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solve.py
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import gje
schedule = [[117, 30, 102, 114, 82, 127, 125, 85, 59, 122, 117, 107, 29, 103, 27, 120, 26, 26, 80, 7, 39, 74, 88, 47, 30, 62, 100, 113, 62, 13, 1, 50, 6, 1, 41, 91, 42, 79, 20, 70, 41, 62, 38, 114, 111, 113, 123, 93, 62, 117, 17, 75, 73, 46, 109, 112, 119, 2, 109, 95, 113, 88, 27, 63], [44, 1, 36, 119, 73, 7, 121, 62, 102, 84, 11, 122, 117, 111, 76, 33, 51, 13, 25, 59, 8, 59, 19, 76, 102, 125, 92, 86, 95, 7, 76, 94, 54, 68, 117, 15, 4, 111, 97, 22, 70, 92, 80, 47, 7, 57, 11, 75, 81, 48, 60, 22, 95, 69, 13, 20, 12, 118, 67, 17, 108, 101, 21, 32], [86, 111, 25, 49, 71, 68, 96, 53, 59, 127, 18, 0, 110, 61, 112, 51, 125, 86, 33, 122, 53, 69, 75, 12, 38, 100, 118, 29, 69, 110, 111, 73, 114, 71, 13, 123, 108, 120, 29, 108, 126, 98, 81, 39, 26, 105, 92, 0, 100, 50, 7, 48, 77, 113, 63, 77, 66, 87, 83, 44, 28, 119, 25, 85], [123, 58, 10, 30, 36, 35, 109, 107, 103, 74, 111, 35, 65, 122, 126, 3, 33, 26, 100, 51, 82, 73, 0, 33, 15, 52, 125, 67, 75, 74, 52, 33, 119, 105, 106, 17, 83, 58, 64, 94, 85, 63, 34, 103, 49, 6, 75, 51, 29, 119, 57, 127, 79, 81, 47, 1, 39, 20, 93, 47, 32, 67, 103, 35], [63, 97, 106, 108, 108, 78, 56, 70, 116, 60, 85, 113, 124, 16, 5, 27, 110, 25, 24, 88, 54, 48, 103, 24, 120, 101, 16, 90, 111, 67, 32, 30, 81, 73, 48, 92, 26, 75, 5, 75, 29, 36, 20, 18, 84, 100, 9, 118, 27, 13, 124, 93, 62, 33, 30, 26, 90, 44, 109, 86, 63, 72, 71, 110], [45, 16, 53, 2, 97, 88, 109, 62, 107, 31, 11, 38, 13, 112, 67, 31, 103, 65, 118, 87, 65, 120, 126, 41, 59, 38, 89, 67, 51, 117, 77, 61, 126, 109, 81, 6, 61, 57, 59, 85, 80, 36, 3, 68, 97, 30, 100, 23, 22, 14, 12, 20, 105, 36, 22, 93, 45, 54, 36, 93, 78, 72, 44, 71], [11, 66, 102, 110, 75, 83, 51, 85, 40, 60, 115, 9, 109, 88, 63, 106, 50, 60, 5, 47, 109, 112, 89, 34, 10, 9, 28, 64, 102, 65, 50, 69, 66, 106, 34, 114, 100, 46, 125, 70, 126, 74, 127, 40, 33, 32, 100, 117, 61, 125, 117, 105, 113, 56, 27, 49, 6, 107, 13, 42, 35, 33, 60, 108], [10, 53, 20, 85, 14, 2, 108, 75, 38, 24, 0, 32, 119, 49, 54, 46, 13, 2, 94, 79, 59, 87, 19, 30, 111, 70, 16, 67, 105, 1, 86, 8, 100, 21, 23, 14, 78, 95, 1, 47, 0, 45, 35, 42, 96, 96, 95, 117, 107, 104, 72, 114, 70, 125, 3, 84, 29, 55, 124, 47, 42, 69, 97, 72], [56, 89, 34, 102, 119, 20, 35, 108, 3, 38, 54, 34, 21, 93, 113, 95, 68, 72, 80, 68, 21, 50, 8, 18, 37, 81, 98, 126, 43, 105, 97, 28, 90, 114, 103, 2, 12, 48, 31, 19, 7, 44, 34, 24, 38, 49, 3, 104, 126, 2, 78, 70, 32, 91, 83, 47, 120, 80, 35, 28, 99, 71, 69, 100], [26, 43, 87, 126, 112, 57, 75, 95, 12, 69, 9, 10, 81, 111, 69, 49, 100, 53, 109, 46, 120, 113, 50, 92, 49, 116, 108, 64, 62, 39, 96, 56, 19, 92, 21, 114, 79, 19, 55, 121, 67, 55, 7, 20, 122, 68, 82, 53, 30, 111, 8, 3, 58, 64, 127, 56, 58, 65, 112, 83, 104, 36, 60, 0], [25, 9, 73, 124, 124, 116, 42, 107, 3, 30, 21, 110, 34, 59, 19, 32, 100, 56, 12, 54, 53, 123, 74, 38, 11, 42, 20, 9, 14, 22, 127, 26, 110, 24, 47, 124, 94, 36, 37, 18, 97, 26, 23, 67, 51, 15, 68, 59, 60, 126, 43, 72, 105, 35, 122, 34, 107, 107, 125, 6, 45, 68, 112, 37], [40, 11, 69, 55, 59, 3, 32, 121, 34, 87, 93, 14, 102, 49, 56, 41, 126, 101, 119, 87, 42, 70, 114, 89, 28, 125, 66, 63, 65, 58, 58, 31, 19, 22, 65, 77, 40, 15, 58, 18, 64, 20, 30, 55, 69, 14, 57, 121, 42, 109, 107, 23, 103, 29, 50, 93, 52, 98, 74, 107, 46, 115, 77, 73], [23, 23, 119, 106, 73, 16, 109, 53, 113, 101, 126, 80, 90, 8, 77, 111, 44, 86, 57, 54, 27, 18, 91, 119, 47, 126, 38, 73, 44, 11, 39, 65, 84, 126, 85, 9, 20, 29, 115, 68, 52, 49, 80, 34, 123, 5, 106, 125, 127, 100, 117, 108, 102, 76, 88, 77, 6, 8, 88, 84, 91, 39, 52, 12], [22, 50, 30, 27, 94, 124, 73, 92, 21, 17, 112, 19, 66, 123, 20, 104, 4, 106, 83, 21, 89, 125, 54, 118, 67, 74, 71, 27, 88, 63, 50, 60, 40, 126, 102, 114, 90, 42, 114, 29, 53, 93, 40, 67, 104, 96, 74, 114, 47, 42, 59, 64, 45, 98, 63, 5, 87, 119, 51, 11, 36, 114, 97, 65], [12, 60, 35, 27, 55, 15, 44, 88, 86, 39, 0, 59, 126, 118, 60, 126, 117, 32, 63, 123, 67, 89, 3, 9, 62, 107, 94, 46, 100, 97, 7, 5, 108, 76, 19, 115, 38, 49, 125, 7, 5, 122, 44, 90, 77, 110, 77, 65, 37, 71, 16, 82, 118, 83, 99, 65, 50, 125, 118, 110, 121, 41, 75, 127], [20, 47, 95, 54, 86, 122, 5, 101, 86, 120, 28, 100, 24, 3, 87, 19, 82, 33, 12, 35, 38, 43, 122, 92, 47, 2, 115, 64, 105, 98, 55, 50, 30, 75, 98, 14, 9, 124, 49, 106, 91, 96, 87, 70, 84, 1, 10, 10, 107, 0, 37, 52, 99, 105, 35, 2, 7, 75, 64, 36, 110, 0, 56, 96], [36, 32, 42, 4, 69, 86, 76, 76, 125, 35, 31, 50, 115, 41, 47, 90, 106, 106, 110, 77, 103, 32, 76, 54, 73, 114, 20, 108, 84, 120, 120, 82, 19, 22, 122, 31, 89, 82, 111, 59, 56, 55, 53, 48, 63, 92, 97, 76, 19, 103, 100, 15, 60, 96, 47, 17, 86, 80, 6, 97, 96, 116, 47, 117], [6, 55, 98, 66, 66, 108, 84, 88, 80, 19, 33, 7, 46, 61, 113, 87, 15, 112, 28, 86, 11, 82, 93, 13, 116, 79, 114, 10, 73, 51, 123, 40, 73, 125, 42, 56, 64, 24, 3, 42, 20, 92, 80, 46, 9, 74, 38, 22, 7, 63, 101, 31, 51, 97, 120, 71, 80, 99, 39, 51, 78, 95, 28, 107], [92, 68, 16, 117, 9, 70, 44, 15, 60, 78, 0, 56, 124, 4, 104, 74, 25, 14, 26, 120, 64, 32, 49, 7, 6, 108, 72, 26, 20, 95, 66, 17, 20, 38, 104, 76, 78, 96, 127, 55, 55, 11, 46, 9, 37, 6, 85, 79, 75, 37, 61, 16, 58, 6, 116, 110, 30, 103, 77, 6, 99, 33, 127, 37], [3, 61, 83, 4, 18, 57, 18, 66, 95, 43, 85, 48, 80, 31, 112, 65, 27, 45, 70, 4, 28, 37, 92, 8, 114, 16, 9, 46, 85, 56, 35, 112, 77, 30, 103, 23, 41, 98, 120, 78, 47, 12, 92, 72, 84, 94, 108, 60, 45, 57, 71, 110, 61, 20, 109, 83, 21, 14, 15, 6, 121, 97, 46, 120], [8, 28, 83, 70, 68, 63, 2, 29, 32, 38, 117, 40, 49, 105, 41, 59, 124, 59, 20, 67, 24, 38, 38, 64, 112, 5, 27, 87, 107, 26, 44, 42, 1, 51, 5, 25, 115, 4, 123, 45, 17, 120, 8, 102, 126, 118, 119, 116, 61, 90, 54, 108, 117, 83, 0, 44, 3, 9, 48, 41, 37, 100, 7, 124], [40, 68, 95, 74, 124, 57, 79, 36, 117, 114, 78, 19, 82, 103, 37, 82, 22, 43, 98, 78, 36, 41, 79, 108, 7, 112, 107, 111, 87, 59, 89, 15, 26, 55, 51, 66, 7, 49, 47, 67, 112, 36, 71, 60, 44, 105, 117, 47, 83, 16, 12, 75, 120, 110, 47, 72, 96, 77, 66, 46, 87, 104, 18, 84], [116, 74, 71, 23, 18, 61, 104, 7, 13, 101, 99, 72, 64, 73, 63, 122, 59, 43, 104, 61, 30, 64, 66, 45, 119, 65, 73, 86, 85, 79, 45, 26, 14, 6, 96, 20, 51, 23, 119, 41, 62, 41, 97, 51, 45, 39, 21, 67, 75, 0, 59, 72, 85, 26, 68, 113, 118, 54, 123, 53, 0, 72, 102, 8], [17, 116, 59, 79, 125, 118, 44, 49, 88, 13, 3, 73, 60, 121, 3, 30, 21, 70, 78, 96, 117, 102, 48, 4, 59, 57, 55, 114, 82, 83, 16, 74, 92, 41, 105, 123, 6, 67, 6, 66, 122, 81, 56, 36, 90, 115, 124, 92, 17, 42, 44, 57, 100, 120, 9, 89, 95, 117, 63, 16, 116, 11, 38, 0], [40, 37, 3, 79, 106, 53, 63, 108, 65, 105, 105, 108, 30, 81, 78, 20, 116, 107, 89, 39, 122, 121, 106, 48, 73, 91, 26, 22, 120, 82, 22, 37, 124, 98, 103, 41, 59, 119, 78, 33, 83, 28, 58, 58, 65, 66, 40, 26, 8, 95, 44, 12, 82, 14, 78, 57, 64, 119, 50, 127, 59, 86, 22, 56], [97, 42, 5, 9, 96, 89, 113, 1, 40, 38, 108, 23, 105, 12, 62, 19, 41, 8, 98, 18, 15, 6, 44, 4, 38, 81, 89, 28, 41, 8, 63, 108, 24, 30, 119, 19, 23, 19, 64, 23, 63, 24, 28, 27, 37, 63, 68, 11, 125, 61, 95, 32, 127, 2, 93, 44, 13, 55, 44, 102, 70, 8, 104, 98], [56, 75, 122, 105, 89, 16, 88, 53, 3, 39, 123, 91, 113, 10, 79, 22, 0, 89, 115, 67, 55, 59, 20, 27, 87, 72, 12, 125, 105, 24, 16, 103, 12, 115, 83, 12, 27, 20, 7, 121, 100, 27, 26, 127, 25, 113, 116, 121, 1, 109, 82, 50, 124, 69, 77, 110, 19, 68, 116, 59, 74, 65, 21, 93], [50, 15, 76, 16, 125, 0, 7, 92, 59, 15, 115, 39, 25, 9, 1, 70, 94, 103, 66, 48, 63, 39, 67, 102, 119, 84, 59, 46, 42, 111, 125, 8, 121, 38, 124, 68, 8, 46, 14, 34, 107, 61, 113, 24, 5, 42, 110, 114, 99, 6, 64, 35, 119, 74, 125, 42, 23, 106, 79, 9, 89, 73, 89, 90], [17, 92, 97, 105, 29, 57, 11, 51, 118, 101, 112, 108, 29, 35, 105, 37, 18, 93, 87, 13, 4, 88, 115, 120, 4, 119, 25, 84, 17, 24, 22, 13, 47, 100, 125, 56, 79, 75, 78, 69, 59, 59, 89, 108, 40, 120, 61, 91, 59, 32, 98, 49, 5, 32, 19, 1, 71, 6, 116, 107, 40, 36, 20, 113], [85, 66, 62, 87, 55, 72, 119, 16, 89, 66, 40, 38, 36, 52, 31, 77, 99, 59, 62, 50, 15, 1, 9, 58, 62, 79, 49, 26, 66, 72, 66, 78, 34, 62, 24, 51, 79, 125, 125, 49, 50, 23, 24, 5, 36, 67, 2, 27, 89, 84, 52, 109, 47, 111, 89, 37, 106, 79, 85, 59, 44, 58, 35, 45], [104, 119, 99, 116, 102, 127, 57, 33, 48, 120, 24, 103, 67, 44, 110, 120, 44, 1, 36, 14, 97, 5, 114, 30, 21, 89, 92, 54, 100, 19, 40, 91, 20, 108, 80, 0, 111, 56, 36, 1, 33, 30, 115, 101, 63, 117, 108, 8, 4, 63, 126, 3, 38, 82, 4, 23, 5, 126, 49, 97, 34, 37, 25, 122], [29, 2, 69, 120, 6, 104, 21, 32, 41, 102, 85, 126, 114, 116, 66, 101, 16, 53, 98, 18, 4, 39, 104, 115, 41, 72, 44, 10, 42, 83, 21, 103, 97, 99, 60, 101, 25, 83, 10, 42, 57, 118, 10, 76, 10, 103, 81, 10, 19, 110, 126, 51, 50, 18, 40, 35, 68, 3, 75, 97, 26, 89, 57, 59], [126, 31, 97, 26, 5, 59, 54, 41, 60, 111, 32, 57, 29, 86, 4, 21, 58, 115, 12, 107, 75, 7, 9, 59, 83, 120, 81, 78, 17, 16, 109, 63, 36, 76, 64, 12, 22, 39, 16, 126, 100, 117, 96, 21, 87, 38, 24, 11, 88, 71, 50, 115, 108, 110, 70, 115, 79, 62, 99, 103, 93, 90, 122, 84], [42, 1, 71, 1, 45, 112, 121, 38, 69, 78, 46, 39, 10, 90, 54, 46, 114, 21, 12, 56, 19, 126, 36, 81, 38, 6, 88, 93, 64, 62, 28, 28, 107, 120, 120, 45, 83, 33, 103, 0, 110, 4, 0, 110, 7, 37, 70, 110, 73, 42, 65, 95, 31, 72, 60, 8, 121, 69, 70, 69, 49, 16, 46, 110], [19, 106, 21, 2, 76, 67, 85, 98, 114, 28, 32, 74, 9, 50, 45, 35, 32, 36, 123, 108, 103, 95, 89, 108, 36, 120, 33, 103, 11, 43, 47, 31, 84, 101, 20, 43, 76, 110, 94, 123, 13, 54, 66, 31, 43, 35, 8, 13, 93, 28, 43, 28, 106, 11, 109, 61, 101, 104, 1, 74, 62, 59, 117, 95], [33, 16, 77, 39, 89, 56, 100, 100, 57, 91, 38, 120, 103, 63, 90, 118, 61, 85, 17, 98, 49, 51, 40, 111, 114, 30, 36, 74, 122, 39, 84, 78, 12, 111, 8, 69, 20, 73, 75, 48, 53, 106, 111, 20, 39, 93, 103, 10, 64, 85, 27, 93, 57, 19, 31, 94, 110, 25, 35, 71, 53, 69, 6, 96], [75, 93, 39, 15, 45, 19, 46, 100, 96, 28, 62, 5, 69, 70, 7, 30, 109, 55, 78, 114, 127, 17, 46, 55, 46, 38, 100, 57, 121, 5, 84, 2, 109, 109, 90, 19, 58, 41, 69, 12, 46, 82, 122, 46, 93, 1, 49, 12, 50, 101, 6, 76, 77, 84, 54, 120, 45, 11, 122, 12, 36, 108, 92, 39], [57, 85, 70, 29, 52, 83, 11, 24, 2, 74, 13, 57, 58, 23, 86, 52, 36, 47, 51, 64, 108, 72, 50, 87, 105, 7, 123, 24, 68, 17, 23, 6, 101, 18, 83, 45, 48, 73, 52, 55, 56, 0, 93, 66, 121, 83, 15, 123, 79, 20, 99, 19, 36, 118, 62, 41, 59, 15, 66, 89, 15, 73, 64, 101], [15, 114, 109, 5, 115, 68, 7, 6, 58, 40, 56, 40, 23, 86, 74, 95, 37, 105, 36, 4, 118, 75, 112, 0, 85, 70, 34, 54, 54, 65, 10, 38, 94, 79, 53, 52, 60, 117, 35, 40, 107, 6, 52, 65, 43, 10, 80, 11, 76, 44, 99, 102, 92, 8, 16, 124, 37, 105, 64, 68, 92, 34, 22, 41], [126, 70, 29, 36, 125, 61, 126, 51, 119, 36, 51, 99, 94, 7, 17, 7, 43, 86, 91, 4, 126, 97, 56, 1, 97, 5, 62, 107, 10, 110, 15, 125, 14, 23, 22, 10, 101, 16, 28, 89, 107, 94, 41, 73, 46, 3, 109, 25, 121, 45, 0, 85, 0, 67, 65, 11, 65, 28, 16, 9, 126, 118, 105, 37], [31, 92, 54, 53, 123, 93, 54, 7, 127, 44, 52, 88, 86, 117, 89, 67, 54, 60, 34, 14, 89, 65, 7, 43, 55, 122, 73, 51, 96, 59, 71, 12, 7, 125, 107, 1, 21, 85, 24, 68, 95, 28, 67, 104, 85, 127, 77, 48, 22, 65, 123, 63, 33, 13, 112, 95, 47, 69, 48, 108, 61, 13, 31, 45], [34, 127, 122, 98, 34, 110, 99, 99, 44, 1, 49, 107, 76, 121, 63, 70, 77, 11, 104, 45, 103, 89, 51, 56, 65, 87, 43, 110, 90, 38, 17, 88, 31, 3, 120, 117, 61, 55, 64, 55, 28, 67, 80, 52, 10, 124, 40, 88, 31, 44, 58, 87, 116, 93, 59, 33, 25, 95, 59, 39, 71, 50, 85, 127], [73, 90, 47, 109, 5, 11, 80, 85, 86, 111, 18, 100, 78, 13, 102, 95, 54, 75, 43, 115, 60, 32, 2, 14, 82, 68, 57, 14, 98, 17, 10, 100, 0, 113, 5, 122, 1, 80, 126, 97, 81, 83, 32, 12, 58, 18, 1, 98, 59, 123, 15, 26, 2, 91, 4, 23, 107, 50, 68, 45, 44, 39, 30, 58], [59, 20, 97, 51, 90, 69, 99, 50, 86, 115, 38, 32, 92, 66, 82, 2, 77, 63, 40, 34, 68, 49, 80, 56, 7, 48, 104, 31, 85, 11, 111, 100, 3, 107, 21, 77, 22, 45, 62, 7, 66, 53, 20, 28, 9, 85, 55, 71, 20, 16, 35, 56, 24, 24, 0, 123, 37, 77, 66, 114, 104, 89, 51, 27], [26, 63, 5, 100, 90, 108, 73, 105, 61, 14, 39, 16, 13, 100, 104, 89, 43, 35, 71, 16, 32, 79, 44, 59, 123, 92, 6, 0, 72, 74, 76, 62, 73, 97, 41, 98, 84, 2, 52, 37, 121, 94, 45, 116, 0, 32, 92, 66, 116, 23, 101, 93, 54, 73, 27, 75, 66, 56, 89, 60, 59, 31, 74, 38], [37, 47, 62, 31, 94, 82, 23, 39, 87, 72, 78, 109, 22, 116, 88, 52, 2, 121, 82, 50, 78, 64, 43, 71, 24, 46, 14, 0, 50, 17, 105, 89, 84, 80, 56, 7, 14, 4, 107, 33, 103, 21, 2, 67, 17, 82, 67, 112, 109, 103, 27, 10, 3, 40, 118, 39, 87, 127, 29, 24, 62, 7, 70, 15], [117, 38, 59, 57, 94, 12, 103, 104, 4, 8, 127, 29, 86, 47, 18, 43, 92, 110, 112, 79, 63, 58, 32, 109, 104, 20, 43, 106, 29, 93, 1, 125, 113, 118, 115, 84, 21, 50, 49, 99, 108, 70, 92, 98, 124, 67, 46, 10, 54, 124, 44, 48, 122, 2, 69, 35, 117, 92, 105, 98, 54, 40, 91, 71], [113, 104, 102, 56, 32, 119, 18, 124, 6, 107, 123, 27, 57, 39, 49, 91, 1, 30, 30, 113, 107, 91, 13, 69, 119, 88, 37, 48, 75, 87, 35, 96, 23, 109, 75, 77, 17, 47, 108, 19, 68, 41, 80, 46, 23, 122, 50, 101, 54, 114, 41, 27, 105, 117, 42, 19, 94, 5, 93, 13, 125, 96, 41, 122], [12, 58, 106, 67, 50, 32, 109, 77, 19, 114, 61, 98, 53, 127, 65, 89, 54, 103, 11, 64, 85, 95, 51, 2, 21, 36, 115, 72, 68, 96, 94, 116, 7, 98, 120, 98, 60, 13, 27, 37, 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101, 117, 95, 40, 66, 110, 39, 87, 34, 57, 48, 24, 79, 74, 46, 10, 0, 41, 9, 40, 4, 90, 36, 98, 30, 79, 49, 94, 100, 105], [72, 13, 73, 3, 21, 127, 123, 43, 23, 20, 83, 100, 22, 116, 19, 18, 61, 22, 70, 100, 60, 19, 30, 121, 0, 82, 76, 29, 83, 46, 116, 35, 9, 53, 95, 15, 66, 15, 127, 114, 49, 65, 79, 30, 125, 41, 114, 9, 112, 73, 102, 5, 47, 34, 101, 38, 45, 71, 69, 107, 113, 8, 30, 89], [70, 54, 103, 89, 114, 32, 57, 92, 50, 80, 3, 49, 105, 87, 123, 62, 10, 41, 95, 1, 50, 47, 75, 85, 78, 29, 31, 22, 114, 66, 125, 93, 87, 99, 90, 1, 36, 57, 103, 107, 118, 10, 16, 85, 36, 53, 120, 42, 112, 85, 89, 66, 32, 79, 118, 84, 44, 2, 37, 119, 5, 104, 53, 11], [65, 42, 85, 25, 64, 28, 86, 120, 65, 1, 46, 43, 81, 34, 98, 18, 106, 83, 35, 109, 116, 59, 16, 17, 125, 36, 32, 31, 28, 37, 81, 26, 9, 91, 122, 34, 108, 23, 107, 55, 27, 107, 34, 75, 49, 59, 45, 90, 78, 102, 40, 62, 85, 115, 70, 28, 9, 83, 92, 118, 0, 114, 8, 58], [36, 31, 26, 62, 62, 93, 4, 120, 3, 33, 28, 48, 94, 62, 96, 123, 126, 78, 5, 76, 53, 117, 63, 34, 21, 10, 101, 84, 36, 66, 77, 80, 102, 16, 26, 30, 113, 62, 45, 61, 96, 64, 44, 34, 25, 47, 96, 49, 31, 57, 3, 24, 121, 114, 92, 124, 32, 100, 115, 126, 29, 1, 83, 87], [2, 4, 48, 97, 120, 66, 52, 18, 65, 108, 91, 13, 56, 88, 15, 60, 19, 37, 8, 47, 35, 64, 54, 67, 32, 72, 121, 83, 9, 3, 14, 49, 37, 84, 21, 91, 12, 4, 83, 37, 33, 88, 36, 67, 122, 59, 25, 60, 61, 86, 59, 42, 93, 8, 77, 99, 16, 62, 78, 16, 49, 58, 77, 116], [86, 0, 61, 49, 51, 49, 82, 52, 100, 15, 14, 34, 18, 42, 68, 93, 53, 101, 91, 16, 12, 89, 82, 33, 30, 95, 123, 50, 10, 23, 125, 13, 42, 108, 32, 91, 98, 28, 38, 88, 123, 119, 104, 119, 66, 119, 72, 80, 72, 14, 68, 86, 21, 47, 13, 15, 54, 45, 105, 31, 41, 72, 76, 76], [65, 48, 67, 51, 109, 90, 17, 82, 94, 5, 96, 22, 48, 68, 49, 14, 88, 127, 62, 72, 49, 99, 17, 94, 31, 86, 105, 70, 25, 71, 53, 125, 25, 62, 15, 30, 98, 6, 50, 65, 17, 61, 64, 123, 63, 75, 112, 69, 110, 121, 121, 118, 79, 90, 69, 88, 2, 127, 99, 34, 30, 110, 29, 63], [111, 93, 55, 38, 59, 108, 53, 108, 36, 118, 99, 89, 16, 60, 99, 73, 25, 11, 106, 70, 55, 3, 93, 105, 48, 108, 121, 122, 37, 73, 118, 112, 43, 48, 32, 61, 66, 103, 3, 3, 75, 76, 49, 96, 113, 42, 75, 68, 115, 56, 68, 47, 1, 123, 16, 104, 104, 53, 40, 31, 99, 113, 98, 5], [75, 110, 29, 118, 61, 101, 52, 44, 40, 27, 97, 85, 28, 111, 39, 104, 6, 23, 50, 29, 40, 119, 58, 115, 113, 74, 78, 95, 127, 109, 32, 11, 120, 74, 114, 18, 11, 63, 76, 52, 83, 64, 52, 91, 51, 9, 69, 11, 122, 83, 88, 9, 85, 8, 91, 49, 94, 125, 100, 115, 35, 93, 83, 66], [108, 127, 127, 62, 22, 68, 62, 111, 24, 23, 14, 69, 17, 15, 13, 53, 16, 52, 117, 119, 25, 68, 14, 34, 6, 49, 3, 17, 82, 13, 91, 90, 86, 100, 122, 122, 89, 54, 119, 62, 37, 125, 113, 35, 27, 44, 68, 93, 91, 15, 49, 104, 116, 76, 44, 6, 22, 18, 7, 61, 90, 125, 48, 5], [24, 67, 62, 14, 30, 71, 45, 81, 77, 91, 102, 25, 123, 12, 6, 94, 19, 5, 92, 18, 97, 59, 17, 46, 1, 36, 5, 106, 38, 1, 11, 14, 119, 1, 53, 58, 51, 85, 57, 28, 17, 98, 96, 87, 81, 75, 9, 77, 67, 106, 113, 10, 112, 87, 118, 0, 60, 121, 28, 17, 91, 50, 25, 16], [120, 19, 85, 109, 79, 112, 47, 71, 16, 56, 45, 29, 70, 84, 90, 0, 69, 98, 54, 16, 127, 28, 65, 66, 121, 82, 110, 110, 78, 81, 105, 7, 23, 37, 96, 58, 81, 46, 44, 50, 18, 51, 22, 37, 58, 62, 59, 32, 66, 82, 111, 121, 56, 73, 79, 102, 50, 77, 95, 91, 96, 117, 123, 33], [75, 92, 17, 111, 106, 48, 20, 61, 5, 114, 117, 72, 104, 67, 99, 101, 124, 48, 65, 125, 86, 70, 12, 63, 69, 16, 70, 90, 74, 31, 111, 38, 59, 73, 27, 91, 42, 84, 104, 47, 39, 42, 11, 89, 29, 71, 75, 83, 121, 110, 126, 35, 126, 49, 91, 74, 14, 93, 52, 100, 21, 107, 17, 12], [120, 95, 30, 17, 78, 23, 106, 126, 98, 19, 101, 100, 121, 54, 81, 9, 49, 97, 40, 94, 96, 47, 61, 38, 82, 112, 29, 111, 112, 80, 39, 55, 29, 116, 79, 40, 6, 84, 52, 17, 122, 22, 108, 12, 102, 75, 28, 24, 46, 121, 76, 23, 104, 57, 121, 77, 7, 4, 110, 42, 8, 25, 70, 73], [111, 22, 63, 61, 36, 77, 32, 53, 66, 34, 93, 81, 52, 21, 57, 27, 76, 31, 79, 105, 39, 110, 74, 113, 127, 94, 47, 54, 43, 1, 25, 14, 32, 16, 32, 39, 127, 112, 69, 59, 15, 46, 98, 82, 93, 60, 53, 113, 109, 63, 2, 115, 53, 122, 120, 62, 44, 109, 80, 17, 69, 44, 104, 46], [124, 54, 94, 81, 63, 5, 61, 33, 55, 63, 110, 4, 40, 98, 27, 36, 71, 35, 80, 77, 69, 12, 84, 90, 84, 122, 11, 73, 16, 72, 105, 0, 36, 88, 6, 123, 50, 83, 20, 60, 17, 100, 24, 28, 105, 32, 84, 0, 126, 47, 64, 34, 99, 26, 97, 0, 97, 92, 126, 98, 70, 28, 41, 23], [6, 24, 106, 26, 123, 57, 105, 43, 69, 34, 28, 0, 50, 97, 5, 94, 125, 126, 53, 67, 125, 2, 102, 92, 66, 44, 12, 26, 92, 56, 91, 100, 44, 2, 93, 52, 15, 110, 42, 93, 45, 56, 124, 68, 78, 79, 1, 24, 116, 49, 55, 19, 114, 18, 95, 52, 56, 99, 2, 60, 97, 67, 31, 70], [24, 80, 106, 71, 108, 14, 66, 4, 63, 68, 105, 94, 11, 107, 10, 14, 45, 9, 37, 6, 0, 68, 2, 122, 103, 31, 6, 20, 58, 3, 4, 46, 35, 7, 120, 95, 37, 43, 110, 33, 86, 10, 126, 78, 43, 31, 78, 77, 126, 51, 46, 13, 2, 6, 51, 117, 95, 116, 73, 111, 93, 7, 18, 5], [29, 73, 3, 73, 108, 98, 114, 106, 42, 67, 3, 24, 60, 23, 70, 91, 41, 15, 36, 10, 125, 60, 61, 127, 37, 38, 83, 29, 110, 51, 86, 64, 64, 78, 13, 25, 79, 22, 123, 42, 57, 100, 71, 104, 38, 82, 114, 15, 47, 94, 64, 77, 23, 88, 78, 48, 57, 70, 63, 39, 99, 63, 84, 19]]
message = bytearray(b"yellow submarine")
def get_bit(b, n):
byte = b[n // 8]
return (byte >> (7 - (n % 8))) & 1
def set_bit(b, n, v):
byte = b[n // 8]
byte &= ~(v << (7 - (n % 8)))
byte |= v << (7 - (n % 8))
b[n // 8] = byte
return b
def bfri(i):
a = hex(i)[2:]
if (len(a) % 2 == 1):
a = "0" + a
return bytes.fromhex(a)
def xor(x1, x2):
assert len(x1) == len(x2)
return b"".join([bfri(x1[i] ^ x2[i]) for i in range(len(x1))])
def band(x1, x2):
assert len(x1) == len(x2)
return b"".join([bfri(x1[i] & x2[i]) for i in range(len(x1))])
def rrot(x1, n):
arr = bytearray(x1)
for i in range(len(x1)):
arr[(i + n) % len(x1)] = x1[i]
return arr
def lrot(x1, n):
arr = bytearray(x1)
for i in range(len(x1)):
arr[i] = x1[(i + n) % len(x1)]
return arr
def keysch(k):
out = bytearray(b"\x00"*16)
print(out)
arr = [0 for i in range(128)]
for i in range(128):
for bit_loc in schedule[i]:
arr[i] ^= get_bit(k, bit_loc)
for i in range(128):
out = set_bit(out, i, arr[i])
return out
def enc(p, k):
dat = bytearray(p)
return xor(p, keysch(k))
def dec(c, k):
dat = bytearray(c)
return xor(c, keysch(k))
def make_matrix(plain, cipher):
matrix = []
for f in range(128):
r = []
for k in range(128):
r.append(0)
matrix.append(r)
xored = xor(plain, cipher)
for i in range(128):
for key_bit_loc in schedule[i]:
matrix[i][key_bit_loc] ^= 1
matrix[i].append(get_bit(xored, i))
return matrix
message= bytearray(b'yellow submarine')
ct= b'\xb7\x8e\xb3\xd9\xfd\xf2\x1f\xa2\xeaz\xe3\x0f\x00xj\x08'
matrix = make_matrix(message, ct)
#for i in matrix:
# print("".join([str(j) for j in i]))
#for i in range(128):
# curr = get_bit(message, i)
# for r in range(128):
# if (matrix[i][r]):
# curr ^= get_bit(key, r)
# assert curr == get_bit(ct, i)
print(len(matrix), len(matrix[0]))
def solve_gje(m, show):
## If there are more than unary xors perform GJE
if len(m[0]) > 2:
m = gje.remove_rows_zeros(m)
m = gje.perform_gauss_jordan_elimination(m, show)
return m
rre = solve_gje(matrix, False)
for i in rre:
print("".join([str(j) for j in i]))
newk = bytearray(b"\x00"*16)
newk2 = bytearray(b"\x00"*16)
set_bit(newk2, 127, 1)
for i in range(127):
newk = set_bit(newk, i, rre[i][128])
newk2 = set_bit(newk2, i, 1 ^ rre[i][128])
print(b"tjctf{"+newk+b"}")
print(b"tjctf{"+newk2+b"}")