Vorticity
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nan 4 3 3 3 3 3 3 3 3 3 3 2 2 2 2 3 3 4 4 4 4 5 5 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 3 3 3 4 4 4 4 5 7 8 11 12 12 10 7 7 7 7 7 7 7 6 6 6 6 6 6 7 7 8 6 2 0 3 8 11 10 8 7 6 6 6 6 6 7 6 6 5 5 4 4 3 3 3 4 4 4 4 4 5 5 5 6 6 5 5 5 5 5 6 6 6 6 5 4 4 4 4 5 5 5 5 4 4 nan
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nan 7 7 7 7 7 8 9 11 11 10 9 8 8 7 7 7 7 7 7 7 8 8 7 8 8 8 8 8 8 8 8 7 8 8 8 8 8 7 7 7 7 7 7 7 7 8 9 9 9 8 8 7 6 6 6 7 8 8 9 9 9 9 8 8 9 9 9 9 8 7 6 5 5 5 6 6 6 7 7 8 7 7 8 8 8 7 7 7 7 7 7 7 6 6 6 7 7 9 12 13 12 10 8 6 5 3 3 5 6 6 6 7 7 7 7 8 8 8 8 8 9 10 11 11 11 11 11 10 10 9 9 9 9 nan
nan 7 7 7 7 8 9 10 11 11 10 9 8 8 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 6 7 7 7 7 7 8 8 9 9 8 8 7 6 6 6 7 8 8 9 9 9 9 8 8 8 9 9 9 8 6 5 6 6 6 5 5 6 7 7 8 9 8 8 8 8 8 8 7 7 7 7 8 7 7 7 7 7 9 12 15 14 12 9 7 5 3 2 3 4 5 6 6 6 7 8 8 9 9 9 9 9 9 10 10 11 11 11 11 10 10 10 9 9 9 nan
nan 7 7 7 8 8 9 11 11 11 9 8 8 7 7 7 7 7 7 7 7 8 8 8 8 7 8 8 8 8 8 8 8 8 8 8 8 7 6 6 6 7 7 7 8 9 9 9 8 8 7 6 6 6 7 8 8 9 9 9 9 8 7 7 8 9 10 9 7 5 5 6 6 5 5 6 7 8 8 9 9 9 8 8 8 8 8 7 6 6 8 9 8 7 7 7 8 10 13 14 13 10 7 4 3 2 2 3 4 5 6 7 7 8 8 9 9 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 nan
nan 7 7 7 7 8 10 11 11 10 9 8 7 7 7 8 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 6 6 6 6 7 7 9 9 9 9 8 7 6 6 6 7 8 9 9 9 9 9 8 7 7 7 9 10 11 8 5 4 5 5 5 4 5 7 8 8 8 8 9 8 8 8 8 8 7 7 6 8 9 9 8 7 7 7 8 9 11 11 10 8 4 2 1 2 2 3 4 6 7 7 8 8 9 10 10 10 11 11 11 10 10 9 9 9 9 9 8 8 8 8 8 9 nan
nan 7 7 7 7 7 9 11 11 9 8 8 8 7 7 7 8 7 7 7 7 7 7 8 8 8 8 8 8 8 7 8 8 9 9 9 9 8 7 6 6 6 7 8 9 10 10 9 8 7 6 7 8 8 9 9 9 9 9 8 7 6 6 8 10 11 10 7 4 4 5 5 4 5 6 8 9 8 8 9 9 9 8 8 8 7 7 7 7 8 9 8 8 8 8 7 7 8 9 9 8 6 3 2 2 3 4 5 5 6 7 7 8 9 9 10 10 11 11 10 10 10 9 8 8 8 8 8 8 7 7 7 7 8 nan
nan 6 6 6 7 7 9 11 10 9 8 8 7 7 7 7 8 8 7 7 7 7 7 8 8 8 8 9 9 8 8 8 9 10 10 10 10 8 7 6 6 6 7 9 10 10 10 9 8 7 7 8 9 9 9 9 9 9 8 7 6 6 7 9 11 11 8 5 4 4 4 5 5 6 8 9 8 8 8 8 9 9 8 8 8 7 6 6 8 9 9 8 7 8 8 7 7 7 8 8 7 6 5 5 5 5 6 6 7 7 7 8 8 9 9 10 11 11 10 10 9 8 8 7 7 7 7 8 8 8 8 8 7 8 nan
nan 6 6 6 7 8 9 10 10 9 8 8 7 7 7 7 7 7 7 7 7 7 7 7 8 8 9 9 9 8 8 8 9 10 10 10 10 8 7 6 6 7 8 9 10 10 10 8 7 7 8 9 10 10 10 10 10 8 7 6 6 7 9 11 12 10 7 4 3 3 4 5 6 7 8 9 8 8 8 8 9 9 8 8 7 7 6 7 9 9 8 8 8 8 8 8 7 7 7 7 7 7 7 8 7 7 7 8 8 8 8 8 8 9 9 10 10 10 9 8 7 7 7 7 7 7 8 8 8 8 8 8 8 8 nan
nan 7 7 7 7 8 9 10 10 9 8 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 9 8 8 8 8 8 9 9 9 9 8 7 7 7 8 9 10 10 10 9 8 7 8 9 10 10 11 11 11 9 7 6 6 7 9 11 12 11 9 5 3 3 3 4 5 7 8 9 9 9 8 8 8 8 8 8 7 7 7 7 8 9 9 8 8 8 8 8 8 7 6 6 7 7 7 8 8 8 9 9 10 10 9 9 8 9 9 10 10 10 9 8 7 6 6 6 7 7 7 8 8 8 8 9 9 9 9 nan
nan 7 7 7 8 8 8 9 10 9 9 7 7 6 6 7 7 7 7 8 7 7 7 8 8 8 9 9 9 8 8 7 7 8 8 8 8 7 7 7 8 9 9 9 9 8 8 7 8 9 10 11 11 11 11 10 9 7 6 7 9 11 11 11 9 7 4 3 2 3 4 7 8 9 9 9 9 8 8 8 8 7 7 7 8 8 9 9 9 9 9 8 8 8 8 7 6 6 6 7 7 8 8 8 9 10 10 10 10 9 9 10 11 12 12 11 10 7 5 5 5 6 6 7 7 8 8 8 8 9 9 9 10 10 nan
nan 8 7 8 7 7 7 8 9 9 9 8 7 6 6 6 7 7 7 7 7 7 7 8 8 8 9 10 10 9 8 7 7 7 8 8 8 8 7 7 8 9 9 9 8 7 7 8 8 10 11 11 11 11 11 9 8 7 7 9 11 12 11 9 7 6 4 3 3 4 6 8 9 9 9 9 8 8 8 8 8 7 7 8 8 9 9 10 9 9 9 8 8 8 7 6 5 6 7 7 8 8 8 8 9 9 10 9 9 10 10 12 15 16 15 12 8 4 2 4 5 6 7 8 8 8 8 8 9 9 9 10 10 11 nan
nan 8 8 8 7 7 7 8 9 9 9 8 7 6 6 6 6 7 7 7 7 8 8 8 8 8 9 10 10 9 9 8 8 8 8 8 8 8 7 7 7 9 9 8 8 7 8 8 9 10 11 11 11 10 10 8 8 8 10 12 13 13 9 6 5 4 3 3 3 5 7 9 9 10 9 8 7 7 8 9 9 8 8 8 9 9 9 9 9 9 9 8 8 7 6 6 6 8 8 8 9 8 8 9 9 9 8 8 9 10 11 13 15 15 13 8 2 -2 0 4 6 7 8 8 8 8 9 9 10 10 10 11 11 11 nan
nan 9 9 8 8 7 7 8 9 9 9 9 8 7 6 6 6 7 7 7 7 7 8 7 7 8 9 9 9 10 9 9 9 9 9 8 8 7 7 7 8 8 8 8 8 8 8 9 10 10 11 10 9 9 8 8 8 10 12 15 15 12 7 3 2 2 2 3 5 7 9 10 10 9 8 7 7 8 9 9 9 8 8 8 8 9 9 8 8 8 8 8 8 7 6 7 8 9 9 9 9 9 9 9 9 8 8 8 8 9 9 10 11 10 6 -1 -7 -6 -0 4 7 8 9 9 9 9 9 10 11 11 12 12 12 13 nan
nan 9 9 8 8 7 7 8 8 9 9 10 9 7 7 7 7 7 7 6 7 8 8 7 7 7 7 8 9 9 9 10 10 10 9 9 8 7 7 7 8 8 8 8 8 8 8 9 10 10 10 9 8 8 8 8 9 12 14 16 14 9 3 0 -1 0 2 5 8 9 10 10 9 8 7 6 7 8 9 9 9 8 8 8 8 8 8 7 7 8 8 8 7 7 7 8 9 9 9 9 9 9 9 9 8 7 7 7 8 8 8 8 8 6 -0 -8 -11 -5 2 7 9 10 10 10 10 10 10 11 12 12 12 13 13 14 nan
nan 9 9 8 8 8 8 7 7 8 9 10 9 8 7 7 7 7 6 6 7 8 8 8 7 7 8 8 8 8 9 9 9 10 10 9 8 8 8 8 8 8 8 8 7 7 8 9 10 10 9 8 8 9 9 9 10 11 13 13 9 3 -1 -2 -1 2 5 8 10 10 10 9 8 7 7 7 8 8 9 10 10 9 8 8 8 8 7 7 7 8 8 8 7 7 8 9 9 9 9 9 10 9 9 9 8 7 7 7 7 7 8 8 7 3 -4 -9 -6 1 7 10 11 11 11 11 10 11 11 11 12 12 13 13 14 15 nan
nan 9 9 9 8 8 8 7 7 8 9 10 10 9 8 7 6 6 6 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 8 8 8 9 9 9 9 8 7 7 7 9 10 10 9 9 9 10 10 9 9 10 10 8 3 -0 -2 -0 3 6 10 12 12 10 8 7 7 7 7 7 8 8 9 10 10 9 8 8 7 7 7 7 7 8 8 8 8 8 10 10 10 10 9 9 9 9 9 9 8 7 7 7 7 7 8 7 5 1 -4 -5 2 10 14 14 12 11 11 11 11 10 11 11 12 13 13 13 13 13 nan
nan 9 9 9 8 8 8 7 7 8 9 9 10 10 9 7 7 6 6 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 10 10 9 8 7 7 7 8 9 10 9 10 10 10 9 9 8 8 6 4 1 -0 1 4 7 10 13 13 11 9 7 7 7 7 7 8 8 9 9 9 9 9 8 7 7 7 7 7 8 8 8 8 9 10 10 10 10 9 9 9 9 9 8 8 8 8 7 7 7 7 7 7 5 3 1 5 13 18 18 15 13 12 11 10 9 9 10 12 13 12 11 10 9 8 nan
nan 9 9 9 8 8 8 8 8 8 9 9 10 10 9 8 7 7 7 7 7 8 8 8 8 8 8 9 9 8 8 7 7 7 8 8 8 8 9 10 10 9 8 7 7 7 7 7 8 8 8 9 9 9 8 8 7 6 4 3 2 3 4 7 10 12 13 12 9 7 7 7 8 7 7 8 8 9 9 9 8 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 7 6 6 6 7 7 7 8 13 18 19 17 14 13 12 10 8 7 7 9 11 12 11 9 7 5 5 nan
nan 8 9 9 9 8 8 8 9 9 9 10 10 10 9 8 7 7 7 6 7 7 8 8 8 8 8 8 9 8 7 7 7 7 7 7 8 9 10 10 10 9 7 7 7 8 8 8 7 7 7 7 7 8 8 7 6 5 4 4 4 5 7 9 11 11 10 8 7 7 8 8 8 8 8 8 8 9 9 8 7 7 7 7 7 7 8 9 8 8 8 9 9 9 9 9 8 8 8 8 8 8 8 8 8 7 7 7 6 6 6 7 9 9 10 13 14 13 12 12 11 9 6 4 4 7 10 10 9 7 5 4 4 5 nan
nan 8 8 9 9 9 9 9 9 9 10 10 9 9 8 8 7 7 7 6 7 7 8 8 8 7 8 8 8 8 8 8 8 8 7 7 8 9 10 10 9 9 8 8 8 9 9 9 9 7 6 5 6 7 8 7 6 5 5 5 5 7 9 10 10 9 7 6 6 8 9 9 9 9 8 8 8 9 8 7 7 7 8 8 7 7 8 8 8 8 8 8 8 9 8 8 8 8 8 8 8 8 8 8 7 7 7 7 6 6 6 7 9 9 9 9 9 9 9 9 8 5 2 -0 2 7 9 8 7 4 3 4 5 6 nan
nan 7 8 9 9 9 9 8 8 9 10 9 9 8 8 8 8 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 8 7 7 8 8 9 9 9 9 9 9 9 10 10 10 8 6 6 7 8 8 7 6 6 6 6 6 8 9 9 8 7 5 6 7 9 10 10 10 9 8 8 8 9 8 7 7 8 8 7 7 7 8 8 8 8 9 8 8 8 8 8 7 8 8 8 9 9 8 8 7 7 6 7 7 7 6 8 8 8 8 8 7 6 5 4 3 -1 -5 -5 1 5 6 6 4 3 3 5 6 7 nan
nan 7 8 8 9 9 9 8 8 9 10 10 9 8 8 8 8 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 8 7 7 8 8 9 9 9 9 9 10 10 10 9 8 8 9 9 8 8 7 7 7 7 7 8 8 8 7 6 6 7 9 10 10 9 9 8 8 8 8 8 7 7 7 8 7 6 6 6 7 8 8 9 8 8 8 8 8 8 8 9 9 9 9 9 8 7 6 6 6 7 7 7 7 8 8 8 8 7 5 2 0 -1 -3 -7 -10 -6 0 4 5 5 4 4 4 5 6 6 nan
nan 8 8 8 9 9 9 8 8 9 10 10 9 9 8 7 7 7 7 7 8 8 7 7 8 9 9 9 9 8 7 7 8 8 9 9 8 7 8 8 8 8 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 8 8 8 7 8 8 8 8 7 7 8 9 9 9 9 9 8 8 8 8 8 8 7 7 7 6 6 6 6 7 8 8 8 7 7 7 7 8 8 9 9 9 9 8 8 7 6 6 6 7 7 7 7 7 8 8 9 8 6 4 2 0 -1 -3 -6 -6 -2 2 4 5 4 4 5 5 5 5 6 nan
nan 8 8 8 8 9 9 8 8 8 9 9 10 10 9 7 6 6 7 8 9 8 7 6 7 8 9 9 8 8 8 8 8 8 8 8 7 7 8 8 8 8 9 9 8 8 8 8 8 7 8 8 8 8 8 8 8 9 9 9 8 8 8 8 9 8 8 8 8 8 8 8 8 8 8 8 9 8 8 7 7 7 7 7 7 8 9 9 9 8 7 7 7 7 8 8 9 8 8 8 8 7 7 7 7 7 8 7 7 7 8 9 9 9 9 8 8 7 6 5 2 -1 0 2 4 4 5 5 5 5 5 5 5 6 nan
nan 8 8 7 8 8 9 8 8 8 8 9 10 10 9 7 6 6 6 8 9 8 6 6 7 7 8 8 8 9 9 9 9 8 8 8 8 8 8 8 8 9 9 8 8 8 8 7 7 7 7 8 9 9 9 9 9 9 9 10 10 10 9 8 8 8 8 8 7 6 6 7 7 8 8 8 8 8 8 7 7 7 8 8 9 9 10 9 8 8 7 7 7 8 8 8 8 8 8 8 7 7 7 8 8 8 8 8 8 8 9 9 9 10 10 10 11 11 10 8 3 0 -0 1 3 5 5 5 5 5 5 5 5 6 nan
nan 8 8 8 8 8 8 9 8 8 9 9 10 10 9 7 6 6 6 8 8 8 7 7 7 7 8 8 9 9 9 9 9 8 8 9 9 8 8 8 8 8 8 8 8 8 7 7 7 7 7 8 8 9 9 9 9 9 9 10 10 10 9 8 7 7 8 7 6 5 6 6 7 7 7 8 8 8 8 7 7 8 8 9 9 9 8 8 7 7 8 8 8 8 8 7 7 7 8 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 11 10 10 10 9 4 -2 -5 -4 0 3 5 5 5 5 5 5 5 6 6 nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan 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
38 42 46 43 37 28 22 17 15 14 13 13 15 14 11 6 7 8 10 11 10 13 16 15 10 6 5 4 3 4 3 5 7 9 10 10 11 14 17 20 20 21 22 24 24 25 25 25 24 23 20 17 13 10 6 4 4 3 2 2 2 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 1 0 0 0 0 2 2 2 2 4 6 9 11 14 15 14 10 6 5 4 3 2 1 2 2 2 2 4 7 8 9 8 7 6 5 3 2 0 0 1 20 127 279 436 420 258 124 64 40 35
50 56 56 50 45 36 27 20 18 18 19 20 22 22 17 7 7 9 8 7 5 8 12 12 9 6 7 6 5 5 4 7 8 9 10 10 11 13 15 16 17 18 20 22 24 25 25 25 26 27 27 26 22 16 12 10 8 6 6 7 10 15 8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 2 3 4 5 6 6 7 8 10 11 10 8 7 5 4 4 3 2 2 2 2 3 3 6 8 9 10 10 9 7 6 3 1 1 1 5 26 71 127 156 125 86 49 36 33
55 66 64 54 48 45 38 31 28 28 29 32 34 31 21 11 12 10 8 9 10 9 7 7 7 7 8 8 7 7 7 8 9 9 9 9 9 10 11 11 15 17 18 20 20 21 22 22 23 25 27 27 27 21 17 15 11 8 8 14 22 26 14 7 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 4 6 7 6 2 3 6 8 8 7 7 6 5 3 2 3 2 2 2 2 3 3 5 7 8 10 12 12 10 9 5 4 3 2 4 10 21 31 44 48 47 35 32 30
68 84 85 74 67 64 58 49 44 43 44 43 40 36 24 17 15 12 10 11 12 11 8 6 5 5 5 6 6 6 5 7 8 8 7 6 8 9 11 11 12 14 15 16 16 17 19 20 21 21 23 22 22 23 21 18 15 11 11 19 27 26 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 1 1 2 3 3 4 5 3 4 6 8 7 7 6 5 4 3 3 2 2 2 2 2 3 3 4 5 6 9 9 10 12 12 10 8 7 7 9 13 18 22 25 29 30 27 25 24
104 120 117 106 100 87 72 60 49 44 43 45 48 48 38 29 23 16 13 13 14 13 11 7 4 2 2 3 3 4 4 5 6 7 6 4 6 8 6 7 9 10 11 12 13 15 17 19 20 20 21 22 23 25 23 21 20 17 16 22 23 14 9 6 2 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 2 4 4 6 7 8 8 7 6 5 4 4 4 3 1 2 2 2 2 2 2 3 4 4 7 7 8 13 16 15 13 12 13 15 20 23 25 23 18 18 19 18 18
136 146 135 128 122 98 72 51 33 24 25 37 55 64 57 45 28 23 22 21 18 13 10 9 5 2 2 2 3 3 3 3 5 5 5 4 4 6 5 3 4 6 7 9 11 13 15 17 17 17 18 20 20 22 23 22 21 20 21 24 17 9 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 1 2 3 3 2 3 7 8 7 7 6 5 4 4 4 4 1 2 3 4 3 3 3 3 3 4 3 4 6 6 7 8 11 15 16 16 14 15 27 23 22 17 12 11 12 13 11
169 167 144 132 117 87 60 35 16 11 21 40 53 67 60 50 40 41 37 29 22 14 9 8 6 1 2 3 2 2 3 4 4 4 5 5 5 5 4 3 5 5 4 5 7 10 12 13 14 14 15 16 16 16 18 18 19 20 24 26 16 10 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 4 5 4 5 8 8 5 4 4 4 4 3 2 4 3 4 5 6 5 4 4 4 4 5 4 5 5 6 7 7 8 11 15 16 14 14 19 14 13 14 13 12 11 11 11
187 156 140 117 91 64 40 23 13 10 17 31 37 50 49 45 61 65 53 43 36 26 16 12 11 6 3 2 1 1 2 3 3 4 5 5 5 6 4 4 5 5 4 3 5 8 8 9 9 10 12 14 13 12 12 13 15 19 23 29 22 16 11 6 3 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 6 6 7 7 6 4 3 3 3 3 1 2 4 5 5 6 7 7 5 5 5 5 5 4 5 6 6 7 7 8 9 11 15 15 17 18 18 19 17 15 15 13 12 12
182 141 107 86 64 46 34 25 16 11 10 14 29 34 35 39 48 56 63 70 72 57 30 27 25 18 9 5 1 1 1 1 2 3 3 7 4 4 4 4 4 4 4 4 5 5 6 7 8 10 11 11 10 9 9 11 15 20 23 30 29 23 16 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 1 3 5 6 6 5 4 3 4 4 3 2 1 2 3 5 7 9 10 9 8 6 6 6 6 5 6 7 8 8 7 8 8 8 12 15 18 20 22 22 21 20 19 17 16 14
155 122 90 67 49 36 29 24 18 13 10 6 21 24 28 39 52 74 99 109 97 75 48 48 39 29 22 15 8 5 4 0 1 1 2 2 2 3 3 4 4 4 4 4 4 4 4 5 5 5 6 7 9 11 11 11 14 18 20 26 29 24 17 14 12 7 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 4 5 5 5 3 3 4 3 2 1 1 2 3 5 7 9 11 12 12 9 7 7 7 7 8 8 9 10 8 10 9 9 11 15 17 20 23 24 30 28 28 27 21 17
118 93 71 52 39 29 22 19 16 13 12 9 18 26 32 51 90 133 155 143 99 69 56 53 47 42 34 25 17 13 8 1 2 1 1 1 1 2 2 3 4 4 3 3 4 3 3 3 3 2 3 3 4 8 8 8 9 11 14 18 23 20 13 11 9 6 3 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 5 5 6 5 4 5 2 2 2 2 2 2 3 5 8 11 13 15 12 9 7 7 8 9 10 12 13 12 13 12 10 11 15 18 21 26 41 42 34 35 31 24 21
84 67 51 37 29 22 16 14 13 11 12 14 24 36 44 66 99 136 157 121 76 51 40 37 39 42 36 28 22 18 11 8 5 2 2 2 1 1 1 2 2 3 3 3 3 3 2 2 2 1 1 1 1 3 3 3 4 6 8 11 15 15 9 6 6 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 5 5 6 6 6 4 3 2 2 3 3 3 4 4 6 10 12 15 14 12 11 11 13 12 13 14 14 14 14 13 13 13 16 19 21 25 30 30 31 33 31 29 26
60 50 38 28 22 17 14 13 12 11 16 21 37 59 77 92 123 158 145 90 54 41 35 35 35 36 34 31 28 22 14 11 7 4 2 2 2 2 1 2 2 3 3 3 2 3 3 2 2 1 0 0 0 0 0 0 1 2 2 4 9 12 9 3 3 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 4 5 6 6 4 4 3 3 4 4 5 6 5 5 8 11 13 15 15 14 14 15 15 14 13 14 14 14 14 14 15 16 17 18 22 22 25 30 32 32 31 31
48 42 37 32 26 20 16 13 13 12 28 36 63 98 123 143 168 171 121 72 60 57 49 47 45 42 39 37 38 33 20 16 11 8 3 2 2 2 1 1 2 2 2 2 2 2 2 2 2 1 1 1 0 0 0 0 0 0 0 1 4 5 1 0 0 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 1 1 2 3 4 5 6 5 4 4 5 5 4 4 6 6 6 8 9 12 13 14 16 14 16 16 15 14 15 14 14 13 14 15 15 17 15 18 22 29 36 39 37 34 38
61 64 66 64 58 46 33 34 33 32 64 94 120 150 169 174 170 145 100 72 65 70 68 62 57 55 54 53 58 63 30 22 19 13 10 11 9 5 3 1 2 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 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 1 2 2 1 2 3 5 6 5 5 5 6 7 6 5 7 6 7 8 8 10 12 13 15 15 16 17 17 16 15 15 15 14 14 15 14 16 16 17 22 31 42 49 49 48 47
93 127 161 154 127 112 85 78 71 77 116 157 205 233 213 186 186 157 114 86 74 70 69 67 65 68 73 79 90 97 56 39 30 22 17 13 8 6 8 2 3 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 2 1 1 2 2 3 5 6 8 11 12 10 9 8 8 7 6 7 7 8 10 10 11 14 15 16 16 16 16 16 16 16 15 16 17 15 14 15 16 18 26 39 50 56 60 64
107 168 228 202 150 160 150 128 103 113 154 201 223 208 170 152 177 158 136 108 87 74 68 66 67 73 82 91 106 92 65 52 44 34 28 20 12 10 8 2 1 1 2 2 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 1 2 2 3 6 8 7 11 7 8 10 11 15 20 23 29 26 25 21 12 11 8 6 7 7 9 9 10 12 15 16 15 14 15 17 19 18 17 17 17 16 15 15 16 17 21 31 42 57 74 87
97 115 137 117 96 139 189 208 169 166 183 228 240 204 160 145 144 130 125 116 100 87 76 70 70 75 82 81 89 78 65 57 53 50 45 39 31 23 14 7 4 3 8 12 13 9 2 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 2 5 8 11 11 10 13 16 18 18 21 21 25 28 33 39 40 40 47 50 52 51 45 31 18 13 12 8 8 8 11 11 12 14 14 15 15 16 20 19 19 18 17 18 18 16 16 18 19 22 33 52 79 102
107 120 114 77 61 93 186 293 298 276 263 279 279 247 214 197 180 160 147 137 122 110 100 91 88 89 92 88 92 94 84 73 67 63 58 52 45 36 34 32 37 30 30 36 35 26 17 16 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 5 9 12 14 14 15 17 19 22 25 28 31 35 39 45 53 57 61 66 72 74 75 75 63 42 34 30 27 11 8 9 10 11 12 13 14 17 18 19 19 22 22 20 20 21 19 20 19 20 21 27 41 63 95
97 106 98 73 58 99 223 326 394 385 354 326 298 273 261 250 226 205 187 170 150 138 131 125 120 121 129 139 131 130 120 124 117 98 89 82 79 81 83 84 102 91 72 62 54 44 40 32 12 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 2 7 12 15 16 15 17 19 22 26 31 35 39 43 48 56 66 78 86 91 102 107 107 106 98 81 61 49 47 28 18 13 9 11 13 13 13 17 18 16 17 27 31 23 31 37 34 38 33 34 33 31 32 39 63
85 92 83 67 62 124 189 294 382 399 401 385 356 336 319 295 266 262 236 216 196 181 175 172 173 178 170 186 163 158 157 156 158 162 150 133 145 155 146 118 108 93 70 50 37 28 27 18 4 0 0 0 1 1 3 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 2 8 13 16 18 18 19 22 26 32 39 47 56 64 65 75 91 103 112 119 129 147 167 173 162 154 112 84 69 54 43 27 12 19 23 21 20 19 17 17 17 23 27 20 41 71 60 68 63 55 52 47 39 36 44
76 79 64 48 32 61 63 129 141 206 309 390 402 362 380 362 337 323 304 284 267 259 259 260 261 279 244 233 205 202 210 220 237 251 235 234 242 219 183 114 60 33 20 14 9 6 5 2 0 0 0 2 4 6 5 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 1 5 12 16 18 19 22 26 32 39 49 61 70 79 86 92 104 117 131 149 172 203 245 277 269 244 189 143 105 79 68 58 40 46 38 35 32 30 27 22 19 20 17 24 65 124 112 87 76 69 66 67 58 55 42
52 46 32 25 9 2 8 18 12 43 110 245 399 424 417 371 409 428 402 368 349 344 362 396 369 382 367 350 310 281 286 314 340 358 380 320 275 226 152 74 23 4 1 0 0 0 0 0 0 2 5 9 11 9 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 2 9 14 18 21 26 33 41 48 58 72 83 90 102 106 116 129 152 188 237 291 330 376 410 357 289 226 168 126 115 88 64 54 45 41 38 36 36 37 37 32 27 35 57 104 116 96 81 78 73 78 73 71 58
17 13 5 1 0 0 2 2 1 5 25 83 143 122 109 155 192 215 268 290 268 248 282 363 365 370 385 397 368 329 318 327 330 348 329 304 248 174 94 35 7 0 0 0 0 0 0 0 0 1 5 12 11 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 1 3 7 14 23 28 35 43 52 61 69 82 93 92 110 121 132 149 180 230 305 392 404 444 485 471 423 356 270 198 167 136 115 88 68 55 45 41 39 40 45 44 39 37 37 52 64 66 66 76 81 89 92 86 64
1 1 0 0 1 0 0 0 0 3 7 12 16 12 5 3 11 22 14 13 31 49 67 107 170 199 226 252 293 330 338 327 326 300 279 251 184 95 35 11 3 0 0 0 0 0 0 0 0 0 3 10 7 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 1 3 10 22 28 33 40 48 58 68 78 86 95 105 109 123 137 151 173 209 273 364 467 496 502 509 517 521 496 411 331 262 211 179 134 102 80 62 58 53 37 42 46 43 38 37 40 44 43 45 62 79 88 86 79 62
0 0 0 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 8 20 43 64 107 189 271 312 319 314 301 262 171 91 37 12 4 0 0 0 0 0 0 0 0 0 0 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 2 5 11 18 24 33 43 52 62 73 85 97 105 113 122 133 149 165 179 202 242 327 425 510 554 565 550 533 540 556 527 491 398 312 256 203 151 114 92 81 70 43 48 54 52 43 38 49 55 52 50 54 62 68 77 89 78
0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 3 14 53 130 216 267 273 257 231 180 76 24 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 3 8 14 25 33 40 45 49 54 64 80 98 112 123 132 144 170 198 215 226 252 294 391 498 586 645 663 635 586 559 553 546 570 511 432 371 316 246 174 152 146 121 86 72 77 78 58 47 60 67 69 69 64 61 63 68 72 66
0 0 0 0 0 1 1 1 1 1 1 1 1 0 2 2 2 2 2 2 2 1 1 1 1 1 10 38 89 152 183 145 95 36 15 8 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 2 6 12 24 29 38 47 57 61 61 61 65 74 102 121 133 144 162 194 230 257 275 308 367 464 584 678 717 719 711 678 639 600 562 587 573 525 482 439 363 268 241 228 196 142 96 86 98 81 72 74 71 68 74 83 83 73 70 78 92
0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 5 17 38 71 104 26 15 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 1 6 21 33 44 47 57 70 83 81 67 64 68 75 101 125 140 151 172 207 241 272 298 338 408 511 635 743 804 815 797 768 742 690 627 610 609 592 562 545 480 406 359 321 277 213 146 112 115 107 99 97 84 75 82 96 100 83 86 81 97
0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 3 6 11 14 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 6 40 64 72 77 84 91 97 95 71 64 68 81 109 131 146 157 177 213 249 277 302 342 410 508 626 740 823 865 874 845 831 783 705 634 596 590 600 607 576 537 502 449 376 310 269 211 175 150 134 129 111 88 93 110 115 91 94 89 91
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