Vorticity
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan 8 9 8 8 9 9 8 7 8 9 10 10 9 9 8 8 8 8 8 8 7 8 7 8 10 10 8 7 7 7 9 9 8 9 10 11 11 10 11 12 10 8 6 6 7 9 9 9 8 7 8 7 7 7 9 10 10 10 8 6 6 6 6 7 10 9 9 11 11 8 7 8 10 11 10 9 9 9 9 7 6 7 8 9 8 7 7 7 8 9 9 9 8 8 8 8 8 8 7 6 6 7 7 8 8 8 8 9 10 10 9 9 9 8 7 7 7 6 6 7 8 8 8 9 8 8 8 7 6 7 8 9 9 9 10 10 11 10 10 10 10 10 9 9 9 9 9 9 9 11 12 12 11 9 9 9 9 8 9 10 9 9 10 12 nan
nan 8 9 8 8 8 9 10 8 7 9 11 12 11 10 9 8 10 9 8 7 8 9 9 9 11 10 9 7 7 7 7 9 10 10 10 10 9 9 10 10 9 8 8 7 7 8 8 8 8 8 8 8 8 9 9 7 7 9 9 8 8 8 7 7 7 8 10 11 11 9 6 7 9 12 12 10 10 9 9 8 7 8 8 8 8 7 6 6 7 9 9 10 9 8 8 8 9 9 10 9 6 6 7 6 7 7 8 8 8 8 8 8 8 8 7 7 6 6 6 6 7 7 8 9 9 9 9 7 5 6 7 8 9 9 8 9 9 10 10 11 10 9 8 10 9 8 8 8 9 10 10 9 8 8 8 9 10 10 10 9 9 9 9 10 nan
nan 8 9 8 8 7 8 9 7 7 8 10 12 13 13 12 11 10 11 9 7 7 9 10 10 11 11 9 8 7 8 8 9 10 10 9 8 8 8 9 9 9 10 10 9 8 8 8 8 8 9 9 9 10 10 9 7 6 8 8 7 8 9 8 7 7 7 9 11 10 8 6 5 6 10 12 12 10 9 8 8 8 8 9 9 8 8 7 5 6 8 9 10 10 8 8 8 9 9 11 11 9 8 7 7 7 7 7 7 7 7 9 8 8 7 8 8 7 6 6 6 7 7 7 8 9 10 9 6 6 7 7 6 6 7 8 9 10 10 10 11 11 9 9 9 10 9 9 9 9 10 9 9 9 9 9 9 10 11 10 8 8 7 7 8 nan
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nan 9 8 8 8 8 7 8 8 7 7 7 7 8 8 7 8 8 8 7 7 7 7 8 9 9 10 12 14 15 14 14 14 14 14 14 14 14 14 13 13 12 12 11 10 10 8 8 8 8 7 7 8 9 10 10 9 9 8 9 10 10 10 10 11 12 13 13 14 14 12 12 12 11 11 10 9 10 10 10 11 10 11 11 11 11 12 12 11 11 11 12 12 13 12 12 11 10 9 8 8 8 9 9 9 10 11 11 11 11 11 12 13 12 12 11 11 11 11 10 10 11 11 12 11 11 11 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 9 9 10 10 11 11 11 11 11 11 11 11 11 11 11 10 10 11 11 11 10 10 nan
nan 11 9 9 8 8 8 7 7 8 7 7 7 8 8 8 8 8 9 9 9 10 10 11 11 12 13 14 15 15 14 14 13 13 13 12 13 13 13 12 11 10 10 9 9 8 8 7 6 6 6 8 9 10 10 10 9 9 10 10 11 10 10 10 10 12 13 14 14 14 13 12 12 11 10 10 10 10 10 11 11 11 10 10 10 11 11 11 11 11 12 12 12 12 12 12 11 10 8 7 7 8 10 11 10 10 10 11 11 11 12 12 12 12 12 11 11 11 11 10 10 11 11 11 11 11 11 10 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 9 10 11 12 11 11 11 11 11 11 11 11 11 11 11 10 9 11 12 12 11 11 nan
nan 13 13 11 9 8 9 8 8 8 9 9 9 9 8 8 9 9 10 10 10 11 12 12 13 14 14 13 14 13 11 11 11 11 11 10 9 10 10 10 10 10 8 7 7 7 7 7 7 7 7 8 10 11 11 10 9 10 10 10 11 11 10 10 10 11 13 14 14 14 13 12 12 11 10 10 10 9 10 10 10 10 10 10 10 11 10 11 11 11 12 11 12 12 12 11 10 9 8 7 8 9 11 12 12 11 10 10 11 11 11 12 12 12 12 11 11 11 12 13 12 12 13 13 12 11 10 10 10 10 11 10 10 10 11 10 10 10 9 10 10 10 10 10 11 11 11 11 11 11 11 11 10 11 12 11 11 11 11 10 11 12 12 13 12 nan
nan 15 14 13 10 9 9 9 9 9 9 10 9 10 9 9 10 10 10 10 10 11 12 13 14 14 13 13 12 11 11 10 10 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 10 11 11 11 11 10 10 10 10 11 11 10 11 11 11 12 13 13 13 12 11 11 10 10 10 9 9 10 10 11 11 10 10 10 10 10 10 10 11 11 12 12 12 11 11 10 9 7 7 8 9 10 11 12 12 11 9 9 11 11 11 12 12 11 11 11 13 14 15 15 14 18 19 15 12 10 10 11 10 10 10 10 10 10 10 10 10 10 10 11 10 9 10 10 10 10 11 11 11 10 11 11 11 11 11 11 11 11 11 11 11 12 12 13 nan
nan 13 14 12 11 11 10 10 9 9 10 10 10 10 10 10 10 11 10 10 11 12 12 13 13 13 12 12 11 10 10 10 10 10 9 8 8 8 8 7 8 8 8 8 9 9 9 9 9 9 10 11 11 11 11 11 11 10 11 11 11 11 11 11 11 11 12 12 12 12 11 10 10 11 10 10 10 10 10 10 10 11 11 11 10 10 10 10 10 10 10 11 12 12 11 10 9 8 8 8 8 9 10 11 12 12 11 9 10 10 11 12 11 11 11 13 15 18 20 21 19 14 19 24 19 13 11 11 11 11 11 11 11 10 10 11 10 10 10 10 9 9 9 9 9 10 10 10 10 10 11 11 11 11 11 11 11 11 11 12 12 11 11 12 11 nan
nan 11 12 11 11 10 10 11 11 11 10 10 10 10 10 10 10 9 10 11 11 12 12 12 12 12 12 11 10 11 10 10 9 9 9 9 9 8 8 8 9 9 9 10 10 10 10 10 10 10 11 11 12 11 11 12 11 11 12 12 12 12 11 11 10 11 11 11 12 11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 11 11 11 10 11 10 10 10 10 10 11 10 10 9 9 9 9 10 11 12 12 12 11 10 10 10 11 11 11 10 11 14 17 20 23 24 19 14 15 20 21 18 14 12 11 12 13 13 12 11 10 11 11 10 10 9 8 8 8 8 10 11 11 11 10 11 11 11 11 12 11 10 11 11 11 11 11 11 11 11 11 nan
nan 10 10 10 11 10 10 10 11 11 11 11 10 11 11 10 9 9 10 10 11 12 11 11 11 11 11 11 11 10 10 9 9 9 9 9 9 9 9 9 9 10 11 11 11 11 11 11 11 11 11 11 11 12 12 11 11 12 12 13 12 12 11 10 10 10 11 11 11 11 11 12 11 12 11 11 11 11 11 11 10 10 11 10 10 11 11 11 11 11 10 9 9 10 11 11 10 10 9 9 10 11 12 13 13 12 11 10 11 10 11 11 11 12 13 15 16 14 13 13 11 8 10 13 17 21 19 14 12 14 15 15 14 11 11 11 11 10 10 9 8 8 9 10 11 11 11 11 10 11 11 11 11 10 10 10 11 11 11 12 11 11 11 10 10 nan
nan 10 10 10 10 10 10 11 11 12 12 12 12 11 11 10 10 10 11 12 12 11 11 11 11 10 10 10 10 9 9 10 10 10 9 9 8 8 9 9 10 11 11 12 12 11 12 12 11 11 11 11 11 11 12 11 11 11 11 11 11 11 10 10 11 10 10 10 11 11 12 12 12 12 12 12 11 11 11 11 11 10 11 11 10 11 11 11 11 11 10 10 10 11 11 11 10 9 9 9 10 11 12 13 13 13 12 12 12 12 12 13 14 16 18 18 17 12 9 7 6 5 6 7 10 15 17 14 12 14 16 15 13 11 11 10 10 10 10 9 8 8 9 11 11 11 11 10 10 11 11 11 11 11 11 11 11 12 12 12 12 12 11 11 10 nan
nan 11 11 11 11 11 11 12 12 12 12 11 11 11 10 10 11 11 12 12 12 12 12 11 10 10 10 10 10 9 9 10 9 9 9 9 9 9 9 9 10 11 12 12 12 12 12 11 10 10 10 11 11 11 11 11 11 10 11 11 11 10 10 10 11 11 11 11 10 11 11 12 12 12 11 12 12 12 11 11 11 11 11 11 11 11 11 11 12 11 10 11 11 11 11 10 9 9 8 9 9 10 11 12 13 14 13 13 13 14 14 15 19 22 23 21 17 14 10 8 7 7 6 6 6 9 11 10 9 10 12 13 11 10 10 10 10 10 9 8 8 9 10 11 11 11 11 10 11 11 11 12 12 12 11 11 11 12 12 12 12 11 11 11 11 nan
nan 11 11 11 12 12 12 13 13 13 12 11 11 11 11 11 11 11 12 12 12 12 11 11 11 10 10 10 11 11 10 10 10 9 9 10 10 10 10 11 11 12 12 12 11 11 11 11 10 10 10 11 11 11 11 11 11 10 10 10 11 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12 13 12 12 12 12 11 11 11 11 11 11 12 11 11 11 11 10 10 10 10 9 8 9 9 10 11 11 12 13 14 14 14 16 17 20 24 25 23 19 13 10 9 9 9 8 7 7 5 5 6 9 9 9 9 10 10 11 11 11 11 11 9 9 9 10 10 11 11 11 10 10 11 12 12 11 12 11 11 10 10 12 12 12 12 11 11 12 11 nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
CAPE
7 19 31 38 39 36 28 18 14 14 16 16 16 16 18 20 22 26 33 42 50 60 73 85 95 103 109 106 104 102 98 86 74 72 70 70 74 79 74 68 46 24 8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 8 15 32 47 53 52 46 41 39 41 42 40 36 27 15 10 8 7 7 8 11 16 16 13 12 16 21 24 28 35 43 49 52 55 59 65 75 88 97 101 96 90 83 74 62 54 54 61 74 89 101 112 130 113 79 54 48 55 69 84 91 91 85 76 73 74 76 74 65 68 68 66 65 66 67 68 67 68 70 72 72 68 63 61 62 64 66 68 67 65 62 58
5 13 25 33 37 35 28 18 13 12 12 13 13 14 16 18 20 22 29 41 47 56 68 81 93 98 101 98 93 91 88 77 69 68 68 70 72 70 58 47 26 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 10 21 32 40 43 41 35 38 47 51 50 46 37 25 17 12 10 8 8 9 12 15 17 20 23 27 28 33 42 53 56 55 54 54 54 55 60 65 73 80 84 84 80 74 67 64 68 81 101 113 119 135 130 108 77 48 46 54 66 78 87 88 82 80 82 87 86 72 66 68 68 66 64 66 69 69 70 71 70 67 61 56 54 56 61 65 66 65 65 65 65
4 9 19 28 32 31 25 18 14 12 12 12 13 12 13 16 20 24 30 41 47 56 67 82 95 98 96 90 83 78 75 69 65 66 68 67 63 54 40 27 13 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 12 20 27 32 33 30 37 46 52 52 49 42 33 25 20 16 13 9 9 10 12 14 17 23 25 26 35 48 61 62 56 52 50 46 43 44 48 54 61 67 71 73 70 67 66 68 79 99 112 117 128 135 125 93 64 52 53 58 63 70 76 76 76 82 91 97 85 73 70 70 67 62 62 64 66 69 72 72 66 59 53 49 50 58 64 66 66 66 68 71
2 6 13 20 24 25 23 20 15 13 12 13 14 12 13 16 23 29 34 41 48 57 69 83 95 98 91 84 76 68 63 61 61 65 64 57 46 36 26 16 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 10 15 18 22 25 31 38 43 46 47 42 34 28 26 24 20 15 12 10 10 9 11 19 22 28 38 51 60 60 54 47 41 36 34 39 45 50 52 55 60 66 67 69 70 72 80 96 110 120 126 128 124 112 94 79 70 64 59 59 63 65 68 74 89 103 93 83 77 72 67 63 60 59 61 66 71 71 67 62 56 53 51 54 58 61 64 66 70 73
1 4 7 12 16 18 18 18 15 14 13 13 14 15 17 20 25 32 38 42 48 56 68 82 96 99 90 80 70 61 54 55 57 58 52 41 31 25 19 11 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 4 7 10 14 18 24 30 38 44 44 33 26 27 28 23 17 13 12 10 9 10 20 30 38 47 56 60 58 54 47 37 28 27 39 47 49 49 50 54 63 70 76 80 83 88 98 111 124 132 131 122 118 112 103 90 77 70 67 65 64 65 68 74 96 94 86 78 70 64 60 57 56 59 68 75 75 71 67 64 62 58 54 53 53 54 57 63 66
0 3 5 8 11 13 14 15 14 13 13 13 16 19 20 22 27 32 36 40 45 51 61 75 90 95 88 77 67 58 49 50 50 46 36 26 21 18 13 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 8 12 15 20 29 38 40 32 26 26 26 21 16 13 13 13 14 18 30 42 51 56 62 62 62 63 59 47 37 38 46 51 52 49 48 52 64 76 86 93 98 102 106 109 117 129 132 122 118 116 112 103 90 89 88 82 73 72 73 73 82 85 80 73 66 63 60 60 63 69 76 81 82 78 73 70 70 70 67 62 54 49 48 51 55
0 2 5 7 9 11 13 13 13 12 12 13 15 17 19 23 27 30 31 32 36 42 49 61 74 83 81 72 64 54 43 42 42 34 22 14 12 12 8 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 12 16 18 23 27 28 26 24 25 22 19 16 14 14 16 19 28 40 53 61 63 63 65 73 79 77 69 60 57 59 62 62 59 55 59 74 91 105 117 124 124 120 114 111 114 120 120 123 124 124 125 108 107 110 106 96 92 95 94 88 81 76 69 64 62 63 68 76 80 84 86 86 85 83 79 77 78 77 71 61 52 48 48 52
0 2 4 6 7 8 9 9 10 10 11 11 12 13 15 20 23 25 24 23 25 28 34 45 57 66 72 69 61 50 39 33 31 23 15 10 9 7 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 8 13 16 17 16 16 17 18 20 19 18 16 15 16 19 24 33 46 58 64 63 60 63 74 85 90 85 77 73 74 76 78 75 73 79 95 114 129 138 142 141 134 123 110 103 112 123 137 147 145 145 132 127 129 128 121 115 114 110 103 95 83 72 65 63 66 72 80 87 88 87 88 93 95 90 87 86 82 76 66 57 51 50 53
0 1 3 4 4 4 4 4 5 6 7 8 8 8 9 12 16 17 16 15 16 17 22 32 41 50 60 64 59 48 34 25 20 14 10 8 7 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 3 6 8 8 8 8 9 10 12 12 14 15 17 18 22 28 36 46 54 56 56 55 57 65 76 85 83 76 74 77 83 88 89 91 98 113 130 144 148 149 147 142 132 118 117 127 140 154 163 158 153 147 145 145 144 132 128 124 115 106 99 91 76 66 63 66 72 75 82 85 85 86 92 96 98 97 92 86 77 67 60 56 57 60
0 0 2 2 2 1 0 0 0 1 2 3 4 4 6 7 9 10 11 11 10 10 13 19 27 37 49 58 56 46 30 18 12 8 7 6 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3 2 2 2 2 1 1 1 0 0 1 2 3 4 4 5 6 6 7 9 12 15 19 25 30 36 42 47 47 48 48 50 56 65 72 72 66 64 67 74 81 87 92 102 117 135 146 148 149 145 137 127 122 127 135 145 156 164 159 154 154 156 154 146 136 134 129 120 114 109 95 78 64 56 63 76 76 79 80 80 80 81 82 83 84 85 80 73 67 65 69 76 77
0 0 1 2 1 0 0 0 0 0 0 1 2 2 3 4 5 6 7 8 8 8 9 12 18 27 41 52 53 42 24 11 6 5 4 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 6 7 7 6 4 2 1 1 0 0 0 0 2 2 2 3 3 4 6 8 9 11 14 20 26 32 38 42 43 44 44 45 49 56 65 65 61 58 58 61 66 71 76 88 109 136 137 132 126 117 106 98 103 113 124 133 142 148 144 148 155 159 154 141 134 134 134 132 127 119 101 79 62 54 61 69 74 75 74 73 72 73 74 72 71 69 71 73 76 82 93 105 104
0 0 0 1 1 0 0 0 0 0 0 0 1 2 2 3 3 3 4 6 7 7 7 8 12 20 34 47 48 34 15 5 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 7 10 12 11 9 6 3 1 0 0 0 0 0 1 1 0 1 2 4 6 8 10 11 12 14 19 25 32 39 40 42 43 45 48 53 59 62 62 61 60 60 59 60 63 73 93 105 104 97 89 80 73 73 81 94 108 118 125 129 129 132 139 145 143 133 122 118 126 139 138 130 109 84 66 59 63 70 75 78 82 86 84 85 86 84 81 76 78 83 92 106 124 134 135
0 0 0 1 1 1 0 0 0 0 0 0 1 2 2 1 1 1 1 2 4 5 5 6 7 14 30 42 39 21 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 9 13 15 15 12 8 5 2 1 0 0 0 0 0 0 0 0 1 3 7 12 15 17 16 14 16 22 27 35 40 43 46 52 58 60 62 62 62 62 63 62 60 59 62 70 78 75 69 63 60 59 63 68 74 82 93 102 108 115 118 119 120 121 124 121 115 107 97 117 130 133 123 100 75 68 71 76 81 87 95 105 113 119 120 112 102 95 94 98 104 114 129 139 141
0 0 0 0 1 1 1 1 0 0 0 0 1 2 2 1 0 0 0 0 1 2 2 3 4 10 25 32 26 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 8 12 13 14 14 10 8 5 3 2 1 0 0 0 0 0 0 0 2 6 14 22 24 23 21 23 27 33 42 49 55 61 66 62 56 52 50 50 54 58 58 57 58 63 68 64 57 50 48 50 56 63 67 70 75 82 92 99 105 109 110 106 109 110 110 110 107 100 104 116 126 129 119 98 86 86 90 92 94 100 112 128 142 147 138 125 108 98 102 109 115 125 134 135
0 0 0 0 1 2 2 2 2 2 2 1 2 3 2 1 0 0 0 0 0 0 0 0 1 6 16 19 14 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 8 10 11 12 11 9 6 4 2 0 0 0 0 0 1 1 3 8 16 26 33 36 38 43 49 57 62 65 65 61 53 45 40 37 36 37 42 45 47 50 54 60 61 53 47 45 48 54 60 64 66 69 72 79 87 95 100 104 108 104 106 108 108 107 109 109 108 111 115 114 113 107 104 103 104 103 102 105 111 118 128 145 144 135 119 104 104 112 117 119 121 122
0 0 0 0 1 2 4 4 4 4 4 2 2 3 2 1 0 0 0 0 0 0 0 0 0 2 7 9 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 4 6 9 12 12 12 9 6 3 2 1 0 0 0 1 3 8 16 26 37 47 56 64 72 77 78 75 70 61 50 39 30 26 26 27 29 32 37 40 44 48 54 50 43 39 40 45 51 55 57 59 61 65 75 85 94 100 104 108 110 111 112 110 108 107 111 114 113 109 104 104 105 105 105 105 108 112 116 112 104 110 131 135 129 120 110 117 126 129 124 114 106
0 0 0 1 2 3 5 6 6 6 5 3 2 2 2 1 0 0 0 0 0 0 0 0 0 1 3 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 8 10 12 13 11 8 6 5 4 2 1 1 3 9 18 30 39 48 58 71 84 93 93 84 72 57 41 28 21 17 18 20 23 27 32 37 41 42 44 47 43 37 32 32 34 40 44 47 50 54 62 72 83 93 101 108 111 112 112 110 108 108 106 107 108 106 102 100 98 95 91 89 90 99 110 118 118 111 113 117 116 110 99 94 103 117 127 124 110 94
0 0 0 2 4 5 6 7 7 6 6 4 2 2 2 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 6 7 9 10 12 12 11 9 8 7 6 5 5 7 13 26 44 60 66 69 74 83 92 96 90 74 53 33 20 15 14 14 15 18 19 23 29 35 39 40 39 37 33 28 24 24 26 30 36 41 47 53 59 67 76 84 92 95 96 97 97 96 98 99 98 95 90 85 83 82 78 72 67 64 68 78 88 95 102 109 111 107 101 91 79 74 78 87 95 102 93 79
0 0 0 2 5 7 7 7 7 6 6 5 4 4 3 3 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 5 8 9 10 11 12 11 10 9 9 9 9 11 18 35 61 88 100 97 92 88 86 83 82 74 58 38 21 13 12 13 14 14 15 15 16 20 26 31 33 30 26 22 18 15 16 18 23 31 39 47 51 54 57 62 68 73 76 78 80 80 80 81 82 85 84 68 62 59 56 53 52 50 49 52 58 65 72 83 92 96 96 95 87 77 72 73 78 84 80 72 61
0 0 1 4 6 8 8 8 7 7 7 7 7 6 6 6 5 5 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 8 8 9 9 11 12 11 11 11 13 15 20 32 55 84 110 113 104 93 83 76 71 70 61 45 27 12 9 9 10 12 12 11 9 9 11 15 18 22 20 17 14 11 9 9 12 17 26 37 41 42 42 42 46 52 56 61 65 68 68 70 69 75 84 83 56 48 45 45 45 47 44 42 43 48 56 66 78 85 88 86 87 84 80 78 81 82 77 65 54 43
0 1 2 5 8 9 9 8 8 8 8 8 9 11 13 13 11 9 7 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 6 5 6 10 11 11 11 13 17 22 30 44 63 86 102 101 93 85 82 86 79 72 60 43 25 13 9 10 11 11 9 6 3 3 5 8 11 12 12 11 10 7 4 4 5 9 14 20 24 26 27 29 32 41 46 52 56 60 65 63 58 61 69 63 49 44 43 43 45 48 46 46 49 54 64 73 82 87 88 86 88 88 86 87 88 78 66 59 52 38
2 4 5 7 9 10 10 9 9 9 9 11 14 19 24 24 20 14 7 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 2 2 2 3 8 11 10 8 7 9 14 22 32 46 64 82 89 84 76 75 86 105 106 94 77 58 44 34 28 26 24 21 14 8 4 3 4 7 10 11 11 10 8 5 1 1 1 2 3 5 8 12 16 19 25 33 40 45 48 50 50 45 40 39 45 44 46 47 48 49 53 54 56 60 67 70 75 81 88 92 92 90 94 95 94 90 82 69 64 67 66 46
4 7 8 9 10 10 10 10 10 11 12 15 20 29 34 32 24 13 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 2 10 12 9 4 2 2 6 14 26 43 62 73 71 64 59 64 80 108 123 121 107 87 68 54 47 45 45 42 34 27 20 15 13 13 13 13 12 10 7 4 1 0 0 0 0 0 2 5 9 13 20 26 30 34 34 31 26 24 27 32 40 47 52 56 61 63 67 67 69 75 84 86 90 93 95 93 91 93 97 101 100 95 80 64 57 60 60 44
5 8 10 11 11 11 11 12 12 13 15 18 25 36 40 34 22 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 8 6 3 0 1 4 13 26 42 59 65 65 65 65 69 78 100 122 134 131 111 85 69 61 58 56 54 50 46 42 38 31 26 22 19 15 12 9 6 3 2 0 0 0 0 0 2 4 9 15 20 24 26 24 21 21 24 30 41 48 58 68 76 78 80 82 82 82 88 95 99 105 109 106 97 94 95 97 96 90 83 68 55 50 54 46 36
5 8 10 11 12 12 12 13 14 16 18 21 27 38 39 30 16 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 3 5 9 17 27 40 52 62 71 78 83 85 84 93 112 132 138 122 99 83 72 64 55 48 44 43 43 44 43 39 34 28 23 18 14 11 8 5 2 0 0 0 0 0 0 7 14 20 25 28 30 30 30 32 40 59 66 77 93 100 96 92 90 90 91 98 100 107 117 122 113 101 96 94 91 83 70 64 56 48 42 41 35 31
4 7 10 11 12 12 13 14 15 16 18 21 27 36 35 25 12 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 8 12 16 22 31 43 59 73 83 86 84 83 92 109 126 132 124 110 94 79 65 53 44 39 35 36 41 44 46 46 44 40 33 27 22 18 12 7 4 4 4 4 4 5 10 17 26 35 43 47 50 52 52 59 73 83 98 118 127 115 104 97 94 97 101 105 111 115 113 104 95 90 85 72 62 53 47 44 41 36 28 22 23
3 6 9 10 11 12 13 14 15 16 17 19 24 34 33 24 12 7 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 10 14 19 27 42 60 74 81 80 77 83 100 121 135 134 123 107 90 73 60 49 41 37 37 40 45 54 59 61 63 64 61 57 51 44 38 30 25 22 20 20 21 22 24 28 32 41 52 59 64 69 73 78 83 93 111 137 135 119 107 101 94 99 106 112 113 104 92 85 81 76 68 52 43 37 33 30 28 24 18 16 19
4 6 8 10 10 11 12 12 13 14 15 16 20 32 33 25 15 8 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 11 16 24 37 56 73 82 82 78 78 89 110 134 148 129 101 75 56 46 40 35 32 32 35 41 47 53 59 64 67 70 72 73 74 71 67 61 56 51 46 42 44 47 47 45 41 45 53 59 66 76 85 92 97 105 122 144 137 123 108 97 89 87 89 91 90 82 74 68 63 57 47 38 32 28 23 20 18 14 13 17 24
6 6 8 9 10 10 10 10 10 11 13 14 21 32 32 24 15 8 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 5 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 7 12 18 28 40 56 74 88 90 80 66 61 70 97 133 146 108 68 39 24 21 21 20 20 22 26 32 40 47 52 57 62 63 64 64 64 66 65 62 58 54 52 50 58 69 80 86 76 71 70 73 77 85 97 107 114 116 122 123 115 103 91 80 70 62 58 55 52 50 46 43 40 38 32 28 26 23 18 17 16 16 19 27 28
8 8 8 8 9 9 8 7 8 9 10 14 24 31 28 20 11 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 6 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 12 20 28 39 52 65 78 91 96 87 65 44 35 44 77 126 120 80 44 23 14 12 10 9 8 10 14 20 30 39 47 54 59 60 58 55 52 50 48 46 44 41 39 43 55 74 97 118 122 113 104 100 98 104 111 114 112 106 100 87 74 62 52 45 38 32 27 24 22 21 20 19 19 20 19 19 19 18 16 17 18 20 22 25 17
9 8 8 8 7 7 6 5 5 6 10 17 26 27 20 12 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 6 9 10 6 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 13 28 42 56 68 80 90 100 106 100 80 51 33 27 42 75 107 87 55 28 14 10 8 5 3 3 6 10 15 22 31 40 49 56 57 54 49 45 40 35 33 33 34 36 43 55 68 84 106 119 122 118 110 104 104 101 92 78 63 48 36 29 24 19 14 10 8 7 6 5 5 4 4 5 6 6 8 9 11 12 14 15 15 15 17 14
8 8 7 6 5 4 3 2 3 6 13 21 25 18 10 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 8 12 16 16 12 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 25 46 66 82 94 103 113 121 121 109 84 59 45 46 62 88 91 64 36 17 10 10 9 6 3 2 4 9 13 18 25 32 40 45 47 44 40 37 32 27 25 27 29 34 41 48 55 60 70 81 87 88 81 71 62 52 40 29 18 11 6 4 4 3 2 1 0 0 0 0 0 0 0 0 1 1 2 3 4 4 6 9 9 8 7 5
7 6 5 4 2 2 1 2 5 11 18 22 17 9 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 5 10 13 16 18 18 14 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 13 34 62 86 104 119 132 143 144 136 119 99 81 73 77 90 100 78 46 21 10 10 14 13 9 5 4 4 8 12 17 23 29 34 37 38 36 33 29 26 23 21 23 26 33 40 43 48 49 49 48 45 41 34 25 17 12 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 5 6 6 4 4
4 4 2 1 0 0 0 2 7 13 17 16 8 5 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 7 10 11 12 13 12 8 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 8 6 3 2 0 0 0 0 0 0 0 0 0 0 0 0 1 4 10 22 51 79 103 123 141 154 162 159 149 134 120 110 108 112 114 101 67 35 17 13 16 16 12 6 3 3 5 8 13 19 26 33 37 39 40 40 34 28 24 22 22 24 26 33 44 45 45 45 43 38 30 18 9 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 2 1 1 3 5 5 6 6 5 1
1 1 1 0 0 0 1 4 9 12 12 9 7 6 4 3 2 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 3 3 4 5 5 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 7 12 9 3 2 0 0 0 0 0 0 0 0 0 0 0 3 7 14 24 42 74 99 119 136 156 168 172 168 159 148 138 130 125 121 113 86 56 36 27 26 27 23 13 3 1 2 4 8 15 23 32 38 41 42 40 34 30 26 24 25 27 30 33 38 48 58 62 58 49 36 25 13 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 1 5 12 16 13 12 14 14 12
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