sss4 = {{1 -> {{0, 0, 1, {"B"}}, {2, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 2 -> {{0, 0, 1, {"A"}}, {1, 0, 3, {"A", "A", "B"}}, {3, 1, 1, {"A"}}, {4, 1, 1, {"B"}}, {7, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 3 -> {{0, 0, 3, {"A", "A", "B"}}, {2, 0, 1, {"A"}}, {7, 1, 1, {"B"}}, {8, 1, 1, {"A"}}, {27, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 4 -> {{2, 0, 1, {"B"}}, {5, 1, 1, {"B"}}, {6, 1, 1, {"A"}}, {10, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 5 -> {{4, 0, 1, {"B"}}, {6, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 6 -> {{4, 0, 1, {"A"}}, {5, 0, 3, {"A", "A", "B"}}, {7, 2, 2, {"A", "A"}}, {9, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 7 -> {{2, 0, 1, {"A"}}, {3, 0, 1, {"B"}}, {6, 0, 2, {"A", "A"}}, {8, 2, 2, {"A", "A"}}, {14, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 8 -> {{3, 0, 1, {"A"}}, {7, 0, 2, {"A", "A"}}, {18, 1, 1, {"B"}}, {26, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 9 -> {{6, 0, 1, {"B"}}, {10, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 10 -> {{4, 0, 1, {"A"}}, {9, 0, 3, {"A", "A", "B"}}, {11, 1, 1, {"B"}}, {14, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 11 -> {{10, 0, 1, {"B"}}, {12, 1, 1, {"B"}}, {13, 1, 1, {"A"}}, {16, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 12 -> {{11, 0, 1, {"B"}}, {13, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 13 -> {{11, 0, 1, {"A"}}, {12, 0, 3, {"A", "A", "B"}}, {14, 1, 1, {"A"}}, {15, 1, 1, {"B"}}, {17, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 14 -> {{7, 0, 1, {"B"}}, {10, 0, 2, {"A", "A"}}, {13, 0, 1, {"A"}}, {17, 1, 1, {"B"}}, {18, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 15 -> {{13, 0, 1, {"B"}}, {16, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 16 -> {{11, 0, 1, {"A"}}, {15, 0, 3, {"A", "A", "B"}}, {17, 2, 2, {"A", "A"}}, {19, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 17 -> {{13, 0, 1, {"A"}}, {14, 0, 1, {"B"}}, {16, 0, 2, {"A", "A"}}, {18, 1, 1, {"A"}}, {24, 1, 1, {"B"}}, {25, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 18 -> {{8, 0, 1, {"B"}}, {14, 0, 2, {"A", "A"}}, {17, 0, 1, {"A"}}, {25, 1, 1, {"B"}}, {26, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 19 -> {{16, 0, 1, {"B"}}, {20, 1, 1, {"B"}}, {21, 1, 1, {"A"}}, {23, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 20 -> {{19, 0, 1, {"B"}}, {21, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 21 -> {{19, 0, 1, {"A"}}, {20, 0, 3, {"A", "A", "B"}}, {22, 1, 1, {"B"}}, {24, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 22 -> {{21, 0, 1, {"B"}}, {23, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 23 -> {{19, 0, 1, {"A"}}, {22, 0, 3, {"A", "A", "B"}}, {24, 1, 1, {"A"}}, {28, 1, 1, {"B"}}, {31, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 24 -> {{17, 0, 1, {"B"}}, {21, 0, 2, {"A", "A"}}, {23, 0, 1, {"A"}}, {25, 2, 2, {"A", "A"}}, {31, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 25 -> {{17, 0, 1, {"A"}}, {18, 0, 1, {"B"}}, {24, 0, 2, {"A", "A"}}, {26, 1, 1, {"A"}}, {38, 1, 1, {"B"}}, {39, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 26 -> {{8, 0, 1, {"B"}}, {18, 0, 2, {"A", "A"}}, {25, 0, 1, {"A"}}, {27, 2, 2, {"A", "A"}}, {39, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 27 -> {{3, 0, 1, {"A"}}, {26, 0, 2, {"A", "A"}}, {56, 1, 1, {"B"}}, {66, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 28 -> {{23, 0, 1, {"B"}}, {29, 1, 1, {"B"}}, {30, 1, 1, {"A"}}, {33, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 29 -> {{28, 0, 1, {"B"}}, {30, 3, 3, {"A", "A", "B"}}, {Infinity, 0, 0, {}}}, 30 -> {{28, 0, 1, {"A"}}, {29, 0, 3, {"A", "A", "B"}}, {31, 2, 2, {"A", "A"}}, {Infinity, 1, 1, {"B"}}}, 31 -> {{23, 0, 1, {"A"}}, {24, 0, 1, {"B"}}, {30, 0, 2, {"A", "A"}}, {37, 1, 1, {"B"}}, {38, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 33 -> {{28, 0, 1, {"A"}}, {37, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "B"}}}, 37 -> {{31, 0, 1, {"B"}}, {33, 0, 2, {"A", "A"}}, {38, 1, 1, {"A"}}, {42, 1, 1, {"B"}}, {43, 1, 1, {"A"}}, {Infinity, 0, 1, {"A"}}}, 38 -> {{25, 0, 1, {"B"}}, {31, 0, 2, {"A", "A"}}, {37, 0, 1, {"A"}}, {39, 2, 2, {"A", "A"}}, {43, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 39 -> {{25, 0, 1, {"A"}}, {26, 0, 1, {"B"}}, {38, 0, 2, {"A", "A"}}, {55, 1, 1, {"B"}}, {56, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 42 -> {{37, 0, 1, {"B"}}, {43, 2, 2, {"A", "A"}}, {49, 1, 1, {"B"}}, {Infinity, 0, 3, {"A", "A", "A"}}}, 43 -> {{37, 0, 1, {"A"}}, {38, 0, 1, {"B"}}, {42, 0, 2, {"A", "A"}}, {54, 1, 1, {"B"}}, {55, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 49 -> {{42, 0, 1, {"B"}}, {54, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 54 -> {{43, 0, 1, {"B"}}, {49, 0, 2, {"A", "A"}}, {55, 1, 1, {"A"}}, {63, 1, 1, {"B"}}, {64, 1, 1, {"A"}}, {Infinity, 0, 1, {"A"}}}, 55 -> {{39, 0, 1, {"B"}}, {43, 0, 2, {"A", "A"}}, {54, 0, 1, {"A"}}, {56, 1, 1, {"A"}}, {64, 1, 1, {"B"}}, {65, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 56 -> {{27, 0, 1, {"B"}}, {39, 0, 2, {"A", "A"}}, {55, 0, 1, {"A"}}, {65, 1, 1, {"B"}}, {66, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 63 -> {{54, 0, 1, {"B"}}, {64, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 64 -> {{54, 0, 1, {"A"}}, {55, 0, 1, {"B"}}, {63, 0, 2, {"A", "A"}}, {65, 2, 2, {"A", "A"}}, {82, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 65 -> {{55, 0, 1, {"A"}}, {56, 0, 1, {"B"}}, {64, 0, 2, {"A", "A"}}, {66, 1, 1, {"A"}}, {94, 1, 1, {"B"}}, {95, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 66 -> {{27, 0, 1, {"B"}}, {56, 0, 2, {"A", "A"}}, {65, 0, 1, {"A"}}, {95, 1, 1, {"B"}}, {96, 1, 1, {"A"}}, {202, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 82 -> {{64, 0, 1, {"B"}}, {93, 1, 1, {"B"}}, {94, 2, 2, {"A", "A"}}, {Infinity, 0, 3, {"A", "A", "A"}}}, 93 -> {{82, 0, 1, {"B"}}, {94, 1, 1, {"A"}}, {116, 1, 1, {"A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 94 -> {{65, 0, 1, {"B"}}, {82, 0, 2, {"A", "A"}}, {93, 0, 1, {"A"}}, {95, 2, 2, {"A", "A"}}, {116, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 95 -> {{65, 0, 1, {"A"}}, {66, 0, 1, {"B"}}, {94, 0, 2, {"A", "A"}}, {96, 2, 2, {"A", "A"}}, {142, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 96 -> {{66, 0, 1, {"A"}}, {95, 0, 2, {"A", "A"}}, {156, 1, 1, {"B"}}, {201, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 116 -> {{93, 0, 1, {"A"}}, {94, 0, 1, {"B"}}, {141, 1, 1, {"B"}}, {142, 2, 2, {"A", "A"}}, {Infinity, 0, 2, {"A", "A"}}}, 141 -> {{116, 0, 1, {"B"}}, {142, 1, 1, {"A"}}, {154, 1, 1, {"B"}}, {155, 1, 1, {"A"}}, {Infinity, 0, 3, {"A", "A", "A"}}}, 142 -> {{95, 0, 1, {"B"}}, {116, 0, 2, {"A", "A"}}, {141, 0, 1, {"A"}}, {155, 1, 1, {"B"}}, {156, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 154 -> {{141, 0, 1, {"B"}}, {155, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 155 -> {{141, 0, 1, {"A"}}, {142, 0, 1, {"B"}}, {154, 0, 2, {"A", "A"}}, {156, 1, 1, {"A"}}, {199, 1, 1, {"B"}}, {200, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 156 -> {{96, 0, 1, {"B"}}, {142, 0, 2, {"A", "A"}}, {155, 0, 1, {"A"}}, {200, 1, 1, {"B"}}, {201, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 199 -> {{155, 0, 1, {"B"}}, {200, 2, 2, {"A", "A"}}, {234, 1, 1, {"B"}}, {Infinity, 0, 3, {"A", "A", "A"}}}, 200 -> {{155, 0, 1, {"A"}}, {156, 0, 1, {"B"}}, {199, 0, 2, {"A", "A"}}, {201, 1, 1, {"A"}}, {274, 1, 1, {"B"}}, {275, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 201 -> {{96, 0, 1, {"B"}}, {156, 0, 2, {"A", "A"}}, {200, 0, 1, {"A"}}, {202, 2, 2, {"A", "A"}}, {275, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 202 -> {{66, 0, 1, {"A"}}, {201, 0, 2, {"A", "A"}}, {361, 1, 1, {"B"}}, {414, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 234 -> {{199, 0, 1, {"B"}}, {274, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 274 -> {{200, 0, 1, {"B"}}, {234, 0, 2, {"A", "A"}}, {275, 2, 2, {"A", "A"}}, {294, 1, 1, {"B"}}, {Infinity, 0, 1, {"A"}}}, 275 -> {{200, 0, 1, {"A"}}, {201, 0, 1, {"B"}}, {274, 0, 2, {"A", "A"}}, {360, 1, 1, {"B"}}, {361, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 294 -> {{274, 0, 1, {"B"}}, {360, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 360 -> {{275, 0, 1, {"B"}}, {294, 0, 2, {"A", "A"}}, {361, 1, 1, {"A"}}, {412, 1, 1, {"B"}}, {413, 1, 1, {"A"}}, {Infinity, 0, 1, {"A"}}}, 361 -> {{202, 0, 1, {"B"}}, {275, 0, 2, {"A", "A"}}, {360, 0, 1, {"A"}}, {413, 1, 1, {"B"}}, {414, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 412 -> {{360, 0, 1, {"B"}}, {413, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 413 -> {{360, 0, 1, {"A"}}, {361, 0, 1, {"B"}}, {412, 0, 2, {"A", "A"}}, {414, 1, 1, {"A"}}, {562, 1, 1, {"B"}}, {563, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 414 -> {{202, 0, 1, {"B"}}, {361, 0, 2, {"A", "A"}}, {413, 0, 1, {"A"}}, {563, 1, 1, {"B"}}, {564, 1, 1, {"A"}}, {1110, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 562 -> {{413, 0, 1, {"B"}}, {563, 2, 2, {"A", "A"}}, {681, 1, 1, {"B"}}, {Infinity, 0, 3, {"A", "A", "A"}}}, 563 -> {{413, 0, 1, {"A"}}, {414, 0, 1, {"B"}}, {562, 0, 2, {"A", "A"}}, {564, 2, 2, {"A", "A"}}, {815, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 564 -> {{414, 0, 1, {"A"}}, {563, 0, 2, {"A", "A"}}, {879, 1, 1, {"B"}}, {1109, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 681 -> {{562, 0, 1, {"B"}}, {815, 2, 2, {"A", "A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 815 -> {{563, 0, 1, {"B"}}, {681, 0, 2, {"A", "A"}}, {878, 1, 1, {"B"}}, {879, 2, 2, {"A", "A"}}, {Infinity, 0, 1, {"A"}}}, 878 -> {{815, 0, 1, {"B"}}, {879, 1, 1, {"A"}}, {1108, 1, 1, {"A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 879 -> {{564, 0, 1, {"B"}}, {815, 0, 2, {"A", "A"}}, {878, 0, 1, {"A"}}, {1108, 1, 1, {"B"}}, {1109, 2, 2, {"A", "A"}}, {Infinity, 0, 0, {}}}, 1108 -> {{878, 0, 1, {"A"}}, {879, 0, 1, {"B"}}, {1109, 1, 1, {"A"}}, {1501, 1, 1, {"A"}}, {Infinity, 1, 3, {"B", "A", "A"}}}, 1109 -> {{564, 0, 1, {"B"}}, {879, 0, 2, {"A", "A"}}, {1108, 0, 1, {"A"}}, {1110, 2, 2, {"A", "A"}}, {1501, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 1110 -> {{414, 0, 1, {"A"}}, {1109, 0, 2, {"A", "A"}}, {1929, 1, 1, {"B"}}, {2199, 1, 1, {"B"}}, {Infinity, 0, 0, {}}}, 1501 -> {{1108, 0, 1, {"A"}}, {1109, 0, 1, {"B"}}, {1929, 2, 2, {"A", "A"}}, {Infinity, 1, 3, {"B", "A", "A"}}}, 1929 -> {{1110, 0, 1, {"B"}}, {1501, 0, 2, {"A", "A"}}, {2198, 1, 1, {"B"}}, {2199, 2, 2, {"A", "A"}}, {Infinity, 0, 1, {"A"}}}, 2198 -> {{1929, 0, 1, {"B"}}, {2199, 1, 1, {"A"}}, {2959, 1, 1, {"A"}}, {Infinity, 1, 4, {"B", "A", "A", "A"}}}, 2199 -> {{1110, 0, 1, {"B"}}, {1929, 0, 2, {"A", "A"}}, {2198, 0, 1, {"A"}}, {2959, 1, 1, {"B"}}, {2960, 1, 1, {"A"}}, {5733, 1, 1, {"A"}}, {Infinity, 0, 0, {}}}, 2959 -> {{2198, 0, 1, {"A"}}, {2199, 0, 1, {"B"}}, {2960, 2, 2, {"A", "A"}}, {Infinity, 1, 3, {"B", "A", "A"}}}, 2960 -> {{2199, 0, 1, {"A"}}, {2959, 0, 2, {"A", "A"}}, {Infinity, 2, 2, {"B", "B"}}}, 5733 -> {{2199, 0, 1, {"A"}}, {Infinity, 2, 4, {"B", "B", "A", "A"}}}}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 37, 38, 39, 42, 43, 49, 54, 55, 56, 63, 64, 65, 66, 82, 93, 94, 95, 96, 116, 141, 142, 154, 155, 156, 199, 200, 201, 202, 234, 274, 275, 294, 360, 361, 412, 413, 414, 562, 563, 564, 681, 815, 878, 879, 1108, 1109, 1110, 1501, 1929, 2198, 2199, 2959, 2960, 5733}, {{1, 0}, {1, 1}, {3, 2}, {1, 2}, {3, 3}, {2, 3}, {2, 2}, {5, 3}, {2, 4}, {1, 3}, {1, 4}, {3, 5}, {2, 5}, {4, 3}, {2, 6}, {1, 5}, {3, 4}, {4, 4}, {1, 6}, {3, 7}, {2, 7}, {2, 8}, {1, 7}, {4, 5}, {5, 5}, {5, 4}, {6, 3}, {1, 8}, {3, 9}, {2, 9}, {3, 6}, {1, 9}, {4, 7}, {4, 6}, {6, 5}, {3, 8}, {5, 7}, {4, 9}, {4, 8}, {5, 6}, {6, 4}, {5, 9}, {6, 7}, {7, 5}, {7, 4}, {5, 8}, {6, 9}, {6, 6}, {8, 5}, {9, 5}, {7, 7}, {6, 8}, {7, 6}, {7, 9}, {8, 7}, {8, 6}, {7, 8}, {9, 7}, {9, 6}, {10, 5}, {8, 9}, {8, 8}, {10, 7}, {9, 9}, {9, 8}, {10, 6}, {10, 9}, {11, 7}, {11, 6}, {10, 8}, {12, 7}, {13, 7}, {11, 9}, {11, 8}, {12, 9}, {12, 8}, {13, 9}, {13, 8}, {14, 7}, {14, 9}, {14, 8}, {15, 9}, {15, 8}, {16, 9}, {17, 9}, {18, 9}}, {{1}, {2}, {4, 7, 3}, {10, 6, 5, 14, 8, 27}, {11, 9, 17, 18, 26, 56, 66}, {16, 13, 12, 24, 25, 39, 65, 95, 96, 202}, {19, 15, 31, 38, 55, 94, 142, 156, 201, 361, 414}, {23, 21, 20, 37, 43, 64, 116, 155, 200, 275, 413, 563, 564, 1110}, {28, 22, 42, 54, 82, 141, 199, 274, 360, 562, 815, 879, 1109, 1929, 2199}, {33, 30, 29, 49, 63, 93, 154, 234, 294, 412, 681, 878, 1108, 1501, 2198, 2959, 2960, 5733}, {32, 34, 53, 76, 115, 181, 273, 359, 502, 814, 1107, 1500, 1928, 2958, 4240, 4564, 5732, 5734}, {35, 36, 41, 62, 81, 121, 198, 293, 411, 561, 877, 1287, 1592, 2197, 3564, 4563, 5731}, {40, 44, 69, 92, 140, 233, 332, 474, 680, 1017, 1499, 1927, 2655, 4239, 5730}, {45, 46, 48, 75, 103, 153, 241, 358, 501, 697, 1106, 1591, 2196, 2957, 4562}, {47, 50, 80, 114, 172, 272, 410, 560, 813, 1286, 1785, 2512, 3563, 5272}, {51, 52, 58, 88, 120, 180, 292, 424, 603, 876, 1322, 1926, 2654, 3635, 5729}, {57, 59, 91, 132, 197, 319, 473, 679, 965, 1498, 2195, 2956, 4238}, {60, 61, 68, 102, 139, 214, 331, 500, 696, 1016, 1590, 2242, 3151, 4561}, {67, 70, 107, 152, 232, 357, 541, 773, 1105, 1725, 2511, 3562, 5003}, {71, 72, 74, 113, 161, 240, 381, 559, 812, 1180, 1784, 2653, 3634, 5271}, {73, 77, 119, 171, 259, 409, 602, 875, 1285, 1925, 2861, 4046, 5728}, {78, 79, 84, 127, 179, 271, 423, 635, 906, 1321, 2047, 2955, 4237}, {83, 85, 131, 192, 291, 453, 678, 964, 1420, 2194, 3150, 4560}, {86, 87, 90, 138, 196, 302, 472, 695, 1015, 1497, 2241, 3330, 4699}, {89, 97, 145, 213, 318, 499, 742, 1082, 1589, 2411, 3561, 5002}, {98, 99, 101, 151, 221, 330, 515, 772, 1104, 1632, 2510, 3633, 5270}, {100, 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{1837, 1838, 1840, 2770, 4152}, {1839, 1844, 2776, 4163}, {1845, 1846, 1850, 2786, 4171}, {1849, 1851, 2790, 4186}, {1852, 1853, 1856, 2797, 4191}, {1855, 1862, 2802, 4203}, {1863, 1864, 1866, 2808, 4211}, {1865, 1871, 2818, 4222}, {1872, 1873, 1876, 2825, 4229}, {1875, 1877, 2828, 4251}, {1878, 1879, 1883, 2837, 4258}, {1882, 1887, 2843, 4269}, {1888, 1889, 1891, 2849, 4276}, {1890, 1893, 2853, 4286}, {1894, 1895, 1904, 2867, 4297}, {1903, 1905, 2871, 4309}, {1906, 1907, 1911, 2881, 4313}, {1910, 1913, 2885, 4327}, {1914, 1915, 1917, 2891, 4336}, {1916, 1930, 2897, 4346}, {1931, 1932, 1937, 2906, 4352}, {1936, 1938, 2909, 4369}, {1939, 1940, 1943, 2916, 4376}, {1942, 1946, 2925, 4392}, {1947, 1948, 1950, 2931, 4397}, {1949, 1955, 2936, 4408}, {1956, 1957, 1960, 2943, 4417}, {1959, 1961, 2947, 4430}, {1962, 1963, 1970, 2966, 4435}, {1969, 1973, 2972, 4446}, {1974, 1975, 1977, 2978, 4457}, {1976, 1979, 2983, 4468}, {1980, 1981, 1986, 2991, 4474}, {1985, 1987, 2994, 4486}, {1988, 1989, 1997, 3004, 4493}, {1996, 1999, 3009, 4509}, {2000, 2001, 2003, 3015, 4517}, {2002, 2006, 3024, 4527}, {2007, 2008, 2014, 3032, 4535}, {2013, 2015, 3036, 4548}, {2016, 2017, 2020, 3043, 4552}, {2019, 2024, 3049, 4575}, {2025, 2026, 2028, 3055, 4583}, {2027, 2031, 3064, 4593}, {2032, 2033, 2036, 3071, 4602}, {2035, 2037, 3074, 4614}, {2038, 2039, 2049, 3082, 4621}, {2048, 2055, 3090, 4633}, {2056, 2057, 2059, 3096, 4640}, {2058, 2061, 3100, 4651}, {2062, 2063, 2067, 3109, 4663}, {2066, 2068, 3113, 4674}, {2069, 2070, 2075, 3121, 4679}, {2074, 2077, 3125, 4691}, {2078, 2079, 2081, 3131, 4706}, {2080, 2086, 3142, 4717}, {2087, 2088, 2092, 3157, 4722}, {2091, 2093, 3160, 4736}, {2094, 2095, 2098, 3167, 4743}, {2097, 2106, 3173, 4755}, {2107, 2108, 2110, 3179, 4761}, {2109, 2114, 3185, 4771}, {2115, 2116, 2119, 3192, 4782}, {2118, 2120, 3196, 4799}, {2121, 2122, 2126, 3206, 4803}, {2125, 2133, 3211, 4815}, {2134, 2135, 2137, 3217, 4824}, {2136, 2139, 3222, 4834}, {2140, 2141, 2147, 3233, 4842}, {2146, 2148, 3236, 4853}, {2149, 2150, 2154, 3245, 4860}, {2153, 2156, 3250, 4876}, {2157, 2158, 2160, 3256, 4882}, {2159, 2164, 3261, 4893}, {2165, 2166, 2173, 3273, 4901}, {2172, 2174, 3277, 4915}, {2175, 2176, 2179, 3284, 4920}, {2178, 2182, 3291, 4933}, {2183, 2184, 2186, 3297, 4941}, {2185, 2200, 3303, 4952}, {2201, 2202, 2205, 3310, 4958}, {2204, 2206, 3313, 4976}, {2207, 2208, 2213, 3322, 4983}, {2212, 2216, 3334, 4994}, {2217, 2218, 2220, 3340, 5008}, {2219, 2222, 3344, 5018}, {2223, 2224, 2230, 3352, 5027}, {2229, 2231, 3356, 5039}, {2232, 2233, 2244, 3367, 5043}, {2243, 2246, 3371, 5057}, {2247, 2248, 2250, 3377, 5068}, {2249, 2253, 3384, 5078}, {2254, 2255, 2260, 3392, 5084}, {2259, 2261, 3395, 5096}, {2262, 2263, 2266, 3402, 5103}, {2265, 2272, 3410, 5119}, {2273, 2274, 2276, 3416, 5124}, {2275, 2279, 3426, 5135}, {2280, 2281, 2284, 3433, 5145}, {2283, 2285, 3437, 5157}, {2286, 2287, 2293, 3445, 5162}, {2292, 2297, 3451, 5173}, {2298, 2299, 2301, 3457, 5186}, {2300, 2303, 3462, 5197}, {2304, 2305, 2309, 3474, 5205}, {2308, 2310, 3477, 5217}, {2311, 2312, 2320, 3485, 5224}, {2319, 2322, 3490, 5236}, {2323, 2324, 2326, 3496, 5244}, {2325, 2334, 3503, 5254}, {2335, 2336, 2340, 3512, 5262}, {2339, 2341, 3516, 5283}, {2342, 2343, 2346, 3523, 5287}, {2345, 2350, 3528, 5300}, {2351, 2352, 2354, 3534, 5308}, {2353, 2359, 3543, 5318}, {2360, 2361, 2364, 3550, 5328}, {2363, 2365, 3553, 5341}, {2366, 2367, 2371, 3570, 5348}, {2370, 2377, 3576, 5360}, {2378, 2379, 2381, 3582, 5366}, {2380, 2383, 3586, 5377}, {2384, 2385, 2390, 3595, 5388}, {2389, 2391, 3599, 5399}, {2392, 2393, 2397, 3609, 5404}, {2396, 2399, 3613, 5421}, {2400, 2401, 2403, 3619, 5430}, {2402, 2412, 3625, 5441}, {2413, 2414, 2420, 3641, 5446}, {2419, 2421, 3644, 5460}, {2422, 2423, 2426, 3651, 5467}, {2425, 2429, 3658, 5483}, {2430, 2431, 2433, 3664, 5489}, {2432, 2437, 3669, 5499}, {2438, 2439, 2442, 3676, 5508}, {2441, 2443, 3680, 5523}, {2444, 2445, 2453, 3691, 5527}, {2452, 2456, 3698, 5539}, {2457, 2458, 2460, 3704, 5549}, {2459, 2462, 3709, 5559}, {2463, 2464, 2471, 3717, 5566}, {2470, 2472, 3720, 5577}, {2473, 2474, 2479, 3729, 5584}, {2478, 2481, 3734, 5600}, {2482, 2483, 2485, 3740, 5612}, {2484, 2488, 3749, 5623}, {2489, 2490, 2496, 3757, 5631}, {2495, 2497, 3761, 5643}, {2498, 2499, 2502, 3768, 5648}, {2501, 2513, 3778, 5661}, {2514, 2515, 2517, 3784, 5669}, {2516, 2520, 3791, 5680}, {2521, 2522, 2525, 3798, 5688}, {2524, 2526, 3801, 5701}, {2527, 2528, 2533, 3809, 5708}, {2532, 2541, 3817, 5719}, {2542, 2543, 2545, 3823}, {2544, 2547, 3827}, {2548, 2549, 2553, 3838}, {2552, 2554, 3842}, {2555, 2556, 2562, 3850}, {2561, 2564, 3854}, {2565, 2566, 2568, 3860}, {2567, 2572, 3867}, {2573, 2574, 2578, 3881}, {2577, 2579, 3884}, {2580, 2581, 2584, 3891}, {2583, 2590, 3897}, {2591, 2592, 2594, 3903}, {2593, 2601, 3910}, {2602, 2603, 2606, 3917}, {2605, 2607, 3921}, {2608, 2609, 2613, 3930}, {2612, 2617, 3935}, {2618, 2619, 2621, 3941}, {2620, 2623, 3946}, {2624, 2625, 2631, 3958}, {2630, 2632, 3961}, {2633, 2634, 2638, 3972}, {2637, 2640, 3977}, {2641, 2642, 2644, 3983}, {2643, 2656, 3988}, {2657, 2658, 2663, 3997}, {2662, 2664, 4001}, {2665, 2666, 2669, 4008}, {2668, 2672, 4015}, {2673, 2674, 2676, 4021}, {2675, 2682, 4027}, {2683, 2684, 2687, 4034}, {2686, 2688, 4037}, {2689, 2690, 2696, 4052}, {2695, 2699, 4059}, {2700, 2701, 2703, 4065}, {2702, 2705, 4069}, {2706, 2707, 2712, 4077}, {2711, 2713, 4081}, {2714, 2715, 2725, 4094}, {2724, 2727, 4098}, {2728, 2729, 2731, 4104}, {2730, 2734, 4112}, {2735, 2736, 2744, 4120}, {2743, 2745, 4123}, {2746, 2747, 2750, 4130}, {2749, 2754, 4137}, {2755, 2756, 2758, 4143}, {2757, 2761, 4151}, {2762, 2763, 2766, 4158}, {2765, 2767, 4162}, {2768, 2769, 2775, 4170}, {2774, 2781, 4179}, {2782, 2783, 2785, 4185}, {2784, 2787, 4190}, {2788, 2789, 2793, 4199}, {2792, 2794, 4202}, {2795, 2796, 2801, 4210}, {2800, 2803, 4215}, {2804, 2805, 2807, 4221}, {2806, 2815, 4228}, {2816, 2817, 2821, 4246}, {2820, 2822, 4250}, {2823, 2824, 2827, 4257}, {2826, 2832, 4262}, {2833, 2834, 2836, 4268}, {2835, 2840, 4275}, {2841, 2842, 2845, 4282}, {2844, 2846, 4285}, {2847, 2848, 2852, 4296}, {2851, 2862, 4302}, {2863, 2864, 2866, 4308}, {2865, 2868, 4312}, {2869, 2870, 2877, 4322}, {2876, 2878, 4326}, {2879, 2880, 2884, 4335}, {2883, 2886, 4339}, {2887, 2888, 2890, 4345}, {2889, 2894, 4351}, {2895, 2896, 2902, 4365}, {2901, 2903, 4368}, {2904, 2905, 2908, 4375}, {2907, 2911, 4385}, {2912, 2913, 2915, 4391}, {2914, 2922, 4396}, {2923, 2924, 2927, 4403}, {2926, 2928, 4407}, {2929, 2930, 2935, 4416}, {2934, 2938, 4423}, {2939, 2940, 2942, 4429}, {2941, 2944, 4434}, {2945, 2946, 2962, 4442}, {2961, 2963, 4445}, {2964, 2965, 2971, 4456}, {2970, 2973, 4461}, {2974, 2975, 2977, 4467}, {2976, 2980, 4473}, {2981, 2982, 2987, 4481}, {2986, 2988, 4485}, {2989, 2990, 2993, 4492}, {2992, 2999, 4502}, {3000, 3001, 3003, 4508}, {3002, 3006, 4516}, {3007, 3008, 3011, 4523}, {3010, 3012, 4526}, {3013, 3014, 3023, 4534}, {3022, 3027, 4541}, {3028, 3029, 3031, 4547}, {3030, 3033, 4551}, {3034, 3035, 3039, 4570}, {3038, 3040, 4574}, {3041, 3042, 3048, 4582}, {3047, 3050, 4586}, {3051, 3052, 3054, 4592}, {3053, 3061, 4601}, {3062, 3063, 3067, 4610}, {3066, 3068, 4613}, {3069, 3070, 3073, 4620}, {3072, 3077, 4626}, {3078, 3079, 3081, 4632}, {3080, 3087, 4639}, {3088, 3089, 3092, 4646}, {3091, 3093, 4650}, {3094, 3095, 3099, 4662}, {3098, 3104, 4667}, {3105, 3106, 3108, 4673}, {3107, 3110, 4678}, {3111, 3112, 3117, 4687}, {3116, 3118, 4690}, {3119, 3120, 3124, 4705}, {3123, 3126, 4710}, {3127, 3128, 3130, 4716}, {3129, 3139, 4721}, {3140, 3141, 3153, 4731}, {3152, 3154, 4735}, {3155, 3156, 3159, 4742}, {3158, 3162, 4748}, {3163, 3164, 3166, 4754}, {3165, 3170, 4760}, {3171, 3172, 3175, 4767}, {3174, 3176, 4770}, {3177, 3178, 3184, 4781}, {3183, 3187, 4792}, {3188, 3189, 3191, 4798}, {3190, 3193, 4802}, {3194, 3195, 3202, 4810}, {3201, 3203, 4814}, {3204, 3205, 3210, 4823}, {3209, 3212, 4827}, {3213, 3214, 3216, 4833}, {3215, 3219, 4841}, {3220, 3221, 3229, 4849}, {3228, 3230, 4852}, {3231, 3232, 3235, 4859}, {3234, 3240, 4869}, {3241, 3242, 3244, 4875}, {3243, 3247, 4881}, {3248, 3249, 3252, 4888}, {3251, 3253, 4892}, {3254, 3255, 3260, 4900}, {3259, 3268, 4908}, {3269, 3270, 3272, 4914}, {3271, 3274, 4919}, {3275, 3276, 3280, 4929}, {3279, 3281, 4932}, {3282, 3283, 3290, 4940}, {3289, 3292, 4945}, {3293, 3294, 3296, 4951}, {3295, 3300, 4957}, {3301, 3302, 3306, 4971}, {3305, 3307, 4975}, {3308, 3309, 3312, 4982}, {3311, 3317, 4987}, {3318, 3319, 3321, 4993}, {3320, 3331, 5007}, {3332, 3333, 3336, 5014}, {3335, 3337, 5017}, {3338, 3339, 3343, 5026}, {3342, 3347, 5032}, {3348, 3349, 3351, 5038}, {3350, 3353, 5042}, {3354, 3355, 3363, 5052}, {3362, 3364, 5056}, {3365, 3366, 3370, 5067}, {3369, 3372, 5071}, {3373, 3374, 3376, 5077}, {3375, 3381, 5083}, {3382, 3383, 3388, 5092}, {3387, 3389, 5095}, {3390, 3391, 3394, 5102}, {3393, 3397, 5112}, {3398, 3399, 3401, 5118}, {3400, 3407, 5123}, {3408, 3409, 3412, 5130}, {3411, 3413, 5134}, {3414, 3415, 3425, 5144}, {3424, 3428, 5150}, {3429, 3430, 3432, 5156}, {3431, 3434, 5161}, {3435, 3436, 3441, 5169}, {3440, 3442, 5172}, {3443, 3444, 3450, 5185}, {3449, 3452, 5190}, {3453, 3454, 3456, 5196}, {3455, 3459, 5204}, {3460, 3461, 3470, 5212}, {3469, 3471, 5216}, {3472, 3473, 3476, 5223}, {3475, 3480, 5229}, {3481, 3482, 3484, 5235}, {3483, 3487, 5243}, {3488, 3489, 3492, 5250}, {3491, 3493, 5253}, {3494, 3495, 3502, 5261}, {3501, 3507, 5276}, {3508, 3509, 3511, 5282}, {3510, 3513, 5286}, {3514, 3515, 3519, 5295}, {3518, 3520, 5299}, {3521, 3522, 3527, 5307}, {3526, 3529, 5311}, {3530, 3531, 3533, 5317}, {3532, 3540, 5327}, {3541, 3542, 3546, 5337}, {3545, 3547, 5340}, {3548, 3549, 3552, 5347}, {3551, 3565, 5353}, {3566, 3567, 3569, 5359}, {3568, 3573, 5365}, {3574, 3575, 3578, 5372}, {3577, 3579, 5376}, {3580, 3581, 3585, 5387}, {3584, 3590, 5392}, {3591, 3592, 3594, 5398}, {3593, 3596, 5403}, {3597, 3598, 3605, 5417}, {3604, 3606, 5420}, {3607, 3608, 3612, 5429}, {3611, 3614, 5434}, {3615, 3616, 3618, 5440}, {3617, 3622, 5445}, {3623, 3624, 3637, 5455}, {3636, 3638, 5459}, {3639, 3640, 3643, 5466}, {3642, 3646, 5476}, {3647, 3648, 3650, 5482}, {3649, 3655, 5488}, {3656, 3657, 3660, 5495}, {3659, 3661, 5498}, {3662, 3663, 3668, 5507}, {3667, 3671, 5516}, {3672, 3673, 3675, 5522}, {3674, 3677, 5526}, {3678, 3679, 3687, 5534}, {3686, 3688, 5538}, {3689, 3690, 3697, 5548}, {3696, 3699, 5552}, {3700, 3701, 3703, 5558}, {3702, 3706, 5565}, {3707, 3708, 3713, 5573}, {3712, 3714, 5576}, {3715, 3716, 3719, 5583}, {3718, 3724, 5593}, {3725, 3726, 3728, 5599}, {3727, 3731, 5611}, {3732, 3733, 3736, 5618}, {3735, 3737, 5622}, {3738, 3739, 3748, 5630}, {3747, 3752, 5636}, {3753, 3754, 3756, 5642}, {3755, 3758, 5647}, {3759, 3760, 3764, 5657}, {3763, 3765, 5660}, {3766, 3767, 3777, 5668}, {3776, 3779, 5673}, {3780, 3781, 3783, 5679}, {3782, 3788, 5687}, {3789, 3790, 3794, 5696}, {3793, 3795, 5700}, {3796, 3797, 3800, 5707}, {3799, 3804, 5712}, {3805, 3806, 3808, 5718}, {3807, 3814}, {3815, 3816, 3819}, {3818, 3820}, {3821, 3822, 3826}, {3825, 3833}, {3834, 3835, 3837}, {3836, 3839}, {3840, 3841, 3846}, {3845, 3847}, {3848, 3849, 3853}, {3852, 3855}, {3856, 3857, 3859}, {3858, 3864}, {3865, 3866, 3877}, {3876, 3878}, {3879, 3880, 3883}, {3882, 3886}, {3887, 3888, 3890}, {3889, 3894}, {3895, 3896, 3899}, {3898, 3900}, {3901, 3902, 3909}, {3908, 3912}, {3913, 3914, 3916}, {3915, 3918}, {3919, 3920, 3926}, {3925, 3927}, {3928, 3929, 3934}, {3933, 3936}, {3937, 3938, 3940}, {3939, 3943}, {3944, 3945, 3954}, {3953, 3955}, {3956, 3957, 3960}, {3959, 3967}, {3968, 3969, 3971}, {3970, 3974}, {3975, 3976, 3979}, {3978, 3980}, {3981, 3982, 3987}, {3986, 3992}, {3993, 3994, 3996}, {3995, 3998}, {3999, 4000, 4004}, {4003, 4005}, {4006, 4007, 4014}, {4013, 4016}, {4017, 4018, 4020}, {4019, 4024}, {4025, 4026, 4030}, {4029, 4031}, {4032, 4033, 4036}, {4035, 4047}, {4048, 4049, 4051}, {4050, 4056}, {4057, 4058, 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