n = 100 m = 150 59 84 45 30 52 74 6 65 67 29 7 66 63 58 55 52 87 65 20 73 92 40 4 53 26 97 7 11 38 61 78 49 46 75 80 50 1 86 68 67 75 86 82 85 42 34 25 59 7 50 51 47 54 57 25 4 64 88 94 78 66 44 24 93 24 26 95 62 94 15 81 22 54 63 7 96 49 84 7 56 34 58 56 41 15 81 97 32 22 91 10 40 35 86 34 11 12 81 73 59 48 54 81 2 69 40 98 19 25 5 27 59 16 83 52 83 17 49 15 39 41 77 79 76 63 65 88 76 98 13 35 47 20 68 49 89 8 0 60 33 57 88 45 25 71 97 9 40 47 76 79 88 54 11 16 17 28 56 45 27 22 32 74 42 0 75 83 61 27 44 94 85 32 91 10 55 89 71 96 88 28 54 38 96 23 67 53 21 94 27 53 20 69 6 95 4 67 23 48 13 60 80 57 22 36 98 46 32 86 46 59 66 0 50 62 75 17 67 96 63 94 2 83 15 8 30 20 27 5 68 92 65 1 49 40 89 47 86 21 85 32 51 84 82 66 59 51 33 56 14 80 10 97 95 18 80 15 97 85 36 89 3 37 91 95 78 90 81 99 28 65 83 31 49 18 97 60 69 31 68 84 11 78 33 58 48 65 26 45 51 62 87 6 51 78 1 29 20 34 80 +++ The input graph 0 -> 50 75 1 -> 49 86 2 -> 3 -> 4 -> 53 5 -> 68 6 -> 51 65 7 -> 11 50 56 66 96 8 -> 0 30 9 -> 40 10 -> 40 55 11 -> 12 -> 81 13 -> 14 -> 15 -> 39 81 97 16 -> 17 83 17 -> 49 67 18 -> 80 97 19 -> 20 -> 27 68 73 21 -> 85 22 -> 32 91 23 -> 67 24 -> 26 93 25 -> 4 5 59 26 -> 97 27 -> 44 59 28 -> 54 56 29 -> 20 30 -> 31 -> 49 68 32 -> 51 91 33 -> 34 -> 11 58 80 35 -> 47 86 36 -> 98 37 -> 91 38 -> 61 96 39 -> 40 -> 89 41 -> 77 42 -> 34 43 -> 44 -> 45 -> 25 27 30 51 46 -> 32 75 47 -> 76 86 48 -> 13 54 49 -> 84 89 50 -> 51 -> 33 47 52 -> 74 83 53 -> 20 21 54 -> 11 57 63 55 -> 52 56 -> 14 41 57 -> 22 88 58 -> 48 59 -> 66 84 60 -> 33 69 80 61 -> 62 -> 75 87 63 -> 58 65 64 -> 88 65 -> 26 83 66 -> 44 59 67 -> 23 29 68 -> 67 69 -> 6 40 70 -> 71 -> 97 72 -> 73 -> 59 74 -> 42 75 -> 86 76 -> 77 -> 78 -> 1 33 49 79 -> 76 88 80 -> 10 50 81 -> 2 22 82 -> 85 83 -> 15 61 84 -> 11 82 85 -> 36 86 -> 46 87 -> 65 88 -> 76 89 -> 3 71 90 -> 81 91 -> 92 -> 40 65 93 -> 94 -> 2 15 27 78 85 95 -> 4 62 78 96 -> 63 88 97 -> 32 95 98 -> 13 19 99 -> 28 +++ The subgroups are --- Subgroup 0: 50 --- Subgroup 1: 33 --- Subgroup 2: 76 --- Subgroup 3: 91 --- Subgroup 4: 47 51 32 46 86 75 --- Subgroup 5: 0 --- Subgroup 6: 11 --- Subgroup 7: 13 --- Subgroup 8: 19 --- Subgroup 9: 98 --- Subgroup 10: 36 --- Subgroup 11: 85 --- Subgroup 12: 82 --- Subgroup 13: 84 --- Subgroup 14: 3 --- Subgroup 15: 44 --- Subgroup 16: 66 59 --- Subgroup 17: 27 --- Subgroup 18: 73 --- Subgroup 19: 29 23 67 68 20 --- Subgroup 20: 21 --- Subgroup 21: 53 --- Subgroup 22: 4 --- Subgroup 23: 39 --- Subgroup 24: 2 --- Subgroup 25: 22 --- Subgroup 26: 81 --- Subgroup 27: 61 --- Subgroup 28: 78 15 83 26 65 87 62 95 97 71 89 49 1 --- Subgroup 29: 5 --- Subgroup 30: 6 --- Subgroup 31: 14 --- Subgroup 32: 77 --- Subgroup 33: 41 --- Subgroup 34: 56 --- Subgroup 35: 88 --- Subgroup 36: 57 --- Subgroup 37: 54 48 58 63 --- Subgroup 38: 96 --- Subgroup 39: 7 --- Subgroup 40: 30 --- Subgroup 41: 8 --- Subgroup 42: 40 --- Subgroup 43: 9 --- Subgroup 44: 80 34 42 74 52 55 10 --- Subgroup 45: 12 --- Subgroup 46: 17 --- Subgroup 47: 16 --- Subgroup 48: 18 --- Subgroup 49: 93 --- Subgroup 50: 24 --- Subgroup 51: 25 --- Subgroup 52: 28 --- Subgroup 53: 31 --- Subgroup 54: 35 --- Subgroup 55: 37 --- Subgroup 56: 38 --- Subgroup 57: 43 --- Subgroup 58: 45 --- Subgroup 59: 69 --- Subgroup 60: 60 --- Subgroup 61: 64 --- Subgroup 62: 70 --- Subgroup 63: 72 --- Subgroup 64: 79 --- Subgroup 65: 90 --- Subgroup 66: 92 --- Subgroup 67: 94 --- Subgroup 68: 99 +++ The essential subgroups are: --- Subgroup 39 is essential --- Subgroup 41 is essential --- Subgroup 43 is essential --- Subgroup 45 is essential --- Subgroup 47 is essential --- Subgroup 48 is essential --- Subgroup 50 is essential --- Subgroup 53 is essential --- Subgroup 54 is essential --- Subgroup 55 is essential --- Subgroup 56 is essential --- Subgroup 57 is essential --- Subgroup 58 is essential --- Subgroup 60 is essential --- Subgroup 61 is essential --- Subgroup 62 is essential --- Subgroup 63 is essential --- Subgroup 64 is essential --- Subgroup 65 is essential --- Subgroup 66 is essential --- Subgroup 67 is essential --- Subgroup 68 is essential Count = 22