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data/dihedral_superset/dataset_dict.json

@@ -0,0 +1 @@
+{"splits": ["train", "test"]}

data/dihedral_superset/metadata.json

@@ -0,0 +1,620 @@
+{
+  "group_type": "dihedral",
+  "max_degree": 20,
+  "subgroups": [
+    {
+      "degree": 3,
+      "order": 6,
+      "name": "D3"
+    },
+    {
+      "degree": 4,
+      "order": 8,
+      "name": "D4"
+    },
+    {
+      "degree": 5,
+      "order": 10,
+      "name": "D5"
+    },
+    {
+      "degree": 6,
+      "order": 12,
+      "name": "D6"
+    },
+    {
+      "degree": 7,
+      "order": 14,
+      "name": "D7"
+    },
+    {
+      "degree": 8,
+      "order": 16,
+      "name": "D8"
+    },
+    {
+      "degree": 9,
+      "order": 18,
+      "name": "D9"
+    },
+    {
+      "degree": 10,
+      "order": 20,
+      "name": "D10"
+    },
+    {
+      "degree": 11,
+      "order": 22,
+      "name": "D11"
+    },
+    {
+      "degree": 12,
+      "order": 24,
+      "name": "D12"
+    },
+    {
+      "degree": 13,
+      "order": 26,
+      "name": "D13"
+    },
+    {
+      "degree": 14,
+      "order": 28,
+      "name": "D14"
+    },
+    {
+      "degree": 15,
+      "order": 30,
+      "name": "D15"
+    },
+    {
+      "degree": 16,
+      "order": 32,
+      "name": "D16"
+    },
+    {
+      "degree": 17,
+      "order": 34,
+      "name": "D17"
+    },
+    {
+      "degree": 18,
+      "order": 36,
+      "name": "D18"
+    },
+    {
+      "degree": 19,
+      "order": 38,
+      "name": "D19"
+    },
+    {
+      "degree": 20,
+      "order": 40,
+      "name": "D20"
+    }
+  ],
+  "mappings": {
+    "3": {
+      "order": 6,
+      "name": "D3",
+      "id_to_perm": {
+        "0": "[0, 1, 2]",
+        "1": "[1, 2, 0]",
+        "2": "[2, 1, 0]",
+        "3": "[0, 2, 1]",
+        "4": "[1, 0, 2]",
+        "5": "[2, 0, 1]"
+      }
+    },
+    "4": {
+      "order": 8,
+      "name": "D4",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3]",
+        "1": "[1, 2, 3, 0]",
+        "2": "[2, 3, 0, 1]",
+        "3": "[3, 2, 1, 0]",
+        "4": "[0, 3, 2, 1]",
+        "5": "[1, 0, 3, 2]",
+        "6": "[2, 1, 0, 3]",
+        "7": "[3, 0, 1, 2]"
+      }
+    },
+    "5": {
+      "order": 10,
+      "name": "D5",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4]",
+        "1": "[1, 2, 3, 4, 0]",
+        "2": "[2, 3, 4, 0, 1]",
+        "3": "[3, 2, 1, 0, 4]",
+        "4": "[4, 3, 2, 1, 0]",
+        "5": "[0, 4, 3, 2, 1]",
+        "6": "[1, 0, 4, 3, 2]",
+        "7": "[2, 1, 0, 4, 3]",
+        "8": "[3, 4, 0, 1, 2]",
+        "9": "[4, 0, 1, 2, 3]"
+      }
+    },
+    "6": {
+      "order": 12,
+      "name": "D6",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5]",
+        "1": "[1, 2, 3, 4, 5, 0]",
+        "2": "[2, 3, 4, 5, 0, 1]",
+        "3": "[3, 4, 5, 0, 1, 2]",
+        "4": "[4, 3, 2, 1, 0, 5]",
+        "5": "[5, 4, 3, 2, 1, 0]",
+        "6": "[0, 5, 4, 3, 2, 1]",
+        "7": "[1, 0, 5, 4, 3, 2]",
+        "8": "[2, 1, 0, 5, 4, 3]",
+        "9": "[3, 2, 1, 0, 5, 4]",
+        "10": "[4, 5, 0, 1, 2, 3]",
+        "11": "[5, 0, 1, 2, 3, 4]"
+      }
+    },
+    "7": {
+      "order": 14,
+      "name": "D7",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6]",
+        "1": "[1, 2, 3, 4, 5, 6, 0]",
+        "2": "[2, 3, 4, 5, 6, 0, 1]",
+        "3": "[3, 4, 5, 6, 0, 1, 2]",
+        "4": "[4, 3, 2, 1, 0, 6, 5]",
+        "5": "[5, 4, 3, 2, 1, 0, 6]",
+        "6": "[6, 5, 4, 3, 2, 1, 0]",
+        "7": "[0, 6, 5, 4, 3, 2, 1]",
+        "8": "[1, 0, 6, 5, 4, 3, 2]",
+        "9": "[2, 1, 0, 6, 5, 4, 3]",
+        "10": "[3, 2, 1, 0, 6, 5, 4]",
+        "11": "[4, 5, 6, 0, 1, 2, 3]",
+        "12": "[5, 6, 0, 1, 2, 3, 4]",
+        "13": "[6, 0, 1, 2, 3, 4, 5]"
+      }
+    },
+    "8": {
+      "order": 16,
+      "name": "D8",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 0, 1, 2, 3]",
+        "5": "[5, 4, 3, 2, 1, 0, 7, 6]",
+        "6": "[6, 5, 4, 3, 2, 1, 0, 7]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0]",
+        "8": "[0, 7, 6, 5, 4, 3, 2, 1]",
+        "9": "[1, 0, 7, 6, 5, 4, 3, 2]",
+        "10": "[2, 1, 0, 7, 6, 5, 4, 3]",
+        "11": "[3, 2, 1, 0, 7, 6, 5, 4]",
+        "12": "[4, 3, 2, 1, 0, 7, 6, 5]",
+        "13": "[5, 6, 7, 0, 1, 2, 3, 4]",
+        "14": "[6, 7, 0, 1, 2, 3, 4, 5]",
+        "15": "[7, 0, 1, 2, 3, 4, 5, 6]"
+      }
+    },
+    "9": {
+      "order": 18,
+      "name": "D9",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 0, 1, 2, 3]",
+        "5": "[5, 4, 3, 2, 1, 0, 8, 7, 6]",
+        "6": "[6, 5, 4, 3, 2, 1, 0, 8, 7]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0, 8]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "9": "[0, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "10": "[1, 0, 8, 7, 6, 5, 4, 3, 2]",
+        "11": "[2, 1, 0, 8, 7, 6, 5, 4, 3]",
+        "12": "[3, 2, 1, 0, 8, 7, 6, 5, 4]",
+        "13": "[4, 3, 2, 1, 0, 8, 7, 6, 5]",
+        "14": "[5, 6, 7, 8, 0, 1, 2, 3, 4]",
+        "15": "[6, 7, 8, 0, 1, 2, 3, 4, 5]",
+        "16": "[7, 8, 0, 1, 2, 3, 4, 5, 6]",
+        "17": "[8, 0, 1, 2, 3, 4, 5, 6, 7]"
+      }
+    },
+    "10": {
+      "order": 20,
+      "name": "D10",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 0, 1, 2, 3, 4]",
+        "6": "[6, 5, 4, 3, 2, 1, 0, 9, 8, 7]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0, 9, 8]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "10": "[0, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "11": "[1, 0, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "12": "[2, 1, 0, 9, 8, 7, 6, 5, 4, 3]",
+        "13": "[3, 2, 1, 0, 9, 8, 7, 6, 5, 4]",
+        "14": "[4, 3, 2, 1, 0, 9, 8, 7, 6, 5]",
+        "15": "[5, 4, 3, 2, 1, 0, 9, 8, 7, 6]",
+        "16": "[6, 7, 8, 9, 0, 1, 2, 3, 4, 5]",
+        "17": "[7, 8, 9, 0, 1, 2, 3, 4, 5, 6]",
+        "18": "[8, 9, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "19": "[9, 0, 1, 2, 3, 4, 5, 6, 7, 8]"
+      }
+    },
+    "11": {
+      "order": 22,
+      "name": "D11",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4]",
+        "6": "[6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "11": "[0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "12": "[1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "13": "[2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "14": "[3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4]",
+        "15": "[4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5]",
+        "16": "[5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6]",
+        "17": "[6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5]",
+        "18": "[7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6]",
+        "19": "[8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "20": "[9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "21": "[10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
+      }
+    },
+    "12": {
+      "order": 24,
+      "name": "D12",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "12": "[0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "13": "[1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "14": "[2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "15": "[3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "16": "[4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5]",
+        "17": "[5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6]",
+        "18": "[6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7]",
+        "19": "[7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6]",
+        "20": "[8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "21": "[9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "22": "[10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "23": "[11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]"
+      }
+    },
+    "13": {
+      "order": 26,
+      "name": "D13",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "13": "[0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "14": "[1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "15": "[2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "16": "[3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "17": "[4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "18": "[5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6]",
+        "19": "[6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7]",
+        "20": "[7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6]",
+        "21": "[8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "22": "[9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "23": "[10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "24": "[11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "25": "[12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]"
+      }
+    },
+    "14": {
+      "order": 28,
+      "name": "D14",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "14": "[0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "15": "[1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "16": "[2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "17": "[3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "18": "[4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "19": "[5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "20": "[6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7]",
+        "21": "[7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8]",
+        "22": "[8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "23": "[9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "24": "[10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "25": "[11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "26": "[12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "27": "[13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]"
+      }
+    },
+    "15": {
+      "order": 30,
+      "name": "D15",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "15": "[0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "16": "[1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "17": "[2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "18": "[3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "19": "[4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "20": "[5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "21": "[6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "22": "[7, 6, 5, 4, 3, 2, 1, 0, 14, 13, 12, 11, 10, 9, 8]",
+        "23": "[8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "24": "[9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "25": "[10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "26": "[11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "27": "[12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "28": "[13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "29": "[14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]"
+      }
+    },
+    "16": {
+      "order": 32,
+      "name": "D16",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15]",
+        "15": "[15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "16": "[0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "17": "[1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "18": "[2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "19": "[3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "20": "[4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "21": "[5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "22": "[6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "23": "[7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8]",
+        "24": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9]",
+        "25": "[9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "26": "[10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "27": "[11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "28": "[12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "29": "[13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "30": "[14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
+        "31": "[15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]"
+      }
+    },
+    "17": {
+      "order": 34,
+      "name": "D17",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "9": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15]",
+        "15": "[15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 16]",
+        "16": "[16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "17": "[0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "18": "[1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "19": "[2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "20": "[3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "21": "[4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "22": "[5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "23": "[6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "24": "[7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9, 8]",
+        "25": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 16, 15, 14, 13, 12, 11, 10, 9]",
+        "26": "[9, 10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "27": "[10, 11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "28": "[11, 12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "29": "[12, 13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "30": "[13, 14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "31": "[14, 15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
+        "32": "[15, 16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]",
+        "33": "[16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]"
+      }
+    },
+    "18": {
+      "order": 36,
+      "name": "D18",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "9": "[9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15]",
+        "15": "[15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16]",
+        "16": "[16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17]",
+        "17": "[17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "18": "[0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "19": "[1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "20": "[2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "21": "[3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "22": "[4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "23": "[5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "24": "[6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "25": "[7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8]",
+        "26": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10, 9]",
+        "27": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 17, 16, 15, 14, 13, 12, 11, 10]",
+        "28": "[10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "29": "[11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "30": "[12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "31": "[13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "32": "[14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
+        "33": "[15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]",
+        "34": "[16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]",
+        "35": "[17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]"
+      }
+    },
+    "19": {
+      "order": 38,
+      "name": "D19",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "9": "[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "10": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15]",
+        "15": "[15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16]",
+        "16": "[16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17]",
+        "17": "[17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18]",
+        "18": "[18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "19": "[0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "20": "[1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "21": "[2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "22": "[3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "23": "[4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "24": "[5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "25": "[6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "26": "[7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8]",
+        "27": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9]",
+        "28": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 18, 17, 16, 15, 14, 13, 12, 11, 10]",
+        "29": "[10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "30": "[11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "31": "[12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "32": "[13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "33": "[14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
+        "34": "[15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]",
+        "35": "[16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]",
+        "36": "[17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]",
+        "37": "[18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]"
+      }
+    },
+    "20": {
+      "order": 40,
+      "name": "D20",
+      "id_to_perm": {
+        "0": "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]",
+        "1": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0]",
+        "2": "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1]",
+        "3": "[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2]",
+        "4": "[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3]",
+        "5": "[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4]",
+        "6": "[6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5]",
+        "7": "[7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6]",
+        "8": "[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7]",
+        "9": "[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8]",
+        "10": "[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]",
+        "11": "[11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12]",
+        "12": "[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13]",
+        "13": "[13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14]",
+        "14": "[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15]",
+        "15": "[15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16]",
+        "16": "[16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17]",
+        "17": "[17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18]",
+        "18": "[18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19]",
+        "19": "[19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]",
+        "20": "[0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]",
+        "21": "[1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]",
+        "22": "[2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]",
+        "23": "[3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4]",
+        "24": "[4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]",
+        "25": "[5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]",
+        "26": "[6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]",
+        "27": "[7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8]",
+        "28": "[8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9]",
+        "29": "[9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]",
+        "30": "[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, 11]",
+        "31": "[11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
+        "32": "[12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]",
+        "33": "[13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]",
+        "34": "[14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]",
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