-------
(10, 352, 5) ALL distance distributions for EXTERNAL point
(5, 352, 5) has 0 possible DDs: {}
(6, 352, 5) has 1 possible DDs: {[0, 66, 0, 220, 0, 66, 0]}
(7, 352, 5) has 6 possible DDs: {[0, 33, 33, 110, 110, 33, 33, 0], [0, 34, 27, 125, 90, 48, 27, 1], [0, 35, 21, 140, 70, 63, 21, 2], [0, 36, 15, 155, 50, 78, 15, 3], [0, 37, 9, 170, 30, 93, 9, 4], [0, 38, 3, 185, 10, 108, 3, 5]}
(8, 352, 5) has 33 possible DDs: {[0, 12, 60, 4, 200, 4, 60, 12, 0], [0, 13, 54, 19, 180, 19, 54, 13, 0], [0, 14, 48, 34, 160, 34, 48, 14, 0], [0, 14, 49, 28, 175, 14, 63, 8, 1], [0, 15, 42, 49, 140, 49, 42, 15, 0], [0, 15, 43, 43, 155, 29, 57, 9, 1], [0, 15, 44, 37, 170, 9, 72, 3, 2], [0, 16, 36, 64, 120, 64, 36, 16, 0], [0, 16, 37, 58, 135, 44, 51, 10, 1], [0, 16, 38, 52, 150, 24, 66, 4, 2], [0, 17, 30, 79, 100, 79, 30, 17, 0], [0, 17, 31, 73, 115, 59, 45, 11, 1], [0, 17, 32, 67, 130, 39, 60, 5, 2], [0, 18, 24, 94, 80, 94, 24, 18, 0], [0, 18, 25, 88, 95, 74, 39, 12, 1], [0, 18, 26, 82, 110, 54, 54, 6, 2], [0, 18, 27, 76, 125, 34, 69, 0, 3], [0, 19, 18, 109, 60, 109, 18, 19, 0], [0, 19, 19, 103, 75, 89, 33, 13, 1], [0, 19, 20, 97, 90, 69, 48, 7, 2], [0, 19, 21, 91, 105, 49, 63, 1, 3], [0, 20, 12, 124, 40, 124, 12, 20, 0], [0, 20, 13, 118, 55, 104, 27, 14, 1], [0, 20, 14, 112, 70, 84, 42, 8, 2], [0, 20, 15, 106, 85, 64, 57, 2, 3], [0, 21, 6, 139, 20, 139, 6, 21, 0], [0, 21, 7, 133, 35, 119, 21, 15, 1], [0, 21, 8, 127, 50, 99, 36, 9, 2], [0, 21, 9, 121, 65, 79, 51, 3, 3], [0, 22, 0, 154, 0, 154, 0, 22, 0], [0, 22, 1, 148, 15, 134, 15, 16, 1], [0, 22, 2, 142, 30, 114, 30, 10, 2], [0, 22, 3, 136, 45, 94, 45, 4, 3]}
(9, 352, 5) has 156 possible DDs: {[0, 3, 51, 5, 117, 117, 5, 51, 3, 0], [0, 4, 46, 14, 112, 112, 14, 46, 4, 0], [0, 4, 47, 8, 127, 92, 29, 40, 5, 0], [0, 4, 48, 2, 142, 72, 44, 34, 6, 0], [0, 4, 48, 3, 136, 87, 24, 49, 0, 1], [0, 5, 40, 29, 92, 127, 8, 47, 4, 0], [0, 5, 41, 23, 107, 107, 23, 41, 5, 0], [0, 5, 42, 17, 122, 87, 38, 35, 6, 0], [0, 5, 42, 18, 116, 102, 18, 50, 0, 1], [0, 5, 43, 11, 137, 67, 53, 29, 7, 0], [0, 5, 43, 12, 131, 82, 33, 44, 1, 1], [0, 5, 44, 5, 152, 47, 68, 23, 8, 0], [0, 5, 44, 6, 146, 62, 48, 38, 2, 1], [0, 5, 45, 0, 161, 42, 63, 32, 3, 1], [0, 6, 34, 44, 72, 142, 2, 48, 4, 0], [0, 6, 35, 38, 87, 122, 17, 42, 5, 0], [0, 6, 36, 32, 102, 102, 32, 36, 6, 0], [0, 6, 36, 33, 96, 117, 12, 51, 0, 1], [0, 6, 37, 26, 117, 82, 47, 30, 7, 0], [0, 6, 37, 27, 111, 97, 27, 45, 1, 1], [0, 6, 38, 20, 132, 62, 62, 24, 8, 0], [0, 6, 38, 21, 126, 77, 42, 39, 2, 1], [0, 6, 39, 14, 147, 42, 77, 18, 9, 0], [0, 6, 39, 15, 141, 57, 57, 33, 3, 1], [0, 6, 40, 8, 162, 22, 92, 12, 10, 0], [0, 6, 40, 9, 156, 37, 72, 27, 4, 1], [0, 6, 41, 2, 177, 2, 107, 6, 11, 0], [0, 6, 41, 3, 171, 17, 87, 21, 5, 1], [0, 7, 29, 53, 67, 137, 11, 43, 5, 0], [0, 7, 30, 47, 82, 117, 26, 37, 6, 0], [0, 7, 30, 48, 76, 132, 6, 52, 0, 1], [0, 7, 31, 41, 97, 97, 41, 31, 7, 0], [0, 7, 31, 42, 91, 112, 21, 46, 1, 1], [0, 7, 32, 35, 112, 77, 56, 25, 8, 0], [0, 7, 32, 36, 106, 92, 36, 40, 2, 1], [0, 7, 33, 29, 127, 57, 71, 19, 9, 0], [0, 7, 33, 30, 121, 72, 51, 34, 3, 1], [0, 7, 34, 23, 142, 37, 86, 13, 10, 0], [0, 7, 34, 24, 136, 52, 66, 28, 4, 1], [0, 7, 35, 17, 157, 17, 101, 7, 11, 0], [0, 7, 35, 18, 151, 32, 81, 22, 5, 1], [0, 7, 36, 12, 166, 12, 96, 16, 6, 1], [0, 7, 36, 13, 160, 27, 76, 31, 0, 2], [0, 7, 37, 7, 175, 7, 91, 25, 1, 2], [0, 8, 23, 68, 47, 152, 5, 44, 5, 0], [0, 8, 24, 62, 62, 132, 20, 38, 6, 0], [0, 8, 24, 63, 56, 147, 0, 53, 0, 1], [0, 8, 25, 56, 77, 112, 35, 32, 7, 0], [0, 8, 25, 57, 71, 127, 15, 47, 1, 1], [0, 8, 26, 50, 92, 92, 50, 26, 8, 0], [0, 8, 26, 51, 86, 107, 30, 41, 2, 1], [0, 8, 27, 44, 107, 72, 65, 20, 9, 0], [0, 8, 27, 45, 101, 87, 45, 35, 3, 1], [0, 8, 28, 38, 122, 52, 80, 14, 10, 0], [0, 8, 28, 39, 116, 67, 60, 29, 4, 1], [0, 8, 29, 32, 137, 32, 95, 8, 11, 0], [0, 8, 29, 33, 131, 47, 75, 23, 5, 1], [0, 8, 30, 26, 152, 12, 110, 2, 12, 0], [0, 8, 30, 27, 146, 27, 90, 17, 6, 1], [0, 8, 30, 28, 140, 42, 70, 32, 0, 2], [0, 8, 31, 21, 161, 7, 105, 11, 7, 1], [0, 8, 31, 22, 155, 22, 85, 26, 1, 2], [0, 8, 32, 16, 170, 2, 100, 20, 2, 2], [0, 9, 18, 77, 42, 147, 14, 39, 6, 0], [0, 9, 19, 71, 57, 127, 29, 33, 7, 0], [0, 9, 19, 72, 51, 142, 9, 48, 1, 1], [0, 9, 20, 65, 72, 107, 44, 27, 8, 0], [0, 9, 20, 66, 66, 122, 24, 42, 2, 1], [0, 9, 21, 59, 87, 87, 59, 21, 9, 0], [0, 9, 21, 60, 81, 102, 39, 36, 3, 1], [0, 9, 22, 53, 102, 67, 74, 15, 10, 0], [0, 9, 22, 54, 96, 82, 54, 30, 4, 1], [0, 9, 23, 47, 117, 47, 89, 9, 11, 0], [0, 9, 23, 48, 111, 62, 69, 24, 5, 1], [0, 9, 24, 41, 132, 27, 104, 3, 12, 0], [0, 9, 24, 42, 126, 42, 84, 18, 6, 1], [0, 9, 24, 43, 120, 57, 64, 33, 0, 2], [0, 9, 25, 36, 141, 22, 99, 12, 7, 1], [0, 9, 25, 37, 135, 37, 79, 27, 1, 2], [0, 9, 26, 30, 156, 2, 114, 6, 8, 1], [0, 9, 26, 31, 150, 17, 94, 21, 2, 2], [0, 10, 12, 92, 22, 162, 8, 40, 6, 0], [0, 10, 13, 86, 37, 142, 23, 34, 7, 0], [0, 10, 13, 87, 31, 157, 3, 49, 1, 1], [0, 10, 14, 80, 52, 122, 38, 28, 8, 0], [0, 10, 14, 81, 46, 137, 18, 43, 2, 1], [0, 10, 15, 74, 67, 102, 53, 22, 9, 0], [0, 10, 15, 75, 61, 117, 33, 37, 3, 1], [0, 10, 16, 68, 82, 82, 68, 16, 10, 0], [0, 10, 16, 69, 76, 97, 48, 31, 4, 1], [0, 10, 17, 62, 97, 62, 83, 10, 11, 0], [0, 10, 17, 63, 91, 77, 63, 25, 5, 1], [0, 10, 18, 56, 112, 42, 98, 4, 12, 0], [0, 10, 18, 57, 106, 57, 78, 19, 6, 1], [0, 10, 18, 58, 100, 72, 58, 34, 0, 2], [0, 10, 19, 51, 121, 37, 93, 13, 7, 1], [0, 10, 19, 52, 115, 52, 73, 28, 1, 2], [0, 10, 20, 45, 136, 17, 108, 7, 8, 1], [0, 10, 20, 46, 130, 32, 88, 22, 2, 2], [0, 10, 21, 40, 145, 12, 103, 16, 3, 2], [0, 11, 6, 107, 2, 177, 2, 41, 6, 0], [0, 11, 7, 101, 17, 157, 17, 35, 7, 0], [0, 11, 8, 95, 32, 137, 32, 29, 8, 0], [0, 11, 8, 96, 26, 152, 12, 44, 2, 1], [0, 11, 9, 89, 47, 117, 47, 23, 9, 0], [0, 11, 9, 90, 41, 132, 27, 38, 3, 1], [0, 11, 10, 83, 62, 97, 62, 17, 10, 0], [0, 11, 10, 84, 56, 112, 42, 32, 4, 1], [0, 11, 11, 77, 77, 77, 77, 11, 11, 0], [0, 11, 11, 78, 71, 92, 57, 26, 5, 1], [0, 11, 12, 71, 92, 57, 92, 5, 12, 0], [0, 11, 12, 72, 86, 72, 72, 20, 6, 1], [0, 11, 12, 73, 80, 87, 52, 35, 0, 2], [0, 11, 13, 66, 101, 52, 87, 14, 7, 1], [0, 11, 13, 67, 95, 67, 67, 29, 1, 2], [0, 11, 14, 60, 116, 32, 102, 8, 8, 1], [0, 11, 14, 61, 110, 47, 82, 23, 2, 2], [0, 11, 15, 54, 131, 12, 117, 2, 9, 1], [0, 11, 15, 55, 125, 27, 97, 17, 3, 2], [0, 11, 16, 49, 140, 7, 112, 11, 4, 2], [0, 12, 2, 110, 12, 152, 26, 30, 8, 0], [0, 12, 2, 111, 6, 167, 6, 45, 2, 1], [0, 12, 3, 104, 27, 132, 41, 24, 9, 0], [0, 12, 3, 105, 21, 147, 21, 39, 3, 1], [0, 12, 4, 98, 42, 112, 56, 18, 10, 0], [0, 12, 4, 99, 36, 127, 36, 33, 4, 1], [0, 12, 5, 92, 57, 92, 71, 12, 11, 0], [0, 12, 5, 93, 51, 107, 51, 27, 5, 1], [0, 12, 6, 86, 72, 72, 86, 6, 12, 0], [0, 12, 6, 87, 66, 87, 66, 21, 6, 1], [0, 12, 6, 88, 60, 102, 46, 36, 0, 2], [0, 12, 7, 80, 87, 52, 101, 0, 13, 0], [0, 12, 7, 81, 81, 67, 81, 15, 7, 1], [0, 12, 7, 82, 75, 82, 61, 30, 1, 2], [0, 12, 8, 75, 96, 47, 96, 9, 8, 1], [0, 12, 8, 76, 90, 62, 76, 24, 2, 2], [0, 12, 9, 69, 111, 27, 111, 3, 9, 1], [0, 12, 9, 70, 105, 42, 91, 18, 3, 2], [0, 12, 10, 64, 120, 22, 106, 12, 4, 2], [0, 12, 11, 58, 135, 2, 121, 6, 5, 2], [0, 13, 0, 101, 52, 87, 80, 7, 12, 0], [0, 13, 0, 102, 46, 102, 60, 22, 6, 1], [0, 13, 0, 103, 40, 117, 40, 37, 0, 2], [0, 13, 1, 95, 67, 67, 95, 1, 13, 0], [0, 13, 1, 96, 61, 82, 75, 16, 7, 1], [0, 13, 1, 97, 55, 97, 55, 31, 1, 2], [0, 13, 2, 90, 76, 62, 90, 10, 8, 1], [0, 13, 2, 91, 70, 77, 70, 25, 2, 2], [0, 13, 3, 84, 91, 42, 105, 4, 9, 1], [0, 13, 3, 85, 85, 57, 85, 19, 3, 2], [0, 13, 4, 79, 100, 37, 100, 13, 4, 2], [0, 13, 5, 73, 115, 17, 115, 7, 5, 2], [0, 13, 6, 68, 124, 12, 110, 16, 0, 3], [0, 14, 0, 82, 110, 12, 124, 2, 6, 2], [0, 14, 0, 83, 104, 27, 104, 17, 0, 3], [0, 14, 1, 77, 119, 7, 119, 11, 1, 3]}
(10, 352, 5) has 688 possible DDs: {[0, 0, 30, 40, 10, 192, 10, 40, 30, 0, 0], [0, 0, 31, 34, 25, 172, 25, 34, 31, 0, 0], [0, 0, 31, 35, 19, 187, 5, 49, 25, 1, 0], [0, 0, 32, 28, 40, 152, 40, 28, 32, 0, 0], [0, 0, 32, 29, 34, 167, 20, 43, 26, 1, 0], [0, 0, 32, 30, 28, 182, 0, 58, 20, 2, 0], [0, 0, 33, 22, 55, 132, 55, 22, 33, 0, 0], [0, 0, 33, 23, 49, 147, 35, 37, 27, 1, 0], [0, 0, 33, 24, 43, 162, 15, 52, 21, 2, 0], [0, 0, 34, 16, 70, 112, 70, 16, 34, 0, 0], [0, 0, 34, 17, 64, 127, 50, 31, 28, 1, 0], [0, 0, 34, 18, 58, 142, 30, 46, 22, 2, 0], [0, 0, 34, 19, 52, 157, 10, 61, 16, 3, 0], [0, 0, 35, 10, 85, 92, 85, 10, 35, 0, 0], [0, 0, 35, 11, 79, 107, 65, 25, 29, 1, 0], [0, 0, 35, 12, 73, 122, 45, 40, 23, 2, 0], [0, 0, 35, 13, 67, 137, 25, 55, 17, 3, 0], [0, 0, 35, 14, 61, 152, 5, 70, 11, 4, 0], [0, 0, 36, 4, 100, 72, 100, 4, 36, 0, 0], [0, 0, 36, 5, 94, 87, 80, 19, 30, 1, 0], [0, 0, 36, 6, 88, 102, 60, 34, 24, 2, 0], [0, 0, 36, 7, 82, 117, 40, 49, 18, 3, 0], [0, 0, 36, 8, 76, 132, 20, 64, 12, 4, 0], [0, 0, 36, 9, 70, 147, 0, 79, 6, 5, 0], [0, 0, 37, 0, 103, 82, 75, 28, 25, 2, 0], [0, 0, 37, 1, 97, 97, 55, 43, 19, 3, 0], [0, 0, 37, 2, 91, 112, 35, 58, 13, 4, 0], [0, 0, 37, 3, 85, 127, 15, 73, 7, 5, 0], [0, 0, 37, 4, 80, 136, 10, 68, 16, 0, 1], [0, 1, 25, 49, 5, 187, 19, 35, 31, 0, 0], [0, 1, 26, 43, 20, 167, 34, 29, 32, 0, 0], [0, 1, 26, 44, 14, 182, 14, 44, 26, 1, 0], [0, 1, 27, 37, 35, 147, 49, 23, 33, 0, 0], [0, 1, 27, 38, 29, 162, 29, 38, 27, 1, 0], [0, 1, 27, 39, 23, 177, 9, 53, 21, 2, 0], [0, 1, 28, 31, 50, 127, 64, 17, 34, 0, 0], [0, 1, 28, 32, 44, 142, 44, 32, 28, 1, 0], [0, 1, 28, 33, 38, 157, 24, 47, 22, 2, 0], [0, 1, 28, 34, 32, 172, 4, 62, 16, 3, 0], [0, 1, 29, 25, 65, 107, 79, 11, 35, 0, 0], [0, 1, 29, 26, 59, 122, 59, 26, 29, 1, 0], [0, 1, 29, 27, 53, 137, 39, 41, 23, 2, 0], [0, 1, 29, 28, 47, 152, 19, 56, 17, 3, 0], [0, 1, 30, 19, 80, 87, 94, 5, 36, 0, 0], [0, 1, 30, 20, 74, 102, 74, 20, 30, 1, 0], [0, 1, 30, 21, 68, 117, 54, 35, 24, 2, 0], [0, 1, 30, 22, 62, 132, 34, 50, 18, 3, 0], [0, 1, 30, 23, 56, 147, 14, 65, 12, 4, 0], [0, 1, 31, 14, 89, 82, 89, 14, 31, 1, 0], [0, 1, 31, 15, 83, 97, 69, 29, 25, 2, 0], [0, 1, 31, 16, 77, 112, 49, 44, 19, 3, 0], [0, 1, 31, 17, 71, 127, 29, 59, 13, 4, 0], [0, 1, 31, 18, 65, 142, 9, 74, 7, 5, 0], [0, 1, 31, 19, 60, 151, 4, 69, 16, 0, 1], [0, 1, 32, 8, 104, 62, 104, 8, 32, 1, 0], [0, 1, 32, 9, 98, 77, 84, 23, 26, 2, 0], [0, 1, 32, 10, 92, 92, 64, 38, 20, 3, 0], [0, 1, 32, 11, 86, 107, 44, 53, 14, 4, 0], [0, 1, 32, 12, 80, 122, 24, 68, 8, 5, 0], [0, 1, 32, 13, 74, 137, 4, 83, 2, 6, 0], [0, 1, 32, 13, 75, 131, 19, 63, 17, 0, 1], [0, 1, 33, 2, 119, 42, 119, 2, 33, 1, 0], [0, 1, 33, 3, 113, 57, 99, 17, 27, 2, 0], [0, 1, 33, 4, 107, 72, 79, 32, 21, 3, 0], [0, 1, 33, 5, 101, 87, 59, 47, 15, 4, 0], [0, 1, 33, 6, 95, 102, 39, 62, 9, 5, 0], [0, 1, 33, 7, 89, 117, 19, 77, 3, 6, 0], [0, 1, 33, 7, 90, 111, 34, 57, 18, 0, 1], [0, 1, 33, 8, 84, 126, 14, 72, 12, 1, 1], [0, 1, 34, 0, 110, 82, 54, 56, 10, 5, 0], [0, 1, 34, 1, 104, 97, 34, 71, 4, 6, 0], [0, 1, 34, 1, 105, 91, 49, 51, 19, 0, 1], [0, 1, 34, 2, 99, 106, 29, 66, 13, 1, 1], [0, 1, 34, 3, 93, 121, 9, 81, 7, 2, 1], [0, 2, 20, 58, 0, 182, 28, 30, 32, 0, 0], [0, 2, 21, 52, 15, 162, 43, 24, 33, 0, 0], [0, 2, 21, 53, 9, 177, 23, 39, 27, 1, 0], [0, 2, 21, 54, 3, 192, 3, 54, 21, 2, 0], [0, 2, 22, 46, 30, 142, 58, 18, 34, 0, 0], [0, 2, 22, 47, 24, 157, 38, 33, 28, 1, 0], [0, 2, 22, 48, 18, 172, 18, 48, 22, 2, 0], [0, 2, 23, 40, 45, 122, 73, 12, 35, 0, 0], [0, 2, 23, 41, 39, 137, 53, 27, 29, 1, 0], [0, 2, 23, 42, 33, 152, 33, 42, 23, 2, 0], [0, 2, 23, 43, 27, 167, 13, 57, 17, 3, 0], [0, 2, 24, 34, 60, 102, 88, 6, 36, 0, 0], [0, 2, 24, 35, 54, 117, 68, 21, 30, 1, 0], [0, 2, 24, 36, 48, 132, 48, 36, 24, 2, 0], [0, 2, 24, 37, 42, 147, 28, 51, 18, 3, 0], [0, 2, 24, 38, 36, 162, 8, 66, 12, 4, 0], [0, 2, 25, 28, 75, 82, 103, 0, 37, 0, 0], [0, 2, 25, 29, 69, 97, 83, 15, 31, 1, 0], [0, 2, 25, 30, 63, 112, 63, 30, 25, 2, 0], [0, 2, 25, 31, 57, 127, 43, 45, 19, 3, 0], [0, 2, 25, 32, 51, 142, 23, 60, 13, 4, 0], [0, 2, 25, 33, 45, 157, 3, 75, 7, 5, 0], [0, 2, 26, 23, 84, 77, 98, 9, 32, 1, 0], [0, 2, 26, 24, 78, 92, 78, 24, 26, 2, 0], [0, 2, 26, 25, 72, 107, 58, 39, 20, 3, 0], [0, 2, 26, 26, 66, 122, 38, 54, 14, 4, 0], [0, 2, 26, 27, 60, 137, 18, 69, 8, 5, 0], [0, 2, 26, 28, 55, 146, 13, 64, 17, 0, 1], [0, 2, 27, 17, 99, 57, 113, 3, 33, 1, 0], [0, 2, 27, 18, 93, 72, 93, 18, 27, 2, 0], [0, 2, 27, 19, 87, 87, 73, 33, 21, 3, 0], [0, 2, 27, 20, 81, 102, 53, 48, 15, 4, 0], [0, 2, 27, 21, 75, 117, 33, 63, 9, 5, 0], [0, 2, 27, 22, 69, 132, 13, 78, 3, 6, 0], [0, 2, 27, 22, 70, 126, 28, 58, 18, 0, 1], [0, 2, 27, 23, 64, 141, 8, 73, 12, 1, 1], [0, 2, 28, 12, 108, 52, 108, 12, 28, 2, 0], [0, 2, 28, 13, 102, 67, 88, 27, 22, 3, 0], [0, 2, 28, 14, 96, 82, 68, 42, 16, 4, 0], [0, 2, 28, 15, 90, 97, 48, 57, 10, 5, 0], [0, 2, 28, 16, 84, 112, 28, 72, 4, 6, 0], [0, 2, 28, 16, 85, 106, 43, 52, 19, 0, 1], [0, 2, 28, 17, 79, 121, 23, 67, 13, 1, 1], [0, 2, 28, 18, 73, 136, 3, 82, 7, 2, 1], [0, 2, 29, 6, 123, 32, 123, 6, 29, 2, 0], [0, 2, 29, 7, 117, 47, 103, 21, 23, 3, 0], [0, 2, 29, 8, 111, 62, 83, 36, 17, 4, 0], [0, 2, 29, 9, 105, 77, 63, 51, 11, 5, 0], [0, 2, 29, 10, 99, 92, 43, 66, 5, 6, 0], [0, 2, 29, 10, 100, 86, 58, 46, 20, 0, 1], [0, 2, 29, 11, 94, 101, 38, 61, 14, 1, 1], [0, 2, 29, 12, 88, 116, 18, 76, 8, 2, 1], [0, 2, 30, 0, 138, 12, 138, 0, 30, 2, 0], [0, 2, 30, 1, 132, 27, 118, 15, 24, 3, 0], [0, 2, 30, 2, 126, 42, 98, 30, 18, 4, 0], [0, 2, 30, 3, 120, 57, 78, 45, 12, 5, 0], [0, 2, 30, 4, 114, 72, 58, 60, 6, 6, 0], [0, 2, 30, 4, 115, 66, 73, 40, 21, 0, 1], [0, 2, 30, 5, 108, 87, 38, 75, 0, 7, 0], [0, 2, 30, 5, 109, 81, 53, 55, 15, 1, 1], [0, 2, 30, 6, 103, 96, 33, 70, 9, 2, 1], [0, 2, 30, 7, 97, 111, 13, 85, 3, 3, 1], [0, 2, 31, 0, 118, 76, 48, 64, 10, 2, 1], [0, 2, 31, 1, 112, 91, 28, 79, 4, 3, 1], [0, 3, 16, 61, 10, 157, 52, 19, 34, 0, 0], [0, 3, 16, 62, 4, 172, 32, 34, 28, 1, 0], [0, 3, 17, 55, 25, 137, 67, 13, 35, 0, 0], [0, 3, 17, 56, 19, 152, 47, 28, 29, 1, 0], [0, 3, 17, 57, 13, 167, 27, 43, 23, 2, 0], [0, 3, 17, 58, 7, 182, 7, 58, 17, 3, 0], [0, 3, 18, 49, 40, 117, 82, 7, 36, 0, 0], [0, 3, 18, 50, 34, 132, 62, 22, 30, 1, 0], [0, 3, 18, 51, 28, 147, 42, 37, 24, 2, 0], [0, 3, 18, 52, 22, 162, 22, 52, 18, 3, 0], [0, 3, 18, 53, 16, 177, 2, 67, 12, 4, 0], [0, 3, 19, 43, 55, 97, 97, 1, 37, 0, 0], [0, 3, 19, 44, 49, 112, 77, 16, 31, 1, 0], [0, 3, 19, 45, 43, 127, 57, 31, 25, 2, 0], [0, 3, 19, 46, 37, 142, 37, 46, 19, 3, 0], [0, 3, 19, 47, 31, 157, 17, 61, 13, 4, 0], [0, 3, 20, 38, 64, 92, 92, 10, 32, 1, 0], [0, 3, 20, 39, 58, 107, 72, 25, 26, 2, 0], [0, 3, 20, 40, 52, 122, 52, 40, 20, 3, 0], [0, 3, 20, 41, 46, 137, 32, 55, 14, 4, 0], [0, 3, 20, 42, 40, 152, 12, 70, 8, 5, 0], [0, 3, 20, 43, 35, 161, 7, 65, 17, 0, 1], [0, 3, 21, 32, 79, 72, 107, 4, 33, 1, 0], [0, 3, 21, 33, 73, 87, 87, 19, 27, 2, 0], [0, 3, 21, 34, 67, 102, 67, 34, 21, 3, 0], [0, 3, 21, 35, 61, 117, 47, 49, 15, 4, 0], [0, 3, 21, 36, 55, 132, 27, 64, 9, 5, 0], [0, 3, 21, 37, 49, 147, 7, 79, 3, 6, 0], [0, 3, 21, 37, 50, 141, 22, 59, 18, 0, 1], [0, 3, 21, 38, 44, 156, 2, 74, 12, 1, 1], [0, 3, 22, 27, 88, 67, 102, 13, 28, 2, 0], [0, 3, 22, 28, 82, 82, 82, 28, 22, 3, 0], [0, 3, 22, 29, 76, 97, 62, 43, 16, 4, 0], [0, 3, 22, 30, 70, 112, 42, 58, 10, 5, 0], [0, 3, 22, 31, 64, 127, 22, 73, 4, 6, 0], [0, 3, 22, 31, 65, 121, 37, 53, 19, 0, 1], [0, 3, 22, 32, 59, 136, 17, 68, 13, 1, 1], [0, 3, 23, 21, 103, 47, 117, 7, 29, 2, 0], [0, 3, 23, 22, 97, 62, 97, 22, 23, 3, 0], [0, 3, 23, 23, 91, 77, 77, 37, 17, 4, 0], [0, 3, 23, 24, 85, 92, 57, 52, 11, 5, 0], [0, 3, 23, 25, 79, 107, 37, 67, 5, 6, 0], [0, 3, 23, 25, 80, 101, 52, 47, 20, 0, 1], [0, 3, 23, 26, 74, 116, 32, 62, 14, 1, 1], [0, 3, 23, 27, 68, 131, 12, 77, 8, 2, 1], [0, 3, 24, 15, 118, 27, 132, 1, 30, 2, 0], [0, 3, 24, 16, 112, 42, 112, 16, 24, 3, 0], [0, 3, 24, 17, 106, 57, 92, 31, 18, 4, 0], [0, 3, 24, 18, 100, 72, 72, 46, 12, 5, 0], [0, 3, 24, 19, 94, 87, 52, 61, 6, 6, 0], [0, 3, 24, 19, 95, 81, 67, 41, 21, 0, 1], [0, 3, 24, 20, 88, 102, 32, 76, 0, 7, 0], [0, 3, 24, 20, 89, 96, 47, 56, 15, 1, 1], [0, 3, 24, 21, 83, 111, 27, 71, 9, 2, 1], [0, 3, 24, 22, 77, 126, 7, 86, 3, 3, 1], [0, 3, 25, 10, 127, 22, 127, 10, 25, 3, 0], [0, 3, 25, 11, 121, 37, 107, 25, 19, 4, 0], [0, 3, 25, 12, 115, 52, 87, 40, 13, 5, 0], [0, 3, 25, 13, 109, 67, 67, 55, 7, 6, 0], [0, 3, 25, 13, 110, 61, 82, 35, 22, 0, 1], [0, 3, 25, 14, 103, 82, 47, 70, 1, 7, 0], [0, 3, 25, 14, 104, 76, 62, 50, 16, 1, 1], [0, 3, 25, 15, 98, 91, 42, 65, 10, 2, 1], [0, 3, 25, 16, 92, 106, 22, 80, 4, 3, 1], [0, 3, 26, 4, 142, 2, 142, 4, 26, 3, 0], [0, 3, 26, 5, 136, 17, 122, 19, 20, 4, 0], [0, 3, 26, 6, 130, 32, 102, 34, 14, 5, 0], [0, 3, 26, 7, 124, 47, 82, 49, 8, 6, 0], [0, 3, 26, 7, 125, 41, 97, 29, 23, 0, 1], [0, 3, 26, 8, 118, 62, 62, 64, 2, 7, 0], [0, 3, 26, 8, 119, 56, 77, 44, 17, 1, 1], [0, 3, 26, 9, 113, 71, 57, 59, 11, 2, 1], [0, 3, 26, 10, 107, 86, 37, 74, 5, 3, 1], [0, 3, 27, 0, 145, 12, 117, 28, 15, 5, 0], [0, 3, 27, 1, 139, 27, 97, 43, 9, 6, 0], [0, 3, 27, 1, 140, 21, 112, 23, 24, 0, 1], [0, 3, 27, 2, 133, 42, 77, 58, 3, 7, 0], [0, 3, 27, 2, 134, 36, 92, 38, 18, 1, 1], [0, 3, 27, 3, 128, 51, 72, 53, 12, 2, 1], [0, 3, 27, 4, 122, 66, 52, 68, 6, 3, 1], [0, 3, 27, 5, 116, 81, 32, 83, 0, 4, 1], [0, 3, 27, 7, 105, 105, 7, 93, 3, 0, 2], [0, 3, 28, 1, 120, 85, 22, 87, 4, 0, 2], [0, 4, 11, 70, 5, 152, 61, 14, 35, 0, 0], [0, 4, 12, 64, 20, 132, 76, 8, 36, 0, 0], [0, 4, 12, 65, 14, 147, 56, 23, 30, 1, 0], [0, 4, 12, 66, 8, 162, 36, 38, 24, 2, 0], [0, 4, 12, 67, 2, 177, 16, 53, 18, 3, 0], [0, 4, 13, 58, 35, 112, 91, 2, 37, 0, 0], [0, 4, 13, 59, 29, 127, 71, 17, 31, 1, 0], [0, 4, 13, 60, 23, 142, 51, 32, 25, 2, 0], [0, 4, 13, 61, 17, 157, 31, 47, 19, 3, 0], [0, 4, 13, 62, 11, 172, 11, 62, 13, 4, 0], [0, 4, 14, 53, 44, 107, 86, 11, 32, 1, 0], [0, 4, 14, 54, 38, 122, 66, 26, 26, 2, 0], [0, 4, 14, 55, 32, 137, 46, 41, 20, 3, 0], [0, 4, 14, 56, 26, 152, 26, 56, 14, 4, 0], [0, 4, 14, 57, 20, 167, 6, 71, 8, 5, 0], [0, 4, 14, 58, 15, 176, 1, 66, 17, 0, 1], [0, 4, 15, 47, 59, 87, 101, 5, 33, 1, 0], [0, 4, 15, 48, 53, 102, 81, 20, 27, 2, 0], [0, 4, 15, 49, 47, 117, 61, 35, 21, 3, 0], [0, 4, 15, 50, 41, 132, 41, 50, 15, 4, 0], [0, 4, 15, 51, 35, 147, 21, 65, 9, 5, 0], [0, 4, 15, 52, 29, 162, 1, 80, 3, 6, 0], [0, 4, 15, 52, 30, 156, 16, 60, 18, 0, 1], [0, 4, 16, 42, 68, 82, 96, 14, 28, 2, 0], [0, 4, 16, 43, 62, 97, 76, 29, 22, 3, 0], [0, 4, 16, 44, 56, 112, 56, 44, 16, 4, 0], [0, 4, 16, 45, 50, 127, 36, 59, 10, 5, 0], [0, 4, 16, 46, 44, 142, 16, 74, 4, 6, 0], [0, 4, 16, 46, 45, 136, 31, 54, 19, 0, 1], [0, 4, 16, 47, 39, 151, 11, 69, 13, 1, 1], [0, 4, 17, 36, 83, 62, 111, 8, 29, 2, 0], [0, 4, 17, 37, 77, 77, 91, 23, 23, 3, 0], [0, 4, 17, 38, 71, 92, 71, 38, 17, 4, 0], [0, 4, 17, 39, 65, 107, 51, 53, 11, 5, 0], [0, 4, 17, 40, 59, 122, 31, 68, 5, 6, 0], [0, 4, 17, 40, 60, 116, 46, 48, 20, 0, 1], [0, 4, 17, 41, 54, 131, 26, 63, 14, 1, 1], [0, 4, 17, 42, 48, 146, 6, 78, 8, 2, 1], [0, 4, 18, 30, 98, 42, 126, 2, 30, 2, 0], [0, 4, 18, 31, 92, 57, 106, 17, 24, 3, 0], [0, 4, 18, 32, 86, 72, 86, 32, 18, 4, 0], [0, 4, 18, 33, 80, 87, 66, 47, 12, 5, 0], [0, 4, 18, 34, 74, 102, 46, 62, 6, 6, 0], [0, 4, 18, 34, 75, 96, 61, 42, 21, 0, 1], [0, 4, 18, 35, 68, 117, 26, 77, 0, 7, 0], [0, 4, 18, 35, 69, 111, 41, 57, 15, 1, 1], [0, 4, 18, 36, 63, 126, 21, 72, 9, 2, 1], [0, 4, 18, 37, 57, 141, 1, 87, 3, 3, 1], [0, 4, 19, 25, 107, 37, 121, 11, 25, 3, 0], [0, 4, 19, 26, 101, 52, 101, 26, 19, 4, 0], [0, 4, 19, 27, 95, 67, 81, 41, 13, 5, 0], [0, 4, 19, 28, 89, 82, 61, 56, 7, 6, 0], [0, 4, 19, 28, 90, 76, 76, 36, 22, 0, 1], [0, 4, 19, 29, 83, 97, 41, 71, 1, 7, 0], [0, 4, 19, 29, 84, 91, 56, 51, 16, 1, 1], [0, 4, 19, 30, 78, 106, 36, 66, 10, 2, 1], [0, 4, 19, 31, 72, 121, 16, 81, 4, 3, 1], [0, 4, 20, 19, 122, 17, 136, 5, 26, 3, 0], [0, 4, 20, 20, 116, 32, 116, 20, 20, 4, 0], [0, 4, 20, 21, 110, 47, 96, 35, 14, 5, 0], [0, 4, 20, 22, 104, 62, 76, 50, 8, 6, 0], [0, 4, 20, 22, 105, 56, 91, 30, 23, 0, 1], [0, 4, 20, 23, 98, 77, 56, 65, 2, 7, 0], [0, 4, 20, 23, 99, 71, 71, 45, 17, 1, 1], [0, 4, 20, 24, 93, 86, 51, 60, 11, 2, 1], [0, 4, 20, 25, 87, 101, 31, 75, 5, 3, 1], [0, 4, 21, 14, 131, 12, 131, 14, 21, 4, 0], [0, 4, 21, 15, 125, 27, 111, 29, 15, 5, 0], [0, 4, 21, 16, 119, 42, 91, 44, 9, 6, 0], [0, 4, 21, 16, 120, 36, 106, 24, 24, 0, 1], [0, 4, 21, 17, 113, 57, 71, 59, 3, 7, 0], [0, 4, 21, 17, 114, 51, 86, 39, 18, 1, 1], [0, 4, 21, 18, 108, 66, 66, 54, 12, 2, 1], [0, 4, 21, 19, 102, 81, 46, 69, 6, 3, 1], [0, 4, 21, 20, 96, 96, 26, 84, 0, 4, 1], [0, 4, 21, 22, 85, 120, 1, 94, 3, 0, 2], [0, 4, 22, 9, 140, 7, 126, 23, 16, 5, 0], [0, 4, 22, 10, 134, 22, 106, 38, 10, 6, 0], [0, 4, 22, 10, 135, 16, 121, 18, 25, 0, 1], [0, 4, 22, 11, 128, 37, 86, 53, 4, 7, 0], [0, 4, 22, 11, 129, 31, 101, 33, 19, 1, 1], [0, 4, 22, 12, 123, 46, 81, 48, 13, 2, 1], [0, 4, 22, 13, 117, 61, 61, 63, 7, 3, 1], [0, 4, 22, 14, 111, 76, 41, 78, 1, 4, 1], [0, 4, 22, 16, 100, 100, 16, 88, 4, 0, 2], [0, 4, 23, 4, 149, 2, 121, 32, 11, 6, 0], [0, 4, 23, 5, 143, 17, 101, 47, 5, 7, 0], [0, 4, 23, 5, 144, 11, 116, 27, 20, 1, 1], [0, 4, 23, 6, 138, 26, 96, 42, 14, 2, 1], [0, 4, 23, 7, 132, 41, 76, 57, 8, 3, 1], [0, 4, 23, 8, 126, 56, 56, 72, 2, 4, 1], [0, 4, 23, 10, 115, 80, 31, 82, 5, 0, 2], [0, 4, 24, 0, 152, 12, 96, 56, 0, 8, 0], [0, 4, 24, 0, 153, 6, 111, 36, 15, 2, 1], [0, 4, 24, 1, 147, 21, 91, 51, 9, 3, 1], [0, 4, 24, 2, 141, 36, 71, 66, 3, 4, 1], [0, 4, 24, 4, 130, 60, 46, 76, 6, 0, 2], [0, 4, 24, 5, 124, 75, 26, 91, 0, 1, 2], [0, 5, 6, 79, 0, 147, 70, 9, 36, 0, 0], [0, 5, 7, 73, 15, 127, 85, 3, 37, 0, 0], [0, 5, 7, 74, 9, 142, 65, 18, 31, 1, 0], [0, 5, 7, 75, 3, 157, 45, 33, 25, 2, 0], [0, 5, 8, 68, 24, 122, 80, 12, 32, 1, 0], [0, 5, 8, 69, 18, 137, 60, 27, 26, 2, 0], [0, 5, 8, 70, 12, 152, 40, 42, 20, 3, 0], [0, 5, 8, 71, 6, 167, 20, 57, 14, 4, 0], [0, 5, 8, 72, 0, 182, 0, 72, 8, 5, 0], [0, 5, 9, 62, 39, 102, 95, 6, 33, 1, 0], [0, 5, 9, 63, 33, 117, 75, 21, 27, 2, 0], [0, 5, 9, 64, 27, 132, 55, 36, 21, 3, 0], [0, 5, 9, 65, 21, 147, 35, 51, 15, 4, 0], [0, 5, 9, 66, 15, 162, 15, 66, 9, 5, 0], [0, 5, 9, 67, 10, 171, 10, 61, 18, 0, 1], [0, 5, 10, 56, 54, 82, 110, 0, 34, 1, 0], [0, 5, 10, 57, 48, 97, 90, 15, 28, 2, 0], [0, 5, 10, 58, 42, 112, 70, 30, 22, 3, 0], [0, 5, 10, 59, 36, 127, 50, 45, 16, 4, 0], [0, 5, 10, 60, 30, 142, 30, 60, 10, 5, 0], [0, 5, 10, 61, 24, 157, 10, 75, 4, 6, 0], [0, 5, 10, 61, 25, 151, 25, 55, 19, 0, 1], [0, 5, 10, 62, 19, 166, 5, 70, 13, 1, 1], [0, 5, 11, 51, 63, 77, 105, 9, 29, 2, 0], [0, 5, 11, 52, 57, 92, 85, 24, 23, 3, 0], [0, 5, 11, 53, 51, 107, 65, 39, 17, 4, 0], [0, 5, 11, 54, 45, 122, 45, 54, 11, 5, 0], [0, 5, 11, 55, 39, 137, 25, 69, 5, 6, 0], [0, 5, 11, 55, 40, 131, 40, 49, 20, 0, 1], [0, 5, 11, 56, 34, 146, 20, 64, 14, 1, 1], [0, 5, 11, 57, 28, 161, 0, 79, 8, 2, 1], [0, 5, 12, 45, 78, 57, 120, 3, 30, 2, 0], [0, 5, 12, 46, 72, 72, 100, 18, 24, 3, 0], [0, 5, 12, 47, 66, 87, 80, 33, 18, 4, 0], [0, 5, 12, 48, 60, 102, 60, 48, 12, 5, 0], [0, 5, 12, 49, 54, 117, 40, 63, 6, 6, 0], [0, 5, 12, 49, 55, 111, 55, 43, 21, 0, 1], [0, 5, 12, 50, 48, 132, 20, 78, 0, 7, 0], [0, 5, 12, 50, 49, 126, 35, 58, 15, 1, 1], [0, 5, 12, 51, 43, 141, 15, 73, 9, 2, 1], [0, 5, 13, 40, 87, 52, 115, 12, 25, 3, 0], [0, 5, 13, 41, 81, 67, 95, 27, 19, 4, 0], [0, 5, 13, 42, 75, 82, 75, 42, 13, 5, 0], [0, 5, 13, 43, 69, 97, 55, 57, 7, 6, 0], [0, 5, 13, 43, 70, 91, 70, 37, 22, 0, 1], [0, 5, 13, 44, 63, 112, 35, 72, 1, 7, 0], [0, 5, 13, 44, 64, 106, 50, 52, 16, 1, 1], [0, 5, 13, 45, 58, 121, 30, 67, 10, 2, 1], [0, 5, 13, 46, 52, 136, 10, 82, 4, 3, 1], [0, 5, 14, 34, 102, 32, 130, 6, 26, 3, 0], [0, 5, 14, 35, 96, 47, 110, 21, 20, 4, 0], [0, 5, 14, 36, 90, 62, 90, 36, 14, 5, 0], [0, 5, 14, 37, 84, 77, 70, 51, 8, 6, 0], [0, 5, 14, 37, 85, 71, 85, 31, 23, 0, 1], [0, 5, 14, 38, 78, 92, 50, 66, 2, 7, 0], [0, 5, 14, 38, 79, 86, 65, 46, 17, 1, 1], [0, 5, 14, 39, 73, 101, 45, 61, 11, 2, 1], [0, 5, 14, 40, 67, 116, 25, 76, 5, 3, 1], [0, 5, 15, 28, 117, 12, 145, 0, 27, 3, 0], [0, 5, 15, 29, 111, 27, 125, 15, 21, 4, 0], [0, 5, 15, 30, 105, 42, 105, 30, 15, 5, 0], [0, 5, 15, 31, 99, 57, 85, 45, 9, 6, 0], [0, 5, 15, 31, 100, 51, 100, 25, 24, 0, 1], [0, 5, 15, 32, 93, 72, 65, 60, 3, 7, 0], [0, 5, 15, 32, 94, 66, 80, 40, 18, 1, 1], [0, 5, 15, 33, 88, 81, 60, 55, 12, 2, 1], [0, 5, 15, 34, 82, 96, 40, 70, 6, 3, 1], [0, 5, 15, 35, 76, 111, 20, 85, 0, 4, 1], [0, 5, 16, 23, 126, 7, 140, 9, 22, 4, 0], [0, 5, 16, 24, 120, 22, 120, 24, 16, 5, 0], [0, 5, 16, 25, 114, 37, 100, 39, 10, 6, 0], [0, 5, 16, 25, 115, 31, 115, 19, 25, 0, 1], [0, 5, 16, 26, 108, 52, 80, 54, 4, 7, 0], [0, 5, 16, 26, 109, 46, 95, 34, 19, 1, 1], [0, 5, 16, 27, 103, 61, 75, 49, 13, 2, 1], [0, 5, 16, 28, 97, 76, 55, 64, 7, 3, 1], [0, 5, 16, 29, 91, 91, 35, 79, 1, 4, 1], [0, 5, 16, 31, 80, 115, 10, 89, 4, 0, 2], [0, 5, 17, 18, 135, 2, 135, 18, 17, 5, 0], [0, 5, 17, 19, 129, 17, 115, 33, 11, 6, 0], [0, 5, 17, 19, 130, 11, 130, 13, 26, 0, 1], [0, 5, 17, 20, 123, 32, 95, 48, 5, 7, 0], [0, 5, 17, 20, 124, 26, 110, 28, 20, 1, 1], [0, 5, 17, 21, 118, 41, 90, 43, 14, 2, 1], [0, 5, 17, 22, 112, 56, 70, 58, 8, 3, 1], [0, 5, 17, 23, 106, 71, 50, 73, 2, 4, 1], [0, 5, 17, 25, 95, 95, 25, 83, 5, 0, 2], [0, 5, 18, 14, 138, 12, 110, 42, 6, 7, 0], [0, 5, 18, 14, 139, 6, 125, 22, 21, 1, 1], [0, 5, 18, 15, 132, 27, 90, 57, 0, 8, 0], [0, 5, 18, 15, 133, 21, 105, 37, 15, 2, 1], [0, 5, 18, 16, 127, 36, 85, 52, 9, 3, 1], [0, 5, 18, 17, 121, 51, 65, 67, 3, 4, 1], [0, 5, 18, 19, 110, 75, 40, 77, 6, 0, 2], [0, 5, 18, 20, 104, 90, 20, 92, 0, 1, 2], [0, 5, 19, 9, 147, 7, 105, 51, 1, 8, 0], [0, 5, 19, 9, 148, 1, 120, 31, 16, 2, 1], [0, 5, 19, 10, 142, 16, 100, 46, 10, 3, 1], [0, 5, 19, 11, 136, 31, 80, 61, 4, 4, 1], [0, 5, 19, 13, 125, 55, 55, 71, 7, 0, 2], [0, 5, 19, 14, 119, 70, 35, 86, 1, 1, 2], [0, 5, 20, 5, 151, 11, 95, 55, 5, 4, 1], [0, 5, 20, 7, 140, 35, 70, 65, 8, 0, 2], [0, 5, 20, 8, 134, 50, 50, 80, 2, 1, 2], [0, 5, 21, 0, 160, 6, 90, 64, 0, 5, 1], [0, 5, 21, 1, 155, 15, 85, 59, 9, 0, 2], [0, 5, 21, 2, 149, 30, 65, 74, 3, 1, 2], [0, 6, 2, 83, 4, 137, 74, 13, 32, 1, 0], [0, 6, 3, 77, 19, 117, 89, 7, 33, 1, 0], [0, 6, 3, 78, 13, 132, 69, 22, 27, 2, 0], [0, 6, 3, 79, 7, 147, 49, 37, 21, 3, 0], [0, 6, 3, 80, 1, 162, 29, 52, 15, 4, 0], [0, 6, 4, 71, 34, 97, 104, 1, 34, 1, 0], [0, 6, 4, 72, 28, 112, 84, 16, 28, 2, 0], [0, 6, 4, 73, 22, 127, 64, 31, 22, 3, 0], [0, 6, 4, 74, 16, 142, 44, 46, 16, 4, 0], [0, 6, 4, 75, 10, 157, 24, 61, 10, 5, 0], [0, 6, 4, 76, 4, 172, 4, 76, 4, 6, 0], [0, 6, 4, 76, 5, 166, 19, 56, 19, 0, 1], [0, 6, 5, 66, 43, 92, 99, 10, 29, 2, 0], [0, 6, 5, 67, 37, 107, 79, 25, 23, 3, 0], [0, 6, 5, 68, 31, 122, 59, 40, 17, 4, 0], [0, 6, 5, 69, 25, 137, 39, 55, 11, 5, 0], [0, 6, 5, 70, 19, 152, 19, 70, 5, 6, 0], [0, 6, 5, 70, 20, 146, 34, 50, 20, 0, 1], [0, 6, 5, 71, 14, 161, 14, 65, 14, 1, 1], [0, 6, 6, 60, 58, 72, 114, 4, 30, 2, 0], [0, 6, 6, 61, 52, 87, 94, 19, 24, 3, 0], [0, 6, 6, 62, 46, 102, 74, 34, 18, 4, 0], [0, 6, 6, 63, 40, 117, 54, 49, 12, 5, 0], [0, 6, 6, 64, 34, 132, 34, 64, 6, 6, 0], [0, 6, 6, 64, 35, 126, 49, 44, 21, 0, 1], [0, 6, 6, 65, 28, 147, 14, 79, 0, 7, 0], [0, 6, 6, 65, 29, 141, 29, 59, 15, 1, 1], [0, 6, 6, 66, 23, 156, 9, 74, 9, 2, 1], [0, 6, 7, 55, 67, 67, 109, 13, 25, 3, 0], [0, 6, 7, 56, 61, 82, 89, 28, 19, 4, 0], [0, 6, 7, 57, 55, 97, 69, 43, 13, 5, 0], [0, 6, 7, 58, 49, 112, 49, 58, 7, 6, 0], [0, 6, 7, 58, 50, 106, 64, 38, 22, 0, 1], [0, 6, 7, 59, 43, 127, 29, 73, 1, 7, 0], [0, 6, 7, 59, 44, 121, 44, 53, 16, 1, 1], [0, 6, 7, 60, 38, 136, 24, 68, 10, 2, 1], [0, 6, 7, 61, 32, 151, 4, 83, 4, 3, 1], [0, 6, 8, 49, 82, 47, 124, 7, 26, 3, 0], [0, 6, 8, 50, 76, 62, 104, 22, 20, 4, 0], [0, 6, 8, 51, 70, 77, 84, 37, 14, 5, 0], [0, 6, 8, 52, 64, 92, 64, 52, 8, 6, 0], [0, 6, 8, 52, 65, 86, 79, 32, 23, 0, 1], [0, 6, 8, 53, 58, 107, 44, 67, 2, 7, 0], [0, 6, 8, 53, 59, 101, 59, 47, 17, 1, 1], [0, 6, 8, 54, 53, 116, 39, 62, 11, 2, 1], [0, 6, 8, 55, 47, 131, 19, 77, 5, 3, 1], [0, 6, 9, 43, 97, 27, 139, 1, 27, 3, 0], [0, 6, 9, 44, 91, 42, 119, 16, 21, 4, 0], [0, 6, 9, 45, 85, 57, 99, 31, 15, 5, 0], [0, 6, 9, 46, 79, 72, 79, 46, 9, 6, 0], [0, 6, 9, 46, 80, 66, 94, 26, 24, 0, 1], [0, 6, 9, 47, 73, 87, 59, 61, 3, 7, 0], [0, 6, 9, 47, 74, 81, 74, 41, 18, 1, 1], [0, 6, 9, 48, 68, 96, 54, 56, 12, 2, 1], [0, 6, 9, 49, 62, 111, 34, 71, 6, 3, 1], [0, 6, 9, 50, 56, 126, 14, 86, 0, 4, 1], [0, 6, 10, 38, 106, 22, 134, 10, 22, 4, 0], [0, 6, 10, 39, 100, 37, 114, 25, 16, 5, 0], [0, 6, 10, 40, 94, 52, 94, 40, 10, 6, 0], [0, 6, 10, 40, 95, 46, 109, 20, 25, 0, 1], [0, 6, 10, 41, 88, 67, 74, 55, 4, 7, 0], [0, 6, 10, 41, 89, 61, 89, 35, 19, 1, 1], [0, 6, 10, 42, 83, 76, 69, 50, 13, 2, 1], [0, 6, 10, 43, 77, 91, 49, 65, 7, 3, 1], [0, 6, 10, 44, 71, 106, 29, 80, 1, 4, 1], [0, 6, 10, 46, 60, 130, 4, 90, 4, 0, 2], [0, 6, 11, 32, 121, 2, 149, 4, 23, 4, 0], [0, 6, 11, 33, 115, 17, 129, 19, 17, 5, 0], [0, 6, 11, 34, 109, 32, 109, 34, 11, 6, 0], [0, 6, 11, 34, 110, 26, 124, 14, 26, 0, 1], [0, 6, 11, 35, 103, 47, 89, 49, 5, 7, 0], [0, 6, 11, 35, 104, 41, 104, 29, 20, 1, 1], [0, 6, 11, 36, 98, 56, 84, 44, 14, 2, 1], [0, 6, 11, 37, 92, 71, 64, 59, 8, 3, 1], [0, 6, 11, 38, 86, 86, 44, 74, 2, 4, 1], [0, 6, 11, 40, 75, 110, 19, 84, 5, 0, 2], [0, 6, 12, 28, 124, 12, 124, 28, 12, 6, 0], [0, 6, 12, 28, 125, 6, 139, 8, 27, 0, 1], [0, 6, 12, 29, 118, 27, 104, 43, 6, 7, 0], [0, 6, 12, 29, 119, 21, 119, 23, 21, 1, 1], [0, 6, 12, 30, 112, 42, 84, 58, 0, 8, 0], [0, 6, 12, 30, 113, 36, 99, 38, 15, 2, 1], [0, 6, 12, 31, 107, 51, 79, 53, 9, 3, 1], [0, 6, 12, 32, 101, 66, 59, 68, 3, 4, 1], [0, 6, 12, 34, 90, 90, 34, 78, 6, 0, 2], [0, 6, 12, 35, 84, 105, 14, 93, 0, 1, 2], [0, 6, 13, 23, 133, 7, 119, 37, 7, 7, 0], [0, 6, 13, 23, 134, 1, 134, 17, 22, 1, 1], [0, 6, 13, 24, 127, 22, 99, 52, 1, 8, 0], [0, 6, 13, 24, 128, 16, 114, 32, 16, 2, 1], [0, 6, 13, 25, 122, 31, 94, 47, 10, 3, 1], [0, 6, 13, 26, 116, 46, 74, 62, 4, 4, 1], [0, 6, 13, 28, 105, 70, 49, 72, 7, 0, 2], [0, 6, 13, 29, 99, 85, 29, 87, 1, 1, 2], [0, 6, 14, 18, 142, 2, 114, 46, 2, 8, 0], [0, 6, 14, 19, 137, 11, 109, 41, 11, 3, 1], [0, 6, 14, 20, 131, 26, 89, 56, 5, 4, 1], [0, 6, 14, 22, 120, 50, 64, 66, 8, 0, 2], [0, 6, 14, 23, 114, 65, 44, 81, 2, 1, 2], [0, 6, 15, 14, 146, 6, 104, 50, 6, 4, 1], [0, 6, 15, 15, 140, 21, 84, 65, 0, 5, 1], [0, 6, 15, 16, 135, 30, 79, 60, 9, 0, 2], [0, 6, 15, 17, 129, 45, 59, 75, 3, 1, 2], [0, 6, 16, 9, 155, 1, 99, 59, 1, 5, 1], [0, 6, 16, 10, 150, 10, 94, 54, 10, 0, 2], [0, 6, 16, 11, 144, 25, 74, 69, 4, 1, 2], [0, 6, 17, 5, 159, 5, 89, 63, 5, 1, 2], [0, 6, 18, 0, 168, 0, 84, 72, 0, 2, 2], [0, 7, 0, 75, 38, 87, 108, 5, 30, 2, 0], [0, 7, 0, 76, 32, 102, 88, 20, 24, 3, 0], [0, 7, 0, 77, 26, 117, 68, 35, 18, 4, 0], [0, 7, 0, 78, 20, 132, 48, 50, 12, 5, 0], [0, 7, 0, 79, 14, 147, 28, 65, 6, 6, 0], [0, 7, 0, 79, 15, 141, 43, 45, 21, 0, 1], [0, 7, 0, 80, 8, 162, 8, 80, 0, 7, 0], [0, 7, 0, 80, 9, 156, 23, 60, 15, 1, 1], [0, 7, 0, 81, 3, 171, 3, 75, 9, 2, 1], [0, 7, 1, 70, 47, 82, 103, 14, 25, 3, 0], [0, 7, 1, 71, 41, 97, 83, 29, 19, 4, 0], [0, 7, 1, 72, 35, 112, 63, 44, 13, 5, 0], [0, 7, 1, 73, 29, 127, 43, 59, 7, 6, 0], [0, 7, 1, 73, 30, 121, 58, 39, 22, 0, 1], [0, 7, 1, 74, 23, 142, 23, 74, 1, 7, 0], [0, 7, 1, 74, 24, 136, 38, 54, 16, 1, 1], [0, 7, 1, 75, 18, 151, 18, 69, 10, 2, 1], [0, 7, 2, 64, 62, 62, 118, 8, 26, 3, 0], [0, 7, 2, 65, 56, 77, 98, 23, 20, 4, 0], [0, 7, 2, 66, 50, 92, 78, 38, 14, 5, 0], [0, 7, 2, 67, 44, 107, 58, 53, 8, 6, 0], [0, 7, 2, 67, 45, 101, 73, 33, 23, 0, 1], [0, 7, 2, 68, 38, 122, 38, 68, 2, 7, 0], [0, 7, 2, 68, 39, 116, 53, 48, 17, 1, 1], [0, 7, 2, 69, 33, 131, 33, 63, 11, 2, 1], [0, 7, 2, 70, 27, 146, 13, 78, 5, 3, 1], [0, 7, 3, 58, 77, 42, 133, 2, 27, 3, 0], [0, 7, 3, 59, 71, 57, 113, 17, 21, 4, 0], [0, 7, 3, 60, 65, 72, 93, 32, 15, 5, 0], [0, 7, 3, 61, 59, 87, 73, 47, 9, 6, 0], [0, 7, 3, 61, 60, 81, 88, 27, 24, 0, 1], [0, 7, 3, 62, 53, 102, 53, 62, 3, 7, 0], [0, 7, 3, 62, 54, 96, 68, 42, 18, 1, 1], [0, 7, 3, 63, 48, 111, 48, 57, 12, 2, 1], [0, 7, 3, 64, 42, 126, 28, 72, 6, 3, 1], [0, 7, 3, 65, 36, 141, 8, 87, 0, 4, 1], [0, 7, 4, 53, 86, 37, 128, 11, 22, 4, 0], [0, 7, 4, 54, 80, 52, 108, 26, 16, 5, 0], [0, 7, 4, 55, 74, 67, 88, 41, 10, 6, 0], [0, 7, 4, 55, 75, 61, 103, 21, 25, 0, 1], [0, 7, 4, 56, 68, 82, 68, 56, 4, 7, 0], [0, 7, 4, 56, 69, 76, 83, 36, 19, 1, 1], [0, 7, 4, 57, 63, 91, 63, 51, 13, 2, 1], [0, 7, 4, 58, 57, 106, 43, 66, 7, 3, 1], [0, 7, 4, 59, 51, 121, 23, 81, 1, 4, 1], [0, 7, 5, 47, 101, 17, 143, 5, 23, 4, 0], [0, 7, 5, 48, 95, 32, 123, 20, 17, 5, 0], [0, 7, 5, 49, 89, 47, 103, 35, 11, 6, 0], [0, 7, 5, 49, 90, 41, 118, 15, 26, 0, 1], [0, 7, 5, 50, 83, 62, 83, 50, 5, 7, 0], [0, 7, 5, 50, 84, 56, 98, 30, 20, 1, 1], [0, 7, 5, 51, 78, 71, 78, 45, 14, 2, 1], [0, 7, 5, 52, 72, 86, 58, 60, 8, 3, 1], [0, 7, 5, 53, 66, 101, 38, 75, 2, 4, 1], [0, 7, 5, 55, 55, 125, 13, 85, 5, 0, 2], [0, 7, 6, 42, 110, 12, 138, 14, 18, 5, 0], [0, 7, 6, 43, 104, 27, 118, 29, 12, 6, 0], [0, 7, 6, 43, 105, 21, 133, 9, 27, 0, 1], [0, 7, 6, 44, 98, 42, 98, 44, 6, 7, 0], [0, 7, 6, 44, 99, 36, 113, 24, 21, 1, 1], [0, 7, 6, 45, 92, 57, 78, 59, 0, 8, 0], [0, 7, 6, 45, 93, 51, 93, 39, 15, 2, 1], [0, 7, 6, 46, 87, 66, 73, 54, 9, 3, 1], [0, 7, 6, 47, 81, 81, 53, 69, 3, 4, 1], [0, 7, 6, 49, 70, 105, 28, 79, 6, 0, 2], [0, 7, 6, 50, 64, 120, 8, 94, 0, 1, 2], [0, 7, 7, 37, 119, 7, 133, 23, 13, 6, 0], [0, 7, 7, 37, 120, 1, 148, 3, 28, 0, 1], [0, 7, 7, 38, 113, 22, 113, 38, 7, 7, 0], [0, 7, 7, 38, 114, 16, 128, 18, 22, 1, 1], [0, 7, 7, 39, 107, 37, 93, 53, 1, 8, 0], [0, 7, 7, 39, 108, 31, 108, 33, 16, 2, 1], [0, 7, 7, 40, 102, 46, 88, 48, 10, 3, 1], [0, 7, 7, 41, 96, 61, 68, 63, 4, 4, 1], [0, 7, 7, 43, 85, 85, 43, 73, 7, 0, 2], [0, 7, 7, 44, 79, 100, 23, 88, 1, 1, 2], [0, 7, 8, 32, 128, 2, 128, 32, 8, 7, 0], [0, 7, 8, 33, 122, 17, 108, 47, 2, 8, 0], [0, 7, 8, 33, 123, 11, 123, 27, 17, 2, 1], [0, 7, 8, 34, 117, 26, 103, 42, 11, 3, 1], [0, 7, 8, 35, 111, 41, 83, 57, 5, 4, 1], [0, 7, 8, 37, 100, 65, 58, 67, 8, 0, 2], [0, 7, 8, 38, 94, 80, 38, 82, 2, 1, 2], [0, 7, 9, 28, 132, 6, 118, 36, 12, 3, 1], [0, 7, 9, 29, 126, 21, 98, 51, 6, 4, 1], [0, 7, 9, 30, 120, 36, 78, 66, 0, 5, 1], [0, 7, 9, 31, 115, 45, 73, 61, 9, 0, 2], [0, 7, 9, 32, 109, 60, 53, 76, 3, 1, 2], [0, 7, 10, 23, 141, 1, 113, 45, 7, 4, 1], [0, 7, 10, 24, 135, 16, 93, 60, 1, 5, 1], [0, 7, 10, 25, 130, 25, 88, 55, 10, 0, 2], [0, 7, 10, 26, 124, 40, 68, 70, 4, 1, 2], [0, 7, 11, 19, 145, 5, 103, 49, 11, 0, 2], [0, 7, 11, 20, 139, 20, 83, 64, 5, 1, 2], [0, 7, 12, 14, 154, 0, 98, 58, 6, 1, 2], [0, 7, 12, 15, 148, 15, 78, 73, 0, 2, 2], [0, 8, 0, 56, 96, 12, 152, 0, 24, 4, 0], [0, 8, 0, 57, 90, 27, 132, 15, 18, 5, 0], [0, 8, 0, 58, 84, 42, 112, 30, 12, 6, 0], [0, 8, 0, 58, 85, 36, 127, 10, 27, 0, 1], [0, 8, 0, 59, 78, 57, 92, 45, 6, 7, 0], [0, 8, 0, 59, 79, 51, 107, 25, 21, 1, 1], [0, 8, 0, 60, 72, 72, 72, 60, 0, 8, 0], [0, 8, 0, 60, 73, 66, 87, 40, 15, 2, 1], [0, 8, 0, 61, 67, 81, 67, 55, 9, 3, 1], [0, 8, 0, 62, 61, 96, 47, 70, 3, 4, 1], [0, 8, 0, 64, 50, 120, 22, 80, 6, 0, 2], [0, 8, 0, 65, 44, 135, 2, 95, 0, 1, 2], [0, 8, 1, 51, 105, 7, 147, 9, 19, 5, 0], [0, 8, 1, 52, 99, 22, 127, 24, 13, 6, 0], [0, 8, 1, 52, 100, 16, 142, 4, 28, 0, 1], [0, 8, 1, 53, 93, 37, 107, 39, 7, 7, 0], [0, 8, 1, 53, 94, 31, 122, 19, 22, 1, 1], [0, 8, 1, 54, 87, 52, 87, 54, 1, 8, 0], [0, 8, 1, 54, 88, 46, 102, 34, 16, 2, 1], [0, 8, 1, 55, 82, 61, 82, 49, 10, 3, 1], [0, 8, 1, 56, 76, 76, 62, 64, 4, 4, 1], [0, 8, 1, 58, 65, 100, 37, 74, 7, 0, 2], [0, 8, 1, 59, 59, 115, 17, 89, 1, 1, 2], [0, 8, 2, 46, 114, 2, 142, 18, 14, 6, 0], [0, 8, 2, 47, 108, 17, 122, 33, 8, 7, 0], [0, 8, 2, 47, 109, 11, 137, 13, 23, 1, 1], [0, 8, 2, 48, 102, 32, 102, 48, 2, 8, 0], [0, 8, 2, 48, 103, 26, 117, 28, 17, 2, 1], [0, 8, 2, 49, 97, 41, 97, 43, 11, 3, 1], [0, 8, 2, 50, 91, 56, 77, 58, 5, 4, 1], [0, 8, 2, 52, 80, 80, 52, 68, 8, 0, 2], [0, 8, 2, 53, 74, 95, 32, 83, 2, 1, 2], [0, 8, 3, 42, 117, 12, 117, 42, 3, 8, 0], [0, 8, 3, 42, 118, 6, 132, 22, 18, 2, 1], [0, 8, 3, 43, 112, 21, 112, 37, 12, 3, 1], [0, 8, 3, 44, 106, 36, 92, 52, 6, 4, 1], [0, 8, 3, 45, 100, 51, 72, 67, 0, 5, 1], [0, 8, 3, 46, 95, 60, 67, 62, 9, 0, 2], [0, 8, 3, 47, 89, 75, 47, 77, 3, 1, 2], [0, 8, 4, 37, 127, 1, 127, 31, 13, 3, 1], [0, 8, 4, 38, 121, 16, 107, 46, 7, 4, 1], [0, 8, 4, 39, 115, 31, 87, 61, 1, 5, 1], [0, 8, 4, 40, 110, 40, 82, 56, 10, 0, 2], [0, 8, 4, 41, 104, 55, 62, 71, 4, 1, 2], [0, 8, 5, 33, 130, 11, 102, 55, 2, 5, 1], [0, 8, 5, 34, 125, 20, 97, 50, 11, 0, 2], [0, 8, 5, 35, 119, 35, 77, 65, 5, 1, 2], [0, 8, 6, 28, 140, 0, 112, 44, 12, 0, 2], [0, 8, 6, 29, 134, 15, 92, 59, 6, 1, 2], [0, 8, 6, 30, 128, 30, 72, 74, 0, 2, 2], [0, 8, 7, 24, 143, 10, 87, 68, 1, 2, 2], [0, 9, 0, 42, 125, 6, 111, 50, 3, 5, 1], [0, 9, 0, 43, 120, 15, 106, 45, 12, 0, 2], [0, 9, 0, 44, 114, 30, 86, 60, 6, 1, 2], [0, 9, 0, 45, 108, 45, 66, 75, 0, 2, 2], [0, 9, 1, 38, 129, 10, 101, 54, 7, 1, 2], [0, 9, 1, 39, 123, 25, 81, 69, 1, 2, 2], [0, 9, 2, 33, 138, 5, 96, 63, 2, 2, 2]}