at that base.
+The predecessor scientific heads are #4597
+`dfeb8ca729a04aea4aa290438f2ed50a37a9c7cb`, #4774
+`a012548529a25a103345e8e8a8afa707a2b3a3e6`, and #4785
+`1c9996b87d497a1690630302a0ac65748affbf16`. Their proofs supply the starting
+point and attribution; their earlier computational receipts are not re-audited.
diff --git a/research/arbitrary-pivot-schur-minimum/RESULT.json b/research/arbitrary-pivot-schur-minimum/RESULT.json
new file mode 100644
index 0000000000..e53984eeb9
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/RESULT.json
@@ -0,0 +1,312 @@
+{
+  "binary_fixture_count": 576,
+  "binary_fixture_sha256": "91f0bc7187b3cb4ee9e6c8ed2d0a51902703ad2c7a704db00ff1c839e866d03d",
+  "counts": {
+    "F2": 594,
+    "F3": 684,
+    "F5": 36,
+    "F7": 36,
+    "Q": 36,
+    "ordered_X_mutation_detected": 1017,
+    "ordered_Y_mutation_detected": 1017
+  },
+  "noncommuting_examples": [
+    {
+      "A": [
+        [
+          "2",
+          "1"
+        ],
+        [
+          "0",
+          "2"
+        ]
+      ],
+      "B": [
+        [
+          "2",
+          "0"
+        ],
+        [
+          "1",
+          "2"
+        ]
+      ],
+      "H": [
+        [
+          "3",
+          "1"
+        ],
+        [
+          "1",
+          "3"
+        ]
+      ],
+      "P": [
+        [
+          "2",
+          "1",
+          "1",
+          "1",
+          "0",
+          "0"
+        ],
+        [
+          "0",
+          "2",
+          "0",
+          "1",
+          "0",
+          "0"
+        ],
+        [
+          "-2",
+          "-1",
+          "-1",
+          "-1",
+          "0",
+          "0"
+        ],
+        [
+          "0",
+          "-2",
+          "0",
+          "-1",
+          "0",
+          "0"
+        ],
+        [
+          "-1",
+          "-1",
+          "-1",
+          "-1",
+          "1",
+          "0"
+        ],
+        [
+          "0",
+          "-1",
+          "0",
+          "-1",
+          "0",
+          "1"
+        ]
+      ],
+      "Q": [
+        [
+          "2",
+          "0",
+          "-1",
+          "-1",
+          "3",
+          "1"
+        ],
+        [
+          "1",
+          "2",
+          "0",
+          "-1",
+          "1",
+          "3"
+        ],
+        [
+          "-1",
+          "0",
+          "2",
+          "1",
+          "-3",
+          "-1"
+        ],
+        [
+          "-1",
+          "-1",
+          "0",
+          "2",
+          "-1",
+          "-3"
+        ],
+        [
+          "-1",
+          "0",
+          "1",
+          "1",
+          "-2",
+          "-1"
+        ],
+        [
+          "-1",
+          "-1",
+          "0",
+          "1",
+          "-1",
+          "-2"
+        ]
+      ],
+      "field": "Q",
+      "n": 6,
+      "rank_p": 4,
+      "rank_q": 4,
+      "sectors": [
+        0,
+        2,
+        2,
+        2
+      ]
+    },
+    {
+      "A": [
+        [
+          2,
+          1
+        ],
+        [
+          0,
+          2
+        ]
+      ],
+      "B": [
+        [
+          2,
+          0
+        ],
+        [
+          1,
+          2
+        ]
+      ],
+      "H": [
+        [
+          0,
+          1
+        ],
+        [
+          1,
+          0
+        ]
+      ],
+      "P": [
+        [
+          2,
+          1,
+          1,
+          1,
+          0,
+          0
+        ],
+        [
+          0,
+          2,
+          0,
+          1,
+          0,
+          0
+        ],
+        [
+          1,
+          2,
+          2,
+          2,
+          0,
+          0
+        ],
+        [
+          0,
+          1,
+          0,
+          2,
+          0,
+          0
+        ],
+        [
+          2,
+          2,
+          2,
+          2,
+          1,
+          0
+        ],
+        [
+          0,
+          2,
+          0,
+          2,
+          0,
+          1
+        ]
+      ],
+      "Q": [
+        [
+          2,
+          0,
+          2,
+          2,
+          0,
+          1
+        ],
+        [
+          1,
+          2,
+          0,
+          2,
+          1,
+          0
+        ],
+        [
+          2,
+          0,
+          2,
+          1,
+          0,
+          2
+        ],
+        [
+          2,
+          2,
+          0,
+          2,
+          2,
+          0
+        ],
+        [
+          2,
+          0,
+          1,
+          1,
+          1,
+          2
+        ],
+        [
+          2,
+          2,
+          0,
+          1,
+          2,
+          1
+        ]
+      ],
+      "field": 3,
+      "n": 6,
+      "rank_p": 4,
+      "rank_q": 4,
+      "sectors": [
+        0,
+        2,
+        2,
+        2
+      ]
+    }
+  ],
+  "rejected_controls": [
+    "sector1_missing_X",
+    "sector1_missing_Y",
+    "sector2_missing_X",
+    "sector2_missing_Y",
+    "sector3_missing_X",
+    "sector3_missing_Y",
+    "singular_A",
+    "singular_B"
+  ],
+  "schema_version": 1,
+  "scope": "Finite corroboration of PROOF.md; no physical admission or new kappa.",
+  "status": "PASS_ARBITRARY_PIVOT_SCHUR_MINIMUM"
+}
diff --git a/research/arbitrary-pivot-schur-minimum/SOURCES.json b/research/arbitrary-pivot-schur-minimum/SOURCES.json
new file mode 100644
index 0000000000..90102f0963
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/SOURCES.json
@@ -0,0 +1,48 @@
+{
+  "schema_version": 1,
+  "base_commit": "81e9bd69e4a5b00ba9c713a1620e36d576d5522e",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/block-schur-commutator/README.md",
+      "usage": "provenance",
+      "git_blob": "79790ccea54cfea1aab611768927651a81f2fb18",
+      "sha256": "945c1420fe9fb5c26dec49e7d6005d77382ca9dc6ca0f424d8baa1500bfc092c"
+    },
+    {
+      "path": "research/unequal-pivot-schur-dimension/README.md",
+      "usage": "provenance",
+      "git_blob": "c34e32931548a9e7b0870d143df11fd55616fbfb",
+      "sha256": "428c8f09221ac4c819e934f6cc4fde3b2d7afdc4f4b36731419ce39cf76e3b7c"
+    },
+    {
+      "path": "research/unequal-pivot-schur-dimension/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "546fdc24fd0e771c57589783b601f31f2179a213",
+      "sha256": "ca1d0454911ebbcf4d2eb48821bdf587f6c5ce6d09d5b61e863c28730313ca8b"
+    },
+    {
+      "path": "research/scalar-block-schur-dimension/README.md",
+      "usage": "provenance",
+      "git_blob": "cbed8b8dd78912e6ef101dd1c5f2cb01a05bfb6a",
+      "sha256": "681c059c2a7bcbe3c522bb8ee56675204072804a28972fb47517520aa6f9ffb3"
+    },
+    {
+      "path": "research/scalar-block-schur-dimension/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "0c4eb58ed9e08522e8d2a054148d069c7879a1ca",
+      "sha256": "a9353583643e35fdcaac8864bb4c2321ca7d8bee3755583a20bee9383626583b"
+    }
+  ]
+}
diff --git a/research/arbitrary-pivot-schur-minimum/TASK.json b/research/arbitrary-pivot-schur-minimum/TASK.json
new file mode 100644
index 0000000000..be40b7a936
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/TASK.json
@@ -0,0 +1,191 @@
+{
+  "schema_version": 1,
+  "task_id": "formal-interface-lemma",
+  "priority_revision": 7,
+  "base_commit": "81e9bd69e4a5b00ba9c713a1620e36d576d5522e",
+  "original_card": {
+    "id": "formal-interface-lemma",
+    "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/gate-operand-parity-lean/README.md",
+      "research/staged544-certified-endpoint/README.md",
+      "research/unconditional-batched-crt/README.md"
+    ],
+    "methods": [
+      "Formalize a missing boundary lemma identified by the selected review.",
+      "Audit a formal theorem-to-certificate binding independently."
+    ],
+    "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.",
+    "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.",
+    "allowed_variations": [
+      "Narrow to one formal lemma or one theorem-to-certificate binding."
+    ],
+    "scope_change_triggers": [
+      "Formalizing already-covered arithmetic and claiming the full multiplication theorem."
+    ],
+    "overlap_terms": [
+      "hyperplane end",
+      "formal interface",
+      "Lean binding",
+      "3807",
+      "3857",
+      "4100",
+      "gate-operand-parity-lean",
+      "staged544-certified-endpoint",
+      "unconditional-batched-crt"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #3807: scoped gate-operand parity formalization.",
+        "evidence": "research/gate-operand-parity-lean/README.md",
+        "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.",
+        "status": "author-checked",
+        "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #3857: certified real-power moment/endpoint arithmetic.",
+        "evidence": "research/staged544-certified-endpoint/README.md",
+        "remaining": "Uniform algorithmic implications, not another endpoint digit.",
+        "status": "author-checked",
+        "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4100: compact-switch formalization proposed as future validation.",
+        "evidence": "research/unconditional-batched-crt/README.md",
+        "remaining": "Audit the statement and assumptions before a formal proof campaign.",
+        "status": "author-checked",
+        "source_commit": "337d04939571a637aeab54a0f58f54fde811663a",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Prove and construct the exact least ambient dimension and input ranks for commuting idempotents with arbitrary prescribed invertible block pivots A,B, prescribed product block H and maximal Schur-commutator rank 2d over any field.",
+  "scope_change_reason": "This is a scoped algebraic side theorem, not a proof-assistant formalization. Open next question 1 of #4774 and #4785 explicitly requests unequal scalar block pivots; the new six-map argument handles arbitrary invertible pivots, without commuting A,B,H. No predecessor census or selected endpoint is re-audited.",
+  "bottleneck_link": "Side result: settles a prescribed-boundary dimension obstruction and gives minimum-size algebraic witnesses. It does not supply or price physical producer/consumer headers, restoration, precision, stock, fixed tapes, recursive compilation or outer transfer, and does not change kappa.",
+  "budget_minutes": 240,
+  "stop_rule": "Stop after one universal theorem, explicit attaining construction, bounded exact verification, separate binary replay and clean export; stop without submission if fresh PR/Discussion checks reveal an overlapping prior claim or proof. Do not extend into physical admission or nonmaximal-rank classification.",
+  "outcome": "completed",
+  "evidence": "PROOF.md gives the all-field six-map equivalence, sector lower bounds and simultaneous attaining construction. verify.py checks 1,386 cases plus two explicit examples and eight rejection controls; binary_check.py independently replays all 576 ordered d=2 binary inputs and seven rejection controls. RESULT.json binds the exact generated fixtures. VERIFY.json registers normal and optimized read-only Python 3.12 replays.",
+  "author": "Krzysztof Wojt",
+  "ai_assistance": "Substantial OpenAI Codex assistance for mathematical derivation, proof, primary exact checker, documentation and integration. A bounded Luna subagent assisted public overlap inventories and separately implemented binary_check.py from the mathematical contract and fixture schema; the primary agent reviewed and ran it. No predecessor code is imported.",
+  "open_questions": [
+    {
+      "question": "For prescribed invertible A,B and arbitrary H, which nonmaximal Schur-commutator ranks are feasible at each ambient dimension?",
+      "why_it_matters": "The six-map equivalence determines the maximal-rank boundary only; smaller ranks could have different dimension obstructions.",
+      "first_step": "Classify rank-two residual commutators for d=2 over F_2 at fixed noncommuting A,B,H, with explicit finite scope before seeking a general theorem.",
+      "blocked_by": "Not addressed by this proof; the rank of the composite L R is no longer determined by injectivity and surjectivity separately."
+    },
+    {
+      "question": "Can the explicit n=6 ternary witness be realized by an admitted complete header with fully priced producer and consumer?",
+      "why_it_matters": "A minimum algebraic representation does not by itself improve multiplication or establish an admissible interface.",
+      "first_step": "Identify an actual caller and list its exact header, restoration, precision and resource requirements before proposing a physical realization.",
+      "blocked_by": "No actual caller or physical implementation is supplied; existing admission and outer-transfer requirements remain."
+    }
+  ],
+  "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/5121",
+  "handoff_pointer": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19143220",
+  "overlap_before_claim": {
+    "open_prs_fetched_at": "2026-10-23T09:46:31.779665+00:00",
+    "open_pr_count": 307,
+    "discussion_records_fetched_at": "2026-10-23T09:47:37.744627+00:00",
+    "discussion_record_count": 4260,
+    "local_notes_searched": 6824,
+    "terms": [
+      "Schur dimension",
+      "unequal pivot",
+      "scalar block",
+      "arbitrary pivot",
+      "noncommuting pivots",
+      "4774",
+      "4785"
+    ],
+    "limits": "Public API snapshot and targeted all-state PR searches, not proof that no concurrent unpublished work exists. Recheck immediately before submission.",
+    "own_recent_claims_excluded": [
+      4999,
+      5006,
+      5030,
+      5086,
+      5094,
+      5100
+    ],
+    "user_excluded_work": [
+      3281,
+      3261,
+      3301,
+      3334,
+      5003,
+      5024,
+      5045,
+      5063,
+      5093,
+      5097
+    ]
+  },
+  "selected_result_sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375",
+  "predecessors": [
+    {
+      "pr": 4597,
+      "scientific_head": "dfeb8ca729a04aea4aa290438f2ed50a37a9c7cb",
+      "use": "Existing ordered arbitrary-pivot Schur factorization; not claimed as new."
+    },
+    {
+      "pr": 4774,
+      "scientific_head": "a012548529a25a103345e8e8a8afa707a2b3a3e6",
+      "use": "Unequal scalar d=1 theorem and open block-pivot question."
+    },
+    {
+      "pr": 4785,
+      "scientific_head": "1c9996b87d497a1690630302a0ac65748affbf16",
+      "use": "Equal scalar-block dimension theorem and open unequal-block question."
+    }
+  ],
+  "overlap_before_submission": {
+    "canonical_main": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba",
+    "coverage": {
+      "local": {
+        "head": "81e9bd69e4a5b00ba9c713a1620e36d576d5522e",
+        "records": 6826,
+        "head_records": 6824,
+        "complete_head_inventory": true,
+        "unsearched_head_paths": []
+      },
+      "open_prs": {
+        "fetched_at": "2026-10-23T10:08:14.848528+00:00",
+        "complete_pagination": true,
+        "records": 311
+      },
+      "discussions": {
+        "fetched_at": "2026-10-23T10:09:18.185089+00:00",
+        "complete_pagination": true,
+        "records": 4281
+      }
+    },
+    "finding": "No same-scope public claim or result found. Current priorities, task catalogue, selected result and cited predecessor files are unchanged between the pinned base and refreshed main. New main research packages do not address this prescribed-pivot minimum. Targeted all-state Schur PR search still identifies the same scalar/identity predecessors.",
+    "own_recent_claims_excluded": [
+      4999,
+      5006,
+      5030,
+      5086,
+      5094,
+      5100,
+      5127
+    ],
+    "limits": "Complete pagination of the recorded open-PR and Discussion snapshots, with targeted all-state PR search and changed-main inspection. Not a certificate covering unpublished work or arbitrary PR diffs."
+  }
+}
diff --git a/research/arbitrary-pivot-schur-minimum/VERIFY.json b/research/arbitrary-pivot-schur-minimum/VERIFY.json
new file mode 100644
index 0000000000..741c22cd46
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/VERIFY.json
@@ -0,0 +1,59 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact all-field constructions on 1,386 finite cases, explicit noncommuting examples, ordered identities, attaining dimensions, singular-pivot and deficient-map controls, and byte-identical receipt regeneration."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact all-field constructions on 1,386 finite cases, explicit noncommuting examples, ordered identities, attaining dimensions, singular-pivot and deficient-map controls, and byte-identical receipt regeneration. Optimized replay: no Python assertions required."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/binary_check.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent bitset replay of all 576 ordered binary triples, full matrix equations and ranks, exact coverage and seven rejection controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/binary_check.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent bitset replay of all 576 ordered binary triples, full matrix equations and ranks, exact coverage and seven rejection controls. Optimized replay: no Python assertions required."
+    }
+  ]
+}
diff --git a/research/arbitrary-pivot-schur-minimum/binary_check.py b/research/arbitrary-pivot-schur-minimum/binary_check.py
new file mode 100644
index 0000000000..d4c5734dd6
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/binary_check.py
@@ -0,0 +1,383 @@
+#!/usr/bin/env python3
+"""Independent exhaustive GF(2) checker for the d=2 arbitrary-pivot fixtures.
+
+Krzysztof Wojt, substantial OpenAI Codex and bounded Luna assistance. Apache-2.0.
+This deliberately uses only raw-matrix arithmetic and the Python standard
+library. Matrix rows are represented as integers, with bit j storing column j.
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import sys
+from pathlib import Path
+from typing import Any, Callable
+
+
+D = 2
+MAX_DIMENSION = 16
+MAX_FILE_BYTES = 2 * 1024 * 1024
+DEFAULT_FIXTURES = Path(__file__).with_name("FIXTURES.json")
+
+
+class CheckError(Exception):
+    """Raised when an input or mathematical check fails."""
+
+
+def fail(message: str) -> None:
+    raise CheckError(message)
+
+
+def require(condition: bool, message: str) -> None:
+    if not condition:
+        fail(message)
+
+
+def mask(width: int) -> int:
+    return (1 << width) - 1
+
+
+def matrix_from_json(value: Any, label: str, dimension: int | None = None) -> tuple[int, ...]:
+    require(type(value) is list, f"{label}: expected a list of rows")
+    size = len(value)
+    require(0 < size <= MAX_DIMENSION, f"{label}: dimension must be in 1..{MAX_DIMENSION}")
+    if dimension is not None:
+        require(size == dimension, f"{label}: expected {dimension} rows, got {size}")
+
+    rows: list[int] = []
+    for row_index, row in enumerate(value):
+        require(type(row) is list, f"{label}[{row_index}]: expected a list")
+        require(len(row) == size, f"{label}[{row_index}]: expected {size} entries")
+        bits = 0
+        for column, entry in enumerate(row):
+            require(type(entry) is int and entry in (0, 1),
+                    f"{label}[{row_index}][{column}]: expected integer bit 0 or 1")
+            bits |= entry << column
+        rows.append(bits)
+    return tuple(rows)
+
+
+def matmul(left: tuple[int, ...], right: tuple[int, ...],
+           output_columns: int) -> tuple[int, ...]:
+    """Multiply bitset-row matrices over GF(2), with explicit output width."""
+    require(len(right) > 0, "matrix product: empty inner dimension")
+    require(0 < output_columns <= MAX_DIMENSION,
+            "matrix product: output width is outside the bounded domain")
+    inner_mask = mask(len(right))
+    out_mask = mask(output_columns)
+    require(all((row & ~out_mask) == 0 for row in right),
+            "matrix product: right operand row exceeds output width")
+    require(all((row & ~inner_mask) == 0 for row in left),
+            "matrix product: left operand row exceeds inner width")
+    output: list[int] = []
+    for row in left:
+        result = 0
+        remaining = row
+        while remaining:
+            bit = remaining & -remaining
+            result ^= right[bit.bit_length() - 1]
+            remaining ^= bit
+        output.append(result & out_mask)
+    return tuple(output)
+
+
+def xor(left: tuple[int, ...], right: tuple[int, ...]) -> tuple[int, ...]:
+    require(len(left) == len(right), "matrix xor: row-count mismatch")
+    return tuple(a ^ b for a, b in zip(left, right))
+
+
+def rank(rows: tuple[int, ...], columns: int) -> int:
+    work = list(rows)
+    pivot_row = 0
+    for column in range(columns):
+        pivot = next((i for i in range(pivot_row, len(work))
+                      if (work[i] >> column) & 1), None)
+        if pivot is None:
+            continue
+        work[pivot_row], work[pivot] = work[pivot], work[pivot_row]
+        for i in range(pivot_row + 1, len(work)):
+            if (work[i] >> column) & 1:
+                work[i] ^= work[pivot_row]
+        pivot_row += 1
+        if pivot_row == len(work):
+            break
+    return pivot_row
+
+
+def inverse(rows: tuple[int, ...], dimension: int, label: str) -> tuple[int, ...]:
+    require(len(rows) == dimension, f"{label}: inverse requires a square matrix")
+    augmented = [rows[i] | (1 << (dimension + i)) for i in range(dimension)]
+    pivot_row = 0
+    for column in range(dimension):
+        pivot = next((i for i in range(pivot_row, dimension)
+                      if (augmented[i] >> column) & 1), None)
+        if pivot is None:
+            fail(f"{label}: singular pivot")
+        augmented[pivot_row], augmented[pivot] = augmented[pivot], augmented[pivot_row]
+        for i in range(dimension):
+            if i != pivot_row and ((augmented[i] >> column) & 1):
+                augmented[i] ^= augmented[pivot_row]
+        pivot_row += 1
+    right_mask = mask(dimension) << dimension
+    return tuple((row & right_mask) >> dimension for row in augmented)
+
+
+def submatrix(rows: tuple[int, ...], row_start: int, column_start: int,
+              row_count: int, column_count: int) -> tuple[int, ...]:
+    column_mask = mask(column_count) << column_start
+    return tuple((rows[i] & column_mask) >> column_start
+                 for i in range(row_start, row_start + row_count))
+
+
+def matrix_key(rows: tuple[int, ...]) -> tuple[int, ...]:
+    return rows
+
+
+def parse_case(value: Any, index: int) -> dict[str, Any]:
+    label = f"fixtures[{index}]"
+    require(type(value) is dict, f"{label}: expected an object")
+    expected_fields = {"A", "B", "H", "P", "Q"}
+    require(set(value) == expected_fields, f"{label}: expected exactly keys {sorted(expected_fields)}")
+    parsed: dict[str, Any] = {name: matrix_from_json(value[name], f"{label}.{name}", D)
+                              for name in ("A", "B", "H")}
+    parsed["P"] = matrix_from_json(value["P"], f"{label}.P")
+    parsed["Q"] = matrix_from_json(value["Q"], f"{label}.Q")
+    n = len(parsed["P"])
+    require(n > D, f"{label}: ambient dimension {n} must exceed d={D}")
+    require(len(parsed["Q"]) == n, f"{label}: P and Q dimensions differ")
+    parsed["n"] = n
+    parsed["label"] = label
+    return parsed
+
+
+def case_key(case: dict[str, Any]) -> tuple[tuple[int, ...], ...]:
+    return tuple(matrix_key(case[name]) for name in ("A", "B", "H"))
+
+
+def exact_case_key(value: Any, index: int) -> tuple[tuple[int, ...], ...]:
+    return case_key(parse_case(value, index))
+
+
+def check_reported_dimension(n: int, minimum: int, label: str) -> None:
+    require(n == minimum, f"{label}: ambient dimension {n} does not equal formula value {minimum}")
+
+
+def check_case(case: dict[str, Any]) -> dict[str, int | bool]:
+    label = case["label"]
+    n = case["n"]
+    m = n - D
+    A, B, H = case["A"], case["B"], case["H"]
+    P, Q = case["P"], case["Q"]
+
+    A_inv = inverse(A, D, f"{label}.A")
+    B_inv = inverse(B, D, f"{label}.B")
+
+    require(matmul(P, P, n) == P, f"{label}: P is not idempotent")
+    require(matmul(Q, Q, n) == Q, f"{label}: Q is not idempotent")
+    PQ = matmul(P, Q, n)
+    QP = matmul(Q, P, n)
+    require(PQ == QP, f"{label}: P and Q do not commute")
+    require(submatrix(P, 0, 0, D, D) == A, f"{label}: leading block of P differs from A")
+    require(submatrix(Q, 0, 0, D, D) == B, f"{label}: leading block of Q differs from B")
+    require(submatrix(PQ, 0, 0, D, D) == H,
+            f"{label}: leading block of PQ differs from H")
+
+    R = submatrix(P, 0, D, D, m)
+    C = submatrix(P, D, 0, m, D)
+    D_block = submatrix(P, D, D, m, m)
+    L = submatrix(Q, 0, D, D, m)
+    E = submatrix(Q, D, 0, m, D)
+    F = submatrix(Q, D, D, m, m)
+    S = xor(D_block, matmul(matmul(C, A_inv, D), R, m))
+    Z = xor(F, matmul(matmul(E, B_inv, D), L, m))
+    rank_S = rank(S, m)
+    rank_Z = rank(Z, m)
+    actual_rank_P = rank(P, n)
+    actual_rank_Q = rank(Q, n)
+    require(actual_rank_P == D + rank_S,
+            f"{label}: rank(P)={actual_rank_P}, Schur elimination gives {D + rank_S}")
+    require(actual_rank_Q == D + rank_Z,
+            f"{label}: rank(Q)={actual_rank_Q}, Schur elimination gives {D + rank_Z}")
+    schur_commutator = xor(matmul(S, Z, m), matmul(Z, S, m))
+    commutator_rank = rank(schur_commutator, m)
+    require(commutator_rank == 2 * D,
+            f"{label}: Schur-complement commutator rank {commutator_rank}, expected {2 * D}")
+
+    null_AH = D - rank(xor(A, H), D)
+    null_BH = D - rank(xor(B, H), D)
+    null_H = D - rank(H, D)
+    expected_rank_P = 2 * D + null_AH + null_H
+    expected_rank_Q = 2 * D + null_BH + null_H
+    require(actual_rank_P == expected_rank_P,
+            f"{label}: rank(P)={actual_rank_P}, formula gives {expected_rank_P}")
+    require(actual_rank_Q == expected_rank_Q,
+            f"{label}: rank(Q)={actual_rank_Q}, formula gives {expected_rank_Q}")
+
+    identity = tuple(1 << i for i in range(D))
+    # In characteristic two, I-A-B+H is I xor A xor B xor H.
+    dimension_term = rank(xor(xor(xor(identity, A), B), H), D)
+    minimum = 3 * D + dimension_term + null_AH + null_BH + null_H
+    check_reported_dimension(n, minimum, label)
+
+    AB, BA = matmul(A, B, D), matmul(B, A, D)
+    AH, HA = matmul(A, H, D), matmul(H, A, D)
+    BH, HB = matmul(B, H, D), matmul(H, B, D)
+    noncommuting_ab = AB != BA
+    all_three_noncommuting = noncommuting_ab and AH != HA and BH != HB
+    return {
+        "minimum": minimum,
+        "commutator_rank": commutator_rank,
+        "noncommuting_ab": noncommuting_ab,
+        "all_three_noncommuting": all_three_noncommuting,
+    }
+
+
+def all_2x2_matrices() -> list[tuple[int, ...]]:
+    return [tuple((code >> (2 * row)) & 3 for row in range(D)) for code in range(1 << 4)]
+
+
+def expected_triples() -> set[tuple[tuple[int, ...], ...]]:
+    matrices = all_2x2_matrices()
+    invertible = [matrix for matrix in matrices if rank(matrix, D) == D]
+    require(len(invertible) == 6, "internal error: GL(2,2) enumeration has wrong size")
+    return {(A, B, H) for A in invertible for B in invertible for H in matrices}
+
+
+def check_exact_coverage(keys: list[tuple[tuple[int, ...], ...]]) -> None:
+    expected = expected_triples()
+    seen: set[tuple[tuple[int, ...], ...]] = set()
+    for index, key in enumerate(keys):
+        require(key in expected, f"coverage: unexpected triple at index {index}")
+        require(key not in seen, f"coverage: duplicate triple at index {index}")
+        seen.add(key)
+    missing = expected - seen
+    require(not missing, f"coverage: {len(missing)} expected triple(s) missing")
+    require(len(seen) == 576, f"coverage: expected 576 distinct triples, got {len(seen)}")
+
+
+def reject_duplicate_object_keys(pairs: list[tuple[str, Any]]) -> dict[str, Any]:
+    result: dict[str, Any] = {}
+    for key, value in pairs:
+        if key in result:
+            fail(f"JSON object has duplicate key {key!r}")
+        result[key] = value
+    return result
+
+
+def reject_nonfinite_constant(value: str) -> None:
+    fail(f"JSON constant {value!r} is not permitted")
+
+
+def load_document(path: Path) -> dict[str, Any]:
+    try:
+        size = path.stat().st_size
+    except OSError as error:
+        fail(f"cannot stat fixture file {path}: {error}")
+    require(size <= MAX_FILE_BYTES, f"fixture file exceeds {MAX_FILE_BYTES} bytes")
+    try:
+        with path.open("rb") as handle:
+            raw = handle.read(MAX_FILE_BYTES + 1)
+    except OSError as error:
+        fail(f"cannot read fixture file {path}: {error}")
+    require(len(raw) <= MAX_FILE_BYTES, f"fixture file exceeds {MAX_FILE_BYTES} bytes")
+    try:
+        source = raw.decode("utf-8")
+        document = json.loads(source, object_pairs_hook=reject_duplicate_object_keys,
+                              parse_constant=reject_nonfinite_constant)
+    except (UnicodeDecodeError, json.JSONDecodeError, RecursionError) as error:
+        fail(f"invalid UTF-8 JSON: {error}")
+    require(type(document) is dict, "document: expected a JSON object")
+    return document
+
+
+def validate_document(document: Any) -> tuple[int, int, int]:
+    require(type(document) is dict, "document: expected a JSON object")
+    expected_fields = {"schema_version", "field", "d", "fixtures"}
+    require(set(document) == expected_fields,
+            f"document: expected exactly keys {sorted(expected_fields)}")
+    require(type(document["schema_version"]) is int and document["schema_version"] == 1,
+            "document.schema_version must be integer 1")
+    require(type(document["field"]) is int and document["field"] == 2,
+            "document.field must be integer 2 for GF(2)")
+    require(type(document["d"]) is int and document["d"] == D,
+            f"document.d must be integer {D}")
+    fixtures = document["fixtures"]
+    require(type(fixtures) is list, "document.fixtures must be a list")
+    require(len(fixtures) == 576, f"document.fixtures must contain 576 entries, got {len(fixtures)}")
+
+    keys: list[tuple[tuple[int, ...], ...]] = []
+    noncommuting_ab = 0
+    all_three_noncommuting = 0
+    for index, value in enumerate(fixtures):
+        case = parse_case(value, index)
+        keys.append(case_key(case))
+        result = check_case(case)
+        noncommuting_ab += int(result["noncommuting_ab"])
+        all_three_noncommuting += int(result["all_three_noncommuting"])
+    check_exact_coverage(keys)
+    return len(fixtures), noncommuting_ab, all_three_noncommuting
+
+
+def expect_rejected(label: str, operation: Callable[[], Any]) -> None:
+    try:
+        operation()
+    except CheckError:
+        return
+    fail(f"rejection control accepted invalid input: {label}")
+
+
+def run_rejection_controls(document: dict[str, Any]) -> int:
+    first = parse_case(document["fixtures"][0], 0)
+    first_raw = document["fixtures"][0]
+
+    mutated_p = json.loads(json.dumps(first_raw))
+    mutated_p["P"][0][0] ^= 1
+    expect_rejected("mutated P", lambda: check_case(parse_case(mutated_p, 0)))
+
+    altered_h = json.loads(json.dumps(first_raw))
+    altered_h["H"][0][0] ^= 1
+    expect_rejected("altered H", lambda: check_case(parse_case(altered_h, 0)))
+
+    expect_rejected("falsely reduced minimum",
+                     lambda: check_reported_dimension(first["n"] - 1,
+                                                      check_case(first)["minimum"],
+                                                      "reduced-minimum control"))
+
+    truncated = json.loads(json.dumps(first_raw))
+    for name in ("P", "Q"):
+        truncated[name] = [row[:-1] for row in truncated[name][:-1]]
+    expect_rejected("truncated P,Q", lambda: check_case(parse_case(truncated, 0)))
+
+    singular = json.loads(json.dumps(first_raw))
+    singular["A"] = [[0, 0], [0, 0]]
+    expect_rejected("singular A pivot", lambda: check_case(parse_case(singular, 0)))
+
+    keys = [exact_case_key(value, index) for index, value in enumerate(document["fixtures"])]
+    duplicate_and_missing = list(keys)
+    duplicate_and_missing[-1] = duplicate_and_missing[0]
+    expect_rejected("duplicate/missing triple", lambda: check_exact_coverage(duplicate_and_missing))
+    expect_rejected("missing triple", lambda: check_exact_coverage(keys[:-1]))
+    return 7
+
+
+def main(argv: list[str] | None = None) -> int:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--fixtures", type=Path, default=DEFAULT_FIXTURES,
+                        help=f"fixture JSON path (default: {DEFAULT_FIXTURES})")
+    arguments = parser.parse_args(argv)
+    try:
+        document = load_document(arguments.fixtures)
+        count, noncommuting_ab, all_three_noncommuting = validate_document(document)
+        controls = run_rejection_controls(document)
+    except CheckError as error:
+        print(f"FAIL_BINARY_ARBITRARY_PIVOT: {error}", file=sys.stderr)
+        return 1
+    print("PASS_BINARY_ARBITRARY_PIVOT "
+          f"fixtures={count} noncommuting_AB={noncommuting_ab} "
+          f"pairwise_noncommuting_ABH={all_three_noncommuting} controls={controls}")
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/research/arbitrary-pivot-schur-minimum/verify.py b/research/arbitrary-pivot-schur-minimum/verify.py
new file mode 100644
index 0000000000..5265bdee80
--- /dev/null
+++ b/research/arbitrary-pivot-schur-minimum/verify.py
@@ -0,0 +1,428 @@
+#!/usr/bin/env python3
+"""Exact new-boundary constructions; no predecessor code is imported.
+
+Krzysztof Wojt, substantial OpenAI Codex assistance. Apache-2.0.
+The proof is in PROOF.md. This finite replay corroborates it, not proves it.
+"""
+from __future__ import annotations
+
+import argparse
+import hashlib
+import itertools
+import json
+from dataclasses import dataclass
+from fractions import Fraction
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+CAP = 48
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def norm(value, prime):
+    return value % prime if prime else Fraction(value)
+
+
+def reciprocal(value, prime):
+    require(value != 0, "zero denominator")
+    return pow(value, -1, prime) if prime else 1 / Fraction(value)
+
+
+@dataclass(frozen=True)
+class Mat:
+    rows: tuple
+    nc: int
+
+    def __post_init__(self):
+        require(0 <= len(self.rows) <= CAP and 0 <= self.nc <= 2 * CAP,
+                "matrix capacity")
+        require(all(len(row) == self.nc for row in self.rows), "ragged matrix")
+
+    @property
+    def nr(self):
+        return len(self.rows)
+
+
+def mat(rows, prime, nc=None):
+    data = tuple(tuple(norm(x, prime) for x in row) for row in rows)
+    return Mat(data, len(data[0]) if data else (0 if nc is None else nc))
+
+
+def zero(nr, nc):
+    return Mat(tuple((0,) * nc for _ in range(nr)), nc)
+
+
+def eye(n):
+    return Mat(tuple(tuple(int(i == j) for j in range(n)) for i in range(n)), n)
+
+
+def add(a, b, prime, sign=1):
+    require((a.nr, a.nc) == (b.nr, b.nc), "addition shape")
+    return mat(([x + sign * y for x, y in zip(ra, rb)]
+                for ra, rb in zip(a.rows, b.rows)), prime, a.nc)
+
+
+def mul(a, b, prime):
+    require(a.nc == b.nr, "product shape")
+    out = [[0] * b.nc for _ in range(a.nr)]
+    for i, row in enumerate(a.rows):
+        for k, x in enumerate(row):
+            if x:
+                for j, y in enumerate(b.rows[k]):
+                    out[i][j] += x * y
+    return mat(out, prime, b.nc)
+
+
+def chain(prime, *items):
+    result = items[0]
+    for item in items[1:]:
+        result = mul(result, item, prime)
+    return result
+
+
+def transpose(a):
+    return Mat(tuple(tuple(a.rows[i][j] for i in range(a.nr))
+                     for j in range(a.nc)), a.nr)
+
+
+def hcat(*items):
+    require(bool(items) and len({a.nr for a in items}) == 1, "horizontal shape")
+    return Mat(tuple(tuple(x for a in items for x in a.rows[i])
+                     for i in range(items[0].nr)), sum(a.nc for a in items))
+
+
+def vcat(*items):
+    require(bool(items) and len({a.nc for a in items}) == 1, "vertical shape")
+    return Mat(tuple(row for a in items for row in a.rows), items[0].nc)
+
+
+def block(a, row_indices, col_indices):
+    rr, cc = tuple(row_indices), tuple(col_indices)
+    return Mat(tuple(tuple(a.rows[i][j] for j in cc) for i in rr), len(cc))
+
+
+def rref(a, prime):
+    rows = [list(row) for row in a.rows]
+    pivots = []
+    for col in range(a.nc):
+        pos = next((i for i in range(len(pivots), a.nr) if rows[i][col]), None)
+        if pos is None:
+            continue
+        lead = len(pivots)
+        rows[lead], rows[pos] = rows[pos], rows[lead]
+        factor = reciprocal(rows[lead][col], prime)
+        rows[lead] = [norm(x * factor, prime) for x in rows[lead]]
+        for i in range(a.nr):
+            if i != lead and rows[i][col]:
+                factor = rows[i][col]
+                rows[i] = [norm(x - factor * y, prime)
+                           for x, y in zip(rows[i], rows[lead])]
+        pivots.append(col)
+        if len(pivots) == a.nr:
+            break
+    return mat(rows, prime, a.nc), tuple(pivots)
+
+
+def rank(a, prime):
+    return len(rref(a, prime)[1])
+
+
+def inverse(a, prime):
+    require(a.nr == a.nc, "inverse shape")
+    reduced, pivots = rref(hcat(a, eye(a.nr)), prime)
+    require(pivots[:a.nr] == tuple(range(a.nr)), "singular pivot")
+    return block(reduced, range(a.nr), range(a.nr, 2 * a.nr))
+
+
+def kernel(a, prime):
+    reduced, pivots = rref(a, prime)
+    free = [j for j in range(a.nc) if j not in pivots]
+    columns = []
+    for col in free:
+        vector = [0] * a.nc
+        vector[col] = 1
+        for i, pivot in enumerate(pivots):
+            vector[pivot] = norm(-reduced.rows[i][col], prime)
+        columns.append(vector)
+    return transpose(mat(columns, prime, a.nc))
+
+
+def rank_factor(t, prime):
+    pivots = rref(t, prime)[1]
+    x = block(t, range(t.nr), pivots)
+    if not pivots:
+        return x, zero(0, t.nc)
+    row_basis = rref(transpose(x), prime)[1]
+    square = block(x, row_basis, range(x.nc))
+    y = mul(inverse(square, prime), block(t, row_basis, range(t.nc)), prime)
+    require(mul(x, y, prime) == t, "rank factor product")
+    return x, y
+
+
+def full_factor(t, prime):
+    require(t.nr == t.nc, "full factor shape")
+    d = t.nr
+    x = t
+    complement = []
+    current_rank = rank(t, prime)
+    for j in range(d):
+        col = block(eye(d), range(d), (j,))
+        candidate = hcat(x, col)
+        new_rank = rank(candidate, prime)
+        if new_rank > current_rank:
+            complement.append(j)
+            x, current_rank = candidate, new_rank
+    y = vcat(eye(d), zero(len(complement), d))
+    require(current_rank == d and mul(x, y, prime) == t, "full factor product")
+    return x, y
+
+
+def products(a, b, h, prime):
+    d = a.nr
+    require(d >= 1 and all(t.nr == d and t.nc == d for t in (a, b, h)),
+            "prescribed block shape")
+    inverse(a, prime)
+    inverse(b, prime)
+    return (add(add(add(eye(d), a, prime, -1), b, prime, -1), h, prime),
+            add(a, h, prime, -1), add(b, h, prime, -1), h)
+
+
+def theorem_data(a, b, h, prime):
+    ts = products(a, b, h, prime)
+    d = a.nr
+    rr = [rank(ts[0], prime)] + [2 * d - rank(t, prime) for t in ts[1:]]
+    return {"sectors": rr, "n": sum(rr), "rank_p": rr[1] + rr[3],
+            "rank_q": rr[2] + rr[3]}
+
+
+def diagonal_on_rows(a, mask, prime):
+    return mat(([x * mask[i] for x in row] for i, row in enumerate(a.rows)),
+               prime, a.nc)
+
+
+def realize(a, b, h, prime, missing=None):
+    ts = products(a, b, h, prime)
+    pairs = [rank_factor(ts[0], prime)] + [full_factor(t, prime) for t in ts[1:]]
+    if missing is not None:
+        sector, which = missing
+        x, y = pairs[sector]
+        require(ts[sector] == zero(a.nr, a.nr), "control requires zero product")
+        if which == "Y":
+            data = [list(row) for row in y.rows]
+            data[0][0] = 0
+            y = mat(data, prime, y.nc)
+        else:
+            data = [list(row) for row in x.rows]
+            data[0][a.nr] = 0
+            x = mat(data, prime, x.nc)
+        pairs[sector] = x, y
+    xs, ys = tuple(pair[0] for pair in pairs), tuple(pair[1] for pair in pairs)
+    projection, inclusion = hcat(*xs), vcat(*ys)
+    require(mul(projection, inclusion, prime) == eye(a.nr), "split projection")
+    change = hcat(inclusion, kernel(projection, prime))
+    undo = inverse(change, prime)
+    sizes = [x.nc for x in xs]
+    pmask = [v for size, v in zip(sizes, (0, 1, 0, 1)) for _ in range(size)]
+    qmask = [v for size, v in zip(sizes, (0, 0, 1, 1)) for _ in range(size)]
+    p = mul(undo, diagonal_on_rows(change, pmask, prime), prime)
+    q = mul(undo, diagonal_on_rows(change, qmask, prime), prime)
+    return {"P": p, "Q": q, "X": xs, "Y": ys, "sectors": sizes}
+
+
+def commutator(a, b, prime):
+    return add(mul(a, b, prime), mul(b, a, prime), prime, -1)
+
+
+def check_pair(a, b, h, prime, witness, sharp=True):
+    p, q = witness["P"], witness["Q"]
+    d, n = a.nr, p.nr
+    rr, tail = range(d), range(d, n)
+    require(p.nc == n and (q.nr, q.nc) == (n, n), "ambient shapes")
+    pq = mul(p, q, prime)
+    require(mul(p, p, prime) == p and mul(q, q, prime) == q, "idempotence")
+    require(pq == mul(q, p, prime), "ambient commutation")
+    require(block(p, rr, rr) == a and block(q, rr, rr) == b, "prescribed pivots")
+    require(block(pq, rr, rr) == h, "prescribed product")
+    c, r = block(p, tail, rr), block(p, rr, tail)
+    e, ell = block(q, tail, rr), block(q, rr, tail)
+    ai, bi = inverse(a, prime), inverse(b, prime)
+    s = add(block(p, tail, tail), chain(prime, c, ai, r), prime, -1)
+    z = add(block(q, tail, tail), chain(prime, e, bi, ell), prime, -1)
+    require(mul(s, s, prime) == s and mul(z, z, prime) == z, "Schur idempotence")
+    k = commutator(s, z, prime)
+    u = add(mul(c, ai, prime), mul(e, bi, prime), prime, -1)
+    v = add(mul(ai, r, prime), mul(bi, ell, prime), prime, -1)
+    w, t = block(pq, tail, rr), block(pq, rr, tail)
+    x = add(w, chain(prime, e, bi, h), prime, -1)
+    y = add(t, chain(prime, h, bi, ell), prime, -1)
+    require(k == add(mul(x, v, prime), mul(u, y, prime), prime, -1), "ordered factors")
+    six = all(rank(t, prime) == d for t in witness["X"][1:] + witness["Y"][1:])
+    rk = rank(k, prime)
+    require((rk == 2 * d) == six, "six-map criterion")
+    require(rank(s, prime) == rank(p, prime) - d, "P rank drop")
+    require(rank(z, prime) == rank(q, prime) - d, "Q rank drop")
+    if sharp:
+        expected = theorem_data(a, b, h, prime)
+        require(rk == 2 * d, "commutator not sharp")
+        require(n == expected["n"] and witness["sectors"] == expected["sectors"],
+                "dimension minimum")
+        require(rank(p, prime) == expected["rank_p"] and
+                rank(q, prime) == expected["rank_q"], "input rank minima")
+    wrong_x = add(w, chain(prime, e, h, bi), prime, -1)
+    wrong_y = add(t, chain(prime, bi, h, ell), prime, -1)
+    errors = (k != add(mul(wrong_x, v, prime), mul(u, y, prime), prime, -1),
+              k != add(mul(x, v, prime), mul(u, wrong_y, prime), prime, -1))
+    return rk, errors
+
+
+def small_matrices(prime, d):
+    for entries in itertools.product(range(prime), repeat=d * d):
+        yield mat([entries[i * d:(i + 1) * d] for i in range(d)], prime)
+
+
+def encode(a):
+    return [list(row) for row in a.rows]
+
+
+def record_case(a, b, h, prime, counts, binary=None):
+    w = realize(a, b, h, prime)
+    _, errors = check_pair(a, b, h, prime, w)
+    key = "Q" if prime == 0 else f"F{prime}"
+    counts[key] = counts.get(key, 0) + 1
+    counts["ordered_X_mutation_detected"] += int(errors[0])
+    counts["ordered_Y_mutation_detected"] += int(errors[1])
+    if binary is not None:
+        binary.append({"A": encode(a), "B": encode(b), "H": encode(h),
+                       "P": encode(w["P"]), "Q": encode(w["Q"])})
+    return w
+
+
+def finite_cases(counts):
+    binary = []
+    matrices = list(small_matrices(2, 2))
+    invertibles = [a for a in matrices if rank(a, 2) == 2]
+    require(len(invertibles) == 6, "GL2 binary census")
+    for a, b, h in itertools.product(invertibles, invertibles, matrices):
+        record_case(a, b, h, 2, counts, binary)
+    ternary = list(small_matrices(3, 2))
+    gl3 = [a for a in ternary if rank(a, 3) == 2]
+    require(len(gl3) == 48, "GL2 ternary census")
+    pairs = [(a, b) for a, b in itertools.product(gl3, gl3)
+             if commutator(a, b, 3) != zero(2, 2)][:8]
+    require(len(pairs) == 8, "ternary pair coverage")
+    for (a, b), h in itertools.product(pairs, ternary):
+        record_case(a, b, h, 3, counts)
+    return {"schema_version": 1, "field": 2, "d": 2, "fixtures": binary}
+
+
+def wider_cases(counts):
+    for prime in (2, 3, 5, 7, 0):
+        for d in (2, 3, 4):
+            for diagonal in (1, 2):
+                if prime and diagonal % prime == 0:
+                    continue
+                a = mat([[diagonal if i == j else int(j == i + 1)
+                          for j in range(d)] for i in range(d)], prime)
+                b = transpose(a)
+                hs = (zero(d, d), eye(d), a, b, mul(a, b, prime),
+                      add(add(a, b, prime), eye(d), prime, -1))
+                for h in hs:
+                    record_case(a, b, h, prime, counts)
+
+
+def rejection_controls():
+    a = mat([[1, 1], [0, 1]], 2)
+    b = transpose(a)
+    controls = []
+    for sector, h in ((1, a), (2, b), (3, zero(2, 2))):
+        for which in ("X", "Y"):
+            w = realize(a, b, h, 2, (sector, which))
+            rk, _ = check_pair(a, b, h, 2, w, sharp=False)
+            require(rk < 4, "missing active map accepted")
+            controls.append(f"sector{sector}_missing_{which}")
+    for pivot in ("A", "B"):
+        aa, bb = (zero(2, 2), b) if pivot == "A" else (a, zero(2, 2))
+        try:
+            realize(aa, bb, eye(2), 2)
+        except ValueError as exc:
+            require(str(exc) == "singular pivot", "unexpected singular-pivot rejection")
+            controls.append(f"singular_{pivot}")
+        else:
+            raise ValueError("singular pivot accepted")
+    return controls
+
+
+def noncommuting_example(prime):
+    a = mat([[2, 1], [0, 2]], prime)
+    b = transpose(a)
+    h = mat([[3, 1], [1, 3]], prime)
+    w = realize(a, b, h, prime)
+    check_pair(a, b, h, prime, w)
+    require(all(commutator(x, y, prime) != zero(2, 2)
+                for x, y in ((a, b), (a, h), (b, h))), "example commutes")
+    info = theorem_data(a, b, h, prime)
+    require(info == {"sectors": [0, 2, 2, 2], "n": 6, "rank_p": 4, "rank_q": 4},
+            "sharp noncommuting example")
+    items = (("A", a), ("B", b), ("H", h), ("P", w["P"]), ("Q", w["Q"]))
+    if prime:
+        matrices = {name: encode(value) for name, value in items}
+    else:
+        matrices = {name: [[str(x) for x in row] for row in value.rows]
+                    for name, value in items}
+    return {"field": prime or "Q", **info, **matrices}
+
+
+def canonical(value):
+    return (json.dumps(value, sort_keys=True, indent=2) + "\n").encode()
+
+
+def fixture_bytes(value):
+    """Keep each raw-matrix fixture on one line for reviewable, bounded receipts."""
+    header = {key: item for key, item in value.items() if key != "fixtures"}
+    prefix = json.dumps(header, sort_keys=True, indent=2).removesuffix("\n}")
+    rows = ["    " + json.dumps(item, sort_keys=True, separators=(",", ":"))
+            for item in value["fixtures"]]
+    return (prefix + ',\n  "fixtures": [\n' + ",\n".join(rows) + "\n  ]\n}\n").encode()
+
+
+def run():
+    counts = {"ordered_X_mutation_detected": 0, "ordered_Y_mutation_detected": 0}
+    fixtures = finite_cases(counts)
+    wider_cases(counts)
+    controls = rejection_controls()
+    require(counts["ordered_X_mutation_detected"] > 0 and
+            counts["ordered_Y_mutation_detected"] > 0, "no factor-order witnesses")
+    result = {"schema_version": 1, "status": "PASS_ARBITRARY_PIVOT_SCHUR_MINIMUM",
+              "counts": counts, "rejected_controls": controls,
+              "binary_fixture_count": len(fixtures["fixtures"]),
+              "binary_fixture_sha256": hashlib.sha256(fixture_bytes(fixtures)).hexdigest(),
+              "noncommuting_examples": [noncommuting_example(0), noncommuting_example(3)],
+              "scope": "Finite corroboration of PROOF.md; no physical admission or new kappa."}
+    return fixtures, result
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--write", action="store_true",
+                        help="regenerate this package's FIXTURES.json and RESULT.json")
+    args = parser.parse_args()
+    fixtures, result = run()
+    for name, value in (("FIXTURES.json", fixtures), ("RESULT.json", result)):
+        expected = fixture_bytes(value) if name == "FIXTURES.json" else canonical(value)
+        path = HERE / name
+        if args.write:
+            path.write_bytes(expected)
+        else:
+            require(path.stat().st_size <= 2 * 1024 * 1024, "receipt size cap")
+            require(path.read_bytes() == expected, f"regenerated payload differs: {name}")
+    print(json.dumps({"status": result["status"], "counts": result["counts"],
+                      "binary_fixture_count": result["binary_fixture_count"],
+                      "rejected_controls": result["rejected_controls"]}, sort_keys=True))
+
+
+if __name__ == "__main__":
+    main()