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 11 10 10 9 10 10 10 10 11 11 12 12 11 11 10 10 9 8 7 7 7 8 9 9 9 8 8 8 8 8 9 9 9 9 9 9 9 8 8 9 9 9 10 11 12 12 11 9 9 9 10 11 11 11 10 10 10 10 10 10 10 10 9 11 16 19 17 8 -2 -3 3 8 10 10 9 9 10 12 15 15 12 9 7 6 6 5 5 6 6 7 7 7 7 7 6 6 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 5 6 6 7 8 8 8 8 7 7 7 8 8 8 7 6 6 6 6 7 7 7 8 8 8 8 8 8 7 6 5 5 nan
nan 10 9 9 9 9 9 10 10 11 11 11 11 11 11 11 10 9 8 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 8 8 8 9 10 11 11 10 10 9 9 10 11 12 12 11 11 11 11 11 10 9 9 9 11 15 19 17 7 -2 -1 3 8 9 9 9 10 11 12 13 13 12 10 8 7 6 5 5 6 6 6 7 7 7 7 7 6 6 6 5 5 5 5 5 5 5 5 5 6 6 6 7 7 6 6 6 6 6 6 5 5 5 4 4 4 3 4 4 4 5 5 6 6 7 8 8 8 7 7 7 7 8 7 6 6 6 6 7 7 7 8 8 8 8 8 8 7 7 6 6 5 nan
nan 10 9 8 8 7 8 9 10 10 11 11 11 11 11 10 10 9 8 8 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 8 8 8 8 9 9 10 10 10 10 9 9 10 11 12 12 12 12 13 13 12 11 9 8 8 9 13 17 17 9 1 1 4 8 9 9 10 11 13 12 9 9 11 12 11 8 7 6 6 6 6 7 7 7 7 7 7 6 6 6 6 6 6 6 5 5 5 5 5 6 6 6 7 7 7 7 7 6 6 6 6 5 5 4 4 3 3 2 2 3 4 5 5 6 6 7 8 8 7 7 6 7 7 6 6 6 7 7 7 7 8 8 8 8 8 8 7 7 6 6 6 6 nan
nan 10 10 9 8 7 7 7 8 9 10 10 10 10 10 10 10 9 8 8 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 8 9 10 10 10 10 10 10 10 11 12 12 12 12 13 14 13 12 10 9 8 8 11 16 16 10 4 2 6 8 8 9 11 14 14 10 5 6 11 15 15 11 8 7 6 6 6 7 7 7 8 7 7 7 7 6 6 6 6 6 6 6 6 5 5 5 6 6 6 7 7 7 7 7 7 6 6 6 5 4 4 3 2 2 2 2 3 4 4 5 6 7 8 8 8 7 6 6 6 6 6 7 7 7 8 8 8 8 8 8 8 8 7 6 6 6 6 6 nan
nan 11 11 10 9 8 7 7 8 8 9 9 9 9 9 9 9 9 9 8 8 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 7 7 6 6 5 5 6 9 10 10 10 10 10 10 11 11 11 11 11 11 12 13 13 13 12 10 10 10 12 15 15 9 4 4 7 9 9 10 13 16 15 9 5 5 11 17 18 16 12 9 7 6 6 7 7 8 8 8 7 7 7 7 7 7 7 6 6 6 6 5 5 5 5 6 6 6 7 7 7 7 7 7 7 6 6 5 4 3 2 2 2 2 3 3 4 4 5 7 8 8 9 8 7 6 6 6 7 7 8 8 9 9 9 8 8 8 8 7 7 6 6 6 6 7 nan
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nan 10 11 11 11 11 11 10 10 9 8 8 8 7 7 8 9 9 10 9 9 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 7 6 5 5 6 6 5 6 7 8 9 10 10 10 11 11 12 12 12 12 12 13 13 12 11 10 10 11 11 12 12 10 7 7 8 10 11 12 12 14 14 13 11 9 8 10 13 16 19 20 18 14 10 8 7 7 8 8 8 7 7 7 7 7 7 7 7 7 6 6 6 6 5 5 5 5 6 6 7 7 8 8 8 7 7 7 7 6 5 4 3 3 3 4 4 3 4 5 7 9 10 11 11 10 9 9 9 9 10 11 11 11 10 9 9 8 8 7 7 7 7 7 7 7 8 nan
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nan 9 10 10 10 10 10 11 11 11 10 9 8 7 8 8 8 8 8 9 9 9 9 8 7 7 8 8 8 8 7 7 7 7 7 7 8 8 7 7 7 7 8 7 6 5 6 7 8 8 8 9 11 12 12 11 10 9 8 9 9 9 9 9 9 9 8 7 7 7 9 10 11 12 12 13 13 12 10 9 9 9 9 10 12 17 20 19 16 12 9 8 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 7 7 7 8 8 8 8 8 8 8 7 6 5 5 6 6 6 6 6 7 9 11 12 12 12 12 12 12 13 14 15 15 15 14 12 11 10 9 8 8 7 8 8 8 9 9 9 nan
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nan 14 13 13 13 13 14 15 15 16 15 14 12 11 10 9 10 11 12 12 11 10 10 11 11 12 11 11 11 11 11 12 12 13 13 14 14 13 13 12 12 12 12 13 13 13 12 11 10 10 9 9 9 9 9 10 10 10 10 11 11 11 12 11 9 8 6 6 6 7 8 9 10 11 11 11 11 12 11 10 10 9 10 11 12 12 13 14 15 16 16 16 15 15 14 13 12 11 10 10 10 10 9 9 9 9 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 7 8 8 8 9 10 12 13 13 12 10 8 7 5 5 6 6 7 7 7 7 8 10 12 14 15 14 12 11 9 8 8 8 8 7 7 7 7 6 6 nan
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nan 10 10 10 10 10 10 11 11 11 11 12 11 10 8 6 5 5 6 6 5 4 4 4 5 6 8 9 9 10 10 9 7 6 6 7 8 8 9 9 9 9 9 9 10 11 11 11 11 11 11 11 11 11 11 10 10 10 9 9 8 8 8 9 10 11 10 10 9 9 8 9 9 10 10 10 9 9 10 11 11 11 10 10 10 10 9 9 9 9 10 10 10 10 10 9 10 10 10 10 11 10 10 11 11 12 13 14 15 17 19 21 21 20 20 20 17 12 9 10 14 16 16 14 12 9 8 7 6 7 7 9 12 14 14 13 13 13 14 13 12 11 10 9 9 9 8 8 7 7 7 7 6 6 7 7 8 8 8 7 7 nan
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nan 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 11 10 10 9 9 10 10 11 11 12 12 12 11 11 10 10 11 12 13 14 14 13 12 12 12 12 11 8 5 4 4 6 7 7 7 7 8 9 9 9 8 7 8 10 12 14 15 14 13 12 12 11 9 8 8 8 9 11 13 13 13 12 11 10 9 9 11 13 13 13 12 12 14 15 14 11 10 10 11 11 10 10 8 7 8 11 13 14 13 11 10 10 10 10 11 12 13 12 12 12 14 17 20 21 18 15 13 11 10 10 9 9 9 10 10 10 10 10 9 9 9 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 6 5 5 6 6 7 8 9 9 nan
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nan 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 11 11 11 11 11 12 11 11 11 11 11 11 10 10 10 10 10 11 11 11 11 12 12 12 12 12 12 12 11 11 12 12 12 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 12 12 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 11 11 11 10 10 10 10 10 10 10 10 11 11 11 11 11 10 10 10 10 10 11 11 12 13 13 13 14 14 15 16 16 16 16 17 17 17 18 18 17 16 15 13 11 10 10 10 10 nan
nan 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 10 10 10 10 10 10 9 9 9 9 9 10 10 10 11 11 11 12 12 12 12 12 12 12 12 13 12 12 12 12 12 12 12 11 12 12 12 12 12 12 12 12 12 11 11 11 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 11 11 11 11 11 10 10 10 11 11 12 12 12 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 10 10 11 11 11 10 9 9 9 10 11 12 13 12 12 12 12 13 14 14 14 14 14 15 17 19 21 21 22 22 20 18 15 14 13 14 nan
nan 11 11 11 11 11 11 11 10 10 10 10 10 10 10 11 11 11 10 10 10 10 11 11 11 11 12 11 11 11 10 10 10 10 10 10 10 10 10 9 10 9 9 9 9 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 11 11 10 10 10 11 11 11 12 12 12 12 12 12 12 13 13 13 13 12 12 11 11 10 10 10 10 11 11 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 10 9 9 9 10 11 12 12 11 11 11 11 12 12 13 12 10 10 11 13 17 19 22 24 25 24 23 22 21 20 20 nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan 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
141 128 116 100 85 74 70 74 66 50 34 21 10 4 3 2 1 0 0 1 5 28 50 58 59 56 54 52 52 56 60 68 87 100 116 151 203 265 313 333 330 319 304 293 277 235 160 91 61 55 62 65 46 15 6 1 0 0 0 0 0 0 0 0 0 0 0 3 16 40 65 19 3 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 1 2 4 5 7 10 17 28 38 55 69 76 87 93 88 76 57 38 29 23 20 19 18 17 19 23 26 29 31 30 31 33 37 46 54 86 131 190 258 343 413 507
121 100 77 58 49 49 48 49 41 29 16 6 2 1 1 2 2 1 2 2 5 16 30 39 37 32 28 26 26 22 23 33 53 75 99 132 164 195 230 261 276 279 269 254 246 222 157 103 68 49 52 67 56 33 15 4 0 0 0 0 0 0 0 0 0 0 0 2 13 43 34 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 5 6 9 16 26 38 53 68 79 84 91 95 90 77 53 39 32 27 24 21 18 19 22 26 29 34 33 34 39 48 53 56 80 119 157 187 237 296 349
122 96 68 45 31 29 31 32 27 18 9 4 2 1 3 6 8 11 12 9 7 9 15 21 19 16 13 12 11 9 14 18 28 49 86 128 151 164 180 205 224 222 207 179 158 154 130 104 80 59 50 59 56 42 24 10 4 2 0 0 0 0 0 0 0 0 0 1 8 46 39 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 2 4 7 13 24 38 48 55 60 63 69 80 88 81 58 43 38 35 31 28 27 26 27 32 34 37 37 37 39 48 51 60 85 129 139 145 158 180 207
168 131 97 65 41 34 29 24 18 13 8 5 4 6 11 17 19 21 19 16 13 12 12 11 10 8 5 4 5 9 11 11 14 25 48 73 116 148 160 166 171 159 144 112 76 69 76 85 83 72 62 59 54 44 30 17 11 6 1 0 0 0 0 0 0 0 0 3 23 44 32 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 2 5 9 17 28 35 37 39 41 45 55 70 68 56 45 43 44 37 36 38 41 45 47 45 43 41 40 42 47 51 55 68 113 117 117 120 123 127
271 216 166 126 90 61 42 31 24 19 12 7 6 10 16 24 29 32 33 30 26 21 19 13 9 5 3 2 3 7 9 9 8 8 12 27 72 123 153 153 154 140 120 91 51 26 33 54 71 78 78 72 58 44 32 22 15 8 2 0 0 0 0 0 0 0 0 0 17 39 27 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 1 1 1 3 6 12 17 18 20 21 22 24 30 46 54 52 45 44 42 39 41 52 58 62 61 58 54 50 48 47 48 49 50 53 75 87 94 101 98 108
325 278 233 189 148 108 77 61 51 37 22 13 11 14 22 33 41 46 49 48 40 33 27 20 13 8 5 3 2 4 7 9 10 6 6 14 39 77 115 142 148 144 134 113 69 26 20 38 64 91 113 111 86 57 36 25 17 8 2 0 0 0 0 0 0 0 0 2 14 35 34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 9 13 13 12 12 12 15 18 29 43 53 45 41 39 43 57 76 74 67 61 60 61 58 54 50 47 48 44 47 55 63 65 73 87 109
337 289 250 218 192 157 125 104 89 64 36 20 16 20 28 40 47 53 61 65 60 50 38 27 19 12 5 3 3 4 7 11 14 10 9 10 16 26 42 80 105 124 142 151 109 59 33 42 83 144 182 175 136 82 39 23 14 7 2 0 0 0 0 0 0 0 0 1 21 29 15 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 6 7 8 8 8 10 14 21 31 47 49 51 58 73 86 81 68 62 65 70 67 61 55 50 45 45 41 40 44 56 59 67 82 109
260 249 234 216 206 192 174 151 125 89 53 32 26 29 34 39 44 51 62 74 78 67 49 34 24 16 9 4 4 7 10 14 15 14 12 10 9 9 13 30 56 93 147 170 148 107 70 57 91 161 209 215 175 101 41 20 11 5 2 0 0 0 0 0 0 0 0 1 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 4 6 6 6 8 10 13 16 22 37 49 61 76 89 73 60 62 85 110 94 76 66 57 53 48 42 40 40 42 49 51 56 65 79
169 194 204 198 197 200 198 184 155 108 71 48 37 36 36 37 36 41 50 59 62 56 47 37 26 18 11 8 7 9 11 12 14 14 12 9 5 2 3 13 35 78 149 173 174 154 113 56 72 126 180 208 192 105 44 18 7 2 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 2 5 6 6 7 9 12 14 19 24 34 44 53 67 76 77 78 80 129 122 91 80 91 64 54 48 45 42 42 43 43 44 49 50 57
104 140 168 174 182 194 203 201 173 123 84 58 44 38 33 27 26 30 35 39 40 38 36 33 28 23 17 13 12 14 14 14 14 14 13 9 5 4 4 8 20 55 119 163 188 190 164 91 70 83 117 153 162 91 44 16 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 6 5 6 9 12 16 19 25 30 36 42 47 62 74 96 143 202 193 135 89 99 104 72 60 59 56 49 45 42 39 39 48 49 59
99 126 150 164 179 197 210 201 173 135 100 73 56 45 31 20 14 16 21 24 26 27 28 30 30 26 18 14 15 16 18 21 22 21 20 16 13 9 7 9 16 48 100 151 193 214 189 139 99 78 78 98 87 58 33 15 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 6 4 5 7 10 15 20 24 29 33 37 40 44 51 64 87 176 211 149 74 94 141 114 84 64 54 55 51 47 43 39 39 45 51 58
91 124 147 166 185 203 214 202 178 144 108 80 68 56 37 20 9 6 8 12 15 18 20 22 26 25 18 11 10 15 22 33 39 39 34 28 24 20 15 15 23 55 104 161 208 229 198 159 121 91 71 73 53 35 22 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 5 7 13 19 24 28 32 34 34 36 40 45 53 75 158 165 108 88 170 194 169 121 66 58 54 50 47 45 42 43 45 50 59
51 88 129 163 191 212 223 216 196 178 162 140 94 65 43 25 13 10 7 7 9 14 19 23 31 33 29 24 19 22 35 52 64 65 56 46 43 39 31 28 40 73 131 203 260 247 193 141 110 96 79 69 55 38 22 15 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 1 4 4 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 1 2 3 4 5 8 16 22 27 31 32 32 33 34 37 43 54 100 184 239 195 234 271 237 164 98 65 60 56 51 46 45 46 46 45 48 57
54 93 136 176 208 228 236 231 222 234 250 189 119 74 45 27 16 14 11 11 14 23 38 47 56 61 63 60 51 51 60 71 81 86 80 76 72 65 54 50 67 101 155 221 267 239 186 138 109 95 81 70 58 44 27 17 12 9 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 1 3 6 6 4 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 2 3 4 5 11 18 25 30 33 33 32 30 30 32 41 54 97 183 337 382 396 307 189 106 72 62 58 54 50 45 44 43 41 42 49 54
91 129 169 207 239 261 266 260 253 262 281 215 141 84 45 24 16 14 14 18 27 44 58 70 77 80 80 77 67 62 60 62 70 77 81 88 92 89 83 87 104 130 164 202 215 197 173 148 119 87 70 60 51 41 31 23 19 16 12 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 1 6 8 8 7 5 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 1 1 2 3 3 6 12 20 28 33 35 34 31 29 28 31 38 50 78 143 297 350 291 179 106 75 64 57 54 54 51 47 45 43 42 46 50 56
126 163 203 244 280 311 323 321 313 305 287 232 159 91 45 28 22 23 25 31 41 57 61 61 59 57 55 50 40 32 29 33 41 54 69 82 91 98 101 111 125 140 154 167 183 183 175 163 129 73 57 51 42 33 26 22 20 20 16 8 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 4 7 8 8 7 6 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 2 1 1 2 7 4 6 11 20 30 33 34 34 32 27 26 27 34 47 68 147 242 254 183 124 117 84 57 54 55 56 55 52 47 47 45 45 49 56
143 176 211 248 289 339 369 374 361 343 319 270 199 129 77 52 44 42 42 42 44 44 41 34 27 23 22 19 15 11 9 10 17 26 36 57 96 120 114 113 118 125 125 122 132 146 156 155 125 67 42 36 28 19 13 14 20 25 23 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 0 0 0 0 2 4 7 8 8 8 6 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 1 0 4 5 7 10 19 27 31 32 33 30 25 23 25 32 45 65 120 187 210 122 145 118 74 50 56 56 55 55 56 54 54 51 47 48 57
124 148 176 211 260 323 361 383 400 415 378 322 252 183 128 93 72 59 48 35 26 20 14 10 6 5 5 5 4 3 1 1 4 12 33 73 132 136 115 95 85 85 80 75 80 92 106 111 92 52 23 16 14 8 10 17 24 32 31 21 9 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 3 5 7 8 8 5 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 1 1 1 1 2 5 8 10 18 25 30 31 32 28 25 23 23 29 43 61 88 139 254 179 160 189 215 106 62 51 49 46 48 50 52 52 51 51 58
65 89 121 162 224 286 332 365 394 422 404 358 298 234 176 131 92 63 42 23 10 2 0 0 0 1 1 1 1 0 0 0 0 3 12 30 59 74 69 56 47 43 38 35 37 46 58 59 45 27 16 16 13 7 8 16 28 38 37 25 11 3 0 0 0 0 0 0 0 0 0 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 6 2 2 4 6 7 7 4 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 1 1 1 1 1 2 5 8 15 22 28 29 29 27 23 20 21 28 41 57 76 96 164 205 256 306 294 165 89 61 56 45 43 44 45 46 49 51 51
17 33 60 99 162 223 273 306 322 357 370 356 316 257 190 132 84 48 24 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 6 11 18 23 26 26 24 20 16 14 14 21 21 18 13 12 16 14 11 13 21 32 35 30 19 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 0 0 0 0 0 0 1 3 7 5 5 5 4 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 3 4 3 2 1 1 1 1 1 1 3 6 13 22 28 27 27 26 24 22 23 29 41 56 76 105 155 216 288 307 266 207 155 116 84 68 50 40 43 43 44 45 44
2 6 18 38 70 109 151 187 204 252 289 301 281 230 158 97 52 22 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 6 8 13 16 18 17 13 8 5 6 7 8 7 6 9 11 14 18 22 22 22 18 11 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 1 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 2 2 1 0 0 0 1 1 1 3 7 17 21 23 25 26 23 22 25 31 41 56 73 94 115 149 207 206 209 201 170 132 81 58 46 38 40 40 42 44 44
0 1 3 8 15 26 47 80 105 142 176 195 186 144 91 47 18 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 6 5 7 10 13 13 10 5 3 2 2 2 4 5 6 10 15 21 23 23 20 14 8 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 1 3 4 2 2 2 1 1 0 0 0 0 1 3 9 15 21 25 27 26 26 28 32 42 57 74 88 100 111 121 150 162 136 107 76 51 37 36 39 40 42 46 48 47
0 0 0 1 3 8 15 26 41 60 74 77 65 47 29 16 6 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 5 9 9 7 6 5 5 6 7 5 3 2 0 0 2 3 5 8 12 19 20 19 14 8 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 0 1 4 3 2 2 2 2 1 1 0 0 0 1 4 9 18 24 26 28 30 31 35 45 56 70 85 96 102 109 114 112 97 87 76 59 37 34 36 40 42 47 49 49
0 0 1 4 7 8 6 5 8 13 14 9 4 6 6 5 3 0 0 0 0 0 0 3 2 1 0 0 0 1 1 1 0 1 5 10 13 14 13 10 5 0 1 2 2 3 2 1 0 0 1 2 3 5 11 11 9 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 0 0 0 0 0 0 0 0 1 2 3 4 3 3 2 2 2 1 0 0 0 1 4 13 20 24 28 31 33 38 46 56 67 79 90 97 99 97 93 87 84 79 67 45 42 47 47 42 45 47 47
0 1 6 8 7 5 4 4 3 2 2 0 0 1 1 1 1 0 0 0 0 0 0 2 2 1 0 0 0 1 1 1 1 7 12 16 18 20 22 18 10 3 1 1 1 1 1 1 0 0 0 0 0 0 2 3 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 0 0 0 0 0 0 0 0 0 0 1 4 6 6 4 4 4 3 1 1 0 0 0 1 7 14 20 25 31 35 39 45 54 65 76 85 91 96 95 91 85 79 74 58 39 35 41 43 43 47 49 46
1 5 9 10 11 11 11 10 7 4 2 1 0 1 3 3 2 1 0 0 1 2 2 2 1 0 0 0 0 0 0 0 2 8 14 18 23 25 24 16 6 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 4 4 5 6 5 3 2 1 1 0 0 1 4 10 20 28 32 35 39 43 52 63 73 80 86 91 90 85 78 73 71 63 45 30 33 39 43 48 52 50
1 5 10 14 17 22 18 14 11 8 6 5 6 11 17 16 10 4 2 5 10 12 11 9 6 1 1 1 0 0 0 0 1 4 9 15 24 26 22 13 4 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 5 5 5 3 2 1 0 0 0 2 6 15 22 29 35 39 42 51 61 70 78 83 84 84 81 76 74 75 64 42 29 39 47 51 54 57 54
5 11 15 18 22 47 34 25 27 36 36 35 35 38 40 36 28 18 13 19 29 31 27 19 10 6 3 1 0 0 1 1 1 2 7 15 21 23 20 13 5 1 0 1 1 1 1 1 1 1 1 1 1 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 0 0 0 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 5 4 2 1 1 0 0 1 4 9 16 25 33 37 41 48 58 67 74 78 79 78 75 72 73 71 61 41 35 42 50 55 58 59 57
9 13 15 15 15 46 45 49 72 105 103 97 90 84 74 60 49 38 32 37 45 49 44 33 20 11 4 1 0 0 0 0 1 2 6 14 18 19 17 12 3 1 0 0 1 0 1 3 4 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 3 2 1 1 1 0 1 3 5 11 20 28 33 37 43 52 62 68 71 72 72 70 71 70 69 63 47 33 32 43 50 56 58 60
25 23 18 11 9 19 30 55 102 155 160 154 142 128 115 93 74 58 47 48 56 61 58 49 37 25 15 7 2 1 0 0 0 1 3 9 13 16 17 14 6 3 1 0 0 1 6 11 15 14 8 3 1 0 0 0 1 1 0 0 0 0 1 3 4 2 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 2 1 1 1 1 1 1 3 8 16 24 29 34 39 48 55 60 62 62 62 64 66 66 65 56 41 31 29 36 45 55 64 72
49 40 29 12 6 4 9 26 59 127 154 159 160 174 148 129 109 88 69 60 63 68 69 63 56 45 35 27 18 11 7 4 3 3 2 4 7 11 14 11 8 6 4 2 2 6 12 17 19 15 6 2 0 0 0 0 1 1 0 0 0 1 6 11 11 6 3 2 3 3 3 3 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 0 1 2 1 1 1 1 1 1 1 2 6 13 21 26 30 35 43 49 51 52 54 57 61 63 64 65 57 40 25 25 30 41 56 71 90
70 58 46 23 7 0 1 4 13 40 56 69 90 122 100 105 118 124 112 90 80 77 76 73 66 57 50 46 37 28 22 19 18 16 13 10 7 5 10 9 10 11 10 7 6 8 11 13 13 8 4 1 0 0 0 0 0 0 0 0 0 3 8 10 11 9 7 7 6 6 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 0 0 1 1 1 1 1 1 1 1 2 5 11 17 23 27 31 37 42 43 43 46 52 58 62 63 62 55 43 40 42 49 61 68 76 85
70 63 51 29 9 0 0 0 1 5 10 17 32 49 56 73 95 111 128 117 108 102 91 87 78 67 59 55 51 44 39 38 39 38 36 35 28 13 11 13 16 17 15 11 8 6 6 5 6 4 2 0 0 0 0 0 0 0 0 0 0 0 2 4 6 8 9 9 10 9 7 5 3 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 2 3 6 9 13 19 24 28 31 36 39 38 41 48 56 60 61 61 60 62 63 66 74 86 93 97 92
54 57 46 25 8 0 0 1 2 5 7 9 15 24 32 40 48 57 84 103 121 135 118 107 96 87 79 73 68 62 59 58 61 62 61 60 56 37 27 26 26 23 17 10 6 3 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 4 6 8 11 11 9 6 4 3 2 2 2 3 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 1 1 1 2 2 1 2 3 4 7 10 16 21 24 27 30 34 36 38 45 53 59 62 63 64 65 67 72 81 92 103 107 103
62 64 41 18 5 0 0 3 7 10 12 13 16 19 23 28 32 41 53 72 93 114 135 135 124 110 96 88 82 78 75 75 77 79 81 82 80 69 58 49 41 35 26 16 7 3 3 4 4 4 2 2 1 1 0 0 0 1 0 0 0 0 0 1 3 5 8 11 10 8 6 4 2 2 1 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 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 2 2 3 5 8 12 16 20 22 25 29 34 40 45 50 55 59 61 63 61 62 67 76 86 96 101 104
77 67 37 16 4 0 2 7 15 19 19 18 20 21 24 27 28 34 42 53 64 75 122 144 144 134 117 106 98 92 90 93 97 102 105 105 101 94 86 77 67 58 45 25 8 7 7 8 9 8 8 7 5 3 1 0 0 0 0 0 0 0 0 1 3 5 7 9 10 10 8 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 0 1 2 2 2 2 2 3 5 8 11 12 16 19 22 25 30 36 41 45 48 52 54 55 55 55 57 64 73 83 90 97
103 76 47 24 9 2 2 14 26 34 35 33 31 29 27 26 27 32 37 43 53 63 78 96 113 127 124 114 104 102 111 108 104 104 110 119 120 117 110 102 94 87 75 59 45 28 18 14 14 13 13 12 10 8 6 4 2 1 1 1 1 0 0 0 1 1 3 5 7 9 9 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 0 0 0 0 0 0 0 2 2 2 2 2 3 4 5 5 7 11 15 18 20 25 29 32 36 39 42 44 45 44 43 44 49 55 60 68 79
169 129 93 59 30 13 15 28 40 44 45 40 35 30 28 27 29 33 36 39 49 60 73 83 89 94 103 102 97 95 101 100 99 103 114 125 130 132 132 132 128 125 116 103 87 67 50 38 29 23 23 23 23 21 17 12 8 6 8 11 8 4 1 0 0 0 0 1 3 6 8 6 3 3 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 3 3 4 6 7 9 11 13 15 19 22 24 26 28 29 30 30 29 27 27 28 30 35 45 57
274 244 208 159 96 48 30 28 33 42 48 48 43 38 36 34 33 34 37 41 49 61 75 85 86 94 100 101 98 91 89 90 93 99 106 109 119 129 138 148 143 148 153 148 143 128 104 79 59 46 41 42 46 43 36 26 18 15 21 31 32 25 12 1 0 0 0 0 1 5 7 8 8 9 7 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 2 2 2 3 3 4 4 5 7 8 10 12 14 15 16 16 17 17 17 15 13 12 12 12 12 17 28 40
411 406 379 324 231 151 97 64 49 55 63 63 59 55 51 43 40 41 46 51 60 69 82 95 102 109 113 112 104 96 89 87 90 97 107 112 115 118 125 140 144 148 153 156 152 138 127 119 100 79 65 61 63 67 63 52 41 35 40 47 54 54 40 20 8 1 0 0 2 4 6 7 7 10 10 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 3 3 4 4 4 5 5 7 8 9 10 10 9 8 7 6 5 4 5 6 4 6 13 22 31
495 519 517 475 379 290 220 167 132 126 118 105 91 79 61 47 44 53 65 69 78 86 94 105 116 127 132 128 118 110 104 99 97 102 110 114 115 116 121 131 139 144 148 152 155 159 160 154 137 117 101 94 94 97 99 91 73 61 60 63 72 83 80 53 26 7 2 2 4 6 8 11 13 12 10 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 2 3 4 4 4 4 5 5 5 6 7 6 4 4 3 2 2 2 2 2 1 4 10 14 19
470 497 508 483 426 370 327 295 269 246 208 166 130 111 96 74 60 61 82 89 98 106 112 119 126 134 142 143 139 133 124 116 117 121 123 124 122 117 125 133 138 141 147 158 169 176 177 168 162 153 146 138 131 135 142 140 120 113 119 118 110 116 103 83 60 32 15 10 7 6 6 8 7 6 4 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 0 0 0 0 1 1 1 1 2 3 3 3 4 4 5 5 5 4 3 3 3 2 2 2 1 1 0 0 1 2 3 5 7
399 409 409 391 375 365 358 351 334 300 252 202 162 145 132 111 87 72 99 111 119 126 134 143 144 145 150 155 161 166 164 156 154 149 145 141 136 140 150 154 152 150 156 170 182 191 198 195 196 196 194 195 196 196 195 192 186 184 179 166 151 152 156 156 138 79 47 28 16 6 4 4 4 3 0 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 0 1 1 1 2 2 2 3 4 5 5 5 5 4 3 3 3 2 2 1 0 0 0 0 0 0 0 0 1
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250 292 325 329 296 269 264 262 246 226 228 260 276 268 240 220 237 222 203 177 154 162 197 226 241 240 227 218 222 234 245 258 265 235 197 184 179 180 181 182 187 195 199 202 207 207 213 221 230 238 242 247 249 251 256 262 266 265 261 258 262 278 291 292 289 247 166 79 35 17 12 13 19 20 14 9 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 2 3 3 4 5 4 4 4 3 3 3 3 2 1 0 0 0 0 0 0 0 0 0 0
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