diff --git "a/data/psl_superset/metadata.json" "b/data/psl_superset/metadata.json"
deleted file mode 100644--- "a/data/psl_superset/metadata.json"
+++ /dev/null
@@ -1,5798 +0,0 @@
-{
-  "group_type": "psl",
-  "max_degree": 8,
-  "subgroups": [
-    {
-      "degree": 6,
-      "order": 60,
-      "name": "PSL(2,5)",
-      "params": [
-        2,
-        5
-      ]
-    },
-    {
-      "degree": 8,
-      "order": 168,
-      "name": "PSL(2,7)",
-      "params": [
-        2,
-        7
-      ]
-    }
-  ],
-  "mappings": {
-    "6": {
-      "order": 60,
-      "name": "PSL(2,5)",
-      "id_to_perm": {
-        "0": "[0, 1, 3, 4, 2, 5]",
-        "1": "[1, 2, 4, 5, 0, 3]",
-        "2": "[2, 0, 5, 3, 1, 4]",
-        "3": "[3, 0, 4, 1, 2, 5]",
-        "4": "[4, 1, 5, 2, 0, 3]",
-        "5": "[5, 2, 3, 0, 1, 4]",
-        "6": "[0, 2, 1, 5, 3, 4]",
-        "7": "[1, 0, 2, 3, 4, 5]",
-        "8": "[2, 1, 0, 4, 5, 3]",
-        "9": "[3, 2, 0, 5, 4, 1]",
-        "10": "[4, 0, 1, 3, 5, 2]",
-        "11": "[5, 1, 2, 4, 3, 0]",
-        "12": "[0, 3, 2, 4, 1, 5]",
-        "13": "[1, 4, 0, 5, 2, 3]",
-        "14": "[2, 5, 1, 3, 0, 4]",
-        "15": "[3, 4, 2, 1, 0, 5]",
-        "16": "[4, 5, 0, 2, 1, 3]",
-        "17": "[5, 3, 1, 0, 2, 4]",
-        "18": "[0, 4, 3, 5, 1, 2]",
-        "19": "[1, 5, 4, 3, 2, 0]",
-        "20": "[2, 3, 5, 4, 0, 1]",
-        "21": "[3, 1, 4, 5, 0, 2]",
-        "22": "[4, 2, 5, 3, 1, 0]",
-        "23": "[5, 0, 3, 4, 2, 1]",
-        "24": "[0, 5, 1, 4, 2, 3]",
-        "25": "[1, 3, 2, 5, 0, 4]",
-        "26": "[2, 4, 0, 3, 1, 5]",
-        "27": "[3, 5, 0, 1, 2, 4]",
-        "28": "[4, 3, 1, 2, 0, 5]",
-        "29": "[5, 4, 2, 0, 1, 3]",
-        "30": "[0, 1, 2, 5, 3, 4]",
-        "31": "[1, 2, 0, 3, 4, 5]",
-        "32": "[2, 0, 1, 4, 5, 3]",
-        "33": "[3, 0, 2, 5, 4, 1]",
-        "34": "[4, 1, 0, 3, 5, 2]",
-        "35": "[5, 2, 1, 4, 3, 0]",
-        "36": "[0, 2, 3, 4, 1, 5]",
-        "37": "[1, 0, 4, 5, 2, 3]",
-        "38": "[2, 1, 5, 3, 0, 4]",
-        "39": "[3, 2, 4, 1, 0, 5]",
-        "40": "[4, 0, 5, 2, 1, 3]",
-        "41": "[5, 1, 3, 0, 2, 4]",
-        "42": "[0, 3, 1, 5, 2, 4]",
-        "43": "[1, 4, 2, 3, 0, 5]",
-        "44": "[2, 5, 0, 4, 1, 3]",
-        "45": "[3, 4, 0, 5, 2, 1]",
-        "46": "[4, 5, 1, 3, 0, 2]",
-        "47": "[5, 3, 2, 4, 1, 0]",
-        "48": "[0, 4, 1, 2, 3, 5]",
-        "49": "[1, 5, 2, 0, 4, 3]",
-        "50": "[2, 3, 0, 1, 5, 4]",
-        "51": "[3, 1, 0, 2, 4, 5]",
-        "52": "[4, 2, 1, 0, 5, 3]",
-        "53": "[5, 0, 2, 1, 3, 4]",
-        "54": "[0, 5, 2, 3, 1, 4]",
-        "55": "[1, 3, 0, 4, 2, 5]",
-        "56": "[2, 4, 1, 5, 0, 3]",
-        "57": "[3, 5, 2, 4, 0, 1]",
-        "58": "[4, 3, 0, 5, 1, 2]",
-        "59": "[5, 4, 1, 3, 2, 0]",
-        "60": "[0, 1, 2, 3, 4, 5]",
-        "61": "[1, 2, 0, 4, 5, 3]",
-        "62": "[2, 0, 1, 5, 3, 4]",
-        "63": "[3, 0, 2, 4, 1, 5]",
-        "64": "[4, 1, 0, 5, 2, 3]",
-        "65": "[5, 2, 1, 3, 0, 4]",
-        "66": "[0, 2, 3, 1, 5, 4]",
-        "67": "[1, 0, 4, 2, 3, 5]",
-        "68": "[2, 1, 5, 0, 4, 3]",
-        "69": "[3, 2, 4, 0, 5, 1]",
-        "70": "[4, 0, 5, 1, 3, 2]",
-        "71": "[5, 1, 3, 2, 4, 0]",
-        "72": "[0, 3, 1, 2, 4, 5]",
-        "73": "[1, 4, 2, 0, 5, 3]",
-        "74": "[2, 5, 0, 1, 3, 4]",
-        "75": "[3, 4, 0, 2, 1, 5]",
-        "76": "[4, 5, 1, 0, 2, 3]",
-        "77": "[5, 3, 2, 1, 0, 4]",
-        "78": "[0, 4, 1, 3, 5, 2]",
-        "79": "[1, 5, 2, 4, 3, 0]",
-        "80": "[2, 3, 0, 5, 4, 1]",
-        "81": "[3, 1, 0, 4, 5, 2]",
-        "82": "[4, 2, 1, 5, 3, 0]",
-        "83": "[5, 0, 2, 3, 4, 1]",
-        "84": "[0, 5, 2, 1, 4, 3]",
-        "85": "[1, 3, 0, 2, 5, 4]",
-        "86": "[2, 4, 1, 0, 3, 5]",
-        "87": "[3, 5, 2, 0, 1, 4]",
-        "88": "[4, 3, 0, 1, 2, 5]",
-        "89": "[5, 4, 1, 2, 0, 3]",
-        "90": "[0, 1, 2, 3, 5, 4]",
-        "91": "[1, 2, 0, 4, 3, 5]",
-        "92": "[2, 0, 1, 5, 4, 3]",
-        "93": "[3, 0, 2, 4, 5, 1]",
-        "94": "[4, 1, 0, 5, 3, 2]",
-        "95": "[5, 2, 1, 3, 4, 0]",
-        "96": "[0, 2, 3, 1, 4, 5]",
-        "97": "[1, 0, 4, 2, 5, 3]",
-        "98": "[2, 1, 5, 0, 3, 4]",
-        "99": "[3, 2, 4, 0, 1, 5]",
-        "100": "[4, 0, 5, 1, 2, 3]",
-        "101": "[5, 1, 3, 2, 0, 4]",
-        "102": "[0, 3, 1, 2, 5, 4]",
-        "103": "[1, 4, 2, 0, 3, 5]",
-        "104": "[2, 5, 0, 1, 4, 3]",
-        "105": "[3, 4, 0, 2, 5, 1]",
-        "106": "[4, 5, 1, 0, 3, 2]",
-        "107": "[5, 3, 2, 1, 4, 0]",
-        "108": "[0, 4, 1, 3, 2, 5]",
-        "109": "[1, 5, 2, 4, 0, 3]",
-        "110": "[2, 3, 0, 5, 1, 4]",
-        "111": "[3, 1, 0, 4, 2, 5]",
-        "112": "[4, 2, 1, 5, 0, 3]",
-        "113": "[5, 0, 2, 3, 1, 4]",
-        "114": "[0, 5, 2, 1, 3, 4]",
-        "115": "[1, 3, 0, 2, 4, 5]",
-        "116": "[2, 4, 1, 0, 5, 3]",
-        "117": "[3, 5, 2, 0, 4, 1]",
-        "118": "[4, 3, 0, 1, 5, 2]",
-        "119": "[5, 4, 1, 2, 3, 0]",
-        "120": "[0, 1, 4, 5, 2, 3]",
-        "121": "[1, 2, 5, 3, 0, 4]",
-        "122": "[2, 0, 3, 4, 1, 5]",
-        "123": "[3, 0, 1, 5, 2, 4]",
-        "124": "[4, 1, 2, 3, 0, 5]",
-        "125": "[5, 2, 0, 4, 1, 3]",
-        "126": "[0, 2, 5, 4, 3, 1]",
-        "127": "[1, 0, 3, 5, 4, 2]",
-        "128": "[2, 1, 4, 3, 5, 0]",
-        "129": "[3, 2, 5, 1, 4, 0]",
-        "130": "[4, 0, 3, 2, 5, 1]",
-        "131": "[5, 1, 4, 0, 3, 2]",
-        "132": "[0, 3, 4, 5, 1, 2]",
-        "133": "[1, 4, 5, 3, 2, 0]",
-        "134": "[2, 5, 3, 4, 0, 1]",
-        "135": "[3, 4, 1, 5, 0, 2]",
-        "136": "[4, 5, 2, 3, 1, 0]",
-        "137": "[5, 3, 0, 4, 2, 1]",
-        "138": "[0, 4, 5, 2, 1, 3]",
-        "139": "[1, 5, 3, 0, 2, 4]",
-        "140": "[2, 3, 4, 1, 0, 5]",
-        "141": "[3, 1, 5, 2, 0, 4]",
-        "142": "[4, 2, 3, 0, 1, 5]",
-        "143": "[5, 0, 4, 1, 2, 3]",
-        "144": "[0, 5, 4, 3, 2, 1]",
-        "145": "[1, 3, 5, 4, 0, 2]",
-        "146": "[2, 4, 3, 5, 1, 0]",
-        "147": "[3, 5, 1, 4, 2, 0]",
-        "148": "[4, 3, 2, 5, 0, 1]",
-        "149": "[5, 4, 0, 3, 1, 2]",
-        "150": "[0, 1, 5, 4, 3, 2]",
-        "151": "[1, 2, 3, 5, 4, 0]",
-        "152": "[2, 0, 4, 3, 5, 1]",
-        "153": "[3, 0, 5, 1, 4, 2]",
-        "154": "[4, 1, 3, 2, 5, 0]",
-        "155": "[5, 2, 4, 0, 3, 1]",
-        "156": "[0, 2, 4, 5, 1, 3]",
-        "157": "[1, 0, 5, 3, 2, 4]",
-        "158": "[2, 1, 3, 4, 0, 5]",
-        "159": "[3, 2, 1, 5, 0, 4]",
-        "160": "[4, 0, 2, 3, 1, 5]",
-        "161": "[5, 1, 0, 4, 2, 3]",
-        "162": "[0, 3, 5, 4, 2, 1]",
-        "163": "[1, 4, 3, 5, 0, 2]",
-        "164": "[2, 5, 4, 3, 1, 0]",
-        "165": "[3, 4, 5, 1, 2, 0]",
-        "166": "[4, 5, 3, 2, 0, 1]",
-        "167": "[5, 3, 4, 0, 1, 2]",
-        "168": "[0, 4, 2, 5, 3, 1]",
-        "169": "[1, 5, 0, 3, 4, 2]",
-        "170": "[2, 3, 1, 4, 5, 0]",
-        "171": "[3, 1, 2, 5, 4, 0]",
-        "172": "[4, 2, 0, 3, 5, 1]",
-        "173": "[5, 0, 1, 4, 3, 2]",
-        "174": "[0, 5, 3, 4, 1, 2]",
-        "175": "[1, 3, 4, 5, 2, 0]",
-        "176": "[2, 4, 5, 3, 0, 1]",
-        "177": "[3, 5, 4, 1, 0, 2]",
-        "178": "[4, 3, 5, 2, 1, 0]",
-        "179": "[5, 4, 3, 0, 2, 1]",
-        "180": "[0, 1, 3, 5, 4, 2]",
-        "181": "[1, 2, 4, 3, 5, 0]",
-        "182": "[2, 0, 5, 4, 3, 1]",
-        "183": "[3, 0, 4, 5, 1, 2]",
-        "184": "[4, 1, 5, 3, 2, 0]",
-        "185": "[5, 2, 3, 4, 0, 1]",
-        "186": "[0, 2, 1, 4, 5, 3]",
-        "187": "[1, 0, 2, 5, 3, 4]",
-        "188": "[2, 1, 0, 3, 4, 5]",
-        "189": "[3, 2, 0, 1, 5, 4]",
-        "190": "[4, 0, 1, 2, 3, 5]",
-        "191": "[5, 1, 2, 0, 4, 3]",
-        "192": "[0, 3, 2, 5, 4, 1]",
-        "193": "[1, 4, 0, 3, 5, 2]",
-        "194": "[2, 5, 1, 4, 3, 0]",
-        "195": "[3, 4, 2, 5, 1, 0]",
-        "196": "[4, 5, 0, 3, 2, 1]",
-        "197": "[5, 3, 1, 4, 0, 2]",
-        "198": "[0, 4, 3, 2, 5, 1]",
-        "199": "[1, 5, 4, 0, 3, 2]",
-        "200": "[2, 3, 5, 1, 4, 0]",
-        "201": "[3, 1, 4, 2, 5, 0]",
-        "202": "[4, 2, 5, 0, 3, 1]",
-        "203": "[5, 0, 3, 1, 4, 2]",
-        "204": "[0, 5, 1, 3, 4, 2]",
-        "205": "[1, 3, 2, 4, 5, 0]",
-        "206": "[2, 4, 0, 5, 3, 1]",
-        "207": "[3, 5, 0, 4, 1, 2]",
-        "208": "[4, 3, 1, 5, 2, 0]",
-        "209": "[5, 4, 2, 3, 0, 1]",
-        "210": "[0, 1, 3, 4, 5, 2]",
-        "211": "[1, 2, 4, 5, 3, 0]",
-        "212": "[2, 0, 5, 3, 4, 1]",
-        "213": "[3, 0, 4, 1, 5, 2]",
-        "214": "[4, 1, 5, 2, 3, 0]",
-        "215": "[5, 2, 3, 0, 4, 1]",
-        "216": "[0, 2, 1, 5, 4, 3]",
-        "217": "[1, 0, 2, 3, 5, 4]",
-        "218": "[2, 1, 0, 4, 3, 5]",
-        "219": "[3, 2, 0, 5, 1, 4]",
-        "220": "[4, 0, 1, 3, 2, 5]",
-        "221": "[5, 1, 2, 4, 0, 3]",
-        "222": "[0, 3, 2, 4, 5, 1]",
-        "223": "[1, 4, 0, 5, 3, 2]",
-        "224": "[2, 5, 1, 3, 4, 0]",
-        "225": "[3, 4, 2, 1, 5, 0]",
-        "226": "[4, 5, 0, 2, 3, 1]",
-        "227": "[5, 3, 1, 0, 4, 2]",
-        "228": "[0, 4, 3, 5, 2, 1]",
-        "229": "[1, 5, 4, 3, 0, 2]",
-        "230": "[2, 3, 5, 4, 1, 0]",
-        "231": "[3, 1, 4, 5, 2, 0]",
-        "232": "[4, 2, 5, 3, 0, 1]",
-        "233": "[5, 0, 3, 4, 1, 2]",
-        "234": "[0, 5, 1, 4, 3, 2]",
-        "235": "[1, 3, 2, 5, 4, 0]",
-        "236": "[2, 4, 0, 3, 5, 1]",
-        "237": "[3, 5, 0, 1, 4, 2]",
-        "238": "[4, 3, 1, 2, 5, 0]",
-        "239": "[5, 4, 2, 0, 3, 1]",
-        "240": "[0, 1, 5, 3, 2, 4]",
-        "241": "[1, 2, 3, 4, 0, 5]",
-        "242": "[2, 0, 4, 5, 1, 3]",
-        "243": "[3, 0, 5, 4, 2, 1]",
-        "244": "[4, 1, 3, 5, 0, 2]",
-        "245": "[5, 2, 4, 3, 1, 0]",
-        "246": "[0, 2, 4, 1, 3, 5]",
-        "247": "[1, 0, 5, 2, 4, 3]",
-        "248": "[2, 1, 3, 0, 5, 4]",
-        "249": "[3, 2, 1, 0, 4, 5]",
-        "250": "[4, 0, 2, 1, 5, 3]",
-        "251": "[5, 1, 0, 2, 3, 4]",
-        "252": "[0, 3, 5, 2, 1, 4]",
-        "253": "[1, 4, 3, 0, 2, 5]",
-        "254": "[2, 5, 4, 1, 0, 3]",
-        "255": "[3, 4, 5, 2, 0, 1]",
-        "256": "[4, 5, 3, 0, 1, 2]",
-        "257": "[5, 3, 4, 1, 2, 0]",
-        "258": "[0, 4, 2, 3, 1, 5]",
-        "259": "[1, 5, 0, 4, 2, 3]",
-        "260": "[2, 3, 1, 5, 0, 4]",
-        "261": "[3, 1, 2, 4, 0, 5]",
-        "262": "[4, 2, 0, 5, 1, 3]",
-        "263": "[5, 0, 1, 3, 2, 4]",
-        "264": "[0, 5, 3, 1, 2, 4]",
-        "265": "[1, 3, 4, 2, 0, 5]",
-        "266": "[2, 4, 5, 0, 1, 3]",
-        "267": "[3, 5, 4, 0, 2, 1]",
-        "268": "[4, 3, 5, 1, 0, 2]",
-        "269": "[5, 4, 3, 2, 1, 0]",
-        "270": "[0, 1, 4, 2, 3, 5]",
-        "271": "[1, 2, 5, 0, 4, 3]",
-        "272": "[2, 0, 3, 1, 5, 4]",
-        "273": "[3, 0, 1, 2, 4, 5]",
-        "274": "[4, 1, 2, 0, 5, 3]",
-        "275": "[5, 2, 0, 1, 3, 4]",
-        "276": "[0, 2, 5, 3, 1, 4]",
-        "277": "[1, 0, 3, 4, 2, 5]",
-        "278": "[2, 1, 4, 5, 0, 3]",
-        "279": "[3, 2, 5, 4, 0, 1]",
-        "280": "[4, 0, 3, 5, 1, 2]",
-        "281": "[5, 1, 4, 3, 2, 0]",
-        "282": "[0, 3, 4, 1, 2, 5]",
-        "283": "[1, 4, 5, 2, 0, 3]",
-        "284": "[2, 5, 3, 0, 1, 4]",
-        "285": "[3, 4, 1, 0, 2, 5]",
-        "286": "[4, 5, 2, 1, 0, 3]",
-        "287": "[5, 3, 0, 2, 1, 4]",
-        "288": "[0, 4, 5, 1, 3, 2]",
-        "289": "[1, 5, 3, 2, 4, 0]",
-        "290": "[2, 3, 4, 0, 5, 1]",
-        "291": "[3, 1, 5, 0, 4, 2]",
-        "292": "[4, 2, 3, 1, 5, 0]",
-        "293": "[5, 0, 4, 2, 3, 1]",
-        "294": "[0, 5, 4, 2, 1, 3]",
-        "295": "[1, 3, 5, 0, 2, 4]",
-        "296": "[2, 4, 3, 1, 0, 5]",
-        "297": "[3, 5, 1, 2, 0, 4]",
-        "298": "[4, 3, 2, 0, 1, 5]",
-        "299": "[5, 4, 0, 1, 2, 3]",
-        "300": "[0, 1, 5, 2, 4, 3]",
-        "301": "[1, 2, 3, 0, 5, 4]",
-        "302": "[2, 0, 4, 1, 3, 5]",
-        "303": "[3, 0, 5, 2, 1, 4]",
-        "304": "[4, 1, 3, 0, 2, 5]",
-        "305": "[5, 2, 4, 1, 0, 3]",
-        "306": "[0, 2, 4, 3, 5, 1]",
-        "307": "[1, 0, 5, 4, 3, 2]",
-        "308": "[2, 1, 3, 5, 4, 0]",
-        "309": "[3, 2, 1, 4, 5, 0]",
-        "310": "[4, 0, 2, 5, 3, 1]",
-        "311": "[5, 1, 0, 3, 4, 2]",
-        "312": "[0, 3, 5, 1, 4, 2]",
-        "313": "[1, 4, 3, 2, 5, 0]",
-        "314": "[2, 5, 4, 0, 3, 1]",
-        "315": "[3, 4, 5, 0, 1, 2]",
-        "316": "[4, 5, 3, 1, 2, 0]",
-        "317": "[5, 3, 4, 2, 0, 1]",
-        "318": "[0, 4, 2, 1, 5, 3]",
-        "319": "[1, 5, 0, 2, 3, 4]",
-        "320": "[2, 3, 1, 0, 4, 5]",
-        "321": "[3, 1, 2, 0, 5, 4]",
-        "322": "[4, 2, 0, 1, 3, 5]",
-        "323": "[5, 0, 1, 2, 4, 3]",
-        "324": "[0, 5, 3, 2, 4, 1]",
-        "325": "[1, 3, 4, 0, 5, 2]",
-        "326": "[2, 4, 5, 1, 3, 0]",
-        "327": "[3, 5, 4, 2, 1, 0]",
-        "328": "[4, 3, 5, 0, 2, 1]",
-        "329": "[5, 4, 3, 1, 0, 2]",
-        "330": "[0, 1, 4, 2, 5, 3]",
-        "331": "[1, 2, 5, 0, 3, 4]",
-        "332": "[2, 0, 3, 1, 4, 5]",
-        "333": "[3, 0, 1, 2, 5, 4]",
-        "334": "[4, 1, 2, 0, 3, 5]",
-        "335": "[5, 2, 0, 1, 4, 3]",
-        "336": "[0, 2, 5, 3, 4, 1]",
-        "337": "[1, 0, 3, 4, 5, 2]",
-        "338": "[2, 1, 4, 5, 3, 0]",
-        "339": "[3, 2, 5, 4, 1, 0]",
-        "340": "[4, 0, 3, 5, 2, 1]",
-        "341": "[5, 1, 4, 3, 0, 2]",
-        "342": "[0, 3, 4, 1, 5, 2]",
-        "343": "[1, 4, 5, 2, 3, 0]",
-        "344": "[2, 5, 3, 0, 4, 1]",
-        "345": "[3, 4, 1, 0, 5, 2]",
-        "346": "[4, 5, 2, 1, 3, 0]",
-        "347": "[5, 3, 0, 2, 4, 1]",
-        "348": "[0, 4, 5, 1, 2, 3]",
-        "349": "[1, 5, 3, 2, 0, 4]",
-        "350": "[2, 3, 4, 0, 1, 5]",
-        "351": "[3, 1, 5, 0, 2, 4]",
-        "352": "[4, 2, 3, 1, 0, 5]",
-        "353": "[5, 0, 4, 2, 1, 3]",
-        "354": "[0, 5, 4, 2, 3, 1]",
-        "355": "[1, 3, 5, 0, 4, 2]",
-        "356": "[2, 4, 3, 1, 5, 0]",
-        "357": "[3, 5, 1, 2, 4, 0]",
-        "358": "[4, 3, 2, 0, 5, 1]",
-        "359": "[5, 4, 0, 1, 3, 2]",
-        "360": "[0, 1, 3, 5, 2, 4]",
-        "361": "[1, 2, 4, 3, 0, 5]",
-        "362": "[2, 0, 5, 4, 1, 3]",
-        "363": "[3, 0, 4, 5, 2, 1]",
-        "364": "[4, 1, 5, 3, 0, 2]",
-        "365": "[5, 2, 3, 4, 1, 0]",
-        "366": "[0, 2, 1, 4, 3, 5]",
-        "367": "[1, 0, 2, 5, 4, 3]",
-        "368": "[2, 1, 0, 3, 5, 4]",
-        "369": "[3, 2, 0, 1, 4, 5]",
-        "370": "[4, 0, 1, 2, 5, 3]",
-        "371": "[5, 1, 2, 0, 3, 4]",
-        "372": "[0, 3, 2, 5, 1, 4]",
-        "373": "[1, 4, 0, 3, 2, 5]",
-        "374": "[2, 5, 1, 4, 0, 3]",
-        "375": "[3, 4, 2, 5, 0, 1]",
-        "376": "[4, 5, 0, 3, 1, 2]",
-        "377": "[5, 3, 1, 4, 2, 0]",
-        "378": "[0, 4, 3, 2, 1, 5]",
-        "379": "[1, 5, 4, 0, 2, 3]",
-        "380": "[2, 3, 5, 1, 0, 4]",
-        "381": "[3, 1, 4, 2, 0, 5]",
-        "382": "[4, 2, 5, 0, 1, 3]",
-        "383": "[5, 0, 3, 1, 2, 4]",
-        "384": "[0, 5, 1, 3, 2, 4]",
-        "385": "[1, 3, 2, 4, 0, 5]",
-        "386": "[2, 4, 0, 5, 1, 3]",
-        "387": "[3, 5, 0, 4, 2, 1]",
-        "388": "[4, 3, 1, 5, 0, 2]",
-        "389": "[5, 4, 2, 3, 1, 0]",
-        "390": "[0, 1, 2, 4, 3, 5]",
-        "391": "[1, 2, 0, 5, 4, 3]",
-        "392": "[2, 0, 1, 3, 5, 4]",
-        "393": "[3, 0, 2, 1, 4, 5]",
-        "394": "[4, 1, 0, 2, 5, 3]",
-        "395": "[5, 2, 1, 0, 3, 4]",
-        "396": "[0, 2, 3, 5, 1, 4]",
-        "397": "[1, 0, 4, 3, 2, 5]",
-        "398": "[2, 1, 5, 4, 0, 3]",
-        "399": "[3, 2, 4, 5, 0, 1]",
-        "400": "[4, 0, 5, 3, 1, 2]",
-        "401": "[5, 1, 3, 4, 2, 0]",
-        "402": "[0, 3, 1, 4, 2, 5]",
-        "403": "[1, 4, 2, 5, 0, 3]",
-        "404": "[2, 5, 0, 3, 1, 4]",
-        "405": "[3, 4, 0, 1, 2, 5]",
-        "406": "[4, 5, 1, 2, 0, 3]",
-        "407": "[5, 3, 2, 0, 1, 4]",
-        "408": "[0, 4, 1, 5, 3, 2]",
-        "409": "[1, 5, 2, 3, 4, 0]",
-        "410": "[2, 3, 0, 4, 5, 1]",
-        "411": "[3, 1, 0, 5, 4, 2]",
-        "412": "[4, 2, 1, 3, 5, 0]",
-        "413": "[5, 0, 2, 4, 3, 1]",
-        "414": "[0, 5, 2, 4, 1, 3]",
-        "415": "[1, 3, 0, 5, 2, 4]",
-        "416": "[2, 4, 1, 3, 0, 5]",
-        "417": "[3, 5, 2, 1, 0, 4]",
-        "418": "[4, 3, 0, 2, 1, 5]",
-        "419": "[5, 4, 1, 0, 2, 3]",
-        "420": "[0, 1, 2, 5, 4, 3]",
-        "421": "[1, 2, 0, 3, 5, 4]",
-        "422": "[2, 0, 1, 4, 3, 5]",
-        "423": "[3, 0, 2, 5, 1, 4]",
-        "424": "[4, 1, 0, 3, 2, 5]",
-        "425": "[5, 2, 1, 4, 0, 3]",
-        "426": "[0, 2, 3, 4, 5, 1]",
-        "427": "[1, 0, 4, 5, 3, 2]",
-        "428": "[2, 1, 5, 3, 4, 0]",
-        "429": "[3, 2, 4, 1, 5, 0]",
-        "430": "[4, 0, 5, 2, 3, 1]",
-        "431": "[5, 1, 3, 0, 4, 2]",
-        "432": "[0, 3, 1, 5, 4, 2]",
-        "433": "[1, 4, 2, 3, 5, 0]",
-        "434": "[2, 5, 0, 4, 3, 1]",
-        "435": "[3, 4, 0, 5, 1, 2]",
-        "436": "[4, 5, 1, 3, 2, 0]",
-        "437": "[5, 3, 2, 4, 0, 1]",
-        "438": "[0, 4, 1, 2, 5, 3]",
-        "439": "[1, 5, 2, 0, 3, 4]",
-        "440": "[2, 3, 0, 1, 4, 5]",
-        "441": "[3, 1, 0, 2, 5, 4]",
-        "442": "[4, 2, 1, 0, 3, 5]",
-        "443": "[5, 0, 2, 1, 4, 3]",
-        "444": "[0, 5, 2, 3, 4, 1]",
-        "445": "[1, 3, 0, 4, 5, 2]",
-        "446": "[2, 4, 1, 5, 3, 0]",
-        "447": "[3, 5, 2, 4, 1, 0]",
-        "448": "[4, 3, 0, 5, 2, 1]",
-        "449": "[5, 4, 1, 3, 0, 2]",
-        "450": "[0, 1, 2, 4, 5, 3]",
-        "451": "[1, 2, 0, 5, 3, 4]",
-        "452": "[2, 0, 1, 3, 4, 5]",
-        "453": "[3, 0, 2, 1, 5, 4]",
-        "454": "[4, 1, 0, 2, 3, 5]",
-        "455": "[5, 2, 1, 0, 4, 3]",
-        "456": "[0, 2, 3, 5, 4, 1]",
-        "457": "[1, 0, 4, 3, 5, 2]",
-        "458": "[2, 1, 5, 4, 3, 0]",
-        "459": "[3, 2, 4, 5, 1, 0]",
-        "460": "[4, 0, 5, 3, 2, 1]",
-        "461": "[5, 1, 3, 4, 0, 2]",
-        "462": "[0, 3, 1, 4, 5, 2]",
-        "463": "[1, 4, 2, 5, 3, 0]",
-        "464": "[2, 5, 0, 3, 4, 1]",
-        "465": "[3, 4, 0, 1, 5, 2]",
-        "466": "[4, 5, 1, 2, 3, 0]",
-        "467": "[5, 3, 2, 0, 4, 1]",
-        "468": "[0, 4, 1, 5, 2, 3]",
-        "469": "[1, 5, 2, 3, 0, 4]",
-        "470": "[2, 3, 0, 4, 1, 5]",
-        "471": "[3, 1, 0, 5, 2, 4]",
-        "472": "[4, 2, 1, 3, 0, 5]",
-        "473": "[5, 0, 2, 4, 1, 3]",
-        "474": "[0, 5, 2, 4, 3, 1]",
-        "475": "[1, 3, 0, 5, 4, 2]",
-        "476": "[2, 4, 1, 3, 5, 0]",
-        "477": "[3, 5, 2, 1, 4, 0]",
-        "478": "[4, 3, 0, 2, 5, 1]",
-        "479": "[5, 4, 1, 0, 3, 2]",
-        "480": "[0, 1, 4, 3, 2, 5]",
-        "481": "[1, 2, 5, 4, 0, 3]",
-        "482": "[2, 0, 3, 5, 1, 4]",
-        "483": "[3, 0, 1, 4, 2, 5]",
-        "484": "[4, 1, 2, 5, 0, 3]",
-        "485": "[5, 2, 0, 3, 1, 4]",
-        "486": "[0, 2, 5, 1, 3, 4]",
-        "487": "[1, 0, 3, 2, 4, 5]",
-        "488": "[2, 1, 4, 0, 5, 3]",
-        "489": "[3, 2, 5, 0, 4, 1]",
-        "490": "[4, 0, 3, 1, 5, 2]",
-        "491": "[5, 1, 4, 2, 3, 0]",
-        "492": "[0, 3, 4, 2, 1, 5]",
-        "493": "[1, 4, 5, 0, 2, 3]",
-        "494": "[2, 5, 3, 1, 0, 4]",
-        "495": "[3, 4, 1, 2, 0, 5]",
-        "496": "[4, 5, 2, 0, 1, 3]",
-        "497": "[5, 3, 0, 1, 2, 4]",
-        "498": "[0, 4, 5, 3, 1, 2]",
-        "499": "[1, 5, 3, 4, 2, 0]",
-        "500": "[2, 3, 4, 5, 0, 1]",
-        "501": "[3, 1, 5, 4, 0, 2]",
-        "502": "[4, 2, 3, 5, 1, 0]",
-        "503": "[5, 0, 4, 3, 2, 1]",
-        "504": "[0, 5, 4, 1, 2, 3]",
-        "505": "[1, 3, 5, 2, 0, 4]",
-        "506": "[2, 4, 3, 0, 1, 5]",
-        "507": "[3, 5, 1, 0, 2, 4]",
-        "508": "[4, 3, 2, 1, 0, 5]",
-        "509": "[5, 4, 0, 2, 1, 3]",
-        "510": "[0, 1, 5, 2, 3, 4]",
-        "511": "[1, 2, 3, 0, 4, 5]",
-        "512": "[2, 0, 4, 1, 5, 3]",
-        "513": "[3, 0, 5, 2, 4, 1]",
-        "514": "[4, 1, 3, 0, 5, 2]",
-        "515": "[5, 2, 4, 1, 3, 0]",
-        "516": "[0, 2, 4, 3, 1, 5]",
-        "517": "[1, 0, 5, 4, 2, 3]",
-        "518": "[2, 1, 3, 5, 0, 4]",
-        "519": "[3, 2, 1, 4, 0, 5]",
-        "520": "[4, 0, 2, 5, 1, 3]",
-        "521": "[5, 1, 0, 3, 2, 4]",
-        "522": "[0, 3, 5, 1, 2, 4]",
-        "523": "[1, 4, 3, 2, 0, 5]",
-        "524": "[2, 5, 4, 0, 1, 3]",
-        "525": "[3, 4, 5, 0, 2, 1]",
-        "526": "[4, 5, 3, 1, 0, 2]",
-        "527": "[5, 3, 4, 2, 1, 0]",
-        "528": "[0, 4, 2, 1, 3, 5]",
-        "529": "[1, 5, 0, 2, 4, 3]",
-        "530": "[2, 3, 1, 0, 5, 4]",
-        "531": "[3, 1, 2, 0, 4, 5]",
-        "532": "[4, 2, 0, 1, 5, 3]",
-        "533": "[5, 0, 1, 2, 3, 4]",
-        "534": "[0, 5, 3, 2, 1, 4]",
-        "535": "[1, 3, 4, 0, 2, 5]",
-        "536": "[2, 4, 5, 1, 0, 3]",
-        "537": "[3, 5, 4, 2, 0, 1]",
-        "538": "[4, 3, 5, 0, 1, 2]",
-        "539": "[5, 4, 3, 1, 2, 0]",
-        "540": "[0, 1, 3, 2, 4, 5]",
-        "541": "[1, 2, 4, 0, 5, 3]",
-        "542": "[2, 0, 5, 1, 3, 4]",
-        "543": "[3, 0, 4, 2, 1, 5]",
-        "544": "[4, 1, 5, 0, 2, 3]",
-        "545": "[5, 2, 3, 1, 0, 4]",
-        "546": "[0, 2, 1, 3, 5, 4]",
-        "547": "[1, 0, 2, 4, 3, 5]",
-        "548": "[2, 1, 0, 5, 4, 3]",
-        "549": "[3, 2, 0, 4, 5, 1]",
-        "550": "[4, 0, 1, 5, 3, 2]",
-        "551": "[5, 1, 2, 3, 4, 0]",
-        "552": "[0, 3, 2, 1, 4, 5]",
-        "553": "[1, 4, 0, 2, 5, 3]",
-        "554": "[2, 5, 1, 0, 3, 4]",
-        "555": "[3, 4, 2, 0, 1, 5]",
-        "556": "[4, 5, 0, 1, 2, 3]",
-        "557": "[5, 3, 1, 2, 0, 4]",
-        "558": "[0, 4, 3, 1, 5, 2]",
-        "559": "[1, 5, 4, 2, 3, 0]",
-        "560": "[2, 3, 5, 0, 4, 1]",
-        "561": "[3, 1, 4, 0, 5, 2]",
-        "562": "[4, 2, 5, 1, 3, 0]",
-        "563": "[5, 0, 3, 2, 4, 1]",
-        "564": "[0, 5, 1, 2, 4, 3]",
-        "565": "[1, 3, 2, 0, 5, 4]",
-        "566": "[2, 4, 0, 1, 3, 5]",
-        "567": "[3, 5, 0, 2, 1, 4]",
-        "568": "[4, 3, 1, 0, 2, 5]",
-        "569": "[5, 4, 2, 1, 0, 3]",
-        "570": "[0, 1, 3, 2, 5, 4]",
-        "571": "[1, 2, 4, 0, 3, 5]",
-        "572": "[2, 0, 5, 1, 4, 3]",
-        "573": "[3, 0, 4, 2, 5, 1]",
-        "574": "[4, 1, 5, 0, 3, 2]",
-        "575": "[5, 2, 3, 1, 4, 0]",
-        "576": "[0, 2, 1, 3, 4, 5]",
-        "577": "[1, 0, 2, 4, 5, 3]",
-        "578": "[2, 1, 0, 5, 3, 4]",
-        "579": "[3, 2, 0, 4, 1, 5]",
-        "580": "[4, 0, 1, 5, 2, 3]",
-        "581": "[5, 1, 2, 3, 0, 4]",
-        "582": "[0, 3, 2, 1, 5, 4]",
-        "583": "[1, 4, 0, 2, 3, 5]",
-        "584": "[2, 5, 1, 0, 4, 3]",
-        "585": "[3, 4, 2, 0, 5, 1]",
-        "586": "[4, 5, 0, 1, 3, 2]",
-        "587": "[5, 3, 1, 2, 4, 0]",
-        "588": "[0, 4, 3, 1, 2, 5]",
-        "589": "[1, 5, 4, 2, 0, 3]",
-        "590": "[2, 3, 5, 0, 1, 4]",
-        "591": "[3, 1, 4, 0, 2, 5]",
-        "592": "[4, 2, 5, 1, 0, 3]",
-        "593": "[5, 0, 3, 2, 1, 4]",
-        "594": "[0, 5, 1, 2, 3, 4]",
-        "595": "[1, 3, 2, 0, 4, 5]",
-        "596": "[2, 4, 0, 1, 5, 3]",
-        "597": "[3, 5, 0, 2, 4, 1]",
-        "598": "[4, 3, 1, 0, 5, 2]",
-        "599": "[5, 4, 2, 1, 3, 0]",
-        "600": "[0, 1, 5, 4, 2, 3]",
-        "601": "[1, 2, 3, 5, 0, 4]",
-        "602": "[2, 0, 4, 3, 1, 5]",
-        "603": "[3, 0, 5, 1, 2, 4]",
-        "604": "[4, 1, 3, 2, 0, 5]",
-        "605": "[5, 2, 4, 0, 1, 3]",
-        "606": "[0, 2, 4, 5, 3, 1]",
-        "607": "[1, 0, 5, 3, 4, 2]",
-        "608": "[2, 1, 3, 4, 5, 0]",
-        "609": "[3, 2, 1, 5, 4, 0]",
-        "610": "[4, 0, 2, 3, 5, 1]",
-        "611": "[5, 1, 0, 4, 3, 2]",
-        "612": "[0, 3, 5, 4, 1, 2]",
-        "613": "[1, 4, 3, 5, 2, 0]",
-        "614": "[2, 5, 4, 3, 0, 1]",
-        "615": "[3, 4, 5, 1, 0, 2]",
-        "616": "[4, 5, 3, 2, 1, 0]",
-        "617": "[5, 3, 4, 0, 2, 1]",
-        "618": "[0, 4, 2, 5, 1, 3]",
-        "619": "[1, 5, 0, 3, 2, 4]",
-        "620": "[2, 3, 1, 4, 0, 5]",
-        "621": "[3, 1, 2, 5, 0, 4]",
-        "622": "[4, 2, 0, 3, 1, 5]",
-        "623": "[5, 0, 1, 4, 2, 3]",
-        "624": "[0, 5, 3, 4, 2, 1]",
-        "625": "[1, 3, 4, 5, 0, 2]",
-        "626": "[2, 4, 5, 3, 1, 0]",
-        "627": "[3, 5, 4, 1, 2, 0]",
-        "628": "[4, 3, 5, 2, 0, 1]",
-        "629": "[5, 4, 3, 0, 1, 2]",
-        "630": "[0, 1, 4, 5, 3, 2]",
-        "631": "[1, 2, 5, 3, 4, 0]",
-        "632": "[2, 0, 3, 4, 5, 1]",
-        "633": "[3, 0, 1, 5, 4, 2]",
-        "634": "[4, 1, 2, 3, 5, 0]",
-        "635": "[5, 2, 0, 4, 3, 1]",
-        "636": "[0, 2, 5, 4, 1, 3]",
-        "637": "[1, 0, 3, 5, 2, 4]",
-        "638": "[2, 1, 4, 3, 0, 5]",
-        "639": "[3, 2, 5, 1, 0, 4]",
-        "640": "[4, 0, 3, 2, 1, 5]",
-        "641": "[5, 1, 4, 0, 2, 3]",
-        "642": "[0, 3, 4, 5, 2, 1]",
-        "643": "[1, 4, 5, 3, 0, 2]",
-        "644": "[2, 5, 3, 4, 1, 0]",
-        "645": "[3, 4, 1, 5, 2, 0]",
-        "646": "[4, 5, 2, 3, 0, 1]",
-        "647": "[5, 3, 0, 4, 1, 2]",
-        "648": "[0, 4, 5, 2, 3, 1]",
-        "649": "[1, 5, 3, 0, 4, 2]",
-        "650": "[2, 3, 4, 1, 5, 0]",
-        "651": "[3, 1, 5, 2, 4, 0]",
-        "652": "[4, 2, 3, 0, 5, 1]",
-        "653": "[5, 0, 4, 1, 3, 2]",
-        "654": "[0, 5, 4, 3, 1, 2]",
-        "655": "[1, 3, 5, 4, 2, 0]",
-        "656": "[2, 4, 3, 5, 0, 1]",
-        "657": "[3, 5, 1, 4, 0, 2]",
-        "658": "[4, 3, 2, 5, 1, 0]",
-        "659": "[5, 4, 0, 3, 2, 1]",
-        "660": "[0, 1, 5, 3, 4, 2]",
-        "661": "[1, 2, 3, 4, 5, 0]",
-        "662": "[2, 0, 4, 5, 3, 1]",
-        "663": "[3, 0, 5, 4, 1, 2]",
-        "664": "[4, 1, 3, 5, 2, 0]",
-        "665": "[5, 2, 4, 3, 0, 1]",
-        "666": "[0, 2, 4, 1, 5, 3]",
-        "667": "[1, 0, 5, 2, 3, 4]",
-        "668": "[2, 1, 3, 0, 4, 5]",
-        "669": "[3, 2, 1, 0, 5, 4]",
-        "670": "[4, 0, 2, 1, 3, 5]",
-        "671": "[5, 1, 0, 2, 4, 3]",
-        "672": "[0, 3, 5, 2, 4, 1]",
-        "673": "[1, 4, 3, 0, 5, 2]",
-        "674": "[2, 5, 4, 1, 3, 0]",
-        "675": "[3, 4, 5, 2, 1, 0]",
-        "676": "[4, 5, 3, 0, 2, 1]",
-        "677": "[5, 3, 4, 1, 0, 2]",
-        "678": "[0, 4, 2, 3, 5, 1]",
-        "679": "[1, 5, 0, 4, 3, 2]",
-        "680": "[2, 3, 1, 5, 4, 0]",
-        "681": "[3, 1, 2, 4, 5, 0]",
-        "682": "[4, 2, 0, 5, 3, 1]",
-        "683": "[5, 0, 1, 3, 4, 2]",
-        "684": "[0, 5, 3, 1, 4, 2]",
-        "685": "[1, 3, 4, 2, 5, 0]",
-        "686": "[2, 4, 5, 0, 3, 1]",
-        "687": "[3, 5, 4, 0, 1, 2]",
-        "688": "[4, 3, 5, 1, 2, 0]",
-        "689": "[5, 4, 3, 2, 0, 1]",
-        "690": "[0, 1, 4, 3, 5, 2]",
-        "691": "[1, 2, 5, 4, 3, 0]",
-        "692": "[2, 0, 3, 5, 4, 1]",
-        "693": "[3, 0, 1, 4, 5, 2]",
-        "694": "[4, 1, 2, 5, 3, 0]",
-        "695": "[5, 2, 0, 3, 4, 1]",
-        "696": "[0, 2, 5, 1, 4, 3]",
-        "697": "[1, 0, 3, 2, 5, 4]",
-        "698": "[2, 1, 4, 0, 3, 5]",
-        "699": "[3, 2, 5, 0, 1, 4]",
-        "700": "[4, 0, 3, 1, 2, 5]",
-        "701": "[5, 1, 4, 2, 0, 3]",
-        "702": "[0, 3, 4, 2, 5, 1]",
-        "703": "[1, 4, 5, 0, 3, 2]",
-        "704": "[2, 5, 3, 1, 4, 0]",
-        "705": "[3, 4, 1, 2, 5, 0]",
-        "706": "[4, 5, 2, 0, 3, 1]",
-        "707": "[5, 3, 0, 1, 4, 2]",
-        "708": "[0, 4, 5, 3, 2, 1]",
-        "709": "[1, 5, 3, 4, 0, 2]",
-        "710": "[2, 3, 4, 5, 1, 0]",
-        "711": "[3, 1, 5, 4, 2, 0]",
-        "712": "[4, 2, 3, 5, 0, 1]",
-        "713": "[5, 0, 4, 3, 1, 2]",
-        "714": "[0, 5, 4, 1, 3, 2]",
-        "715": "[1, 3, 5, 2, 4, 0]",
-        "716": "[2, 4, 3, 0, 5, 1]",
-        "717": "[3, 5, 1, 0, 4, 2]",
-        "718": "[4, 3, 2, 1, 5, 0]",
-        "719": "[5, 4, 0, 2, 3, 1]"
-      }
-    },
-    "8": {
-      "order": 168,
-      "name": "PSL(2,7)",
-      "id_to_perm": {
-        "0": "[0, 1, 2, 3, 6, 4, 5, 7]",
-        "1": "[1, 2, 3, 4, 0, 5, 6, 7]",
-        "2": "[2, 3, 4, 5, 1, 6, 0, 7]",
-        "3": "[3, 1, 5, 2, 0, 6, 4, 7]",
-        "4": "[4, 5, 3, 6, 1, 2, 0, 7]",
-        "5": "[5, 3, 6, 1, 0, 4, 2, 7]",
-        "6": "[6, 5, 3, 4, 1, 2, 0, 7]",
-        "7": "[0, 2, 3, 5, 6, 1, 4, 7]",
-        "8": "[1, 3, 4, 6, 0, 2, 5, 7]",
-        "9": "[2, 4, 5, 0, 1, 3, 6, 7]",
-        "10": "[3, 5, 2, 4, 0, 1, 6, 7]",
-        "11": "[4, 3, 6, 0, 1, 5, 2, 7]",
-        "12": "[5, 6, 1, 2, 0, 3, 4, 7]",
-        "13": "[6, 3, 4, 0, 1, 5, 2, 7]",
-        "14": "[0, 3, 1, 5, 4, 2, 6, 7]",
-        "15": "[1, 4, 2, 6, 5, 3, 0, 7]",
-        "16": "[2, 5, 3, 0, 6, 4, 1, 7]",
-        "17": "[3, 2, 1, 4, 6, 5, 0, 7]",
-        "18": "[4, 6, 5, 0, 2, 3, 1, 7]",
-        "19": "[5, 1, 3, 2, 4, 6, 0, 7]",
-        "20": "[6, 4, 5, 0, 2, 3, 1, 7]",
-        "21": "[0, 4, 1, 3, 5, 2, 6, 7]",
-        "22": "[1, 5, 2, 4, 6, 3, 0, 7]",
-        "23": "[2, 6, 3, 5, 0, 4, 1, 7]",
-        "24": "[3, 6, 1, 2, 4, 5, 0, 7]",
-        "25": "[4, 2, 5, 6, 0, 3, 1, 7]",
-        "26": "[5, 4, 3, 1, 2, 6, 0, 7]",
-        "27": "[6, 2, 5, 4, 0, 3, 1, 7]",
-        "28": "[0, 5, 3, 6, 2, 1, 4, 7]",
-        "29": "[1, 6, 4, 0, 3, 2, 5, 7]",
-        "30": "[2, 0, 5, 1, 4, 3, 6, 7]",
-        "31": "[3, 4, 2, 0, 5, 1, 6, 7]",
-        "32": "[4, 0, 6, 1, 3, 5, 2, 7]",
-        "33": "[5, 2, 1, 0, 6, 3, 4, 7]",
-        "34": "[6, 0, 4, 1, 3, 5, 2, 7]",
-        "35": "[0, 6, 1, 3, 5, 2, 4, 7]",
-        "36": "[1, 0, 2, 4, 6, 3, 5, 7]",
-        "37": "[2, 1, 3, 5, 0, 4, 6, 7]",
-        "38": "[3, 0, 1, 2, 4, 5, 6, 7]",
-        "39": "[4, 1, 5, 6, 0, 3, 2, 7]",
-        "40": "[5, 0, 3, 1, 2, 6, 4, 7]",
-        "41": "[6, 1, 5, 4, 0, 3, 2, 7]",
-        "42": "[0, 1, 3, 4, 6, 5, 2, 7]",
-        "43": "[1, 2, 4, 5, 0, 6, 3, 7]",
-        "44": "[2, 3, 5, 6, 1, 0, 4, 7]",
-        "45": "[3, 1, 2, 6, 0, 4, 5, 7]",
-        "46": "[4, 5, 6, 2, 1, 0, 3, 7]",
-        "47": "[5, 3, 1, 4, 0, 2, 6, 7]",
-        "48": "[6, 5, 4, 2, 1, 0, 3, 7]",
-        "49": "[0, 2, 5, 1, 6, 4, 3, 7]",
-        "50": "[1, 3, 6, 2, 0, 5, 4, 7]",
-        "51": "[2, 4, 0, 3, 1, 6, 5, 7]",
-        "52": "[3, 5, 4, 1, 0, 6, 2, 7]",
-        "53": "[4, 3, 0, 5, 1, 2, 6, 7]",
-        "54": "[5, 6, 2, 3, 0, 4, 1, 7]",
-        "55": "[6, 3, 0, 5, 1, 2, 4, 7]",
-        "56": "[0, 3, 5, 2, 4, 6, 1, 7]",
-        "57": "[1, 4, 6, 3, 5, 0, 2, 7]",
-        "58": "[2, 5, 0, 4, 6, 1, 3, 7]",
-        "59": "[3, 2, 4, 5, 6, 0, 1, 7]",
-        "60": "[4, 6, 0, 3, 2, 1, 5, 7]",
-        "61": "[5, 1, 2, 6, 4, 0, 3, 7]",
-        "62": "[6, 4, 0, 3, 2, 1, 5, 7]",
-        "63": "[0, 4, 3, 2, 5, 6, 1, 7]",
-        "64": "[1, 5, 4, 3, 6, 0, 2, 7]",
-        "65": "[2, 6, 5, 4, 0, 1, 3, 7]",
-        "66": "[3, 6, 2, 5, 4, 0, 1, 7]",
-        "67": "[4, 2, 6, 3, 0, 1, 5, 7]",
-        "68": "[5, 4, 1, 6, 2, 0, 3, 7]",
-        "69": "[6, 2, 4, 3, 0, 1, 5, 7]",
-        "70": "[0, 5, 6, 1, 2, 4, 3, 7]",
-        "71": "[1, 6, 0, 2, 3, 5, 4, 7]",
-        "72": "[2, 0, 1, 3, 4, 6, 5, 7]",
-        "73": "[3, 4, 0, 1, 5, 6, 2, 7]",
-        "74": "[4, 0, 1, 5, 3, 2, 6, 7]",
-        "75": "[5, 2, 0, 3, 6, 4, 1, 7]",
-        "76": "[6, 0, 1, 5, 3, 2, 4, 7]",
-        "77": "[0, 6, 3, 2, 5, 4, 1, 7]",
-        "78": "[1, 0, 4, 3, 6, 5, 2, 7]",
-        "79": "[2, 1, 5, 4, 0, 6, 3, 7]",
-        "80": "[3, 0, 2, 5, 4, 6, 1, 7]",
-        "81": "[4, 1, 6, 3, 0, 2, 5, 7]",
-        "82": "[5, 0, 1, 6, 2, 4, 3, 7]",
-        "83": "[6, 1, 4, 3, 0, 2, 5, 7]",
-        "84": "[0, 1, 4, 5, 2, 3, 6, 7]",
-        "85": "[1, 2, 5, 6, 3, 4, 0, 7]",
-        "86": "[2, 3, 6, 0, 4, 5, 1, 7]",
-        "87": "[3, 1, 6, 4, 5, 2, 0, 7]",
-        "88": "[4, 5, 2, 0, 3, 6, 1, 7]",
-        "89": "[5, 3, 4, 2, 6, 1, 0, 7]",
-        "90": "[6, 5, 2, 0, 3, 4, 1, 7]",
-        "91": "[0, 2, 1, 4, 3, 5, 6, 7]",
-        "92": "[1, 3, 2, 5, 4, 6, 0, 7]",
-        "93": "[2, 4, 3, 6, 5, 0, 1, 7]",
-        "94": "[3, 5, 1, 6, 2, 4, 0, 7]",
-        "95": "[4, 3, 5, 2, 6, 0, 1, 7]",
-        "96": "[5, 6, 3, 4, 1, 2, 0, 7]",
-        "97": "[6, 3, 5, 2, 4, 0, 1, 7]",
-        "98": "[0, 3, 2, 6, 1, 5, 4, 7]",
-        "99": "[1, 4, 3, 0, 2, 6, 5, 7]",
-        "100": "[2, 5, 4, 1, 3, 0, 6, 7]",
-        "101": "[3, 2, 5, 0, 1, 4, 6, 7]",
-        "102": "[4, 6, 3, 1, 5, 0, 2, 7]",
-        "103": "[5, 1, 6, 0, 3, 2, 4, 7]",
-        "104": "[6, 4, 3, 1, 5, 0, 2, 7]",
-        "105": "[0, 4, 2, 6, 1, 3, 5, 7]",
-        "106": "[1, 5, 3, 0, 2, 4, 6, 7]",
-        "107": "[2, 6, 4, 1, 3, 5, 0, 7]",
-        "108": "[3, 6, 5, 0, 1, 2, 4, 7]",
-        "109": "[4, 2, 3, 1, 5, 6, 0, 7]",
-        "110": "[5, 4, 6, 0, 3, 1, 2, 7]",
-        "111": "[6, 2, 3, 1, 5, 4, 0, 7]",
-        "112": "[0, 5, 1, 4, 3, 6, 2, 7]",
-        "113": "[1, 6, 2, 5, 4, 0, 3, 7]",
-        "114": "[2, 0, 3, 6, 5, 1, 4, 7]",
-        "115": "[3, 4, 1, 6, 2, 0, 5, 7]",
-        "116": "[4, 0, 5, 2, 6, 1, 3, 7]",
-        "117": "[5, 2, 3, 4, 1, 0, 6, 7]",
-        "118": "[6, 0, 5, 2, 4, 1, 3, 7]",
-        "119": "[0, 6, 2, 4, 1, 3, 5, 7]",
-        "120": "[1, 0, 3, 5, 2, 4, 6, 7]",
-        "121": "[2, 1, 4, 6, 3, 5, 0, 7]",
-        "122": "[3, 0, 5, 6, 1, 2, 4, 7]",
-        "123": "[4, 1, 3, 2, 5, 6, 0, 7]",
-        "124": "[5, 0, 6, 4, 3, 1, 2, 7]",
-        "125": "[6, 1, 3, 2, 5, 4, 0, 7]",
-        "126": "[0, 1, 5, 6, 2, 3, 4, 7]",
-        "127": "[1, 2, 6, 0, 3, 4, 5, 7]",
-        "128": "[2, 3, 0, 1, 4, 5, 6, 7]",
-        "129": "[3, 1, 4, 0, 5, 2, 6, 7]",
-        "130": "[4, 5, 0, 1, 3, 6, 2, 7]",
-        "131": "[5, 3, 2, 0, 6, 1, 4, 7]",
-        "132": "[6, 5, 0, 1, 3, 4, 2, 7]",
-        "133": "[0, 2, 4, 6, 3, 5, 1, 7]",
-        "134": "[1, 3, 5, 0, 4, 6, 2, 7]",
-        "135": "[2, 4, 6, 1, 5, 0, 3, 7]",
-        "136": "[3, 5, 6, 0, 2, 4, 1, 7]",
-        "137": "[4, 3, 2, 1, 6, 0, 5, 7]",
-        "138": "[5, 6, 4, 0, 1, 2, 3, 7]",
-        "139": "[6, 3, 2, 1, 4, 0, 5, 7]",
-        "140": "[0, 3, 6, 4, 1, 5, 2, 7]",
-        "141": "[1, 4, 0, 5, 2, 6, 3, 7]",
-        "142": "[2, 5, 1, 6, 3, 0, 4, 7]",
-        "143": "[3, 2, 0, 6, 1, 4, 5, 7]",
-        "144": "[4, 6, 1, 2, 5, 0, 3, 7]",
-        "145": "[5, 1, 0, 4, 3, 2, 6, 7]",
-        "146": "[6, 4, 1, 2, 5, 0, 3, 7]",
-        "147": "[0, 4, 6, 5, 1, 3, 2, 7]",
-        "148": "[1, 5, 0, 6, 2, 4, 3, 7]",
-        "149": "[2, 6, 1, 0, 3, 5, 4, 7]",
-        "150": "[3, 6, 0, 4, 1, 2, 5, 7]",
-        "151": "[4, 2, 1, 0, 5, 6, 3, 7]",
-        "152": "[5, 4, 0, 2, 3, 1, 6, 7]",
-        "153": "[6, 2, 1, 0, 5, 4, 3, 7]",
-        "154": "[0, 5, 4, 2, 3, 6, 1, 7]",
-        "155": "[1, 6, 5, 3, 4, 0, 2, 7]",
-        "156": "[2, 0, 6, 4, 5, 1, 3, 7]",
-        "157": "[3, 4, 6, 5, 2, 0, 1, 7]",
-        "158": "[4, 0, 2, 3, 6, 1, 5, 7]",
-        "159": "[5, 2, 4, 6, 1, 0, 3, 7]",
-        "160": "[6, 0, 2, 3, 4, 1, 5, 7]",
-        "161": "[0, 6, 4, 5, 1, 3, 2, 7]",
-        "162": "[1, 0, 5, 6, 2, 4, 3, 7]",
-        "163": "[2, 1, 6, 0, 3, 5, 4, 7]",
-        "164": "[3, 0, 6, 4, 1, 2, 5, 7]",
-        "165": "[4, 1, 2, 0, 5, 6, 3, 7]",
-        "166": "[5, 0, 4, 2, 3, 1, 6, 7]",
-        "167": "[6, 1, 2, 0, 5, 4, 3, 7]",
-        "168": "[0, 1, 6, 5, 2, 3, 4, 7]",
-        "169": "[1, 2, 0, 6, 3, 4, 5, 7]",
-        "170": "[2, 3, 1, 0, 4, 5, 6, 7]",
-        "171": "[3, 1, 0, 4, 5, 2, 6, 7]",
-        "172": "[4, 5, 1, 0, 3, 6, 2, 7]",
-        "173": "[5, 3, 0, 2, 6, 1, 4, 7]",
-        "174": "[6, 5, 1, 0, 3, 4, 2, 7]",
-        "175": "[0, 2, 6, 4, 3, 5, 1, 7]",
-        "176": "[1, 3, 0, 5, 4, 6, 2, 7]",
-        "177": "[2, 4, 1, 6, 5, 0, 3, 7]",
-        "178": "[3, 5, 0, 6, 2, 4, 1, 7]",
-        "179": "[4, 3, 1, 2, 6, 0, 5, 7]",
-        "180": "[5, 6, 0, 4, 1, 2, 3, 7]",
-        "181": "[6, 3, 1, 2, 4, 0, 5, 7]",
-        "182": "[0, 3, 4, 6, 1, 5, 2, 7]",
-        "183": "[1, 4, 5, 0, 2, 6, 3, 7]",
-        "184": "[2, 5, 6, 1, 3, 0, 4, 7]",
-        "185": "[3, 2, 6, 0, 1, 4, 5, 7]",
-        "186": "[4, 6, 2, 1, 5, 0, 3, 7]",
-        "187": "[5, 1, 4, 0, 3, 2, 6, 7]",
-        "188": "[6, 4, 2, 1, 5, 0, 3, 7]",
-        "189": "[0, 4, 5, 6, 1, 3, 2, 7]",
-        "190": "[1, 5, 6, 0, 2, 4, 3, 7]",
-        "191": "[2, 6, 0, 1, 3, 5, 4, 7]",
-        "192": "[3, 6, 4, 0, 1, 2, 5, 7]",
-        "193": "[4, 2, 0, 1, 5, 6, 3, 7]",
-        "194": "[5, 4, 2, 0, 3, 1, 6, 7]",
-        "195": "[6, 2, 0, 1, 5, 4, 3, 7]",
-        "196": "[0, 5, 2, 4, 3, 6, 1, 7]",
-        "197": "[1, 6, 3, 5, 4, 0, 2, 7]",
-        "198": "[2, 0, 4, 6, 5, 1, 3, 7]",
-        "199": "[3, 4, 5, 6, 2, 0, 1, 7]",
-        "200": "[4, 0, 3, 2, 6, 1, 5, 7]",
-        "201": "[5, 2, 6, 4, 1, 0, 3, 7]",
-        "202": "[6, 0, 3, 2, 4, 1, 5, 7]",
-        "203": "[0, 6, 5, 4, 1, 3, 2, 7]",
-        "204": "[1, 0, 6, 5, 2, 4, 3, 7]",
-        "205": "[2, 1, 0, 6, 3, 5, 4, 7]",
-        "206": "[3, 0, 4, 6, 1, 2, 5, 7]",
-        "207": "[4, 1, 0, 2, 5, 6, 3, 7]",
-        "208": "[5, 0, 2, 4, 3, 1, 6, 7]",
-        "209": "[6, 1, 0, 2, 5, 4, 3, 7]",
-        "210": "[0, 1, 2, 4, 6, 5, 3, 7]",
-        "211": "[1, 2, 3, 5, 0, 6, 4, 7]",
-        "212": "[2, 3, 4, 6, 1, 0, 5, 7]",
-        "213": "[3, 1, 5, 6, 0, 4, 2, 7]",
-        "214": "[4, 5, 3, 2, 1, 0, 6, 7]",
-        "215": "[5, 3, 6, 4, 0, 2, 1, 7]",
-        "216": "[6, 5, 3, 2, 1, 0, 4, 7]",
-        "217": "[0, 2, 3, 1, 6, 4, 5, 7]",
-        "218": "[1, 3, 4, 2, 0, 5, 6, 7]",
-        "219": "[2, 4, 5, 3, 1, 6, 0, 7]",
-        "220": "[3, 5, 2, 1, 0, 6, 4, 7]",
-        "221": "[4, 3, 6, 5, 1, 2, 0, 7]",
-        "222": "[5, 6, 1, 3, 0, 4, 2, 7]",
-        "223": "[6, 3, 4, 5, 1, 2, 0, 7]",
-        "224": "[0, 3, 1, 2, 4, 6, 5, 7]",
-        "225": "[1, 4, 2, 3, 5, 0, 6, 7]",
-        "226": "[2, 5, 3, 4, 6, 1, 0, 7]",
-        "227": "[3, 2, 1, 5, 6, 0, 4, 7]",
-        "228": "[4, 6, 5, 3, 2, 1, 0, 7]",
-        "229": "[5, 1, 3, 6, 4, 0, 2, 7]",
-        "230": "[6, 4, 5, 3, 2, 1, 0, 7]",
-        "231": "[0, 4, 1, 2, 5, 6, 3, 7]",
-        "232": "[1, 5, 2, 3, 6, 0, 4, 7]",
-        "233": "[2, 6, 3, 4, 0, 1, 5, 7]",
-        "234": "[3, 6, 1, 5, 4, 0, 2, 7]",
-        "235": "[4, 2, 5, 3, 0, 1, 6, 7]",
-        "236": "[5, 4, 3, 6, 2, 0, 1, 7]",
-        "237": "[6, 2, 5, 3, 0, 1, 4, 7]",
-        "238": "[0, 5, 3, 1, 2, 4, 6, 7]",
-        "239": "[1, 6, 4, 2, 3, 5, 0, 7]",
-        "240": "[2, 0, 5, 3, 4, 6, 1, 7]",
-        "241": "[3, 4, 2, 1, 5, 6, 0, 7]",
-        "242": "[4, 0, 6, 5, 3, 2, 1, 7]",
-        "243": "[5, 2, 1, 3, 6, 4, 0, 7]",
-        "244": "[6, 0, 4, 5, 3, 2, 1, 7]",
-        "245": "[0, 6, 1, 2, 5, 4, 3, 7]",
-        "246": "[1, 0, 2, 3, 6, 5, 4, 7]",
-        "247": "[2, 1, 3, 4, 0, 6, 5, 7]",
-        "248": "[3, 0, 1, 5, 4, 6, 2, 7]",
-        "249": "[4, 1, 5, 3, 0, 2, 6, 7]",
-        "250": "[5, 0, 3, 6, 2, 4, 1, 7]",
-        "251": "[6, 1, 5, 3, 0, 2, 4, 7]",
-        "252": "[0, 1, 3, 5, 6, 2, 4, 7]",
-        "253": "[1, 2, 4, 6, 0, 3, 5, 7]",
-        "254": "[2, 3, 5, 0, 1, 4, 6, 7]",
-        "255": "[3, 1, 2, 4, 0, 5, 6, 7]",
-        "256": "[4, 5, 6, 0, 1, 3, 2, 7]",
-        "257": "[5, 3, 1, 2, 0, 6, 4, 7]",
-        "258": "[6, 5, 4, 0, 1, 3, 2, 7]",
-        "259": "[0, 2, 5, 4, 6, 3, 1, 7]",
-        "260": "[1, 3, 6, 5, 0, 4, 2, 7]",
-        "261": "[2, 4, 0, 6, 1, 5, 3, 7]",
-        "262": "[3, 5, 4, 6, 0, 2, 1, 7]",
-        "263": "[4, 3, 0, 2, 1, 6, 5, 7]",
-        "264": "[5, 6, 2, 4, 0, 1, 3, 7]",
-        "265": "[6, 3, 0, 2, 1, 4, 5, 7]",
-        "266": "[0, 3, 5, 6, 4, 1, 2, 7]",
-        "267": "[1, 4, 6, 0, 5, 2, 3, 7]",
-        "268": "[2, 5, 0, 1, 6, 3, 4, 7]",
-        "269": "[3, 2, 4, 0, 6, 1, 5, 7]",
-        "270": "[4, 6, 0, 1, 2, 5, 3, 7]",
-        "271": "[5, 1, 2, 0, 4, 3, 6, 7]",
-        "272": "[6, 4, 0, 1, 2, 5, 3, 7]",
-        "273": "[0, 4, 3, 6, 5, 1, 2, 7]",
-        "274": "[1, 5, 4, 0, 6, 2, 3, 7]",
-        "275": "[2, 6, 5, 1, 0, 3, 4, 7]",
-        "276": "[3, 6, 2, 0, 4, 1, 5, 7]",
-        "277": "[4, 2, 6, 1, 0, 5, 3, 7]",
-        "278": "[5, 4, 1, 0, 2, 3, 6, 7]",
-        "279": "[6, 2, 4, 1, 0, 5, 3, 7]",
-        "280": "[0, 5, 6, 4, 2, 3, 1, 7]",
-        "281": "[1, 6, 0, 5, 3, 4, 2, 7]",
-        "282": "[2, 0, 1, 6, 4, 5, 3, 7]",
-        "283": "[3, 4, 0, 6, 5, 2, 1, 7]",
-        "284": "[4, 0, 1, 2, 3, 6, 5, 7]",
-        "285": "[5, 2, 0, 4, 6, 1, 3, 7]",
-        "286": "[6, 0, 1, 2, 3, 4, 5, 7]",
-        "287": "[0, 6, 3, 4, 5, 1, 2, 7]",
-        "288": "[1, 0, 4, 5, 6, 2, 3, 7]",
-        "289": "[2, 1, 5, 6, 0, 3, 4, 7]",
-        "290": "[3, 0, 2, 6, 4, 1, 5, 7]",
-        "291": "[4, 1, 6, 2, 0, 5, 3, 7]",
-        "292": "[5, 0, 1, 4, 2, 3, 6, 7]",
-        "293": "[6, 1, 4, 2, 0, 5, 3, 7]",
-        "294": "[0, 1, 4, 3, 2, 6, 5, 7]",
-        "295": "[1, 2, 5, 4, 3, 0, 6, 7]",
-        "296": "[2, 3, 6, 5, 4, 1, 0, 7]",
-        "297": "[3, 1, 6, 2, 5, 0, 4, 7]",
-        "298": "[4, 5, 2, 6, 3, 1, 0, 7]",
-        "299": "[5, 3, 4, 1, 6, 0, 2, 7]",
-        "300": "[6, 5, 2, 4, 3, 1, 0, 7]",
-        "301": "[0, 2, 1, 5, 3, 6, 4, 7]",
-        "302": "[1, 3, 2, 6, 4, 0, 5, 7]",
-        "303": "[2, 4, 3, 0, 5, 1, 6, 7]",
-        "304": "[3, 5, 1, 4, 2, 0, 6, 7]",
-        "305": "[4, 3, 5, 0, 6, 1, 2, 7]",
-        "306": "[5, 6, 3, 2, 1, 0, 4, 7]",
-        "307": "[6, 3, 5, 0, 4, 1, 2, 7]",
-        "308": "[0, 3, 2, 5, 1, 4, 6, 7]",
-        "309": "[1, 4, 3, 6, 2, 5, 0, 7]",
-        "310": "[2, 5, 4, 0, 3, 6, 1, 7]",
-        "311": "[3, 2, 5, 4, 1, 6, 0, 7]",
-        "312": "[4, 6, 3, 0, 5, 2, 1, 7]",
-        "313": "[5, 1, 6, 2, 3, 4, 0, 7]",
-        "314": "[6, 4, 3, 0, 5, 2, 1, 7]",
-        "315": "[0, 4, 2, 3, 1, 5, 6, 7]",
-        "316": "[1, 5, 3, 4, 2, 6, 0, 7]",
-        "317": "[2, 6, 4, 5, 3, 0, 1, 7]",
-        "318": "[3, 6, 5, 2, 1, 4, 0, 7]",
-        "319": "[4, 2, 3, 6, 5, 0, 1, 7]",
-        "320": "[5, 4, 6, 1, 3, 2, 0, 7]",
-        "321": "[6, 2, 3, 4, 5, 0, 1, 7]",
-        "322": "[0, 5, 1, 6, 3, 2, 4, 7]",
-        "323": "[1, 6, 2, 0, 4, 3, 5, 7]",
-        "324": "[2, 0, 3, 1, 5, 4, 6, 7]",
-        "325": "[3, 4, 1, 0, 2, 5, 6, 7]",
-        "326": "[4, 0, 5, 1, 6, 3, 2, 7]",
-        "327": "[5, 2, 3, 0, 1, 6, 4, 7]",
-        "328": "[6, 0, 5, 1, 4, 3, 2, 7]",
-        "329": "[0, 6, 2, 3, 1, 5, 4, 7]",
-        "330": "[1, 0, 3, 4, 2, 6, 5, 7]",
-        "331": "[2, 1, 4, 5, 3, 0, 6, 7]",
-        "332": "[3, 0, 5, 2, 1, 4, 6, 7]",
-        "333": "[4, 1, 3, 6, 5, 0, 2, 7]",
-        "334": "[5, 0, 6, 1, 3, 2, 4, 7]",
-        "335": "[6, 1, 3, 4, 5, 0, 2, 7]",
-        "336": "[0, 1, 5, 3, 2, 4, 6, 7]",
-        "337": "[1, 2, 6, 4, 3, 5, 0, 7]",
-        "338": "[2, 3, 0, 5, 4, 6, 1, 7]",
-        "339": "[3, 1, 4, 2, 5, 6, 0, 7]",
-        "340": "[4, 5, 0, 6, 3, 2, 1, 7]",
-        "341": "[5, 3, 2, 1, 6, 4, 0, 7]",
-        "342": "[6, 5, 0, 4, 3, 2, 1, 7]",
-        "343": "[0, 2, 4, 5, 3, 1, 6, 7]",
-        "344": "[1, 3, 5, 6, 4, 2, 0, 7]",
-        "345": "[2, 4, 6, 0, 5, 3, 1, 7]",
-        "346": "[3, 5, 6, 4, 2, 1, 0, 7]",
-        "347": "[4, 3, 2, 0, 6, 5, 1, 7]",
-        "348": "[5, 6, 4, 2, 1, 3, 0, 7]",
-        "349": "[6, 3, 2, 0, 4, 5, 1, 7]",
-        "350": "[0, 3, 6, 5, 1, 2, 4, 7]",
-        "351": "[1, 4, 0, 6, 2, 3, 5, 7]",
-        "352": "[2, 5, 1, 0, 3, 4, 6, 7]",
-        "353": "[3, 2, 0, 4, 1, 5, 6, 7]",
-        "354": "[4, 6, 1, 0, 5, 3, 2, 7]",
-        "355": "[5, 1, 0, 2, 3, 6, 4, 7]",
-        "356": "[6, 4, 1, 0, 5, 3, 2, 7]",
-        "357": "[0, 4, 6, 3, 1, 2, 5, 7]",
-        "358": "[1, 5, 0, 4, 2, 3, 6, 7]",
-        "359": "[2, 6, 1, 5, 3, 4, 0, 7]",
-        "360": "[3, 6, 0, 2, 1, 5, 4, 7]",
-        "361": "[4, 2, 1, 6, 5, 3, 0, 7]",
-        "362": "[5, 4, 0, 1, 3, 6, 2, 7]",
-        "363": "[6, 2, 1, 4, 5, 3, 0, 7]",
-        "364": "[0, 5, 4, 6, 3, 1, 2, 7]",
-        "365": "[1, 6, 5, 0, 4, 2, 3, 7]",
-        "366": "[2, 0, 6, 1, 5, 3, 4, 7]",
-        "367": "[3, 4, 6, 0, 2, 1, 5, 7]",
-        "368": "[4, 0, 2, 1, 6, 5, 3, 7]",
-        "369": "[5, 2, 4, 0, 1, 3, 6, 7]",
-        "370": "[6, 0, 2, 1, 4, 5, 3, 7]",
-        "371": "[0, 6, 4, 3, 1, 2, 5, 7]",
-        "372": "[1, 0, 5, 4, 2, 3, 6, 7]",
-        "373": "[2, 1, 6, 5, 3, 4, 0, 7]",
-        "374": "[3, 0, 6, 2, 1, 5, 4, 7]",
-        "375": "[4, 1, 2, 6, 5, 3, 0, 7]",
-        "376": "[5, 0, 4, 1, 3, 6, 2, 7]",
-        "377": "[6, 1, 2, 4, 5, 3, 0, 7]",
-        "378": "[0, 1, 6, 3, 2, 4, 5, 7]",
-        "379": "[1, 2, 0, 4, 3, 5, 6, 7]",
-        "380": "[2, 3, 1, 5, 4, 6, 0, 7]",
-        "381": "[3, 1, 0, 2, 5, 6, 4, 7]",
-        "382": "[4, 5, 1, 6, 3, 2, 0, 7]",
-        "383": "[5, 3, 0, 1, 6, 4, 2, 7]",
-        "384": "[6, 5, 1, 4, 3, 2, 0, 7]",
-        "385": "[0, 2, 6, 5, 3, 1, 4, 7]",
-        "386": "[1, 3, 0, 6, 4, 2, 5, 7]",
-        "387": "[2, 4, 1, 0, 5, 3, 6, 7]",
-        "388": "[3, 5, 0, 4, 2, 1, 6, 7]",
-        "389": "[4, 3, 1, 0, 6, 5, 2, 7]",
-        "390": "[5, 6, 0, 2, 1, 3, 4, 7]",
-        "391": "[6, 3, 1, 0, 4, 5, 2, 7]",
-        "392": "[0, 3, 4, 5, 1, 2, 6, 7]",
-        "393": "[1, 4, 5, 6, 2, 3, 0, 7]",
-        "394": "[2, 5, 6, 0, 3, 4, 1, 7]",
-        "395": "[3, 2, 6, 4, 1, 5, 0, 7]",
-        "396": "[4, 6, 2, 0, 5, 3, 1, 7]",
-        "397": "[5, 1, 4, 2, 3, 6, 0, 7]",
-        "398": "[6, 4, 2, 0, 5, 3, 1, 7]",
-        "399": "[0, 4, 5, 3, 1, 2, 6, 7]",
-        "400": "[1, 5, 6, 4, 2, 3, 0, 7]",
-        "401": "[2, 6, 0, 5, 3, 4, 1, 7]",
-        "402": "[3, 6, 4, 2, 1, 5, 0, 7]",
-        "403": "[4, 2, 0, 6, 5, 3, 1, 7]",
-        "404": "[5, 4, 2, 1, 3, 6, 0, 7]",
-        "405": "[6, 2, 0, 4, 5, 3, 1, 7]",
-        "406": "[0, 5, 2, 6, 3, 1, 4, 7]",
-        "407": "[1, 6, 3, 0, 4, 2, 5, 7]",
-        "408": "[2, 0, 4, 1, 5, 3, 6, 7]",
-        "409": "[3, 4, 5, 0, 2, 1, 6, 7]",
-        "410": "[4, 0, 3, 1, 6, 5, 2, 7]",
-        "411": "[5, 2, 6, 0, 1, 3, 4, 7]",
-        "412": "[6, 0, 3, 1, 4, 5, 2, 7]",
-        "413": "[0, 6, 5, 3, 1, 2, 4, 7]",
-        "414": "[1, 0, 6, 4, 2, 3, 5, 7]",
-        "415": "[2, 1, 0, 5, 3, 4, 6, 7]",
-        "416": "[3, 0, 4, 2, 1, 5, 6, 7]",
-        "417": "[4, 1, 0, 6, 5, 3, 2, 7]",
-        "418": "[5, 0, 2, 1, 3, 6, 4, 7]",
-        "419": "[6, 1, 0, 4, 5, 3, 2, 7]",
-        "420": "[0, 1, 2, 5, 6, 3, 4, 7]",
-        "421": "[1, 2, 3, 6, 0, 4, 5, 7]",
-        "422": "[2, 3, 4, 0, 1, 5, 6, 7]",
-        "423": "[3, 1, 5, 4, 0, 2, 6, 7]",
-        "424": "[4, 5, 3, 0, 1, 6, 2, 7]",
-        "425": "[5, 3, 6, 2, 0, 1, 4, 7]",
-        "426": "[6, 5, 3, 0, 1, 4, 2, 7]",
-        "427": "[0, 2, 3, 4, 6, 5, 1, 7]",
-        "428": "[1, 3, 4, 5, 0, 6, 2, 7]",
-        "429": "[2, 4, 5, 6, 1, 0, 3, 7]",
-        "430": "[3, 5, 2, 6, 0, 4, 1, 7]",
-        "431": "[4, 3, 6, 2, 1, 0, 5, 7]",
-        "432": "[5, 6, 1, 4, 0, 2, 3, 7]",
-        "433": "[6, 3, 4, 2, 1, 0, 5, 7]",
-        "434": "[0, 3, 1, 6, 4, 5, 2, 7]",
-        "435": "[1, 4, 2, 0, 5, 6, 3, 7]",
-        "436": "[2, 5, 3, 1, 6, 0, 4, 7]",
-        "437": "[3, 2, 1, 0, 6, 4, 5, 7]",
-        "438": "[4, 6, 5, 1, 2, 0, 3, 7]",
-        "439": "[5, 1, 3, 0, 4, 2, 6, 7]",
-        "440": "[6, 4, 5, 1, 2, 0, 3, 7]",
-        "441": "[0, 4, 1, 6, 5, 3, 2, 7]",
-        "442": "[1, 5, 2, 0, 6, 4, 3, 7]",
-        "443": "[2, 6, 3, 1, 0, 5, 4, 7]",
-        "444": "[3, 6, 1, 0, 4, 2, 5, 7]",
-        "445": "[4, 2, 5, 1, 0, 6, 3, 7]",
-        "446": "[5, 4, 3, 0, 2, 1, 6, 7]",
-        "447": "[6, 2, 5, 1, 0, 4, 3, 7]",
-        "448": "[0, 5, 3, 4, 2, 6, 1, 7]",
-        "449": "[1, 6, 4, 5, 3, 0, 2, 7]",
-        "450": "[2, 0, 5, 6, 4, 1, 3, 7]",
-        "451": "[3, 4, 2, 6, 5, 0, 1, 7]",
-        "452": "[4, 0, 6, 2, 3, 1, 5, 7]",
-        "453": "[5, 2, 1, 4, 6, 0, 3, 7]",
-        "454": "[6, 0, 4, 2, 3, 1, 5, 7]",
-        "455": "[0, 6, 1, 4, 5, 3, 2, 7]",
-        "456": "[1, 0, 2, 5, 6, 4, 3, 7]",
-        "457": "[2, 1, 3, 6, 0, 5, 4, 7]",
-        "458": "[3, 0, 1, 6, 4, 2, 5, 7]",
-        "459": "[4, 1, 5, 2, 0, 6, 3, 7]",
-        "460": "[5, 0, 3, 4, 2, 1, 6, 7]",
-        "461": "[6, 1, 5, 2, 0, 4, 3, 7]",
-        "462": "[0, 1, 3, 2, 6, 4, 5, 7]",
-        "463": "[1, 2, 4, 3, 0, 5, 6, 7]",
-        "464": "[2, 3, 5, 4, 1, 6, 0, 7]",
-        "465": "[3, 1, 2, 5, 0, 6, 4, 7]",
-        "466": "[4, 5, 6, 3, 1, 2, 0, 7]",
-        "467": "[5, 3, 1, 6, 0, 4, 2, 7]",
-        "468": "[6, 5, 4, 3, 1, 2, 0, 7]",
-        "469": "[0, 2, 5, 3, 6, 1, 4, 7]",
-        "470": "[1, 3, 6, 4, 0, 2, 5, 7]",
-        "471": "[2, 4, 0, 5, 1, 3, 6, 7]",
-        "472": "[3, 5, 4, 2, 0, 1, 6, 7]",
-        "473": "[4, 3, 0, 6, 1, 5, 2, 7]",
-        "474": "[5, 6, 2, 1, 0, 3, 4, 7]",
-        "475": "[6, 3, 0, 4, 1, 5, 2, 7]",
-        "476": "[0, 3, 5, 1, 4, 2, 6, 7]",
-        "477": "[1, 4, 6, 2, 5, 3, 0, 7]",
-        "478": "[2, 5, 0, 3, 6, 4, 1, 7]",
-        "479": "[3, 2, 4, 1, 6, 5, 0, 7]",
-        "480": "[4, 6, 0, 5, 2, 3, 1, 7]",
-        "481": "[5, 1, 2, 3, 4, 6, 0, 7]",
-        "482": "[6, 4, 0, 5, 2, 3, 1, 7]",
-        "483": "[0, 4, 3, 1, 5, 2, 6, 7]",
-        "484": "[1, 5, 4, 2, 6, 3, 0, 7]",
-        "485": "[2, 6, 5, 3, 0, 4, 1, 7]",
-        "486": "[3, 6, 2, 1, 4, 5, 0, 7]",
-        "487": "[4, 2, 6, 5, 0, 3, 1, 7]",
-        "488": "[5, 4, 1, 3, 2, 6, 0, 7]",
-        "489": "[6, 2, 4, 5, 0, 3, 1, 7]",
-        "490": "[0, 5, 6, 3, 2, 1, 4, 7]",
-        "491": "[1, 6, 0, 4, 3, 2, 5, 7]",
-        "492": "[2, 0, 1, 5, 4, 3, 6, 7]",
-        "493": "[3, 4, 0, 2, 5, 1, 6, 7]",
-        "494": "[4, 0, 1, 6, 3, 5, 2, 7]",
-        "495": "[5, 2, 0, 1, 6, 3, 4, 7]",
-        "496": "[6, 0, 1, 4, 3, 5, 2, 7]",
-        "497": "[0, 6, 3, 1, 5, 2, 4, 7]",
-        "498": "[1, 0, 4, 2, 6, 3, 5, 7]",
-        "499": "[2, 1, 5, 3, 0, 4, 6, 7]",
-        "500": "[3, 0, 2, 1, 4, 5, 6, 7]",
-        "501": "[4, 1, 6, 5, 0, 3, 2, 7]",
-        "502": "[5, 0, 1, 3, 2, 6, 4, 7]",
-        "503": "[6, 1, 4, 5, 0, 3, 2, 7]",
-        "504": "[0, 1, 4, 6, 2, 5, 3, 7]",
-        "505": "[1, 2, 5, 0, 3, 6, 4, 7]",
-        "506": "[2, 3, 6, 1, 4, 0, 5, 7]",
-        "507": "[3, 1, 6, 0, 5, 4, 2, 7]",
-        "508": "[4, 5, 2, 1, 3, 0, 6, 7]",
-        "509": "[5, 3, 4, 0, 6, 2, 1, 7]",
-        "510": "[6, 5, 2, 1, 3, 0, 4, 7]",
-        "511": "[0, 2, 1, 6, 3, 4, 5, 7]",
-        "512": "[1, 3, 2, 0, 4, 5, 6, 7]",
-        "513": "[2, 4, 3, 1, 5, 6, 0, 7]",
-        "514": "[3, 5, 1, 0, 2, 6, 4, 7]",
-        "515": "[4, 3, 5, 1, 6, 2, 0, 7]",
-        "516": "[5, 6, 3, 0, 1, 4, 2, 7]",
-        "517": "[6, 3, 5, 1, 4, 2, 0, 7]",
-        "518": "[0, 3, 2, 4, 1, 6, 5, 7]",
-        "519": "[1, 4, 3, 5, 2, 0, 6, 7]",
-        "520": "[2, 5, 4, 6, 3, 1, 0, 7]",
-        "521": "[3, 2, 5, 6, 1, 0, 4, 7]",
-        "522": "[4, 6, 3, 2, 5, 1, 0, 7]",
-        "523": "[5, 1, 6, 4, 3, 0, 2, 7]",
-        "524": "[6, 4, 3, 2, 5, 1, 0, 7]",
-        "525": "[0, 4, 2, 5, 1, 6, 3, 7]",
-        "526": "[1, 5, 3, 6, 2, 0, 4, 7]",
-        "527": "[2, 6, 4, 0, 3, 1, 5, 7]",
-        "528": "[3, 6, 5, 4, 1, 0, 2, 7]",
-        "529": "[4, 2, 3, 0, 5, 1, 6, 7]",
-        "530": "[5, 4, 6, 2, 3, 0, 1, 7]",
-        "531": "[6, 2, 3, 0, 5, 1, 4, 7]",
-        "532": "[0, 5, 1, 2, 3, 4, 6, 7]",
-        "533": "[1, 6, 2, 3, 4, 5, 0, 7]",
-        "534": "[2, 0, 3, 4, 5, 6, 1, 7]",
-        "535": "[3, 4, 1, 5, 2, 6, 0, 7]",
-        "536": "[4, 0, 5, 3, 6, 2, 1, 7]",
-        "537": "[5, 2, 3, 6, 1, 4, 0, 7]",
-        "538": "[6, 0, 5, 3, 4, 2, 1, 7]",
-        "539": "[0, 6, 2, 5, 1, 4, 3, 7]",
-        "540": "[1, 0, 3, 6, 2, 5, 4, 7]",
-        "541": "[2, 1, 4, 0, 3, 6, 5, 7]",
-        "542": "[3, 0, 5, 4, 1, 6, 2, 7]",
-        "543": "[4, 1, 3, 0, 5, 2, 6, 7]",
-        "544": "[5, 0, 6, 2, 3, 4, 1, 7]",
-        "545": "[6, 1, 3, 0, 5, 2, 4, 7]",
-        "546": "[0, 1, 5, 4, 2, 6, 3, 7]",
-        "547": "[1, 2, 6, 5, 3, 0, 4, 7]",
-        "548": "[2, 3, 0, 6, 4, 1, 5, 7]",
-        "549": "[3, 1, 4, 6, 5, 0, 2, 7]",
-        "550": "[4, 5, 0, 2, 3, 1, 6, 7]",
-        "551": "[5, 3, 2, 4, 6, 0, 1, 7]",
-        "552": "[6, 5, 0, 2, 3, 1, 4, 7]",
-        "553": "[0, 2, 4, 1, 3, 6, 5, 7]",
-        "554": "[1, 3, 5, 2, 4, 0, 6, 7]",
-        "555": "[2, 4, 6, 3, 5, 1, 0, 7]",
-        "556": "[3, 5, 6, 1, 2, 0, 4, 7]",
-        "557": "[4, 3, 2, 5, 6, 1, 0, 7]",
-        "558": "[5, 6, 4, 3, 1, 0, 2, 7]",
-        "559": "[6, 3, 2, 5, 4, 1, 0, 7]",
-        "560": "[0, 3, 6, 2, 1, 4, 5, 7]",
-        "561": "[1, 4, 0, 3, 2, 5, 6, 7]",
-        "562": "[2, 5, 1, 4, 3, 6, 0, 7]",
-        "563": "[3, 2, 0, 5, 1, 6, 4, 7]",
-        "564": "[4, 6, 1, 3, 5, 2, 0, 7]",
-        "565": "[5, 1, 0, 6, 3, 4, 2, 7]",
-        "566": "[6, 4, 1, 3, 5, 2, 0, 7]",
-        "567": "[0, 4, 6, 2, 1, 5, 3, 7]",
-        "568": "[1, 5, 0, 3, 2, 6, 4, 7]",
-        "569": "[2, 6, 1, 4, 3, 0, 5, 7]",
-        "570": "[3, 6, 0, 5, 1, 4, 2, 7]",
-        "571": "[4, 2, 1, 3, 5, 0, 6, 7]",
-        "572": "[5, 4, 0, 6, 3, 2, 1, 7]",
-        "573": "[6, 2, 1, 3, 5, 0, 4, 7]",
-        "574": "[0, 5, 4, 1, 3, 2, 6, 7]",
-        "575": "[1, 6, 5, 2, 4, 3, 0, 7]",
-        "576": "[2, 0, 6, 3, 5, 4, 1, 7]",
-        "577": "[3, 4, 6, 1, 2, 5, 0, 7]",
-        "578": "[4, 0, 2, 5, 6, 3, 1, 7]",
-        "579": "[5, 2, 4, 3, 1, 6, 0, 7]",
-        "580": "[6, 0, 2, 5, 4, 3, 1, 7]",
-        "581": "[0, 6, 4, 2, 1, 5, 3, 7]",
-        "582": "[1, 0, 5, 3, 2, 6, 4, 7]",
-        "583": "[2, 1, 6, 4, 3, 0, 5, 7]",
-        "584": "[3, 0, 6, 5, 1, 4, 2, 7]",
-        "585": "[4, 1, 2, 3, 5, 0, 6, 7]",
-        "586": "[5, 0, 4, 6, 3, 2, 1, 7]",
-        "587": "[6, 1, 2, 3, 5, 0, 4, 7]",
-        "588": "[0, 1, 6, 4, 2, 5, 3, 7]",
-        "589": "[1, 2, 0, 5, 3, 6, 4, 7]",
-        "590": "[2, 3, 1, 6, 4, 0, 5, 7]",
-        "591": "[3, 1, 0, 6, 5, 4, 2, 7]",
-        "592": "[4, 5, 1, 2, 3, 0, 6, 7]",
-        "593": "[5, 3, 0, 4, 6, 2, 1, 7]",
-        "594": "[6, 5, 1, 2, 3, 0, 4, 7]",
-        "595": "[0, 2, 6, 1, 3, 4, 5, 7]",
-        "596": "[1, 3, 0, 2, 4, 5, 6, 7]",
-        "597": "[2, 4, 1, 3, 5, 6, 0, 7]",
-        "598": "[3, 5, 0, 1, 2, 6, 4, 7]",
-        "599": "[4, 3, 1, 5, 6, 2, 0, 7]",
-        "600": "[5, 6, 0, 3, 1, 4, 2, 7]",
-        "601": "[6, 3, 1, 5, 4, 2, 0, 7]",
-        "602": "[0, 3, 4, 2, 1, 6, 5, 7]",
-        "603": "[1, 4, 5, 3, 2, 0, 6, 7]",
-        "604": "[2, 5, 6, 4, 3, 1, 0, 7]",
-        "605": "[3, 2, 6, 5, 1, 0, 4, 7]",
-        "606": "[4, 6, 2, 3, 5, 1, 0, 7]",
-        "607": "[5, 1, 4, 6, 3, 0, 2, 7]",
-        "608": "[6, 4, 2, 3, 5, 1, 0, 7]",
-        "609": "[0, 4, 5, 2, 1, 6, 3, 7]",
-        "610": "[1, 5, 6, 3, 2, 0, 4, 7]",
-        "611": "[2, 6, 0, 4, 3, 1, 5, 7]",
-        "612": "[3, 6, 4, 5, 1, 0, 2, 7]",
-        "613": "[4, 2, 0, 3, 5, 1, 6, 7]",
-        "614": "[5, 4, 2, 6, 3, 0, 1, 7]",
-        "615": "[6, 2, 0, 3, 5, 1, 4, 7]",
-        "616": "[0, 5, 2, 1, 3, 4, 6, 7]",
-        "617": "[1, 6, 3, 2, 4, 5, 0, 7]",
-        "618": "[2, 0, 4, 3, 5, 6, 1, 7]",
-        "619": "[3, 4, 5, 1, 2, 6, 0, 7]",
-        "620": "[4, 0, 3, 5, 6, 2, 1, 7]",
-        "621": "[5, 2, 6, 3, 1, 4, 0, 7]",
-        "622": "[6, 0, 3, 5, 4, 2, 1, 7]",
-        "623": "[0, 6, 5, 2, 1, 4, 3, 7]",
-        "624": "[1, 0, 6, 3, 2, 5, 4, 7]",
-        "625": "[2, 1, 0, 4, 3, 6, 5, 7]",
-        "626": "[3, 0, 4, 5, 1, 6, 2, 7]",
-        "627": "[4, 1, 0, 3, 5, 2, 6, 7]",
-        "628": "[5, 0, 2, 6, 3, 4, 1, 7]",
-        "629": "[6, 1, 0, 3, 5, 2, 4, 7]",
-        "630": "[0, 1, 2, 6, 4, 5, 3, 7]",
-        "631": "[1, 2, 3, 0, 5, 6, 4, 7]",
-        "632": "[2, 3, 4, 1, 6, 0, 5, 7]",
-        "633": "[3, 1, 5, 0, 6, 4, 2, 7]",
-        "634": "[4, 5, 3, 1, 2, 0, 6, 7]",
-        "635": "[5, 3, 6, 0, 4, 2, 1, 7]",
-        "636": "[6, 5, 3, 1, 2, 0, 4, 7]",
-        "637": "[0, 2, 3, 6, 1, 4, 5, 7]",
-        "638": "[1, 3, 4, 0, 2, 5, 6, 7]",
-        "639": "[2, 4, 5, 1, 3, 6, 0, 7]",
-        "640": "[3, 5, 2, 0, 1, 6, 4, 7]",
-        "641": "[4, 3, 6, 1, 5, 2, 0, 7]",
-        "642": "[5, 6, 1, 0, 3, 4, 2, 7]",
-        "643": "[6, 3, 4, 1, 5, 2, 0, 7]",
-        "644": "[0, 3, 1, 4, 2, 6, 5, 7]",
-        "645": "[1, 4, 2, 5, 3, 0, 6, 7]",
-        "646": "[2, 5, 3, 6, 4, 1, 0, 7]",
-        "647": "[3, 2, 1, 6, 5, 0, 4, 7]",
-        "648": "[4, 6, 5, 2, 3, 1, 0, 7]",
-        "649": "[5, 1, 3, 4, 6, 0, 2, 7]",
-        "650": "[6, 4, 5, 2, 3, 1, 0, 7]",
-        "651": "[0, 4, 1, 5, 2, 6, 3, 7]",
-        "652": "[1, 5, 2, 6, 3, 0, 4, 7]",
-        "653": "[2, 6, 3, 0, 4, 1, 5, 7]",
-        "654": "[3, 6, 1, 4, 5, 0, 2, 7]",
-        "655": "[4, 2, 5, 0, 3, 1, 6, 7]",
-        "656": "[5, 4, 3, 2, 6, 0, 1, 7]",
-        "657": "[6, 2, 5, 0, 3, 1, 4, 7]",
-        "658": "[0, 5, 3, 2, 1, 4, 6, 7]",
-        "659": "[1, 6, 4, 3, 2, 5, 0, 7]",
-        "660": "[2, 0, 5, 4, 3, 6, 1, 7]",
-        "661": "[3, 4, 2, 5, 1, 6, 0, 7]",
-        "662": "[4, 0, 6, 3, 5, 2, 1, 7]",
-        "663": "[5, 2, 1, 6, 3, 4, 0, 7]",
-        "664": "[6, 0, 4, 3, 5, 2, 1, 7]",
-        "665": "[0, 6, 1, 5, 2, 4, 3, 7]",
-        "666": "[1, 0, 2, 6, 3, 5, 4, 7]",
-        "667": "[2, 1, 3, 0, 4, 6, 5, 7]",
-        "668": "[3, 0, 1, 4, 5, 6, 2, 7]",
-        "669": "[4, 1, 5, 0, 3, 2, 6, 7]",
-        "670": "[5, 0, 3, 2, 6, 4, 1, 7]",
-        "671": "[6, 1, 5, 0, 3, 2, 4, 7]",
-        "672": "[0, 1, 3, 6, 5, 2, 4, 7]",
-        "673": "[1, 2, 4, 0, 6, 3, 5, 7]",
-        "674": "[2, 3, 5, 1, 0, 4, 6, 7]",
-        "675": "[3, 1, 2, 0, 4, 5, 6, 7]",
-        "676": "[4, 5, 6, 1, 0, 3, 2, 7]",
-        "677": "[5, 3, 1, 0, 2, 6, 4, 7]",
-        "678": "[6, 5, 4, 1, 0, 3, 2, 7]",
-        "679": "[0, 2, 5, 6, 4, 3, 1, 7]",
-        "680": "[1, 3, 6, 0, 5, 4, 2, 7]",
-        "681": "[2, 4, 0, 1, 6, 5, 3, 7]",
-        "682": "[3, 5, 4, 0, 6, 2, 1, 7]",
-        "683": "[4, 3, 0, 1, 2, 6, 5, 7]",
-        "684": "[5, 6, 2, 0, 4, 1, 3, 7]",
-        "685": "[6, 3, 0, 1, 2, 4, 5, 7]",
-        "686": "[0, 3, 5, 4, 6, 1, 2, 7]",
-        "687": "[1, 4, 6, 5, 0, 2, 3, 7]",
-        "688": "[2, 5, 0, 6, 1, 3, 4, 7]",
-        "689": "[3, 2, 4, 6, 0, 1, 5, 7]",
-        "690": "[4, 6, 0, 2, 1, 5, 3, 7]",
-        "691": "[5, 1, 2, 4, 0, 3, 6, 7]",
-        "692": "[6, 4, 0, 2, 1, 5, 3, 7]",
-        "693": "[0, 4, 3, 5, 6, 1, 2, 7]",
-        "694": "[1, 5, 4, 6, 0, 2, 3, 7]",
-        "695": "[2, 6, 5, 0, 1, 3, 4, 7]",
-        "696": "[3, 6, 2, 4, 0, 1, 5, 7]",
-        "697": "[4, 2, 6, 0, 1, 5, 3, 7]",
-        "698": "[5, 4, 1, 2, 0, 3, 6, 7]",
-        "699": "[6, 2, 4, 0, 1, 5, 3, 7]",
-        "700": "[0, 5, 6, 2, 4, 3, 1, 7]",
-        "701": "[1, 6, 0, 3, 5, 4, 2, 7]",
-        "702": "[2, 0, 1, 4, 6, 5, 3, 7]",
-        "703": "[3, 4, 0, 5, 6, 2, 1, 7]",
-        "704": "[4, 0, 1, 3, 2, 6, 5, 7]",
-        "705": "[5, 2, 0, 6, 4, 1, 3, 7]",
-        "706": "[6, 0, 1, 3, 2, 4, 5, 7]",
-        "707": "[0, 6, 3, 5, 4, 1, 2, 7]",
-        "708": "[1, 0, 4, 6, 5, 2, 3, 7]",
-        "709": "[2, 1, 5, 0, 6, 3, 4, 7]",
-        "710": "[3, 0, 2, 4, 6, 1, 5, 7]",
-        "711": "[4, 1, 6, 0, 2, 5, 3, 7]",
-        "712": "[5, 0, 1, 2, 4, 3, 6, 7]",
-        "713": "[6, 1, 4, 0, 2, 5, 3, 7]",
-        "714": "[0, 1, 4, 2, 3, 6, 5, 7]",
-        "715": "[1, 2, 5, 3, 4, 0, 6, 7]",
-        "716": "[2, 3, 6, 4, 5, 1, 0, 7]",
-        "717": "[3, 1, 6, 5, 2, 0, 4, 7]",
-        "718": "[4, 5, 2, 3, 6, 1, 0, 7]",
-        "719": "[5, 3, 4, 6, 1, 0, 2, 7]",
-        "720": "[6, 5, 2, 3, 4, 1, 0, 7]",
-        "721": "[0, 2, 1, 3, 5, 6, 4, 7]",
-        "722": "[1, 3, 2, 4, 6, 0, 5, 7]",
-        "723": "[2, 4, 3, 5, 0, 1, 6, 7]",
-        "724": "[3, 5, 1, 2, 4, 0, 6, 7]",
-        "725": "[4, 3, 5, 6, 0, 1, 2, 7]",
-        "726": "[5, 6, 3, 1, 2, 0, 4, 7]",
-        "727": "[6, 3, 5, 4, 0, 1, 2, 7]",
-        "728": "[0, 3, 2, 1, 5, 4, 6, 7]",
-        "729": "[1, 4, 3, 2, 6, 5, 0, 7]",
-        "730": "[2, 5, 4, 3, 0, 6, 1, 7]",
-        "731": "[3, 2, 5, 1, 4, 6, 0, 7]",
-        "732": "[4, 6, 3, 5, 0, 2, 1, 7]",
-        "733": "[5, 1, 6, 3, 2, 4, 0, 7]",
-        "734": "[6, 4, 3, 5, 0, 2, 1, 7]",
-        "735": "[0, 4, 2, 1, 3, 5, 6, 7]",
-        "736": "[1, 5, 3, 2, 4, 6, 0, 7]",
-        "737": "[2, 6, 4, 3, 5, 0, 1, 7]",
-        "738": "[3, 6, 5, 1, 2, 4, 0, 7]",
-        "739": "[4, 2, 3, 5, 6, 0, 1, 7]",
-        "740": "[5, 4, 6, 3, 1, 2, 0, 7]",
-        "741": "[6, 2, 3, 5, 4, 0, 1, 7]",
-        "742": "[0, 5, 1, 3, 6, 2, 4, 7]",
-        "743": "[1, 6, 2, 4, 0, 3, 5, 7]",
-        "744": "[2, 0, 3, 5, 1, 4, 6, 7]",
-        "745": "[3, 4, 1, 2, 0, 5, 6, 7]",
-        "746": "[4, 0, 5, 6, 1, 3, 2, 7]",
-        "747": "[5, 2, 3, 1, 0, 6, 4, 7]",
-        "748": "[6, 0, 5, 4, 1, 3, 2, 7]",
-        "749": "[0, 6, 2, 1, 3, 5, 4, 7]",
-        "750": "[1, 0, 3, 2, 4, 6, 5, 7]",
-        "751": "[2, 1, 4, 3, 5, 0, 6, 7]",
-        "752": "[3, 0, 5, 1, 2, 4, 6, 7]",
-        "753": "[4, 1, 3, 5, 6, 0, 2, 7]",
-        "754": "[5, 0, 6, 3, 1, 2, 4, 7]",
-        "755": "[6, 1, 3, 5, 4, 0, 2, 7]",
-        "756": "[0, 1, 5, 2, 3, 4, 6, 7]",
-        "757": "[1, 2, 6, 3, 4, 5, 0, 7]",
-        "758": "[2, 3, 0, 4, 5, 6, 1, 7]",
-        "759": "[3, 1, 4, 5, 2, 6, 0, 7]",
-        "760": "[4, 5, 0, 3, 6, 2, 1, 7]",
-        "761": "[5, 3, 2, 6, 1, 4, 0, 7]",
-        "762": "[6, 5, 0, 3, 4, 2, 1, 7]",
-        "763": "[0, 2, 4, 3, 5, 1, 6, 7]",
-        "764": "[1, 3, 5, 4, 6, 2, 0, 7]",
-        "765": "[2, 4, 6, 5, 0, 3, 1, 7]",
-        "766": "[3, 5, 6, 2, 4, 1, 0, 7]",
-        "767": "[4, 3, 2, 6, 0, 5, 1, 7]",
-        "768": "[5, 6, 4, 1, 2, 3, 0, 7]",
-        "769": "[6, 3, 2, 4, 0, 5, 1, 7]",
-        "770": "[0, 3, 6, 1, 5, 2, 4, 7]",
-        "771": "[1, 4, 0, 2, 6, 3, 5, 7]",
-        "772": "[2, 5, 1, 3, 0, 4, 6, 7]",
-        "773": "[3, 2, 0, 1, 4, 5, 6, 7]",
-        "774": "[4, 6, 1, 5, 0, 3, 2, 7]",
-        "775": "[5, 1, 0, 3, 2, 6, 4, 7]",
-        "776": "[6, 4, 1, 5, 0, 3, 2, 7]",
-        "777": "[0, 4, 6, 1, 3, 2, 5, 7]",
-        "778": "[1, 5, 0, 2, 4, 3, 6, 7]",
-        "779": "[2, 6, 1, 3, 5, 4, 0, 7]",
-        "780": "[3, 6, 0, 1, 2, 5, 4, 7]",
-        "781": "[4, 2, 1, 5, 6, 3, 0, 7]",
-        "782": "[5, 4, 0, 3, 1, 6, 2, 7]",
-        "783": "[6, 2, 1, 5, 4, 3, 0, 7]",
-        "784": "[0, 5, 4, 3, 6, 1, 2, 7]",
-        "785": "[1, 6, 5, 4, 0, 2, 3, 7]",
-        "786": "[2, 0, 6, 5, 1, 3, 4, 7]",
-        "787": "[3, 4, 6, 2, 0, 1, 5, 7]",
-        "788": "[4, 0, 2, 6, 1, 5, 3, 7]",
-        "789": "[5, 2, 4, 1, 0, 3, 6, 7]",
-        "790": "[6, 0, 2, 4, 1, 5, 3, 7]",
-        "791": "[0, 6, 4, 1, 3, 2, 5, 7]",
-        "792": "[1, 0, 5, 2, 4, 3, 6, 7]",
-        "793": "[2, 1, 6, 3, 5, 4, 0, 7]",
-        "794": "[3, 0, 6, 1, 2, 5, 4, 7]",
-        "795": "[4, 1, 2, 5, 6, 3, 0, 7]",
-        "796": "[5, 0, 4, 3, 1, 6, 2, 7]",
-        "797": "[6, 1, 2, 5, 4, 3, 0, 7]",
-        "798": "[0, 1, 6, 2, 3, 4, 5, 7]",
-        "799": "[1, 2, 0, 3, 4, 5, 6, 7]",
-        "800": "[2, 3, 1, 4, 5, 6, 0, 7]",
-        "801": "[3, 1, 0, 5, 2, 6, 4, 7]",
-        "802": "[4, 5, 1, 3, 6, 2, 0, 7]",
-        "803": "[5, 3, 0, 6, 1, 4, 2, 7]",
-        "804": "[6, 5, 1, 3, 4, 2, 0, 7]",
-        "805": "[0, 2, 6, 3, 5, 1, 4, 7]",
-        "806": "[1, 3, 0, 4, 6, 2, 5, 7]",
-        "807": "[2, 4, 1, 5, 0, 3, 6, 7]",
-        "808": "[3, 5, 0, 2, 4, 1, 6, 7]",
-        "809": "[4, 3, 1, 6, 0, 5, 2, 7]",
-        "810": "[5, 6, 0, 1, 2, 3, 4, 7]",
-        "811": "[6, 3, 1, 4, 0, 5, 2, 7]",
-        "812": "[0, 3, 4, 1, 5, 2, 6, 7]",
-        "813": "[1, 4, 5, 2, 6, 3, 0, 7]",
-        "814": "[2, 5, 6, 3, 0, 4, 1, 7]",
-        "815": "[3, 2, 6, 1, 4, 5, 0, 7]",
-        "816": "[4, 6, 2, 5, 0, 3, 1, 7]",
-        "817": "[5, 1, 4, 3, 2, 6, 0, 7]",
-        "818": "[6, 4, 2, 5, 0, 3, 1, 7]",
-        "819": "[0, 4, 5, 1, 3, 2, 6, 7]",
-        "820": "[1, 5, 6, 2, 4, 3, 0, 7]",
-        "821": "[2, 6, 0, 3, 5, 4, 1, 7]",
-        "822": "[3, 6, 4, 1, 2, 5, 0, 7]",
-        "823": "[4, 2, 0, 5, 6, 3, 1, 7]",
-        "824": "[5, 4, 2, 3, 1, 6, 0, 7]",
-        "825": "[6, 2, 0, 5, 4, 3, 1, 7]",
-        "826": "[0, 5, 2, 3, 6, 1, 4, 7]",
-        "827": "[1, 6, 3, 4, 0, 2, 5, 7]",
-        "828": "[2, 0, 4, 5, 1, 3, 6, 7]",
-        "829": "[3, 4, 5, 2, 0, 1, 6, 7]",
-        "830": "[4, 0, 3, 6, 1, 5, 2, 7]",
-        "831": "[5, 2, 6, 1, 0, 3, 4, 7]",
-        "832": "[6, 0, 3, 4, 1, 5, 2, 7]",
-        "833": "[0, 6, 5, 1, 3, 2, 4, 7]",
-        "834": "[1, 0, 6, 2, 4, 3, 5, 7]",
-        "835": "[2, 1, 0, 3, 5, 4, 6, 7]",
-        "836": "[3, 0, 4, 1, 2, 5, 6, 7]",
-        "837": "[4, 1, 0, 5, 6, 3, 2, 7]",
-        "838": "[5, 0, 2, 3, 1, 6, 4, 7]",
-        "839": "[6, 1, 0, 5, 4, 3, 2, 7]",
-        "840": "[0, 1, 2, 3, 4, 5, 6, 7]",
-        "841": "[1, 2, 3, 4, 5, 6, 0, 7]",
-        "842": "[2, 3, 4, 5, 6, 0, 1, 7]",
-        "843": "[3, 1, 5, 2, 6, 4, 0, 7]",
-        "844": "[4, 5, 3, 6, 2, 0, 1, 7]",
-        "845": "[5, 3, 6, 1, 4, 2, 0, 7]",
-        "846": "[6, 5, 3, 4, 2, 0, 1, 7]",
-        "847": "[0, 2, 3, 5, 1, 4, 6, 7]",
-        "848": "[1, 3, 4, 6, 2, 5, 0, 7]",
-        "849": "[2, 4, 5, 0, 3, 6, 1, 7]",
-        "850": "[3, 5, 2, 4, 1, 6, 0, 7]",
-        "851": "[4, 3, 6, 0, 5, 2, 1, 7]",
-        "852": "[5, 6, 1, 2, 3, 4, 0, 7]",
-        "853": "[6, 3, 4, 0, 5, 2, 1, 7]",
-        "854": "[0, 3, 1, 5, 2, 6, 4, 7]",
-        "855": "[1, 4, 2, 6, 3, 0, 5, 7]",
-        "856": "[2, 5, 3, 0, 4, 1, 6, 7]",
-        "857": "[3, 2, 1, 4, 5, 0, 6, 7]",
-        "858": "[4, 6, 5, 0, 3, 1, 2, 7]",
-        "859": "[5, 1, 3, 2, 6, 0, 4, 7]",
-        "860": "[6, 4, 5, 0, 3, 1, 2, 7]",
-        "861": "[0, 4, 1, 3, 2, 6, 5, 7]",
-        "862": "[1, 5, 2, 4, 3, 0, 6, 7]",
-        "863": "[2, 6, 3, 5, 4, 1, 0, 7]",
-        "864": "[3, 6, 1, 2, 5, 0, 4, 7]",
-        "865": "[4, 2, 5, 6, 3, 1, 0, 7]",
-        "866": "[5, 4, 3, 1, 6, 0, 2, 7]",
-        "867": "[6, 2, 5, 4, 3, 1, 0, 7]",
-        "868": "[0, 5, 3, 6, 1, 4, 2, 7]",
-        "869": "[1, 6, 4, 0, 2, 5, 3, 7]",
-        "870": "[2, 0, 5, 1, 3, 6, 4, 7]",
-        "871": "[3, 4, 2, 0, 1, 6, 5, 7]",
-        "872": "[4, 0, 6, 1, 5, 2, 3, 7]",
-        "873": "[5, 2, 1, 0, 3, 4, 6, 7]",
-        "874": "[6, 0, 4, 1, 5, 2, 3, 7]",
-        "875": "[0, 6, 1, 3, 2, 4, 5, 7]",
-        "876": "[1, 0, 2, 4, 3, 5, 6, 7]",
-        "877": "[2, 1, 3, 5, 4, 6, 0, 7]",
-        "878": "[3, 0, 1, 2, 5, 6, 4, 7]",
-        "879": "[4, 1, 5, 6, 3, 2, 0, 7]",
-        "880": "[5, 0, 3, 1, 6, 4, 2, 7]",
-        "881": "[6, 1, 5, 4, 3, 2, 0, 7]",
-        "882": "[0, 1, 3, 4, 5, 2, 6, 7]",
-        "883": "[1, 2, 4, 5, 6, 3, 0, 7]",
-        "884": "[2, 3, 5, 6, 0, 4, 1, 7]",
-        "885": "[3, 1, 2, 6, 4, 5, 0, 7]",
-        "886": "[4, 5, 6, 2, 0, 3, 1, 7]",
-        "887": "[5, 3, 1, 4, 2, 6, 0, 7]",
-        "888": "[6, 5, 4, 2, 0, 3, 1, 7]",
-        "889": "[0, 2, 5, 1, 4, 3, 6, 7]",
-        "890": "[1, 3, 6, 2, 5, 4, 0, 7]",
-        "891": "[2, 4, 0, 3, 6, 5, 1, 7]",
-        "892": "[3, 5, 4, 1, 6, 2, 0, 7]",
-        "893": "[4, 3, 0, 5, 2, 6, 1, 7]",
-        "894": "[5, 6, 2, 3, 4, 1, 0, 7]",
-        "895": "[6, 3, 0, 5, 2, 4, 1, 7]",
-        "896": "[0, 3, 5, 2, 6, 1, 4, 7]",
-        "897": "[1, 4, 6, 3, 0, 2, 5, 7]",
-        "898": "[2, 5, 0, 4, 1, 3, 6, 7]",
-        "899": "[3, 2, 4, 5, 0, 1, 6, 7]",
-        "900": "[4, 6, 0, 3, 1, 5, 2, 7]",
-        "901": "[5, 1, 2, 6, 0, 3, 4, 7]",
-        "902": "[6, 4, 0, 3, 1, 5, 2, 7]",
-        "903": "[0, 4, 3, 2, 6, 1, 5, 7]",
-        "904": "[1, 5, 4, 3, 0, 2, 6, 7]",
-        "905": "[2, 6, 5, 4, 1, 3, 0, 7]",
-        "906": "[3, 6, 2, 5, 0, 1, 4, 7]",
-        "907": "[4, 2, 6, 3, 1, 5, 0, 7]",
-        "908": "[5, 4, 1, 6, 0, 3, 2, 7]",
-        "909": "[6, 2, 4, 3, 1, 5, 0, 7]",
-        "910": "[0, 5, 6, 1, 4, 3, 2, 7]",
-        "911": "[1, 6, 0, 2, 5, 4, 3, 7]",
-        "912": "[2, 0, 1, 3, 6, 5, 4, 7]",
-        "913": "[3, 4, 0, 1, 6, 2, 5, 7]",
-        "914": "[4, 0, 1, 5, 2, 6, 3, 7]",
-        "915": "[5, 2, 0, 3, 4, 1, 6, 7]",
-        "916": "[6, 0, 1, 5, 2, 4, 3, 7]",
-        "917": "[0, 6, 3, 2, 4, 1, 5, 7]",
-        "918": "[1, 0, 4, 3, 5, 2, 6, 7]",
-        "919": "[2, 1, 5, 4, 6, 3, 0, 7]",
-        "920": "[3, 0, 2, 5, 6, 1, 4, 7]",
-        "921": "[4, 1, 6, 3, 2, 5, 0, 7]",
-        "922": "[5, 0, 1, 6, 4, 3, 2, 7]",
-        "923": "[6, 1, 4, 3, 2, 5, 0, 7]",
-        "924": "[0, 1, 4, 5, 3, 6, 2, 7]",
-        "925": "[1, 2, 5, 6, 4, 0, 3, 7]",
-        "926": "[2, 3, 6, 0, 5, 1, 4, 7]",
-        "927": "[3, 1, 6, 4, 2, 0, 5, 7]",
-        "928": "[4, 5, 2, 0, 6, 1, 3, 7]",
-        "929": "[5, 3, 4, 2, 1, 0, 6, 7]",
-        "930": "[6, 5, 2, 0, 4, 1, 3, 7]",
-        "931": "[0, 2, 1, 4, 5, 6, 3, 7]",
-        "932": "[1, 3, 2, 5, 6, 0, 4, 7]",
-        "933": "[2, 4, 3, 6, 0, 1, 5, 7]",
-        "934": "[3, 5, 1, 6, 4, 0, 2, 7]",
-        "935": "[4, 3, 5, 2, 0, 1, 6, 7]",
-        "936": "[5, 6, 3, 4, 2, 0, 1, 7]",
-        "937": "[6, 3, 5, 2, 0, 1, 4, 7]",
-        "938": "[0, 3, 2, 6, 5, 4, 1, 7]",
-        "939": "[1, 4, 3, 0, 6, 5, 2, 7]",
-        "940": "[2, 5, 4, 1, 0, 6, 3, 7]",
-        "941": "[3, 2, 5, 0, 4, 6, 1, 7]",
-        "942": "[4, 6, 3, 1, 0, 2, 5, 7]",
-        "943": "[5, 1, 6, 0, 2, 4, 3, 7]",
-        "944": "[6, 4, 3, 1, 0, 2, 5, 7]",
-        "945": "[0, 4, 2, 6, 3, 5, 1, 7]",
-        "946": "[1, 5, 3, 0, 4, 6, 2, 7]",
-        "947": "[2, 6, 4, 1, 5, 0, 3, 7]",
-        "948": "[3, 6, 5, 0, 2, 4, 1, 7]",
-        "949": "[4, 2, 3, 1, 6, 0, 5, 7]",
-        "950": "[5, 4, 6, 0, 1, 2, 3, 7]",
-        "951": "[6, 2, 3, 1, 4, 0, 5, 7]",
-        "952": "[0, 5, 1, 4, 6, 2, 3, 7]",
-        "953": "[1, 6, 2, 5, 0, 3, 4, 7]",
-        "954": "[2, 0, 3, 6, 1, 4, 5, 7]",
-        "955": "[3, 4, 1, 6, 0, 5, 2, 7]",
-        "956": "[4, 0, 5, 2, 1, 3, 6, 7]",
-        "957": "[5, 2, 3, 4, 0, 6, 1, 7]",
-        "958": "[6, 0, 5, 2, 1, 3, 4, 7]",
-        "959": "[0, 6, 2, 4, 3, 5, 1, 7]",
-        "960": "[1, 0, 3, 5, 4, 6, 2, 7]",
-        "961": "[2, 1, 4, 6, 5, 0, 3, 7]",
-        "962": "[3, 0, 5, 6, 2, 4, 1, 7]",
-        "963": "[4, 1, 3, 2, 6, 0, 5, 7]",
-        "964": "[5, 0, 6, 4, 1, 2, 3, 7]",
-        "965": "[6, 1, 3, 2, 4, 0, 5, 7]",
-        "966": "[0, 1, 5, 6, 3, 4, 2, 7]",
-        "967": "[1, 2, 6, 0, 4, 5, 3, 7]",
-        "968": "[2, 3, 0, 1, 5, 6, 4, 7]",
-        "969": "[3, 1, 4, 0, 2, 6, 5, 7]",
-        "970": "[4, 5, 0, 1, 6, 2, 3, 7]",
-        "971": "[5, 3, 2, 0, 1, 4, 6, 7]",
-        "972": "[6, 5, 0, 1, 4, 2, 3, 7]",
-        "973": "[0, 2, 4, 6, 5, 1, 3, 7]",
-        "974": "[1, 3, 5, 0, 6, 2, 4, 7]",
-        "975": "[2, 4, 6, 1, 0, 3, 5, 7]",
-        "976": "[3, 5, 6, 0, 4, 1, 2, 7]",
-        "977": "[4, 3, 2, 1, 0, 5, 6, 7]",
-        "978": "[5, 6, 4, 0, 2, 3, 1, 7]",
-        "979": "[6, 3, 2, 1, 0, 5, 4, 7]",
-        "980": "[0, 3, 6, 4, 5, 2, 1, 7]",
-        "981": "[1, 4, 0, 5, 6, 3, 2, 7]",
-        "982": "[2, 5, 1, 6, 0, 4, 3, 7]",
-        "983": "[3, 2, 0, 6, 4, 5, 1, 7]",
-        "984": "[4, 6, 1, 2, 0, 3, 5, 7]",
-        "985": "[5, 1, 0, 4, 2, 6, 3, 7]",
-        "986": "[6, 4, 1, 2, 0, 3, 5, 7]",
-        "987": "[0, 4, 6, 5, 3, 2, 1, 7]",
-        "988": "[1, 5, 0, 6, 4, 3, 2, 7]",
-        "989": "[2, 6, 1, 0, 5, 4, 3, 7]",
-        "990": "[3, 6, 0, 4, 2, 5, 1, 7]",
-        "991": "[4, 2, 1, 0, 6, 3, 5, 7]",
-        "992": "[5, 4, 0, 2, 1, 6, 3, 7]",
-        "993": "[6, 2, 1, 0, 4, 3, 5, 7]",
-        "994": "[0, 5, 4, 2, 6, 1, 3, 7]",
-        "995": "[1, 6, 5, 3, 0, 2, 4, 7]",
-        "996": "[2, 0, 6, 4, 1, 3, 5, 7]",
-        "997": "[3, 4, 6, 5, 0, 1, 2, 7]",
-        "998": "[4, 0, 2, 3, 1, 5, 6, 7]",
-        "999": "[5, 2, 4, 6, 0, 3, 1, 7]",
-        "1000": "[6, 0, 2, 3, 1, 5, 4, 7]",
-        "1001": "[0, 6, 4, 5, 3, 2, 1, 7]",
-        "1002": "[1, 0, 5, 6, 4, 3, 2, 7]",
-        "1003": "[2, 1, 6, 0, 5, 4, 3, 7]",
-        "1004": "[3, 0, 6, 4, 2, 5, 1, 7]",
-        "1005": "[4, 1, 2, 0, 6, 3, 5, 7]",
-        "1006": "[5, 0, 4, 2, 1, 6, 3, 7]",
-        "1007": "[6, 1, 2, 0, 4, 3, 5, 7]",
-        "1008": "[0, 1, 6, 5, 3, 4, 2, 7]",
-        "1009": "[1, 2, 0, 6, 4, 5, 3, 7]",
-        "1010": "[2, 3, 1, 0, 5, 6, 4, 7]",
-        "1011": "[3, 1, 0, 4, 2, 6, 5, 7]",
-        "1012": "[4, 5, 1, 0, 6, 2, 3, 7]",
-        "1013": "[5, 3, 0, 2, 1, 4, 6, 7]",
-        "1014": "[6, 5, 1, 0, 4, 2, 3, 7]",
-        "1015": "[0, 2, 6, 4, 5, 1, 3, 7]",
-        "1016": "[1, 3, 0, 5, 6, 2, 4, 7]",
-        "1017": "[2, 4, 1, 6, 0, 3, 5, 7]",
-        "1018": "[3, 5, 0, 6, 4, 1, 2, 7]",
-        "1019": "[4, 3, 1, 2, 0, 5, 6, 7]",
-        "1020": "[5, 6, 0, 4, 2, 3, 1, 7]",
-        "1021": "[6, 3, 1, 2, 0, 5, 4, 7]",
-        "1022": "[0, 3, 4, 6, 5, 2, 1, 7]",
-        "1023": "[1, 4, 5, 0, 6, 3, 2, 7]",
-        "1024": "[2, 5, 6, 1, 0, 4, 3, 7]",
-        "1025": "[3, 2, 6, 0, 4, 5, 1, 7]",
-        "1026": "[4, 6, 2, 1, 0, 3, 5, 7]",
-        "1027": "[5, 1, 4, 0, 2, 6, 3, 7]",
-        "1028": "[6, 4, 2, 1, 0, 3, 5, 7]",
-        "1029": "[0, 4, 5, 6, 3, 2, 1, 7]",
-        "1030": "[1, 5, 6, 0, 4, 3, 2, 7]",
-        "1031": "[2, 6, 0, 1, 5, 4, 3, 7]",
-        "1032": "[3, 6, 4, 0, 2, 5, 1, 7]",
-        "1033": "[4, 2, 0, 1, 6, 3, 5, 7]",
-        "1034": "[5, 4, 2, 0, 1, 6, 3, 7]",
-        "1035": "[6, 2, 0, 1, 4, 3, 5, 7]",
-        "1036": "[0, 5, 2, 4, 6, 1, 3, 7]",
-        "1037": "[1, 6, 3, 5, 0, 2, 4, 7]",
-        "1038": "[2, 0, 4, 6, 1, 3, 5, 7]",
-        "1039": "[3, 4, 5, 6, 0, 1, 2, 7]",
-        "1040": "[4, 0, 3, 2, 1, 5, 6, 7]",
-        "1041": "[5, 2, 6, 4, 0, 3, 1, 7]",
-        "1042": "[6, 0, 3, 2, 1, 5, 4, 7]",
-        "1043": "[0, 6, 5, 4, 3, 2, 1, 7]",
-        "1044": "[1, 0, 6, 5, 4, 3, 2, 7]",
-        "1045": "[2, 1, 0, 6, 5, 4, 3, 7]",
-        "1046": "[3, 0, 4, 6, 2, 5, 1, 7]",
-        "1047": "[4, 1, 0, 2, 6, 3, 5, 7]",
-        "1048": "[5, 0, 2, 4, 1, 6, 3, 7]",
-        "1049": "[6, 1, 0, 2, 4, 3, 5, 7]",
-        "1050": "[0, 1, 2, 4, 5, 3, 6, 7]",
-        "1051": "[1, 2, 3, 5, 6, 4, 0, 7]",
-        "1052": "[2, 3, 4, 6, 0, 5, 1, 7]",
-        "1053": "[3, 1, 5, 6, 4, 2, 0, 7]",
-        "1054": "[4, 5, 3, 2, 0, 6, 1, 7]",
-        "1055": "[5, 3, 6, 4, 2, 1, 0, 7]",
-        "1056": "[6, 5, 3, 2, 0, 4, 1, 7]",
-        "1057": "[0, 2, 3, 1, 4, 5, 6, 7]",
-        "1058": "[1, 3, 4, 2, 5, 6, 0, 7]",
-        "1059": "[2, 4, 5, 3, 6, 0, 1, 7]",
-        "1060": "[3, 5, 2, 1, 6, 4, 0, 7]",
-        "1061": "[4, 3, 6, 5, 2, 0, 1, 7]",
-        "1062": "[5, 6, 1, 3, 4, 2, 0, 7]",
-        "1063": "[6, 3, 4, 5, 2, 0, 1, 7]",
-        "1064": "[0, 3, 1, 2, 6, 5, 4, 7]",
-        "1065": "[1, 4, 2, 3, 0, 6, 5, 7]",
-        "1066": "[2, 5, 3, 4, 1, 0, 6, 7]",
-        "1067": "[3, 2, 1, 5, 0, 4, 6, 7]",
-        "1068": "[4, 6, 5, 3, 1, 0, 2, 7]",
-        "1069": "[5, 1, 3, 6, 0, 2, 4, 7]",
-        "1070": "[6, 4, 5, 3, 1, 0, 2, 7]",
-        "1071": "[0, 4, 1, 2, 6, 3, 5, 7]",
-        "1072": "[1, 5, 2, 3, 0, 4, 6, 7]",
-        "1073": "[2, 6, 3, 4, 1, 5, 0, 7]",
-        "1074": "[3, 6, 1, 5, 0, 2, 4, 7]",
-        "1075": "[4, 2, 5, 3, 1, 6, 0, 7]",
-        "1076": "[5, 4, 3, 6, 0, 1, 2, 7]",
-        "1077": "[6, 2, 5, 3, 1, 4, 0, 7]",
-        "1078": "[0, 5, 3, 1, 4, 6, 2, 7]",
-        "1079": "[1, 6, 4, 2, 5, 0, 3, 7]",
-        "1080": "[2, 0, 5, 3, 6, 1, 4, 7]",
-        "1081": "[3, 4, 2, 1, 6, 0, 5, 7]",
-        "1082": "[4, 0, 6, 5, 2, 1, 3, 7]",
-        "1083": "[5, 2, 1, 3, 4, 0, 6, 7]",
-        "1084": "[6, 0, 4, 5, 2, 1, 3, 7]",
-        "1085": "[0, 6, 1, 2, 4, 3, 5, 7]",
-        "1086": "[1, 0, 2, 3, 5, 4, 6, 7]",
-        "1087": "[2, 1, 3, 4, 6, 5, 0, 7]",
-        "1088": "[3, 0, 1, 5, 6, 2, 4, 7]",
-        "1089": "[4, 1, 5, 3, 2, 6, 0, 7]",
-        "1090": "[5, 0, 3, 6, 4, 1, 2, 7]",
-        "1091": "[6, 1, 5, 3, 2, 4, 0, 7]",
-        "1092": "[0, 1, 3, 5, 2, 4, 6, 7]",
-        "1093": "[1, 2, 4, 6, 3, 5, 0, 7]",
-        "1094": "[2, 3, 5, 0, 4, 6, 1, 7]",
-        "1095": "[3, 1, 2, 4, 5, 6, 0, 7]",
-        "1096": "[4, 5, 6, 0, 3, 2, 1, 7]",
-        "1097": "[5, 3, 1, 2, 6, 4, 0, 7]",
-        "1098": "[6, 5, 4, 0, 3, 2, 1, 7]",
-        "1099": "[0, 2, 5, 4, 3, 1, 6, 7]",
-        "1100": "[1, 3, 6, 5, 4, 2, 0, 7]",
-        "1101": "[2, 4, 0, 6, 5, 3, 1, 7]",
-        "1102": "[3, 5, 4, 6, 2, 1, 0, 7]",
-        "1103": "[4, 3, 0, 2, 6, 5, 1, 7]",
-        "1104": "[5, 6, 2, 4, 1, 3, 0, 7]",
-        "1105": "[6, 3, 0, 2, 4, 5, 1, 7]",
-        "1106": "[0, 3, 5, 6, 1, 2, 4, 7]",
-        "1107": "[1, 4, 6, 0, 2, 3, 5, 7]",
-        "1108": "[2, 5, 0, 1, 3, 4, 6, 7]",
-        "1109": "[3, 2, 4, 0, 1, 5, 6, 7]",
-        "1110": "[4, 6, 0, 1, 5, 3, 2, 7]",
-        "1111": "[5, 1, 2, 0, 3, 6, 4, 7]",
-        "1112": "[6, 4, 0, 1, 5, 3, 2, 7]",
-        "1113": "[0, 4, 3, 6, 1, 2, 5, 7]",
-        "1114": "[1, 5, 4, 0, 2, 3, 6, 7]",
-        "1115": "[2, 6, 5, 1, 3, 4, 0, 7]",
-        "1116": "[3, 6, 2, 0, 1, 5, 4, 7]",
-        "1117": "[4, 2, 6, 1, 5, 3, 0, 7]",
-        "1118": "[5, 4, 1, 0, 3, 6, 2, 7]",
-        "1119": "[6, 2, 4, 1, 5, 3, 0, 7]",
-        "1120": "[0, 5, 6, 4, 3, 1, 2, 7]",
-        "1121": "[1, 6, 0, 5, 4, 2, 3, 7]",
-        "1122": "[2, 0, 1, 6, 5, 3, 4, 7]",
-        "1123": "[3, 4, 0, 6, 2, 1, 5, 7]",
-        "1124": "[4, 0, 1, 2, 6, 5, 3, 7]",
-        "1125": "[5, 2, 0, 4, 1, 3, 6, 7]",
-        "1126": "[6, 0, 1, 2, 4, 5, 3, 7]",
-        "1127": "[0, 6, 3, 4, 1, 2, 5, 7]",
-        "1128": "[1, 0, 4, 5, 2, 3, 6, 7]",
-        "1129": "[2, 1, 5, 6, 3, 4, 0, 7]",
-        "1130": "[3, 0, 2, 6, 1, 5, 4, 7]",
-        "1131": "[4, 1, 6, 2, 5, 3, 0, 7]",
-        "1132": "[5, 0, 1, 4, 3, 6, 2, 7]",
-        "1133": "[6, 1, 4, 2, 5, 3, 0, 7]",
-        "1134": "[0, 1, 4, 3, 6, 5, 2, 7]",
-        "1135": "[1, 2, 5, 4, 0, 6, 3, 7]",
-        "1136": "[2, 3, 6, 5, 1, 0, 4, 7]",
-        "1137": "[3, 1, 6, 2, 0, 4, 5, 7]",
-        "1138": "[4, 5, 2, 6, 1, 0, 3, 7]",
-        "1139": "[5, 3, 4, 1, 0, 2, 6, 7]",
-        "1140": "[6, 5, 2, 4, 1, 0, 3, 7]",
-        "1141": "[0, 2, 1, 5, 6, 4, 3, 7]",
-        "1142": "[1, 3, 2, 6, 0, 5, 4, 7]",
-        "1143": "[2, 4, 3, 0, 1, 6, 5, 7]",
-        "1144": "[3, 5, 1, 4, 0, 6, 2, 7]",
-        "1145": "[4, 3, 5, 0, 1, 2, 6, 7]",
-        "1146": "[5, 6, 3, 2, 0, 4, 1, 7]",
-        "1147": "[6, 3, 5, 0, 1, 2, 4, 7]",
-        "1148": "[0, 3, 2, 5, 4, 6, 1, 7]",
-        "1149": "[1, 4, 3, 6, 5, 0, 2, 7]",
-        "1150": "[2, 5, 4, 0, 6, 1, 3, 7]",
-        "1151": "[3, 2, 5, 4, 6, 0, 1, 7]",
-        "1152": "[4, 6, 3, 0, 2, 1, 5, 7]",
-        "1153": "[5, 1, 6, 2, 4, 0, 3, 7]",
-        "1154": "[6, 4, 3, 0, 2, 1, 5, 7]",
-        "1155": "[0, 4, 2, 3, 5, 6, 1, 7]",
-        "1156": "[1, 5, 3, 4, 6, 0, 2, 7]",
-        "1157": "[2, 6, 4, 5, 0, 1, 3, 7]",
-        "1158": "[3, 6, 5, 2, 4, 0, 1, 7]",
-        "1159": "[4, 2, 3, 6, 0, 1, 5, 7]",
-        "1160": "[5, 4, 6, 1, 2, 0, 3, 7]",
-        "1161": "[6, 2, 3, 4, 0, 1, 5, 7]",
-        "1162": "[0, 5, 1, 6, 2, 4, 3, 7]",
-        "1163": "[1, 6, 2, 0, 3, 5, 4, 7]",
-        "1164": "[2, 0, 3, 1, 4, 6, 5, 7]",
-        "1165": "[3, 4, 1, 0, 5, 6, 2, 7]",
-        "1166": "[4, 0, 5, 1, 3, 2, 6, 7]",
-        "1167": "[5, 2, 3, 0, 6, 4, 1, 7]",
-        "1168": "[6, 0, 5, 1, 3, 2, 4, 7]",
-        "1169": "[0, 6, 2, 3, 5, 4, 1, 7]",
-        "1170": "[1, 0, 3, 4, 6, 5, 2, 7]",
-        "1171": "[2, 1, 4, 5, 0, 6, 3, 7]",
-        "1172": "[3, 0, 5, 2, 4, 6, 1, 7]",
-        "1173": "[4, 1, 3, 6, 0, 2, 5, 7]",
-        "1174": "[5, 0, 6, 1, 2, 4, 3, 7]",
-        "1175": "[6, 1, 3, 4, 0, 2, 5, 7]",
-        "1176": "[0, 1, 5, 3, 4, 6, 2, 7]",
-        "1177": "[1, 2, 6, 4, 5, 0, 3, 7]",
-        "1178": "[2, 3, 0, 5, 6, 1, 4, 7]",
-        "1179": "[3, 1, 4, 2, 6, 0, 5, 7]",
-        "1180": "[4, 5, 0, 6, 2, 1, 3, 7]",
-        "1181": "[5, 3, 2, 1, 4, 0, 6, 7]",
-        "1182": "[6, 5, 0, 4, 2, 1, 3, 7]",
-        "1183": "[0, 2, 4, 5, 1, 6, 3, 7]",
-        "1184": "[1, 3, 5, 6, 2, 0, 4, 7]",
-        "1185": "[2, 4, 6, 0, 3, 1, 5, 7]",
-        "1186": "[3, 5, 6, 4, 1, 0, 2, 7]",
-        "1187": "[4, 3, 2, 0, 5, 1, 6, 7]",
-        "1188": "[5, 6, 4, 2, 3, 0, 1, 7]",
-        "1189": "[6, 3, 2, 0, 5, 1, 4, 7]",
-        "1190": "[0, 3, 6, 5, 2, 4, 1, 7]",
-        "1191": "[1, 4, 0, 6, 3, 5, 2, 7]",
-        "1192": "[2, 5, 1, 0, 4, 6, 3, 7]",
-        "1193": "[3, 2, 0, 4, 5, 6, 1, 7]",
-        "1194": "[4, 6, 1, 0, 3, 2, 5, 7]",
-        "1195": "[5, 1, 0, 2, 6, 4, 3, 7]",
-        "1196": "[6, 4, 1, 0, 3, 2, 5, 7]",
-        "1197": "[0, 4, 6, 3, 2, 5, 1, 7]",
-        "1198": "[1, 5, 0, 4, 3, 6, 2, 7]",
-        "1199": "[2, 6, 1, 5, 4, 0, 3, 7]",
-        "1200": "[3, 6, 0, 2, 5, 4, 1, 7]",
-        "1201": "[4, 2, 1, 6, 3, 0, 5, 7]",
-        "1202": "[5, 4, 0, 1, 6, 2, 3, 7]",
-        "1203": "[6, 2, 1, 4, 3, 0, 5, 7]",
-        "1204": "[0, 5, 4, 6, 1, 2, 3, 7]",
-        "1205": "[1, 6, 5, 0, 2, 3, 4, 7]",
-        "1206": "[2, 0, 6, 1, 3, 4, 5, 7]",
-        "1207": "[3, 4, 6, 0, 1, 5, 2, 7]",
-        "1208": "[4, 0, 2, 1, 5, 3, 6, 7]",
-        "1209": "[5, 2, 4, 0, 3, 6, 1, 7]",
-        "1210": "[6, 0, 2, 1, 5, 3, 4, 7]",
-        "1211": "[0, 6, 4, 3, 2, 5, 1, 7]",
-        "1212": "[1, 0, 5, 4, 3, 6, 2, 7]",
-        "1213": "[2, 1, 6, 5, 4, 0, 3, 7]",
-        "1214": "[3, 0, 6, 2, 5, 4, 1, 7]",
-        "1215": "[4, 1, 2, 6, 3, 0, 5, 7]",
-        "1216": "[5, 0, 4, 1, 6, 2, 3, 7]",
-        "1217": "[6, 1, 2, 4, 3, 0, 5, 7]",
-        "1218": "[0, 1, 6, 3, 4, 5, 2, 7]",
-        "1219": "[1, 2, 0, 4, 5, 6, 3, 7]",
-        "1220": "[2, 3, 1, 5, 6, 0, 4, 7]",
-        "1221": "[3, 1, 0, 2, 6, 4, 5, 7]",
-        "1222": "[4, 5, 1, 6, 2, 0, 3, 7]",
-        "1223": "[5, 3, 0, 1, 4, 2, 6, 7]",
-        "1224": "[6, 5, 1, 4, 2, 0, 3, 7]",
-        "1225": "[0, 2, 6, 5, 1, 4, 3, 7]",
-        "1226": "[1, 3, 0, 6, 2, 5, 4, 7]",
-        "1227": "[2, 4, 1, 0, 3, 6, 5, 7]",
-        "1228": "[3, 5, 0, 4, 1, 6, 2, 7]",
-        "1229": "[4, 3, 1, 0, 5, 2, 6, 7]",
-        "1230": "[5, 6, 0, 2, 3, 4, 1, 7]",
-        "1231": "[6, 3, 1, 0, 5, 2, 4, 7]",
-        "1232": "[0, 3, 4, 5, 2, 6, 1, 7]",
-        "1233": "[1, 4, 5, 6, 3, 0, 2, 7]",
-        "1234": "[2, 5, 6, 0, 4, 1, 3, 7]",
-        "1235": "[3, 2, 6, 4, 5, 0, 1, 7]",
-        "1236": "[4, 6, 2, 0, 3, 1, 5, 7]",
-        "1237": "[5, 1, 4, 2, 6, 0, 3, 7]",
-        "1238": "[6, 4, 2, 0, 3, 1, 5, 7]",
-        "1239": "[0, 4, 5, 3, 2, 6, 1, 7]",
-        "1240": "[1, 5, 6, 4, 3, 0, 2, 7]",
-        "1241": "[2, 6, 0, 5, 4, 1, 3, 7]",
-        "1242": "[3, 6, 4, 2, 5, 0, 1, 7]",
-        "1243": "[4, 2, 0, 6, 3, 1, 5, 7]",
-        "1244": "[5, 4, 2, 1, 6, 0, 3, 7]",
-        "1245": "[6, 2, 0, 4, 3, 1, 5, 7]",
-        "1246": "[0, 5, 2, 6, 1, 4, 3, 7]",
-        "1247": "[1, 6, 3, 0, 2, 5, 4, 7]",
-        "1248": "[2, 0, 4, 1, 3, 6, 5, 7]",
-        "1249": "[3, 4, 5, 0, 1, 6, 2, 7]",
-        "1250": "[4, 0, 3, 1, 5, 2, 6, 7]",
-        "1251": "[5, 2, 6, 0, 3, 4, 1, 7]",
-        "1252": "[6, 0, 3, 1, 5, 2, 4, 7]",
-        "1253": "[0, 6, 5, 3, 2, 4, 1, 7]",
-        "1254": "[1, 0, 6, 4, 3, 5, 2, 7]",
-        "1255": "[2, 1, 0, 5, 4, 6, 3, 7]",
-        "1256": "[3, 0, 4, 2, 5, 6, 1, 7]",
-        "1257": "[4, 1, 0, 6, 3, 2, 5, 7]",
-        "1258": "[5, 0, 2, 1, 6, 4, 3, 7]",
-        "1259": "[6, 1, 0, 4, 3, 2, 5, 7]",
-        "1260": "[0, 1, 2, 5, 3, 4, 6, 7]",
-        "1261": "[1, 2, 3, 6, 4, 5, 0, 7]",
-        "1262": "[2, 3, 4, 0, 5, 6, 1, 7]",
-        "1263": "[3, 1, 5, 4, 2, 6, 0, 7]",
-        "1264": "[4, 5, 3, 0, 6, 2, 1, 7]",
-        "1265": "[5, 3, 6, 2, 1, 4, 0, 7]",
-        "1266": "[6, 5, 3, 0, 4, 2, 1, 7]",
-        "1267": "[0, 2, 3, 4, 5, 1, 6, 7]",
-        "1268": "[1, 3, 4, 5, 6, 2, 0, 7]",
-        "1269": "[2, 4, 5, 6, 0, 3, 1, 7]",
-        "1270": "[3, 5, 2, 6, 4, 1, 0, 7]",
-        "1271": "[4, 3, 6, 2, 0, 5, 1, 7]",
-        "1272": "[5, 6, 1, 4, 2, 3, 0, 7]",
-        "1273": "[6, 3, 4, 2, 0, 5, 1, 7]",
-        "1274": "[0, 3, 1, 6, 5, 2, 4, 7]",
-        "1275": "[1, 4, 2, 0, 6, 3, 5, 7]",
-        "1276": "[2, 5, 3, 1, 0, 4, 6, 7]",
-        "1277": "[3, 2, 1, 0, 4, 5, 6, 7]",
-        "1278": "[4, 6, 5, 1, 0, 3, 2, 7]",
-        "1279": "[5, 1, 3, 0, 2, 6, 4, 7]",
-        "1280": "[6, 4, 5, 1, 0, 3, 2, 7]",
-        "1281": "[0, 4, 1, 6, 3, 2, 5, 7]",
-        "1282": "[1, 5, 2, 0, 4, 3, 6, 7]",
-        "1283": "[2, 6, 3, 1, 5, 4, 0, 7]",
-        "1284": "[3, 6, 1, 0, 2, 5, 4, 7]",
-        "1285": "[4, 2, 5, 1, 6, 3, 0, 7]",
-        "1286": "[5, 4, 3, 0, 1, 6, 2, 7]",
-        "1287": "[6, 2, 5, 1, 4, 3, 0, 7]",
-        "1288": "[0, 5, 3, 4, 6, 1, 2, 7]",
-        "1289": "[1, 6, 4, 5, 0, 2, 3, 7]",
-        "1290": "[2, 0, 5, 6, 1, 3, 4, 7]",
-        "1291": "[3, 4, 2, 6, 0, 1, 5, 7]",
-        "1292": "[4, 0, 6, 2, 1, 5, 3, 7]",
-        "1293": "[5, 2, 1, 4, 0, 3, 6, 7]",
-        "1294": "[6, 0, 4, 2, 1, 5, 3, 7]",
-        "1295": "[0, 6, 1, 4, 3, 2, 5, 7]",
-        "1296": "[1, 0, 2, 5, 4, 3, 6, 7]",
-        "1297": "[2, 1, 3, 6, 5, 4, 0, 7]",
-        "1298": "[3, 0, 1, 6, 2, 5, 4, 7]",
-        "1299": "[4, 1, 5, 2, 6, 3, 0, 7]",
-        "1300": "[5, 0, 3, 4, 1, 6, 2, 7]",
-        "1301": "[6, 1, 5, 2, 4, 3, 0, 7]",
-        "1302": "[0, 1, 3, 2, 4, 5, 6, 7]",
-        "1303": "[1, 2, 4, 3, 5, 6, 0, 7]",
-        "1304": "[2, 3, 5, 4, 6, 0, 1, 7]",
-        "1305": "[3, 1, 2, 5, 6, 4, 0, 7]",
-        "1306": "[4, 5, 6, 3, 2, 0, 1, 7]",
-        "1307": "[5, 3, 1, 6, 4, 2, 0, 7]",
-        "1308": "[6, 5, 4, 3, 2, 0, 1, 7]",
-        "1309": "[0, 2, 5, 3, 1, 4, 6, 7]",
-        "1310": "[1, 3, 6, 4, 2, 5, 0, 7]",
-        "1311": "[2, 4, 0, 5, 3, 6, 1, 7]",
-        "1312": "[3, 5, 4, 2, 1, 6, 0, 7]",
-        "1313": "[4, 3, 0, 6, 5, 2, 1, 7]",
-        "1314": "[5, 6, 2, 1, 3, 4, 0, 7]",
-        "1315": "[6, 3, 0, 4, 5, 2, 1, 7]",
-        "1316": "[0, 3, 5, 1, 2, 6, 4, 7]",
-        "1317": "[1, 4, 6, 2, 3, 0, 5, 7]",
-        "1318": "[2, 5, 0, 3, 4, 1, 6, 7]",
-        "1319": "[3, 2, 4, 1, 5, 0, 6, 7]",
-        "1320": "[4, 6, 0, 5, 3, 1, 2, 7]",
-        "1321": "[5, 1, 2, 3, 6, 0, 4, 7]",
-        "1322": "[6, 4, 0, 5, 3, 1, 2, 7]",
-        "1323": "[0, 4, 3, 1, 2, 6, 5, 7]",
-        "1324": "[1, 5, 4, 2, 3, 0, 6, 7]",
-        "1325": "[2, 6, 5, 3, 4, 1, 0, 7]",
-        "1326": "[3, 6, 2, 1, 5, 0, 4, 7]",
-        "1327": "[4, 2, 6, 5, 3, 1, 0, 7]",
-        "1328": "[5, 4, 1, 3, 6, 0, 2, 7]",
-        "1329": "[6, 2, 4, 5, 3, 1, 0, 7]",
-        "1330": "[0, 5, 6, 3, 1, 4, 2, 7]",
-        "1331": "[1, 6, 0, 4, 2, 5, 3, 7]",
-        "1332": "[2, 0, 1, 5, 3, 6, 4, 7]",
-        "1333": "[3, 4, 0, 2, 1, 6, 5, 7]",
-        "1334": "[4, 0, 1, 6, 5, 2, 3, 7]",
-        "1335": "[5, 2, 0, 1, 3, 4, 6, 7]",
-        "1336": "[6, 0, 1, 4, 5, 2, 3, 7]",
-        "1337": "[0, 6, 3, 1, 2, 4, 5, 7]",
-        "1338": "[1, 0, 4, 2, 3, 5, 6, 7]",
-        "1339": "[2, 1, 5, 3, 4, 6, 0, 7]",
-        "1340": "[3, 0, 2, 1, 5, 6, 4, 7]",
-        "1341": "[4, 1, 6, 5, 3, 2, 0, 7]",
-        "1342": "[5, 0, 1, 3, 6, 4, 2, 7]",
-        "1343": "[6, 1, 4, 5, 3, 2, 0, 7]",
-        "1344": "[0, 1, 4, 6, 5, 3, 2, 7]",
-        "1345": "[1, 2, 5, 0, 6, 4, 3, 7]",
-        "1346": "[2, 3, 6, 1, 0, 5, 4, 7]",
-        "1347": "[3, 1, 6, 0, 4, 2, 5, 7]",
-        "1348": "[4, 5, 2, 1, 0, 6, 3, 7]",
-        "1349": "[5, 3, 4, 0, 2, 1, 6, 7]",
-        "1350": "[6, 5, 2, 1, 0, 4, 3, 7]",
-        "1351": "[0, 2, 1, 6, 4, 5, 3, 7]",
-        "1352": "[1, 3, 2, 0, 5, 6, 4, 7]",
-        "1353": "[2, 4, 3, 1, 6, 0, 5, 7]",
-        "1354": "[3, 5, 1, 0, 6, 4, 2, 7]",
-        "1355": "[4, 3, 5, 1, 2, 0, 6, 7]",
-        "1356": "[5, 6, 3, 0, 4, 2, 1, 7]",
-        "1357": "[6, 3, 5, 1, 2, 0, 4, 7]",
-        "1358": "[0, 3, 2, 4, 6, 5, 1, 7]",
-        "1359": "[1, 4, 3, 5, 0, 6, 2, 7]",
-        "1360": "[2, 5, 4, 6, 1, 0, 3, 7]",
-        "1361": "[3, 2, 5, 6, 0, 4, 1, 7]",
-        "1362": "[4, 6, 3, 2, 1, 0, 5, 7]",
-        "1363": "[5, 1, 6, 4, 0, 2, 3, 7]",
-        "1364": "[6, 4, 3, 2, 1, 0, 5, 7]",
-        "1365": "[0, 4, 2, 5, 6, 3, 1, 7]",
-        "1366": "[1, 5, 3, 6, 0, 4, 2, 7]",
-        "1367": "[2, 6, 4, 0, 1, 5, 3, 7]",
-        "1368": "[3, 6, 5, 4, 0, 2, 1, 7]",
-        "1369": "[4, 2, 3, 0, 1, 6, 5, 7]",
-        "1370": "[5, 4, 6, 2, 0, 1, 3, 7]",
-        "1371": "[6, 2, 3, 0, 1, 4, 5, 7]",
-        "1372": "[0, 5, 1, 2, 4, 6, 3, 7]",
-        "1373": "[1, 6, 2, 3, 5, 0, 4, 7]",
-        "1374": "[2, 0, 3, 4, 6, 1, 5, 7]",
-        "1375": "[3, 4, 1, 5, 6, 0, 2, 7]",
-        "1376": "[4, 0, 5, 3, 2, 1, 6, 7]",
-        "1377": "[5, 2, 3, 6, 4, 0, 1, 7]",
-        "1378": "[6, 0, 5, 3, 2, 1, 4, 7]",
-        "1379": "[0, 6, 2, 5, 4, 3, 1, 7]",
-        "1380": "[1, 0, 3, 6, 5, 4, 2, 7]",
-        "1381": "[2, 1, 4, 0, 6, 5, 3, 7]",
-        "1382": "[3, 0, 5, 4, 6, 2, 1, 7]",
-        "1383": "[4, 1, 3, 0, 2, 6, 5, 7]",
-        "1384": "[5, 0, 6, 2, 4, 1, 3, 7]",
-        "1385": "[6, 1, 3, 0, 2, 4, 5, 7]",
-        "1386": "[0, 1, 5, 4, 6, 3, 2, 7]",
-        "1387": "[1, 2, 6, 5, 0, 4, 3, 7]",
-        "1388": "[2, 3, 0, 6, 1, 5, 4, 7]",
-        "1389": "[3, 1, 4, 6, 0, 2, 5, 7]",
-        "1390": "[4, 5, 0, 2, 1, 6, 3, 7]",
-        "1391": "[5, 3, 2, 4, 0, 1, 6, 7]",
-        "1392": "[6, 5, 0, 2, 1, 4, 3, 7]",
-        "1393": "[0, 2, 4, 1, 6, 5, 3, 7]",
-        "1394": "[1, 3, 5, 2, 0, 6, 4, 7]",
-        "1395": "[2, 4, 6, 3, 1, 0, 5, 7]",
-        "1396": "[3, 5, 6, 1, 0, 4, 2, 7]",
-        "1397": "[4, 3, 2, 5, 1, 0, 6, 7]",
-        "1398": "[5, 6, 4, 3, 0, 2, 1, 7]",
-        "1399": "[6, 3, 2, 5, 1, 0, 4, 7]",
-        "1400": "[0, 3, 6, 2, 4, 5, 1, 7]",
-        "1401": "[1, 4, 0, 3, 5, 6, 2, 7]",
-        "1402": "[2, 5, 1, 4, 6, 0, 3, 7]",
-        "1403": "[3, 2, 0, 5, 6, 4, 1, 7]",
-        "1404": "[4, 6, 1, 3, 2, 0, 5, 7]",
-        "1405": "[5, 1, 0, 6, 4, 2, 3, 7]",
-        "1406": "[6, 4, 1, 3, 2, 0, 5, 7]",
-        "1407": "[0, 4, 6, 2, 5, 3, 1, 7]",
-        "1408": "[1, 5, 0, 3, 6, 4, 2, 7]",
-        "1409": "[2, 6, 1, 4, 0, 5, 3, 7]",
-        "1410": "[3, 6, 0, 5, 4, 2, 1, 7]",
-        "1411": "[4, 2, 1, 3, 0, 6, 5, 7]",
-        "1412": "[5, 4, 0, 6, 2, 1, 3, 7]",
-        "1413": "[6, 2, 1, 3, 0, 4, 5, 7]",
-        "1414": "[0, 5, 4, 1, 2, 6, 3, 7]",
-        "1415": "[1, 6, 5, 2, 3, 0, 4, 7]",
-        "1416": "[2, 0, 6, 3, 4, 1, 5, 7]",
-        "1417": "[3, 4, 6, 1, 5, 0, 2, 7]",
-        "1418": "[4, 0, 2, 5, 3, 1, 6, 7]",
-        "1419": "[5, 2, 4, 3, 6, 0, 1, 7]",
-        "1420": "[6, 0, 2, 5, 3, 1, 4, 7]",
-        "1421": "[0, 6, 4, 2, 5, 3, 1, 7]",
-        "1422": "[1, 0, 5, 3, 6, 4, 2, 7]",
-        "1423": "[2, 1, 6, 4, 0, 5, 3, 7]",
-        "1424": "[3, 0, 6, 5, 4, 2, 1, 7]",
-        "1425": "[4, 1, 2, 3, 0, 6, 5, 7]",
-        "1426": "[5, 0, 4, 6, 2, 1, 3, 7]",
-        "1427": "[6, 1, 2, 3, 0, 4, 5, 7]",
-        "1428": "[0, 1, 6, 4, 5, 3, 2, 7]",
-        "1429": "[1, 2, 0, 5, 6, 4, 3, 7]",
-        "1430": "[2, 3, 1, 6, 0, 5, 4, 7]",
-        "1431": "[3, 1, 0, 6, 4, 2, 5, 7]",
-        "1432": "[4, 5, 1, 2, 0, 6, 3, 7]",
-        "1433": "[5, 3, 0, 4, 2, 1, 6, 7]",
-        "1434": "[6, 5, 1, 2, 0, 4, 3, 7]",
-        "1435": "[0, 2, 6, 1, 4, 5, 3, 7]",
-        "1436": "[1, 3, 0, 2, 5, 6, 4, 7]",
-        "1437": "[2, 4, 1, 3, 6, 0, 5, 7]",
-        "1438": "[3, 5, 0, 1, 6, 4, 2, 7]",
-        "1439": "[4, 3, 1, 5, 2, 0, 6, 7]",
-        "1440": "[5, 6, 0, 3, 4, 2, 1, 7]",
-        "1441": "[6, 3, 1, 5, 2, 0, 4, 7]",
-        "1442": "[0, 3, 4, 2, 6, 5, 1, 7]",
-        "1443": "[1, 4, 5, 3, 0, 6, 2, 7]",
-        "1444": "[2, 5, 6, 4, 1, 0, 3, 7]",
-        "1445": "[3, 2, 6, 5, 0, 4, 1, 7]",
-        "1446": "[4, 6, 2, 3, 1, 0, 5, 7]",
-        "1447": "[5, 1, 4, 6, 0, 2, 3, 7]",
-        "1448": "[6, 4, 2, 3, 1, 0, 5, 7]",
-        "1449": "[0, 4, 5, 2, 6, 3, 1, 7]",
-        "1450": "[1, 5, 6, 3, 0, 4, 2, 7]",
-        "1451": "[2, 6, 0, 4, 1, 5, 3, 7]",
-        "1452": "[3, 6, 4, 5, 0, 2, 1, 7]",
-        "1453": "[4, 2, 0, 3, 1, 6, 5, 7]",
-        "1454": "[5, 4, 2, 6, 0, 1, 3, 7]",
-        "1455": "[6, 2, 0, 3, 1, 4, 5, 7]",
-        "1456": "[0, 5, 2, 1, 4, 6, 3, 7]",
-        "1457": "[1, 6, 3, 2, 5, 0, 4, 7]",
-        "1458": "[2, 0, 4, 3, 6, 1, 5, 7]",
-        "1459": "[3, 4, 5, 1, 6, 0, 2, 7]",
-        "1460": "[4, 0, 3, 5, 2, 1, 6, 7]",
-        "1461": "[5, 2, 6, 3, 4, 0, 1, 7]",
-        "1462": "[6, 0, 3, 5, 2, 1, 4, 7]",
-        "1463": "[0, 6, 5, 2, 4, 3, 1, 7]",
-        "1464": "[1, 0, 6, 3, 5, 4, 2, 7]",
-        "1465": "[2, 1, 0, 4, 6, 5, 3, 7]",
-        "1466": "[3, 0, 4, 5, 6, 2, 1, 7]",
-        "1467": "[4, 1, 0, 3, 2, 6, 5, 7]",
-        "1468": "[5, 0, 2, 6, 4, 1, 3, 7]",
-        "1469": "[6, 1, 0, 3, 2, 4, 5, 7]",
-        "1470": "[0, 1, 2, 6, 5, 3, 4, 7]",
-        "1471": "[1, 2, 3, 0, 6, 4, 5, 7]",
-        "1472": "[2, 3, 4, 1, 0, 5, 6, 7]",
-        "1473": "[3, 1, 5, 0, 4, 2, 6, 7]",
-        "1474": "[4, 5, 3, 1, 0, 6, 2, 7]",
-        "1475": "[5, 3, 6, 0, 2, 1, 4, 7]",
-        "1476": "[6, 5, 3, 1, 0, 4, 2, 7]",
-        "1477": "[0, 2, 3, 6, 4, 5, 1, 7]",
-        "1478": "[1, 3, 4, 0, 5, 6, 2, 7]",
-        "1479": "[2, 4, 5, 1, 6, 0, 3, 7]",
-        "1480": "[3, 5, 2, 0, 6, 4, 1, 7]",
-        "1481": "[4, 3, 6, 1, 2, 0, 5, 7]",
-        "1482": "[5, 6, 1, 0, 4, 2, 3, 7]",
-        "1483": "[6, 3, 4, 1, 2, 0, 5, 7]",
-        "1484": "[0, 3, 1, 4, 6, 5, 2, 7]",
-        "1485": "[1, 4, 2, 5, 0, 6, 3, 7]",
-        "1486": "[2, 5, 3, 6, 1, 0, 4, 7]",
-        "1487": "[3, 2, 1, 6, 0, 4, 5, 7]",
-        "1488": "[4, 6, 5, 2, 1, 0, 3, 7]",
-        "1489": "[5, 1, 3, 4, 0, 2, 6, 7]",
-        "1490": "[6, 4, 5, 2, 1, 0, 3, 7]",
-        "1491": "[0, 4, 1, 5, 6, 3, 2, 7]",
-        "1492": "[1, 5, 2, 6, 0, 4, 3, 7]",
-        "1493": "[2, 6, 3, 0, 1, 5, 4, 7]",
-        "1494": "[3, 6, 1, 4, 0, 2, 5, 7]",
-        "1495": "[4, 2, 5, 0, 1, 6, 3, 7]",
-        "1496": "[5, 4, 3, 2, 0, 1, 6, 7]",
-        "1497": "[6, 2, 5, 0, 1, 4, 3, 7]",
-        "1498": "[0, 5, 3, 2, 4, 6, 1, 7]",
-        "1499": "[1, 6, 4, 3, 5, 0, 2, 7]",
-        "1500": "[2, 0, 5, 4, 6, 1, 3, 7]",
-        "1501": "[3, 4, 2, 5, 6, 0, 1, 7]",
-        "1502": "[4, 0, 6, 3, 2, 1, 5, 7]",
-        "1503": "[5, 2, 1, 6, 4, 0, 3, 7]",
-        "1504": "[6, 0, 4, 3, 2, 1, 5, 7]",
-        "1505": "[0, 6, 1, 5, 4, 3, 2, 7]",
-        "1506": "[1, 0, 2, 6, 5, 4, 3, 7]",
-        "1507": "[2, 1, 3, 0, 6, 5, 4, 7]",
-        "1508": "[3, 0, 1, 4, 6, 2, 5, 7]",
-        "1509": "[4, 1, 5, 0, 2, 6, 3, 7]",
-        "1510": "[5, 0, 3, 2, 4, 1, 6, 7]",
-        "1511": "[6, 1, 5, 0, 2, 4, 3, 7]",
-        "1512": "[0, 1, 3, 6, 2, 4, 5, 7]",
-        "1513": "[1, 2, 4, 0, 3, 5, 6, 7]",
-        "1514": "[2, 3, 5, 1, 4, 6, 0, 7]",
-        "1515": "[3, 1, 2, 0, 5, 6, 4, 7]",
-        "1516": "[4, 5, 6, 1, 3, 2, 0, 7]",
-        "1517": "[5, 3, 1, 0, 6, 4, 2, 7]",
-        "1518": "[6, 5, 4, 1, 3, 2, 0, 7]",
-        "1519": "[0, 2, 5, 6, 3, 1, 4, 7]",
-        "1520": "[1, 3, 6, 0, 4, 2, 5, 7]",
-        "1521": "[2, 4, 0, 1, 5, 3, 6, 7]",
-        "1522": "[3, 5, 4, 0, 2, 1, 6, 7]",
-        "1523": "[4, 3, 0, 1, 6, 5, 2, 7]",
-        "1524": "[5, 6, 2, 0, 1, 3, 4, 7]",
-        "1525": "[6, 3, 0, 1, 4, 5, 2, 7]",
-        "1526": "[0, 3, 5, 4, 1, 2, 6, 7]",
-        "1527": "[1, 4, 6, 5, 2, 3, 0, 7]",
-        "1528": "[2, 5, 0, 6, 3, 4, 1, 7]",
-        "1529": "[3, 2, 4, 6, 1, 5, 0, 7]",
-        "1530": "[4, 6, 0, 2, 5, 3, 1, 7]",
-        "1531": "[5, 1, 2, 4, 3, 6, 0, 7]",
-        "1532": "[6, 4, 0, 2, 5, 3, 1, 7]",
-        "1533": "[0, 4, 3, 5, 1, 2, 6, 7]",
-        "1534": "[1, 5, 4, 6, 2, 3, 0, 7]",
-        "1535": "[2, 6, 5, 0, 3, 4, 1, 7]",
-        "1536": "[3, 6, 2, 4, 1, 5, 0, 7]",
-        "1537": "[4, 2, 6, 0, 5, 3, 1, 7]",
-        "1538": "[5, 4, 1, 2, 3, 6, 0, 7]",
-        "1539": "[6, 2, 4, 0, 5, 3, 1, 7]",
-        "1540": "[0, 5, 6, 2, 3, 1, 4, 7]",
-        "1541": "[1, 6, 0, 3, 4, 2, 5, 7]",
-        "1542": "[2, 0, 1, 4, 5, 3, 6, 7]",
-        "1543": "[3, 4, 0, 5, 2, 1, 6, 7]",
-        "1544": "[4, 0, 1, 3, 6, 5, 2, 7]",
-        "1545": "[5, 2, 0, 6, 1, 3, 4, 7]",
-        "1546": "[6, 0, 1, 3, 4, 5, 2, 7]",
-        "1547": "[0, 6, 3, 5, 1, 2, 4, 7]",
-        "1548": "[1, 0, 4, 6, 2, 3, 5, 7]",
-        "1549": "[2, 1, 5, 0, 3, 4, 6, 7]",
-        "1550": "[3, 0, 2, 4, 1, 5, 6, 7]",
-        "1551": "[4, 1, 6, 0, 5, 3, 2, 7]",
-        "1552": "[5, 0, 1, 2, 3, 6, 4, 7]",
-        "1553": "[6, 1, 4, 0, 5, 3, 2, 7]",
-        "1554": "[0, 1, 4, 2, 6, 5, 3, 7]",
-        "1555": "[1, 2, 5, 3, 0, 6, 4, 7]",
-        "1556": "[2, 3, 6, 4, 1, 0, 5, 7]",
-        "1557": "[3, 1, 6, 5, 0, 4, 2, 7]",
-        "1558": "[4, 5, 2, 3, 1, 0, 6, 7]",
-        "1559": "[5, 3, 4, 6, 0, 2, 1, 7]",
-        "1560": "[6, 5, 2, 3, 1, 0, 4, 7]",
-        "1561": "[0, 2, 1, 3, 6, 4, 5, 7]",
-        "1562": "[1, 3, 2, 4, 0, 5, 6, 7]",
-        "1563": "[2, 4, 3, 5, 1, 6, 0, 7]",
-        "1564": "[3, 5, 1, 2, 0, 6, 4, 7]",
-        "1565": "[4, 3, 5, 6, 1, 2, 0, 7]",
-        "1566": "[5, 6, 3, 1, 0, 4, 2, 7]",
-        "1567": "[6, 3, 5, 4, 1, 2, 0, 7]",
-        "1568": "[0, 3, 2, 1, 4, 6, 5, 7]",
-        "1569": "[1, 4, 3, 2, 5, 0, 6, 7]",
-        "1570": "[2, 5, 4, 3, 6, 1, 0, 7]",
-        "1571": "[3, 2, 5, 1, 6, 0, 4, 7]",
-        "1572": "[4, 6, 3, 5, 2, 1, 0, 7]",
-        "1573": "[5, 1, 6, 3, 4, 0, 2, 7]",
-        "1574": "[6, 4, 3, 5, 2, 1, 0, 7]",
-        "1575": "[0, 4, 2, 1, 5, 6, 3, 7]",
-        "1576": "[1, 5, 3, 2, 6, 0, 4, 7]",
-        "1577": "[2, 6, 4, 3, 0, 1, 5, 7]",
-        "1578": "[3, 6, 5, 1, 4, 0, 2, 7]",
-        "1579": "[4, 2, 3, 5, 0, 1, 6, 7]",
-        "1580": "[5, 4, 6, 3, 2, 0, 1, 7]",
-        "1581": "[6, 2, 3, 5, 0, 1, 4, 7]",
-        "1582": "[0, 5, 1, 3, 2, 4, 6, 7]",
-        "1583": "[1, 6, 2, 4, 3, 5, 0, 7]",
-        "1584": "[2, 0, 3, 5, 4, 6, 1, 7]",
-        "1585": "[3, 4, 1, 2, 5, 6, 0, 7]",
-        "1586": "[4, 0, 5, 6, 3, 2, 1, 7]",
-        "1587": "[5, 2, 3, 1, 6, 4, 0, 7]",
-        "1588": "[6, 0, 5, 4, 3, 2, 1, 7]",
-        "1589": "[0, 6, 2, 1, 5, 4, 3, 7]",
-        "1590": "[1, 0, 3, 2, 6, 5, 4, 7]",
-        "1591": "[2, 1, 4, 3, 0, 6, 5, 7]",
-        "1592": "[3, 0, 5, 1, 4, 6, 2, 7]",
-        "1593": "[4, 1, 3, 5, 0, 2, 6, 7]",
-        "1594": "[5, 0, 6, 3, 2, 4, 1, 7]",
-        "1595": "[6, 1, 3, 5, 0, 2, 4, 7]",
-        "1596": "[0, 1, 5, 2, 4, 6, 3, 7]",
-        "1597": "[1, 2, 6, 3, 5, 0, 4, 7]",
-        "1598": "[2, 3, 0, 4, 6, 1, 5, 7]",
-        "1599": "[3, 1, 4, 5, 6, 0, 2, 7]",
-        "1600": "[4, 5, 0, 3, 2, 1, 6, 7]",
-        "1601": "[5, 3, 2, 6, 4, 0, 1, 7]",
-        "1602": "[6, 5, 0, 3, 2, 1, 4, 7]",
-        "1603": "[0, 2, 4, 3, 1, 6, 5, 7]",
-        "1604": "[1, 3, 5, 4, 2, 0, 6, 7]",
-        "1605": "[2, 4, 6, 5, 3, 1, 0, 7]",
-        "1606": "[3, 5, 6, 2, 1, 0, 4, 7]",
-        "1607": "[4, 3, 2, 6, 5, 1, 0, 7]",
-        "1608": "[5, 6, 4, 1, 3, 0, 2, 7]",
-        "1609": "[6, 3, 2, 4, 5, 1, 0, 7]",
-        "1610": "[0, 3, 6, 1, 2, 4, 5, 7]",
-        "1611": "[1, 4, 0, 2, 3, 5, 6, 7]",
-        "1612": "[2, 5, 1, 3, 4, 6, 0, 7]",
-        "1613": "[3, 2, 0, 1, 5, 6, 4, 7]",
-        "1614": "[4, 6, 1, 5, 3, 2, 0, 7]",
-        "1615": "[5, 1, 0, 3, 6, 4, 2, 7]",
-        "1616": "[6, 4, 1, 5, 3, 2, 0, 7]",
-        "1617": "[0, 4, 6, 1, 2, 5, 3, 7]",
-        "1618": "[1, 5, 0, 2, 3, 6, 4, 7]",
-        "1619": "[2, 6, 1, 3, 4, 0, 5, 7]",
-        "1620": "[3, 6, 0, 1, 5, 4, 2, 7]",
-        "1621": "[4, 2, 1, 5, 3, 0, 6, 7]",
-        "1622": "[5, 4, 0, 3, 6, 2, 1, 7]",
-        "1623": "[6, 2, 1, 5, 3, 0, 4, 7]",
-        "1624": "[0, 5, 4, 3, 1, 2, 6, 7]",
-        "1625": "[1, 6, 5, 4, 2, 3, 0, 7]",
-        "1626": "[2, 0, 6, 5, 3, 4, 1, 7]",
-        "1627": "[3, 4, 6, 2, 1, 5, 0, 7]",
-        "1628": "[4, 0, 2, 6, 5, 3, 1, 7]",
-        "1629": "[5, 2, 4, 1, 3, 6, 0, 7]",
-        "1630": "[6, 0, 2, 4, 5, 3, 1, 7]",
-        "1631": "[0, 6, 4, 1, 2, 5, 3, 7]",
-        "1632": "[1, 0, 5, 2, 3, 6, 4, 7]",
-        "1633": "[2, 1, 6, 3, 4, 0, 5, 7]",
-        "1634": "[3, 0, 6, 1, 5, 4, 2, 7]",
-        "1635": "[4, 1, 2, 5, 3, 0, 6, 7]",
-        "1636": "[5, 0, 4, 3, 6, 2, 1, 7]",
-        "1637": "[6, 1, 2, 5, 3, 0, 4, 7]",
-        "1638": "[0, 1, 6, 2, 4, 5, 3, 7]",
-        "1639": "[1, 2, 0, 3, 5, 6, 4, 7]",
-        "1640": "[2, 3, 1, 4, 6, 0, 5, 7]",
-        "1641": "[3, 1, 0, 5, 6, 4, 2, 7]",
-        "1642": "[4, 5, 1, 3, 2, 0, 6, 7]",
-        "1643": "[5, 3, 0, 6, 4, 2, 1, 7]",
-        "1644": "[6, 5, 1, 3, 2, 0, 4, 7]",
-        "1645": "[0, 2, 6, 3, 1, 4, 5, 7]",
-        "1646": "[1, 3, 0, 4, 2, 5, 6, 7]",
-        "1647": "[2, 4, 1, 5, 3, 6, 0, 7]",
-        "1648": "[3, 5, 0, 2, 1, 6, 4, 7]",
-        "1649": "[4, 3, 1, 6, 5, 2, 0, 7]",
-        "1650": "[5, 6, 0, 1, 3, 4, 2, 7]",
-        "1651": "[6, 3, 1, 4, 5, 2, 0, 7]",
-        "1652": "[0, 3, 4, 1, 2, 6, 5, 7]",
-        "1653": "[1, 4, 5, 2, 3, 0, 6, 7]",
-        "1654": "[2, 5, 6, 3, 4, 1, 0, 7]",
-        "1655": "[3, 2, 6, 1, 5, 0, 4, 7]",
-        "1656": "[4, 6, 2, 5, 3, 1, 0, 7]",
-        "1657": "[5, 1, 4, 3, 6, 0, 2, 7]",
-        "1658": "[6, 4, 2, 5, 3, 1, 0, 7]",
-        "1659": "[0, 4, 5, 1, 2, 6, 3, 7]",
-        "1660": "[1, 5, 6, 2, 3, 0, 4, 7]",
-        "1661": "[2, 6, 0, 3, 4, 1, 5, 7]",
-        "1662": "[3, 6, 4, 1, 5, 0, 2, 7]",
-        "1663": "[4, 2, 0, 5, 3, 1, 6, 7]",
-        "1664": "[5, 4, 2, 3, 6, 0, 1, 7]",
-        "1665": "[6, 2, 0, 5, 3, 1, 4, 7]",
-        "1666": "[0, 5, 2, 3, 1, 4, 6, 7]",
-        "1667": "[1, 6, 3, 4, 2, 5, 0, 7]",
-        "1668": "[2, 0, 4, 5, 3, 6, 1, 7]",
-        "1669": "[3, 4, 5, 2, 1, 6, 0, 7]",
-        "1670": "[4, 0, 3, 6, 5, 2, 1, 7]",
-        "1671": "[5, 2, 6, 1, 3, 4, 0, 7]",
-        "1672": "[6, 0, 3, 4, 5, 2, 1, 7]",
-        "1673": "[0, 6, 5, 1, 2, 4, 3, 7]",
-        "1674": "[1, 0, 6, 2, 3, 5, 4, 7]",
-        "1675": "[2, 1, 0, 3, 4, 6, 5, 7]",
-        "1676": "[3, 0, 4, 1, 5, 6, 2, 7]",
-        "1677": "[4, 1, 0, 5, 3, 2, 6, 7]",
-        "1678": "[5, 0, 2, 3, 6, 4, 1, 7]",
-        "1679": "[6, 1, 0, 5, 3, 2, 4, 7]",
-        "1680": "[0, 1, 2, 3, 4, 6, 5, 7]",
-        "1681": "[1, 2, 3, 4, 5, 0, 6, 7]",
-        "1682": "[2, 3, 4, 5, 6, 1, 0, 7]",
-        "1683": "[3, 1, 5, 2, 6, 0, 4, 7]",
-        "1684": "[4, 5, 3, 6, 2, 1, 0, 7]",
-        "1685": "[5, 3, 6, 1, 4, 0, 2, 7]",
-        "1686": "[6, 5, 3, 4, 2, 1, 0, 7]",
-        "1687": "[0, 2, 3, 5, 1, 6, 4, 7]",
-        "1688": "[1, 3, 4, 6, 2, 0, 5, 7]",
-        "1689": "[2, 4, 5, 0, 3, 1, 6, 7]",
-        "1690": "[3, 5, 2, 4, 1, 0, 6, 7]",
-        "1691": "[4, 3, 6, 0, 5, 1, 2, 7]",
-        "1692": "[5, 6, 1, 2, 3, 0, 4, 7]",
-        "1693": "[6, 3, 4, 0, 5, 1, 2, 7]",
-        "1694": "[0, 3, 1, 5, 2, 4, 6, 7]",
-        "1695": "[1, 4, 2, 6, 3, 5, 0, 7]",
-        "1696": "[2, 5, 3, 0, 4, 6, 1, 7]",
-        "1697": "[3, 2, 1, 4, 5, 6, 0, 7]",
-        "1698": "[4, 6, 5, 0, 3, 2, 1, 7]",
-        "1699": "[5, 1, 3, 2, 6, 4, 0, 7]",
-        "1700": "[6, 4, 5, 0, 3, 2, 1, 7]",
-        "1701": "[0, 4, 1, 3, 2, 5, 6, 7]",
-        "1702": "[1, 5, 2, 4, 3, 6, 0, 7]",
-        "1703": "[2, 6, 3, 5, 4, 0, 1, 7]",
-        "1704": "[3, 6, 1, 2, 5, 4, 0, 7]",
-        "1705": "[4, 2, 5, 6, 3, 0, 1, 7]",
-        "1706": "[5, 4, 3, 1, 6, 2, 0, 7]",
-        "1707": "[6, 2, 5, 4, 3, 0, 1, 7]",
-        "1708": "[0, 5, 3, 6, 1, 2, 4, 7]",
-        "1709": "[1, 6, 4, 0, 2, 3, 5, 7]",
-        "1710": "[2, 0, 5, 1, 3, 4, 6, 7]",
-        "1711": "[3, 4, 2, 0, 1, 5, 6, 7]",
-        "1712": "[4, 0, 6, 1, 5, 3, 2, 7]",
-        "1713": "[5, 2, 1, 0, 3, 6, 4, 7]",
-        "1714": "[6, 0, 4, 1, 5, 3, 2, 7]",
-        "1715": "[0, 6, 1, 3, 2, 5, 4, 7]",
-        "1716": "[1, 0, 2, 4, 3, 6, 5, 7]",
-        "1717": "[2, 1, 3, 5, 4, 0, 6, 7]",
-        "1718": "[3, 0, 1, 2, 5, 4, 6, 7]",
-        "1719": "[4, 1, 5, 6, 3, 0, 2, 7]",
-        "1720": "[5, 0, 3, 1, 6, 2, 4, 7]",
-        "1721": "[6, 1, 5, 4, 3, 0, 2, 7]",
-        "1722": "[0, 1, 3, 4, 5, 6, 2, 7]",
-        "1723": "[1, 2, 4, 5, 6, 0, 3, 7]",
-        "1724": "[2, 3, 5, 6, 0, 1, 4, 7]",
-        "1725": "[3, 1, 2, 6, 4, 0, 5, 7]",
-        "1726": "[4, 5, 6, 2, 0, 1, 3, 7]",
-        "1727": "[5, 3, 1, 4, 2, 0, 6, 7]",
-        "1728": "[6, 5, 4, 2, 0, 1, 3, 7]",
-        "1729": "[0, 2, 5, 1, 4, 6, 3, 7]",
-        "1730": "[1, 3, 6, 2, 5, 0, 4, 7]",
-        "1731": "[2, 4, 0, 3, 6, 1, 5, 7]",
-        "1732": "[3, 5, 4, 1, 6, 0, 2, 7]",
-        "1733": "[4, 3, 0, 5, 2, 1, 6, 7]",
-        "1734": "[5, 6, 2, 3, 4, 0, 1, 7]",
-        "1735": "[6, 3, 0, 5, 2, 1, 4, 7]",
-        "1736": "[0, 3, 5, 2, 6, 4, 1, 7]",
-        "1737": "[1, 4, 6, 3, 0, 5, 2, 7]",
-        "1738": "[2, 5, 0, 4, 1, 6, 3, 7]",
-        "1739": "[3, 2, 4, 5, 0, 6, 1, 7]",
-        "1740": "[4, 6, 0, 3, 1, 2, 5, 7]",
-        "1741": "[5, 1, 2, 6, 0, 4, 3, 7]",
-        "1742": "[6, 4, 0, 3, 1, 2, 5, 7]",
-        "1743": "[0, 4, 3, 2, 6, 5, 1, 7]",
-        "1744": "[1, 5, 4, 3, 0, 6, 2, 7]",
-        "1745": "[2, 6, 5, 4, 1, 0, 3, 7]",
-        "1746": "[3, 6, 2, 5, 0, 4, 1, 7]",
-        "1747": "[4, 2, 6, 3, 1, 0, 5, 7]",
-        "1748": "[5, 4, 1, 6, 0, 2, 3, 7]",
-        "1749": "[6, 2, 4, 3, 1, 0, 5, 7]",
-        "1750": "[0, 5, 6, 1, 4, 2, 3, 7]",
-        "1751": "[1, 6, 0, 2, 5, 3, 4, 7]",
-        "1752": "[2, 0, 1, 3, 6, 4, 5, 7]",
-        "1753": "[3, 4, 0, 1, 6, 5, 2, 7]",
-        "1754": "[4, 0, 1, 5, 2, 3, 6, 7]",
-        "1755": "[5, 2, 0, 3, 4, 6, 1, 7]",
-        "1756": "[6, 0, 1, 5, 2, 3, 4, 7]",
-        "1757": "[0, 6, 3, 2, 4, 5, 1, 7]",
-        "1758": "[1, 0, 4, 3, 5, 6, 2, 7]",
-        "1759": "[2, 1, 5, 4, 6, 0, 3, 7]",
-        "1760": "[3, 0, 2, 5, 6, 4, 1, 7]",
-        "1761": "[4, 1, 6, 3, 2, 0, 5, 7]",
-        "1762": "[5, 0, 1, 6, 4, 2, 3, 7]",
-        "1763": "[6, 1, 4, 3, 2, 0, 5, 7]",
-        "1764": "[0, 1, 4, 5, 3, 2, 6, 7]",
-        "1765": "[1, 2, 5, 6, 4, 3, 0, 7]",
-        "1766": "[2, 3, 6, 0, 5, 4, 1, 7]",
-        "1767": "[3, 1, 6, 4, 2, 5, 0, 7]",
-        "1768": "[4, 5, 2, 0, 6, 3, 1, 7]",
-        "1769": "[5, 3, 4, 2, 1, 6, 0, 7]",
-        "1770": "[6, 5, 2, 0, 4, 3, 1, 7]",
-        "1771": "[0, 2, 1, 4, 5, 3, 6, 7]",
-        "1772": "[1, 3, 2, 5, 6, 4, 0, 7]",
-        "1773": "[2, 4, 3, 6, 0, 5, 1, 7]",
-        "1774": "[3, 5, 1, 6, 4, 2, 0, 7]",
-        "1775": "[4, 3, 5, 2, 0, 6, 1, 7]",
-        "1776": "[5, 6, 3, 4, 2, 1, 0, 7]",
-        "1777": "[6, 3, 5, 2, 0, 4, 1, 7]",
-        "1778": "[0, 3, 2, 6, 5, 1, 4, 7]",
-        "1779": "[1, 4, 3, 0, 6, 2, 5, 7]",
-        "1780": "[2, 5, 4, 1, 0, 3, 6, 7]",
-        "1781": "[3, 2, 5, 0, 4, 1, 6, 7]",
-        "1782": "[4, 6, 3, 1, 0, 5, 2, 7]",
-        "1783": "[5, 1, 6, 0, 2, 3, 4, 7]",
-        "1784": "[6, 4, 3, 1, 0, 5, 2, 7]",
-        "1785": "[0, 4, 2, 6, 3, 1, 5, 7]",
-        "1786": "[1, 5, 3, 0, 4, 2, 6, 7]",
-        "1787": "[2, 6, 4, 1, 5, 3, 0, 7]",
-        "1788": "[3, 6, 5, 0, 2, 1, 4, 7]",
-        "1789": "[4, 2, 3, 1, 6, 5, 0, 7]",
-        "1790": "[5, 4, 6, 0, 1, 3, 2, 7]",
-        "1791": "[6, 2, 3, 1, 4, 5, 0, 7]",
-        "1792": "[0, 5, 1, 4, 6, 3, 2, 7]",
-        "1793": "[1, 6, 2, 5, 0, 4, 3, 7]",
-        "1794": "[2, 0, 3, 6, 1, 5, 4, 7]",
-        "1795": "[3, 4, 1, 6, 0, 2, 5, 7]",
-        "1796": "[4, 0, 5, 2, 1, 6, 3, 7]",
-        "1797": "[5, 2, 3, 4, 0, 1, 6, 7]",
-        "1798": "[6, 0, 5, 2, 1, 4, 3, 7]",
-        "1799": "[0, 6, 2, 4, 3, 1, 5, 7]",
-        "1800": "[1, 0, 3, 5, 4, 2, 6, 7]",
-        "1801": "[2, 1, 4, 6, 5, 3, 0, 7]",
-        "1802": "[3, 0, 5, 6, 2, 1, 4, 7]",
-        "1803": "[4, 1, 3, 2, 6, 5, 0, 7]",
-        "1804": "[5, 0, 6, 4, 1, 3, 2, 7]",
-        "1805": "[6, 1, 3, 2, 4, 5, 0, 7]",
-        "1806": "[0, 1, 5, 6, 3, 2, 4, 7]",
-        "1807": "[1, 2, 6, 0, 4, 3, 5, 7]",
-        "1808": "[2, 3, 0, 1, 5, 4, 6, 7]",
-        "1809": "[3, 1, 4, 0, 2, 5, 6, 7]",
-        "1810": "[4, 5, 0, 1, 6, 3, 2, 7]",
-        "1811": "[5, 3, 2, 0, 1, 6, 4, 7]",
-        "1812": "[6, 5, 0, 1, 4, 3, 2, 7]",
-        "1813": "[0, 2, 4, 6, 5, 3, 1, 7]",
-        "1814": "[1, 3, 5, 0, 6, 4, 2, 7]",
-        "1815": "[2, 4, 6, 1, 0, 5, 3, 7]",
-        "1816": "[3, 5, 6, 0, 4, 2, 1, 7]",
-        "1817": "[4, 3, 2, 1, 0, 6, 5, 7]",
-        "1818": "[5, 6, 4, 0, 2, 1, 3, 7]",
-        "1819": "[6, 3, 2, 1, 0, 4, 5, 7]",
-        "1820": "[0, 3, 6, 4, 5, 1, 2, 7]",
-        "1821": "[1, 4, 0, 5, 6, 2, 3, 7]",
-        "1822": "[2, 5, 1, 6, 0, 3, 4, 7]",
-        "1823": "[3, 2, 0, 6, 4, 1, 5, 7]",
-        "1824": "[4, 6, 1, 2, 0, 5, 3, 7]",
-        "1825": "[5, 1, 0, 4, 2, 3, 6, 7]",
-        "1826": "[6, 4, 1, 2, 0, 5, 3, 7]",
-        "1827": "[0, 4, 6, 5, 3, 1, 2, 7]",
-        "1828": "[1, 5, 0, 6, 4, 2, 3, 7]",
-        "1829": "[2, 6, 1, 0, 5, 3, 4, 7]",
-        "1830": "[3, 6, 0, 4, 2, 1, 5, 7]",
-        "1831": "[4, 2, 1, 0, 6, 5, 3, 7]",
-        "1832": "[5, 4, 0, 2, 1, 3, 6, 7]",
-        "1833": "[6, 2, 1, 0, 4, 5, 3, 7]",
-        "1834": "[0, 5, 4, 2, 6, 3, 1, 7]",
-        "1835": "[1, 6, 5, 3, 0, 4, 2, 7]",
-        "1836": "[2, 0, 6, 4, 1, 5, 3, 7]",
-        "1837": "[3, 4, 6, 5, 0, 2, 1, 7]",
-        "1838": "[4, 0, 2, 3, 1, 6, 5, 7]",
-        "1839": "[5, 2, 4, 6, 0, 1, 3, 7]",
-        "1840": "[6, 0, 2, 3, 1, 4, 5, 7]",
-        "1841": "[0, 6, 4, 5, 3, 1, 2, 7]",
-        "1842": "[1, 0, 5, 6, 4, 2, 3, 7]",
-        "1843": "[2, 1, 6, 0, 5, 3, 4, 7]",
-        "1844": "[3, 0, 6, 4, 2, 1, 5, 7]",
-        "1845": "[4, 1, 2, 0, 6, 5, 3, 7]",
-        "1846": "[5, 0, 4, 2, 1, 3, 6, 7]",
-        "1847": "[6, 1, 2, 0, 4, 5, 3, 7]",
-        "1848": "[0, 1, 6, 5, 3, 2, 4, 7]",
-        "1849": "[1, 2, 0, 6, 4, 3, 5, 7]",
-        "1850": "[2, 3, 1, 0, 5, 4, 6, 7]",
-        "1851": "[3, 1, 0, 4, 2, 5, 6, 7]",
-        "1852": "[4, 5, 1, 0, 6, 3, 2, 7]",
-        "1853": "[5, 3, 0, 2, 1, 6, 4, 7]",
-        "1854": "[6, 5, 1, 0, 4, 3, 2, 7]",
-        "1855": "[0, 2, 6, 4, 5, 3, 1, 7]",
-        "1856": "[1, 3, 0, 5, 6, 4, 2, 7]",
-        "1857": "[2, 4, 1, 6, 0, 5, 3, 7]",
-        "1858": "[3, 5, 0, 6, 4, 2, 1, 7]",
-        "1859": "[4, 3, 1, 2, 0, 6, 5, 7]",
-        "1860": "[5, 6, 0, 4, 2, 1, 3, 7]",
-        "1861": "[6, 3, 1, 2, 0, 4, 5, 7]",
-        "1862": "[0, 3, 4, 6, 5, 1, 2, 7]",
-        "1863": "[1, 4, 5, 0, 6, 2, 3, 7]",
-        "1864": "[2, 5, 6, 1, 0, 3, 4, 7]",
-        "1865": "[3, 2, 6, 0, 4, 1, 5, 7]",
-        "1866": "[4, 6, 2, 1, 0, 5, 3, 7]",
-        "1867": "[5, 1, 4, 0, 2, 3, 6, 7]",
-        "1868": "[6, 4, 2, 1, 0, 5, 3, 7]",
-        "1869": "[0, 4, 5, 6, 3, 1, 2, 7]",
-        "1870": "[1, 5, 6, 0, 4, 2, 3, 7]",
-        "1871": "[2, 6, 0, 1, 5, 3, 4, 7]",
-        "1872": "[3, 6, 4, 0, 2, 1, 5, 7]",
-        "1873": "[4, 2, 0, 1, 6, 5, 3, 7]",
-        "1874": "[5, 4, 2, 0, 1, 3, 6, 7]",
-        "1875": "[6, 2, 0, 1, 4, 5, 3, 7]",
-        "1876": "[0, 5, 2, 4, 6, 3, 1, 7]",
-        "1877": "[1, 6, 3, 5, 0, 4, 2, 7]",
-        "1878": "[2, 0, 4, 6, 1, 5, 3, 7]",
-        "1879": "[3, 4, 5, 6, 0, 2, 1, 7]",
-        "1880": "[4, 0, 3, 2, 1, 6, 5, 7]",
-        "1881": "[5, 2, 6, 4, 0, 1, 3, 7]",
-        "1882": "[6, 0, 3, 2, 1, 4, 5, 7]",
-        "1883": "[0, 6, 5, 4, 3, 1, 2, 7]",
-        "1884": "[1, 0, 6, 5, 4, 2, 3, 7]",
-        "1885": "[2, 1, 0, 6, 5, 3, 4, 7]",
-        "1886": "[3, 0, 4, 6, 2, 1, 5, 7]",
-        "1887": "[4, 1, 0, 2, 6, 5, 3, 7]",
-        "1888": "[5, 0, 2, 4, 1, 3, 6, 7]",
-        "1889": "[6, 1, 0, 2, 4, 5, 3, 7]",
-        "1890": "[0, 1, 2, 4, 5, 6, 3, 7]",
-        "1891": "[1, 2, 3, 5, 6, 0, 4, 7]",
-        "1892": "[2, 3, 4, 6, 0, 1, 5, 7]",
-        "1893": "[3, 1, 5, 6, 4, 0, 2, 7]",
-        "1894": "[4, 5, 3, 2, 0, 1, 6, 7]",
-        "1895": "[5, 3, 6, 4, 2, 0, 1, 7]",
-        "1896": "[6, 5, 3, 2, 0, 1, 4, 7]",
-        "1897": "[0, 2, 3, 1, 4, 6, 5, 7]",
-        "1898": "[1, 3, 4, 2, 5, 0, 6, 7]",
-        "1899": "[2, 4, 5, 3, 6, 1, 0, 7]",
-        "1900": "[3, 5, 2, 1, 6, 0, 4, 7]",
-        "1901": "[4, 3, 6, 5, 2, 1, 0, 7]",
-        "1902": "[5, 6, 1, 3, 4, 0, 2, 7]",
-        "1903": "[6, 3, 4, 5, 2, 1, 0, 7]",
-        "1904": "[0, 3, 1, 2, 6, 4, 5, 7]",
-        "1905": "[1, 4, 2, 3, 0, 5, 6, 7]",
-        "1906": "[2, 5, 3, 4, 1, 6, 0, 7]",
-        "1907": "[3, 2, 1, 5, 0, 6, 4, 7]",
-        "1908": "[4, 6, 5, 3, 1, 2, 0, 7]",
-        "1909": "[5, 1, 3, 6, 0, 4, 2, 7]",
-        "1910": "[6, 4, 5, 3, 1, 2, 0, 7]",
-        "1911": "[0, 4, 1, 2, 6, 5, 3, 7]",
-        "1912": "[1, 5, 2, 3, 0, 6, 4, 7]",
-        "1913": "[2, 6, 3, 4, 1, 0, 5, 7]",
-        "1914": "[3, 6, 1, 5, 0, 4, 2, 7]",
-        "1915": "[4, 2, 5, 3, 1, 0, 6, 7]",
-        "1916": "[5, 4, 3, 6, 0, 2, 1, 7]",
-        "1917": "[6, 2, 5, 3, 1, 0, 4, 7]",
-        "1918": "[0, 5, 3, 1, 4, 2, 6, 7]",
-        "1919": "[1, 6, 4, 2, 5, 3, 0, 7]",
-        "1920": "[2, 0, 5, 3, 6, 4, 1, 7]",
-        "1921": "[3, 4, 2, 1, 6, 5, 0, 7]",
-        "1922": "[4, 0, 6, 5, 2, 3, 1, 7]",
-        "1923": "[5, 2, 1, 3, 4, 6, 0, 7]",
-        "1924": "[6, 0, 4, 5, 2, 3, 1, 7]",
-        "1925": "[0, 6, 1, 2, 4, 5, 3, 7]",
-        "1926": "[1, 0, 2, 3, 5, 6, 4, 7]",
-        "1927": "[2, 1, 3, 4, 6, 0, 5, 7]",
-        "1928": "[3, 0, 1, 5, 6, 4, 2, 7]",
-        "1929": "[4, 1, 5, 3, 2, 0, 6, 7]",
-        "1930": "[5, 0, 3, 6, 4, 2, 1, 7]",
-        "1931": "[6, 1, 5, 3, 2, 0, 4, 7]",
-        "1932": "[0, 1, 3, 5, 2, 6, 4, 7]",
-        "1933": "[1, 2, 4, 6, 3, 0, 5, 7]",
-        "1934": "[2, 3, 5, 0, 4, 1, 6, 7]",
-        "1935": "[3, 1, 2, 4, 5, 0, 6, 7]",
-        "1936": "[4, 5, 6, 0, 3, 1, 2, 7]",
-        "1937": "[5, 3, 1, 2, 6, 0, 4, 7]",
-        "1938": "[6, 5, 4, 0, 3, 1, 2, 7]",
-        "1939": "[0, 2, 5, 4, 3, 6, 1, 7]",
-        "1940": "[1, 3, 6, 5, 4, 0, 2, 7]",
-        "1941": "[2, 4, 0, 6, 5, 1, 3, 7]",
-        "1942": "[3, 5, 4, 6, 2, 0, 1, 7]",
-        "1943": "[4, 3, 0, 2, 6, 1, 5, 7]",
-        "1944": "[5, 6, 2, 4, 1, 0, 3, 7]",
-        "1945": "[6, 3, 0, 2, 4, 1, 5, 7]",
-        "1946": "[0, 3, 5, 6, 1, 4, 2, 7]",
-        "1947": "[1, 4, 6, 0, 2, 5, 3, 7]",
-        "1948": "[2, 5, 0, 1, 3, 6, 4, 7]",
-        "1949": "[3, 2, 4, 0, 1, 6, 5, 7]",
-        "1950": "[4, 6, 0, 1, 5, 2, 3, 7]",
-        "1951": "[5, 1, 2, 0, 3, 4, 6, 7]",
-        "1952": "[6, 4, 0, 1, 5, 2, 3, 7]",
-        "1953": "[0, 4, 3, 6, 1, 5, 2, 7]",
-        "1954": "[1, 5, 4, 0, 2, 6, 3, 7]",
-        "1955": "[2, 6, 5, 1, 3, 0, 4, 7]",
-        "1956": "[3, 6, 2, 0, 1, 4, 5, 7]",
-        "1957": "[4, 2, 6, 1, 5, 0, 3, 7]",
-        "1958": "[5, 4, 1, 0, 3, 2, 6, 7]",
-        "1959": "[6, 2, 4, 1, 5, 0, 3, 7]",
-        "1960": "[0, 5, 6, 4, 3, 2, 1, 7]",
-        "1961": "[1, 6, 0, 5, 4, 3, 2, 7]",
-        "1962": "[2, 0, 1, 6, 5, 4, 3, 7]",
-        "1963": "[3, 4, 0, 6, 2, 5, 1, 7]",
-        "1964": "[4, 0, 1, 2, 6, 3, 5, 7]",
-        "1965": "[5, 2, 0, 4, 1, 6, 3, 7]",
-        "1966": "[6, 0, 1, 2, 4, 3, 5, 7]",
-        "1967": "[0, 6, 3, 4, 1, 5, 2, 7]",
-        "1968": "[1, 0, 4, 5, 2, 6, 3, 7]",
-        "1969": "[2, 1, 5, 6, 3, 0, 4, 7]",
-        "1970": "[3, 0, 2, 6, 1, 4, 5, 7]",
-        "1971": "[4, 1, 6, 2, 5, 0, 3, 7]",
-        "1972": "[5, 0, 1, 4, 3, 2, 6, 7]",
-        "1973": "[6, 1, 4, 2, 5, 0, 3, 7]",
-        "1974": "[0, 1, 4, 3, 6, 2, 5, 7]",
-        "1975": "[1, 2, 5, 4, 0, 3, 6, 7]",
-        "1976": "[2, 3, 6, 5, 1, 4, 0, 7]",
-        "1977": "[3, 1, 6, 2, 0, 5, 4, 7]",
-        "1978": "[4, 5, 2, 6, 1, 3, 0, 7]",
-        "1979": "[5, 3, 4, 1, 0, 6, 2, 7]",
-        "1980": "[6, 5, 2, 4, 1, 3, 0, 7]",
-        "1981": "[0, 2, 1, 5, 6, 3, 4, 7]",
-        "1982": "[1, 3, 2, 6, 0, 4, 5, 7]",
-        "1983": "[2, 4, 3, 0, 1, 5, 6, 7]",
-        "1984": "[3, 5, 1, 4, 0, 2, 6, 7]",
-        "1985": "[4, 3, 5, 0, 1, 6, 2, 7]",
-        "1986": "[5, 6, 3, 2, 0, 1, 4, 7]",
-        "1987": "[6, 3, 5, 0, 1, 4, 2, 7]",
-        "1988": "[0, 3, 2, 5, 4, 1, 6, 7]",
-        "1989": "[1, 4, 3, 6, 5, 2, 0, 7]",
-        "1990": "[2, 5, 4, 0, 6, 3, 1, 7]",
-        "1991": "[3, 2, 5, 4, 6, 1, 0, 7]",
-        "1992": "[4, 6, 3, 0, 2, 5, 1, 7]",
-        "1993": "[5, 1, 6, 2, 4, 3, 0, 7]",
-        "1994": "[6, 4, 3, 0, 2, 5, 1, 7]",
-        "1995": "[0, 4, 2, 3, 5, 1, 6, 7]",
-        "1996": "[1, 5, 3, 4, 6, 2, 0, 7]",
-        "1997": "[2, 6, 4, 5, 0, 3, 1, 7]",
-        "1998": "[3, 6, 5, 2, 4, 1, 0, 7]",
-        "1999": "[4, 2, 3, 6, 0, 5, 1, 7]",
-        "2000": "[5, 4, 6, 1, 2, 3, 0, 7]",
-        "2001": "[6, 2, 3, 4, 0, 5, 1, 7]",
-        "2002": "[0, 5, 1, 6, 2, 3, 4, 7]",
-        "2003": "[1, 6, 2, 0, 3, 4, 5, 7]",
-        "2004": "[2, 0, 3, 1, 4, 5, 6, 7]",
-        "2005": "[3, 4, 1, 0, 5, 2, 6, 7]",
-        "2006": "[4, 0, 5, 1, 3, 6, 2, 7]",
-        "2007": "[5, 2, 3, 0, 6, 1, 4, 7]",
-        "2008": "[6, 0, 5, 1, 3, 4, 2, 7]",
-        "2009": "[0, 6, 2, 3, 5, 1, 4, 7]",
-        "2010": "[1, 0, 3, 4, 6, 2, 5, 7]",
-        "2011": "[2, 1, 4, 5, 0, 3, 6, 7]",
-        "2012": "[3, 0, 5, 2, 4, 1, 6, 7]",
-        "2013": "[4, 1, 3, 6, 0, 5, 2, 7]",
-        "2014": "[5, 0, 6, 1, 2, 3, 4, 7]",
-        "2015": "[6, 1, 3, 4, 0, 5, 2, 7]",
-        "2016": "[0, 1, 5, 3, 4, 2, 6, 7]",
-        "2017": "[1, 2, 6, 4, 5, 3, 0, 7]",
-        "2018": "[2, 3, 0, 5, 6, 4, 1, 7]",
-        "2019": "[3, 1, 4, 2, 6, 5, 0, 7]",
-        "2020": "[4, 5, 0, 6, 2, 3, 1, 7]",
-        "2021": "[5, 3, 2, 1, 4, 6, 0, 7]",
-        "2022": "[6, 5, 0, 4, 2, 3, 1, 7]",
-        "2023": "[0, 2, 4, 5, 1, 3, 6, 7]",
-        "2024": "[1, 3, 5, 6, 2, 4, 0, 7]",
-        "2025": "[2, 4, 6, 0, 3, 5, 1, 7]",
-        "2026": "[3, 5, 6, 4, 1, 2, 0, 7]",
-        "2027": "[4, 3, 2, 0, 5, 6, 1, 7]",
-        "2028": "[5, 6, 4, 2, 3, 1, 0, 7]",
-        "2029": "[6, 3, 2, 0, 5, 4, 1, 7]",
-        "2030": "[0, 3, 6, 5, 2, 1, 4, 7]",
-        "2031": "[1, 4, 0, 6, 3, 2, 5, 7]",
-        "2032": "[2, 5, 1, 0, 4, 3, 6, 7]",
-        "2033": "[3, 2, 0, 4, 5, 1, 6, 7]",
-        "2034": "[4, 6, 1, 0, 3, 5, 2, 7]",
-        "2035": "[5, 1, 0, 2, 6, 3, 4, 7]",
-        "2036": "[6, 4, 1, 0, 3, 5, 2, 7]",
-        "2037": "[0, 4, 6, 3, 2, 1, 5, 7]",
-        "2038": "[1, 5, 0, 4, 3, 2, 6, 7]",
-        "2039": "[2, 6, 1, 5, 4, 3, 0, 7]",
-        "2040": "[3, 6, 0, 2, 5, 1, 4, 7]",
-        "2041": "[4, 2, 1, 6, 3, 5, 0, 7]",
-        "2042": "[5, 4, 0, 1, 6, 3, 2, 7]",
-        "2043": "[6, 2, 1, 4, 3, 5, 0, 7]",
-        "2044": "[0, 5, 4, 6, 1, 3, 2, 7]",
-        "2045": "[1, 6, 5, 0, 2, 4, 3, 7]",
-        "2046": "[2, 0, 6, 1, 3, 5, 4, 7]",
-        "2047": "[3, 4, 6, 0, 1, 2, 5, 7]",
-        "2048": "[4, 0, 2, 1, 5, 6, 3, 7]",
-        "2049": "[5, 2, 4, 0, 3, 1, 6, 7]",
-        "2050": "[6, 0, 2, 1, 5, 4, 3, 7]",
-        "2051": "[0, 6, 4, 3, 2, 1, 5, 7]",
-        "2052": "[1, 0, 5, 4, 3, 2, 6, 7]",
-        "2053": "[2, 1, 6, 5, 4, 3, 0, 7]",
-        "2054": "[3, 0, 6, 2, 5, 1, 4, 7]",
-        "2055": "[4, 1, 2, 6, 3, 5, 0, 7]",
-        "2056": "[5, 0, 4, 1, 6, 3, 2, 7]",
-        "2057": "[6, 1, 2, 4, 3, 5, 0, 7]",
-        "2058": "[0, 1, 6, 3, 4, 2, 5, 7]",
-        "2059": "[1, 2, 0, 4, 5, 3, 6, 7]",
-        "2060": "[2, 3, 1, 5, 6, 4, 0, 7]",
-        "2061": "[3, 1, 0, 2, 6, 5, 4, 7]",
-        "2062": "[4, 5, 1, 6, 2, 3, 0, 7]",
-        "2063": "[5, 3, 0, 1, 4, 6, 2, 7]",
-        "2064": "[6, 5, 1, 4, 2, 3, 0, 7]",
-        "2065": "[0, 2, 6, 5, 1, 3, 4, 7]",
-        "2066": "[1, 3, 0, 6, 2, 4, 5, 7]",
-        "2067": "[2, 4, 1, 0, 3, 5, 6, 7]",
-        "2068": "[3, 5, 0, 4, 1, 2, 6, 7]",
-        "2069": "[4, 3, 1, 0, 5, 6, 2, 7]",
-        "2070": "[5, 6, 0, 2, 3, 1, 4, 7]",
-        "2071": "[6, 3, 1, 0, 5, 4, 2, 7]",
-        "2072": "[0, 3, 4, 5, 2, 1, 6, 7]",
-        "2073": "[1, 4, 5, 6, 3, 2, 0, 7]",
-        "2074": "[2, 5, 6, 0, 4, 3, 1, 7]",
-        "2075": "[3, 2, 6, 4, 5, 1, 0, 7]",
-        "2076": "[4, 6, 2, 0, 3, 5, 1, 7]",
-        "2077": "[5, 1, 4, 2, 6, 3, 0, 7]",
-        "2078": "[6, 4, 2, 0, 3, 5, 1, 7]",
-        "2079": "[0, 4, 5, 3, 2, 1, 6, 7]",
-        "2080": "[1, 5, 6, 4, 3, 2, 0, 7]",
-        "2081": "[2, 6, 0, 5, 4, 3, 1, 7]",
-        "2082": "[3, 6, 4, 2, 5, 1, 0, 7]",
-        "2083": "[4, 2, 0, 6, 3, 5, 1, 7]",
-        "2084": "[5, 4, 2, 1, 6, 3, 0, 7]",
-        "2085": "[6, 2, 0, 4, 3, 5, 1, 7]",
-        "2086": "[0, 5, 2, 6, 1, 3, 4, 7]",
-        "2087": "[1, 6, 3, 0, 2, 4, 5, 7]",
-        "2088": "[2, 0, 4, 1, 3, 5, 6, 7]",
-        "2089": "[3, 4, 5, 0, 1, 2, 6, 7]",
-        "2090": "[4, 0, 3, 1, 5, 6, 2, 7]",
-        "2091": "[5, 2, 6, 0, 3, 1, 4, 7]",
-        "2092": "[6, 0, 3, 1, 5, 4, 2, 7]",
-        "2093": "[0, 6, 5, 3, 2, 1, 4, 7]",
-        "2094": "[1, 0, 6, 4, 3, 2, 5, 7]",
-        "2095": "[2, 1, 0, 5, 4, 3, 6, 7]",
-        "2096": "[3, 0, 4, 2, 5, 1, 6, 7]",
-        "2097": "[4, 1, 0, 6, 3, 5, 2, 7]",
-        "2098": "[5, 0, 2, 1, 6, 3, 4, 7]",
-        "2099": "[6, 1, 0, 4, 3, 5, 2, 7]",
-        "2100": "[0, 1, 2, 5, 3, 6, 4, 7]",
-        "2101": "[1, 2, 3, 6, 4, 0, 5, 7]",
-        "2102": "[2, 3, 4, 0, 5, 1, 6, 7]",
-        "2103": "[3, 1, 5, 4, 2, 0, 6, 7]",
-        "2104": "[4, 5, 3, 0, 6, 1, 2, 7]",
-        "2105": "[5, 3, 6, 2, 1, 0, 4, 7]",
-        "2106": "[6, 5, 3, 0, 4, 1, 2, 7]",
-        "2107": "[0, 2, 3, 4, 5, 6, 1, 7]",
-        "2108": "[1, 3, 4, 5, 6, 0, 2, 7]",
-        "2109": "[2, 4, 5, 6, 0, 1, 3, 7]",
-        "2110": "[3, 5, 2, 6, 4, 0, 1, 7]",
-        "2111": "[4, 3, 6, 2, 0, 1, 5, 7]",
-        "2112": "[5, 6, 1, 4, 2, 0, 3, 7]",
-        "2113": "[6, 3, 4, 2, 0, 1, 5, 7]",
-        "2114": "[0, 3, 1, 6, 5, 4, 2, 7]",
-        "2115": "[1, 4, 2, 0, 6, 5, 3, 7]",
-        "2116": "[2, 5, 3, 1, 0, 6, 4, 7]",
-        "2117": "[3, 2, 1, 0, 4, 6, 5, 7]",
-        "2118": "[4, 6, 5, 1, 0, 2, 3, 7]",
-        "2119": "[5, 1, 3, 0, 2, 4, 6, 7]",
-        "2120": "[6, 4, 5, 1, 0, 2, 3, 7]",
-        "2121": "[0, 4, 1, 6, 3, 5, 2, 7]",
-        "2122": "[1, 5, 2, 0, 4, 6, 3, 7]",
-        "2123": "[2, 6, 3, 1, 5, 0, 4, 7]",
-        "2124": "[3, 6, 1, 0, 2, 4, 5, 7]",
-        "2125": "[4, 2, 5, 1, 6, 0, 3, 7]",
-        "2126": "[5, 4, 3, 0, 1, 2, 6, 7]",
-        "2127": "[6, 2, 5, 1, 4, 0, 3, 7]",
-        "2128": "[0, 5, 3, 4, 6, 2, 1, 7]",
-        "2129": "[1, 6, 4, 5, 0, 3, 2, 7]",
-        "2130": "[2, 0, 5, 6, 1, 4, 3, 7]",
-        "2131": "[3, 4, 2, 6, 0, 5, 1, 7]",
-        "2132": "[4, 0, 6, 2, 1, 3, 5, 7]",
-        "2133": "[5, 2, 1, 4, 0, 6, 3, 7]",
-        "2134": "[6, 0, 4, 2, 1, 3, 5, 7]",
-        "2135": "[0, 6, 1, 4, 3, 5, 2, 7]",
-        "2136": "[1, 0, 2, 5, 4, 6, 3, 7]",
-        "2137": "[2, 1, 3, 6, 5, 0, 4, 7]",
-        "2138": "[3, 0, 1, 6, 2, 4, 5, 7]",
-        "2139": "[4, 1, 5, 2, 6, 0, 3, 7]",
-        "2140": "[5, 0, 3, 4, 1, 2, 6, 7]",
-        "2141": "[6, 1, 5, 2, 4, 0, 3, 7]",
-        "2142": "[0, 1, 3, 2, 4, 6, 5, 7]",
-        "2143": "[1, 2, 4, 3, 5, 0, 6, 7]",
-        "2144": "[2, 3, 5, 4, 6, 1, 0, 7]",
-        "2145": "[3, 1, 2, 5, 6, 0, 4, 7]",
-        "2146": "[4, 5, 6, 3, 2, 1, 0, 7]",
-        "2147": "[5, 3, 1, 6, 4, 0, 2, 7]",
-        "2148": "[6, 5, 4, 3, 2, 1, 0, 7]",
-        "2149": "[0, 2, 5, 3, 1, 6, 4, 7]",
-        "2150": "[1, 3, 6, 4, 2, 0, 5, 7]",
-        "2151": "[2, 4, 0, 5, 3, 1, 6, 7]",
-        "2152": "[3, 5, 4, 2, 1, 0, 6, 7]",
-        "2153": "[4, 3, 0, 6, 5, 1, 2, 7]",
-        "2154": "[5, 6, 2, 1, 3, 0, 4, 7]",
-        "2155": "[6, 3, 0, 4, 5, 1, 2, 7]",
-        "2156": "[0, 3, 5, 1, 2, 4, 6, 7]",
-        "2157": "[1, 4, 6, 2, 3, 5, 0, 7]",
-        "2158": "[2, 5, 0, 3, 4, 6, 1, 7]",
-        "2159": "[3, 2, 4, 1, 5, 6, 0, 7]",
-        "2160": "[4, 6, 0, 5, 3, 2, 1, 7]",
-        "2161": "[5, 1, 2, 3, 6, 4, 0, 7]",
-        "2162": "[6, 4, 0, 5, 3, 2, 1, 7]",
-        "2163": "[0, 4, 3, 1, 2, 5, 6, 7]",
-        "2164": "[1, 5, 4, 2, 3, 6, 0, 7]",
-        "2165": "[2, 6, 5, 3, 4, 0, 1, 7]",
-        "2166": "[3, 6, 2, 1, 5, 4, 0, 7]",
-        "2167": "[4, 2, 6, 5, 3, 0, 1, 7]",
-        "2168": "[5, 4, 1, 3, 6, 2, 0, 7]",
-        "2169": "[6, 2, 4, 5, 3, 0, 1, 7]",
-        "2170": "[0, 5, 6, 3, 1, 2, 4, 7]",
-        "2171": "[1, 6, 0, 4, 2, 3, 5, 7]",
-        "2172": "[2, 0, 1, 5, 3, 4, 6, 7]",
-        "2173": "[3, 4, 0, 2, 1, 5, 6, 7]",
-        "2174": "[4, 0, 1, 6, 5, 3, 2, 7]",
-        "2175": "[5, 2, 0, 1, 3, 6, 4, 7]",
-        "2176": "[6, 0, 1, 4, 5, 3, 2, 7]",
-        "2177": "[0, 6, 3, 1, 2, 5, 4, 7]",
-        "2178": "[1, 0, 4, 2, 3, 6, 5, 7]",
-        "2179": "[2, 1, 5, 3, 4, 0, 6, 7]",
-        "2180": "[3, 0, 2, 1, 5, 4, 6, 7]",
-        "2181": "[4, 1, 6, 5, 3, 0, 2, 7]",
-        "2182": "[5, 0, 1, 3, 6, 2, 4, 7]",
-        "2183": "[6, 1, 4, 5, 3, 0, 2, 7]",
-        "2184": "[0, 1, 4, 6, 5, 2, 3, 7]",
-        "2185": "[1, 2, 5, 0, 6, 3, 4, 7]",
-        "2186": "[2, 3, 6, 1, 0, 4, 5, 7]",
-        "2187": "[3, 1, 6, 0, 4, 5, 2, 7]",
-        "2188": "[4, 5, 2, 1, 0, 3, 6, 7]",
-        "2189": "[5, 3, 4, 0, 2, 6, 1, 7]",
-        "2190": "[6, 5, 2, 1, 0, 3, 4, 7]",
-        "2191": "[0, 2, 1, 6, 4, 3, 5, 7]",
-        "2192": "[1, 3, 2, 0, 5, 4, 6, 7]",
-        "2193": "[2, 4, 3, 1, 6, 5, 0, 7]",
-        "2194": "[3, 5, 1, 0, 6, 2, 4, 7]",
-        "2195": "[4, 3, 5, 1, 2, 6, 0, 7]",
-        "2196": "[5, 6, 3, 0, 4, 1, 2, 7]",
-        "2197": "[6, 3, 5, 1, 2, 4, 0, 7]",
-        "2198": "[0, 3, 2, 4, 6, 1, 5, 7]",
-        "2199": "[1, 4, 3, 5, 0, 2, 6, 7]",
-        "2200": "[2, 5, 4, 6, 1, 3, 0, 7]",
-        "2201": "[3, 2, 5, 6, 0, 1, 4, 7]",
-        "2202": "[4, 6, 3, 2, 1, 5, 0, 7]",
-        "2203": "[5, 1, 6, 4, 0, 3, 2, 7]",
-        "2204": "[6, 4, 3, 2, 1, 5, 0, 7]",
-        "2205": "[0, 4, 2, 5, 6, 1, 3, 7]",
-        "2206": "[1, 5, 3, 6, 0, 2, 4, 7]",
-        "2207": "[2, 6, 4, 0, 1, 3, 5, 7]",
-        "2208": "[3, 6, 5, 4, 0, 1, 2, 7]",
-        "2209": "[4, 2, 3, 0, 1, 5, 6, 7]",
-        "2210": "[5, 4, 6, 2, 0, 3, 1, 7]",
-        "2211": "[6, 2, 3, 0, 1, 5, 4, 7]",
-        "2212": "[0, 5, 1, 2, 4, 3, 6, 7]",
-        "2213": "[1, 6, 2, 3, 5, 4, 0, 7]",
-        "2214": "[2, 0, 3, 4, 6, 5, 1, 7]",
-        "2215": "[3, 4, 1, 5, 6, 2, 0, 7]",
-        "2216": "[4, 0, 5, 3, 2, 6, 1, 7]",
-        "2217": "[5, 2, 3, 6, 4, 1, 0, 7]",
-        "2218": "[6, 0, 5, 3, 2, 4, 1, 7]",
-        "2219": "[0, 6, 2, 5, 4, 1, 3, 7]",
-        "2220": "[1, 0, 3, 6, 5, 2, 4, 7]",
-        "2221": "[2, 1, 4, 0, 6, 3, 5, 7]",
-        "2222": "[3, 0, 5, 4, 6, 1, 2, 7]",
-        "2223": "[4, 1, 3, 0, 2, 5, 6, 7]",
-        "2224": "[5, 0, 6, 2, 4, 3, 1, 7]",
-        "2225": "[6, 1, 3, 0, 2, 5, 4, 7]",
-        "2226": "[0, 1, 5, 4, 6, 2, 3, 7]",
-        "2227": "[1, 2, 6, 5, 0, 3, 4, 7]",
-        "2228": "[2, 3, 0, 6, 1, 4, 5, 7]",
-        "2229": "[3, 1, 4, 6, 0, 5, 2, 7]",
-        "2230": "[4, 5, 0, 2, 1, 3, 6, 7]",
-        "2231": "[5, 3, 2, 4, 0, 6, 1, 7]",
-        "2232": "[6, 5, 0, 2, 1, 3, 4, 7]",
-        "2233": "[0, 2, 4, 1, 6, 3, 5, 7]",
-        "2234": "[1, 3, 5, 2, 0, 4, 6, 7]",
-        "2235": "[2, 4, 6, 3, 1, 5, 0, 7]",
-        "2236": "[3, 5, 6, 1, 0, 2, 4, 7]",
-        "2237": "[4, 3, 2, 5, 1, 6, 0, 7]",
-        "2238": "[5, 6, 4, 3, 0, 1, 2, 7]",
-        "2239": "[6, 3, 2, 5, 1, 4, 0, 7]",
-        "2240": "[0, 3, 6, 2, 4, 1, 5, 7]",
-        "2241": "[1, 4, 0, 3, 5, 2, 6, 7]",
-        "2242": "[2, 5, 1, 4, 6, 3, 0, 7]",
-        "2243": "[3, 2, 0, 5, 6, 1, 4, 7]",
-        "2244": "[4, 6, 1, 3, 2, 5, 0, 7]",
-        "2245": "[5, 1, 0, 6, 4, 3, 2, 7]",
-        "2246": "[6, 4, 1, 3, 2, 5, 0, 7]",
-        "2247": "[0, 4, 6, 2, 5, 1, 3, 7]",
-        "2248": "[1, 5, 0, 3, 6, 2, 4, 7]",
-        "2249": "[2, 6, 1, 4, 0, 3, 5, 7]",
-        "2250": "[3, 6, 0, 5, 4, 1, 2, 7]",
-        "2251": "[4, 2, 1, 3, 0, 5, 6, 7]",
-        "2252": "[5, 4, 0, 6, 2, 3, 1, 7]",
-        "2253": "[6, 2, 1, 3, 0, 5, 4, 7]",
-        "2254": "[0, 5, 4, 1, 2, 3, 6, 7]",
-        "2255": "[1, 6, 5, 2, 3, 4, 0, 7]",
-        "2256": "[2, 0, 6, 3, 4, 5, 1, 7]",
-        "2257": "[3, 4, 6, 1, 5, 2, 0, 7]",
-        "2258": "[4, 0, 2, 5, 3, 6, 1, 7]",
-        "2259": "[5, 2, 4, 3, 6, 1, 0, 7]",
-        "2260": "[6, 0, 2, 5, 3, 4, 1, 7]",
-        "2261": "[0, 6, 4, 2, 5, 1, 3, 7]",
-        "2262": "[1, 0, 5, 3, 6, 2, 4, 7]",
-        "2263": "[2, 1, 6, 4, 0, 3, 5, 7]",
-        "2264": "[3, 0, 6, 5, 4, 1, 2, 7]",
-        "2265": "[4, 1, 2, 3, 0, 5, 6, 7]",
-        "2266": "[5, 0, 4, 6, 2, 3, 1, 7]",
-        "2267": "[6, 1, 2, 3, 0, 5, 4, 7]",
-        "2268": "[0, 1, 6, 4, 5, 2, 3, 7]",
-        "2269": "[1, 2, 0, 5, 6, 3, 4, 7]",
-        "2270": "[2, 3, 1, 6, 0, 4, 5, 7]",
-        "2271": "[3, 1, 0, 6, 4, 5, 2, 7]",
-        "2272": "[4, 5, 1, 2, 0, 3, 6, 7]",
-        "2273": "[5, 3, 0, 4, 2, 6, 1, 7]",
-        "2274": "[6, 5, 1, 2, 0, 3, 4, 7]",
-        "2275": "[0, 2, 6, 1, 4, 3, 5, 7]",
-        "2276": "[1, 3, 0, 2, 5, 4, 6, 7]",
-        "2277": "[2, 4, 1, 3, 6, 5, 0, 7]",
-        "2278": "[3, 5, 0, 1, 6, 2, 4, 7]",
-        "2279": "[4, 3, 1, 5, 2, 6, 0, 7]",
-        "2280": "[5, 6, 0, 3, 4, 1, 2, 7]",
-        "2281": "[6, 3, 1, 5, 2, 4, 0, 7]",
-        "2282": "[0, 3, 4, 2, 6, 1, 5, 7]",
-        "2283": "[1, 4, 5, 3, 0, 2, 6, 7]",
-        "2284": "[2, 5, 6, 4, 1, 3, 0, 7]",
-        "2285": "[3, 2, 6, 5, 0, 1, 4, 7]",
-        "2286": "[4, 6, 2, 3, 1, 5, 0, 7]",
-        "2287": "[5, 1, 4, 6, 0, 3, 2, 7]",
-        "2288": "[6, 4, 2, 3, 1, 5, 0, 7]",
-        "2289": "[0, 4, 5, 2, 6, 1, 3, 7]",
-        "2290": "[1, 5, 6, 3, 0, 2, 4, 7]",
-        "2291": "[2, 6, 0, 4, 1, 3, 5, 7]",
-        "2292": "[3, 6, 4, 5, 0, 1, 2, 7]",
-        "2293": "[4, 2, 0, 3, 1, 5, 6, 7]",
-        "2294": "[5, 4, 2, 6, 0, 3, 1, 7]",
-        "2295": "[6, 2, 0, 3, 1, 5, 4, 7]",
-        "2296": "[0, 5, 2, 1, 4, 3, 6, 7]",
-        "2297": "[1, 6, 3, 2, 5, 4, 0, 7]",
-        "2298": "[2, 0, 4, 3, 6, 5, 1, 7]",
-        "2299": "[3, 4, 5, 1, 6, 2, 0, 7]",
-        "2300": "[4, 0, 3, 5, 2, 6, 1, 7]",
-        "2301": "[5, 2, 6, 3, 4, 1, 0, 7]",
-        "2302": "[6, 0, 3, 5, 2, 4, 1, 7]",
-        "2303": "[0, 6, 5, 2, 4, 1, 3, 7]",
-        "2304": "[1, 0, 6, 3, 5, 2, 4, 7]",
-        "2305": "[2, 1, 0, 4, 6, 3, 5, 7]",
-        "2306": "[3, 0, 4, 5, 6, 1, 2, 7]",
-        "2307": "[4, 1, 0, 3, 2, 5, 6, 7]",
-        "2308": "[5, 0, 2, 6, 4, 3, 1, 7]",
-        "2309": "[6, 1, 0, 3, 2, 5, 4, 7]",
-        "2310": "[0, 1, 2, 6, 5, 4, 3, 7]",
-        "2311": "[1, 2, 3, 0, 6, 5, 4, 7]",
-        "2312": "[2, 3, 4, 1, 0, 6, 5, 7]",
-        "2313": "[3, 1, 5, 0, 4, 6, 2, 7]",
-        "2314": "[4, 5, 3, 1, 0, 2, 6, 7]",
-        "2315": "[5, 3, 6, 0, 2, 4, 1, 7]",
-        "2316": "[6, 5, 3, 1, 0, 2, 4, 7]",
-        "2317": "[0, 2, 3, 6, 4, 1, 5, 7]",
-        "2318": "[1, 3, 4, 0, 5, 2, 6, 7]",
-        "2319": "[2, 4, 5, 1, 6, 3, 0, 7]",
-        "2320": "[3, 5, 2, 0, 6, 1, 4, 7]",
-        "2321": "[4, 3, 6, 1, 2, 5, 0, 7]",
-        "2322": "[5, 6, 1, 0, 4, 3, 2, 7]",
-        "2323": "[6, 3, 4, 1, 2, 5, 0, 7]",
-        "2324": "[0, 3, 1, 4, 6, 2, 5, 7]",
-        "2325": "[1, 4, 2, 5, 0, 3, 6, 7]",
-        "2326": "[2, 5, 3, 6, 1, 4, 0, 7]",
-        "2327": "[3, 2, 1, 6, 0, 5, 4, 7]",
-        "2328": "[4, 6, 5, 2, 1, 3, 0, 7]",
-        "2329": "[5, 1, 3, 4, 0, 6, 2, 7]",
-        "2330": "[6, 4, 5, 2, 1, 3, 0, 7]",
-        "2331": "[0, 4, 1, 5, 6, 2, 3, 7]",
-        "2332": "[1, 5, 2, 6, 0, 3, 4, 7]",
-        "2333": "[2, 6, 3, 0, 1, 4, 5, 7]",
-        "2334": "[3, 6, 1, 4, 0, 5, 2, 7]",
-        "2335": "[4, 2, 5, 0, 1, 3, 6, 7]",
-        "2336": "[5, 4, 3, 2, 0, 6, 1, 7]",
-        "2337": "[6, 2, 5, 0, 1, 3, 4, 7]",
-        "2338": "[0, 5, 3, 2, 4, 1, 6, 7]",
-        "2339": "[1, 6, 4, 3, 5, 2, 0, 7]",
-        "2340": "[2, 0, 5, 4, 6, 3, 1, 7]",
-        "2341": "[3, 4, 2, 5, 6, 1, 0, 7]",
-        "2342": "[4, 0, 6, 3, 2, 5, 1, 7]",
-        "2343": "[5, 2, 1, 6, 4, 3, 0, 7]",
-        "2344": "[6, 0, 4, 3, 2, 5, 1, 7]",
-        "2345": "[0, 6, 1, 5, 4, 2, 3, 7]",
-        "2346": "[1, 0, 2, 6, 5, 3, 4, 7]",
-        "2347": "[2, 1, 3, 0, 6, 4, 5, 7]",
-        "2348": "[3, 0, 1, 4, 6, 5, 2, 7]",
-        "2349": "[4, 1, 5, 0, 2, 3, 6, 7]",
-        "2350": "[5, 0, 3, 2, 4, 6, 1, 7]",
-        "2351": "[6, 1, 5, 0, 2, 3, 4, 7]",
-        "2352": "[0, 1, 3, 6, 2, 5, 4, 7]",
-        "2353": "[1, 2, 4, 0, 3, 6, 5, 7]",
-        "2354": "[2, 3, 5, 1, 4, 0, 6, 7]",
-        "2355": "[3, 1, 2, 0, 5, 4, 6, 7]",
-        "2356": "[4, 5, 6, 1, 3, 0, 2, 7]",
-        "2357": "[5, 3, 1, 0, 6, 2, 4, 7]",
-        "2358": "[6, 5, 4, 1, 3, 0, 2, 7]",
-        "2359": "[0, 2, 5, 6, 3, 4, 1, 7]",
-        "2360": "[1, 3, 6, 0, 4, 5, 2, 7]",
-        "2361": "[2, 4, 0, 1, 5, 6, 3, 7]",
-        "2362": "[3, 5, 4, 0, 2, 6, 1, 7]",
-        "2363": "[4, 3, 0, 1, 6, 2, 5, 7]",
-        "2364": "[5, 6, 2, 0, 1, 4, 3, 7]",
-        "2365": "[6, 3, 0, 1, 4, 2, 5, 7]",
-        "2366": "[0, 3, 5, 4, 1, 6, 2, 7]",
-        "2367": "[1, 4, 6, 5, 2, 0, 3, 7]",
-        "2368": "[2, 5, 0, 6, 3, 1, 4, 7]",
-        "2369": "[3, 2, 4, 6, 1, 0, 5, 7]",
-        "2370": "[4, 6, 0, 2, 5, 1, 3, 7]",
-        "2371": "[5, 1, 2, 4, 3, 0, 6, 7]",
-        "2372": "[6, 4, 0, 2, 5, 1, 3, 7]",
-        "2373": "[0, 4, 3, 5, 1, 6, 2, 7]",
-        "2374": "[1, 5, 4, 6, 2, 0, 3, 7]",
-        "2375": "[2, 6, 5, 0, 3, 1, 4, 7]",
-        "2376": "[3, 6, 2, 4, 1, 0, 5, 7]",
-        "2377": "[4, 2, 6, 0, 5, 1, 3, 7]",
-        "2378": "[5, 4, 1, 2, 3, 0, 6, 7]",
-        "2379": "[6, 2, 4, 0, 5, 1, 3, 7]",
-        "2380": "[0, 5, 6, 2, 3, 4, 1, 7]",
-        "2381": "[1, 6, 0, 3, 4, 5, 2, 7]",
-        "2382": "[2, 0, 1, 4, 5, 6, 3, 7]",
-        "2383": "[3, 4, 0, 5, 2, 6, 1, 7]",
-        "2384": "[4, 0, 1, 3, 6, 2, 5, 7]",
-        "2385": "[5, 2, 0, 6, 1, 4, 3, 7]",
-        "2386": "[6, 0, 1, 3, 4, 2, 5, 7]",
-        "2387": "[0, 6, 3, 5, 1, 4, 2, 7]",
-        "2388": "[1, 0, 4, 6, 2, 5, 3, 7]",
-        "2389": "[2, 1, 5, 0, 3, 6, 4, 7]",
-        "2390": "[3, 0, 2, 4, 1, 6, 5, 7]",
-        "2391": "[4, 1, 6, 0, 5, 2, 3, 7]",
-        "2392": "[5, 0, 1, 2, 3, 4, 6, 7]",
-        "2393": "[6, 1, 4, 0, 5, 2, 3, 7]",
-        "2394": "[0, 1, 4, 2, 6, 3, 5, 7]",
-        "2395": "[1, 2, 5, 3, 0, 4, 6, 7]",
-        "2396": "[2, 3, 6, 4, 1, 5, 0, 7]",
-        "2397": "[3, 1, 6, 5, 0, 2, 4, 7]",
-        "2398": "[4, 5, 2, 3, 1, 6, 0, 7]",
-        "2399": "[5, 3, 4, 6, 0, 1, 2, 7]",
-        "2400": "[6, 5, 2, 3, 1, 4, 0, 7]",
-        "2401": "[0, 2, 1, 3, 6, 5, 4, 7]",
-        "2402": "[1, 3, 2, 4, 0, 6, 5, 7]",
-        "2403": "[2, 4, 3, 5, 1, 0, 6, 7]",
-        "2404": "[3, 5, 1, 2, 0, 4, 6, 7]",
-        "2405": "[4, 3, 5, 6, 1, 0, 2, 7]",
-        "2406": "[5, 6, 3, 1, 0, 2, 4, 7]",
-        "2407": "[6, 3, 5, 4, 1, 0, 2, 7]",
-        "2408": "[0, 3, 2, 1, 4, 5, 6, 7]",
-        "2409": "[1, 4, 3, 2, 5, 6, 0, 7]",
-        "2410": "[2, 5, 4, 3, 6, 0, 1, 7]",
-        "2411": "[3, 2, 5, 1, 6, 4, 0, 7]",
-        "2412": "[4, 6, 3, 5, 2, 0, 1, 7]",
-        "2413": "[5, 1, 6, 3, 4, 2, 0, 7]",
-        "2414": "[6, 4, 3, 5, 2, 0, 1, 7]",
-        "2415": "[0, 4, 2, 1, 5, 3, 6, 7]",
-        "2416": "[1, 5, 3, 2, 6, 4, 0, 7]",
-        "2417": "[2, 6, 4, 3, 0, 5, 1, 7]",
-        "2418": "[3, 6, 5, 1, 4, 2, 0, 7]",
-        "2419": "[4, 2, 3, 5, 0, 6, 1, 7]",
-        "2420": "[5, 4, 6, 3, 2, 1, 0, 7]",
-        "2421": "[6, 2, 3, 5, 0, 4, 1, 7]",
-        "2422": "[0, 5, 1, 3, 2, 6, 4, 7]",
-        "2423": "[1, 6, 2, 4, 3, 0, 5, 7]",
-        "2424": "[2, 0, 3, 5, 4, 1, 6, 7]",
-        "2425": "[3, 4, 1, 2, 5, 0, 6, 7]",
-        "2426": "[4, 0, 5, 6, 3, 1, 2, 7]",
-        "2427": "[5, 2, 3, 1, 6, 0, 4, 7]",
-        "2428": "[6, 0, 5, 4, 3, 1, 2, 7]",
-        "2429": "[0, 6, 2, 1, 5, 3, 4, 7]",
-        "2430": "[1, 0, 3, 2, 6, 4, 5, 7]",
-        "2431": "[2, 1, 4, 3, 0, 5, 6, 7]",
-        "2432": "[3, 0, 5, 1, 4, 2, 6, 7]",
-        "2433": "[4, 1, 3, 5, 0, 6, 2, 7]",
-        "2434": "[5, 0, 6, 3, 2, 1, 4, 7]",
-        "2435": "[6, 1, 3, 5, 0, 4, 2, 7]",
-        "2436": "[0, 1, 5, 2, 4, 3, 6, 7]",
-        "2437": "[1, 2, 6, 3, 5, 4, 0, 7]",
-        "2438": "[2, 3, 0, 4, 6, 5, 1, 7]",
-        "2439": "[3, 1, 4, 5, 6, 2, 0, 7]",
-        "2440": "[4, 5, 0, 3, 2, 6, 1, 7]",
-        "2441": "[5, 3, 2, 6, 4, 1, 0, 7]",
-        "2442": "[6, 5, 0, 3, 2, 4, 1, 7]",
-        "2443": "[0, 2, 4, 3, 1, 5, 6, 7]",
-        "2444": "[1, 3, 5, 4, 2, 6, 0, 7]",
-        "2445": "[2, 4, 6, 5, 3, 0, 1, 7]",
-        "2446": "[3, 5, 6, 2, 1, 4, 0, 7]",
-        "2447": "[4, 3, 2, 6, 5, 0, 1, 7]",
-        "2448": "[5, 6, 4, 1, 3, 2, 0, 7]",
-        "2449": "[6, 3, 2, 4, 5, 0, 1, 7]",
-        "2450": "[0, 3, 6, 1, 2, 5, 4, 7]",
-        "2451": "[1, 4, 0, 2, 3, 6, 5, 7]",
-        "2452": "[2, 5, 1, 3, 4, 0, 6, 7]",
-        "2453": "[3, 2, 0, 1, 5, 4, 6, 7]",
-        "2454": "[4, 6, 1, 5, 3, 0, 2, 7]",
-        "2455": "[5, 1, 0, 3, 6, 2, 4, 7]",
-        "2456": "[6, 4, 1, 5, 3, 0, 2, 7]",
-        "2457": "[0, 4, 6, 1, 2, 3, 5, 7]",
-        "2458": "[1, 5, 0, 2, 3, 4, 6, 7]",
-        "2459": "[2, 6, 1, 3, 4, 5, 0, 7]",
-        "2460": "[3, 6, 0, 1, 5, 2, 4, 7]",
-        "2461": "[4, 2, 1, 5, 3, 6, 0, 7]",
-        "2462": "[5, 4, 0, 3, 6, 1, 2, 7]",
-        "2463": "[6, 2, 1, 5, 3, 4, 0, 7]",
-        "2464": "[0, 5, 4, 3, 1, 6, 2, 7]",
-        "2465": "[1, 6, 5, 4, 2, 0, 3, 7]",
-        "2466": "[2, 0, 6, 5, 3, 1, 4, 7]",
-        "2467": "[3, 4, 6, 2, 1, 0, 5, 7]",
-        "2468": "[4, 0, 2, 6, 5, 1, 3, 7]",
-        "2469": "[5, 2, 4, 1, 3, 0, 6, 7]",
-        "2470": "[6, 0, 2, 4, 5, 1, 3, 7]",
-        "2471": "[0, 6, 4, 1, 2, 3, 5, 7]",
-        "2472": "[1, 0, 5, 2, 3, 4, 6, 7]",
-        "2473": "[2, 1, 6, 3, 4, 5, 0, 7]",
-        "2474": "[3, 0, 6, 1, 5, 2, 4, 7]",
-        "2475": "[4, 1, 2, 5, 3, 6, 0, 7]",
-        "2476": "[5, 0, 4, 3, 6, 1, 2, 7]",
-        "2477": "[6, 1, 2, 5, 3, 4, 0, 7]",
-        "2478": "[0, 1, 6, 2, 4, 3, 5, 7]",
-        "2479": "[1, 2, 0, 3, 5, 4, 6, 7]",
-        "2480": "[2, 3, 1, 4, 6, 5, 0, 7]",
-        "2481": "[3, 1, 0, 5, 6, 2, 4, 7]",
-        "2482": "[4, 5, 1, 3, 2, 6, 0, 7]",
-        "2483": "[5, 3, 0, 6, 4, 1, 2, 7]",
-        "2484": "[6, 5, 1, 3, 2, 4, 0, 7]",
-        "2485": "[0, 2, 6, 3, 1, 5, 4, 7]",
-        "2486": "[1, 3, 0, 4, 2, 6, 5, 7]",
-        "2487": "[2, 4, 1, 5, 3, 0, 6, 7]",
-        "2488": "[3, 5, 0, 2, 1, 4, 6, 7]",
-        "2489": "[4, 3, 1, 6, 5, 0, 2, 7]",
-        "2490": "[5, 6, 0, 1, 3, 2, 4, 7]",
-        "2491": "[6, 3, 1, 4, 5, 0, 2, 7]",
-        "2492": "[0, 3, 4, 1, 2, 5, 6, 7]",
-        "2493": "[1, 4, 5, 2, 3, 6, 0, 7]",
-        "2494": "[2, 5, 6, 3, 4, 0, 1, 7]",
-        "2495": "[3, 2, 6, 1, 5, 4, 0, 7]",
-        "2496": "[4, 6, 2, 5, 3, 0, 1, 7]",
-        "2497": "[5, 1, 4, 3, 6, 2, 0, 7]",
-        "2498": "[6, 4, 2, 5, 3, 0, 1, 7]",
-        "2499": "[0, 4, 5, 1, 2, 3, 6, 7]",
-        "2500": "[1, 5, 6, 2, 3, 4, 0, 7]",
-        "2501": "[2, 6, 0, 3, 4, 5, 1, 7]",
-        "2502": "[3, 6, 4, 1, 5, 2, 0, 7]",
-        "2503": "[4, 2, 0, 5, 3, 6, 1, 7]",
-        "2504": "[5, 4, 2, 3, 6, 1, 0, 7]",
-        "2505": "[6, 2, 0, 5, 3, 4, 1, 7]",
-        "2506": "[0, 5, 2, 3, 1, 6, 4, 7]",
-        "2507": "[1, 6, 3, 4, 2, 0, 5, 7]",
-        "2508": "[2, 0, 4, 5, 3, 1, 6, 7]",
-        "2509": "[3, 4, 5, 2, 1, 0, 6, 7]",
-        "2510": "[4, 0, 3, 6, 5, 1, 2, 7]",
-        "2511": "[5, 2, 6, 1, 3, 0, 4, 7]",
-        "2512": "[6, 0, 3, 4, 5, 1, 2, 7]",
-        "2513": "[0, 6, 5, 1, 2, 3, 4, 7]",
-        "2514": "[1, 0, 6, 2, 3, 4, 5, 7]",
-        "2515": "[2, 1, 0, 3, 4, 5, 6, 7]",
-        "2516": "[3, 0, 4, 1, 5, 2, 6, 7]",
-        "2517": "[4, 1, 0, 5, 3, 6, 2, 7]",
-        "2518": "[5, 0, 2, 3, 6, 1, 4, 7]",
-        "2519": "[6, 1, 0, 5, 3, 4, 2, 7]",
-        "2520": "[0, 1, 2, 3, 5, 4, 6, 7]",
-        "2521": "[1, 2, 3, 4, 6, 5, 0, 7]",
-        "2522": "[2, 3, 4, 5, 0, 6, 1, 7]",
-        "2523": "[3, 1, 5, 2, 4, 6, 0, 7]",
-        "2524": "[4, 5, 3, 6, 0, 2, 1, 7]",
-        "2525": "[5, 3, 6, 1, 2, 4, 0, 7]",
-        "2526": "[6, 5, 3, 4, 0, 2, 1, 7]",
-        "2527": "[0, 2, 3, 5, 4, 1, 6, 7]",
-        "2528": "[1, 3, 4, 6, 5, 2, 0, 7]",
-        "2529": "[2, 4, 5, 0, 6, 3, 1, 7]",
-        "2530": "[3, 5, 2, 4, 6, 1, 0, 7]",
-        "2531": "[4, 3, 6, 0, 2, 5, 1, 7]",
-        "2532": "[5, 6, 1, 2, 4, 3, 0, 7]",
-        "2533": "[6, 3, 4, 0, 2, 5, 1, 7]",
-        "2534": "[0, 3, 1, 5, 6, 2, 4, 7]",
-        "2535": "[1, 4, 2, 6, 0, 3, 5, 7]",
-        "2536": "[2, 5, 3, 0, 1, 4, 6, 7]",
-        "2537": "[3, 2, 1, 4, 0, 5, 6, 7]",
-        "2538": "[4, 6, 5, 0, 1, 3, 2, 7]",
-        "2539": "[5, 1, 3, 2, 0, 6, 4, 7]",
-        "2540": "[6, 4, 5, 0, 1, 3, 2, 7]",
-        "2541": "[0, 4, 1, 3, 6, 2, 5, 7]",
-        "2542": "[1, 5, 2, 4, 0, 3, 6, 7]",
-        "2543": "[2, 6, 3, 5, 1, 4, 0, 7]",
-        "2544": "[3, 6, 1, 2, 0, 5, 4, 7]",
-        "2545": "[4, 2, 5, 6, 1, 3, 0, 7]",
-        "2546": "[5, 4, 3, 1, 0, 6, 2, 7]",
-        "2547": "[6, 2, 5, 4, 1, 3, 0, 7]",
-        "2548": "[0, 5, 3, 6, 4, 1, 2, 7]",
-        "2549": "[1, 6, 4, 0, 5, 2, 3, 7]",
-        "2550": "[2, 0, 5, 1, 6, 3, 4, 7]",
-        "2551": "[3, 4, 2, 0, 6, 1, 5, 7]",
-        "2552": "[4, 0, 6, 1, 2, 5, 3, 7]",
-        "2553": "[5, 2, 1, 0, 4, 3, 6, 7]",
-        "2554": "[6, 0, 4, 1, 2, 5, 3, 7]",
-        "2555": "[0, 6, 1, 3, 4, 2, 5, 7]",
-        "2556": "[1, 0, 2, 4, 5, 3, 6, 7]",
-        "2557": "[2, 1, 3, 5, 6, 4, 0, 7]",
-        "2558": "[3, 0, 1, 2, 6, 5, 4, 7]",
-        "2559": "[4, 1, 5, 6, 2, 3, 0, 7]",
-        "2560": "[5, 0, 3, 1, 4, 6, 2, 7]",
-        "2561": "[6, 1, 5, 4, 2, 3, 0, 7]",
-        "2562": "[0, 1, 3, 4, 2, 5, 6, 7]",
-        "2563": "[1, 2, 4, 5, 3, 6, 0, 7]",
-        "2564": "[2, 3, 5, 6, 4, 0, 1, 7]",
-        "2565": "[3, 1, 2, 6, 5, 4, 0, 7]",
-        "2566": "[4, 5, 6, 2, 3, 0, 1, 7]",
-        "2567": "[5, 3, 1, 4, 6, 2, 0, 7]",
-        "2568": "[6, 5, 4, 2, 3, 0, 1, 7]",
-        "2569": "[0, 2, 5, 1, 3, 4, 6, 7]",
-        "2570": "[1, 3, 6, 2, 4, 5, 0, 7]",
-        "2571": "[2, 4, 0, 3, 5, 6, 1, 7]",
-        "2572": "[3, 5, 4, 1, 2, 6, 0, 7]",
-        "2573": "[4, 3, 0, 5, 6, 2, 1, 7]",
-        "2574": "[5, 6, 2, 3, 1, 4, 0, 7]",
-        "2575": "[6, 3, 0, 5, 4, 2, 1, 7]",
-        "2576": "[0, 3, 5, 2, 1, 6, 4, 7]",
-        "2577": "[1, 4, 6, 3, 2, 0, 5, 7]",
-        "2578": "[2, 5, 0, 4, 3, 1, 6, 7]",
-        "2579": "[3, 2, 4, 5, 1, 0, 6, 7]",
-        "2580": "[4, 6, 0, 3, 5, 1, 2, 7]",
-        "2581": "[5, 1, 2, 6, 3, 0, 4, 7]",
-        "2582": "[6, 4, 0, 3, 5, 1, 2, 7]",
-        "2583": "[0, 4, 3, 2, 1, 6, 5, 7]",
-        "2584": "[1, 5, 4, 3, 2, 0, 6, 7]",
-        "2585": "[2, 6, 5, 4, 3, 1, 0, 7]",
-        "2586": "[3, 6, 2, 5, 1, 0, 4, 7]",
-        "2587": "[4, 2, 6, 3, 5, 1, 0, 7]",
-        "2588": "[5, 4, 1, 6, 3, 0, 2, 7]",
-        "2589": "[6, 2, 4, 3, 5, 1, 0, 7]",
-        "2590": "[0, 5, 6, 1, 3, 4, 2, 7]",
-        "2591": "[1, 6, 0, 2, 4, 5, 3, 7]",
-        "2592": "[2, 0, 1, 3, 5, 6, 4, 7]",
-        "2593": "[3, 4, 0, 1, 2, 6, 5, 7]",
-        "2594": "[4, 0, 1, 5, 6, 2, 3, 7]",
-        "2595": "[5, 2, 0, 3, 1, 4, 6, 7]",
-        "2596": "[6, 0, 1, 5, 4, 2, 3, 7]",
-        "2597": "[0, 6, 3, 2, 1, 4, 5, 7]",
-        "2598": "[1, 0, 4, 3, 2, 5, 6, 7]",
-        "2599": "[2, 1, 5, 4, 3, 6, 0, 7]",
-        "2600": "[3, 0, 2, 5, 1, 6, 4, 7]",
-        "2601": "[4, 1, 6, 3, 5, 2, 0, 7]",
-        "2602": "[5, 0, 1, 6, 3, 4, 2, 7]",
-        "2603": "[6, 1, 4, 3, 5, 2, 0, 7]",
-        "2604": "[0, 1, 4, 5, 6, 3, 2, 7]",
-        "2605": "[1, 2, 5, 6, 0, 4, 3, 7]",
-        "2606": "[2, 3, 6, 0, 1, 5, 4, 7]",
-        "2607": "[3, 1, 6, 4, 0, 2, 5, 7]",
-        "2608": "[4, 5, 2, 0, 1, 6, 3, 7]",
-        "2609": "[5, 3, 4, 2, 0, 1, 6, 7]",
-        "2610": "[6, 5, 2, 0, 1, 4, 3, 7]",
-        "2611": "[0, 2, 1, 4, 6, 5, 3, 7]",
-        "2612": "[1, 3, 2, 5, 0, 6, 4, 7]",
-        "2613": "[2, 4, 3, 6, 1, 0, 5, 7]",
-        "2614": "[3, 5, 1, 6, 0, 4, 2, 7]",
-        "2615": "[4, 3, 5, 2, 1, 0, 6, 7]",
-        "2616": "[5, 6, 3, 4, 0, 2, 1, 7]",
-        "2617": "[6, 3, 5, 2, 1, 0, 4, 7]",
-        "2618": "[0, 3, 2, 6, 4, 5, 1, 7]",
-        "2619": "[1, 4, 3, 0, 5, 6, 2, 7]",
-        "2620": "[2, 5, 4, 1, 6, 0, 3, 7]",
-        "2621": "[3, 2, 5, 0, 6, 4, 1, 7]",
-        "2622": "[4, 6, 3, 1, 2, 0, 5, 7]",
-        "2623": "[5, 1, 6, 0, 4, 2, 3, 7]",
-        "2624": "[6, 4, 3, 1, 2, 0, 5, 7]",
-        "2625": "[0, 4, 2, 6, 5, 3, 1, 7]",
-        "2626": "[1, 5, 3, 0, 6, 4, 2, 7]",
-        "2627": "[2, 6, 4, 1, 0, 5, 3, 7]",
-        "2628": "[3, 6, 5, 0, 4, 2, 1, 7]",
-        "2629": "[4, 2, 3, 1, 0, 6, 5, 7]",
-        "2630": "[5, 4, 6, 0, 2, 1, 3, 7]",
-        "2631": "[6, 2, 3, 1, 0, 4, 5, 7]",
-        "2632": "[0, 5, 1, 4, 2, 6, 3, 7]",
-        "2633": "[1, 6, 2, 5, 3, 0, 4, 7]",
-        "2634": "[2, 0, 3, 6, 4, 1, 5, 7]",
-        "2635": "[3, 4, 1, 6, 5, 0, 2, 7]",
-        "2636": "[4, 0, 5, 2, 3, 1, 6, 7]",
-        "2637": "[5, 2, 3, 4, 6, 0, 1, 7]",
-        "2638": "[6, 0, 5, 2, 3, 1, 4, 7]",
-        "2639": "[0, 6, 2, 4, 5, 3, 1, 7]",
-        "2640": "[1, 0, 3, 5, 6, 4, 2, 7]",
-        "2641": "[2, 1, 4, 6, 0, 5, 3, 7]",
-        "2642": "[3, 0, 5, 6, 4, 2, 1, 7]",
-        "2643": "[4, 1, 3, 2, 0, 6, 5, 7]",
-        "2644": "[5, 0, 6, 4, 2, 1, 3, 7]",
-        "2645": "[6, 1, 3, 2, 0, 4, 5, 7]",
-        "2646": "[0, 1, 5, 6, 4, 3, 2, 7]",
-        "2647": "[1, 2, 6, 0, 5, 4, 3, 7]",
-        "2648": "[2, 3, 0, 1, 6, 5, 4, 7]",
-        "2649": "[3, 1, 4, 0, 6, 2, 5, 7]",
-        "2650": "[4, 5, 0, 1, 2, 6, 3, 7]",
-        "2651": "[5, 3, 2, 0, 4, 1, 6, 7]",
-        "2652": "[6, 5, 0, 1, 2, 4, 3, 7]",
-        "2653": "[0, 2, 4, 6, 1, 5, 3, 7]",
-        "2654": "[1, 3, 5, 0, 2, 6, 4, 7]",
-        "2655": "[2, 4, 6, 1, 3, 0, 5, 7]",
-        "2656": "[3, 5, 6, 0, 1, 4, 2, 7]",
-        "2657": "[4, 3, 2, 1, 5, 0, 6, 7]",
-        "2658": "[5, 6, 4, 0, 3, 2, 1, 7]",
-        "2659": "[6, 3, 2, 1, 5, 0, 4, 7]",
-        "2660": "[0, 3, 6, 4, 2, 5, 1, 7]",
-        "2661": "[1, 4, 0, 5, 3, 6, 2, 7]",
-        "2662": "[2, 5, 1, 6, 4, 0, 3, 7]",
-        "2663": "[3, 2, 0, 6, 5, 4, 1, 7]",
-        "2664": "[4, 6, 1, 2, 3, 0, 5, 7]",
-        "2665": "[5, 1, 0, 4, 6, 2, 3, 7]",
-        "2666": "[6, 4, 1, 2, 3, 0, 5, 7]",
-        "2667": "[0, 4, 6, 5, 2, 3, 1, 7]",
-        "2668": "[1, 5, 0, 6, 3, 4, 2, 7]",
-        "2669": "[2, 6, 1, 0, 4, 5, 3, 7]",
-        "2670": "[3, 6, 0, 4, 5, 2, 1, 7]",
-        "2671": "[4, 2, 1, 0, 3, 6, 5, 7]",
-        "2672": "[5, 4, 0, 2, 6, 1, 3, 7]",
-        "2673": "[6, 2, 1, 0, 3, 4, 5, 7]",
-        "2674": "[0, 5, 4, 2, 1, 6, 3, 7]",
-        "2675": "[1, 6, 5, 3, 2, 0, 4, 7]",
-        "2676": "[2, 0, 6, 4, 3, 1, 5, 7]",
-        "2677": "[3, 4, 6, 5, 1, 0, 2, 7]",
-        "2678": "[4, 0, 2, 3, 5, 1, 6, 7]",
-        "2679": "[5, 2, 4, 6, 3, 0, 1, 7]",
-        "2680": "[6, 0, 2, 3, 5, 1, 4, 7]",
-        "2681": "[0, 6, 4, 5, 2, 3, 1, 7]",
-        "2682": "[1, 0, 5, 6, 3, 4, 2, 7]",
-        "2683": "[2, 1, 6, 0, 4, 5, 3, 7]",
-        "2684": "[3, 0, 6, 4, 5, 2, 1, 7]",
-        "2685": "[4, 1, 2, 0, 3, 6, 5, 7]",
-        "2686": "[5, 0, 4, 2, 6, 1, 3, 7]",
-        "2687": "[6, 1, 2, 0, 3, 4, 5, 7]",
-        "2688": "[0, 1, 6, 5, 4, 3, 2, 7]",
-        "2689": "[1, 2, 0, 6, 5, 4, 3, 7]",
-        "2690": "[2, 3, 1, 0, 6, 5, 4, 7]",
-        "2691": "[3, 1, 0, 4, 6, 2, 5, 7]",
-        "2692": "[4, 5, 1, 0, 2, 6, 3, 7]",
-        "2693": "[5, 3, 0, 2, 4, 1, 6, 7]",
-        "2694": "[6, 5, 1, 0, 2, 4, 3, 7]",
-        "2695": "[0, 2, 6, 4, 1, 5, 3, 7]",
-        "2696": "[1, 3, 0, 5, 2, 6, 4, 7]",
-        "2697": "[2, 4, 1, 6, 3, 0, 5, 7]",
-        "2698": "[3, 5, 0, 6, 1, 4, 2, 7]",
-        "2699": "[4, 3, 1, 2, 5, 0, 6, 7]",
-        "2700": "[5, 6, 0, 4, 3, 2, 1, 7]",
-        "2701": "[6, 3, 1, 2, 5, 0, 4, 7]",
-        "2702": "[0, 3, 4, 6, 2, 5, 1, 7]",
-        "2703": "[1, 4, 5, 0, 3, 6, 2, 7]",
-        "2704": "[2, 5, 6, 1, 4, 0, 3, 7]",
-        "2705": "[3, 2, 6, 0, 5, 4, 1, 7]",
-        "2706": "[4, 6, 2, 1, 3, 0, 5, 7]",
-        "2707": "[5, 1, 4, 0, 6, 2, 3, 7]",
-        "2708": "[6, 4, 2, 1, 3, 0, 5, 7]",
-        "2709": "[0, 4, 5, 6, 2, 3, 1, 7]",
-        "2710": "[1, 5, 6, 0, 3, 4, 2, 7]",
-        "2711": "[2, 6, 0, 1, 4, 5, 3, 7]",
-        "2712": "[3, 6, 4, 0, 5, 2, 1, 7]",
-        "2713": "[4, 2, 0, 1, 3, 6, 5, 7]",
-        "2714": "[5, 4, 2, 0, 6, 1, 3, 7]",
-        "2715": "[6, 2, 0, 1, 3, 4, 5, 7]",
-        "2716": "[0, 5, 2, 4, 1, 6, 3, 7]",
-        "2717": "[1, 6, 3, 5, 2, 0, 4, 7]",
-        "2718": "[2, 0, 4, 6, 3, 1, 5, 7]",
-        "2719": "[3, 4, 5, 6, 1, 0, 2, 7]",
-        "2720": "[4, 0, 3, 2, 5, 1, 6, 7]",
-        "2721": "[5, 2, 6, 4, 3, 0, 1, 7]",
-        "2722": "[6, 0, 3, 2, 5, 1, 4, 7]",
-        "2723": "[0, 6, 5, 4, 2, 3, 1, 7]",
-        "2724": "[1, 0, 6, 5, 3, 4, 2, 7]",
-        "2725": "[2, 1, 0, 6, 4, 5, 3, 7]",
-        "2726": "[3, 0, 4, 6, 5, 2, 1, 7]",
-        "2727": "[4, 1, 0, 2, 3, 6, 5, 7]",
-        "2728": "[5, 0, 2, 4, 6, 1, 3, 7]",
-        "2729": "[6, 1, 0, 2, 3, 4, 5, 7]",
-        "2730": "[0, 1, 2, 4, 3, 5, 6, 7]",
-        "2731": "[1, 2, 3, 5, 4, 6, 0, 7]",
-        "2732": "[2, 3, 4, 6, 5, 0, 1, 7]",
-        "2733": "[3, 1, 5, 6, 2, 4, 0, 7]",
-        "2734": "[4, 5, 3, 2, 6, 0, 1, 7]",
-        "2735": "[5, 3, 6, 4, 1, 2, 0, 7]",
-        "2736": "[6, 5, 3, 2, 4, 0, 1, 7]",
-        "2737": "[0, 2, 3, 1, 5, 4, 6, 7]",
-        "2738": "[1, 3, 4, 2, 6, 5, 0, 7]",
-        "2739": "[2, 4, 5, 3, 0, 6, 1, 7]",
-        "2740": "[3, 5, 2, 1, 4, 6, 0, 7]",
-        "2741": "[4, 3, 6, 5, 0, 2, 1, 7]",
-        "2742": "[5, 6, 1, 3, 2, 4, 0, 7]",
-        "2743": "[6, 3, 4, 5, 0, 2, 1, 7]",
-        "2744": "[0, 3, 1, 2, 5, 6, 4, 7]",
-        "2745": "[1, 4, 2, 3, 6, 0, 5, 7]",
-        "2746": "[2, 5, 3, 4, 0, 1, 6, 7]",
-        "2747": "[3, 2, 1, 5, 4, 0, 6, 7]",
-        "2748": "[4, 6, 5, 3, 0, 1, 2, 7]",
-        "2749": "[5, 1, 3, 6, 2, 0, 4, 7]",
-        "2750": "[6, 4, 5, 3, 0, 1, 2, 7]",
-        "2751": "[0, 4, 1, 2, 3, 6, 5, 7]",
-        "2752": "[1, 5, 2, 3, 4, 0, 6, 7]",
-        "2753": "[2, 6, 3, 4, 5, 1, 0, 7]",
-        "2754": "[3, 6, 1, 5, 2, 0, 4, 7]",
-        "2755": "[4, 2, 5, 3, 6, 1, 0, 7]",
-        "2756": "[5, 4, 3, 6, 1, 0, 2, 7]",
-        "2757": "[6, 2, 5, 3, 4, 1, 0, 7]",
-        "2758": "[0, 5, 3, 1, 6, 4, 2, 7]",
-        "2759": "[1, 6, 4, 2, 0, 5, 3, 7]",
-        "2760": "[2, 0, 5, 3, 1, 6, 4, 7]",
-        "2761": "[3, 4, 2, 1, 0, 6, 5, 7]",
-        "2762": "[4, 0, 6, 5, 1, 2, 3, 7]",
-        "2763": "[5, 2, 1, 3, 0, 4, 6, 7]",
-        "2764": "[6, 0, 4, 5, 1, 2, 3, 7]",
-        "2765": "[0, 6, 1, 2, 3, 4, 5, 7]",
-        "2766": "[1, 0, 2, 3, 4, 5, 6, 7]",
-        "2767": "[2, 1, 3, 4, 5, 6, 0, 7]",
-        "2768": "[3, 0, 1, 5, 2, 6, 4, 7]",
-        "2769": "[4, 1, 5, 3, 6, 2, 0, 7]",
-        "2770": "[5, 0, 3, 6, 1, 4, 2, 7]",
-        "2771": "[6, 1, 5, 3, 4, 2, 0, 7]",
-        "2772": "[0, 1, 3, 5, 4, 2, 6, 7]",
-        "2773": "[1, 2, 4, 6, 5, 3, 0, 7]",
-        "2774": "[2, 3, 5, 0, 6, 4, 1, 7]",
-        "2775": "[3, 1, 2, 4, 6, 5, 0, 7]",
-        "2776": "[4, 5, 6, 0, 2, 3, 1, 7]",
-        "2777": "[5, 3, 1, 2, 4, 6, 0, 7]",
-        "2778": "[6, 5, 4, 0, 2, 3, 1, 7]",
-        "2779": "[0, 2, 5, 4, 1, 3, 6, 7]",
-        "2780": "[1, 3, 6, 5, 2, 4, 0, 7]",
-        "2781": "[2, 4, 0, 6, 3, 5, 1, 7]",
-        "2782": "[3, 5, 4, 6, 1, 2, 0, 7]",
-        "2783": "[4, 3, 0, 2, 5, 6, 1, 7]",
-        "2784": "[5, 6, 2, 4, 3, 1, 0, 7]",
-        "2785": "[6, 3, 0, 2, 5, 4, 1, 7]",
-        "2786": "[0, 3, 5, 6, 2, 1, 4, 7]",
-        "2787": "[1, 4, 6, 0, 3, 2, 5, 7]",
-        "2788": "[2, 5, 0, 1, 4, 3, 6, 7]",
-        "2789": "[3, 2, 4, 0, 5, 1, 6, 7]",
-        "2790": "[4, 6, 0, 1, 3, 5, 2, 7]",
-        "2791": "[5, 1, 2, 0, 6, 3, 4, 7]",
-        "2792": "[6, 4, 0, 1, 3, 5, 2, 7]",
-        "2793": "[0, 4, 3, 6, 2, 1, 5, 7]",
-        "2794": "[1, 5, 4, 0, 3, 2, 6, 7]",
-        "2795": "[2, 6, 5, 1, 4, 3, 0, 7]",
-        "2796": "[3, 6, 2, 0, 5, 1, 4, 7]",
-        "2797": "[4, 2, 6, 1, 3, 5, 0, 7]",
-        "2798": "[5, 4, 1, 0, 6, 3, 2, 7]",
-        "2799": "[6, 2, 4, 1, 3, 5, 0, 7]",
-        "2800": "[0, 5, 6, 4, 1, 3, 2, 7]",
-        "2801": "[1, 6, 0, 5, 2, 4, 3, 7]",
-        "2802": "[2, 0, 1, 6, 3, 5, 4, 7]",
-        "2803": "[3, 4, 0, 6, 1, 2, 5, 7]",
-        "2804": "[4, 0, 1, 2, 5, 6, 3, 7]",
-        "2805": "[5, 2, 0, 4, 3, 1, 6, 7]",
-        "2806": "[6, 0, 1, 2, 5, 4, 3, 7]",
-        "2807": "[0, 6, 3, 4, 2, 1, 5, 7]",
-        "2808": "[1, 0, 4, 5, 3, 2, 6, 7]",
-        "2809": "[2, 1, 5, 6, 4, 3, 0, 7]",
-        "2810": "[3, 0, 2, 6, 5, 1, 4, 7]",
-        "2811": "[4, 1, 6, 2, 3, 5, 0, 7]",
-        "2812": "[5, 0, 1, 4, 6, 3, 2, 7]",
-        "2813": "[6, 1, 4, 2, 3, 5, 0, 7]",
-        "2814": "[0, 1, 4, 3, 5, 6, 2, 7]",
-        "2815": "[1, 2, 5, 4, 6, 0, 3, 7]",
-        "2816": "[2, 3, 6, 5, 0, 1, 4, 7]",
-        "2817": "[3, 1, 6, 2, 4, 0, 5, 7]",
-        "2818": "[4, 5, 2, 6, 0, 1, 3, 7]",
-        "2819": "[5, 3, 4, 1, 2, 0, 6, 7]",
-        "2820": "[6, 5, 2, 4, 0, 1, 3, 7]",
-        "2821": "[0, 2, 1, 5, 4, 6, 3, 7]",
-        "2822": "[1, 3, 2, 6, 5, 0, 4, 7]",
-        "2823": "[2, 4, 3, 0, 6, 1, 5, 7]",
-        "2824": "[3, 5, 1, 4, 6, 0, 2, 7]",
-        "2825": "[4, 3, 5, 0, 2, 1, 6, 7]",
-        "2826": "[5, 6, 3, 2, 4, 0, 1, 7]",
-        "2827": "[6, 3, 5, 0, 2, 1, 4, 7]",
-        "2828": "[0, 3, 2, 5, 6, 4, 1, 7]",
-        "2829": "[1, 4, 3, 6, 0, 5, 2, 7]",
-        "2830": "[2, 5, 4, 0, 1, 6, 3, 7]",
-        "2831": "[3, 2, 5, 4, 0, 6, 1, 7]",
-        "2832": "[4, 6, 3, 0, 1, 2, 5, 7]",
-        "2833": "[5, 1, 6, 2, 0, 4, 3, 7]",
-        "2834": "[6, 4, 3, 0, 1, 2, 5, 7]",
-        "2835": "[0, 4, 2, 3, 6, 5, 1, 7]",
-        "2836": "[1, 5, 3, 4, 0, 6, 2, 7]",
-        "2837": "[2, 6, 4, 5, 1, 0, 3, 7]",
-        "2838": "[3, 6, 5, 2, 0, 4, 1, 7]",
-        "2839": "[4, 2, 3, 6, 1, 0, 5, 7]",
-        "2840": "[5, 4, 6, 1, 0, 2, 3, 7]",
-        "2841": "[6, 2, 3, 4, 1, 0, 5, 7]",
-        "2842": "[0, 5, 1, 6, 4, 2, 3, 7]",
-        "2843": "[1, 6, 2, 0, 5, 3, 4, 7]",
-        "2844": "[2, 0, 3, 1, 6, 4, 5, 7]",
-        "2845": "[3, 4, 1, 0, 6, 5, 2, 7]",
-        "2846": "[4, 0, 5, 1, 2, 3, 6, 7]",
-        "2847": "[5, 2, 3, 0, 4, 6, 1, 7]",
-        "2848": "[6, 0, 5, 1, 2, 3, 4, 7]",
-        "2849": "[0, 6, 2, 3, 4, 5, 1, 7]",
-        "2850": "[1, 0, 3, 4, 5, 6, 2, 7]",
-        "2851": "[2, 1, 4, 5, 6, 0, 3, 7]",
-        "2852": "[3, 0, 5, 2, 6, 4, 1, 7]",
-        "2853": "[4, 1, 3, 6, 2, 0, 5, 7]",
-        "2854": "[5, 0, 6, 1, 4, 2, 3, 7]",
-        "2855": "[6, 1, 3, 4, 2, 0, 5, 7]",
-        "2856": "[0, 1, 5, 3, 6, 4, 2, 7]",
-        "2857": "[1, 2, 6, 4, 0, 5, 3, 7]",
-        "2858": "[2, 3, 0, 5, 1, 6, 4, 7]",
-        "2859": "[3, 1, 4, 2, 0, 6, 5, 7]",
-        "2860": "[4, 5, 0, 6, 1, 2, 3, 7]",
-        "2861": "[5, 3, 2, 1, 0, 4, 6, 7]",
-        "2862": "[6, 5, 0, 4, 1, 2, 3, 7]",
-        "2863": "[0, 2, 4, 5, 6, 1, 3, 7]",
-        "2864": "[1, 3, 5, 6, 0, 2, 4, 7]",
-        "2865": "[2, 4, 6, 0, 1, 3, 5, 7]",
-        "2866": "[3, 5, 6, 4, 0, 1, 2, 7]",
-        "2867": "[4, 3, 2, 0, 1, 5, 6, 7]",
-        "2868": "[5, 6, 4, 2, 0, 3, 1, 7]",
-        "2869": "[6, 3, 2, 0, 1, 5, 4, 7]",
-        "2870": "[0, 3, 6, 5, 4, 2, 1, 7]",
-        "2871": "[1, 4, 0, 6, 5, 3, 2, 7]",
-        "2872": "[2, 5, 1, 0, 6, 4, 3, 7]",
-        "2873": "[3, 2, 0, 4, 6, 5, 1, 7]",
-        "2874": "[4, 6, 1, 0, 2, 3, 5, 7]",
-        "2875": "[5, 1, 0, 2, 4, 6, 3, 7]",
-        "2876": "[6, 4, 1, 0, 2, 3, 5, 7]",
-        "2877": "[0, 4, 6, 3, 5, 2, 1, 7]",
-        "2878": "[1, 5, 0, 4, 6, 3, 2, 7]",
-        "2879": "[2, 6, 1, 5, 0, 4, 3, 7]",
-        "2880": "[3, 6, 0, 2, 4, 5, 1, 7]",
-        "2881": "[4, 2, 1, 6, 0, 3, 5, 7]",
-        "2882": "[5, 4, 0, 1, 2, 6, 3, 7]",
-        "2883": "[6, 2, 1, 4, 0, 3, 5, 7]",
-        "2884": "[0, 5, 4, 6, 2, 1, 3, 7]",
-        "2885": "[1, 6, 5, 0, 3, 2, 4, 7]",
-        "2886": "[2, 0, 6, 1, 4, 3, 5, 7]",
-        "2887": "[3, 4, 6, 0, 5, 1, 2, 7]",
-        "2888": "[4, 0, 2, 1, 3, 5, 6, 7]",
-        "2889": "[5, 2, 4, 0, 6, 3, 1, 7]",
-        "2890": "[6, 0, 2, 1, 3, 5, 4, 7]",
-        "2891": "[0, 6, 4, 3, 5, 2, 1, 7]",
-        "2892": "[1, 0, 5, 4, 6, 3, 2, 7]",
-        "2893": "[2, 1, 6, 5, 0, 4, 3, 7]",
-        "2894": "[3, 0, 6, 2, 4, 5, 1, 7]",
-        "2895": "[4, 1, 2, 6, 0, 3, 5, 7]",
-        "2896": "[5, 0, 4, 1, 2, 6, 3, 7]",
-        "2897": "[6, 1, 2, 4, 0, 3, 5, 7]",
-        "2898": "[0, 1, 6, 3, 5, 4, 2, 7]",
-        "2899": "[1, 2, 0, 4, 6, 5, 3, 7]",
-        "2900": "[2, 3, 1, 5, 0, 6, 4, 7]",
-        "2901": "[3, 1, 0, 2, 4, 6, 5, 7]",
-        "2902": "[4, 5, 1, 6, 0, 2, 3, 7]",
-        "2903": "[5, 3, 0, 1, 2, 4, 6, 7]",
-        "2904": "[6, 5, 1, 4, 0, 2, 3, 7]",
-        "2905": "[0, 2, 6, 5, 4, 1, 3, 7]",
-        "2906": "[1, 3, 0, 6, 5, 2, 4, 7]",
-        "2907": "[2, 4, 1, 0, 6, 3, 5, 7]",
-        "2908": "[3, 5, 0, 4, 6, 1, 2, 7]",
-        "2909": "[4, 3, 1, 0, 2, 5, 6, 7]",
-        "2910": "[5, 6, 0, 2, 4, 3, 1, 7]",
-        "2911": "[6, 3, 1, 0, 2, 5, 4, 7]",
-        "2912": "[0, 3, 4, 5, 6, 2, 1, 7]",
-        "2913": "[1, 4, 5, 6, 0, 3, 2, 7]",
-        "2914": "[2, 5, 6, 0, 1, 4, 3, 7]",
-        "2915": "[3, 2, 6, 4, 0, 5, 1, 7]",
-        "2916": "[4, 6, 2, 0, 1, 3, 5, 7]",
-        "2917": "[5, 1, 4, 2, 0, 6, 3, 7]",
-        "2918": "[6, 4, 2, 0, 1, 3, 5, 7]",
-        "2919": "[0, 4, 5, 3, 6, 2, 1, 7]",
-        "2920": "[1, 5, 6, 4, 0, 3, 2, 7]",
-        "2921": "[2, 6, 0, 5, 1, 4, 3, 7]",
-        "2922": "[3, 6, 4, 2, 0, 5, 1, 7]",
-        "2923": "[4, 2, 0, 6, 1, 3, 5, 7]",
-        "2924": "[5, 4, 2, 1, 0, 6, 3, 7]",
-        "2925": "[6, 2, 0, 4, 1, 3, 5, 7]",
-        "2926": "[0, 5, 2, 6, 4, 1, 3, 7]",
-        "2927": "[1, 6, 3, 0, 5, 2, 4, 7]",
-        "2928": "[2, 0, 4, 1, 6, 3, 5, 7]",
-        "2929": "[3, 4, 5, 0, 6, 1, 2, 7]",
-        "2930": "[4, 0, 3, 1, 2, 5, 6, 7]",
-        "2931": "[5, 2, 6, 0, 4, 3, 1, 7]",
-        "2932": "[6, 0, 3, 1, 2, 5, 4, 7]",
-        "2933": "[0, 6, 5, 3, 4, 2, 1, 7]",
-        "2934": "[1, 0, 6, 4, 5, 3, 2, 7]",
-        "2935": "[2, 1, 0, 5, 6, 4, 3, 7]",
-        "2936": "[3, 0, 4, 2, 6, 5, 1, 7]",
-        "2937": "[4, 1, 0, 6, 2, 3, 5, 7]",
-        "2938": "[5, 0, 2, 1, 4, 6, 3, 7]",
-        "2939": "[6, 1, 0, 4, 2, 3, 5, 7]",
-        "2940": "[0, 1, 2, 5, 4, 3, 6, 7]",
-        "2941": "[1, 2, 3, 6, 5, 4, 0, 7]",
-        "2942": "[2, 3, 4, 0, 6, 5, 1, 7]",
-        "2943": "[3, 1, 5, 4, 6, 2, 0, 7]",
-        "2944": "[4, 5, 3, 0, 2, 6, 1, 7]",
-        "2945": "[5, 3, 6, 2, 4, 1, 0, 7]",
-        "2946": "[6, 5, 3, 0, 2, 4, 1, 7]",
-        "2947": "[0, 2, 3, 4, 1, 5, 6, 7]",
-        "2948": "[1, 3, 4, 5, 2, 6, 0, 7]",
-        "2949": "[2, 4, 5, 6, 3, 0, 1, 7]",
-        "2950": "[3, 5, 2, 6, 1, 4, 0, 7]",
-        "2951": "[4, 3, 6, 2, 5, 0, 1, 7]",
-        "2952": "[5, 6, 1, 4, 3, 2, 0, 7]",
-        "2953": "[6, 3, 4, 2, 5, 0, 1, 7]",
-        "2954": "[0, 3, 1, 6, 2, 5, 4, 7]",
-        "2955": "[1, 4, 2, 0, 3, 6, 5, 7]",
-        "2956": "[2, 5, 3, 1, 4, 0, 6, 7]",
-        "2957": "[3, 2, 1, 0, 5, 4, 6, 7]",
-        "2958": "[4, 6, 5, 1, 3, 0, 2, 7]",
-        "2959": "[5, 1, 3, 0, 6, 2, 4, 7]",
-        "2960": "[6, 4, 5, 1, 3, 0, 2, 7]",
-        "2961": "[0, 4, 1, 6, 2, 3, 5, 7]",
-        "2962": "[1, 5, 2, 0, 3, 4, 6, 7]",
-        "2963": "[2, 6, 3, 1, 4, 5, 0, 7]",
-        "2964": "[3, 6, 1, 0, 5, 2, 4, 7]",
-        "2965": "[4, 2, 5, 1, 3, 6, 0, 7]",
-        "2966": "[5, 4, 3, 0, 6, 1, 2, 7]",
-        "2967": "[6, 2, 5, 1, 3, 4, 0, 7]",
-        "2968": "[0, 5, 3, 4, 1, 6, 2, 7]",
-        "2969": "[1, 6, 4, 5, 2, 0, 3, 7]",
-        "2970": "[2, 0, 5, 6, 3, 1, 4, 7]",
-        "2971": "[3, 4, 2, 6, 1, 0, 5, 7]",
-        "2972": "[4, 0, 6, 2, 5, 1, 3, 7]",
-        "2973": "[5, 2, 1, 4, 3, 0, 6, 7]",
-        "2974": "[6, 0, 4, 2, 5, 1, 3, 7]",
-        "2975": "[0, 6, 1, 4, 2, 3, 5, 7]",
-        "2976": "[1, 0, 2, 5, 3, 4, 6, 7]",
-        "2977": "[2, 1, 3, 6, 4, 5, 0, 7]",
-        "2978": "[3, 0, 1, 6, 5, 2, 4, 7]",
-        "2979": "[4, 1, 5, 2, 3, 6, 0, 7]",
-        "2980": "[5, 0, 3, 4, 6, 1, 2, 7]",
-        "2981": "[6, 1, 5, 2, 3, 4, 0, 7]",
-        "2982": "[0, 1, 3, 2, 5, 4, 6, 7]",
-        "2983": "[1, 2, 4, 3, 6, 5, 0, 7]",
-        "2984": "[2, 3, 5, 4, 0, 6, 1, 7]",
-        "2985": "[3, 1, 2, 5, 4, 6, 0, 7]",
-        "2986": "[4, 5, 6, 3, 0, 2, 1, 7]",
-        "2987": "[5, 3, 1, 6, 2, 4, 0, 7]",
-        "2988": "[6, 5, 4, 3, 0, 2, 1, 7]",
-        "2989": "[0, 2, 5, 3, 4, 1, 6, 7]",
-        "2990": "[1, 3, 6, 4, 5, 2, 0, 7]",
-        "2991": "[2, 4, 0, 5, 6, 3, 1, 7]",
-        "2992": "[3, 5, 4, 2, 6, 1, 0, 7]",
-        "2993": "[4, 3, 0, 6, 2, 5, 1, 7]",
-        "2994": "[5, 6, 2, 1, 4, 3, 0, 7]",
-        "2995": "[6, 3, 0, 4, 2, 5, 1, 7]",
-        "2996": "[0, 3, 5, 1, 6, 2, 4, 7]",
-        "2997": "[1, 4, 6, 2, 0, 3, 5, 7]",
-        "2998": "[2, 5, 0, 3, 1, 4, 6, 7]",
-        "2999": "[3, 2, 4, 1, 0, 5, 6, 7]",
-        "3000": "[4, 6, 0, 5, 1, 3, 2, 7]",
-        "3001": "[5, 1, 2, 3, 0, 6, 4, 7]",
-        "3002": "[6, 4, 0, 5, 1, 3, 2, 7]",
-        "3003": "[0, 4, 3, 1, 6, 2, 5, 7]",
-        "3004": "[1, 5, 4, 2, 0, 3, 6, 7]",
-        "3005": "[2, 6, 5, 3, 1, 4, 0, 7]",
-        "3006": "[3, 6, 2, 1, 0, 5, 4, 7]",
-        "3007": "[4, 2, 6, 5, 1, 3, 0, 7]",
-        "3008": "[5, 4, 1, 3, 0, 6, 2, 7]",
-        "3009": "[6, 2, 4, 5, 1, 3, 0, 7]",
-        "3010": "[0, 5, 6, 3, 4, 1, 2, 7]",
-        "3011": "[1, 6, 0, 4, 5, 2, 3, 7]",
-        "3012": "[2, 0, 1, 5, 6, 3, 4, 7]",
-        "3013": "[3, 4, 0, 2, 6, 1, 5, 7]",
-        "3014": "[4, 0, 1, 6, 2, 5, 3, 7]",
-        "3015": "[5, 2, 0, 1, 4, 3, 6, 7]",
-        "3016": "[6, 0, 1, 4, 2, 5, 3, 7]",
-        "3017": "[0, 6, 3, 1, 4, 2, 5, 7]",
-        "3018": "[1, 0, 4, 2, 5, 3, 6, 7]",
-        "3019": "[2, 1, 5, 3, 6, 4, 0, 7]",
-        "3020": "[3, 0, 2, 1, 6, 5, 4, 7]",
-        "3021": "[4, 1, 6, 5, 2, 3, 0, 7]",
-        "3022": "[5, 0, 1, 3, 4, 6, 2, 7]",
-        "3023": "[6, 1, 4, 5, 2, 3, 0, 7]",
-        "3024": "[0, 1, 4, 6, 3, 5, 2, 7]",
-        "3025": "[1, 2, 5, 0, 4, 6, 3, 7]",
-        "3026": "[2, 3, 6, 1, 5, 0, 4, 7]",
-        "3027": "[3, 1, 6, 0, 2, 4, 5, 7]",
-        "3028": "[4, 5, 2, 1, 6, 0, 3, 7]",
-        "3029": "[5, 3, 4, 0, 1, 2, 6, 7]",
-        "3030": "[6, 5, 2, 1, 4, 0, 3, 7]",
-        "3031": "[0, 2, 1, 6, 5, 4, 3, 7]",
-        "3032": "[1, 3, 2, 0, 6, 5, 4, 7]",
-        "3033": "[2, 4, 3, 1, 0, 6, 5, 7]",
-        "3034": "[3, 5, 1, 0, 4, 6, 2, 7]",
-        "3035": "[4, 3, 5, 1, 0, 2, 6, 7]",
-        "3036": "[5, 6, 3, 0, 2, 4, 1, 7]",
-        "3037": "[6, 3, 5, 1, 0, 2, 4, 7]",
-        "3038": "[0, 3, 2, 4, 5, 6, 1, 7]",
-        "3039": "[1, 4, 3, 5, 6, 0, 2, 7]",
-        "3040": "[2, 5, 4, 6, 0, 1, 3, 7]",
-        "3041": "[3, 2, 5, 6, 4, 0, 1, 7]",
-        "3042": "[4, 6, 3, 2, 0, 1, 5, 7]",
-        "3043": "[5, 1, 6, 4, 2, 0, 3, 7]",
-        "3044": "[6, 4, 3, 2, 0, 1, 5, 7]",
-        "3045": "[0, 4, 2, 5, 3, 6, 1, 7]",
-        "3046": "[1, 5, 3, 6, 4, 0, 2, 7]",
-        "3047": "[2, 6, 4, 0, 5, 1, 3, 7]",
-        "3048": "[3, 6, 5, 4, 2, 0, 1, 7]",
-        "3049": "[4, 2, 3, 0, 6, 1, 5, 7]",
-        "3050": "[5, 4, 6, 2, 1, 0, 3, 7]",
-        "3051": "[6, 2, 3, 0, 4, 1, 5, 7]",
-        "3052": "[0, 5, 1, 2, 6, 4, 3, 7]",
-        "3053": "[1, 6, 2, 3, 0, 5, 4, 7]",
-        "3054": "[2, 0, 3, 4, 1, 6, 5, 7]",
-        "3055": "[3, 4, 1, 5, 0, 6, 2, 7]",
-        "3056": "[4, 0, 5, 3, 1, 2, 6, 7]",
-        "3057": "[5, 2, 3, 6, 0, 4, 1, 7]",
-        "3058": "[6, 0, 5, 3, 1, 2, 4, 7]",
-        "3059": "[0, 6, 2, 5, 3, 4, 1, 7]",
-        "3060": "[1, 0, 3, 6, 4, 5, 2, 7]",
-        "3061": "[2, 1, 4, 0, 5, 6, 3, 7]",
-        "3062": "[3, 0, 5, 4, 2, 6, 1, 7]",
-        "3063": "[4, 1, 3, 0, 6, 2, 5, 7]",
-        "3064": "[5, 0, 6, 2, 1, 4, 3, 7]",
-        "3065": "[6, 1, 3, 0, 4, 2, 5, 7]",
-        "3066": "[0, 1, 5, 4, 3, 6, 2, 7]",
-        "3067": "[1, 2, 6, 5, 4, 0, 3, 7]",
-        "3068": "[2, 3, 0, 6, 5, 1, 4, 7]",
-        "3069": "[3, 1, 4, 6, 2, 0, 5, 7]",
-        "3070": "[4, 5, 0, 2, 6, 1, 3, 7]",
-        "3071": "[5, 3, 2, 4, 1, 0, 6, 7]",
-        "3072": "[6, 5, 0, 2, 4, 1, 3, 7]",
-        "3073": "[0, 2, 4, 1, 5, 6, 3, 7]",
-        "3074": "[1, 3, 5, 2, 6, 0, 4, 7]",
-        "3075": "[2, 4, 6, 3, 0, 1, 5, 7]",
-        "3076": "[3, 5, 6, 1, 4, 0, 2, 7]",
-        "3077": "[4, 3, 2, 5, 0, 1, 6, 7]",
-        "3078": "[5, 6, 4, 3, 2, 0, 1, 7]",
-        "3079": "[6, 3, 2, 5, 0, 1, 4, 7]",
-        "3080": "[0, 3, 6, 2, 5, 4, 1, 7]",
-        "3081": "[1, 4, 0, 3, 6, 5, 2, 7]",
-        "3082": "[2, 5, 1, 4, 0, 6, 3, 7]",
-        "3083": "[3, 2, 0, 5, 4, 6, 1, 7]",
-        "3084": "[4, 6, 1, 3, 0, 2, 5, 7]",
-        "3085": "[5, 1, 0, 6, 2, 4, 3, 7]",
-        "3086": "[6, 4, 1, 3, 0, 2, 5, 7]",
-        "3087": "[0, 4, 6, 2, 3, 5, 1, 7]",
-        "3088": "[1, 5, 0, 3, 4, 6, 2, 7]",
-        "3089": "[2, 6, 1, 4, 5, 0, 3, 7]",
-        "3090": "[3, 6, 0, 5, 2, 4, 1, 7]",
-        "3091": "[4, 2, 1, 3, 6, 0, 5, 7]",
-        "3092": "[5, 4, 0, 6, 1, 2, 3, 7]",
-        "3093": "[6, 2, 1, 3, 4, 0, 5, 7]",
-        "3094": "[0, 5, 4, 1, 6, 2, 3, 7]",
-        "3095": "[1, 6, 5, 2, 0, 3, 4, 7]",
-        "3096": "[2, 0, 6, 3, 1, 4, 5, 7]",
-        "3097": "[3, 4, 6, 1, 0, 5, 2, 7]",
-        "3098": "[4, 0, 2, 5, 1, 3, 6, 7]",
-        "3099": "[5, 2, 4, 3, 0, 6, 1, 7]",
-        "3100": "[6, 0, 2, 5, 1, 3, 4, 7]",
-        "3101": "[0, 6, 4, 2, 3, 5, 1, 7]",
-        "3102": "[1, 0, 5, 3, 4, 6, 2, 7]",
-        "3103": "[2, 1, 6, 4, 5, 0, 3, 7]",
-        "3104": "[3, 0, 6, 5, 2, 4, 1, 7]",
-        "3105": "[4, 1, 2, 3, 6, 0, 5, 7]",
-        "3106": "[5, 0, 4, 6, 1, 2, 3, 7]",
-        "3107": "[6, 1, 2, 3, 4, 0, 5, 7]",
-        "3108": "[0, 1, 6, 4, 3, 5, 2, 7]",
-        "3109": "[1, 2, 0, 5, 4, 6, 3, 7]",
-        "3110": "[2, 3, 1, 6, 5, 0, 4, 7]",
-        "3111": "[3, 1, 0, 6, 2, 4, 5, 7]",
-        "3112": "[4, 5, 1, 2, 6, 0, 3, 7]",
-        "3113": "[5, 3, 0, 4, 1, 2, 6, 7]",
-        "3114": "[6, 5, 1, 2, 4, 0, 3, 7]",
-        "3115": "[0, 2, 6, 1, 5, 4, 3, 7]",
-        "3116": "[1, 3, 0, 2, 6, 5, 4, 7]",
-        "3117": "[2, 4, 1, 3, 0, 6, 5, 7]",
-        "3118": "[3, 5, 0, 1, 4, 6, 2, 7]",
-        "3119": "[4, 3, 1, 5, 0, 2, 6, 7]",
-        "3120": "[5, 6, 0, 3, 2, 4, 1, 7]",
-        "3121": "[6, 3, 1, 5, 0, 2, 4, 7]",
-        "3122": "[0, 3, 4, 2, 5, 6, 1, 7]",
-        "3123": "[1, 4, 5, 3, 6, 0, 2, 7]",
-        "3124": "[2, 5, 6, 4, 0, 1, 3, 7]",
-        "3125": "[3, 2, 6, 5, 4, 0, 1, 7]",
-        "3126": "[4, 6, 2, 3, 0, 1, 5, 7]",
-        "3127": "[5, 1, 4, 6, 2, 0, 3, 7]",
-        "3128": "[6, 4, 2, 3, 0, 1, 5, 7]",
-        "3129": "[0, 4, 5, 2, 3, 6, 1, 7]",
-        "3130": "[1, 5, 6, 3, 4, 0, 2, 7]",
-        "3131": "[2, 6, 0, 4, 5, 1, 3, 7]",
-        "3132": "[3, 6, 4, 5, 2, 0, 1, 7]",
-        "3133": "[4, 2, 0, 3, 6, 1, 5, 7]",
-        "3134": "[5, 4, 2, 6, 1, 0, 3, 7]",
-        "3135": "[6, 2, 0, 3, 4, 1, 5, 7]",
-        "3136": "[0, 5, 2, 1, 6, 4, 3, 7]",
-        "3137": "[1, 6, 3, 2, 0, 5, 4, 7]",
-        "3138": "[2, 0, 4, 3, 1, 6, 5, 7]",
-        "3139": "[3, 4, 5, 1, 0, 6, 2, 7]",
-        "3140": "[4, 0, 3, 5, 1, 2, 6, 7]",
-        "3141": "[5, 2, 6, 3, 0, 4, 1, 7]",
-        "3142": "[6, 0, 3, 5, 1, 2, 4, 7]",
-        "3143": "[0, 6, 5, 2, 3, 4, 1, 7]",
-        "3144": "[1, 0, 6, 3, 4, 5, 2, 7]",
-        "3145": "[2, 1, 0, 4, 5, 6, 3, 7]",
-        "3146": "[3, 0, 4, 5, 2, 6, 1, 7]",
-        "3147": "[4, 1, 0, 3, 6, 2, 5, 7]",
-        "3148": "[5, 0, 2, 6, 1, 4, 3, 7]",
-        "3149": "[6, 1, 0, 3, 4, 2, 5, 7]",
-        "3150": "[0, 1, 2, 6, 3, 5, 4, 7]",
-        "3151": "[1, 2, 3, 0, 4, 6, 5, 7]",
-        "3152": "[2, 3, 4, 1, 5, 0, 6, 7]",
-        "3153": "[3, 1, 5, 0, 2, 4, 6, 7]",
-        "3154": "[4, 5, 3, 1, 6, 0, 2, 7]",
-        "3155": "[5, 3, 6, 0, 1, 2, 4, 7]",
-        "3156": "[6, 5, 3, 1, 4, 0, 2, 7]",
-        "3157": "[0, 2, 3, 6, 5, 4, 1, 7]",
-        "3158": "[1, 3, 4, 0, 6, 5, 2, 7]",
-        "3159": "[2, 4, 5, 1, 0, 6, 3, 7]",
-        "3160": "[3, 5, 2, 0, 4, 6, 1, 7]",
-        "3161": "[4, 3, 6, 1, 0, 2, 5, 7]",
-        "3162": "[5, 6, 1, 0, 2, 4, 3, 7]",
-        "3163": "[6, 3, 4, 1, 0, 2, 5, 7]",
-        "3164": "[0, 3, 1, 4, 5, 6, 2, 7]",
-        "3165": "[1, 4, 2, 5, 6, 0, 3, 7]",
-        "3166": "[2, 5, 3, 6, 0, 1, 4, 7]",
-        "3167": "[3, 2, 1, 6, 4, 0, 5, 7]",
-        "3168": "[4, 6, 5, 2, 0, 1, 3, 7]",
-        "3169": "[5, 1, 3, 4, 2, 0, 6, 7]",
-        "3170": "[6, 4, 5, 2, 0, 1, 3, 7]",
-        "3171": "[0, 4, 1, 5, 3, 6, 2, 7]",
-        "3172": "[1, 5, 2, 6, 4, 0, 3, 7]",
-        "3173": "[2, 6, 3, 0, 5, 1, 4, 7]",
-        "3174": "[3, 6, 1, 4, 2, 0, 5, 7]",
-        "3175": "[4, 2, 5, 0, 6, 1, 3, 7]",
-        "3176": "[5, 4, 3, 2, 1, 0, 6, 7]",
-        "3177": "[6, 2, 5, 0, 4, 1, 3, 7]",
-        "3178": "[0, 5, 3, 2, 6, 4, 1, 7]",
-        "3179": "[1, 6, 4, 3, 0, 5, 2, 7]",
-        "3180": "[2, 0, 5, 4, 1, 6, 3, 7]",
-        "3181": "[3, 4, 2, 5, 0, 6, 1, 7]",
-        "3182": "[4, 0, 6, 3, 1, 2, 5, 7]",
-        "3183": "[5, 2, 1, 6, 0, 4, 3, 7]",
-        "3184": "[6, 0, 4, 3, 1, 2, 5, 7]",
-        "3185": "[0, 6, 1, 5, 3, 4, 2, 7]",
-        "3186": "[1, 0, 2, 6, 4, 5, 3, 7]",
-        "3187": "[2, 1, 3, 0, 5, 6, 4, 7]",
-        "3188": "[3, 0, 1, 4, 2, 6, 5, 7]",
-        "3189": "[4, 1, 5, 0, 6, 2, 3, 7]",
-        "3190": "[5, 0, 3, 2, 1, 4, 6, 7]",
-        "3191": "[6, 1, 5, 0, 4, 2, 3, 7]",
-        "3192": "[0, 1, 3, 6, 4, 2, 5, 7]",
-        "3193": "[1, 2, 4, 0, 5, 3, 6, 7]",
-        "3194": "[2, 3, 5, 1, 6, 4, 0, 7]",
-        "3195": "[3, 1, 2, 0, 6, 5, 4, 7]",
-        "3196": "[4, 5, 6, 1, 2, 3, 0, 7]",
-        "3197": "[5, 3, 1, 0, 4, 6, 2, 7]",
-        "3198": "[6, 5, 4, 1, 2, 3, 0, 7]",
-        "3199": "[0, 2, 5, 6, 1, 3, 4, 7]",
-        "3200": "[1, 3, 6, 0, 2, 4, 5, 7]",
-        "3201": "[2, 4, 0, 1, 3, 5, 6, 7]",
-        "3202": "[3, 5, 4, 0, 1, 2, 6, 7]",
-        "3203": "[4, 3, 0, 1, 5, 6, 2, 7]",
-        "3204": "[5, 6, 2, 0, 3, 1, 4, 7]",
-        "3205": "[6, 3, 0, 1, 5, 4, 2, 7]",
-        "3206": "[0, 3, 5, 4, 2, 1, 6, 7]",
-        "3207": "[1, 4, 6, 5, 3, 2, 0, 7]",
-        "3208": "[2, 5, 0, 6, 4, 3, 1, 7]",
-        "3209": "[3, 2, 4, 6, 5, 1, 0, 7]",
-        "3210": "[4, 6, 0, 2, 3, 5, 1, 7]",
-        "3211": "[5, 1, 2, 4, 6, 3, 0, 7]",
-        "3212": "[6, 4, 0, 2, 3, 5, 1, 7]",
-        "3213": "[0, 4, 3, 5, 2, 1, 6, 7]",
-        "3214": "[1, 5, 4, 6, 3, 2, 0, 7]",
-        "3215": "[2, 6, 5, 0, 4, 3, 1, 7]",
-        "3216": "[3, 6, 2, 4, 5, 1, 0, 7]",
-        "3217": "[4, 2, 6, 0, 3, 5, 1, 7]",
-        "3218": "[5, 4, 1, 2, 6, 3, 0, 7]",
-        "3219": "[6, 2, 4, 0, 3, 5, 1, 7]",
-        "3220": "[0, 5, 6, 2, 1, 3, 4, 7]",
-        "3221": "[1, 6, 0, 3, 2, 4, 5, 7]",
-        "3222": "[2, 0, 1, 4, 3, 5, 6, 7]",
-        "3223": "[3, 4, 0, 5, 1, 2, 6, 7]",
-        "3224": "[4, 0, 1, 3, 5, 6, 2, 7]",
-        "3225": "[5, 2, 0, 6, 3, 1, 4, 7]",
-        "3226": "[6, 0, 1, 3, 5, 4, 2, 7]",
-        "3227": "[0, 6, 3, 5, 2, 1, 4, 7]",
-        "3228": "[1, 0, 4, 6, 3, 2, 5, 7]",
-        "3229": "[2, 1, 5, 0, 4, 3, 6, 7]",
-        "3230": "[3, 0, 2, 4, 5, 1, 6, 7]",
-        "3231": "[4, 1, 6, 0, 3, 5, 2, 7]",
-        "3232": "[5, 0, 1, 2, 6, 3, 4, 7]",
-        "3233": "[6, 1, 4, 0, 3, 5, 2, 7]",
-        "3234": "[0, 1, 4, 2, 5, 6, 3, 7]",
-        "3235": "[1, 2, 5, 3, 6, 0, 4, 7]",
-        "3236": "[2, 3, 6, 4, 0, 1, 5, 7]",
-        "3237": "[3, 1, 6, 5, 4, 0, 2, 7]",
-        "3238": "[4, 5, 2, 3, 0, 1, 6, 7]",
-        "3239": "[5, 3, 4, 6, 2, 0, 1, 7]",
-        "3240": "[6, 5, 2, 3, 0, 1, 4, 7]",
-        "3241": "[0, 2, 1, 3, 4, 6, 5, 7]",
-        "3242": "[1, 3, 2, 4, 5, 0, 6, 7]",
-        "3243": "[2, 4, 3, 5, 6, 1, 0, 7]",
-        "3244": "[3, 5, 1, 2, 6, 0, 4, 7]",
-        "3245": "[4, 3, 5, 6, 2, 1, 0, 7]",
-        "3246": "[5, 6, 3, 1, 4, 0, 2, 7]",
-        "3247": "[6, 3, 5, 4, 2, 1, 0, 7]",
-        "3248": "[0, 3, 2, 1, 6, 4, 5, 7]",
-        "3249": "[1, 4, 3, 2, 0, 5, 6, 7]",
-        "3250": "[2, 5, 4, 3, 1, 6, 0, 7]",
-        "3251": "[3, 2, 5, 1, 0, 6, 4, 7]",
-        "3252": "[4, 6, 3, 5, 1, 2, 0, 7]",
-        "3253": "[5, 1, 6, 3, 0, 4, 2, 7]",
-        "3254": "[6, 4, 3, 5, 1, 2, 0, 7]",
-        "3255": "[0, 4, 2, 1, 6, 5, 3, 7]",
-        "3256": "[1, 5, 3, 2, 0, 6, 4, 7]",
-        "3257": "[2, 6, 4, 3, 1, 0, 5, 7]",
-        "3258": "[3, 6, 5, 1, 0, 4, 2, 7]",
-        "3259": "[4, 2, 3, 5, 1, 0, 6, 7]",
-        "3260": "[5, 4, 6, 3, 0, 2, 1, 7]",
-        "3261": "[6, 2, 3, 5, 1, 0, 4, 7]",
-        "3262": "[0, 5, 1, 3, 4, 2, 6, 7]",
-        "3263": "[1, 6, 2, 4, 5, 3, 0, 7]",
-        "3264": "[2, 0, 3, 5, 6, 4, 1, 7]",
-        "3265": "[3, 4, 1, 2, 6, 5, 0, 7]",
-        "3266": "[4, 0, 5, 6, 2, 3, 1, 7]",
-        "3267": "[5, 2, 3, 1, 4, 6, 0, 7]",
-        "3268": "[6, 0, 5, 4, 2, 3, 1, 7]",
-        "3269": "[0, 6, 2, 1, 4, 5, 3, 7]",
-        "3270": "[1, 0, 3, 2, 5, 6, 4, 7]",
-        "3271": "[2, 1, 4, 3, 6, 0, 5, 7]",
-        "3272": "[3, 0, 5, 1, 6, 4, 2, 7]",
-        "3273": "[4, 1, 3, 5, 2, 0, 6, 7]",
-        "3274": "[5, 0, 6, 3, 4, 2, 1, 7]",
-        "3275": "[6, 1, 3, 5, 2, 0, 4, 7]",
-        "3276": "[0, 1, 5, 2, 6, 4, 3, 7]",
-        "3277": "[1, 2, 6, 3, 0, 5, 4, 7]",
-        "3278": "[2, 3, 0, 4, 1, 6, 5, 7]",
-        "3279": "[3, 1, 4, 5, 0, 6, 2, 7]",
-        "3280": "[4, 5, 0, 3, 1, 2, 6, 7]",
-        "3281": "[5, 3, 2, 6, 0, 4, 1, 7]",
-        "3282": "[6, 5, 0, 3, 1, 2, 4, 7]",
-        "3283": "[0, 2, 4, 3, 6, 1, 5, 7]",
-        "3284": "[1, 3, 5, 4, 0, 2, 6, 7]",
-        "3285": "[2, 4, 6, 5, 1, 3, 0, 7]",
-        "3286": "[3, 5, 6, 2, 0, 1, 4, 7]",
-        "3287": "[4, 3, 2, 6, 1, 5, 0, 7]",
-        "3288": "[5, 6, 4, 1, 0, 3, 2, 7]",
-        "3289": "[6, 3, 2, 4, 1, 5, 0, 7]",
-        "3290": "[0, 3, 6, 1, 4, 2, 5, 7]",
-        "3291": "[1, 4, 0, 2, 5, 3, 6, 7]",
-        "3292": "[2, 5, 1, 3, 6, 4, 0, 7]",
-        "3293": "[3, 2, 0, 1, 6, 5, 4, 7]",
-        "3294": "[4, 6, 1, 5, 2, 3, 0, 7]",
-        "3295": "[5, 1, 0, 3, 4, 6, 2, 7]",
-        "3296": "[6, 4, 1, 5, 2, 3, 0, 7]",
-        "3297": "[0, 4, 6, 1, 5, 2, 3, 7]",
-        "3298": "[1, 5, 0, 2, 6, 3, 4, 7]",
-        "3299": "[2, 6, 1, 3, 0, 4, 5, 7]",
-        "3300": "[3, 6, 0, 1, 4, 5, 2, 7]",
-        "3301": "[4, 2, 1, 5, 0, 3, 6, 7]",
-        "3302": "[5, 4, 0, 3, 2, 6, 1, 7]",
-        "3303": "[6, 2, 1, 5, 0, 3, 4, 7]",
-        "3304": "[0, 5, 4, 3, 2, 1, 6, 7]",
-        "3305": "[1, 6, 5, 4, 3, 2, 0, 7]",
-        "3306": "[2, 0, 6, 5, 4, 3, 1, 7]",
-        "3307": "[3, 4, 6, 2, 5, 1, 0, 7]",
-        "3308": "[4, 0, 2, 6, 3, 5, 1, 7]",
-        "3309": "[5, 2, 4, 1, 6, 3, 0, 7]",
-        "3310": "[6, 0, 2, 4, 3, 5, 1, 7]",
-        "3311": "[0, 6, 4, 1, 5, 2, 3, 7]",
-        "3312": "[1, 0, 5, 2, 6, 3, 4, 7]",
-        "3313": "[2, 1, 6, 3, 0, 4, 5, 7]",
-        "3314": "[3, 0, 6, 1, 4, 5, 2, 7]",
-        "3315": "[4, 1, 2, 5, 0, 3, 6, 7]",
-        "3316": "[5, 0, 4, 3, 2, 6, 1, 7]",
-        "3317": "[6, 1, 2, 5, 0, 3, 4, 7]",
-        "3318": "[0, 1, 6, 2, 5, 4, 3, 7]",
-        "3319": "[1, 2, 0, 3, 6, 5, 4, 7]",
-        "3320": "[2, 3, 1, 4, 0, 6, 5, 7]",
-        "3321": "[3, 1, 0, 5, 4, 6, 2, 7]",
-        "3322": "[4, 5, 1, 3, 0, 2, 6, 7]",
-        "3323": "[5, 3, 0, 6, 2, 4, 1, 7]",
-        "3324": "[6, 5, 1, 3, 0, 2, 4, 7]",
-        "3325": "[0, 2, 6, 3, 4, 1, 5, 7]",
-        "3326": "[1, 3, 0, 4, 5, 2, 6, 7]",
-        "3327": "[2, 4, 1, 5, 6, 3, 0, 7]",
-        "3328": "[3, 5, 0, 2, 6, 1, 4, 7]",
-        "3329": "[4, 3, 1, 6, 2, 5, 0, 7]",
-        "3330": "[5, 6, 0, 1, 4, 3, 2, 7]",
-        "3331": "[6, 3, 1, 4, 2, 5, 0, 7]",
-        "3332": "[0, 3, 4, 1, 6, 2, 5, 7]",
-        "3333": "[1, 4, 5, 2, 0, 3, 6, 7]",
-        "3334": "[2, 5, 6, 3, 1, 4, 0, 7]",
-        "3335": "[3, 2, 6, 1, 0, 5, 4, 7]",
-        "3336": "[4, 6, 2, 5, 1, 3, 0, 7]",
-        "3337": "[5, 1, 4, 3, 0, 6, 2, 7]",
-        "3338": "[6, 4, 2, 5, 1, 3, 0, 7]",
-        "3339": "[0, 4, 5, 1, 6, 2, 3, 7]",
-        "3340": "[1, 5, 6, 2, 0, 3, 4, 7]",
-        "3341": "[2, 6, 0, 3, 1, 4, 5, 7]",
-        "3342": "[3, 6, 4, 1, 0, 5, 2, 7]",
-        "3343": "[4, 2, 0, 5, 1, 3, 6, 7]",
-        "3344": "[5, 4, 2, 3, 0, 6, 1, 7]",
-        "3345": "[6, 2, 0, 5, 1, 3, 4, 7]",
-        "3346": "[0, 5, 2, 3, 4, 1, 6, 7]",
-        "3347": "[1, 6, 3, 4, 5, 2, 0, 7]",
-        "3348": "[2, 0, 4, 5, 6, 3, 1, 7]",
-        "3349": "[3, 4, 5, 2, 6, 1, 0, 7]",
-        "3350": "[4, 0, 3, 6, 2, 5, 1, 7]",
-        "3351": "[5, 2, 6, 1, 4, 3, 0, 7]",
-        "3352": "[6, 0, 3, 4, 2, 5, 1, 7]",
-        "3353": "[0, 6, 5, 1, 4, 2, 3, 7]",
-        "3354": "[1, 0, 6, 2, 5, 3, 4, 7]",
-        "3355": "[2, 1, 0, 3, 6, 4, 5, 7]",
-        "3356": "[3, 0, 4, 1, 6, 5, 2, 7]",
-        "3357": "[4, 1, 0, 5, 2, 3, 6, 7]",
-        "3358": "[5, 0, 2, 3, 4, 6, 1, 7]",
-        "3359": "[6, 1, 0, 5, 2, 3, 4, 7]",
-        "3360": "[0, 1, 2, 3, 6, 5, 4, 7]",
-        "3361": "[1, 2, 3, 4, 0, 6, 5, 7]",
-        "3362": "[2, 3, 4, 5, 1, 0, 6, 7]",
-        "3363": "[3, 1, 5, 2, 0, 4, 6, 7]",
-        "3364": "[4, 5, 3, 6, 1, 0, 2, 7]",
-        "3365": "[5, 3, 6, 1, 0, 2, 4, 7]",
-        "3366": "[6, 5, 3, 4, 1, 0, 2, 7]",
-        "3367": "[0, 2, 3, 5, 6, 4, 1, 7]",
-        "3368": "[1, 3, 4, 6, 0, 5, 2, 7]",
-        "3369": "[2, 4, 5, 0, 1, 6, 3, 7]",
-        "3370": "[3, 5, 2, 4, 0, 6, 1, 7]",
-        "3371": "[4, 3, 6, 0, 1, 2, 5, 7]",
-        "3372": "[5, 6, 1, 2, 0, 4, 3, 7]",
-        "3373": "[6, 3, 4, 0, 1, 2, 5, 7]",
-        "3374": "[0, 3, 1, 5, 4, 6, 2, 7]",
-        "3375": "[1, 4, 2, 6, 5, 0, 3, 7]",
-        "3376": "[2, 5, 3, 0, 6, 1, 4, 7]",
-        "3377": "[3, 2, 1, 4, 6, 0, 5, 7]",
-        "3378": "[4, 6, 5, 0, 2, 1, 3, 7]",
-        "3379": "[5, 1, 3, 2, 4, 0, 6, 7]",
-        "3380": "[6, 4, 5, 0, 2, 1, 3, 7]",
-        "3381": "[0, 4, 1, 3, 5, 6, 2, 7]",
-        "3382": "[1, 5, 2, 4, 6, 0, 3, 7]",
-        "3383": "[2, 6, 3, 5, 0, 1, 4, 7]",
-        "3384": "[3, 6, 1, 2, 4, 0, 5, 7]",
-        "3385": "[4, 2, 5, 6, 0, 1, 3, 7]",
-        "3386": "[5, 4, 3, 1, 2, 0, 6, 7]",
-        "3387": "[6, 2, 5, 4, 0, 1, 3, 7]",
-        "3388": "[0, 5, 3, 6, 2, 4, 1, 7]",
-        "3389": "[1, 6, 4, 0, 3, 5, 2, 7]",
-        "3390": "[2, 0, 5, 1, 4, 6, 3, 7]",
-        "3391": "[3, 4, 2, 0, 5, 6, 1, 7]",
-        "3392": "[4, 0, 6, 1, 3, 2, 5, 7]",
-        "3393": "[5, 2, 1, 0, 6, 4, 3, 7]",
-        "3394": "[6, 0, 4, 1, 3, 2, 5, 7]",
-        "3395": "[0, 6, 1, 3, 5, 4, 2, 7]",
-        "3396": "[1, 0, 2, 4, 6, 5, 3, 7]",
-        "3397": "[2, 1, 3, 5, 0, 6, 4, 7]",
-        "3398": "[3, 0, 1, 2, 4, 6, 5, 7]",
-        "3399": "[4, 1, 5, 6, 0, 2, 3, 7]",
-        "3400": "[5, 0, 3, 1, 2, 4, 6, 7]",
-        "3401": "[6, 1, 5, 4, 0, 2, 3, 7]",
-        "3402": "[0, 1, 3, 4, 6, 2, 5, 7]",
-        "3403": "[1, 2, 4, 5, 0, 3, 6, 7]",
-        "3404": "[2, 3, 5, 6, 1, 4, 0, 7]",
-        "3405": "[3, 1, 2, 6, 0, 5, 4, 7]",
-        "3406": "[4, 5, 6, 2, 1, 3, 0, 7]",
-        "3407": "[5, 3, 1, 4, 0, 6, 2, 7]",
-        "3408": "[6, 5, 4, 2, 1, 3, 0, 7]",
-        "3409": "[0, 2, 5, 1, 6, 3, 4, 7]",
-        "3410": "[1, 3, 6, 2, 0, 4, 5, 7]",
-        "3411": "[2, 4, 0, 3, 1, 5, 6, 7]",
-        "3412": "[3, 5, 4, 1, 0, 2, 6, 7]",
-        "3413": "[4, 3, 0, 5, 1, 6, 2, 7]",
-        "3414": "[5, 6, 2, 3, 0, 1, 4, 7]",
-        "3415": "[6, 3, 0, 5, 1, 4, 2, 7]",
-        "3416": "[0, 3, 5, 2, 4, 1, 6, 7]",
-        "3417": "[1, 4, 6, 3, 5, 2, 0, 7]",
-        "3418": "[2, 5, 0, 4, 6, 3, 1, 7]",
-        "3419": "[3, 2, 4, 5, 6, 1, 0, 7]",
-        "3420": "[4, 6, 0, 3, 2, 5, 1, 7]",
-        "3421": "[5, 1, 2, 6, 4, 3, 0, 7]",
-        "3422": "[6, 4, 0, 3, 2, 5, 1, 7]",
-        "3423": "[0, 4, 3, 2, 5, 1, 6, 7]",
-        "3424": "[1, 5, 4, 3, 6, 2, 0, 7]",
-        "3425": "[2, 6, 5, 4, 0, 3, 1, 7]",
-        "3426": "[3, 6, 2, 5, 4, 1, 0, 7]",
-        "3427": "[4, 2, 6, 3, 0, 5, 1, 7]",
-        "3428": "[5, 4, 1, 6, 2, 3, 0, 7]",
-        "3429": "[6, 2, 4, 3, 0, 5, 1, 7]",
-        "3430": "[0, 5, 6, 1, 2, 3, 4, 7]",
-        "3431": "[1, 6, 0, 2, 3, 4, 5, 7]",
-        "3432": "[2, 0, 1, 3, 4, 5, 6, 7]",
-        "3433": "[3, 4, 0, 1, 5, 2, 6, 7]",
-        "3434": "[4, 0, 1, 5, 3, 6, 2, 7]",
-        "3435": "[5, 2, 0, 3, 6, 1, 4, 7]",
-        "3436": "[6, 0, 1, 5, 3, 4, 2, 7]",
-        "3437": "[0, 6, 3, 2, 5, 1, 4, 7]",
-        "3438": "[1, 0, 4, 3, 6, 2, 5, 7]",
-        "3439": "[2, 1, 5, 4, 0, 3, 6, 7]",
-        "3440": "[3, 0, 2, 5, 4, 1, 6, 7]",
-        "3441": "[4, 1, 6, 3, 0, 5, 2, 7]",
-        "3442": "[5, 0, 1, 6, 2, 3, 4, 7]",
-        "3443": "[6, 1, 4, 3, 0, 5, 2, 7]",
-        "3444": "[0, 1, 4, 5, 2, 6, 3, 7]",
-        "3445": "[1, 2, 5, 6, 3, 0, 4, 7]",
-        "3446": "[2, 3, 6, 0, 4, 1, 5, 7]",
-        "3447": "[3, 1, 6, 4, 5, 0, 2, 7]",
-        "3448": "[4, 5, 2, 0, 3, 1, 6, 7]",
-        "3449": "[5, 3, 4, 2, 6, 0, 1, 7]",
-        "3450": "[6, 5, 2, 0, 3, 1, 4, 7]",
-        "3451": "[0, 2, 1, 4, 3, 6, 5, 7]",
-        "3452": "[1, 3, 2, 5, 4, 0, 6, 7]",
-        "3453": "[2, 4, 3, 6, 5, 1, 0, 7]",
-        "3454": "[3, 5, 1, 6, 2, 0, 4, 7]",
-        "3455": "[4, 3, 5, 2, 6, 1, 0, 7]",
-        "3456": "[5, 6, 3, 4, 1, 0, 2, 7]",
-        "3457": "[6, 3, 5, 2, 4, 1, 0, 7]",
-        "3458": "[0, 3, 2, 6, 1, 4, 5, 7]",
-        "3459": "[1, 4, 3, 0, 2, 5, 6, 7]",
-        "3460": "[2, 5, 4, 1, 3, 6, 0, 7]",
-        "3461": "[3, 2, 5, 0, 1, 6, 4, 7]",
-        "3462": "[4, 6, 3, 1, 5, 2, 0, 7]",
-        "3463": "[5, 1, 6, 0, 3, 4, 2, 7]",
-        "3464": "[6, 4, 3, 1, 5, 2, 0, 7]",
-        "3465": "[0, 4, 2, 6, 1, 5, 3, 7]",
-        "3466": "[1, 5, 3, 0, 2, 6, 4, 7]",
-        "3467": "[2, 6, 4, 1, 3, 0, 5, 7]",
-        "3468": "[3, 6, 5, 0, 1, 4, 2, 7]",
-        "3469": "[4, 2, 3, 1, 5, 0, 6, 7]",
-        "3470": "[5, 4, 6, 0, 3, 2, 1, 7]",
-        "3471": "[6, 2, 3, 1, 5, 0, 4, 7]",
-        "3472": "[0, 5, 1, 4, 3, 2, 6, 7]",
-        "3473": "[1, 6, 2, 5, 4, 3, 0, 7]",
-        "3474": "[2, 0, 3, 6, 5, 4, 1, 7]",
-        "3475": "[3, 4, 1, 6, 2, 5, 0, 7]",
-        "3476": "[4, 0, 5, 2, 6, 3, 1, 7]",
-        "3477": "[5, 2, 3, 4, 1, 6, 0, 7]",
-        "3478": "[6, 0, 5, 2, 4, 3, 1, 7]",
-        "3479": "[0, 6, 2, 4, 1, 5, 3, 7]",
-        "3480": "[1, 0, 3, 5, 2, 6, 4, 7]",
-        "3481": "[2, 1, 4, 6, 3, 0, 5, 7]",
-        "3482": "[3, 0, 5, 6, 1, 4, 2, 7]",
-        "3483": "[4, 1, 3, 2, 5, 0, 6, 7]",
-        "3484": "[5, 0, 6, 4, 3, 2, 1, 7]",
-        "3485": "[6, 1, 3, 2, 5, 0, 4, 7]",
-        "3486": "[0, 1, 5, 6, 2, 4, 3, 7]",
-        "3487": "[1, 2, 6, 0, 3, 5, 4, 7]",
-        "3488": "[2, 3, 0, 1, 4, 6, 5, 7]",
-        "3489": "[3, 1, 4, 0, 5, 6, 2, 7]",
-        "3490": "[4, 5, 0, 1, 3, 2, 6, 7]",
-        "3491": "[5, 3, 2, 0, 6, 4, 1, 7]",
-        "3492": "[6, 5, 0, 1, 3, 2, 4, 7]",
-        "3493": "[0, 2, 4, 6, 3, 1, 5, 7]",
-        "3494": "[1, 3, 5, 0, 4, 2, 6, 7]",
-        "3495": "[2, 4, 6, 1, 5, 3, 0, 7]",
-        "3496": "[3, 5, 6, 0, 2, 1, 4, 7]",
-        "3497": "[4, 3, 2, 1, 6, 5, 0, 7]",
-        "3498": "[5, 6, 4, 0, 1, 3, 2, 7]",
-        "3499": "[6, 3, 2, 1, 4, 5, 0, 7]",
-        "3500": "[0, 3, 6, 4, 1, 2, 5, 7]",
-        "3501": "[1, 4, 0, 5, 2, 3, 6, 7]",
-        "3502": "[2, 5, 1, 6, 3, 4, 0, 7]",
-        "3503": "[3, 2, 0, 6, 1, 5, 4, 7]",
-        "3504": "[4, 6, 1, 2, 5, 3, 0, 7]",
-        "3505": "[5, 1, 0, 4, 3, 6, 2, 7]",
-        "3506": "[6, 4, 1, 2, 5, 3, 0, 7]",
-        "3507": "[0, 4, 6, 5, 1, 2, 3, 7]",
-        "3508": "[1, 5, 0, 6, 2, 3, 4, 7]",
-        "3509": "[2, 6, 1, 0, 3, 4, 5, 7]",
-        "3510": "[3, 6, 0, 4, 1, 5, 2, 7]",
-        "3511": "[4, 2, 1, 0, 5, 3, 6, 7]",
-        "3512": "[5, 4, 0, 2, 3, 6, 1, 7]",
-        "3513": "[6, 2, 1, 0, 5, 3, 4, 7]",
-        "3514": "[0, 5, 4, 2, 3, 1, 6, 7]",
-        "3515": "[1, 6, 5, 3, 4, 2, 0, 7]",
-        "3516": "[2, 0, 6, 4, 5, 3, 1, 7]",
-        "3517": "[3, 4, 6, 5, 2, 1, 0, 7]",
-        "3518": "[4, 0, 2, 3, 6, 5, 1, 7]",
-        "3519": "[5, 2, 4, 6, 1, 3, 0, 7]",
-        "3520": "[6, 0, 2, 3, 4, 5, 1, 7]",
-        "3521": "[0, 6, 4, 5, 1, 2, 3, 7]",
-        "3522": "[1, 0, 5, 6, 2, 3, 4, 7]",
-        "3523": "[2, 1, 6, 0, 3, 4, 5, 7]",
-        "3524": "[3, 0, 6, 4, 1, 5, 2, 7]",
-        "3525": "[4, 1, 2, 0, 5, 3, 6, 7]",
-        "3526": "[5, 0, 4, 2, 3, 6, 1, 7]",
-        "3527": "[6, 1, 2, 0, 5, 3, 4, 7]",
-        "3528": "[0, 1, 6, 5, 2, 4, 3, 7]",
-        "3529": "[1, 2, 0, 6, 3, 5, 4, 7]",
-        "3530": "[2, 3, 1, 0, 4, 6, 5, 7]",
-        "3531": "[3, 1, 0, 4, 5, 6, 2, 7]",
-        "3532": "[4, 5, 1, 0, 3, 2, 6, 7]",
-        "3533": "[5, 3, 0, 2, 6, 4, 1, 7]",
-        "3534": "[6, 5, 1, 0, 3, 2, 4, 7]",
-        "3535": "[0, 2, 6, 4, 3, 1, 5, 7]",
-        "3536": "[1, 3, 0, 5, 4, 2, 6, 7]",
-        "3537": "[2, 4, 1, 6, 5, 3, 0, 7]",
-        "3538": "[3, 5, 0, 6, 2, 1, 4, 7]",
-        "3539": "[4, 3, 1, 2, 6, 5, 0, 7]",
-        "3540": "[5, 6, 0, 4, 1, 3, 2, 7]",
-        "3541": "[6, 3, 1, 2, 4, 5, 0, 7]",
-        "3542": "[0, 3, 4, 6, 1, 2, 5, 7]",
-        "3543": "[1, 4, 5, 0, 2, 3, 6, 7]",
-        "3544": "[2, 5, 6, 1, 3, 4, 0, 7]",
-        "3545": "[3, 2, 6, 0, 1, 5, 4, 7]",
-        "3546": "[4, 6, 2, 1, 5, 3, 0, 7]",
-        "3547": "[5, 1, 4, 0, 3, 6, 2, 7]",
-        "3548": "[6, 4, 2, 1, 5, 3, 0, 7]",
-        "3549": "[0, 4, 5, 6, 1, 2, 3, 7]",
-        "3550": "[1, 5, 6, 0, 2, 3, 4, 7]",
-        "3551": "[2, 6, 0, 1, 3, 4, 5, 7]",
-        "3552": "[3, 6, 4, 0, 1, 5, 2, 7]",
-        "3553": "[4, 2, 0, 1, 5, 3, 6, 7]",
-        "3554": "[5, 4, 2, 0, 3, 6, 1, 7]",
-        "3555": "[6, 2, 0, 1, 5, 3, 4, 7]",
-        "3556": "[0, 5, 2, 4, 3, 1, 6, 7]",
-        "3557": "[1, 6, 3, 5, 4, 2, 0, 7]",
-        "3558": "[2, 0, 4, 6, 5, 3, 1, 7]",
-        "3559": "[3, 4, 5, 6, 2, 1, 0, 7]",
-        "3560": "[4, 0, 3, 2, 6, 5, 1, 7]",
-        "3561": "[5, 2, 6, 4, 1, 3, 0, 7]",
-        "3562": "[6, 0, 3, 2, 4, 5, 1, 7]",
-        "3563": "[0, 6, 5, 4, 1, 2, 3, 7]",
-        "3564": "[1, 0, 6, 5, 2, 3, 4, 7]",
-        "3565": "[2, 1, 0, 6, 3, 4, 5, 7]",
-        "3566": "[3, 0, 4, 6, 1, 5, 2, 7]",
-        "3567": "[4, 1, 0, 2, 5, 3, 6, 7]",
-        "3568": "[5, 0, 2, 4, 3, 6, 1, 7]",
-        "3569": "[6, 1, 0, 2, 5, 3, 4, 7]",
-        "3570": "[0, 1, 2, 4, 6, 3, 5, 7]",
-        "3571": "[1, 2, 3, 5, 0, 4, 6, 7]",
-        "3572": "[2, 3, 4, 6, 1, 5, 0, 7]",
-        "3573": "[3, 1, 5, 6, 0, 2, 4, 7]",
-        "3574": "[4, 5, 3, 2, 1, 6, 0, 7]",
-        "3575": "[5, 3, 6, 4, 0, 1, 2, 7]",
-        "3576": "[6, 5, 3, 2, 1, 4, 0, 7]",
-        "3577": "[0, 2, 3, 1, 6, 5, 4, 7]",
-        "3578": "[1, 3, 4, 2, 0, 6, 5, 7]",
-        "3579": "[2, 4, 5, 3, 1, 0, 6, 7]",
-        "3580": "[3, 5, 2, 1, 0, 4, 6, 7]",
-        "3581": "[4, 3, 6, 5, 1, 0, 2, 7]",
-        "3582": "[5, 6, 1, 3, 0, 2, 4, 7]",
-        "3583": "[6, 3, 4, 5, 1, 0, 2, 7]",
-        "3584": "[0, 3, 1, 2, 4, 5, 6, 7]",
-        "3585": "[1, 4, 2, 3, 5, 6, 0, 7]",
-        "3586": "[2, 5, 3, 4, 6, 0, 1, 7]",
-        "3587": "[3, 2, 1, 5, 6, 4, 0, 7]",
-        "3588": "[4, 6, 5, 3, 2, 0, 1, 7]",
-        "3589": "[5, 1, 3, 6, 4, 2, 0, 7]",
-        "3590": "[6, 4, 5, 3, 2, 0, 1, 7]",
-        "3591": "[0, 4, 1, 2, 5, 3, 6, 7]",
-        "3592": "[1, 5, 2, 3, 6, 4, 0, 7]",
-        "3593": "[2, 6, 3, 4, 0, 5, 1, 7]",
-        "3594": "[3, 6, 1, 5, 4, 2, 0, 7]",
-        "3595": "[4, 2, 5, 3, 0, 6, 1, 7]",
-        "3596": "[5, 4, 3, 6, 2, 1, 0, 7]",
-        "3597": "[6, 2, 5, 3, 0, 4, 1, 7]",
-        "3598": "[0, 5, 3, 1, 2, 6, 4, 7]",
-        "3599": "[1, 6, 4, 2, 3, 0, 5, 7]",
-        "3600": "[2, 0, 5, 3, 4, 1, 6, 7]",
-        "3601": "[3, 4, 2, 1, 5, 0, 6, 7]",
-        "3602": "[4, 0, 6, 5, 3, 1, 2, 7]",
-        "3603": "[5, 2, 1, 3, 6, 0, 4, 7]",
-        "3604": "[6, 0, 4, 5, 3, 1, 2, 7]",
-        "3605": "[0, 6, 1, 2, 5, 3, 4, 7]",
-        "3606": "[1, 0, 2, 3, 6, 4, 5, 7]",
-        "3607": "[2, 1, 3, 4, 0, 5, 6, 7]",
-        "3608": "[3, 0, 1, 5, 4, 2, 6, 7]",
-        "3609": "[4, 1, 5, 3, 0, 6, 2, 7]",
-        "3610": "[5, 0, 3, 6, 2, 1, 4, 7]",
-        "3611": "[6, 1, 5, 3, 0, 4, 2, 7]",
-        "3612": "[0, 1, 3, 5, 6, 4, 2, 7]",
-        "3613": "[1, 2, 4, 6, 0, 5, 3, 7]",
-        "3614": "[2, 3, 5, 0, 1, 6, 4, 7]",
-        "3615": "[3, 1, 2, 4, 0, 6, 5, 7]",
-        "3616": "[4, 5, 6, 0, 1, 2, 3, 7]",
-        "3617": "[5, 3, 1, 2, 0, 4, 6, 7]",
-        "3618": "[6, 5, 4, 0, 1, 2, 3, 7]",
-        "3619": "[0, 2, 5, 4, 6, 1, 3, 7]",
-        "3620": "[1, 3, 6, 5, 0, 2, 4, 7]",
-        "3621": "[2, 4, 0, 6, 1, 3, 5, 7]",
-        "3622": "[3, 5, 4, 6, 0, 1, 2, 7]",
-        "3623": "[4, 3, 0, 2, 1, 5, 6, 7]",
-        "3624": "[5, 6, 2, 4, 0, 3, 1, 7]",
-        "3625": "[6, 3, 0, 2, 1, 5, 4, 7]",
-        "3626": "[0, 3, 5, 6, 4, 2, 1, 7]",
-        "3627": "[1, 4, 6, 0, 5, 3, 2, 7]",
-        "3628": "[2, 5, 0, 1, 6, 4, 3, 7]",
-        "3629": "[3, 2, 4, 0, 6, 5, 1, 7]",
-        "3630": "[4, 6, 0, 1, 2, 3, 5, 7]",
-        "3631": "[5, 1, 2, 0, 4, 6, 3, 7]",
-        "3632": "[6, 4, 0, 1, 2, 3, 5, 7]",
-        "3633": "[0, 4, 3, 6, 5, 2, 1, 7]",
-        "3634": "[1, 5, 4, 0, 6, 3, 2, 7]",
-        "3635": "[2, 6, 5, 1, 0, 4, 3, 7]",
-        "3636": "[3, 6, 2, 0, 4, 5, 1, 7]",
-        "3637": "[4, 2, 6, 1, 0, 3, 5, 7]",
-        "3638": "[5, 4, 1, 0, 2, 6, 3, 7]",
-        "3639": "[6, 2, 4, 1, 0, 3, 5, 7]",
-        "3640": "[0, 5, 6, 4, 2, 1, 3, 7]",
-        "3641": "[1, 6, 0, 5, 3, 2, 4, 7]",
-        "3642": "[2, 0, 1, 6, 4, 3, 5, 7]",
-        "3643": "[3, 4, 0, 6, 5, 1, 2, 7]",
-        "3644": "[4, 0, 1, 2, 3, 5, 6, 7]",
-        "3645": "[5, 2, 0, 4, 6, 3, 1, 7]",
-        "3646": "[6, 0, 1, 2, 3, 5, 4, 7]",
-        "3647": "[0, 6, 3, 4, 5, 2, 1, 7]",
-        "3648": "[1, 0, 4, 5, 6, 3, 2, 7]",
-        "3649": "[2, 1, 5, 6, 0, 4, 3, 7]",
-        "3650": "[3, 0, 2, 6, 4, 5, 1, 7]",
-        "3651": "[4, 1, 6, 2, 0, 3, 5, 7]",
-        "3652": "[5, 0, 1, 4, 2, 6, 3, 7]",
-        "3653": "[6, 1, 4, 2, 0, 3, 5, 7]",
-        "3654": "[0, 1, 4, 3, 2, 5, 6, 7]",
-        "3655": "[1, 2, 5, 4, 3, 6, 0, 7]",
-        "3656": "[2, 3, 6, 5, 4, 0, 1, 7]",
-        "3657": "[3, 1, 6, 2, 5, 4, 0, 7]",
-        "3658": "[4, 5, 2, 6, 3, 0, 1, 7]",
-        "3659": "[5, 3, 4, 1, 6, 2, 0, 7]",
-        "3660": "[6, 5, 2, 4, 3, 0, 1, 7]",
-        "3661": "[0, 2, 1, 5, 3, 4, 6, 7]",
-        "3662": "[1, 3, 2, 6, 4, 5, 0, 7]",
-        "3663": "[2, 4, 3, 0, 5, 6, 1, 7]",
-        "3664": "[3, 5, 1, 4, 2, 6, 0, 7]",
-        "3665": "[4, 3, 5, 0, 6, 2, 1, 7]",
-        "3666": "[5, 6, 3, 2, 1, 4, 0, 7]",
-        "3667": "[6, 3, 5, 0, 4, 2, 1, 7]",
-        "3668": "[0, 3, 2, 5, 1, 6, 4, 7]",
-        "3669": "[1, 4, 3, 6, 2, 0, 5, 7]",
-        "3670": "[2, 5, 4, 0, 3, 1, 6, 7]",
-        "3671": "[3, 2, 5, 4, 1, 0, 6, 7]",
-        "3672": "[4, 6, 3, 0, 5, 1, 2, 7]",
-        "3673": "[5, 1, 6, 2, 3, 0, 4, 7]",
-        "3674": "[6, 4, 3, 0, 5, 1, 2, 7]",
-        "3675": "[0, 4, 2, 3, 1, 6, 5, 7]",
-        "3676": "[1, 5, 3, 4, 2, 0, 6, 7]",
-        "3677": "[2, 6, 4, 5, 3, 1, 0, 7]",
-        "3678": "[3, 6, 5, 2, 1, 0, 4, 7]",
-        "3679": "[4, 2, 3, 6, 5, 1, 0, 7]",
-        "3680": "[5, 4, 6, 1, 3, 0, 2, 7]",
-        "3681": "[6, 2, 3, 4, 5, 1, 0, 7]",
-        "3682": "[0, 5, 1, 6, 3, 4, 2, 7]",
-        "3683": "[1, 6, 2, 0, 4, 5, 3, 7]",
-        "3684": "[2, 0, 3, 1, 5, 6, 4, 7]",
-        "3685": "[3, 4, 1, 0, 2, 6, 5, 7]",
-        "3686": "[4, 0, 5, 1, 6, 2, 3, 7]",
-        "3687": "[5, 2, 3, 0, 1, 4, 6, 7]",
-        "3688": "[6, 0, 5, 1, 4, 2, 3, 7]",
-        "3689": "[0, 6, 2, 3, 1, 4, 5, 7]",
-        "3690": "[1, 0, 3, 4, 2, 5, 6, 7]",
-        "3691": "[2, 1, 4, 5, 3, 6, 0, 7]",
-        "3692": "[3, 0, 5, 2, 1, 6, 4, 7]",
-        "3693": "[4, 1, 3, 6, 5, 2, 0, 7]",
-        "3694": "[5, 0, 6, 1, 3, 4, 2, 7]",
-        "3695": "[6, 1, 3, 4, 5, 2, 0, 7]",
-        "3696": "[0, 1, 5, 3, 2, 6, 4, 7]",
-        "3697": "[1, 2, 6, 4, 3, 0, 5, 7]",
-        "3698": "[2, 3, 0, 5, 4, 1, 6, 7]",
-        "3699": "[3, 1, 4, 2, 5, 0, 6, 7]",
-        "3700": "[4, 5, 0, 6, 3, 1, 2, 7]",
-        "3701": "[5, 3, 2, 1, 6, 0, 4, 7]",
-        "3702": "[6, 5, 0, 4, 3, 1, 2, 7]",
-        "3703": "[0, 2, 4, 5, 3, 6, 1, 7]",
-        "3704": "[1, 3, 5, 6, 4, 0, 2, 7]",
-        "3705": "[2, 4, 6, 0, 5, 1, 3, 7]",
-        "3706": "[3, 5, 6, 4, 2, 0, 1, 7]",
-        "3707": "[4, 3, 2, 0, 6, 1, 5, 7]",
-        "3708": "[5, 6, 4, 2, 1, 0, 3, 7]",
-        "3709": "[6, 3, 2, 0, 4, 1, 5, 7]",
-        "3710": "[0, 3, 6, 5, 1, 4, 2, 7]",
-        "3711": "[1, 4, 0, 6, 2, 5, 3, 7]",
-        "3712": "[2, 5, 1, 0, 3, 6, 4, 7]",
-        "3713": "[3, 2, 0, 4, 1, 6, 5, 7]",
-        "3714": "[4, 6, 1, 0, 5, 2, 3, 7]",
-        "3715": "[5, 1, 0, 2, 3, 4, 6, 7]",
-        "3716": "[6, 4, 1, 0, 5, 2, 3, 7]",
-        "3717": "[0, 4, 6, 3, 1, 5, 2, 7]",
-        "3718": "[1, 5, 0, 4, 2, 6, 3, 7]",
-        "3719": "[2, 6, 1, 5, 3, 0, 4, 7]",
-        "3720": "[3, 6, 0, 2, 1, 4, 5, 7]",
-        "3721": "[4, 2, 1, 6, 5, 0, 3, 7]",
-        "3722": "[5, 4, 0, 1, 3, 2, 6, 7]",
-        "3723": "[6, 2, 1, 4, 5, 0, 3, 7]",
-        "3724": "[0, 5, 4, 6, 3, 2, 1, 7]",
-        "3725": "[1, 6, 5, 0, 4, 3, 2, 7]",
-        "3726": "[2, 0, 6, 1, 5, 4, 3, 7]",
-        "3727": "[3, 4, 6, 0, 2, 5, 1, 7]",
-        "3728": "[4, 0, 2, 1, 6, 3, 5, 7]",
-        "3729": "[5, 2, 4, 0, 1, 6, 3, 7]",
-        "3730": "[6, 0, 2, 1, 4, 3, 5, 7]",
-        "3731": "[0, 6, 4, 3, 1, 5, 2, 7]",
-        "3732": "[1, 0, 5, 4, 2, 6, 3, 7]",
-        "3733": "[2, 1, 6, 5, 3, 0, 4, 7]",
-        "3734": "[3, 0, 6, 2, 1, 4, 5, 7]",
-        "3735": "[4, 1, 2, 6, 5, 0, 3, 7]",
-        "3736": "[5, 0, 4, 1, 3, 2, 6, 7]",
-        "3737": "[6, 1, 2, 4, 5, 0, 3, 7]",
-        "3738": "[0, 1, 6, 3, 2, 5, 4, 7]",
-        "3739": "[1, 2, 0, 4, 3, 6, 5, 7]",
-        "3740": "[2, 3, 1, 5, 4, 0, 6, 7]",
-        "3741": "[3, 1, 0, 2, 5, 4, 6, 7]",
-        "3742": "[4, 5, 1, 6, 3, 0, 2, 7]",
-        "3743": "[5, 3, 0, 1, 6, 2, 4, 7]",
-        "3744": "[6, 5, 1, 4, 3, 0, 2, 7]",
-        "3745": "[0, 2, 6, 5, 3, 4, 1, 7]",
-        "3746": "[1, 3, 0, 6, 4, 5, 2, 7]",
-        "3747": "[2, 4, 1, 0, 5, 6, 3, 7]",
-        "3748": "[3, 5, 0, 4, 2, 6, 1, 7]",
-        "3749": "[4, 3, 1, 0, 6, 2, 5, 7]",
-        "3750": "[5, 6, 0, 2, 1, 4, 3, 7]",
-        "3751": "[6, 3, 1, 0, 4, 2, 5, 7]",
-        "3752": "[0, 3, 4, 5, 1, 6, 2, 7]",
-        "3753": "[1, 4, 5, 6, 2, 0, 3, 7]",
-        "3754": "[2, 5, 6, 0, 3, 1, 4, 7]",
-        "3755": "[3, 2, 6, 4, 1, 0, 5, 7]",
-        "3756": "[4, 6, 2, 0, 5, 1, 3, 7]",
-        "3757": "[5, 1, 4, 2, 3, 0, 6, 7]",
-        "3758": "[6, 4, 2, 0, 5, 1, 3, 7]",
-        "3759": "[0, 4, 5, 3, 1, 6, 2, 7]",
-        "3760": "[1, 5, 6, 4, 2, 0, 3, 7]",
-        "3761": "[2, 6, 0, 5, 3, 1, 4, 7]",
-        "3762": "[3, 6, 4, 2, 1, 0, 5, 7]",
-        "3763": "[4, 2, 0, 6, 5, 1, 3, 7]",
-        "3764": "[5, 4, 2, 1, 3, 0, 6, 7]",
-        "3765": "[6, 2, 0, 4, 5, 1, 3, 7]",
-        "3766": "[0, 5, 2, 6, 3, 4, 1, 7]",
-        "3767": "[1, 6, 3, 0, 4, 5, 2, 7]",
-        "3768": "[2, 0, 4, 1, 5, 6, 3, 7]",
-        "3769": "[3, 4, 5, 0, 2, 6, 1, 7]",
-        "3770": "[4, 0, 3, 1, 6, 2, 5, 7]",
-        "3771": "[5, 2, 6, 0, 1, 4, 3, 7]",
-        "3772": "[6, 0, 3, 1, 4, 2, 5, 7]",
-        "3773": "[0, 6, 5, 3, 1, 4, 2, 7]",
-        "3774": "[1, 0, 6, 4, 2, 5, 3, 7]",
-        "3775": "[2, 1, 0, 5, 3, 6, 4, 7]",
-        "3776": "[3, 0, 4, 2, 1, 6, 5, 7]",
-        "3777": "[4, 1, 0, 6, 5, 2, 3, 7]",
-        "3778": "[5, 0, 2, 1, 3, 4, 6, 7]",
-        "3779": "[6, 1, 0, 4, 5, 2, 3, 7]",
-        "3780": "[0, 1, 2, 5, 6, 4, 3, 7]",
-        "3781": "[1, 2, 3, 6, 0, 5, 4, 7]",
-        "3782": "[2, 3, 4, 0, 1, 6, 5, 7]",
-        "3783": "[3, 1, 5, 4, 0, 6, 2, 7]",
-        "3784": "[4, 5, 3, 0, 1, 2, 6, 7]",
-        "3785": "[5, 3, 6, 2, 0, 4, 1, 7]",
-        "3786": "[6, 5, 3, 0, 1, 2, 4, 7]",
-        "3787": "[0, 2, 3, 4, 6, 1, 5, 7]",
-        "3788": "[1, 3, 4, 5, 0, 2, 6, 7]",
-        "3789": "[2, 4, 5, 6, 1, 3, 0, 7]",
-        "3790": "[3, 5, 2, 6, 0, 1, 4, 7]",
-        "3791": "[4, 3, 6, 2, 1, 5, 0, 7]",
-        "3792": "[5, 6, 1, 4, 0, 3, 2, 7]",
-        "3793": "[6, 3, 4, 2, 1, 5, 0, 7]",
-        "3794": "[0, 3, 1, 6, 4, 2, 5, 7]",
-        "3795": "[1, 4, 2, 0, 5, 3, 6, 7]",
-        "3796": "[2, 5, 3, 1, 6, 4, 0, 7]",
-        "3797": "[3, 2, 1, 0, 6, 5, 4, 7]",
-        "3798": "[4, 6, 5, 1, 2, 3, 0, 7]",
-        "3799": "[5, 1, 3, 0, 4, 6, 2, 7]",
-        "3800": "[6, 4, 5, 1, 2, 3, 0, 7]",
-        "3801": "[0, 4, 1, 6, 5, 2, 3, 7]",
-        "3802": "[1, 5, 2, 0, 6, 3, 4, 7]",
-        "3803": "[2, 6, 3, 1, 0, 4, 5, 7]",
-        "3804": "[3, 6, 1, 0, 4, 5, 2, 7]",
-        "3805": "[4, 2, 5, 1, 0, 3, 6, 7]",
-        "3806": "[5, 4, 3, 0, 2, 6, 1, 7]",
-        "3807": "[6, 2, 5, 1, 0, 3, 4, 7]",
-        "3808": "[0, 5, 3, 4, 2, 1, 6, 7]",
-        "3809": "[1, 6, 4, 5, 3, 2, 0, 7]",
-        "3810": "[2, 0, 5, 6, 4, 3, 1, 7]",
-        "3811": "[3, 4, 2, 6, 5, 1, 0, 7]",
-        "3812": "[4, 0, 6, 2, 3, 5, 1, 7]",
-        "3813": "[5, 2, 1, 4, 6, 3, 0, 7]",
-        "3814": "[6, 0, 4, 2, 3, 5, 1, 7]",
-        "3815": "[0, 6, 1, 4, 5, 2, 3, 7]",
-        "3816": "[1, 0, 2, 5, 6, 3, 4, 7]",
-        "3817": "[2, 1, 3, 6, 0, 4, 5, 7]",
-        "3818": "[3, 0, 1, 6, 4, 5, 2, 7]",
-        "3819": "[4, 1, 5, 2, 0, 3, 6, 7]",
-        "3820": "[5, 0, 3, 4, 2, 6, 1, 7]",
-        "3821": "[6, 1, 5, 2, 0, 3, 4, 7]",
-        "3822": "[0, 1, 3, 2, 6, 5, 4, 7]",
-        "3823": "[1, 2, 4, 3, 0, 6, 5, 7]",
-        "3824": "[2, 3, 5, 4, 1, 0, 6, 7]",
-        "3825": "[3, 1, 2, 5, 0, 4, 6, 7]",
-        "3826": "[4, 5, 6, 3, 1, 0, 2, 7]",
-        "3827": "[5, 3, 1, 6, 0, 2, 4, 7]",
-        "3828": "[6, 5, 4, 3, 1, 0, 2, 7]",
-        "3829": "[0, 2, 5, 3, 6, 4, 1, 7]",
-        "3830": "[1, 3, 6, 4, 0, 5, 2, 7]",
-        "3831": "[2, 4, 0, 5, 1, 6, 3, 7]",
-        "3832": "[3, 5, 4, 2, 0, 6, 1, 7]",
-        "3833": "[4, 3, 0, 6, 1, 2, 5, 7]",
-        "3834": "[5, 6, 2, 1, 0, 4, 3, 7]",
-        "3835": "[6, 3, 0, 4, 1, 2, 5, 7]",
-        "3836": "[0, 3, 5, 1, 4, 6, 2, 7]",
-        "3837": "[1, 4, 6, 2, 5, 0, 3, 7]",
-        "3838": "[2, 5, 0, 3, 6, 1, 4, 7]",
-        "3839": "[3, 2, 4, 1, 6, 0, 5, 7]",
-        "3840": "[4, 6, 0, 5, 2, 1, 3, 7]",
-        "3841": "[5, 1, 2, 3, 4, 0, 6, 7]",
-        "3842": "[6, 4, 0, 5, 2, 1, 3, 7]",
-        "3843": "[0, 4, 3, 1, 5, 6, 2, 7]",
-        "3844": "[1, 5, 4, 2, 6, 0, 3, 7]",
-        "3845": "[2, 6, 5, 3, 0, 1, 4, 7]",
-        "3846": "[3, 6, 2, 1, 4, 0, 5, 7]",
-        "3847": "[4, 2, 6, 5, 0, 1, 3, 7]",
-        "3848": "[5, 4, 1, 3, 2, 0, 6, 7]",
-        "3849": "[6, 2, 4, 5, 0, 1, 3, 7]",
-        "3850": "[0, 5, 6, 3, 2, 4, 1, 7]",
-        "3851": "[1, 6, 0, 4, 3, 5, 2, 7]",
-        "3852": "[2, 0, 1, 5, 4, 6, 3, 7]",
-        "3853": "[3, 4, 0, 2, 5, 6, 1, 7]",
-        "3854": "[4, 0, 1, 6, 3, 2, 5, 7]",
-        "3855": "[5, 2, 0, 1, 6, 4, 3, 7]",
-        "3856": "[6, 0, 1, 4, 3, 2, 5, 7]",
-        "3857": "[0, 6, 3, 1, 5, 4, 2, 7]",
-        "3858": "[1, 0, 4, 2, 6, 5, 3, 7]",
-        "3859": "[2, 1, 5, 3, 0, 6, 4, 7]",
-        "3860": "[3, 0, 2, 1, 4, 6, 5, 7]",
-        "3861": "[4, 1, 6, 5, 0, 2, 3, 7]",
-        "3862": "[5, 0, 1, 3, 2, 4, 6, 7]",
-        "3863": "[6, 1, 4, 5, 0, 2, 3, 7]",
-        "3864": "[0, 1, 4, 6, 2, 3, 5, 7]",
-        "3865": "[1, 2, 5, 0, 3, 4, 6, 7]",
-        "3866": "[2, 3, 6, 1, 4, 5, 0, 7]",
-        "3867": "[3, 1, 6, 0, 5, 2, 4, 7]",
-        "3868": "[4, 5, 2, 1, 3, 6, 0, 7]",
-        "3869": "[5, 3, 4, 0, 6, 1, 2, 7]",
-        "3870": "[6, 5, 2, 1, 3, 4, 0, 7]",
-        "3871": "[0, 2, 1, 6, 3, 5, 4, 7]",
-        "3872": "[1, 3, 2, 0, 4, 6, 5, 7]",
-        "3873": "[2, 4, 3, 1, 5, 0, 6, 7]",
-        "3874": "[3, 5, 1, 0, 2, 4, 6, 7]",
-        "3875": "[4, 3, 5, 1, 6, 0, 2, 7]",
-        "3876": "[5, 6, 3, 0, 1, 2, 4, 7]",
-        "3877": "[6, 3, 5, 1, 4, 0, 2, 7]",
-        "3878": "[0, 3, 2, 4, 1, 5, 6, 7]",
-        "3879": "[1, 4, 3, 5, 2, 6, 0, 7]",
-        "3880": "[2, 5, 4, 6, 3, 0, 1, 7]",
-        "3881": "[3, 2, 5, 6, 1, 4, 0, 7]",
-        "3882": "[4, 6, 3, 2, 5, 0, 1, 7]",
-        "3883": "[5, 1, 6, 4, 3, 2, 0, 7]",
-        "3884": "[6, 4, 3, 2, 5, 0, 1, 7]",
-        "3885": "[0, 4, 2, 5, 1, 3, 6, 7]",
-        "3886": "[1, 5, 3, 6, 2, 4, 0, 7]",
-        "3887": "[2, 6, 4, 0, 3, 5, 1, 7]",
-        "3888": "[3, 6, 5, 4, 1, 2, 0, 7]",
-        "3889": "[4, 2, 3, 0, 5, 6, 1, 7]",
-        "3890": "[5, 4, 6, 2, 3, 1, 0, 7]",
-        "3891": "[6, 2, 3, 0, 5, 4, 1, 7]",
-        "3892": "[0, 5, 1, 2, 3, 6, 4, 7]",
-        "3893": "[1, 6, 2, 3, 4, 0, 5, 7]",
-        "3894": "[2, 0, 3, 4, 5, 1, 6, 7]",
-        "3895": "[3, 4, 1, 5, 2, 0, 6, 7]",
-        "3896": "[4, 0, 5, 3, 6, 1, 2, 7]",
-        "3897": "[5, 2, 3, 6, 1, 0, 4, 7]",
-        "3898": "[6, 0, 5, 3, 4, 1, 2, 7]",
-        "3899": "[0, 6, 2, 5, 1, 3, 4, 7]",
-        "3900": "[1, 0, 3, 6, 2, 4, 5, 7]",
-        "3901": "[2, 1, 4, 0, 3, 5, 6, 7]",
-        "3902": "[3, 0, 5, 4, 1, 2, 6, 7]",
-        "3903": "[4, 1, 3, 0, 5, 6, 2, 7]",
-        "3904": "[5, 0, 6, 2, 3, 1, 4, 7]",
-        "3905": "[6, 1, 3, 0, 5, 4, 2, 7]",
-        "3906": "[0, 1, 5, 4, 2, 3, 6, 7]",
-        "3907": "[1, 2, 6, 5, 3, 4, 0, 7]",
-        "3908": "[2, 3, 0, 6, 4, 5, 1, 7]",
-        "3909": "[3, 1, 4, 6, 5, 2, 0, 7]",
-        "3910": "[4, 5, 0, 2, 3, 6, 1, 7]",
-        "3911": "[5, 3, 2, 4, 6, 1, 0, 7]",
-        "3912": "[6, 5, 0, 2, 3, 4, 1, 7]",
-        "3913": "[0, 2, 4, 1, 3, 5, 6, 7]",
-        "3914": "[1, 3, 5, 2, 4, 6, 0, 7]",
-        "3915": "[2, 4, 6, 3, 5, 0, 1, 7]",
-        "3916": "[3, 5, 6, 1, 2, 4, 0, 7]",
-        "3917": "[4, 3, 2, 5, 6, 0, 1, 7]",
-        "3918": "[5, 6, 4, 3, 1, 2, 0, 7]",
-        "3919": "[6, 3, 2, 5, 4, 0, 1, 7]",
-        "3920": "[0, 3, 6, 2, 1, 5, 4, 7]",
-        "3921": "[1, 4, 0, 3, 2, 6, 5, 7]",
-        "3922": "[2, 5, 1, 4, 3, 0, 6, 7]",
-        "3923": "[3, 2, 0, 5, 1, 4, 6, 7]",
-        "3924": "[4, 6, 1, 3, 5, 0, 2, 7]",
-        "3925": "[5, 1, 0, 6, 3, 2, 4, 7]",
-        "3926": "[6, 4, 1, 3, 5, 0, 2, 7]",
-        "3927": "[0, 4, 6, 2, 1, 3, 5, 7]",
-        "3928": "[1, 5, 0, 3, 2, 4, 6, 7]",
-        "3929": "[2, 6, 1, 4, 3, 5, 0, 7]",
-        "3930": "[3, 6, 0, 5, 1, 2, 4, 7]",
-        "3931": "[4, 2, 1, 3, 5, 6, 0, 7]",
-        "3932": "[5, 4, 0, 6, 3, 1, 2, 7]",
-        "3933": "[6, 2, 1, 3, 5, 4, 0, 7]",
-        "3934": "[0, 5, 4, 1, 3, 6, 2, 7]",
-        "3935": "[1, 6, 5, 2, 4, 0, 3, 7]",
-        "3936": "[2, 0, 6, 3, 5, 1, 4, 7]",
-        "3937": "[3, 4, 6, 1, 2, 0, 5, 7]",
-        "3938": "[4, 0, 2, 5, 6, 1, 3, 7]",
-        "3939": "[5, 2, 4, 3, 1, 0, 6, 7]",
-        "3940": "[6, 0, 2, 5, 4, 1, 3, 7]",
-        "3941": "[0, 6, 4, 2, 1, 3, 5, 7]",
-        "3942": "[1, 0, 5, 3, 2, 4, 6, 7]",
-        "3943": "[2, 1, 6, 4, 3, 5, 0, 7]",
-        "3944": "[3, 0, 6, 5, 1, 2, 4, 7]",
-        "3945": "[4, 1, 2, 3, 5, 6, 0, 7]",
-        "3946": "[5, 0, 4, 6, 3, 1, 2, 7]",
-        "3947": "[6, 1, 2, 3, 5, 4, 0, 7]",
-        "3948": "[0, 1, 6, 4, 2, 3, 5, 7]",
-        "3949": "[1, 2, 0, 5, 3, 4, 6, 7]",
-        "3950": "[2, 3, 1, 6, 4, 5, 0, 7]",
-        "3951": "[3, 1, 0, 6, 5, 2, 4, 7]",
-        "3952": "[4, 5, 1, 2, 3, 6, 0, 7]",
-        "3953": "[5, 3, 0, 4, 6, 1, 2, 7]",
-        "3954": "[6, 5, 1, 2, 3, 4, 0, 7]",
-        "3955": "[0, 2, 6, 1, 3, 5, 4, 7]",
-        "3956": "[1, 3, 0, 2, 4, 6, 5, 7]",
-        "3957": "[2, 4, 1, 3, 5, 0, 6, 7]",
-        "3958": "[3, 5, 0, 1, 2, 4, 6, 7]",
-        "3959": "[4, 3, 1, 5, 6, 0, 2, 7]",
-        "3960": "[5, 6, 0, 3, 1, 2, 4, 7]",
-        "3961": "[6, 3, 1, 5, 4, 0, 2, 7]",
-        "3962": "[0, 3, 4, 2, 1, 5, 6, 7]",
-        "3963": "[1, 4, 5, 3, 2, 6, 0, 7]",
-        "3964": "[2, 5, 6, 4, 3, 0, 1, 7]",
-        "3965": "[3, 2, 6, 5, 1, 4, 0, 7]",
-        "3966": "[4, 6, 2, 3, 5, 0, 1, 7]",
-        "3967": "[5, 1, 4, 6, 3, 2, 0, 7]",
-        "3968": "[6, 4, 2, 3, 5, 0, 1, 7]",
-        "3969": "[0, 4, 5, 2, 1, 3, 6, 7]",
-        "3970": "[1, 5, 6, 3, 2, 4, 0, 7]",
-        "3971": "[2, 6, 0, 4, 3, 5, 1, 7]",
-        "3972": "[3, 6, 4, 5, 1, 2, 0, 7]",
-        "3973": "[4, 2, 0, 3, 5, 6, 1, 7]",
-        "3974": "[5, 4, 2, 6, 3, 1, 0, 7]",
-        "3975": "[6, 2, 0, 3, 5, 4, 1, 7]",
-        "3976": "[0, 5, 2, 1, 3, 6, 4, 7]",
-        "3977": "[1, 6, 3, 2, 4, 0, 5, 7]",
-        "3978": "[2, 0, 4, 3, 5, 1, 6, 7]",
-        "3979": "[3, 4, 5, 1, 2, 0, 6, 7]",
-        "3980": "[4, 0, 3, 5, 6, 1, 2, 7]",
-        "3981": "[5, 2, 6, 3, 1, 0, 4, 7]",
-        "3982": "[6, 0, 3, 5, 4, 1, 2, 7]",
-        "3983": "[0, 6, 5, 2, 1, 3, 4, 7]",
-        "3984": "[1, 0, 6, 3, 2, 4, 5, 7]",
-        "3985": "[2, 1, 0, 4, 3, 5, 6, 7]",
-        "3986": "[3, 0, 4, 5, 1, 2, 6, 7]",
-        "3987": "[4, 1, 0, 3, 5, 6, 2, 7]",
-        "3988": "[5, 0, 2, 6, 3, 1, 4, 7]",
-        "3989": "[6, 1, 0, 3, 5, 4, 2, 7]",
-        "3990": "[0, 1, 2, 6, 4, 3, 5, 7]",
-        "3991": "[1, 2, 3, 0, 5, 4, 6, 7]",
-        "3992": "[2, 3, 4, 1, 6, 5, 0, 7]",
-        "3993": "[3, 1, 5, 0, 6, 2, 4, 7]",
-        "3994": "[4, 5, 3, 1, 2, 6, 0, 7]",
-        "3995": "[5, 3, 6, 0, 4, 1, 2, 7]",
-        "3996": "[6, 5, 3, 1, 2, 4, 0, 7]",
-        "3997": "[0, 2, 3, 6, 1, 5, 4, 7]",
-        "3998": "[1, 3, 4, 0, 2, 6, 5, 7]",
-        "3999": "[2, 4, 5, 1, 3, 0, 6, 7]",
-        "4000": "[3, 5, 2, 0, 1, 4, 6, 7]",
-        "4001": "[4, 3, 6, 1, 5, 0, 2, 7]",
-        "4002": "[5, 6, 1, 0, 3, 2, 4, 7]",
-        "4003": "[6, 3, 4, 1, 5, 0, 2, 7]",
-        "4004": "[0, 3, 1, 4, 2, 5, 6, 7]",
-        "4005": "[1, 4, 2, 5, 3, 6, 0, 7]",
-        "4006": "[2, 5, 3, 6, 4, 0, 1, 7]",
-        "4007": "[3, 2, 1, 6, 5, 4, 0, 7]",
-        "4008": "[4, 6, 5, 2, 3, 0, 1, 7]",
-        "4009": "[5, 1, 3, 4, 6, 2, 0, 7]",
-        "4010": "[6, 4, 5, 2, 3, 0, 1, 7]",
-        "4011": "[0, 4, 1, 5, 2, 3, 6, 7]",
-        "4012": "[1, 5, 2, 6, 3, 4, 0, 7]",
-        "4013": "[2, 6, 3, 0, 4, 5, 1, 7]",
-        "4014": "[3, 6, 1, 4, 5, 2, 0, 7]",
-        "4015": "[4, 2, 5, 0, 3, 6, 1, 7]",
-        "4016": "[5, 4, 3, 2, 6, 1, 0, 7]",
-        "4017": "[6, 2, 5, 0, 3, 4, 1, 7]",
-        "4018": "[0, 5, 3, 2, 1, 6, 4, 7]",
-        "4019": "[1, 6, 4, 3, 2, 0, 5, 7]",
-        "4020": "[2, 0, 5, 4, 3, 1, 6, 7]",
-        "4021": "[3, 4, 2, 5, 1, 0, 6, 7]",
-        "4022": "[4, 0, 6, 3, 5, 1, 2, 7]",
-        "4023": "[5, 2, 1, 6, 3, 0, 4, 7]",
-        "4024": "[6, 0, 4, 3, 5, 1, 2, 7]",
-        "4025": "[0, 6, 1, 5, 2, 3, 4, 7]",
-        "4026": "[1, 0, 2, 6, 3, 4, 5, 7]",
-        "4027": "[2, 1, 3, 0, 4, 5, 6, 7]",
-        "4028": "[3, 0, 1, 4, 5, 2, 6, 7]",
-        "4029": "[4, 1, 5, 0, 3, 6, 2, 7]",
-        "4030": "[5, 0, 3, 2, 6, 1, 4, 7]",
-        "4031": "[6, 1, 5, 0, 3, 4, 2, 7]",
-        "4032": "[0, 1, 3, 6, 5, 4, 2, 7]",
-        "4033": "[1, 2, 4, 0, 6, 5, 3, 7]",
-        "4034": "[2, 3, 5, 1, 0, 6, 4, 7]",
-        "4035": "[3, 1, 2, 0, 4, 6, 5, 7]",
-        "4036": "[4, 5, 6, 1, 0, 2, 3, 7]",
-        "4037": "[5, 3, 1, 0, 2, 4, 6, 7]",
-        "4038": "[6, 5, 4, 1, 0, 2, 3, 7]",
-        "4039": "[0, 2, 5, 6, 4, 1, 3, 7]",
-        "4040": "[1, 3, 6, 0, 5, 2, 4, 7]",
-        "4041": "[2, 4, 0, 1, 6, 3, 5, 7]",
-        "4042": "[3, 5, 4, 0, 6, 1, 2, 7]",
-        "4043": "[4, 3, 0, 1, 2, 5, 6, 7]",
-        "4044": "[5, 6, 2, 0, 4, 3, 1, 7]",
-        "4045": "[6, 3, 0, 1, 2, 5, 4, 7]",
-        "4046": "[0, 3, 5, 4, 6, 2, 1, 7]",
-        "4047": "[1, 4, 6, 5, 0, 3, 2, 7]",
-        "4048": "[2, 5, 0, 6, 1, 4, 3, 7]",
-        "4049": "[3, 2, 4, 6, 0, 5, 1, 7]",
-        "4050": "[4, 6, 0, 2, 1, 3, 5, 7]",
-        "4051": "[5, 1, 2, 4, 0, 6, 3, 7]",
-        "4052": "[6, 4, 0, 2, 1, 3, 5, 7]",
-        "4053": "[0, 4, 3, 5, 6, 2, 1, 7]",
-        "4054": "[1, 5, 4, 6, 0, 3, 2, 7]",
-        "4055": "[2, 6, 5, 0, 1, 4, 3, 7]",
-        "4056": "[3, 6, 2, 4, 0, 5, 1, 7]",
-        "4057": "[4, 2, 6, 0, 1, 3, 5, 7]",
-        "4058": "[5, 4, 1, 2, 0, 6, 3, 7]",
-        "4059": "[6, 2, 4, 0, 1, 3, 5, 7]",
-        "4060": "[0, 5, 6, 2, 4, 1, 3, 7]",
-        "4061": "[1, 6, 0, 3, 5, 2, 4, 7]",
-        "4062": "[2, 0, 1, 4, 6, 3, 5, 7]",
-        "4063": "[3, 4, 0, 5, 6, 1, 2, 7]",
-        "4064": "[4, 0, 1, 3, 2, 5, 6, 7]",
-        "4065": "[5, 2, 0, 6, 4, 3, 1, 7]",
-        "4066": "[6, 0, 1, 3, 2, 5, 4, 7]",
-        "4067": "[0, 6, 3, 5, 4, 2, 1, 7]",
-        "4068": "[1, 0, 4, 6, 5, 3, 2, 7]",
-        "4069": "[2, 1, 5, 0, 6, 4, 3, 7]",
-        "4070": "[3, 0, 2, 4, 6, 5, 1, 7]",
-        "4071": "[4, 1, 6, 0, 2, 3, 5, 7]",
-        "4072": "[5, 0, 1, 2, 4, 6, 3, 7]",
-        "4073": "[6, 1, 4, 0, 2, 3, 5, 7]",
-        "4074": "[0, 1, 4, 2, 3, 5, 6, 7]",
-        "4075": "[1, 2, 5, 3, 4, 6, 0, 7]",
-        "4076": "[2, 3, 6, 4, 5, 0, 1, 7]",
-        "4077": "[3, 1, 6, 5, 2, 4, 0, 7]",
-        "4078": "[4, 5, 2, 3, 6, 0, 1, 7]",
-        "4079": "[5, 3, 4, 6, 1, 2, 0, 7]",
-        "4080": "[6, 5, 2, 3, 4, 0, 1, 7]",
-        "4081": "[0, 2, 1, 3, 5, 4, 6, 7]",
-        "4082": "[1, 3, 2, 4, 6, 5, 0, 7]",
-        "4083": "[2, 4, 3, 5, 0, 6, 1, 7]",
-        "4084": "[3, 5, 1, 2, 4, 6, 0, 7]",
-        "4085": "[4, 3, 5, 6, 0, 2, 1, 7]",
-        "4086": "[5, 6, 3, 1, 2, 4, 0, 7]",
-        "4087": "[6, 3, 5, 4, 0, 2, 1, 7]",
-        "4088": "[0, 3, 2, 1, 5, 6, 4, 7]",
-        "4089": "[1, 4, 3, 2, 6, 0, 5, 7]",
-        "4090": "[2, 5, 4, 3, 0, 1, 6, 7]",
-        "4091": "[3, 2, 5, 1, 4, 0, 6, 7]",
-        "4092": "[4, 6, 3, 5, 0, 1, 2, 7]",
-        "4093": "[5, 1, 6, 3, 2, 0, 4, 7]",
-        "4094": "[6, 4, 3, 5, 0, 1, 2, 7]",
-        "4095": "[0, 4, 2, 1, 3, 6, 5, 7]",
-        "4096": "[1, 5, 3, 2, 4, 0, 6, 7]",
-        "4097": "[2, 6, 4, 3, 5, 1, 0, 7]",
-        "4098": "[3, 6, 5, 1, 2, 0, 4, 7]",
-        "4099": "[4, 2, 3, 5, 6, 1, 0, 7]",
-        "4100": "[5, 4, 6, 3, 1, 0, 2, 7]",
-        "4101": "[6, 2, 3, 5, 4, 1, 0, 7]",
-        "4102": "[0, 5, 1, 3, 6, 4, 2, 7]",
-        "4103": "[1, 6, 2, 4, 0, 5, 3, 7]",
-        "4104": "[2, 0, 3, 5, 1, 6, 4, 7]",
-        "4105": "[3, 4, 1, 2, 0, 6, 5, 7]",
-        "4106": "[4, 0, 5, 6, 1, 2, 3, 7]",
-        "4107": "[5, 2, 3, 1, 0, 4, 6, 7]",
-        "4108": "[6, 0, 5, 4, 1, 2, 3, 7]",
-        "4109": "[0, 6, 2, 1, 3, 4, 5, 7]",
-        "4110": "[1, 0, 3, 2, 4, 5, 6, 7]",
-        "4111": "[2, 1, 4, 3, 5, 6, 0, 7]",
-        "4112": "[3, 0, 5, 1, 2, 6, 4, 7]",
-        "4113": "[4, 1, 3, 5, 6, 2, 0, 7]",
-        "4114": "[5, 0, 6, 3, 1, 4, 2, 7]",
-        "4115": "[6, 1, 3, 5, 4, 2, 0, 7]",
-        "4116": "[0, 1, 5, 2, 3, 6, 4, 7]",
-        "4117": "[1, 2, 6, 3, 4, 0, 5, 7]",
-        "4118": "[2, 3, 0, 4, 5, 1, 6, 7]",
-        "4119": "[3, 1, 4, 5, 2, 0, 6, 7]",
-        "4120": "[4, 5, 0, 3, 6, 1, 2, 7]",
-        "4121": "[5, 3, 2, 6, 1, 0, 4, 7]",
-        "4122": "[6, 5, 0, 3, 4, 1, 2, 7]",
-        "4123": "[0, 2, 4, 3, 5, 6, 1, 7]",
-        "4124": "[1, 3, 5, 4, 6, 0, 2, 7]",
-        "4125": "[2, 4, 6, 5, 0, 1, 3, 7]",
-        "4126": "[3, 5, 6, 2, 4, 0, 1, 7]",
-        "4127": "[4, 3, 2, 6, 0, 1, 5, 7]",
-        "4128": "[5, 6, 4, 1, 2, 0, 3, 7]",
-        "4129": "[6, 3, 2, 4, 0, 1, 5, 7]",
-        "4130": "[0, 3, 6, 1, 5, 4, 2, 7]",
-        "4131": "[1, 4, 0, 2, 6, 5, 3, 7]",
-        "4132": "[2, 5, 1, 3, 0, 6, 4, 7]",
-        "4133": "[3, 2, 0, 1, 4, 6, 5, 7]",
-        "4134": "[4, 6, 1, 5, 0, 2, 3, 7]",
-        "4135": "[5, 1, 0, 3, 2, 4, 6, 7]",
-        "4136": "[6, 4, 1, 5, 0, 2, 3, 7]",
-        "4137": "[0, 4, 6, 1, 3, 5, 2, 7]",
-        "4138": "[1, 5, 0, 2, 4, 6, 3, 7]",
-        "4139": "[2, 6, 1, 3, 5, 0, 4, 7]",
-        "4140": "[3, 6, 0, 1, 2, 4, 5, 7]",
-        "4141": "[4, 2, 1, 5, 6, 0, 3, 7]",
-        "4142": "[5, 4, 0, 3, 1, 2, 6, 7]",
-        "4143": "[6, 2, 1, 5, 4, 0, 3, 7]",
-        "4144": "[0, 5, 4, 3, 6, 2, 1, 7]",
-        "4145": "[1, 6, 5, 4, 0, 3, 2, 7]",
-        "4146": "[2, 0, 6, 5, 1, 4, 3, 7]",
-        "4147": "[3, 4, 6, 2, 0, 5, 1, 7]",
-        "4148": "[4, 0, 2, 6, 1, 3, 5, 7]",
-        "4149": "[5, 2, 4, 1, 0, 6, 3, 7]",
-        "4150": "[6, 0, 2, 4, 1, 3, 5, 7]",
-        "4151": "[0, 6, 4, 1, 3, 5, 2, 7]",
-        "4152": "[1, 0, 5, 2, 4, 6, 3, 7]",
-        "4153": "[2, 1, 6, 3, 5, 0, 4, 7]",
-        "4154": "[3, 0, 6, 1, 2, 4, 5, 7]",
-        "4155": "[4, 1, 2, 5, 6, 0, 3, 7]",
-        "4156": "[5, 0, 4, 3, 1, 2, 6, 7]",
-        "4157": "[6, 1, 2, 5, 4, 0, 3, 7]",
-        "4158": "[0, 1, 6, 2, 3, 5, 4, 7]",
-        "4159": "[1, 2, 0, 3, 4, 6, 5, 7]",
-        "4160": "[2, 3, 1, 4, 5, 0, 6, 7]",
-        "4161": "[3, 1, 0, 5, 2, 4, 6, 7]",
-        "4162": "[4, 5, 1, 3, 6, 0, 2, 7]",
-        "4163": "[5, 3, 0, 6, 1, 2, 4, 7]",
-        "4164": "[6, 5, 1, 3, 4, 0, 2, 7]",
-        "4165": "[0, 2, 6, 3, 5, 4, 1, 7]",
-        "4166": "[1, 3, 0, 4, 6, 5, 2, 7]",
-        "4167": "[2, 4, 1, 5, 0, 6, 3, 7]",
-        "4168": "[3, 5, 0, 2, 4, 6, 1, 7]",
-        "4169": "[4, 3, 1, 6, 0, 2, 5, 7]",
-        "4170": "[5, 6, 0, 1, 2, 4, 3, 7]",
-        "4171": "[6, 3, 1, 4, 0, 2, 5, 7]",
-        "4172": "[0, 3, 4, 1, 5, 6, 2, 7]",
-        "4173": "[1, 4, 5, 2, 6, 0, 3, 7]",
-        "4174": "[2, 5, 6, 3, 0, 1, 4, 7]",
-        "4175": "[3, 2, 6, 1, 4, 0, 5, 7]",
-        "4176": "[4, 6, 2, 5, 0, 1, 3, 7]",
-        "4177": "[5, 1, 4, 3, 2, 0, 6, 7]",
-        "4178": "[6, 4, 2, 5, 0, 1, 3, 7]",
-        "4179": "[0, 4, 5, 1, 3, 6, 2, 7]",
-        "4180": "[1, 5, 6, 2, 4, 0, 3, 7]",
-        "4181": "[2, 6, 0, 3, 5, 1, 4, 7]",
-        "4182": "[3, 6, 4, 1, 2, 0, 5, 7]",
-        "4183": "[4, 2, 0, 5, 6, 1, 3, 7]",
-        "4184": "[5, 4, 2, 3, 1, 0, 6, 7]",
-        "4185": "[6, 2, 0, 5, 4, 1, 3, 7]",
-        "4186": "[0, 5, 2, 3, 6, 4, 1, 7]",
-        "4187": "[1, 6, 3, 4, 0, 5, 2, 7]",
-        "4188": "[2, 0, 4, 5, 1, 6, 3, 7]",
-        "4189": "[3, 4, 5, 2, 0, 6, 1, 7]",
-        "4190": "[4, 0, 3, 6, 1, 2, 5, 7]",
-        "4191": "[5, 2, 6, 1, 0, 4, 3, 7]",
-        "4192": "[6, 0, 3, 4, 1, 2, 5, 7]",
-        "4193": "[0, 6, 5, 1, 3, 4, 2, 7]",
-        "4194": "[1, 0, 6, 2, 4, 5, 3, 7]",
-        "4195": "[2, 1, 0, 3, 5, 6, 4, 7]",
-        "4196": "[3, 0, 4, 1, 2, 6, 5, 7]",
-        "4197": "[4, 1, 0, 5, 6, 2, 3, 7]",
-        "4198": "[5, 0, 2, 3, 1, 4, 6, 7]",
-        "4199": "[6, 1, 0, 5, 4, 2, 3, 7]",
-        "4200": "[0, 1, 2, 3, 5, 6, 4, 7]",
-        "4201": "[1, 2, 3, 4, 6, 0, 5, 7]",
-        "4202": "[2, 3, 4, 5, 0, 1, 6, 7]",
-        "4203": "[3, 1, 5, 2, 4, 0, 6, 7]",
-        "4204": "[4, 5, 3, 6, 0, 1, 2, 7]",
-        "4205": "[5, 3, 6, 1, 2, 0, 4, 7]",
-        "4206": "[6, 5, 3, 4, 0, 1, 2, 7]",
-        "4207": "[0, 2, 3, 5, 4, 6, 1, 7]",
-        "4208": "[1, 3, 4, 6, 5, 0, 2, 7]",
-        "4209": "[2, 4, 5, 0, 6, 1, 3, 7]",
-        "4210": "[3, 5, 2, 4, 6, 0, 1, 7]",
-        "4211": "[4, 3, 6, 0, 2, 1, 5, 7]",
-        "4212": "[5, 6, 1, 2, 4, 0, 3, 7]",
-        "4213": "[6, 3, 4, 0, 2, 1, 5, 7]",
-        "4214": "[0, 3, 1, 5, 6, 4, 2, 7]",
-        "4215": "[1, 4, 2, 6, 0, 5, 3, 7]",
-        "4216": "[2, 5, 3, 0, 1, 6, 4, 7]",
-        "4217": "[3, 2, 1, 4, 0, 6, 5, 7]",
-        "4218": "[4, 6, 5, 0, 1, 2, 3, 7]",
-        "4219": "[5, 1, 3, 2, 0, 4, 6, 7]",
-        "4220": "[6, 4, 5, 0, 1, 2, 3, 7]",
-        "4221": "[0, 4, 1, 3, 6, 5, 2, 7]",
-        "4222": "[1, 5, 2, 4, 0, 6, 3, 7]",
-        "4223": "[2, 6, 3, 5, 1, 0, 4, 7]",
-        "4224": "[3, 6, 1, 2, 0, 4, 5, 7]",
-        "4225": "[4, 2, 5, 6, 1, 0, 3, 7]",
-        "4226": "[5, 4, 3, 1, 0, 2, 6, 7]",
-        "4227": "[6, 2, 5, 4, 1, 0, 3, 7]",
-        "4228": "[0, 5, 3, 6, 4, 2, 1, 7]",
-        "4229": "[1, 6, 4, 0, 5, 3, 2, 7]",
-        "4230": "[2, 0, 5, 1, 6, 4, 3, 7]",
-        "4231": "[3, 4, 2, 0, 6, 5, 1, 7]",
-        "4232": "[4, 0, 6, 1, 2, 3, 5, 7]",
-        "4233": "[5, 2, 1, 0, 4, 6, 3, 7]",
-        "4234": "[6, 0, 4, 1, 2, 3, 5, 7]",
-        "4235": "[0, 6, 1, 3, 4, 5, 2, 7]",
-        "4236": "[1, 0, 2, 4, 5, 6, 3, 7]",
-        "4237": "[2, 1, 3, 5, 6, 0, 4, 7]",
-        "4238": "[3, 0, 1, 2, 6, 4, 5, 7]",
-        "4239": "[4, 1, 5, 6, 2, 0, 3, 7]",
-        "4240": "[5, 0, 3, 1, 4, 2, 6, 7]",
-        "4241": "[6, 1, 5, 4, 2, 0, 3, 7]",
-        "4242": "[0, 1, 3, 4, 2, 6, 5, 7]",
-        "4243": "[1, 2, 4, 5, 3, 0, 6, 7]",
-        "4244": "[2, 3, 5, 6, 4, 1, 0, 7]",
-        "4245": "[3, 1, 2, 6, 5, 0, 4, 7]",
-        "4246": "[4, 5, 6, 2, 3, 1, 0, 7]",
-        "4247": "[5, 3, 1, 4, 6, 0, 2, 7]",
-        "4248": "[6, 5, 4, 2, 3, 1, 0, 7]",
-        "4249": "[0, 2, 5, 1, 3, 6, 4, 7]",
-        "4250": "[1, 3, 6, 2, 4, 0, 5, 7]",
-        "4251": "[2, 4, 0, 3, 5, 1, 6, 7]",
-        "4252": "[3, 5, 4, 1, 2, 0, 6, 7]",
-        "4253": "[4, 3, 0, 5, 6, 1, 2, 7]",
-        "4254": "[5, 6, 2, 3, 1, 0, 4, 7]",
-        "4255": "[6, 3, 0, 5, 4, 1, 2, 7]",
-        "4256": "[0, 3, 5, 2, 1, 4, 6, 7]",
-        "4257": "[1, 4, 6, 3, 2, 5, 0, 7]",
-        "4258": "[2, 5, 0, 4, 3, 6, 1, 7]",
-        "4259": "[3, 2, 4, 5, 1, 6, 0, 7]",
-        "4260": "[4, 6, 0, 3, 5, 2, 1, 7]",
-        "4261": "[5, 1, 2, 6, 3, 4, 0, 7]",
-        "4262": "[6, 4, 0, 3, 5, 2, 1, 7]",
-        "4263": "[0, 4, 3, 2, 1, 5, 6, 7]",
-        "4264": "[1, 5, 4, 3, 2, 6, 0, 7]",
-        "4265": "[2, 6, 5, 4, 3, 0, 1, 7]",
-        "4266": "[3, 6, 2, 5, 1, 4, 0, 7]",
-        "4267": "[4, 2, 6, 3, 5, 0, 1, 7]",
-        "4268": "[5, 4, 1, 6, 3, 2, 0, 7]",
-        "4269": "[6, 2, 4, 3, 5, 0, 1, 7]",
-        "4270": "[0, 5, 6, 1, 3, 2, 4, 7]",
-        "4271": "[1, 6, 0, 2, 4, 3, 5, 7]",
-        "4272": "[2, 0, 1, 3, 5, 4, 6, 7]",
-        "4273": "[3, 4, 0, 1, 2, 5, 6, 7]",
-        "4274": "[4, 0, 1, 5, 6, 3, 2, 7]",
-        "4275": "[5, 2, 0, 3, 1, 6, 4, 7]",
-        "4276": "[6, 0, 1, 5, 4, 3, 2, 7]",
-        "4277": "[0, 6, 3, 2, 1, 5, 4, 7]",
-        "4278": "[1, 0, 4, 3, 2, 6, 5, 7]",
-        "4279": "[2, 1, 5, 4, 3, 0, 6, 7]",
-        "4280": "[3, 0, 2, 5, 1, 4, 6, 7]",
-        "4281": "[4, 1, 6, 3, 5, 0, 2, 7]",
-        "4282": "[5, 0, 1, 6, 3, 2, 4, 7]",
-        "4283": "[6, 1, 4, 3, 5, 0, 2, 7]",
-        "4284": "[0, 1, 4, 5, 6, 2, 3, 7]",
-        "4285": "[1, 2, 5, 6, 0, 3, 4, 7]",
-        "4286": "[2, 3, 6, 0, 1, 4, 5, 7]",
-        "4287": "[3, 1, 6, 4, 0, 5, 2, 7]",
-        "4288": "[4, 5, 2, 0, 1, 3, 6, 7]",
-        "4289": "[5, 3, 4, 2, 0, 6, 1, 7]",
-        "4290": "[6, 5, 2, 0, 1, 3, 4, 7]",
-        "4291": "[0, 2, 1, 4, 6, 3, 5, 7]",
-        "4292": "[1, 3, 2, 5, 0, 4, 6, 7]",
-        "4293": "[2, 4, 3, 6, 1, 5, 0, 7]",
-        "4294": "[3, 5, 1, 6, 0, 2, 4, 7]",
-        "4295": "[4, 3, 5, 2, 1, 6, 0, 7]",
-        "4296": "[5, 6, 3, 4, 0, 1, 2, 7]",
-        "4297": "[6, 3, 5, 2, 1, 4, 0, 7]",
-        "4298": "[0, 3, 2, 6, 4, 1, 5, 7]",
-        "4299": "[1, 4, 3, 0, 5, 2, 6, 7]",
-        "4300": "[2, 5, 4, 1, 6, 3, 0, 7]",
-        "4301": "[3, 2, 5, 0, 6, 1, 4, 7]",
-        "4302": "[4, 6, 3, 1, 2, 5, 0, 7]",
-        "4303": "[5, 1, 6, 0, 4, 3, 2, 7]",
-        "4304": "[6, 4, 3, 1, 2, 5, 0, 7]",
-        "4305": "[0, 4, 2, 6, 5, 1, 3, 7]",
-        "4306": "[1, 5, 3, 0, 6, 2, 4, 7]",
-        "4307": "[2, 6, 4, 1, 0, 3, 5, 7]",
-        "4308": "[3, 6, 5, 0, 4, 1, 2, 7]",
-        "4309": "[4, 2, 3, 1, 0, 5, 6, 7]",
-        "4310": "[5, 4, 6, 0, 2, 3, 1, 7]",
-        "4311": "[6, 2, 3, 1, 0, 5, 4, 7]",
-        "4312": "[0, 5, 1, 4, 2, 3, 6, 7]",
-        "4313": "[1, 6, 2, 5, 3, 4, 0, 7]",
-        "4314": "[2, 0, 3, 6, 4, 5, 1, 7]",
-        "4315": "[3, 4, 1, 6, 5, 2, 0, 7]",
-        "4316": "[4, 0, 5, 2, 3, 6, 1, 7]",
-        "4317": "[5, 2, 3, 4, 6, 1, 0, 7]",
-        "4318": "[6, 0, 5, 2, 3, 4, 1, 7]",
-        "4319": "[0, 6, 2, 4, 5, 1, 3, 7]",
-        "4320": "[1, 0, 3, 5, 6, 2, 4, 7]",
-        "4321": "[2, 1, 4, 6, 0, 3, 5, 7]",
-        "4322": "[3, 0, 5, 6, 4, 1, 2, 7]",
-        "4323": "[4, 1, 3, 2, 0, 5, 6, 7]",
-        "4324": "[5, 0, 6, 4, 2, 3, 1, 7]",
-        "4325": "[6, 1, 3, 2, 0, 5, 4, 7]",
-        "4326": "[0, 1, 5, 6, 4, 2, 3, 7]",
-        "4327": "[1, 2, 6, 0, 5, 3, 4, 7]",
-        "4328": "[2, 3, 0, 1, 6, 4, 5, 7]",
-        "4329": "[3, 1, 4, 0, 6, 5, 2, 7]",
-        "4330": "[4, 5, 0, 1, 2, 3, 6, 7]",
-        "4331": "[5, 3, 2, 0, 4, 6, 1, 7]",
-        "4332": "[6, 5, 0, 1, 2, 3, 4, 7]",
-        "4333": "[0, 2, 4, 6, 1, 3, 5, 7]",
-        "4334": "[1, 3, 5, 0, 2, 4, 6, 7]",
-        "4335": "[2, 4, 6, 1, 3, 5, 0, 7]",
-        "4336": "[3, 5, 6, 0, 1, 2, 4, 7]",
-        "4337": "[4, 3, 2, 1, 5, 6, 0, 7]",
-        "4338": "[5, 6, 4, 0, 3, 1, 2, 7]",
-        "4339": "[6, 3, 2, 1, 5, 4, 0, 7]",
-        "4340": "[0, 3, 6, 4, 2, 1, 5, 7]",
-        "4341": "[1, 4, 0, 5, 3, 2, 6, 7]",
-        "4342": "[2, 5, 1, 6, 4, 3, 0, 7]",
-        "4343": "[3, 2, 0, 6, 5, 1, 4, 7]",
-        "4344": "[4, 6, 1, 2, 3, 5, 0, 7]",
-        "4345": "[5, 1, 0, 4, 6, 3, 2, 7]",
-        "4346": "[6, 4, 1, 2, 3, 5, 0, 7]",
-        "4347": "[0, 4, 6, 5, 2, 1, 3, 7]",
-        "4348": "[1, 5, 0, 6, 3, 2, 4, 7]",
-        "4349": "[2, 6, 1, 0, 4, 3, 5, 7]",
-        "4350": "[3, 6, 0, 4, 5, 1, 2, 7]",
-        "4351": "[4, 2, 1, 0, 3, 5, 6, 7]",
-        "4352": "[5, 4, 0, 2, 6, 3, 1, 7]",
-        "4353": "[6, 2, 1, 0, 3, 5, 4, 7]",
-        "4354": "[0, 5, 4, 2, 1, 3, 6, 7]",
-        "4355": "[1, 6, 5, 3, 2, 4, 0, 7]",
-        "4356": "[2, 0, 6, 4, 3, 5, 1, 7]",
-        "4357": "[3, 4, 6, 5, 1, 2, 0, 7]",
-        "4358": "[4, 0, 2, 3, 5, 6, 1, 7]",
-        "4359": "[5, 2, 4, 6, 3, 1, 0, 7]",
-        "4360": "[6, 0, 2, 3, 5, 4, 1, 7]",
-        "4361": "[0, 6, 4, 5, 2, 1, 3, 7]",
-        "4362": "[1, 0, 5, 6, 3, 2, 4, 7]",
-        "4363": "[2, 1, 6, 0, 4, 3, 5, 7]",
-        "4364": "[3, 0, 6, 4, 5, 1, 2, 7]",
-        "4365": "[4, 1, 2, 0, 3, 5, 6, 7]",
-        "4366": "[5, 0, 4, 2, 6, 3, 1, 7]",
-        "4367": "[6, 1, 2, 0, 3, 5, 4, 7]",
-        "4368": "[0, 1, 6, 5, 4, 2, 3, 7]",
-        "4369": "[1, 2, 0, 6, 5, 3, 4, 7]",
-        "4370": "[2, 3, 1, 0, 6, 4, 5, 7]",
-        "4371": "[3, 1, 0, 4, 6, 5, 2, 7]",
-        "4372": "[4, 5, 1, 0, 2, 3, 6, 7]",
-        "4373": "[5, 3, 0, 2, 4, 6, 1, 7]",
-        "4374": "[6, 5, 1, 0, 2, 3, 4, 7]",
-        "4375": "[0, 2, 6, 4, 1, 3, 5, 7]",
-        "4376": "[1, 3, 0, 5, 2, 4, 6, 7]",
-        "4377": "[2, 4, 1, 6, 3, 5, 0, 7]",
-        "4378": "[3, 5, 0, 6, 1, 2, 4, 7]",
-        "4379": "[4, 3, 1, 2, 5, 6, 0, 7]",
-        "4380": "[5, 6, 0, 4, 3, 1, 2, 7]",
-        "4381": "[6, 3, 1, 2, 5, 4, 0, 7]",
-        "4382": "[0, 3, 4, 6, 2, 1, 5, 7]",
-        "4383": "[1, 4, 5, 0, 3, 2, 6, 7]",
-        "4384": "[2, 5, 6, 1, 4, 3, 0, 7]",
-        "4385": "[3, 2, 6, 0, 5, 1, 4, 7]",
-        "4386": "[4, 6, 2, 1, 3, 5, 0, 7]",
-        "4387": "[5, 1, 4, 0, 6, 3, 2, 7]",
-        "4388": "[6, 4, 2, 1, 3, 5, 0, 7]",
-        "4389": "[0, 4, 5, 6, 2, 1, 3, 7]",
-        "4390": "[1, 5, 6, 0, 3, 2, 4, 7]",
-        "4391": "[2, 6, 0, 1, 4, 3, 5, 7]",
-        "4392": "[3, 6, 4, 0, 5, 1, 2, 7]",
-        "4393": "[4, 2, 0, 1, 3, 5, 6, 7]",
-        "4394": "[5, 4, 2, 0, 6, 3, 1, 7]",
-        "4395": "[6, 2, 0, 1, 3, 5, 4, 7]",
-        "4396": "[0, 5, 2, 4, 1, 3, 6, 7]",
-        "4397": "[1, 6, 3, 5, 2, 4, 0, 7]",
-        "4398": "[2, 0, 4, 6, 3, 5, 1, 7]",
-        "4399": "[3, 4, 5, 6, 1, 2, 0, 7]",
-        "4400": "[4, 0, 3, 2, 5, 6, 1, 7]",
-        "4401": "[5, 2, 6, 4, 3, 1, 0, 7]",
-        "4402": "[6, 0, 3, 2, 5, 4, 1, 7]",
-        "4403": "[0, 6, 5, 4, 2, 1, 3, 7]",
-        "4404": "[1, 0, 6, 5, 3, 2, 4, 7]",
-        "4405": "[2, 1, 0, 6, 4, 3, 5, 7]",
-        "4406": "[3, 0, 4, 6, 5, 1, 2, 7]",
-        "4407": "[4, 1, 0, 2, 3, 5, 6, 7]",
-        "4408": "[5, 0, 2, 4, 6, 3, 1, 7]",
-        "4409": "[6, 1, 0, 2, 3, 5, 4, 7]",
-        "4410": "[0, 1, 2, 4, 3, 6, 5, 7]",
-        "4411": "[1, 2, 3, 5, 4, 0, 6, 7]",
-        "4412": "[2, 3, 4, 6, 5, 1, 0, 7]",
-        "4413": "[3, 1, 5, 6, 2, 0, 4, 7]",
-        "4414": "[4, 5, 3, 2, 6, 1, 0, 7]",
-        "4415": "[5, 3, 6, 4, 1, 0, 2, 7]",
-        "4416": "[6, 5, 3, 2, 4, 1, 0, 7]",
-        "4417": "[0, 2, 3, 1, 5, 6, 4, 7]",
-        "4418": "[1, 3, 4, 2, 6, 0, 5, 7]",
-        "4419": "[2, 4, 5, 3, 0, 1, 6, 7]",
-        "4420": "[3, 5, 2, 1, 4, 0, 6, 7]",
-        "4421": "[4, 3, 6, 5, 0, 1, 2, 7]",
-        "4422": "[5, 6, 1, 3, 2, 0, 4, 7]",
-        "4423": "[6, 3, 4, 5, 0, 1, 2, 7]",
-        "4424": "[0, 3, 1, 2, 5, 4, 6, 7]",
-        "4425": "[1, 4, 2, 3, 6, 5, 0, 7]",
-        "4426": "[2, 5, 3, 4, 0, 6, 1, 7]",
-        "4427": "[3, 2, 1, 5, 4, 6, 0, 7]",
-        "4428": "[4, 6, 5, 3, 0, 2, 1, 7]",
-        "4429": "[5, 1, 3, 6, 2, 4, 0, 7]",
-        "4430": "[6, 4, 5, 3, 0, 2, 1, 7]",
-        "4431": "[0, 4, 1, 2, 3, 5, 6, 7]",
-        "4432": "[1, 5, 2, 3, 4, 6, 0, 7]",
-        "4433": "[2, 6, 3, 4, 5, 0, 1, 7]",
-        "4434": "[3, 6, 1, 5, 2, 4, 0, 7]",
-        "4435": "[4, 2, 5, 3, 6, 0, 1, 7]",
-        "4436": "[5, 4, 3, 6, 1, 2, 0, 7]",
-        "4437": "[6, 2, 5, 3, 4, 0, 1, 7]",
-        "4438": "[0, 5, 3, 1, 6, 2, 4, 7]",
-        "4439": "[1, 6, 4, 2, 0, 3, 5, 7]",
-        "4440": "[2, 0, 5, 3, 1, 4, 6, 7]",
-        "4441": "[3, 4, 2, 1, 0, 5, 6, 7]",
-        "4442": "[4, 0, 6, 5, 1, 3, 2, 7]",
-        "4443": "[5, 2, 1, 3, 0, 6, 4, 7]",
-        "4444": "[6, 0, 4, 5, 1, 3, 2, 7]",
-        "4445": "[0, 6, 1, 2, 3, 5, 4, 7]",
-        "4446": "[1, 0, 2, 3, 4, 6, 5, 7]",
-        "4447": "[2, 1, 3, 4, 5, 0, 6, 7]",
-        "4448": "[3, 0, 1, 5, 2, 4, 6, 7]",
-        "4449": "[4, 1, 5, 3, 6, 0, 2, 7]",
-        "4450": "[5, 0, 3, 6, 1, 2, 4, 7]",
-        "4451": "[6, 1, 5, 3, 4, 0, 2, 7]",
-        "4452": "[0, 1, 3, 5, 4, 6, 2, 7]",
-        "4453": "[1, 2, 4, 6, 5, 0, 3, 7]",
-        "4454": "[2, 3, 5, 0, 6, 1, 4, 7]",
-        "4455": "[3, 1, 2, 4, 6, 0, 5, 7]",
-        "4456": "[4, 5, 6, 0, 2, 1, 3, 7]",
-        "4457": "[5, 3, 1, 2, 4, 0, 6, 7]",
-        "4458": "[6, 5, 4, 0, 2, 1, 3, 7]",
-        "4459": "[0, 2, 5, 4, 1, 6, 3, 7]",
-        "4460": "[1, 3, 6, 5, 2, 0, 4, 7]",
-        "4461": "[2, 4, 0, 6, 3, 1, 5, 7]",
-        "4462": "[3, 5, 4, 6, 1, 0, 2, 7]",
-        "4463": "[4, 3, 0, 2, 5, 1, 6, 7]",
-        "4464": "[5, 6, 2, 4, 3, 0, 1, 7]",
-        "4465": "[6, 3, 0, 2, 5, 1, 4, 7]",
-        "4466": "[0, 3, 5, 6, 2, 4, 1, 7]",
-        "4467": "[1, 4, 6, 0, 3, 5, 2, 7]",
-        "4468": "[2, 5, 0, 1, 4, 6, 3, 7]",
-        "4469": "[3, 2, 4, 0, 5, 6, 1, 7]",
-        "4470": "[4, 6, 0, 1, 3, 2, 5, 7]",
-        "4471": "[5, 1, 2, 0, 6, 4, 3, 7]",
-        "4472": "[6, 4, 0, 1, 3, 2, 5, 7]",
-        "4473": "[0, 4, 3, 6, 2, 5, 1, 7]",
-        "4474": "[1, 5, 4, 0, 3, 6, 2, 7]",
-        "4475": "[2, 6, 5, 1, 4, 0, 3, 7]",
-        "4476": "[3, 6, 2, 0, 5, 4, 1, 7]",
-        "4477": "[4, 2, 6, 1, 3, 0, 5, 7]",
-        "4478": "[5, 4, 1, 0, 6, 2, 3, 7]",
-        "4479": "[6, 2, 4, 1, 3, 0, 5, 7]",
-        "4480": "[0, 5, 6, 4, 1, 2, 3, 7]",
-        "4481": "[1, 6, 0, 5, 2, 3, 4, 7]",
-        "4482": "[2, 0, 1, 6, 3, 4, 5, 7]",
-        "4483": "[3, 4, 0, 6, 1, 5, 2, 7]",
-        "4484": "[4, 0, 1, 2, 5, 3, 6, 7]",
-        "4485": "[5, 2, 0, 4, 3, 6, 1, 7]",
-        "4486": "[6, 0, 1, 2, 5, 3, 4, 7]",
-        "4487": "[0, 6, 3, 4, 2, 5, 1, 7]",
-        "4488": "[1, 0, 4, 5, 3, 6, 2, 7]",
-        "4489": "[2, 1, 5, 6, 4, 0, 3, 7]",
-        "4490": "[3, 0, 2, 6, 5, 4, 1, 7]",
-        "4491": "[4, 1, 6, 2, 3, 0, 5, 7]",
-        "4492": "[5, 0, 1, 4, 6, 2, 3, 7]",
-        "4493": "[6, 1, 4, 2, 3, 0, 5, 7]",
-        "4494": "[0, 1, 4, 3, 5, 2, 6, 7]",
-        "4495": "[1, 2, 5, 4, 6, 3, 0, 7]",
-        "4496": "[2, 3, 6, 5, 0, 4, 1, 7]",
-        "4497": "[3, 1, 6, 2, 4, 5, 0, 7]",
-        "4498": "[4, 5, 2, 6, 0, 3, 1, 7]",
-        "4499": "[5, 3, 4, 1, 2, 6, 0, 7]",
-        "4500": "[6, 5, 2, 4, 0, 3, 1, 7]",
-        "4501": "[0, 2, 1, 5, 4, 3, 6, 7]",
-        "4502": "[1, 3, 2, 6, 5, 4, 0, 7]",
-        "4503": "[2, 4, 3, 0, 6, 5, 1, 7]",
-        "4504": "[3, 5, 1, 4, 6, 2, 0, 7]",
-        "4505": "[4, 3, 5, 0, 2, 6, 1, 7]",
-        "4506": "[5, 6, 3, 2, 4, 1, 0, 7]",
-        "4507": "[6, 3, 5, 0, 2, 4, 1, 7]",
-        "4508": "[0, 3, 2, 5, 6, 1, 4, 7]",
-        "4509": "[1, 4, 3, 6, 0, 2, 5, 7]",
-        "4510": "[2, 5, 4, 0, 1, 3, 6, 7]",
-        "4511": "[3, 2, 5, 4, 0, 1, 6, 7]",
-        "4512": "[4, 6, 3, 0, 1, 5, 2, 7]",
-        "4513": "[5, 1, 6, 2, 0, 3, 4, 7]",
-        "4514": "[6, 4, 3, 0, 1, 5, 2, 7]",
-        "4515": "[0, 4, 2, 3, 6, 1, 5, 7]",
-        "4516": "[1, 5, 3, 4, 0, 2, 6, 7]",
-        "4517": "[2, 6, 4, 5, 1, 3, 0, 7]",
-        "4518": "[3, 6, 5, 2, 0, 1, 4, 7]",
-        "4519": "[4, 2, 3, 6, 1, 5, 0, 7]",
-        "4520": "[5, 4, 6, 1, 0, 3, 2, 7]",
-        "4521": "[6, 2, 3, 4, 1, 5, 0, 7]",
-        "4522": "[0, 5, 1, 6, 4, 3, 2, 7]",
-        "4523": "[1, 6, 2, 0, 5, 4, 3, 7]",
-        "4524": "[2, 0, 3, 1, 6, 5, 4, 7]",
-        "4525": "[3, 4, 1, 0, 6, 2, 5, 7]",
-        "4526": "[4, 0, 5, 1, 2, 6, 3, 7]",
-        "4527": "[5, 2, 3, 0, 4, 1, 6, 7]",
-        "4528": "[6, 0, 5, 1, 2, 4, 3, 7]",
-        "4529": "[0, 6, 2, 3, 4, 1, 5, 7]",
-        "4530": "[1, 0, 3, 4, 5, 2, 6, 7]",
-        "4531": "[2, 1, 4, 5, 6, 3, 0, 7]",
-        "4532": "[3, 0, 5, 2, 6, 1, 4, 7]",
-        "4533": "[4, 1, 3, 6, 2, 5, 0, 7]",
-        "4534": "[5, 0, 6, 1, 4, 3, 2, 7]",
-        "4535": "[6, 1, 3, 4, 2, 5, 0, 7]",
-        "4536": "[0, 1, 5, 3, 6, 2, 4, 7]",
-        "4537": "[1, 2, 6, 4, 0, 3, 5, 7]",
-        "4538": "[2, 3, 0, 5, 1, 4, 6, 7]",
-        "4539": "[3, 1, 4, 2, 0, 5, 6, 7]",
-        "4540": "[4, 5, 0, 6, 1, 3, 2, 7]",
-        "4541": "[5, 3, 2, 1, 0, 6, 4, 7]",
-        "4542": "[6, 5, 0, 4, 1, 3, 2, 7]",
-        "4543": "[0, 2, 4, 5, 6, 3, 1, 7]",
-        "4544": "[1, 3, 5, 6, 0, 4, 2, 7]",
-        "4545": "[2, 4, 6, 0, 1, 5, 3, 7]",
-        "4546": "[3, 5, 6, 4, 0, 2, 1, 7]",
-        "4547": "[4, 3, 2, 0, 1, 6, 5, 7]",
-        "4548": "[5, 6, 4, 2, 0, 1, 3, 7]",
-        "4549": "[6, 3, 2, 0, 1, 4, 5, 7]",
-        "4550": "[0, 3, 6, 5, 4, 1, 2, 7]",
-        "4551": "[1, 4, 0, 6, 5, 2, 3, 7]",
-        "4552": "[2, 5, 1, 0, 6, 3, 4, 7]",
-        "4553": "[3, 2, 0, 4, 6, 1, 5, 7]",
-        "4554": "[4, 6, 1, 0, 2, 5, 3, 7]",
-        "4555": "[5, 1, 0, 2, 4, 3, 6, 7]",
-        "4556": "[6, 4, 1, 0, 2, 5, 3, 7]",
-        "4557": "[0, 4, 6, 3, 5, 1, 2, 7]",
-        "4558": "[1, 5, 0, 4, 6, 2, 3, 7]",
-        "4559": "[2, 6, 1, 5, 0, 3, 4, 7]",
-        "4560": "[3, 6, 0, 2, 4, 1, 5, 7]",
-        "4561": "[4, 2, 1, 6, 0, 5, 3, 7]",
-        "4562": "[5, 4, 0, 1, 2, 3, 6, 7]",
-        "4563": "[6, 2, 1, 4, 0, 5, 3, 7]",
-        "4564": "[0, 5, 4, 6, 2, 3, 1, 7]",
-        "4565": "[1, 6, 5, 0, 3, 4, 2, 7]",
-        "4566": "[2, 0, 6, 1, 4, 5, 3, 7]",
-        "4567": "[3, 4, 6, 0, 5, 2, 1, 7]",
-        "4568": "[4, 0, 2, 1, 3, 6, 5, 7]",
-        "4569": "[5, 2, 4, 0, 6, 1, 3, 7]",
-        "4570": "[6, 0, 2, 1, 3, 4, 5, 7]",
-        "4571": "[0, 6, 4, 3, 5, 1, 2, 7]",
-        "4572": "[1, 0, 5, 4, 6, 2, 3, 7]",
-        "4573": "[2, 1, 6, 5, 0, 3, 4, 7]",
-        "4574": "[3, 0, 6, 2, 4, 1, 5, 7]",
-        "4575": "[4, 1, 2, 6, 0, 5, 3, 7]",
-        "4576": "[5, 0, 4, 1, 2, 3, 6, 7]",
-        "4577": "[6, 1, 2, 4, 0, 5, 3, 7]",
-        "4578": "[0, 1, 6, 3, 5, 2, 4, 7]",
-        "4579": "[1, 2, 0, 4, 6, 3, 5, 7]",
-        "4580": "[2, 3, 1, 5, 0, 4, 6, 7]",
-        "4581": "[3, 1, 0, 2, 4, 5, 6, 7]",
-        "4582": "[4, 5, 1, 6, 0, 3, 2, 7]",
-        "4583": "[5, 3, 0, 1, 2, 6, 4, 7]",
-        "4584": "[6, 5, 1, 4, 0, 3, 2, 7]",
-        "4585": "[0, 2, 6, 5, 4, 3, 1, 7]",
-        "4586": "[1, 3, 0, 6, 5, 4, 2, 7]",
-        "4587": "[2, 4, 1, 0, 6, 5, 3, 7]",
-        "4588": "[3, 5, 0, 4, 6, 2, 1, 7]",
-        "4589": "[4, 3, 1, 0, 2, 6, 5, 7]",
-        "4590": "[5, 6, 0, 2, 4, 1, 3, 7]",
-        "4591": "[6, 3, 1, 0, 2, 4, 5, 7]",
-        "4592": "[0, 3, 4, 5, 6, 1, 2, 7]",
-        "4593": "[1, 4, 5, 6, 0, 2, 3, 7]",
-        "4594": "[2, 5, 6, 0, 1, 3, 4, 7]",
-        "4595": "[3, 2, 6, 4, 0, 1, 5, 7]",
-        "4596": "[4, 6, 2, 0, 1, 5, 3, 7]",
-        "4597": "[5, 1, 4, 2, 0, 3, 6, 7]",
-        "4598": "[6, 4, 2, 0, 1, 5, 3, 7]",
-        "4599": "[0, 4, 5, 3, 6, 1, 2, 7]",
-        "4600": "[1, 5, 6, 4, 0, 2, 3, 7]",
-        "4601": "[2, 6, 0, 5, 1, 3, 4, 7]",
-        "4602": "[3, 6, 4, 2, 0, 1, 5, 7]",
-        "4603": "[4, 2, 0, 6, 1, 5, 3, 7]",
-        "4604": "[5, 4, 2, 1, 0, 3, 6, 7]",
-        "4605": "[6, 2, 0, 4, 1, 5, 3, 7]",
-        "4606": "[0, 5, 2, 6, 4, 3, 1, 7]",
-        "4607": "[1, 6, 3, 0, 5, 4, 2, 7]",
-        "4608": "[2, 0, 4, 1, 6, 5, 3, 7]",
-        "4609": "[3, 4, 5, 0, 6, 2, 1, 7]",
-        "4610": "[4, 0, 3, 1, 2, 6, 5, 7]",
-        "4611": "[5, 2, 6, 0, 4, 1, 3, 7]",
-        "4612": "[6, 0, 3, 1, 2, 4, 5, 7]",
-        "4613": "[0, 6, 5, 3, 4, 1, 2, 7]",
-        "4614": "[1, 0, 6, 4, 5, 2, 3, 7]",
-        "4615": "[2, 1, 0, 5, 6, 3, 4, 7]",
-        "4616": "[3, 0, 4, 2, 6, 1, 5, 7]",
-        "4617": "[4, 1, 0, 6, 2, 5, 3, 7]",
-        "4618": "[5, 0, 2, 1, 4, 3, 6, 7]",
-        "4619": "[6, 1, 0, 4, 2, 5, 3, 7]",
-        "4620": "[0, 1, 2, 5, 4, 6, 3, 7]",
-        "4621": "[1, 2, 3, 6, 5, 0, 4, 7]",
-        "4622": "[2, 3, 4, 0, 6, 1, 5, 7]",
-        "4623": "[3, 1, 5, 4, 6, 0, 2, 7]",
-        "4624": "[4, 5, 3, 0, 2, 1, 6, 7]",
-        "4625": "[5, 3, 6, 2, 4, 0, 1, 7]",
-        "4626": "[6, 5, 3, 0, 2, 1, 4, 7]",
-        "4627": "[0, 2, 3, 4, 1, 6, 5, 7]",
-        "4628": "[1, 3, 4, 5, 2, 0, 6, 7]",
-        "4629": "[2, 4, 5, 6, 3, 1, 0, 7]",
-        "4630": "[3, 5, 2, 6, 1, 0, 4, 7]",
-        "4631": "[4, 3, 6, 2, 5, 1, 0, 7]",
-        "4632": "[5, 6, 1, 4, 3, 0, 2, 7]",
-        "4633": "[6, 3, 4, 2, 5, 1, 0, 7]",
-        "4634": "[0, 3, 1, 6, 2, 4, 5, 7]",
-        "4635": "[1, 4, 2, 0, 3, 5, 6, 7]",
-        "4636": "[2, 5, 3, 1, 4, 6, 0, 7]",
-        "4637": "[3, 2, 1, 0, 5, 6, 4, 7]",
-        "4638": "[4, 6, 5, 1, 3, 2, 0, 7]",
-        "4639": "[5, 1, 3, 0, 6, 4, 2, 7]",
-        "4640": "[6, 4, 5, 1, 3, 2, 0, 7]",
-        "4641": "[0, 4, 1, 6, 2, 5, 3, 7]",
-        "4642": "[1, 5, 2, 0, 3, 6, 4, 7]",
-        "4643": "[2, 6, 3, 1, 4, 0, 5, 7]",
-        "4644": "[3, 6, 1, 0, 5, 4, 2, 7]",
-        "4645": "[4, 2, 5, 1, 3, 0, 6, 7]",
-        "4646": "[5, 4, 3, 0, 6, 2, 1, 7]",
-        "4647": "[6, 2, 5, 1, 3, 0, 4, 7]",
-        "4648": "[0, 5, 3, 4, 1, 2, 6, 7]",
-        "4649": "[1, 6, 4, 5, 2, 3, 0, 7]",
-        "4650": "[2, 0, 5, 6, 3, 4, 1, 7]",
-        "4651": "[3, 4, 2, 6, 1, 5, 0, 7]",
-        "4652": "[4, 0, 6, 2, 5, 3, 1, 7]",
-        "4653": "[5, 2, 1, 4, 3, 6, 0, 7]",
-        "4654": "[6, 0, 4, 2, 5, 3, 1, 7]",
-        "4655": "[0, 6, 1, 4, 2, 5, 3, 7]",
-        "4656": "[1, 0, 2, 5, 3, 6, 4, 7]",
-        "4657": "[2, 1, 3, 6, 4, 0, 5, 7]",
-        "4658": "[3, 0, 1, 6, 5, 4, 2, 7]",
-        "4659": "[4, 1, 5, 2, 3, 0, 6, 7]",
-        "4660": "[5, 0, 3, 4, 6, 2, 1, 7]",
-        "4661": "[6, 1, 5, 2, 3, 0, 4, 7]",
-        "4662": "[0, 1, 3, 2, 5, 6, 4, 7]",
-        "4663": "[1, 2, 4, 3, 6, 0, 5, 7]",
-        "4664": "[2, 3, 5, 4, 0, 1, 6, 7]",
-        "4665": "[3, 1, 2, 5, 4, 0, 6, 7]",
-        "4666": "[4, 5, 6, 3, 0, 1, 2, 7]",
-        "4667": "[5, 3, 1, 6, 2, 0, 4, 7]",
-        "4668": "[6, 5, 4, 3, 0, 1, 2, 7]",
-        "4669": "[0, 2, 5, 3, 4, 6, 1, 7]",
-        "4670": "[1, 3, 6, 4, 5, 0, 2, 7]",
-        "4671": "[2, 4, 0, 5, 6, 1, 3, 7]",
-        "4672": "[3, 5, 4, 2, 6, 0, 1, 7]",
-        "4673": "[4, 3, 0, 6, 2, 1, 5, 7]",
-        "4674": "[5, 6, 2, 1, 4, 0, 3, 7]",
-        "4675": "[6, 3, 0, 4, 2, 1, 5, 7]",
-        "4676": "[0, 3, 5, 1, 6, 4, 2, 7]",
-        "4677": "[1, 4, 6, 2, 0, 5, 3, 7]",
-        "4678": "[2, 5, 0, 3, 1, 6, 4, 7]",
-        "4679": "[3, 2, 4, 1, 0, 6, 5, 7]",
-        "4680": "[4, 6, 0, 5, 1, 2, 3, 7]",
-        "4681": "[5, 1, 2, 3, 0, 4, 6, 7]",
-        "4682": "[6, 4, 0, 5, 1, 2, 3, 7]",
-        "4683": "[0, 4, 3, 1, 6, 5, 2, 7]",
-        "4684": "[1, 5, 4, 2, 0, 6, 3, 7]",
-        "4685": "[2, 6, 5, 3, 1, 0, 4, 7]",
-        "4686": "[3, 6, 2, 1, 0, 4, 5, 7]",
-        "4687": "[4, 2, 6, 5, 1, 0, 3, 7]",
-        "4688": "[5, 4, 1, 3, 0, 2, 6, 7]",
-        "4689": "[6, 2, 4, 5, 1, 0, 3, 7]",
-        "4690": "[0, 5, 6, 3, 4, 2, 1, 7]",
-        "4691": "[1, 6, 0, 4, 5, 3, 2, 7]",
-        "4692": "[2, 0, 1, 5, 6, 4, 3, 7]",
-        "4693": "[3, 4, 0, 2, 6, 5, 1, 7]",
-        "4694": "[4, 0, 1, 6, 2, 3, 5, 7]",
-        "4695": "[5, 2, 0, 1, 4, 6, 3, 7]",
-        "4696": "[6, 0, 1, 4, 2, 3, 5, 7]",
-        "4697": "[0, 6, 3, 1, 4, 5, 2, 7]",
-        "4698": "[1, 0, 4, 2, 5, 6, 3, 7]",
-        "4699": "[2, 1, 5, 3, 6, 0, 4, 7]",
-        "4700": "[3, 0, 2, 1, 6, 4, 5, 7]",
-        "4701": "[4, 1, 6, 5, 2, 0, 3, 7]",
-        "4702": "[5, 0, 1, 3, 4, 2, 6, 7]",
-        "4703": "[6, 1, 4, 5, 2, 0, 3, 7]",
-        "4704": "[0, 1, 4, 6, 3, 2, 5, 7]",
-        "4705": "[1, 2, 5, 0, 4, 3, 6, 7]",
-        "4706": "[2, 3, 6, 1, 5, 4, 0, 7]",
-        "4707": "[3, 1, 6, 0, 2, 5, 4, 7]",
-        "4708": "[4, 5, 2, 1, 6, 3, 0, 7]",
-        "4709": "[5, 3, 4, 0, 1, 6, 2, 7]",
-        "4710": "[6, 5, 2, 1, 4, 3, 0, 7]",
-        "4711": "[0, 2, 1, 6, 5, 3, 4, 7]",
-        "4712": "[1, 3, 2, 0, 6, 4, 5, 7]",
-        "4713": "[2, 4, 3, 1, 0, 5, 6, 7]",
-        "4714": "[3, 5, 1, 0, 4, 2, 6, 7]",
-        "4715": "[4, 3, 5, 1, 0, 6, 2, 7]",
-        "4716": "[5, 6, 3, 0, 2, 1, 4, 7]",
-        "4717": "[6, 3, 5, 1, 0, 4, 2, 7]",
-        "4718": "[0, 3, 2, 4, 5, 1, 6, 7]",
-        "4719": "[1, 4, 3, 5, 6, 2, 0, 7]",
-        "4720": "[2, 5, 4, 6, 0, 3, 1, 7]",
-        "4721": "[3, 2, 5, 6, 4, 1, 0, 7]",
-        "4722": "[4, 6, 3, 2, 0, 5, 1, 7]",
-        "4723": "[5, 1, 6, 4, 2, 3, 0, 7]",
-        "4724": "[6, 4, 3, 2, 0, 5, 1, 7]",
-        "4725": "[0, 4, 2, 5, 3, 1, 6, 7]",
-        "4726": "[1, 5, 3, 6, 4, 2, 0, 7]",
-        "4727": "[2, 6, 4, 0, 5, 3, 1, 7]",
-        "4728": "[3, 6, 5, 4, 2, 1, 0, 7]",
-        "4729": "[4, 2, 3, 0, 6, 5, 1, 7]",
-        "4730": "[5, 4, 6, 2, 1, 3, 0, 7]",
-        "4731": "[6, 2, 3, 0, 4, 5, 1, 7]",
-        "4732": "[0, 5, 1, 2, 6, 3, 4, 7]",
-        "4733": "[1, 6, 2, 3, 0, 4, 5, 7]",
-        "4734": "[2, 0, 3, 4, 1, 5, 6, 7]",
-        "4735": "[3, 4, 1, 5, 0, 2, 6, 7]",
-        "4736": "[4, 0, 5, 3, 1, 6, 2, 7]",
-        "4737": "[5, 2, 3, 6, 0, 1, 4, 7]",
-        "4738": "[6, 0, 5, 3, 1, 4, 2, 7]",
-        "4739": "[0, 6, 2, 5, 3, 1, 4, 7]",
-        "4740": "[1, 0, 3, 6, 4, 2, 5, 7]",
-        "4741": "[2, 1, 4, 0, 5, 3, 6, 7]",
-        "4742": "[3, 0, 5, 4, 2, 1, 6, 7]",
-        "4743": "[4, 1, 3, 0, 6, 5, 2, 7]",
-        "4744": "[5, 0, 6, 2, 1, 3, 4, 7]",
-        "4745": "[6, 1, 3, 0, 4, 5, 2, 7]",
-        "4746": "[0, 1, 5, 4, 3, 2, 6, 7]",
-        "4747": "[1, 2, 6, 5, 4, 3, 0, 7]",
-        "4748": "[2, 3, 0, 6, 5, 4, 1, 7]",
-        "4749": "[3, 1, 4, 6, 2, 5, 0, 7]",
-        "4750": "[4, 5, 0, 2, 6, 3, 1, 7]",
-        "4751": "[5, 3, 2, 4, 1, 6, 0, 7]",
-        "4752": "[6, 5, 0, 2, 4, 3, 1, 7]",
-        "4753": "[0, 2, 4, 1, 5, 3, 6, 7]",
-        "4754": "[1, 3, 5, 2, 6, 4, 0, 7]",
-        "4755": "[2, 4, 6, 3, 0, 5, 1, 7]",
-        "4756": "[3, 5, 6, 1, 4, 2, 0, 7]",
-        "4757": "[4, 3, 2, 5, 0, 6, 1, 7]",
-        "4758": "[5, 6, 4, 3, 2, 1, 0, 7]",
-        "4759": "[6, 3, 2, 5, 0, 4, 1, 7]",
-        "4760": "[0, 3, 6, 2, 5, 1, 4, 7]",
-        "4761": "[1, 4, 0, 3, 6, 2, 5, 7]",
-        "4762": "[2, 5, 1, 4, 0, 3, 6, 7]",
-        "4763": "[3, 2, 0, 5, 4, 1, 6, 7]",
-        "4764": "[4, 6, 1, 3, 0, 5, 2, 7]",
-        "4765": "[5, 1, 0, 6, 2, 3, 4, 7]",
-        "4766": "[6, 4, 1, 3, 0, 5, 2, 7]",
-        "4767": "[0, 4, 6, 2, 3, 1, 5, 7]",
-        "4768": "[1, 5, 0, 3, 4, 2, 6, 7]",
-        "4769": "[2, 6, 1, 4, 5, 3, 0, 7]",
-        "4770": "[3, 6, 0, 5, 2, 1, 4, 7]",
-        "4771": "[4, 2, 1, 3, 6, 5, 0, 7]",
-        "4772": "[5, 4, 0, 6, 1, 3, 2, 7]",
-        "4773": "[6, 2, 1, 3, 4, 5, 0, 7]",
-        "4774": "[0, 5, 4, 1, 6, 3, 2, 7]",
-        "4775": "[1, 6, 5, 2, 0, 4, 3, 7]",
-        "4776": "[2, 0, 6, 3, 1, 5, 4, 7]",
-        "4777": "[3, 4, 6, 1, 0, 2, 5, 7]",
-        "4778": "[4, 0, 2, 5, 1, 6, 3, 7]",
-        "4779": "[5, 2, 4, 3, 0, 1, 6, 7]",
-        "4780": "[6, 0, 2, 5, 1, 4, 3, 7]",
-        "4781": "[0, 6, 4, 2, 3, 1, 5, 7]",
-        "4782": "[1, 0, 5, 3, 4, 2, 6, 7]",
-        "4783": "[2, 1, 6, 4, 5, 3, 0, 7]",
-        "4784": "[3, 0, 6, 5, 2, 1, 4, 7]",
-        "4785": "[4, 1, 2, 3, 6, 5, 0, 7]",
-        "4786": "[5, 0, 4, 6, 1, 3, 2, 7]",
-        "4787": "[6, 1, 2, 3, 4, 5, 0, 7]",
-        "4788": "[0, 1, 6, 4, 3, 2, 5, 7]",
-        "4789": "[1, 2, 0, 5, 4, 3, 6, 7]",
-        "4790": "[2, 3, 1, 6, 5, 4, 0, 7]",
-        "4791": "[3, 1, 0, 6, 2, 5, 4, 7]",
-        "4792": "[4, 5, 1, 2, 6, 3, 0, 7]",
-        "4793": "[5, 3, 0, 4, 1, 6, 2, 7]",
-        "4794": "[6, 5, 1, 2, 4, 3, 0, 7]",
-        "4795": "[0, 2, 6, 1, 5, 3, 4, 7]",
-        "4796": "[1, 3, 0, 2, 6, 4, 5, 7]",
-        "4797": "[2, 4, 1, 3, 0, 5, 6, 7]",
-        "4798": "[3, 5, 0, 1, 4, 2, 6, 7]",
-        "4799": "[4, 3, 1, 5, 0, 6, 2, 7]",
-        "4800": "[5, 6, 0, 3, 2, 1, 4, 7]",
-        "4801": "[6, 3, 1, 5, 0, 4, 2, 7]",
-        "4802": "[0, 3, 4, 2, 5, 1, 6, 7]",
-        "4803": "[1, 4, 5, 3, 6, 2, 0, 7]",
-        "4804": "[2, 5, 6, 4, 0, 3, 1, 7]",
-        "4805": "[3, 2, 6, 5, 4, 1, 0, 7]",
-        "4806": "[4, 6, 2, 3, 0, 5, 1, 7]",
-        "4807": "[5, 1, 4, 6, 2, 3, 0, 7]",
-        "4808": "[6, 4, 2, 3, 0, 5, 1, 7]",
-        "4809": "[0, 4, 5, 2, 3, 1, 6, 7]",
-        "4810": "[1, 5, 6, 3, 4, 2, 0, 7]",
-        "4811": "[2, 6, 0, 4, 5, 3, 1, 7]",
-        "4812": "[3, 6, 4, 5, 2, 1, 0, 7]",
-        "4813": "[4, 2, 0, 3, 6, 5, 1, 7]",
-        "4814": "[5, 4, 2, 6, 1, 3, 0, 7]",
-        "4815": "[6, 2, 0, 3, 4, 5, 1, 7]",
-        "4816": "[0, 5, 2, 1, 6, 3, 4, 7]",
-        "4817": "[1, 6, 3, 2, 0, 4, 5, 7]",
-        "4818": "[2, 0, 4, 3, 1, 5, 6, 7]",
-        "4819": "[3, 4, 5, 1, 0, 2, 6, 7]",
-        "4820": "[4, 0, 3, 5, 1, 6, 2, 7]",
-        "4821": "[5, 2, 6, 3, 0, 1, 4, 7]",
-        "4822": "[6, 0, 3, 5, 1, 4, 2, 7]",
-        "4823": "[0, 6, 5, 2, 3, 1, 4, 7]",
-        "4824": "[1, 0, 6, 3, 4, 2, 5, 7]",
-        "4825": "[2, 1, 0, 4, 5, 3, 6, 7]",
-        "4826": "[3, 0, 4, 5, 2, 1, 6, 7]",
-        "4827": "[4, 1, 0, 3, 6, 5, 2, 7]",
-        "4828": "[5, 0, 2, 6, 1, 3, 4, 7]",
-        "4829": "[6, 1, 0, 3, 4, 5, 2, 7]",
-        "4830": "[0, 1, 2, 6, 3, 4, 5, 7]",
-        "4831": "[1, 2, 3, 0, 4, 5, 6, 7]",
-        "4832": "[2, 3, 4, 1, 5, 6, 0, 7]",
-        "4833": "[3, 1, 5, 0, 2, 6, 4, 7]",
-        "4834": "[4, 5, 3, 1, 6, 2, 0, 7]",
-        "4835": "[5, 3, 6, 0, 1, 4, 2, 7]",
-        "4836": "[6, 5, 3, 1, 4, 2, 0, 7]",
-        "4837": "[0, 2, 3, 6, 5, 1, 4, 7]",
-        "4838": "[1, 3, 4, 0, 6, 2, 5, 7]",
-        "4839": "[2, 4, 5, 1, 0, 3, 6, 7]",
-        "4840": "[3, 5, 2, 0, 4, 1, 6, 7]",
-        "4841": "[4, 3, 6, 1, 0, 5, 2, 7]",
-        "4842": "[5, 6, 1, 0, 2, 3, 4, 7]",
-        "4843": "[6, 3, 4, 1, 0, 5, 2, 7]",
-        "4844": "[0, 3, 1, 4, 5, 2, 6, 7]",
-        "4845": "[1, 4, 2, 5, 6, 3, 0, 7]",
-        "4846": "[2, 5, 3, 6, 0, 4, 1, 7]",
-        "4847": "[3, 2, 1, 6, 4, 5, 0, 7]",
-        "4848": "[4, 6, 5, 2, 0, 3, 1, 7]",
-        "4849": "[5, 1, 3, 4, 2, 6, 0, 7]",
-        "4850": "[6, 4, 5, 2, 0, 3, 1, 7]",
-        "4851": "[0, 4, 1, 5, 3, 2, 6, 7]",
-        "4852": "[1, 5, 2, 6, 4, 3, 0, 7]",
-        "4853": "[2, 6, 3, 0, 5, 4, 1, 7]",
-        "4854": "[3, 6, 1, 4, 2, 5, 0, 7]",
-        "4855": "[4, 2, 5, 0, 6, 3, 1, 7]",
-        "4856": "[5, 4, 3, 2, 1, 6, 0, 7]",
-        "4857": "[6, 2, 5, 0, 4, 3, 1, 7]",
-        "4858": "[0, 5, 3, 2, 6, 1, 4, 7]",
-        "4859": "[1, 6, 4, 3, 0, 2, 5, 7]",
-        "4860": "[2, 0, 5, 4, 1, 3, 6, 7]",
-        "4861": "[3, 4, 2, 5, 0, 1, 6, 7]",
-        "4862": "[4, 0, 6, 3, 1, 5, 2, 7]",
-        "4863": "[5, 2, 1, 6, 0, 3, 4, 7]",
-        "4864": "[6, 0, 4, 3, 1, 5, 2, 7]",
-        "4865": "[0, 6, 1, 5, 3, 2, 4, 7]",
-        "4866": "[1, 0, 2, 6, 4, 3, 5, 7]",
-        "4867": "[2, 1, 3, 0, 5, 4, 6, 7]",
-        "4868": "[3, 0, 1, 4, 2, 5, 6, 7]",
-        "4869": "[4, 1, 5, 0, 6, 3, 2, 7]",
-        "4870": "[5, 0, 3, 2, 1, 6, 4, 7]",
-        "4871": "[6, 1, 5, 0, 4, 3, 2, 7]",
-        "4872": "[0, 1, 3, 6, 4, 5, 2, 7]",
-        "4873": "[1, 2, 4, 0, 5, 6, 3, 7]",
-        "4874": "[2, 3, 5, 1, 6, 0, 4, 7]",
-        "4875": "[3, 1, 2, 0, 6, 4, 5, 7]",
-        "4876": "[4, 5, 6, 1, 2, 0, 3, 7]",
-        "4877": "[5, 3, 1, 0, 4, 2, 6, 7]",
-        "4878": "[6, 5, 4, 1, 2, 0, 3, 7]",
-        "4879": "[0, 2, 5, 6, 1, 4, 3, 7]",
-        "4880": "[1, 3, 6, 0, 2, 5, 4, 7]",
-        "4881": "[2, 4, 0, 1, 3, 6, 5, 7]",
-        "4882": "[3, 5, 4, 0, 1, 6, 2, 7]",
-        "4883": "[4, 3, 0, 1, 5, 2, 6, 7]",
-        "4884": "[5, 6, 2, 0, 3, 4, 1, 7]",
-        "4885": "[6, 3, 0, 1, 5, 2, 4, 7]",
-        "4886": "[0, 3, 5, 4, 2, 6, 1, 7]",
-        "4887": "[1, 4, 6, 5, 3, 0, 2, 7]",
-        "4888": "[2, 5, 0, 6, 4, 1, 3, 7]",
-        "4889": "[3, 2, 4, 6, 5, 0, 1, 7]",
-        "4890": "[4, 6, 0, 2, 3, 1, 5, 7]",
-        "4891": "[5, 1, 2, 4, 6, 0, 3, 7]",
-        "4892": "[6, 4, 0, 2, 3, 1, 5, 7]",
-        "4893": "[0, 4, 3, 5, 2, 6, 1, 7]",
-        "4894": "[1, 5, 4, 6, 3, 0, 2, 7]",
-        "4895": "[2, 6, 5, 0, 4, 1, 3, 7]",
-        "4896": "[3, 6, 2, 4, 5, 0, 1, 7]",
-        "4897": "[4, 2, 6, 0, 3, 1, 5, 7]",
-        "4898": "[5, 4, 1, 2, 6, 0, 3, 7]",
-        "4899": "[6, 2, 4, 0, 3, 1, 5, 7]",
-        "4900": "[0, 5, 6, 2, 1, 4, 3, 7]",
-        "4901": "[1, 6, 0, 3, 2, 5, 4, 7]",
-        "4902": "[2, 0, 1, 4, 3, 6, 5, 7]",
-        "4903": "[3, 4, 0, 5, 1, 6, 2, 7]",
-        "4904": "[4, 0, 1, 3, 5, 2, 6, 7]",
-        "4905": "[5, 2, 0, 6, 3, 4, 1, 7]",
-        "4906": "[6, 0, 1, 3, 5, 2, 4, 7]",
-        "4907": "[0, 6, 3, 5, 2, 4, 1, 7]",
-        "4908": "[1, 0, 4, 6, 3, 5, 2, 7]",
-        "4909": "[2, 1, 5, 0, 4, 6, 3, 7]",
-        "4910": "[3, 0, 2, 4, 5, 6, 1, 7]",
-        "4911": "[4, 1, 6, 0, 3, 2, 5, 7]",
-        "4912": "[5, 0, 1, 2, 6, 4, 3, 7]",
-        "4913": "[6, 1, 4, 0, 3, 2, 5, 7]",
-        "4914": "[0, 1, 4, 2, 5, 3, 6, 7]",
-        "4915": "[1, 2, 5, 3, 6, 4, 0, 7]",
-        "4916": "[2, 3, 6, 4, 0, 5, 1, 7]",
-        "4917": "[3, 1, 6, 5, 4, 2, 0, 7]",
-        "4918": "[4, 5, 2, 3, 0, 6, 1, 7]",
-        "4919": "[5, 3, 4, 6, 2, 1, 0, 7]",
-        "4920": "[6, 5, 2, 3, 0, 4, 1, 7]",
-        "4921": "[0, 2, 1, 3, 4, 5, 6, 7]",
-        "4922": "[1, 3, 2, 4, 5, 6, 0, 7]",
-        "4923": "[2, 4, 3, 5, 6, 0, 1, 7]",
-        "4924": "[3, 5, 1, 2, 6, 4, 0, 7]",
-        "4925": "[4, 3, 5, 6, 2, 0, 1, 7]",
-        "4926": "[5, 6, 3, 1, 4, 2, 0, 7]",
-        "4927": "[6, 3, 5, 4, 2, 0, 1, 7]",
-        "4928": "[0, 3, 2, 1, 6, 5, 4, 7]",
-        "4929": "[1, 4, 3, 2, 0, 6, 5, 7]",
-        "4930": "[2, 5, 4, 3, 1, 0, 6, 7]",
-        "4931": "[3, 2, 5, 1, 0, 4, 6, 7]",
-        "4932": "[4, 6, 3, 5, 1, 0, 2, 7]",
-        "4933": "[5, 1, 6, 3, 0, 2, 4, 7]",
-        "4934": "[6, 4, 3, 5, 1, 0, 2, 7]",
-        "4935": "[0, 4, 2, 1, 6, 3, 5, 7]",
-        "4936": "[1, 5, 3, 2, 0, 4, 6, 7]",
-        "4937": "[2, 6, 4, 3, 1, 5, 0, 7]",
-        "4938": "[3, 6, 5, 1, 0, 2, 4, 7]",
-        "4939": "[4, 2, 3, 5, 1, 6, 0, 7]",
-        "4940": "[5, 4, 6, 3, 0, 1, 2, 7]",
-        "4941": "[6, 2, 3, 5, 1, 4, 0, 7]",
-        "4942": "[0, 5, 1, 3, 4, 6, 2, 7]",
-        "4943": "[1, 6, 2, 4, 5, 0, 3, 7]",
-        "4944": "[2, 0, 3, 5, 6, 1, 4, 7]",
-        "4945": "[3, 4, 1, 2, 6, 0, 5, 7]",
-        "4946": "[4, 0, 5, 6, 2, 1, 3, 7]",
-        "4947": "[5, 2, 3, 1, 4, 0, 6, 7]",
-        "4948": "[6, 0, 5, 4, 2, 1, 3, 7]",
-        "4949": "[0, 6, 2, 1, 4, 3, 5, 7]",
-        "4950": "[1, 0, 3, 2, 5, 4, 6, 7]",
-        "4951": "[2, 1, 4, 3, 6, 5, 0, 7]",
-        "4952": "[3, 0, 5, 1, 6, 2, 4, 7]",
-        "4953": "[4, 1, 3, 5, 2, 6, 0, 7]",
-        "4954": "[5, 0, 6, 3, 4, 1, 2, 7]",
-        "4955": "[6, 1, 3, 5, 2, 4, 0, 7]",
-        "4956": "[0, 1, 5, 2, 6, 3, 4, 7]",
-        "4957": "[1, 2, 6, 3, 0, 4, 5, 7]",
-        "4958": "[2, 3, 0, 4, 1, 5, 6, 7]",
-        "4959": "[3, 1, 4, 5, 0, 2, 6, 7]",
-        "4960": "[4, 5, 0, 3, 1, 6, 2, 7]",
-        "4961": "[5, 3, 2, 6, 0, 1, 4, 7]",
-        "4962": "[6, 5, 0, 3, 1, 4, 2, 7]",
-        "4963": "[0, 2, 4, 3, 6, 5, 1, 7]",
-        "4964": "[1, 3, 5, 4, 0, 6, 2, 7]",
-        "4965": "[2, 4, 6, 5, 1, 0, 3, 7]",
-        "4966": "[3, 5, 6, 2, 0, 4, 1, 7]",
-        "4967": "[4, 3, 2, 6, 1, 0, 5, 7]",
-        "4968": "[5, 6, 4, 1, 0, 2, 3, 7]",
-        "4969": "[6, 3, 2, 4, 1, 0, 5, 7]",
-        "4970": "[0, 3, 6, 1, 4, 5, 2, 7]",
-        "4971": "[1, 4, 0, 2, 5, 6, 3, 7]",
-        "4972": "[2, 5, 1, 3, 6, 0, 4, 7]",
-        "4973": "[3, 2, 0, 1, 6, 4, 5, 7]",
-        "4974": "[4, 6, 1, 5, 2, 0, 3, 7]",
-        "4975": "[5, 1, 0, 3, 4, 2, 6, 7]",
-        "4976": "[6, 4, 1, 5, 2, 0, 3, 7]",
-        "4977": "[0, 4, 6, 1, 5, 3, 2, 7]",
-        "4978": "[1, 5, 0, 2, 6, 4, 3, 7]",
-        "4979": "[2, 6, 1, 3, 0, 5, 4, 7]",
-        "4980": "[3, 6, 0, 1, 4, 2, 5, 7]",
-        "4981": "[4, 2, 1, 5, 0, 6, 3, 7]",
-        "4982": "[5, 4, 0, 3, 2, 1, 6, 7]",
-        "4983": "[6, 2, 1, 5, 0, 4, 3, 7]",
-        "4984": "[0, 5, 4, 3, 2, 6, 1, 7]",
-        "4985": "[1, 6, 5, 4, 3, 0, 2, 7]",
-        "4986": "[2, 0, 6, 5, 4, 1, 3, 7]",
-        "4987": "[3, 4, 6, 2, 5, 0, 1, 7]",
-        "4988": "[4, 0, 2, 6, 3, 1, 5, 7]",
-        "4989": "[5, 2, 4, 1, 6, 0, 3, 7]",
-        "4990": "[6, 0, 2, 4, 3, 1, 5, 7]",
-        "4991": "[0, 6, 4, 1, 5, 3, 2, 7]",
-        "4992": "[1, 0, 5, 2, 6, 4, 3, 7]",
-        "4993": "[2, 1, 6, 3, 0, 5, 4, 7]",
-        "4994": "[3, 0, 6, 1, 4, 2, 5, 7]",
-        "4995": "[4, 1, 2, 5, 0, 6, 3, 7]",
-        "4996": "[5, 0, 4, 3, 2, 1, 6, 7]",
-        "4997": "[6, 1, 2, 5, 0, 4, 3, 7]",
-        "4998": "[0, 1, 6, 2, 5, 3, 4, 7]",
-        "4999": "[1, 2, 0, 3, 6, 4, 5, 7]",
-        "5000": "[2, 3, 1, 4, 0, 5, 6, 7]",
-        "5001": "[3, 1, 0, 5, 4, 2, 6, 7]",
-        "5002": "[4, 5, 1, 3, 0, 6, 2, 7]",
-        "5003": "[5, 3, 0, 6, 2, 1, 4, 7]",
-        "5004": "[6, 5, 1, 3, 0, 4, 2, 7]",
-        "5005": "[0, 2, 6, 3, 4, 5, 1, 7]",
-        "5006": "[1, 3, 0, 4, 5, 6, 2, 7]",
-        "5007": "[2, 4, 1, 5, 6, 0, 3, 7]",
-        "5008": "[3, 5, 0, 2, 6, 4, 1, 7]",
-        "5009": "[4, 3, 1, 6, 2, 0, 5, 7]",
-        "5010": "[5, 6, 0, 1, 4, 2, 3, 7]",
-        "5011": "[6, 3, 1, 4, 2, 0, 5, 7]",
-        "5012": "[0, 3, 4, 1, 6, 5, 2, 7]",
-        "5013": "[1, 4, 5, 2, 0, 6, 3, 7]",
-        "5014": "[2, 5, 6, 3, 1, 0, 4, 7]",
-        "5015": "[3, 2, 6, 1, 0, 4, 5, 7]",
-        "5016": "[4, 6, 2, 5, 1, 0, 3, 7]",
-        "5017": "[5, 1, 4, 3, 0, 2, 6, 7]",
-        "5018": "[6, 4, 2, 5, 1, 0, 3, 7]",
-        "5019": "[0, 4, 5, 1, 6, 3, 2, 7]",
-        "5020": "[1, 5, 6, 2, 0, 4, 3, 7]",
-        "5021": "[2, 6, 0, 3, 1, 5, 4, 7]",
-        "5022": "[3, 6, 4, 1, 0, 2, 5, 7]",
-        "5023": "[4, 2, 0, 5, 1, 6, 3, 7]",
-        "5024": "[5, 4, 2, 3, 0, 1, 6, 7]",
-        "5025": "[6, 2, 0, 5, 1, 4, 3, 7]",
-        "5026": "[0, 5, 2, 3, 4, 6, 1, 7]",
-        "5027": "[1, 6, 3, 4, 5, 0, 2, 7]",
-        "5028": "[2, 0, 4, 5, 6, 1, 3, 7]",
-        "5029": "[3, 4, 5, 2, 6, 0, 1, 7]",
-        "5030": "[4, 0, 3, 6, 2, 1, 5, 7]",
-        "5031": "[5, 2, 6, 1, 4, 0, 3, 7]",
-        "5032": "[6, 0, 3, 4, 2, 1, 5, 7]",
-        "5033": "[0, 6, 5, 1, 4, 3, 2, 7]",
-        "5034": "[1, 0, 6, 2, 5, 4, 3, 7]",
-        "5035": "[2, 1, 0, 3, 6, 5, 4, 7]",
-        "5036": "[3, 0, 4, 1, 6, 2, 5, 7]",
-        "5037": "[4, 1, 0, 5, 2, 6, 3, 7]",
-        "5038": "[5, 0, 2, 3, 4, 1, 6, 7]",
-        "5039": "[6, 1, 0, 5, 2, 4, 3, 7]"
-      }
-    }
-  }
-}
\ No newline at end of file