Vorticity
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nan 6 7 7 7 6 6 6 6 6 7 7 7 7 7 7 6 6 6 6 6 6 7 6 6 6 7 8 9 9 9 8 7 6 5 5 5 5 5 6 5 5 4 5 7 7 8 8 8 8 7 6 6 5 6 6 7 8 9 8 8 8 8 8 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 7 7 7 8 8 7 6 6 6 6 6 6 6 6 6 6 6 5 5 4 4 5 5 6 6 7 6 6 6 5 6 7 8 8 8 7 6 4 4 4 5 5 6 7 7 7 7 7 6 6 6 6 6 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 6 6 6 6 7 7 7 7 6 5 5 4 5 5 7 8 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 nan
nan 7 7 9 9 8 7 7 7 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6 7 7 8 8 8 8 8 7 6 5 5 5 5 5 6 5 6 7 7 8 8 8 7 7 6 6 6 6 6 5 6 6 7 7 8 8 8 8 9 9 10 10 10 9 9 8 8 8 8 9 9 10 9 8 7 7 8 8 8 7 6 6 6 6 5 5 6 6 6 6 5 5 4 4 4 5 6 6 7 7 6 6 6 7 7 8 8 8 7 6 4 4 4 5 6 6 7 7 7 7 7 6 6 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 8 8 8 7 7 7 7 6 6 6 6 6 7 7 6 6 5 5 4 4 4 5 7 7 7 7 6 6 6 6 6 6 6 5 6 6 6 6 5 5 5 nan
nan 8 8 9 9 9 8 8 8 8 8 7 7 6 6 6 6 7 7 7 6 6 6 6 6 6 7 7 7 7 7 8 8 7 6 5 5 5 6 7 7 7 7 7 7 7 6 6 6 6 6 6 7 7 7 6 5 5 5 5 6 7 8 8 9 9 10 11 11 11 11 10 9 8 8 9 9 10 10 8 7 6 7 8 9 9 8 7 6 6 6 6 6 6 7 6 6 5 5 4 4 4 5 6 7 7 7 6 7 7 7 7 8 8 7 6 5 5 5 6 6 7 7 7 8 7 7 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 5 5 5 5 4 4 5 6 7 7 7 7 7 7 7 6 6 6 6 5 5 5 5 5 5 5 nan
nan 8 8 8 9 9 9 9 8 8 7 7 6 6 6 6 6 6 7 7 7 7 6 6 7 7 7 7 6 6 7 7 7 7 6 5 4 5 6 8 8 7 6 6 5 5 5 5 5 5 6 7 7 7 7 7 6 6 5 5 5 6 7 7 8 8 9 9 11 11 11 11 10 9 9 8 7 7 7 6 5 5 6 8 10 10 10 8 7 6 6 6 6 6 7 7 7 6 5 5 4 4 5 6 7 7 7 7 7 7 7 8 8 8 7 6 6 6 6 6 6 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 6 7 7 8 7 7 7 7 7 6 6 5 5 5 5 5 6 5 5 nan
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nan 9 8 6 5 4 5 6 7 7 8 8 9 9 10 9 8 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 7 7 6 6 6 6 6 6 7 7 7 8 8 9 10 10 10 9 9 9 9 8 8 7 6 6 6 7 8 7 7 8 8 8 8 8 8 8 8 8 7 7 7 7 8 8 9 9 9 9 9 8 8 9 10 9 9 8 8 7 7 6 6 6 6 7 6 6 7 9 11 13 13 13 11 11 11 12 12 10 8 7 7 6 6 7 7 8 9 9 9 9 8 7 6 5 4 4 3 4 6 9 12 15 16 15 12 10 8 6 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 6 6 5 5 nan
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nan 9 9 9 10 10 10 10 11 11 10 10 10 10 9 9 9 9 9 9 9 9 9 10 10 10 9 9 10 10 10 10 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 10 10 10 10 10 10 10 10 9 9 9 8 8 7 7 7 8 8 8 8 9 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 10 10 11 12 13 13 13 13 13 13 12 11 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 8 7 7 7 7 7 8 8 9 10 10 10 10 9 9 8 9 9 9 8 7 7 6 6 6 7 7 7 7 8 7 8 8 9 9 10 10 11 11 12 12 12 12 12 13 13 13 12 12 11 11 10 10 9 9 9 8 8 8 9 9 9 9 9 nan
nan 9 9 10 10 10 10 10 10 10 10 10 10 9 10 10 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 10 10 10 10 10 10 11 11 10 10 9 9 8 7 7 7 7 8 8 8 8 9 10 10 10 10 10 10 10 10 9 9 8 8 8 8 9 10 10 10 11 12 13 13 14 14 13 12 11 10 10 10 10 10 10 10 10 9 9 9 8 8 8 8 9 10 11 10 9 9 8 8 8 8 8 8 8 9 9 10 10 10 10 10 10 10 9 8 8 8 8 8 7 7 8 8 8 8 8 8 8 9 9 9 10 11 12 12 12 12 13 13 13 14 14 14 13 12 11 10 10 9 9 8 8 8 8 8 8 8 8 9 nan
nan 9 9 10 10 10 10 10 10 10 10 10 10 9 9 10 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 10 10 10 10 10 10 9 8 8 8 8 9 9 9 9 9 10 10 10 10 10 10 9 8 7 7 8 8 9 9 9 9 9 9 9 10 11 12 13 13 12 11 11 10 10 10 10 10 10 9 9 9 9 8 8 8 8 8 9 11 12 11 11 10 9 9 9 9 9 9 8 8 8 9 9 10 11 11 11 9 8 7 7 8 9 10 9 8 8 8 9 9 10 10 10 10 9 9 10 11 11 10 10 10 11 11 12 12 13 13 12 12 11 10 9 9 8 8 8 8 8 8 9 9 9 9 nan
nan 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 8 8 9 10 11 11 11 11 10 10 9 9 9 9 8 8 8 8 9 9 9 9 8 7 7 8 9 9 10 9 9 9 8 8 9 10 10 11 11 11 11 10 10 10 10 10 10 10 10 9 9 9 9 8 8 8 8 8 9 10 11 12 11 11 10 10 9 9 9 8 8 8 8 8 9 10 10 10 9 8 7 6 6 7 8 9 9 8 6 6 6 7 9 10 10 9 9 8 9 9 8 7 7 7 8 8 9 9 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 nan
nan 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 10 10 10 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 8 8 8 8 8 8 8 8 8 9 9 9 9 8 8 7 7 7 8 10 11 12 13 12 11 10 9 8 7 7 6 6 6 7 8 8 8 8 8 9 9 10 10 10 9 8 8 8 9 9 10 10 10 9 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 8 9 9 10 11 11 10 10 10 9 9 8 8 7 7 7 8 9 10 9 8 7 7 7 6 6 6 7 8 8 7 5 4 3 4 5 6 7 7 7 7 8 8 7 6 6 6 7 7 7 8 8 9 9 9 9 9 10 10 10 10 10 10 10 10 9 10 10 9 nan
nan 10 11 11 11 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 8 8 8 8 7 7 8 8 7 8 8 8 8 9 9 9 8 8 8 7 8 9 10 11 12 12 12 10 9 7 6 6 6 6 7 7 7 7 8 9 10 10 10 10 10 10 9 8 8 8 9 9 9 9 9 9 9 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8 8 8 8 8 9 8 7 6 6 7 7 7 7 7 7 8 8 7 6 5 4 3 3 4 5 6 6 7 8 8 7 7 7 8 8 8 8 9 9 9 10 10 11 12 12 12 12 11 11 10 10 10 10 10 10 10 nan
nan 10 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 9 9 9 9 8 8 8 8 8 8 8 7 8 8 8 8 8 8 8 8 8 9 9 9 10 10 10 10 10 11 12 14 14 14 13 11 9 8 8 9 10 9 9 8 8 9 11 11 11 10 10 10 10 10 9 9 8 8 8 8 8 9 9 9 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 10 10 10 9 9 9 8 8 8 8 8 9 9 9 9 9 9 9 9 9 8 7 6 5 6 6 8 8 9 8 8 8 8 8 6 6 5 4 5 6 6 7 8 8 8 8 8 9 9 10 10 10 10 11 11 12 12 13 14 14 13 12 11 11 10 10 10 10 10 10 10 nan
nan 11 11 12 12 11 11 11 10 10 9 10 10 10 10 10 10 9 9 9 8 8 9 9 9 9 10 10 10 10 10 9 9 9 9 9 9 8 8 8 8 8 8 7 7 7 7 8 8 8 7 8 8 8 8 8 8 8 9 10 10 11 13 13 14 15 16 17 19 18 17 15 14 13 14 14 14 13 12 10 10 11 13 13 12 11 11 10 10 10 10 9 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 9 9 9 8 8 8 9 9 10 10 10 10 10 10 9 9 8 7 6 5 4 5 7 8 9 9 9 9 9 8 8 7 7 7 6 7 7 8 8 9 9 9 9 10 10 10 11 11 11 12 13 13 14 14 14 14 12 11 11 11 11 11 11 11 11 11 11 nan
nan 11 12 12 12 12 11 11 10 10 9 9 10 10 10 9 9 9 9 9 8 8 8 8 9 10 12 13 13 12 11 10 9 9 8 8 8 8 8 8 8 8 8 8 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 10 10 11 13 15 17 17 18 19 19 20 19 18 17 17 17 17 16 15 13 12 12 13 14 15 14 13 11 11 11 10 10 9 9 9 9 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 11 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 9 8 8 7 7 6 5 4 5 6 7 8 8 9 9 9 9 9 8 8 8 7 7 7 8 9 9 10 10 10 10 10 10 10 11 11 11 12 13 13 13 13 13 12 11 11 12 12 12 12 11 11 10 11 nan
nan 11 11 11 11 11 11 11 11 10 10 10 9 9 9 9 9 9 8 8 8 8 8 8 10 12 14 15 15 14 12 12 11 10 8 8 8 8 8 8 9 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 10 10 9 9 10 11 13 14 15 15 16 17 17 17 16 15 15 15 14 14 13 12 11 12 14 15 15 14 12 11 11 11 11 11 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 11 11 11 11 11 12 12 11 11 11 11 11 10 10 9 9 8 7 7 6 6 6 7 6 6 5 5 5 6 7 8 8 9 9 9 9 9 8 8 8 8 9 9 10 11 11 11 11 11 11 10 10 10 10 11 12 12 11 12 12 11 11 11 11 11 11 10 10 9 10 10 nan
nan 11 11 11 11 11 11 11 11 11 10 10 9 9 8 8 8 8 8 8 8 8 9 10 13 15 16 16 14 13 13 12 11 10 9 8 8 8 8 8 8 8 9 9 9 9 8 8 8 8 8 8 8 7 7 8 8 9 9 9 8 7 6 5 6 7 9 11 12 13 14 13 12 12 11 11 12 12 12 12 11 12 13 14 15 15 13 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 10 10 10 11 11 12 12 12 12 12 11 11 11 10 10 9 8 8 8 7 6 6 6 6 7 7 8 7 7 6 4 5 6 7 7 8 9 10 10 10 9 9 8 9 9 10 11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 10 9 8 7 7 7 8 8 8 9 9 9 nan
nan 10 10 10 11 11 11 11 11 11 10 10 9 8 8 8 8 8 8 8 8 9 10 13 16 17 15 13 12 11 11 11 11 10 10 9 8 8 7 7 7 8 9 9 9 8 7 7 8 8 8 7 7 7 7 7 7 8 8 8 7 5 4 2 1 2 4 6 8 10 11 11 10 10 10 10 10 10 11 11 11 12 12 13 15 16 15 14 12 11 10 10 10 11 11 11 11 11 10 10 10 10 10 10 9 9 10 11 11 11 11 11 11 11 11 11 11 10 10 9 9 9 9 9 9 9 8 8 7 7 6 6 5 5 6 6 7 8 9 9 8 7 5 5 5 5 6 7 9 10 11 10 9 9 9 9 9 10 10 11 11 11 11 11 11 10 10 10 10 10 9 9 9 8 8 7 6 5 6 6 7 8 8 9 9 10 nan
nan 10 10 10 10 11 11 11 11 11 11 11 10 9 9 9 9 8 8 8 9 10 12 14 16 15 13 11 10 9 9 9 9 9 9 8 8 8 7 7 7 8 9 9 8 7 7 8 8 8 7 7 7 7 7 7 7 7 8 7 6 6 5 4 3 2 2 3 6 8 9 9 9 9 10 9 9 10 10 10 11 11 11 12 13 15 16 16 15 13 11 10 10 10 11 11 11 11 10 10 10 10 10 10 10 10 11 12 12 13 13 12 11 10 9 8 8 7 6 6 6 6 6 7 7 7 7 6 6 6 5 5 5 5 6 7 8 9 10 10 9 7 6 5 4 3 4 6 8 11 12 11 10 9 9 9 9 10 10 11 11 11 11 11 10 10 9 9 9 9 8 8 7 7 6 5 5 6 8 9 9 10 10 10 10 10 nan
nan 9 10 10 10 10 10 10 11 11 11 11 11 11 11 11 10 10 10 10 10 11 13 16 16 14 11 9 9 8 8 8 8 7 6 6 7 7 8 8 8 8 8 7 7 7 8 9 9 8 7 7 6 6 5 6 7 8 8 8 8 8 8 8 7 6 5 6 7 9 9 8 8 9 9 9 9 10 10 10 10 10 11 11 12 13 14 15 15 15 14 14 13 12 11 11 10 10 10 10 10 10 9 9 9 10 11 12 12 13 12 10 8 6 5 4 4 3 3 3 4 4 4 5 5 6 6 5 5 5 5 5 6 6 6 7 8 9 10 10 9 7 6 4 3 2 3 5 8 11 12 11 11 10 10 9 9 10 10 11 11 11 10 10 9 9 9 8 8 7 7 6 6 5 5 5 6 8 9 10 10 10 10 10 10 10 nan
nan 9 10 10 10 10 10 10 11 11 11 12 12 13 13 12 12 11 11 11 12 13 15 17 16 13 11 9 9 8 8 7 7 6 5 5 6 7 8 9 9 9 9 8 8 9 10 10 9 9 8 7 6 5 4 5 7 9 10 10 10 9 9 10 10 10 10 10 10 11 10 8 7 7 8 8 8 9 9 9 9 10 11 11 12 12 13 13 14 15 16 17 17 16 13 12 10 9 9 10 10 9 9 9 10 10 11 11 11 11 9 7 5 3 2 2 2 2 2 3 3 4 4 4 5 5 6 6 6 6 6 7 7 7 7 8 8 9 10 10 9 7 5 3 2 2 3 5 8 10 11 12 11 11 10 10 10 10 10 10 10 10 10 9 9 8 8 8 7 7 7 6 5 4 4 5 7 8 9 9 10 10 10 10 10 10 nan
nan 9 9 9 10 10 10 11 11 11 11 11 12 12 12 12 12 12 12 12 13 15 17 18 16 13 11 10 10 10 9 9 8 7 6 5 6 7 8 9 9 9 9 10 10 11 10 9 8 7 7 7 6 5 5 6 8 9 10 10 11 10 10 11 11 11 10 11 11 11 11 10 8 7 6 5 5 6 8 8 8 9 9 10 12 12 13 13 13 14 14 15 16 17 15 13 12 11 10 10 10 10 10 10 10 10 10 10 10 10 8 6 4 3 3 3 3 3 3 4 5 5 6 6 6 6 7 8 8 9 9 10 10 10 9 9 10 10 10 9 8 7 6 4 3 3 4 6 9 11 12 12 12 11 10 10 10 10 10 9 9 9 9 9 9 9 8 8 8 8 9 7 6 5 6 7 8 8 9 9 9 9 10 10 10 10 nan
nan 9 9 9 9 10 10 11 10 10 10 10 10 10 10 10 10 11 11 12 14 16 18 17 15 13 11 11 11 11 11 12 11 10 8 7 7 8 8 9 9 8 8 9 9 9 7 6 5 5 5 5 5 5 6 7 7 8 8 9 9 10 10 10 10 9 9 8 9 9 10 10 8 6 5 3 3 3 3 5 5 6 7 8 9 10 12 13 13 13 13 12 13 14 15 15 14 13 13 12 11 10 10 11 11 11 10 10 10 9 8 7 6 5 6 6 6 6 6 6 7 7 7 7 7 7 8 10 11 13 13 13 13 12 12 11 11 11 10 9 8 7 6 5 5 5 6 7 9 11 12 12 12 11 10 10 10 10 10 9 9 9 9 9 9 9 8 8 9 9 10 9 8 8 8 9 9 8 8 9 9 10 10 10 11 11 nan
nan 9 9 9 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 11 12 15 15 14 13 12 11 11 12 12 12 12 12 10 9 8 8 8 9 9 9 8 8 7 6 5 4 4 5 5 5 5 5 6 8 8 8 8 7 7 8 9 9 10 10 9 8 6 6 7 8 9 9 8 6 5 3 2 1 1 2 3 4 5 6 7 9 11 12 12 12 11 11 11 12 13 14 14 14 14 13 12 12 12 12 11 11 10 10 9 8 7 6 7 7 8 9 9 9 9 9 9 8 7 7 7 9 12 13 14 14 14 13 12 11 10 10 10 9 8 8 7 6 5 6 7 8 9 10 10 11 11 11 10 10 11 10 10 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 9 8 8 9 9 10 11 11 11 12 12 nan
nan 9 9 10 10 10 10 10 9 9 9 9 9 9 9 8 8 8 9 10 12 13 13 12 11 11 11 11 11 12 12 12 11 10 9 8 7 8 9 10 10 9 9 8 6 5 5 6 7 8 8 8 8 9 9 9 9 8 7 7 7 8 9 11 11 11 9 7 6 7 8 9 10 9 8 7 6 4 3 3 2 3 4 5 6 7 8 9 10 10 10 10 10 10 11 11 12 12 12 13 13 12 12 11 11 11 11 11 11 10 8 7 7 7 7 9 10 10 11 10 10 9 7 7 6 7 9 11 12 12 12 12 11 9 8 8 8 8 8 8 7 6 6 6 8 10 11 11 10 9 10 10 10 10 10 10 10 10 9 9 9 9 10 10 10 9 9 9 9 9 9 9 9 8 7 7 7 8 10 11 11 12 12 13 13 13 nan
nan 9 9 10 10 10 9 9 9 10 10 10 10 10 9 9 9 10 11 12 13 13 13 12 11 10 10 10 10 11 11 11 10 9 8 7 7 8 9 10 10 10 10 9 8 7 8 8 9 9 9 9 9 9 9 9 8 7 5 5 6 7 9 11 11 11 10 9 8 8 9 9 10 10 10 9 8 8 8 7 6 5 6 7 8 8 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 12 12 12 11 9 7 6 6 6 7 8 9 10 10 9 8 7 7 6 7 8 8 9 10 10 9 7 6 6 6 7 7 7 7 7 7 7 8 10 12 13 12 9 9 9 9 9 10 10 9 9 9 9 9 9 10 10 10 10 9 9 9 9 9 9 9 8 6 6 6 8 10 11 12 13 13 14 14 14 14 nan
nan 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 12 12 13 14 14 14 12 10 9 9 9 9 9 10 10 9 8 7 6 5 6 8 9 9 9 8 9 9 9 9 9 9 9 9 9 9 9 9 9 8 6 5 4 5 6 8 9 9 9 9 9 9 9 9 9 9 9 10 11 11 11 10 9 8 7 7 7 8 9 9 9 9 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 10 10 11 11 11 10 9 7 6 6 6 7 7 8 8 9 9 8 8 7 7 8 8 8 7 7 6 5 4 4 5 6 7 6 6 7 9 9 10 10 12 13 13 11 10 9 9 8 9 9 9 9 9 8 8 9 9 10 11 10 10 9 9 8 9 9 9 9 8 7 7 8 10 12 13 14 14 15 15 15 15 15 nan
nan 9 8 8 8 9 10 10 10 10 10 10 9 9 10 11 11 12 12 12 13 12 11 10 9 8 8 8 8 8 9 9 8 8 6 4 2 4 6 7 9 9 9 10 10 10 10 11 11 11 11 10 10 10 10 10 9 9 8 7 7 7 7 7 7 8 8 9 10 10 10 10 9 9 10 10 11 10 9 8 8 7 7 7 7 7 7 8 8 10 11 10 9 8 8 8 9 9 9 9 9 9 9 8 8 9 9 10 9 9 8 8 7 7 7 7 7 8 9 9 10 10 10 9 9 9 9 9 7 6 5 4 4 6 7 8 8 8 9 11 12 13 13 13 14 14 14 12 11 10 9 8 8 8 8 8 8 8 8 9 9 10 10 10 9 9 8 8 8 9 9 9 9 9 10 11 13 13 14 15 15 16 16 16 16 16 nan
nan 9 8 8 9 10 11 11 11 10 10 9 9 9 10 10 11 11 11 10 10 10 10 9 8 8 7 7 7 7 8 8 8 7 5 3 1 2 4 7 9 10 11 11 11 11 11 12 12 12 12 12 12 11 11 11 11 11 11 10 9 8 8 7 7 7 8 8 9 10 12 12 11 11 10 8 8 7 7 7 7 7 7 6 6 6 6 6 7 9 10 10 9 7 6 7 9 10 10 9 8 8 8 8 7 8 8 9 8 8 8 8 8 7 8 8 9 11 11 11 12 13 12 12 12 12 12 12 11 10 9 9 10 10 10 10 10 11 12 13 13 14 15 15 15 15 14 13 13 11 9 8 8 8 8 8 8 8 8 9 10 10 10 9 9 8 8 9 9 9 10 10 10 11 11 12 13 14 14 15 15 16 16 15 15 15 nan
nan 9 8 8 9 11 12 12 11 11 10 9 9 9 9 9 9 9 8 7 8 9 10 10 9 8 7 7 7 7 7 8 7 7 4 2 0 1 4 7 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 10 9 8 8 7 7 7 7 7 8 8 10 12 13 13 12 10 7 6 6 6 6 7 7 7 7 7 7 7 7 7 9 10 10 9 6 6 7 8 10 9 8 7 7 7 7 7 7 7 8 8 8 7 7 7 8 8 9 10 12 12 12 12 12 13 13 13 13 13 14 15 14 14 14 13 13 12 11 11 11 11 11 11 12 12 13 13 13 13 13 12 11 9 8 8 8 8 8 8 9 10 10 10 10 9 9 8 8 9 9 9 10 10 11 11 11 11 12 13 13 14 14 14 14 14 14 14 14 nan
nan 9 9 9 10 11 11 11 10 10 9 8 7 7 7 8 8 7 6 5 6 8 10 10 9 8 8 8 8 8 8 8 8 6 4 1 1 3 6 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 10 10 10 9 8 7 7 7 6 7 7 7 7 7 7 9 11 12 13 14 11 8 6 6 6 7 7 8 8 9 9 9 9 9 9 9 10 10 10 8 7 7 7 7 7 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 9 10 10 10 9 9 10 10 11 11 11 11 12 12 13 13 13 12 12 11 11 10 9 9 8 9 9 10 10 10 11 12 12 11 9 8 7 7 8 8 8 9 9 10 10 10 9 8 8 8 8 9 9 10 10 10 11 11 11 11 11 11 12 12 12 12 11 11 11 11 11 nan
nan 9 9 9 9 10 10 10 9 9 7 5 5 5 5 6 7 7 6 6 8 9 10 10 9 8 8 9 9 9 9 9 9 7 5 3 4 7 8 9 8 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 7 7 7 6 6 7 7 7 7 7 8 9 11 13 15 13 11 8 6 5 6 7 7 7 8 9 10 10 10 10 10 10 10 10 9 8 6 6 6 5 5 5 6 6 6 7 7 7 7 7 7 7 7 7 8 9 10 10 10 9 8 7 8 8 8 8 7 7 8 8 9 9 10 10 10 10 9 8 7 7 7 8 9 9 9 10 10 10 10 9 8 7 7 7 7 8 8 9 10 10 9 8 7 7 8 8 9 9 10 11 11 11 11 11 11 11 11 10 10 10 10 9 9 9 9 9 10 nan
nan 9 9 9 9 9 9 9 8 7 5 3 3 3 5 6 7 8 8 9 10 11 11 11 10 9 9 9 9 10 10 11 10 9 7 6 8 9 9 8 8 8 8 8 8 8 8 7 7 7 8 8 8 8 8 8 8 8 8 7 7 7 6 6 6 7 7 7 7 7 8 9 13 16 16 14 11 6 3 4 5 6 6 7 8 9 9 10 10 10 10 10 10 9 8 7 7 7 7 7 6 7 7 8 8 8 8 8 8 8 8 8 8 9 9 10 11 11 10 9 8 7 7 6 6 6 6 6 6 6 7 8 9 9 8 7 6 6 6 7 8 9 9 9 10 10 10 10 10 9 9 8 8 8 8 8 9 9 9 8 7 7 7 8 9 9 10 11 12 12 12 12 11 11 11 10 10 9 8 7 7 8 8 9 9 10 nan
nan 8 8 8 8 8 8 7 5 4 2 3 4 5 6 7 8 9 9 9 9 10 10 10 10 9 9 9 9 10 11 11 11 11 10 9 10 9 9 8 9 10 10 11 10 10 9 8 8 8 9 9 9 9 9 8 8 7 7 7 6 6 6 6 6 6 6 6 6 6 6 8 11 15 15 15 11 5 1 2 3 5 6 7 7 7 8 9 10 10 10 10 9 9 8 9 9 8 8 8 9 9 9 9 9 10 10 9 9 9 9 9 9 10 10 11 11 12 11 11 10 9 8 8 8 8 8 7 7 7 8 8 9 8 7 6 6 6 7 8 8 8 9 9 10 10 10 11 12 12 12 11 9 8 8 8 9 9 8 7 7 7 8 9 9 10 12 13 13 13 13 12 11 11 11 10 10 9 8 7 7 8 9 10 11 11 nan
nan 7 7 7 8 7 6 4 2 2 3 6 8 8 7 7 8 9 9 8 8 8 9 9 10 9 9 8 9 9 10 11 11 11 10 10 10 9 9 9 10 11 11 11 11 10 10 9 9 10 10 10 10 10 9 9 8 7 7 6 6 6 6 5 5 5 5 6 5 5 5 6 9 11 13 14 10 5 2 2 3 6 7 7 7 7 8 9 9 10 9 8 8 7 7 8 8 8 9 9 9 10 10 10 9 9 9 9 9 9 9 9 9 10 11 12 13 13 12 12 11 11 10 10 10 10 9 8 8 7 7 8 8 7 7 7 7 8 8 8 8 8 8 9 10 10 11 13 15 16 15 13 9 7 7 7 8 8 7 7 7 8 9 9 10 11 13 14 14 14 13 12 11 11 11 10 9 9 8 8 10 11 12 12 13 13 nan
nan 6 7 7 8 7 4 3 2 4 7 9 10 9 7 7 8 9 9 8 8 8 9 10 10 9 8 8 8 8 9 10 10 10 9 9 9 9 9 10 11 11 11 10 10 10 10 10 10 11 11 11 11 11 10 10 9 9 9 8 7 7 6 6 5 5 5 5 5 5 5 5 6 8 10 11 10 8 6 5 6 8 9 8 8 8 8 9 9 9 9 8 6 6 5 5 6 6 7 8 9 9 9 9 8 7 7 7 7 8 8 9 9 10 12 13 13 13 13 13 13 13 13 13 13 13 12 11 9 9 8 9 9 9 9 9 9 9 9 8 8 8 8 9 9 10 13 15 17 19 18 14 9 7 5 6 6 7 7 7 8 8 9 9 10 11 13 14 14 13 13 13 12 11 11 10 9 8 8 10 11 13 13 13 14 15 nan
nan 7 8 8 8 7 5 4 4 6 9 11 11 10 8 7 7 8 9 9 9 9 10 11 11 9 8 7 7 8 8 8 9 9 8 8 8 8 10 11 11 11 10 9 9 9 9 10 10 11 11 12 12 12 11 11 11 11 11 10 9 9 8 7 6 6 5 5 5 5 5 5 5 6 8 10 10 10 10 9 9 9 9 9 8 8 8 8 8 8 8 8 7 6 5 5 5 6 6 7 8 8 8 7 6 6 5 6 6 7 7 8 10 11 12 13 13 13 13 13 14 15 15 15 16 16 16 15 14 12 12 13 14 14 14 13 12 11 10 9 9 9 9 9 9 10 12 15 17 19 17 13 8 5 3 4 5 6 7 7 8 8 8 8 9 10 12 12 12 12 12 13 12 12 10 9 8 8 9 10 11 11 12 12 13 15 nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan 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
45 40 35 32 31 29 23 20 18 15 11 9 8 8 7 6 4 2 1 2 2 2 2 3 2 2 2 2 2 3 3 3 3 3 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 2 6 4 1 1 6 10 9 5 5 5 14 32 68 93 101 95 77 57 43 42 41 47 51 51 45 37 28 24 22 20 18 17 20 25 24 23 21 17 13 11 10 10 13 15 17 20 19 19 20 21 22 20 18 17 17 17 17 18 20 19 19 20 23 31 39 41 41 41 40 30 22 18 14 12 15 24 25 16 9 7 6 6 5 4 9 15 18 16 13 12 13 13 16 23 27
57 51 44 38 36 34 27 25 24 17 11 9 9 8 8 5 4 2 2 2 2 2 2 2 2 1 2 2 2 3 3 3 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 0 0 0 0 0 0 0 0 0 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 5 1 1 4 7 8 9 8 4 6 10 30 48 63 75 77 70 69 68 70 75 77 74 65 55 40 30 26 23 22 21 23 28 30 29 27 21 13 8 8 9 10 11 15 18 18 19 21 23 28 25 22 19 18 20 24 28 26 23 23 22 22 28 35 39 43 40 32 23 18 16 15 16 23 35 32 23 13 8 6 6 6 6 9 14 18 16 12 12 13 12 17 23 27
61 56 52 49 44 40 34 32 28 21 15 10 8 8 6 3 3 3 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 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 1 2 2 2 6 6 3 1 3 5 7 10 12 6 5 6 11 20 32 48 59 64 71 79 88 94 98 95 85 74 54 38 30 28 28 28 27 32 35 36 35 30 21 12 9 11 10 10 13 15 17 19 22 21 22 23 23 21 20 21 23 24 25 27 26 22 21 28 38 46 39 29 21 17 14 12 12 21 33 42 40 30 19 10 8 8 7 7 10 14 16 13 10 10 10 11 17 22 26
62 61 58 52 46 42 38 36 32 25 17 12 8 8 10 6 5 4 3 2 1 1 1 2 1 2 2 3 2 2 3 3 2 2 2 3 3 2 1 1 0 0 0 0 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 1 2 4 4 6 9 7 5 3 1 3 9 18 15 10 6 6 9 15 24 37 50 64 78 92 104 113 113 103 88 69 53 44 41 41 36 35 40 42 41 39 34 27 20 12 11 10 10 12 14 17 19 23 22 21 21 22 22 21 20 22 26 29 28 24 21 22 28 31 29 25 20 18 16 12 10 17 29 39 46 46 37 29 18 13 10 9 7 8 13 15 13 9 7 7 11 16 21 25
61 61 58 53 47 40 39 36 32 25 18 13 11 10 11 9 7 6 4 1 0 1 0 1 1 2 2 2 1 2 3 2 1 1 2 2 2 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 8 9 10 10 9 6 3 1 9 20 22 16 9 5 9 13 17 27 42 59 75 90 105 121 126 121 108 92 79 69 65 61 54 51 54 55 52 47 41 34 26 16 12 11 12 14 15 18 18 21 21 20 20 22 22 22 21 23 26 28 26 22 21 23 25 24 21 19 18 17 14 10 12 22 32 40 45 48 44 39 29 20 14 10 9 11 14 14 12 8 5 5 7 12 19 22
61 61 61 60 51 39 38 35 30 25 21 16 12 11 13 11 9 7 6 3 1 1 0 0 0 1 1 1 1 1 2 1 1 1 1 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 6 11 12 10 10 11 11 12 19 24 26 25 18 9 14 16 17 23 32 46 64 84 104 124 136 141 134 121 107 94 88 83 77 72 69 69 68 63 56 44 33 23 16 13 13 15 15 18 20 22 21 20 21 21 21 21 21 22 23 22 21 21 20 22 21 19 18 19 20 18 13 13 18 26 33 38 42 47 48 44 36 28 19 12 10 13 15 12 10 7 5 5 6 12 17 19
63 63 62 60 55 38 37 34 31 28 24 20 18 15 12 11 9 9 8 4 3 2 1 0 0 0 0 0 1 0 1 1 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 0 0 0 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 10 13 11 11 16 20 23 24 26 30 33 30 18 18 19 19 22 28 38 55 74 104 126 138 148 151 140 125 112 110 105 99 89 80 76 78 77 71 57 43 30 18 12 12 14 16 19 21 24 24 23 23 21 21 21 21 22 22 23 23 22 22 23 22 22 25 27 27 22 18 21 30 37 39 39 40 45 49 46 41 34 25 15 9 14 14 11 8 6 5 5 8 13 16 17
63 63 58 49 48 38 36 34 32 29 27 25 23 20 14 12 10 7 5 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 11 12 11 15 21 26 28 27 30 35 36 29 20 20 19 18 21 29 41 62 96 126 153 174 183 174 153 143 144 142 135 121 101 86 86 84 80 70 55 37 23 16 14 16 18 20 23 26 27 26 25 23 22 21 21 21 21 22 21 23 24 26 29 33 35 34 32 26 22 25 38 51 47 42 42 46 49 46 43 39 28 13 9 12 12 9 6 6 6 6 10 14 17 17
59 61 58 51 46 41 37 35 34 31 28 26 25 20 17 15 13 10 7 6 8 4 2 2 2 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 1 1 2 8 13 15 12 13 19 25 28 28 32 38 36 26 19 15 11 14 23 39 53 76 105 142 192 251 281 260 245 230 213 196 174 133 106 98 93 89 82 67 46 33 24 20 20 21 22 25 29 31 29 27 26 24 22 21 21 22 23 23 24 26 28 32 43 44 42 38 32 28 31 42 48 45 42 43 46 50 50 50 48 30 15 11 12 10 6 5 5 5 7 11 14 16 17
52 56 60 56 53 45 39 35 33 31 30 28 27 22 17 17 16 14 10 9 10 5 5 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 13 10 7 10 18 24 28 28 34 37 34 26 16 6 5 15 27 37 51 77 125 213 350 416 425 405 373 339 306 280 214 161 126 105 101 99 87 59 41 33 28 25 25 26 28 31 33 29 28 26 24 23 22 24 24 24 24 26 27 29 31 39 42 45 43 38 35 34 35 40 41 43 45 48 50 53 65 55 32 17 13 12 10 6 6 5 5 7 10 13 15 16
45 47 53 52 47 40 37 34 31 30 30 29 27 24 20 18 16 13 11 13 14 12 9 7 5 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 0 0 0 0 0 0 0 0 2 5 7 8 6 6 8 15 27 24 28 33 36 36 27 6 3 9 16 24 35 56 91 158 342 431 475 500 509 508 495 479 402 290 192 133 119 116 104 76 53 40 33 30 30 31 32 32 33 28 24 23 23 23 24 25 25 25 26 27 28 30 29 31 36 43 47 45 43 36 35 44 44 43 47 50 50 46 61 49 29 14 10 13 10 7 6 6 6 6 11 12 14 15
36 39 46 48 40 36 36 34 31 27 26 25 26 25 20 17 16 15 13 20 21 20 17 12 8 4 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 1 1 1 2 3 3 2 4 12 23 23 22 24 31 39 41 21 13 10 10 14 23 36 53 86 162 260 379 494 571 620 667 726 719 566 368 238 180 140 114 92 72 53 40 35 34 36 37 37 31 23 19 19 19 20 23 24 26 26 27 29 30 29 29 30 31 37 46 49 46 39 41 45 45 44 46 50 48 44 46 42 31 16 14 13 10 8 7 9 9 11 13 12 14 15
28 32 41 53 47 39 36 34 31 27 22 20 23 27 26 27 28 22 18 22 25 25 22 17 11 6 5 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 0 0 0 0 0 0 1 1 3 6 13 18 19 19 21 31 39 39 32 24 18 13 14 20 30 44 67 114 225 408 596 697 743 825 953 911 672 490 352 225 158 121 101 84 64 49 45 42 43 40 31 20 14 15 16 18 21 24 26 27 28 30 30 30 29 29 29 32 42 48 49 45 48 51 47 43 42 45 43 43 46 46 39 21 14 10 9 8 8 10 11 12 12 13 14 15
23 25 33 40 39 36 33 30 28 24 21 19 17 19 20 24 29 27 23 25 27 25 24 23 19 15 11 6 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 0 0 0 0 0 0 1 2 3 6 12 16 15 19 24 30 36 42 44 37 25 20 18 18 21 25 44 112 266 482 643 740 810 909 985 915 807 655 432 292 218 172 134 95 72 60 51 47 41 29 13 8 9 13 17 21 24 25 27 27 28 29 30 30 30 30 32 36 40 37 38 46 50 46 43 41 43 43 43 45 48 44 28 19 14 11 10 9 11 14 15 16 16 15 15
17 18 25 29 30 29 27 24 23 22 21 20 15 17 21 25 27 29 28 29 28 26 27 27 25 23 17 10 5 1 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 0 0 0 0 0 0 0 0 0 0 0 0 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 6 11 12 17 22 27 29 34 42 46 41 37 28 21 17 15 19 42 105 207 379 596 801 948 1049 1088 1143 1025 770 536 371 259 193 141 106 81 64 54 46 33 9 5 6 9 16 23 28 29 28 26 25 27 29 29 30 31 31 31 32 32 35 42 46 40 39 39 39 39 40 44 50 45 31 19 14 14 16 14 14 16 18 18 17 15 14
14 15 21 24 24 23 21 19 19 19 15 17 14 15 17 20 23 26 30 30 29 27 25 23 21 19 14 11 7 3 1 0 0 0 0 0 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 2 6 8 13 17 23 27 27 32 38 42 43 39 35 29 18 13 17 31 60 168 371 600 777 924 1113 1321 1279 1081 841 603 403 298 225 161 114 85 67 55 37 15 7 4 6 12 23 28 28 26 25 24 24 25 26 26 26 26 26 27 30 35 40 38 33 32 32 32 32 32 37 43 40 29 19 16 20 21 18 17 19 19 18 16 14 13
12 16 22 25 26 23 20 18 14 13 11 13 13 13 14 17 19 22 28 27 24 20 18 16 15 14 10 11 9 5 4 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 0 0 0 0 0 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 5 6 11 19 22 26 29 34 37 39 39 38 35 31 18 13 21 61 148 292 524 748 946 1147 1280 1292 1149 913 665 485 347 248 180 133 94 67 50 34 16 5 4 8 13 18 25 27 25 22 21 22 23 23 23 23 22 23 24 31 36 33 28 26 27 27 25 26 29 32 30 24 17 14 18 20 19 19 21 20 18 15 14 13
10 13 19 23 24 22 20 19 17 14 13 13 12 13 15 17 17 18 22 21 19 17 15 14 14 16 13 12 11 10 9 9 6 2 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 0 0 0 0 0 0 0 0 0 0 1 1 1 3 9 15 21 23 28 31 33 35 38 41 42 28 16 12 17 39 86 267 456 637 886 1167 1357 1344 1159 945 728 551 411 300 219 141 90 62 40 19 6 4 5 7 10 17 21 20 17 18 20 21 21 21 21 21 22 21 26 30 31 27 23 24 24 22 25 27 27 24 21 18 21 24 22 20 20 23 23 19 16 14 13
8 9 12 17 18 17 17 17 17 17 16 14 13 14 14 15 16 16 16 16 17 17 16 15 15 17 17 16 15 15 15 12 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 0 0 0 0 0 0 0 0 0 0 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 14 17 21 25 27 32 36 36 41 37 28 18 8 10 31 97 217 393 620 890 1101 1120 1126 1142 1063 889 688 505 355 227 128 73 45 22 9 5 4 5 7 9 11 12 14 15 18 20 21 21 22 22 21 21 24 28 29 26 22 23 24 28 34 34 28 22 18 19 25 27 24 20 19 20 20 18 16 15 14
5 8 9 12 13 13 11 10 9 10 10 11 13 14 14 13 13 12 12 12 13 14 14 13 14 16 19 20 19 18 18 18 16 10 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 8 11 13 14 15 18 24 28 32 35 34 28 12 11 17 30 58 118 248 500 700 839 999 1183 1276 1219 1055 819 561 333 175 92 51 26 12 6 4 4 4 5 7 9 11 13 16 18 19 18 20 21 20 20 20 21 24 23 23 25 27 33 39 38 29 22 21 22 24 26 24 19 18 19 19 18 16 14 15
4 6 6 8 10 11 10 8 7 11 8 9 11 12 12 11 10 8 8 8 8 8 10 10 10 11 14 15 16 16 17 19 18 15 11 6 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 4 7 11 16 20 23 26 27 20 19 16 13 15 28 73 211 363 548 733 934 1166 1325 1317 1158 854 528 284 139 66 35 19 10 5 4 4 4 6 7 8 9 11 12 14 14 16 17 17 18 19 20 22 22 24 28 31 33 34 31 27 23 21 22 26 29 25 19 18 19 19 17 17 15 17
6 4 2 2 5 9 11 10 11 15 13 11 12 13 13 13 12 8 6 6 5 5 6 7 6 7 8 10 11 11 13 15 16 17 18 14 7 4 2 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 6 11 12 14 16 21 29 30 22 13 12 24 69 141 251 380 538 794 998 1233 1343 1183 859 537 257 113 61 34 18 10 5 5 4 4 4 5 6 8 9 11 11 12 13 15 16 17 18 20 21 24 29 32 32 31 30 27 24 23 26 31 32 25 20 18 18 18 16 18 20 21
7 4 1 1 3 7 12 12 14 18 18 16 14 13 12 12 12 11 10 9 8 9 10 9 6 5 5 6 7 9 11 14 18 20 22 22 20 18 11 6 3 2 3 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 2 3 6 15 23 26 24 18 12 20 33 59 108 177 293 436 610 915 1146 1219 1124 857 455 245 132 67 31 17 8 5 4 4 4 4 5 6 7 8 9 11 13 15 17 17 18 21 23 24 28 30 31 30 30 28 24 22 24 26 29 26 21 17 18 20 20 21 22 24
5 3 1 2 5 8 12 12 14 18 19 16 12 10 8 8 9 12 13 13 13 13 15 13 7 4 3 4 7 11 16 20 21 22 23 25 26 27 25 20 9 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 17 23 28 23 17 27 35 43 59 79 122 215 361 523 718 971 1237 1267 906 576 331 155 58 31 19 12 8 6 5 4 4 4 5 6 9 11 12 14 14 15 18 22 24 24 25 29 30 30 28 26 24 25 28 31 31 31 27 20 20 22 23 23 23 23
5 4 4 3 6 13 15 13 14 16 15 14 12 12 12 11 11 12 13 13 12 12 13 12 8 7 7 8 9 13 20 28 27 26 27 29 32 34 41 38 21 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 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 20 22 23 21 25 33 39 46 39 70 148 232 317 438 649 1054 1248 1188 957 665 361 148 81 45 27 19 13 7 5 4 4 4 5 7 8 10 11 10 10 13 18 21 22 21 25 27 27 26 25 25 27 27 28 32 38 37 27 24 24 24 24 23 23
8 4 4 4 6 13 18 18 18 19 20 20 19 17 15 15 14 13 12 11 9 12 14 12 10 11 10 9 10 13 22 28 30 30 32 36 40 45 50 47 34 18 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 14 16 21 24 25 28 31 41 33 43 81 139 210 290 446 718 925 1056 1093 998 691 419 240 117 51 32 24 16 11 8 5 4 5 6 8 8 9 9 9 11 14 17 18 19 21 22 23 24 24 23 23 23 26 31 42 41 33 27 25 24 24 23 24
12 5 1 1 3 9 16 18 22 25 25 22 18 16 12 11 12 11 9 7 6 8 12 14 14 13 13 12 12 15 25 32 35 35 36 41 46 47 48 48 41 27 11 2 1 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 0 0 2 5 8 9 12 18 23 25 20 27 30 32 45 76 130 209 337 475 592 738 938 1097 955 761 528 293 122 71 46 36 26 16 9 6 5 6 7 7 9 10 10 10 12 14 16 17 18 18 18 21 21 20 20 22 27 31 37 37 34 30 28 27 25 25 27
14 8 4 2 2 4 10 16 26 32 32 27 21 16 10 6 9 10 8 5 4 5 10 15 16 14 13 17 24 26 31 37 41 39 36 42 45 44 46 46 42 33 20 18 13 10 7 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 0 0 0 0 0 0 3 3 3 5 10 17 21 17 18 21 25 29 37 73 152 257 334 363 416 603 835 946 951 823 585 349 201 114 70 48 33 20 11 8 8 7 8 8 10 11 10 12 14 16 16 16 17 17 19 21 21 21 22 27 31 33 32 30 29 30 30 28 29 30
13 12 9 6 3 2 7 20 29 32 30 26 24 21 14 8 8 8 8 5 2 3 8 13 14 14 15 18 21 26 33 39 41 39 35 36 38 40 40 40 39 37 29 27 28 26 20 11 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 0 0 0 0 0 0 0 0 0 1 3 8 13 12 8 6 14 26 32 54 105 183 245 239 272 397 586 789 938 963 839 651 454 279 166 104 67 41 24 17 12 9 8 9 10 11 11 13 15 16 16 17 17 17 19 22 22 22 24 27 30 32 31 29 30 33 33 33 33 33
18 14 10 6 4 1 8 19 26 28 26 25 29 28 19 12 7 5 4 4 3 5 8 12 14 15 17 20 23 28 35 41 41 36 30 29 32 35 35 31 28 31 32 31 32 33 34 24 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 0 0 0 0 0 0 0 0 0 1 3 6 7 5 1 6 18 28 44 70 114 176 214 276 367 506 686 851 956 970 881 721 543 386 255 141 75 47 37 28 18 12 11 12 11 11 12 15 17 16 17 18 19 21 23 24 23 24 26 29 30 29 28 30 36 38 38 37 36
20 16 10 8 11 11 10 16 23 26 28 31 34 27 16 10 6 4 4 6 9 13 14 17 19 18 18 19 25 29 34 42 50 50 43 35 32 32 31 30 27 28 31 34 36 37 38 32 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 8 4 8 14 24 37 54 78 107 164 262 354 475 633 769 849 895 919 879 785 650 474 301 176 111 81 58 41 20 15 13 12 12 14 17 17 17 18 20 22 24 24 25 24 24 26 28 28 27 29 33 39 43 42 41 38
19 22 22 18 17 16 15 18 22 24 24 25 25 21 16 12 11 11 10 12 16 21 24 26 25 22 21 28 27 23 27 37 49 56 54 43 33 30 33 36 38 35 30 29 32 34 30 25 10 2 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 2 5 10 15 16 21 36 55 72 84 115 205 319 443 602 712 740 774 834 884 896 864 724 563 405 271 179 117 87 54 35 23 17 16 16 16 16 16 17 21 26 27 26 26 24 23 25 28 28 27 28 33 40 44 46 47 44
20 21 22 22 19 17 18 23 25 23 20 22 24 27 24 22 21 20 17 18 23 27 29 29 27 25 26 30 20 18 25 33 40 47 47 39 33 32 37 42 45 41 33 25 22 18 12 10 5 1 0 0 0 0 0 0 0 0 0 0 0 0 2 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 1 1 0 0 1 3 10 17 21 20 19 30 47 67 80 100 162 278 420 580 666 688 696 726 786 884 964 927 826 680 515 371 254 189 130 83 52 34 24 21 19 19 21 22 26 29 30 30 28 25 24 25 29 32 32 34 38 42 45 50 53 52
14 19 23 23 23 24 24 27 28 26 25 25 29 32 32 30 29 29 25 24 26 29 32 32 30 27 33 27 22 23 29 34 39 42 40 36 34 35 40 46 51 46 38 29 18 7 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 2 5 10 14 17 17 15 15 26 46 64 88 139 228 352 510 617 673 692 692 701 800 922 1007 1029 962 801 633 485 360 246 150 95 75 57 45 35 30 31 29 30 31 32 32 30 28 29 32 36 38 39 39 40 44 47 54 58 58
6 10 15 20 24 30 27 27 29 32 35 38 39 39 40 41 41 41 35 27 26 29 32 33 32 30 32 29 27 29 34 39 45 46 42 36 34 35 40 46 56 54 45 36 27 16 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 10 13 17 18 13 15 30 57 98 151 198 286 418 550 662 733 713 675 708 796 920 1056 1160 1063 908 743 576 408 249 158 125 105 86 67 52 45 36 33 34 35 33 31 31 34 38 41 42 42 41 41 46 52 58 63 63
9 10 12 14 19 22 23 24 26 31 37 43 43 44 47 50 51 50 43 32 30 31 34 35 31 29 33 34 35 37 41 45 51 51 46 38 35 39 43 47 57 57 51 47 43 32 4 1 0 0 0 0 0 0 0 0 0 0 0 2 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 0 0 0 0 0 0 0 0 0 0 1 3 6 11 14 18 16 16 25 43 73 127 176 248 350 480 626 774 745 696 663 665 727 884 1087 1163 1143 1014 805 610 417 294 216 169 136 108 87 74 63 56 48 42 39 36 36 39 42 45 45 46 45 45 48 54 61 67 67
14 11 12 13 15 13 13 15 17 19 22 33 39 42 45 50 53 54 50 40 37 36 36 38 37 42 47 46 47 49 50 54 58 59 55 47 43 48 50 52 58 56 50 47 45 40 16 6 1 0 0 0 0 0 0 0 0 0 1 3 6 3 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 5 6 11 12 13 17 23 30 73 129 202 292 389 495 642 703 711 675 600 542 624 822 1041 1210 1227 1042 836 622 453 334 253 199 162 139 121 105 88 74 64 54 48 45 45 47 50 50 51 50 49 51 55 59 66 65
12 10 11 13 13 10 10 13 15 14 18 29 37 39 41 44 48 48 47 45 40 38 39 42 48 55 61 64 66 68 69 68 66 67 63 57 54 56 55 53 48 40 35 34 35 36 25 14 5 0 0 0 0 0 0 0 0 0 0 1 2 2 1 0 0 1 4 2 1 0 0 1 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 1 1 3 4 4 3 9 13 33 73 141 233 293 352 457 577 674 695 593 447 383 453 695 1027 1252 1221 1040 816 615 465 354 276 231 201 174 150 134 118 95 71 56 47 46 50 54 56 58 60 60 57 54 55 59 61
4 3 5 6 7 9 13 18 21 21 25 34 39 37 33 34 40 41 46 43 40 39 37 37 45 55 65 69 70 75 79 76 73 74 74 71 64 55 50 44 34 26 23 27 32 37 34 25 12 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 2 2 2 1 1 1 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 1 4 14 37 85 176 230 275 335 440 575 649 575 416 241 128 248 623 969 1166 1173 1026 820 647 493 378 312 260 218 191 174 151 117 90 71 60 56 55 60 65 69 69 66 60 53 54 58 63
2 2 1 2 4 6 9 16 22 23 26 33 36 34 30 31 38 36 40 39 36 34 34 35 45 55 63 66 68 72 79 78 80 81 79 68 49 35 38 39 34 25 23 30 34 35 34 29 17 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 18 62 140 199 235 263 327 463 549 534 421 243 79 51 241 541 899 1119 1126 999 809 645 513 421 351 298 263 219 180 144 116 95 80 71 68 71 75 74 71 64 60 59 62 66 70
2 3 3 4 5 5 6 10 20 25 28 31 35 35 31 28 34 31 36 42 43 41 43 39 47 55 61 67 71 74 78 76 77 72 60 46 36 31 37 46 45 38 34 32 28 25 25 23 15 7 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 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 0 0 0 1 7 48 107 166 202 215 261 361 455 487 425 285 132 36 65 208 528 898 1129 1175 1020 846 697 575 472 380 321 254 202 165 138 112 88 78 79 81 80 73 70 66 65 66 69 71 71
3 4 5 5 5 6 6 8 14 20 27 31 36 38 34 30 34 39 48 56 57 50 45 39 44 50 57 65 73 75 77 67 56 44 34 29 43 34 38 45 46 39 30 23 18 13 11 10 8 7 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 4 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 3 21 54 96 139 167 217 296 386 437 413 322 194 71 22 64 240 570 972 1228 1204 1075 916 758 615 464 350 263 207 173 148 116 97 90 88 89 87 82 76 72 69 67 69 69 68
1 1 1 3 4 4 4 5 7 9 15 20 27 32 33 34 37 40 40 35 31 31 32 33 37 42 48 52 57 63 63 50 35 23 16 15 26 28 29 27 23 16 12 11 9 7 5 3 4 7 6 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 2 2 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 0 0 0 0 0 1 3 10 24 44 73 114 182 276 373 429 417 352 248 130 61 53 96 239 644 995 1187 1227 1149 987 767 551 379 270 214 185 161 137 116 101 96 97 101 101 97 89 77 71 72 73 72
0 0 0 0 1 1 1 2 2 2 4 7 10 14 15 16 17 19 18 14 11 13 16 19 20 21 21 21 25 30 29 21 14 10 6 5 5 6 7 7 5 3 4 3 3 3 3 2 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 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 1 2 3 5 10 17 28 44 77 172 312 432 464 411 359 276 185 117 84 76 117 369 714 1034 1245 1274 1121 898 663 457 314 239 200 166 137 116 109 110 118 126 124 113 98 85 85 87 84 79
0 0 0 0 0 0 0 0 0 0 1 2 2 3 3 2 2 4 4 2 1 1 3 4 5 4 3 3 5 6 5 3 2 2 1 1 0 0 1 1 0 2 3 2 2 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 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 0 1 2 5 8 12 18 27 41 88 215 392 512 485 389 306 231 165 118 99 93 116 241 462 731 1012 1133 1112 990 794 561 380 282 215 177 159 152 151 157 159 155 144 123 104 98 101 98 89 81
0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1 1 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 1 2 3 2 2 3 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 1 1 1 0 0 0 0 3 9 16 23 31 48 117 262 456 523 451 337 230 148 101 74 74 86 118 186 285 404 687 958 1152 1199 1029 708 486 325 232 194 182 189 198 198 187 166 142 120 106 110 110 104 95 91
1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 2 4 6 6 6 6 5 4 3 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 1 2 3 3 4 2 2 3 6 12 20 29 39 64 139 295 494 498 393 259 149 84 56 38 43 63 96 138 194 295 495 782 1099 1318 1220 915 634 407 266 232 221 223 225 222 206 180 155 135 121 116 112 108 107 105
1 1 1 1 1 1 1 1 2 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 4 6 7 8 10 10 9 8 7 5 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 1 2 3 4 5 5 6 9 14 19 24 30 43 83 188 363 482 444 321 189 93 50 31 23 27 43 74 114 182 248 341 498 754 992 1055 976 783 532 343 277 255 251 243 228 206 184 164 146 131 120 115 117 114 106
1 1 2 2 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 2 3 1 1 2 3 3 2 2 3 4 3 2 1 1 1 1 1 0 0 0 0 0 1 4 7 9 11 14 15 14 13 11 8 6 4 3 2 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 0 0 0 0 0 0 0 0 0 0 1 1 1 3 4 5 6 10 15 21 25 26 34 60 137 284 416 453 394 271 136 73 42 24 19 27 47 85 140 196 244 281 324 441 603 756 880 861 651 456 332 275 251 232 213 194 178 161 145 136 129 126 126 117 106
2 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 3 6 8 8 9 11 11 10 9 6 5 5 3 3 2 2 2 3 4 6 9 12 14 17 17 17 16 15 13 11 9 8 6 3 0 0 0 0 0 2 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 1 3 5 6 7 10 15 22 27 29 31 49 111 265 389 452 444 371 242 120 67 40 26 25 45 80 128 181 227 263 298 327 369 448 567 727 835 723 563 408 312 278 251 226 208 195 181 165 157 150 145 136 125 120
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2 2 2 2 2 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 5 7 10 13 14 15 15 16 17 18 17 17 16 15 16 16 17 19 22 23 22 23 23 21 20 19 17 17 18 16 14 10 8 5 1 1 1 2 3 4 3 4 4 3 1 0 0 0 1 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 7 11 15 18 21 26 30 32 33 46 118 227 310 361 385 375 299 203 134 94 82 94 118 174 252 332 379 370 329 301 288 296 326 372 435 486 492 455 410 393 361 323 308 294 273 253 237 207 182 162 149 144 147
3 2 2 2 2 2 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 2 4 5 5 5 5 6 9 12 13 14 16 17 18 18 18 19 20 20 20 21 23 24 26 26 25 25 25 24 25 25 23 21 19 16 13 10 6 4 4 2 2 2 2 3 3 3 2 2 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 3 5 8 12 16 20 22 26 32 39 47 72 133 188 225 250 274 274 228 177 136 119 134 168 217 277 333 369 363 328 276 236 211 202 207 224 248 289 304 295 280 274 276 260 244 230 213 193 174 152 131 115 107 113 121
3 3 3 3 2 2 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 6 7 8 9 8 8 8 10 13 17 19 19 18 18 18 18 19 21 21 21 24 27 28 29 28 26 25 26 27 29 29 28 24 20 16 14 11 8 8 6 3 1 2 1 2 3 2 2 3 2 2 2 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 2 2 3 4 6 8 11 15 18 24 33 45 55 64 92 133 166 183 191 205 197 175 155 149 164 206 243 269 286 290 268 229 188 158 135 118 107 107 117 134 155 177 191 199 203 188 170 157 144 138 120 102 88 76 67 66 72 80
2 2 3 3 3 3 2 1 1 1 0 0 0 0 1 1 1 2 1 0 0 1 1 2 2 2 2 2 2 1 1 1 2 2 2 2 2 1 1 2 2 2 2 2 1 1 1 1 1 1 1 1 2 3 4 5 7 9 11 12 13 14 15 17 18 18 18 18 17 18 17 16 17 20 22 22 24 28 30 30 28 28 26 27 28 29 30 30 27 21 16 13 11 9 7 4 2 2 2 1 0 1 2 3 4 3 3 3 2 1 1 1 0 0 0 0 1 1 2 2 2 2 3 2 2 2 2 2 3 4 5 5 6 7 8 11 14 24 38 55 70 74 78 91 118 147 161 170 175 165 157 165 194 239 263 257 232 201 168 133 105 81 66 57 50 46 47 59 76 94 108 120 129 127 118 103 83 75 69 59 51 47 43 38 37 41 48
3 3 3 3 3 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 3 3 4 5 7 8 11 13 14 16 19 22 23 23 22 21 19 19 17 16 17 21 25 26 27 29 31 31 30 29 28 28 29 29 28 27 25 22 18 15 12 10 8 5 3 2 1 0 0 1 3 3 3 3 3 3 3 2 1 1 1 2 1 1 2 2 3 4 3 4 5 5 4 3 3 3 4 6 7 8 8 10 14 21 30 47 67 83 89 87 94 107 120 136 150 169 177 177 186 215 247 253 227 187 150 117 85 63 49 38 31 25 24 24 26 31 40 48 54 63 68 69 66 52 39 35 30 24 21 20 20 18 18 20 24
3 3 3 3 4 4 2 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 2 2 2 2 2 3 4 4 4 3 3 3 2 2 2 2 2 1 1 2 1 2 2 2 2 2 3 3 5 6 7 9 12 15 15 18 22 24 25 25 22 18 15 14 14 18 22 26 29 32 34 35 34 32 30 29 29 31 32 28 23 21 20 18 15 11 9 7 5 2 0 0 1 1 1 2 2 3 3 3 3 3 3 3 2 3 3 3 3 3 4 5 5 4 5 6 6 5 4 4 4 5 8 11 14 16 23 33 47 61 78 93 98 98 109 123 135 147 159 175 189 193 199 221 224 191 151 116 91 77 59 40 32 28 23 20 18 18 19 19 21 24 28 35 41 45 44 38 29 23 20 16 12 10 10 10 10 10 9 11
3 3 3 3 3 3 3 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 1 1 2 3 3 3 3 3 3 3 4 4 4 4 3 4 4 3 2 3 3 2 2 2 2 3 3 2 2 2 3 3 3 4 5 6 8 12 16 19 21 22 22 21 18 14 10 8 7 7 12 18 22 26 28 31 32 34 32 31 30 29 29 27 24 20 18 16 15 11 8 6 5 4 2 0 0 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 4 5 5 5 5 6 5 6 6 6 5 5 7 9 12 15 18 21 28 45 59 69 79 85 88 83 80 85 94 105 115 128 142 145 138 124 106 88 73 61 51 42 35 29 23 19 16 16 15 15 16 17 17 18 21 25 29 34 38 38 32 25 20 15 12 10 8 7 6 4 4 3 5
2 2 2 2 2 3 3 2 2 2 1 1 2 2 2 3 3 2 2 2 1 1 1 1 1 2 3 4 4 4 4 4 5 6 6 5 4 4 4 4 4 4 5 3 2 3 5 7 6 5 6 6 5 5 4 3 4 5 7 9 12 15 17 17 15 12 7 3 2 2 2 2 5 10 13 15 18 22 25 26 26 26 25 23 19 17 14 12 11 9 8 7 5 4 3 3 2 0 1 1 1 1 0 1 1 1 1 1 2 2 3 3 3 3 4 5 6 6 6 6 7 6 5 6 7 10 15 21 23 22 20 17 24 41 56 65 63 58 52 45 40 37 34 33 42 44 48 53 53 46 36 27 26 26 26 23 20 19 17 15 13 13 13 13 14 15 17 19 20 22 24 26 32 31 26 22 17 13 11 10 8 6 4 2 1 0 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 1 1 1 1 1 2 2 3 3 3 4 5 5 6 6 7 6 6 6 5 5 6 6 6 4 3 4 5 7 6 7 7 7 7 6 5 4 4 4 4 4 5 6 8 9 9 6 3 1 1 1 0 0 2 3 4 4 5 6 9 12 13 13 12 11 8 6 5 3 1 2 2 2 1 1 2 3 2 1 1 1 0 0 0 1 1 1 0 0 1 2 3 3 3 4 5 5 6 6 7 7 7 6 6 9 14 21 25 28 25 18 10 6 12 27 38 40 35 27 21 17 16 15 14 13 16 19 21 22 23 23 22 21 20 18 17 16 15 14 13 12 11 11 11 12 12 12 13 14 14 15 15 16 19 19 19 18 15 12 10 9 9 7 6 4 3 2 1
2 1 1 1 2 2 3 3 3 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 3 3 4 5 5 6 6 7 7 7 6 5 6 8 8 8 7 6 4 3 2 4 6 7 8 8 6 4 3 3 3 2 1 1 2 4 5 4 3 1 1 1 0 0 0 1 1 1 1 1 2 2 3 4 4 5 4 3 2 1 1 0 0 1 1 1 2 3 2 1 1 1 1 0 1 1 1 1 0 0 0 1 3 3 3 4 5 6 6 7 8 8 8 7 7 8 12 19 27 27 20 11 4 0 1 5 10 13 12 18 16 14 12 11 12 13 14 16 17 19 20 21 21 20 18 16 14 13 12 11 11 11 10 10 10 9 9 10 10 9 9 8 8 9 10 11 13 15 15 14 12 11 11 11 9 8 7 6 6 6
2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4 5 6 6 5 5 6 8 9 9 8 6 4 2 4 6 7 7 6 5 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 2 3 3 3 3 2 2 1 0 0 0 0 1 2 2 1 1 1 1 0 0 1 1 1 1 0 0 0 1 2 3 3 5 6 8 9 11 13 11 10 9 9 9 12 18 17 10 4 1 0 0 0 1 3 6 8 14 15 13 11 12 12 13 14 15 17 19 20 20 20 20 20 18 15 13 12 11 10 9 8 8 7 6 5 5 5 5 4 4 5 6 7 8 9 11 11 12 12 12 13 12 10 9 9 8 8 9
3 3 2 1 1 2 2 2 2 2 2 2 2 2 2 2 3 2 1 1 1 2 1 1 2 2 2 2 3 3 3 3 3 4 4 5 6 5 5 5 7 9 9 8 6 5 4 6 7 7 6 3 2 1 1 1 0 0 1 1 1 1 1 1 2 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3 3 2 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 2 3 3 5 7 9 10 13 15 14 12 10 8 9 13 14 9 3 1 0 0 0 0 1 4 8 10 13 15 14 13 13 13 13 14 15 17 19 20 21 21 21 20 19 17 14 12 10 8 6 5 4 4 3 3 3 3 3 2 2 3 3 4 5 6 7 8 9 10 10 11 10 9 8 9 10 11 12
2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 1 2 2 3 3 3 3 3 3 3 4 5 5 6 6 6 5 6 7 9 9 8 7 6 5 5 6 6 5 2 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 2 3 3 3 3 3 2 2 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 2 3 4 6 8 10 11 14 15 13 10 7 6 10 12 10 6 2 0 0 0 0 0 2 6 10 12 14 15 14 14 13 13 12 11 13 13 15 16 17 18 17 15 14 12 11 9 7 5 4 3 3 2 1 1 1 1 0 1 1 1 1 2 3 3 5 6 6 7 7 8 8 8 8 9 10 11 12
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3 2 3 1 1 2 3 4 3 3 4 4 5 5 5 5 4 4 4 4 3 3 3 3 3 3 3 4 5 7 6 6 6 7 7 7 7 8 8 9 8 8 7 7 6 5 5 4 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 4 4 5 4 3 3 2 1 1 1 1 1 1 2 2 2 1 1 2 3 2 2 2 2 3 6 10 9 6 3 2 2 4 5 5 5 5 4 2 1 0 0 0 0 0 1 3 6 7 5 3 3 2 2 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 2 3 4 4 5 6 7 8 9 10 12 14 18
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3 3 3 2 1 1 1 2 3 2 3 4 5 5 5 4 4 4 3 2 4 4 4 4 4 5 5 5 5 5 5 5 5 6 7 8 7 6 5 5 5 4 3 1 1 1 2 2 2 2 2 1 1 1 1 1 0 0 0 1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 2 2 2 2 3 3 2 3 3 3 2 2 1 1 1 1 1 2 2 2 2 2 3 3 4 4 3 2 2 3 2 2 1 1 1 1 1 1 1 1 2 1 1 1 1 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 1 2 4 6 7 9 12 15 18 21 25 30
3 3 2 1 1 1 2 2 1 1 2 3 3 3 3 3 3 2 2 1 2 3 3 4 5 5 5 5 5 5 5 5 5 6 7 8 7 5 4 4 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 3 4 4 4 3 2 1 2 2 2 2 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 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 0 0 1 0 0 0 0 0 0 1 2 2 3 5 7 9 11 14 18 22 26 30
2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 4 4 3 4 4 4 5 6 6 6 7 7 6 4 3 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 2 2 2 2 3 3 3 4 3 3 1 1 1 2 2 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 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 4 5 7 8 10 13 16 20 25 30 34 37
1 1 1 0 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 2 2 3 3 4 5 6 6 6 5 4 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 3 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 3 3 2 1 2 2 2 2 2 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 1 0 0 0 0 0 0 0 1 2 2 1 1 1 1 1 1 2 2 2 2 3 4 4 4 4 5 6 6 7 7 9 9 10 12 15 18 22 26 32 37 42 42 45
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1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 3 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 0 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 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 1 1 1 1 1 1 1 1 1 2 2 1 2 2 3 4 5 6 6 7 9 11 13 15 17 19 21 22 25 30 34 35 37 41 45 42 43 45 46
1 0 0 1 1 1 1 1 1 1 2 2 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 1 2 2 2 2 1 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 8 10 9 11 13 16 19 22 24 27 32 39 38 39 39 40 44 51 43 40 43 45
0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 2 2 2 2 1 1 1 2 2 2 2 2 2 2 3 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 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 1 1 1 1 1 1 1 1 1 2 2 3 4 5 6 8 10 11 12 14 18 21 25 27 29 33 40 39 38 37 38 40 43 40 37 38 37
1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 1 1 2 2 3 3 3 2 2 3 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 0 0 0 0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 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 1 1 1 1 1 2 3 3 3 4 5 6 8 10 11 13 15 16 19 21 23 24 26 29 30 30 29 29 28 27 27 28 28 27
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