-------
(8, 120, 3) Remaining distance distributions
(3, 120, 3) has 1 possible DDs: {[15, 45, 45, 15]}
(4, 120, 3) has 16 possible DDs: {[0, 60, 0, 60, 0], [1, 56, 6, 56, 1], [2, 52, 12, 52, 2], [3, 48, 18, 48, 3], [4, 44, 24, 44, 4], [5, 40, 30, 40, 5], [6, 36, 36, 36, 6], [7, 32, 42, 32, 7], [8, 28, 48, 28, 8], [9, 24, 54, 24, 9], [10, 20, 60, 20, 10], [11, 16, 66, 16, 11], [12, 12, 72, 12, 12], [13, 8, 78, 8, 13], [14, 4, 84, 4, 14], [15, 0, 90, 0, 15]}
(5, 120, 3) has 83 possible DDs: {[0, 30, 30, 30, 30, 0], [0, 31, 26, 36, 26, 1], [0, 32, 22, 42, 22, 2], [0, 33, 18, 48, 18, 3], [0, 34, 14, 54, 14, 4], [0, 35, 10, 60, 10, 5], [0, 36, 6, 66, 6, 6], [1, 26, 36, 26, 31, 0], [1, 27, 32, 32, 27, 1], [1, 28, 28, 38, 23, 2], [1, 29, 24, 44, 19, 3], [1, 30, 20, 50, 15, 4], [1, 31, 16, 56, 11, 5], [1, 32, 12, 62, 7, 6], [1, 33, 8, 68, 3, 7], [2, 22, 42, 22, 32, 0], [2, 23, 38, 28, 28, 1], [2, 24, 34, 34, 24, 2], [2, 25, 30, 40, 20, 3], [2, 26, 26, 46, 16, 4], [2, 27, 22, 52, 12, 5], [2, 28, 18, 58, 8, 6], [2, 29, 14, 64, 4, 7], [2, 30, 10, 70, 0, 8], [3, 18, 48, 18, 33, 0], [3, 19, 44, 24, 29, 1], [3, 20, 40, 30, 25, 2], [3, 21, 36, 36, 21, 3], [3, 22, 32, 42, 17, 4], [3, 23, 28, 48, 13, 5], [3, 24, 24, 54, 9, 6], [3, 25, 20, 60, 5, 7], [3, 26, 16, 66, 1, 8], [4, 14, 54, 14, 34, 0], [4, 15, 50, 20, 30, 1], [4, 16, 46, 26, 26, 2], [4, 17, 42, 32, 22, 3], [4, 18, 38, 38, 18, 4], [4, 19, 34, 44, 14, 5], [4, 20, 30, 50, 10, 6], [4, 21, 26, 56, 6, 7], [4, 22, 22, 62, 2, 8], [5, 10, 60, 10, 35, 0], [5, 11, 56, 16, 31, 1], [5, 12, 52, 22, 27, 2], [5, 13, 48, 28, 23, 3], [5, 14, 44, 34, 19, 4], [5, 15, 40, 40, 15, 5], [5, 16, 36, 46, 11, 6], [5, 17, 32, 52, 7, 7], [5, 18, 28, 58, 3, 8], [6, 6, 66, 6, 36, 0], [6, 7, 62, 12, 32, 1], [6, 8, 58, 18, 28, 2], [6, 9, 54, 24, 24, 3], [6, 10, 50, 30, 20, 4], [6, 11, 46, 36, 16, 5], [6, 12, 42, 42, 12, 6], [6, 13, 38, 48, 8, 7], [6, 14, 34, 54, 4, 8], [6, 15, 30, 60, 0, 9], [7, 3, 68, 8, 33, 1], [7, 4, 64, 14, 29, 2], [7, 5, 60, 20, 25, 3], [7, 6, 56, 26, 21, 4], [7, 7, 52, 32, 17, 5], [7, 8, 48, 38, 13, 6], [7, 9, 44, 44, 9, 7], [7, 10, 40, 50, 5, 8], [7, 11, 36, 56, 1, 9], [8, 0, 70, 10, 30, 2], [8, 1, 66, 16, 26, 3], [8, 2, 62, 22, 22, 4], [8, 3, 58, 28, 18, 5], [8, 4, 54, 34, 14, 6], [8, 5, 50, 40, 10, 7], [8, 6, 46, 46, 6, 8], [8, 7, 42, 52, 2, 9], [9, 0, 60, 30, 15, 6], [9, 1, 56, 36, 11, 7], [9, 2, 52, 42, 7, 8], [9, 3, 48, 48, 3, 9], [10, 0, 50, 50, 0, 10]}
(6, 120, 3) has 473 possible DDs: {[0, 10, 50, 0, 50, 10, 0], [0, 11, 46, 6, 46, 11, 0], [0, 12, 42, 12, 42, 12, 0], [0, 12, 43, 8, 48, 8, 1], [0, 12, 44, 4, 54, 4, 2], [0, 12, 45, 0, 60, 0, 3], [0, 13, 38, 18, 38, 13, 0], [0, 13, 39, 14, 44, 9, 1], [0, 13, 40, 10, 50, 5, 2], [0, 13, 41, 6, 56, 1, 3], [0, 14, 34, 24, 34, 14, 0], [0, 14, 35, 20, 40, 10, 1], [0, 14, 36, 16, 46, 6, 2], [0, 14, 37, 12, 52, 2, 3], [0, 15, 30, 30, 30, 15, 0], [0, 15, 31, 26, 36, 11, 1], [0, 15, 32, 22, 42, 7, 2], [0, 15, 33, 18, 48, 3, 3], [0, 16, 26, 36, 26, 16, 0], [0, 16, 27, 32, 32, 12, 1], [0, 16, 28, 28, 38, 8, 2], [0, 16, 29, 24, 44, 4, 3], [0, 16, 30, 20, 50, 0, 4], [0, 17, 22, 42, 22, 17, 0], [0, 17, 23, 38, 28, 13, 1], [0, 17, 24, 34, 34, 9, 2], [0, 17, 25, 30, 40, 5, 3], [0, 17, 26, 26, 46, 1, 4], [0, 18, 18, 48, 18, 18, 0], [0, 18, 19, 44, 24, 14, 1], [0, 18, 20, 40, 30, 10, 2], [0, 18, 21, 36, 36, 6, 3], [0, 18, 22, 32, 42, 2, 4], [0, 19, 14, 54, 14, 19, 0], [0, 19, 15, 50, 20, 15, 1], [0, 19, 16, 46, 26, 11, 2], [0, 19, 17, 42, 32, 7, 3], [0, 19, 18, 38, 38, 3, 4], [0, 20, 10, 60, 10, 20, 0], [0, 20, 11, 56, 16, 16, 1], [0, 20, 12, 52, 22, 12, 2], [0, 20, 13, 48, 28, 8, 3], [0, 20, 14, 44, 34, 4, 4], [0, 20, 15, 40, 40, 0, 5], [0, 21, 6, 66, 6, 21, 0], [0, 21, 7, 62, 12, 17, 1], [0, 21, 8, 58, 18, 13, 2], [0, 21, 9, 54, 24, 9, 3], [0, 21, 10, 50, 30, 5, 4], [0, 21, 11, 46, 36, 1, 5], [0, 22, 2, 72, 2, 22, 0], [0, 22, 3, 68, 8, 18, 1], [0, 22, 4, 64, 14, 14, 2], [0, 22, 5, 60, 20, 10, 3], [0, 22, 6, 56, 26, 6, 4], [0, 22, 7, 52, 32, 2, 5], [0, 23, 0, 70, 10, 15, 2], [0, 23, 1, 66, 16, 11, 3], [0, 23, 2, 62, 22, 7, 4], [0, 23, 3, 58, 28, 3, 5], [0, 24, 0, 60, 30, 0, 6], [1, 8, 48, 8, 43, 12, 0], [1, 8, 49, 4, 49, 8, 1], [1, 9, 44, 14, 39, 13, 0], [1, 9, 45, 10, 45, 9, 1], [1, 9, 46, 6, 51, 5, 2], [1, 10, 40, 20, 35, 14, 0], [1, 10, 41, 16, 41, 10, 1], [1, 10, 42, 12, 47, 6, 2], [1, 10, 43, 8, 53, 2, 3], [1, 11, 36, 26, 31, 15, 0], [1, 11, 37, 22, 37, 11, 1], [1, 11, 38, 18, 43, 7, 2], [1, 11, 39, 14, 49, 3, 3], [1, 12, 32, 32, 27, 16, 0], [1, 12, 33, 28, 33, 12, 1], [1, 12, 34, 24, 39, 8, 2], [1, 12, 35, 20, 45, 4, 3], [1, 12, 36, 16, 51, 0, 4], [1, 13, 28, 38, 23, 17, 0], [1, 13, 29, 34, 29, 13, 1], [1, 13, 30, 30, 35, 9, 2], [1, 13, 31, 26, 41, 5, 3], [1, 13, 32, 22, 47, 1, 4], [1, 14, 24, 44, 19, 18, 0], [1, 14, 25, 40, 25, 14, 1], [1, 14, 26, 36, 31, 10, 2], [1, 14, 27, 32, 37, 6, 3], [1, 14, 28, 28, 43, 2, 4], [1, 15, 20, 50, 15, 19, 0], [1, 15, 21, 46, 21, 15, 1], [1, 15, 22, 42, 27, 11, 2], [1, 15, 23, 38, 33, 7, 3], [1, 15, 24, 34, 39, 3, 4], [1, 16, 16, 56, 11, 20, 0], [1, 16, 17, 52, 17, 16, 1], [1, 16, 18, 48, 23, 12, 2], [1, 16, 19, 44, 29, 8, 3], [1, 16, 20, 40, 35, 4, 4], [1, 16, 21, 36, 41, 0, 5], [1, 17, 12, 62, 7, 21, 0], [1, 17, 13, 58, 13, 17, 1], [1, 17, 14, 54, 19, 13, 2], [1, 17, 15, 50, 25, 9, 3], [1, 17, 16, 46, 31, 5, 4], [1, 17, 17, 42, 37, 1, 5], [1, 18, 8, 68, 3, 22, 0], [1, 18, 9, 64, 9, 18, 1], [1, 18, 10, 60, 15, 14, 2], [1, 18, 11, 56, 21, 10, 3], [1, 18, 12, 52, 27, 6, 4], [1, 18, 13, 48, 33, 2, 5], [1, 19, 5, 70, 5, 19, 1], [1, 19, 6, 66, 11, 15, 2], [1, 19, 7, 62, 17, 11, 3], [1, 19, 8, 58, 23, 7, 4], [1, 19, 9, 54, 29, 3, 5], [1, 20, 3, 68, 13, 12, 3], [1, 20, 4, 64, 19, 8, 4], [1, 20, 5, 60, 25, 4, 5], [1, 20, 6, 56, 31, 0, 6], [2, 4, 54, 4, 44, 12, 0], [2, 5, 50, 10, 40, 13, 0], [2, 5, 51, 6, 46, 9, 1], [2, 5, 52, 2, 52, 5, 2], [2, 6, 46, 16, 36, 14, 0], [2, 6, 47, 12, 42, 10, 1], [2, 6, 48, 8, 48, 6, 2], [2, 6, 49, 4, 54, 2, 3], [2, 7, 42, 22, 32, 15, 0], [2, 7, 43, 18, 38, 11, 1], [2, 7, 44, 14, 44, 7, 2], [2, 7, 45, 10, 50, 3, 3], [2, 8, 38, 28, 28, 16, 0], [2, 8, 39, 24, 34, 12, 1], [2, 8, 40, 20, 40, 8, 2], [2, 8, 41, 16, 46, 4, 3], [2, 8, 42, 12, 52, 0, 4], [2, 9, 34, 34, 24, 17, 0], [2, 9, 35, 30, 30, 13, 1], [2, 9, 36, 26, 36, 9, 2], [2, 9, 37, 22, 42, 5, 3], [2, 9, 38, 18, 48, 1, 4], [2, 10, 30, 40, 20, 18, 0], [2, 10, 31, 36, 26, 14, 1], [2, 10, 32, 32, 32, 10, 2], [2, 10, 33, 28, 38, 6, 3], [2, 10, 34, 24, 44, 2, 4], [2, 11, 26, 46, 16, 19, 0], [2, 11, 27, 42, 22, 15, 1], [2, 11, 28, 38, 28, 11, 2], [2, 11, 29, 34, 34, 7, 3], [2, 11, 30, 30, 40, 3, 4], [2, 12, 22, 52, 12, 20, 0], [2, 12, 23, 48, 18, 16, 1], [2, 12, 24, 44, 24, 12, 2], [2, 12, 25, 40, 30, 8, 3], [2, 12, 26, 36, 36, 4, 4], [2, 12, 27, 32, 42, 0, 5], [2, 13, 18, 58, 8, 21, 0], [2, 13, 19, 54, 14, 17, 1], [2, 13, 20, 50, 20, 13, 2], [2, 13, 21, 46, 26, 9, 3], [2, 13, 22, 42, 32, 5, 4], [2, 13, 23, 38, 38, 1, 5], [2, 14, 14, 64, 4, 22, 0], [2, 14, 15, 60, 10, 18, 1], [2, 14, 16, 56, 16, 14, 2], [2, 14, 17, 52, 22, 10, 3], [2, 14, 18, 48, 28, 6, 4], [2, 14, 19, 44, 34, 2, 5], [2, 15, 10, 70, 0, 23, 0], [2, 15, 11, 66, 6, 19, 1], [2, 15, 12, 62, 12, 15, 2], [2, 15, 13, 58, 18, 11, 3], [2, 15, 14, 54, 24, 7, 4], [2, 15, 15, 50, 30, 3, 5], [2, 16, 8, 68, 8, 16, 2], [2, 16, 9, 64, 14, 12, 3], [2, 16, 10, 60, 20, 8, 4], [2, 16, 11, 56, 26, 4, 5], [2, 16, 12, 52, 32, 0, 6], [2, 17, 4, 74, 4, 17, 2], [2, 17, 5, 70, 10, 13, 3], [2, 17, 6, 66, 16, 9, 4], [2, 17, 7, 62, 22, 5, 5], [2, 17, 8, 58, 28, 1, 6], [2, 18, 0, 80, 0, 18, 2], [2, 18, 1, 76, 6, 14, 3], [2, 18, 2, 72, 12, 10, 4], [2, 18, 3, 68, 18, 6, 5], [2, 18, 4, 64, 24, 2, 6], [2, 19, 0, 70, 20, 3, 6], [3, 0, 60, 0, 45, 12, 0], [3, 1, 56, 6, 41, 13, 0], [3, 2, 52, 12, 37, 14, 0], [3, 2, 53, 8, 43, 10, 1], [3, 2, 54, 4, 49, 6, 2], [3, 2, 55, 0, 55, 2, 3], [3, 3, 48, 18, 33, 15, 0], [3, 3, 49, 14, 39, 11, 1], [3, 3, 50, 10, 45, 7, 2], [3, 3, 51, 6, 51, 3, 3], [3, 4, 44, 24, 29, 16, 0], [3, 4, 45, 20, 35, 12, 1], [3, 4, 46, 16, 41, 8, 2], [3, 4, 47, 12, 47, 4, 3], [3, 4, 48, 8, 53, 0, 4], [3, 5, 40, 30, 25, 17, 0], [3, 5, 41, 26, 31, 13, 1], [3, 5, 42, 22, 37, 9, 2], [3, 5, 43, 18, 43, 5, 3], [3, 5, 44, 14, 49, 1, 4], [3, 6, 36, 36, 21, 18, 0], [3, 6, 37, 32, 27, 14, 1], [3, 6, 38, 28, 33, 10, 2], [3, 6, 39, 24, 39, 6, 3], [3, 6, 40, 20, 45, 2, 4], [3, 7, 32, 42, 17, 19, 0], [3, 7, 33, 38, 23, 15, 1], [3, 7, 34, 34, 29, 11, 2], [3, 7, 35, 30, 35, 7, 3], [3, 7, 36, 26, 41, 3, 4], [3, 8, 28, 48, 13, 20, 0], [3, 8, 29, 44, 19, 16, 1], [3, 8, 30, 40, 25, 12, 2], [3, 8, 31, 36, 31, 8, 3], [3, 8, 32, 32, 37, 4, 4], [3, 8, 33, 28, 43, 0, 5], [3, 9, 24, 54, 9, 21, 0], [3, 9, 25, 50, 15, 17, 1], [3, 9, 26, 46, 21, 13, 2], [3, 9, 27, 42, 27, 9, 3], [3, 9, 28, 38, 33, 5, 4], [3, 9, 29, 34, 39, 1, 5], [3, 10, 20, 60, 5, 22, 0], [3, 10, 21, 56, 11, 18, 1], [3, 10, 22, 52, 17, 14, 2], [3, 10, 23, 48, 23, 10, 3], [3, 10, 24, 44, 29, 6, 4], [3, 10, 25, 40, 35, 2, 5], [3, 11, 16, 66, 1, 23, 0], [3, 11, 17, 62, 7, 19, 1], [3, 11, 18, 58, 13, 15, 2], [3, 11, 19, 54, 19, 11, 3], [3, 11, 20, 50, 25, 7, 4], [3, 11, 21, 46, 31, 3, 5], [3, 12, 13, 68, 3, 20, 1], [3, 12, 14, 64, 9, 16, 2], [3, 12, 15, 60, 15, 12, 3], [3, 12, 16, 56, 21, 8, 4], [3, 12, 17, 52, 27, 4, 5], [3, 12, 18, 48, 33, 0, 6], [3, 13, 10, 70, 5, 17, 2], [3, 13, 11, 66, 11, 13, 3], [3, 13, 12, 62, 17, 9, 4], [3, 13, 13, 58, 23, 5, 5], [3, 13, 14, 54, 29, 1, 6], [3, 14, 6, 76, 1, 18, 2], [3, 14, 7, 72, 7, 14, 3], [3, 14, 8, 68, 13, 10, 4], [3, 14, 9, 64, 19, 6, 5], [3, 14, 10, 60, 25, 2, 6], [3, 15, 3, 78, 3, 15, 3], [3, 15, 4, 74, 9, 11, 4], [3, 15, 5, 70, 15, 7, 5], [3, 15, 6, 66, 21, 3, 6], [3, 16, 1, 76, 11, 8, 5], [3, 16, 2, 72, 17, 4, 6], [3, 16, 3, 68, 23, 0, 7], [4, 0, 50, 20, 30, 16, 0], [4, 0, 51, 16, 36, 12, 1], [4, 0, 52, 12, 42, 8, 2], [4, 0, 53, 8, 48, 4, 3], [4, 0, 54, 4, 54, 0, 4], [4, 1, 46, 26, 26, 17, 0], [4, 1, 47, 22, 32, 13, 1], [4, 1, 48, 18, 38, 9, 2], [4, 1, 49, 14, 44, 5, 3], [4, 1, 50, 10, 50, 1, 4], [4, 2, 42, 32, 22, 18, 0], [4, 2, 43, 28, 28, 14, 1], [4, 2, 44, 24, 34, 10, 2], [4, 2, 45, 20, 40, 6, 3], [4, 2, 46, 16, 46, 2, 4], [4, 3, 38, 38, 18, 19, 0], [4, 3, 39, 34, 24, 15, 1], [4, 3, 40, 30, 30, 11, 2], [4, 3, 41, 26, 36, 7, 3], [4, 3, 42, 22, 42, 3, 4], [4, 4, 34, 44, 14, 20, 0], [4, 4, 35, 40, 20, 16, 1], [4, 4, 36, 36, 26, 12, 2], [4, 4, 37, 32, 32, 8, 3], [4, 4, 38, 28, 38, 4, 4], [4, 4, 39, 24, 44, 0, 5], [4, 5, 30, 50, 10, 21, 0], [4, 5, 31, 46, 16, 17, 1], [4, 5, 32, 42, 22, 13, 2], [4, 5, 33, 38, 28, 9, 3], [4, 5, 34, 34, 34, 5, 4], [4, 5, 35, 30, 40, 1, 5], [4, 6, 26, 56, 6, 22, 0], [4, 6, 27, 52, 12, 18, 1], [4, 6, 28, 48, 18, 14, 2], [4, 6, 29, 44, 24, 10, 3], [4, 6, 30, 40, 30, 6, 4], [4, 6, 31, 36, 36, 2, 5], [4, 7, 22, 62, 2, 23, 0], [4, 7, 23, 58, 8, 19, 1], [4, 7, 24, 54, 14, 15, 2], [4, 7, 25, 50, 20, 11, 3], [4, 7, 26, 46, 26, 7, 4], [4, 7, 27, 42, 32, 3, 5], [4, 8, 19, 64, 4, 20, 1], [4, 8, 20, 60, 10, 16, 2], [4, 8, 21, 56, 16, 12, 3], [4, 8, 22, 52, 22, 8, 4], [4, 8, 23, 48, 28, 4, 5], [4, 8, 24, 44, 34, 0, 6], [4, 9, 16, 66, 6, 17, 2], [4, 9, 17, 62, 12, 13, 3], [4, 9, 18, 58, 18, 9, 4], [4, 9, 19, 54, 24, 5, 5], [4, 9, 20, 50, 30, 1, 6], [4, 10, 12, 72, 2, 18, 2], [4, 10, 13, 68, 8, 14, 3], [4, 10, 14, 64, 14, 10, 4], [4, 10, 15, 60, 20, 6, 5], [4, 10, 16, 56, 26, 2, 6], [4, 11, 9, 74, 4, 15, 3], [4, 11, 10, 70, 10, 11, 4], [4, 11, 11, 66, 16, 7, 5], [4, 11, 12, 62, 22, 3, 6], [4, 12, 6, 76, 6, 12, 4], [4, 12, 7, 72, 12, 8, 5], [4, 12, 8, 68, 18, 4, 6], [4, 12, 9, 64, 24, 0, 7], [4, 13, 4, 74, 14, 5, 6], [4, 13, 5, 70, 20, 1, 7], [5, 0, 40, 40, 15, 20, 0], [5, 0, 41, 36, 21, 16, 1], [5, 0, 42, 32, 27, 12, 2], [5, 0, 43, 28, 33, 8, 3], [5, 0, 44, 24, 39, 4, 4], [5, 0, 45, 20, 45, 0, 5], [5, 1, 36, 46, 11, 21, 0], [5, 1, 37, 42, 17, 17, 1], [5, 1, 38, 38, 23, 13, 2], [5, 1, 39, 34, 29, 9, 3], [5, 1, 40, 30, 35, 5, 4], [5, 1, 41, 26, 41, 1, 5], [5, 2, 32, 52, 7, 22, 0], [5, 2, 33, 48, 13, 18, 1], [5, 2, 34, 44, 19, 14, 2], [5, 2, 35, 40, 25, 10, 3], [5, 2, 36, 36, 31, 6, 4], [5, 2, 37, 32, 37, 2, 5], [5, 3, 28, 58, 3, 23, 0], [5, 3, 29, 54, 9, 19, 1], [5, 3, 30, 50, 15, 15, 2], [5, 3, 31, 46, 21, 11, 3], [5, 3, 32, 42, 27, 7, 4], [5, 3, 33, 38, 33, 3, 5], [5, 4, 25, 60, 5, 20, 1], [5, 4, 26, 56, 11, 16, 2], [5, 4, 27, 52, 17, 12, 3], [5, 4, 28, 48, 23, 8, 4], [5, 4, 29, 44, 29, 4, 5], [5, 4, 30, 40, 35, 0, 6], [5, 5, 22, 62, 7, 17, 2], [5, 5, 23, 58, 13, 13, 3], 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