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Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>3 [2,1,3]=>3 [2,3,1]=>2 [3,1,2]=>2 [3,2,1]=>3 [1,2,3,4]=>1 [1,2,4,3]=>6 [1,3,2,4]=>6 [1,3,4,2]=>8 [1,4,2,3]=>8 [1,4,3,2]=>6 [2,1,3,4]=>6 [2,1,4,3]=>9 [2,3,1,4]=>8 [2,3,4,1]=>9 [2,4,1,3]=>9 [2,4,3,1]=>8 [3,1,2,4]=>8 [3,1,4,2]=>9 [3,2,1,4]=>6 [3,2,4,1]=>8 [3,4,1,2]=>9 [3,4,2,1]=>9 [4,1,2,3]=>9 [4,1,3,2]=>8 [4,2,1,3]=>8 [4,2,3,1]=>6 [4,3,1,2]=>9 [4,3,2,1]=>9 [1,2,3,4,5]=>1 [1,2,3,5,4]=>10 [1,2,4,3,5]=>10 [1,2,4,5,3]=>20 [1,2,5,3,4]=>20 [1,2,5,4,3]=>10 [1,3,2,4,5]=>10 [1,3,2,5,4]=>45 [1,3,4,2,5]=>20 [1,3,4,5,2]=>45 [1,3,5,2,4]=>45 [1,3,5,4,2]=>20 [1,4,2,3,5]=>20 [1,4,2,5,3]=>45 [1,4,3,2,5]=>10 [1,4,3,5,2]=>20 [1,4,5,2,3]=>45 [1,4,5,3,2]=>45 [1,5,2,3,4]=>45 [1,5,2,4,3]=>20 [1,5,3,2,4]=>20 [1,5,3,4,2]=>10 [1,5,4,2,3]=>45 [1,5,4,3,2]=>45 [2,1,3,4,5]=>10 [2,1,3,5,4]=>45 [2,1,4,3,5]=>45 [2,1,4,5,3]=>44 [2,1,5,3,4]=>44 [2,1,5,4,3]=>45 [2,3,1,4,5]=>20 [2,3,1,5,4]=>44 [2,3,4,1,5]=>45 [2,3,4,5,1]=>44 [2,3,5,1,4]=>44 [2,3,5,4,1]=>45 [2,4,1,3,5]=>45 [2,4,1,5,3]=>44 [2,4,3,1,5]=>20 [2,4,3,5,1]=>45 [2,4,5,1,3]=>44 [2,4,5,3,1]=>44 [2,5,1,3,4]=>44 [2,5,1,4,3]=>45 [2,5,3,1,4]=>45 [2,5,3,4,1]=>20 [2,5,4,1,3]=>44 [2,5,4,3,1]=>44 [3,1,2,4,5]=>20 [3,1,2,5,4]=>44 [3,1,4,2,5]=>45 [3,1,4,5,2]=>44 [3,1,5,2,4]=>44 [3,1,5,4,2]=>45 [3,2,1,4,5]=>10 [3,2,1,5,4]=>45 [3,2,4,1,5]=>20 [3,2,4,5,1]=>45 [3,2,5,1,4]=>45 [3,2,5,4,1]=>20 [3,4,1,2,5]=>45 [3,4,1,5,2]=>44 [3,4,2,1,5]=>45 [3,4,2,5,1]=>44 [3,4,5,1,2]=>44 [3,4,5,2,1]=>44 [3,5,1,2,4]=>44 [3,5,1,4,2]=>45 [3,5,2,1,4]=>44 [3,5,2,4,1]=>45 [3,5,4,1,2]=>44 [3,5,4,2,1]=>44 [4,1,2,3,5]=>45 [4,1,2,5,3]=>44 [4,1,3,2,5]=>20 [4,1,3,5,2]=>45 [4,1,5,2,3]=>44 [4,1,5,3,2]=>44 [4,2,1,3,5]=>20 [4,2,1,5,3]=>45 [4,2,3,1,5]=>10 [4,2,3,5,1]=>20 [4,2,5,1,3]=>45 [4,2,5,3,1]=>45 [4,3,1,2,5]=>45 [4,3,1,5,2]=>44 [4,3,2,1,5]=>45 [4,3,2,5,1]=>44 [4,3,5,1,2]=>44 [4,3,5,2,1]=>44 [4,5,1,2,3]=>44 [4,5,1,3,2]=>44 [4,5,2,1,3]=>44 [4,5,2,3,1]=>44 [4,5,3,1,2]=>45 [4,5,3,2,1]=>45 [5,1,2,3,4]=>44 [5,1,2,4,3]=>45 [5,1,3,2,4]=>45 [5,1,3,4,2]=>20 [5,1,4,2,3]=>44 [5,1,4,3,2]=>44 [5,2,1,3,4]=>45 [5,2,1,4,3]=>20 [5,2,3,1,4]=>20 [5,2,3,4,1]=>10 [5,2,4,1,3]=>45 [5,2,4,3,1]=>45 [5,3,1,2,4]=>44 [5,3,1,4,2]=>45 [5,3,2,1,4]=>44 [5,3,2,4,1]=>45 [5,3,4,1,2]=>44 [5,3,4,2,1]=>44 [5,4,1,2,3]=>44 [5,4,1,3,2]=>44 [5,4,2,1,3]=>44 [5,4,2,3,1]=>44 [5,4,3,1,2]=>45 [5,4,3,2,1]=>45 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>15 [1,2,3,5,4,6]=>15 [1,2,3,5,6,4]=>40 [1,2,3,6,4,5]=>40 [1,2,3,6,5,4]=>15 [1,2,4,3,5,6]=>15 [1,2,4,3,6,5]=>135 [1,2,4,5,3,6]=>40 [1,2,4,5,6,3]=>135 [1,2,4,6,3,5]=>135 [1,2,4,6,5,3]=>40 [1,2,5,3,4,6]=>40 [1,2,5,3,6,4]=>135 [1,2,5,4,3,6]=>15 [1,2,5,4,6,3]=>40 [1,2,5,6,3,4]=>135 [1,2,5,6,4,3]=>135 [1,2,6,3,4,5]=>135 [1,2,6,3,5,4]=>40 [1,2,6,4,3,5]=>40 [1,2,6,4,5,3]=>15 [1,2,6,5,3,4]=>135 [1,2,6,5,4,3]=>135 [1,3,2,4,5,6]=>15 [1,3,2,4,6,5]=>135 [1,3,2,5,4,6]=>135 [1,3,2,5,6,4]=>264 [1,3,2,6,4,5]=>264 [1,3,2,6,5,4]=>135 [1,3,4,2,5,6]=>40 [1,3,4,2,6,5]=>264 [1,3,4,5,2,6]=>135 [1,3,4,5,6,2]=>264 [1,3,4,6,2,5]=>264 [1,3,4,6,5,2]=>135 [1,3,5,2,4,6]=>135 [1,3,5,2,6,4]=>264 [1,3,5,4,2,6]=>40 [1,3,5,4,6,2]=>135 [1,3,5,6,2,4]=>264 [1,3,5,6,4,2]=>264 [1,3,6,2,4,5]=>264 [1,3,6,2,5,4]=>135 [1,3,6,4,2,5]=>135 [1,3,6,4,5,2]=>40 [1,3,6,5,2,4]=>264 [1,3,6,5,4,2]=>264 [1,4,2,3,5,6]=>40 [1,4,2,3,6,5]=>264 [1,4,2,5,3,6]=>135 [1,4,2,5,6,3]=>264 [1,4,2,6,3,5]=>264 [1,4,2,6,5,3]=>135 [1,4,3,2,5,6]=>15 [1,4,3,2,6,5]=>135 [1,4,3,5,2,6]=>40 [1,4,3,5,6,2]=>135 [1,4,3,6,2,5]=>135 [1,4,3,6,5,2]=>40 [1,4,5,2,3,6]=>135 [1,4,5,2,6,3]=>264 [1,4,5,3,2,6]=>135 [1,4,5,3,6,2]=>264 [1,4,5,6,2,3]=>264 [1,4,5,6,3,2]=>264 [1,4,6,2,3,5]=>264 [1,4,6,2,5,3]=>135 [1,4,6,3,2,5]=>264 [1,4,6,3,5,2]=>135 [1,4,6,5,2,3]=>264 [1,4,6,5,3,2]=>264 [1,5,2,3,4,6]=>135 [1,5,2,3,6,4]=>264 [1,5,2,4,3,6]=>40 [1,5,2,4,6,3]=>135 [1,5,2,6,3,4]=>264 [1,5,2,6,4,3]=>264 [1,5,3,2,4,6]=>40 [1,5,3,2,6,4]=>135 [1,5,3,4,2,6]=>15 [1,5,3,4,6,2]=>40 [1,5,3,6,2,4]=>135 [1,5,3,6,4,2]=>135 [1,5,4,2,3,6]=>135 [1,5,4,2,6,3]=>264 [1,5,4,3,2,6]=>135 [1,5,4,3,6,2]=>264 [1,5,4,6,2,3]=>264 [1,5,4,6,3,2]=>264 [1,5,6,2,3,4]=>264 [1,5,6,2,4,3]=>264 [1,5,6,3,2,4]=>264 [1,5,6,3,4,2]=>264 [1,5,6,4,2,3]=>135 [1,5,6,4,3,2]=>135 [1,6,2,3,4,5]=>264 [1,6,2,3,5,4]=>135 [1,6,2,4,3,5]=>135 [1,6,2,4,5,3]=>40 [1,6,2,5,3,4]=>264 [1,6,2,5,4,3]=>264 [1,6,3,2,4,5]=>135 [1,6,3,2,5,4]=>40 [1,6,3,4,2,5]=>40 [1,6,3,4,5,2]=>15 [1,6,3,5,2,4]=>135 [1,6,3,5,4,2]=>135 [1,6,4,2,3,5]=>264 [1,6,4,2,5,3]=>135 [1,6,4,3,2,5]=>264 [1,6,4,3,5,2]=>135 [1,6,4,5,2,3]=>264 [1,6,4,5,3,2]=>264 [1,6,5,2,3,4]=>264 [1,6,5,2,4,3]=>264 [1,6,5,3,2,4]=>264 [1,6,5,3,4,2]=>264 [1,6,5,4,2,3]=>135 [1,6,5,4,3,2]=>135 [2,1,3,4,5,6]=>15 [2,1,3,4,6,5]=>135 [2,1,3,5,4,6]=>135 [2,1,3,5,6,4]=>264 [2,1,3,6,4,5]=>264 [2,1,3,6,5,4]=>135 [2,1,4,3,5,6]=>135 [2,1,4,3,6,5]=>265 [2,1,4,5,3,6]=>264 [2,1,4,5,6,3]=>265 [2,1,4,6,3,5]=>265 [2,1,4,6,5,3]=>264 [2,1,5,3,4,6]=>264 [2,1,5,3,6,4]=>265 [2,1,5,4,3,6]=>135 [2,1,5,4,6,3]=>264 [2,1,5,6,3,4]=>265 [2,1,5,6,4,3]=>265 [2,1,6,3,4,5]=>265 [2,1,6,3,5,4]=>264 [2,1,6,4,3,5]=>264 [2,1,6,4,5,3]=>135 [2,1,6,5,3,4]=>265 [2,1,6,5,4,3]=>265 [2,3,1,4,5,6]=>40 [2,3,1,4,6,5]=>264 [2,3,1,5,4,6]=>264 [2,3,1,5,6,4]=>265 [2,3,1,6,4,5]=>265 [2,3,1,6,5,4]=>264 [2,3,4,1,5,6]=>135 [2,3,4,1,6,5]=>265 [2,3,4,5,1,6]=>264 [2,3,4,5,6,1]=>265 [2,3,4,6,1,5]=>265 [2,3,4,6,5,1]=>264 [2,3,5,1,4,6]=>264 [2,3,5,1,6,4]=>265 [2,3,5,4,1,6]=>135 [2,3,5,4,6,1]=>264 [2,3,5,6,1,4]=>265 [2,3,5,6,4,1]=>265 [2,3,6,1,4,5]=>265 [2,3,6,1,5,4]=>264 [2,3,6,4,1,5]=>264 [2,3,6,4,5,1]=>135 [2,3,6,5,1,4]=>265 [2,3,6,5,4,1]=>265 [2,4,1,3,5,6]=>135 [2,4,1,3,6,5]=>265 [2,4,1,5,3,6]=>264 [2,4,1,5,6,3]=>265 [2,4,1,6,3,5]=>265 [2,4,1,6,5,3]=>264 [2,4,3,1,5,6]=>40 [2,4,3,1,6,5]=>264 [2,4,3,5,1,6]=>135 [2,4,3,5,6,1]=>264 [2,4,3,6,1,5]=>264 [2,4,3,6,5,1]=>135 [2,4,5,1,3,6]=>264 [2,4,5,1,6,3]=>265 [2,4,5,3,1,6]=>264 [2,4,5,3,6,1]=>265 [2,4,5,6,1,3]=>265 [2,4,5,6,3,1]=>265 [2,4,6,1,3,5]=>265 [2,4,6,1,5,3]=>264 [2,4,6,3,1,5]=>265 [2,4,6,3,5,1]=>264 [2,4,6,5,1,3]=>265 [2,4,6,5,3,1]=>265 [2,5,1,3,4,6]=>264 [2,5,1,3,6,4]=>265 [2,5,1,4,3,6]=>135 [2,5,1,4,6,3]=>264 [2,5,1,6,3,4]=>265 [2,5,1,6,4,3]=>265 [2,5,3,1,4,6]=>135 [2,5,3,1,6,4]=>264 [2,5,3,4,1,6]=>40 [2,5,3,4,6,1]=>135 [2,5,3,6,1,4]=>264 [2,5,3,6,4,1]=>264 [2,5,4,1,3,6]=>264 [2,5,4,1,6,3]=>265 [2,5,4,3,1,6]=>264 [2,5,4,3,6,1]=>265 [2,5,4,6,1,3]=>265 [2,5,4,6,3,1]=>265 [2,5,6,1,3,4]=>265 [2,5,6,1,4,3]=>265 [2,5,6,3,1,4]=>265 [2,5,6,3,4,1]=>265 [2,5,6,4,1,3]=>264 [2,5,6,4,3,1]=>264 [2,6,1,3,4,5]=>265 [2,6,1,3,5,4]=>264 [2,6,1,4,3,5]=>264 [2,6,1,4,5,3]=>135 [2,6,1,5,3,4]=>265 [2,6,1,5,4,3]=>265 [2,6,3,1,4,5]=>264 [2,6,3,1,5,4]=>135 [2,6,3,4,1,5]=>135 [2,6,3,4,5,1]=>40 [2,6,3,5,1,4]=>264 [2,6,3,5,4,1]=>264 [2,6,4,1,3,5]=>265 [2,6,4,1,5,3]=>264 [2,6,4,3,1,5]=>265 [2,6,4,3,5,1]=>264 [2,6,4,5,1,3]=>265 [2,6,4,5,3,1]=>265 [2,6,5,1,3,4]=>265 [2,6,5,1,4,3]=>265 [2,6,5,3,1,4]=>265 [2,6,5,3,4,1]=>265 [2,6,5,4,1,3]=>264 [2,6,5,4,3,1]=>264 [3,1,2,4,5,6]=>40 [3,1,2,4,6,5]=>264 [3,1,2,5,4,6]=>264 [3,1,2,5,6,4]=>265 [3,1,2,6,4,5]=>265 [3,1,2,6,5,4]=>264 [3,1,4,2,5,6]=>135 [3,1,4,2,6,5]=>265 [3,1,4,5,2,6]=>264 [3,1,4,5,6,2]=>265 [3,1,4,6,2,5]=>265 [3,1,4,6,5,2]=>264 [3,1,5,2,4,6]=>264 [3,1,5,2,6,4]=>265 [3,1,5,4,2,6]=>135 [3,1,5,4,6,2]=>264 [3,1,5,6,2,4]=>265 [3,1,5,6,4,2]=>265 [3,1,6,2,4,5]=>265 [3,1,6,2,5,4]=>264 [3,1,6,4,2,5]=>264 [3,1,6,4,5,2]=>135 [3,1,6,5,2,4]=>265 [3,1,6,5,4,2]=>265 [3,2,1,4,5,6]=>15 [3,2,1,4,6,5]=>135 [3,2,1,5,4,6]=>135 [3,2,1,5,6,4]=>264 [3,2,1,6,4,5]=>264 [3,2,1,6,5,4]=>135 [3,2,4,1,5,6]=>40 [3,2,4,1,6,5]=>264 [3,2,4,5,1,6]=>135 [3,2,4,5,6,1]=>264 [3,2,4,6,1,5]=>264 [3,2,4,6,5,1]=>135 [3,2,5,1,4,6]=>135 [3,2,5,1,6,4]=>264 [3,2,5,4,1,6]=>40 [3,2,5,4,6,1]=>135 [3,2,5,6,1,4]=>264 [3,2,5,6,4,1]=>264 [3,2,6,1,4,5]=>264 [3,2,6,1,5,4]=>135 [3,2,6,4,1,5]=>135 [3,2,6,4,5,1]=>40 [3,2,6,5,1,4]=>264 [3,2,6,5,4,1]=>264 [3,4,1,2,5,6]=>135 [3,4,1,2,6,5]=>265 [3,4,1,5,2,6]=>264 [3,4,1,5,6,2]=>265 [3,4,1,6,2,5]=>265 [3,4,1,6,5,2]=>264 [3,4,2,1,5,6]=>135 [3,4,2,1,6,5]=>265 [3,4,2,5,1,6]=>264 [3,4,2,5,6,1]=>265 [3,4,2,6,1,5]=>265 [3,4,2,6,5,1]=>264 [3,4,5,1,2,6]=>264 [3,4,5,1,6,2]=>265 [3,4,5,2,1,6]=>264 [3,4,5,2,6,1]=>265 [3,4,5,6,1,2]=>265 [3,4,5,6,2,1]=>265 [3,4,6,1,2,5]=>265 [3,4,6,1,5,2]=>264 [3,4,6,2,1,5]=>265 [3,4,6,2,5,1]=>264 [3,4,6,5,1,2]=>265 [3,4,6,5,2,1]=>265 [3,5,1,2,4,6]=>264 [3,5,1,2,6,4]=>265 [3,5,1,4,2,6]=>135 [3,5,1,4,6,2]=>264 [3,5,1,6,2,4]=>265 [3,5,1,6,4,2]=>265 [3,5,2,1,4,6]=>264 [3,5,2,1,6,4]=>265 [3,5,2,4,1,6]=>135 [3,5,2,4,6,1]=>264 [3,5,2,6,1,4]=>265 [3,5,2,6,4,1]=>265 [3,5,4,1,2,6]=>264 [3,5,4,1,6,2]=>265 [3,5,4,2,1,6]=>264 [3,5,4,2,6,1]=>265 [3,5,4,6,1,2]=>265 [3,5,4,6,2,1]=>265 [3,5,6,1,2,4]=>265 [3,5,6,1,4,2]=>265 [3,5,6,2,1,4]=>265 [3,5,6,2,4,1]=>265 [3,5,6,4,1,2]=>264 [3,5,6,4,2,1]=>264 [3,6,1,2,4,5]=>265 [3,6,1,2,5,4]=>264 [3,6,1,4,2,5]=>264 [3,6,1,4,5,2]=>135 [3,6,1,5,2,4]=>265 [3,6,1,5,4,2]=>265 [3,6,2,1,4,5]=>265 [3,6,2,1,5,4]=>264 [3,6,2,4,1,5]=>264 [3,6,2,4,5,1]=>135 [3,6,2,5,1,4]=>265 [3,6,2,5,4,1]=>265 [3,6,4,1,2,5]=>265 [3,6,4,1,5,2]=>264 [3,6,4,2,1,5]=>265 [3,6,4,2,5,1]=>264 [3,6,4,5,1,2]=>265 [3,6,4,5,2,1]=>265 [3,6,5,1,2,4]=>265 [3,6,5,1,4,2]=>265 [3,6,5,2,1,4]=>265 [3,6,5,2,4,1]=>265 [3,6,5,4,1,2]=>264 [3,6,5,4,2,1]=>264 [4,1,2,3,5,6]=>135 [4,1,2,3,6,5]=>265 [4,1,2,5,3,6]=>264 [4,1,2,5,6,3]=>265 [4,1,2,6,3,5]=>265 [4,1,2,6,5,3]=>264 [4,1,3,2,5,6]=>40 [4,1,3,2,6,5]=>264 [4,1,3,5,2,6]=>135 [4,1,3,5,6,2]=>264 [4,1,3,6,2,5]=>264 [4,1,3,6,5,2]=>135 [4,1,5,2,3,6]=>264 [4,1,5,2,6,3]=>265 [4,1,5,3,2,6]=>264 [4,1,5,3,6,2]=>265 [4,1,5,6,2,3]=>265 [4,1,5,6,3,2]=>265 [4,1,6,2,3,5]=>265 [4,1,6,2,5,3]=>264 [4,1,6,3,2,5]=>265 [4,1,6,3,5,2]=>264 [4,1,6,5,2,3]=>265 [4,1,6,5,3,2]=>265 [4,2,1,3,5,6]=>40 [4,2,1,3,6,5]=>264 [4,2,1,5,3,6]=>135 [4,2,1,5,6,3]=>264 [4,2,1,6,3,5]=>264 [4,2,1,6,5,3]=>135 [4,2,3,1,5,6]=>15 [4,2,3,1,6,5]=>135 [4,2,3,5,1,6]=>40 [4,2,3,5,6,1]=>135 [4,2,3,6,1,5]=>135 [4,2,3,6,5,1]=>40 [4,2,5,1,3,6]=>135 [4,2,5,1,6,3]=>264 [4,2,5,3,1,6]=>135 [4,2,5,3,6,1]=>264 [4,2,5,6,1,3]=>264 [4,2,5,6,3,1]=>264 [4,2,6,1,3,5]=>264 [4,2,6,1,5,3]=>135 [4,2,6,3,1,5]=>264 [4,2,6,3,5,1]=>135 [4,2,6,5,1,3]=>264 [4,2,6,5,3,1]=>264 [4,3,1,2,5,6]=>135 [4,3,1,2,6,5]=>265 [4,3,1,5,2,6]=>264 [4,3,1,5,6,2]=>265 [4,3,1,6,2,5]=>265 [4,3,1,6,5,2]=>264 [4,3,2,1,5,6]=>135 [4,3,2,1,6,5]=>265 [4,3,2,5,1,6]=>264 [4,3,2,5,6,1]=>265 [4,3,2,6,1,5]=>265 [4,3,2,6,5,1]=>264 [4,3,5,1,2,6]=>264 [4,3,5,1,6,2]=>265 [4,3,5,2,1,6]=>264 [4,3,5,2,6,1]=>265 [4,3,5,6,1,2]=>265 [4,3,5,6,2,1]=>265 [4,3,6,1,2,5]=>265 [4,3,6,1,5,2]=>264 [4,3,6,2,1,5]=>265 [4,3,6,2,5,1]=>264 [4,3,6,5,1,2]=>265 [4,3,6,5,2,1]=>265 [4,5,1,2,3,6]=>264 [4,5,1,2,6,3]=>265 [4,5,1,3,2,6]=>264 [4,5,1,3,6,2]=>265 [4,5,1,6,2,3]=>265 [4,5,1,6,3,2]=>265 [4,5,2,1,3,6]=>264 [4,5,2,1,6,3]=>265 [4,5,2,3,1,6]=>264 [4,5,2,3,6,1]=>265 [4,5,2,6,1,3]=>265 [4,5,2,6,3,1]=>265 [4,5,3,1,2,6]=>135 [4,5,3,1,6,2]=>264 [4,5,3,2,1,6]=>135 [4,5,3,2,6,1]=>264 [4,5,3,6,1,2]=>264 [4,5,3,6,2,1]=>264 [4,5,6,1,2,3]=>265 [4,5,6,1,3,2]=>265 [4,5,6,2,1,3]=>265 [4,5,6,2,3,1]=>265 [4,5,6,3,1,2]=>265 [4,5,6,3,2,1]=>265 [4,6,1,2,3,5]=>265 [4,6,1,2,5,3]=>264 [4,6,1,3,2,5]=>265 [4,6,1,3,5,2]=>264 [4,6,1,5,2,3]=>265 [4,6,1,5,3,2]=>265 [4,6,2,1,3,5]=>265 [4,6,2,1,5,3]=>264 [4,6,2,3,1,5]=>265 [4,6,2,3,5,1]=>264 [4,6,2,5,1,3]=>265 [4,6,2,5,3,1]=>265 [4,6,3,1,2,5]=>264 [4,6,3,1,5,2]=>135 [4,6,3,2,1,5]=>264 [4,6,3,2,5,1]=>135 [4,6,3,5,1,2]=>264 [4,6,3,5,2,1]=>264 [4,6,5,1,2,3]=>265 [4,6,5,1,3,2]=>265 [4,6,5,2,1,3]=>265 [4,6,5,2,3,1]=>265 [4,6,5,3,1,2]=>265 [4,6,5,3,2,1]=>265 [5,1,2,3,4,6]=>264 [5,1,2,3,6,4]=>265 [5,1,2,4,3,6]=>135 [5,1,2,4,6,3]=>264 [5,1,2,6,3,4]=>265 [5,1,2,6,4,3]=>265 [5,1,3,2,4,6]=>135 [5,1,3,2,6,4]=>264 [5,1,3,4,2,6]=>40 [5,1,3,4,6,2]=>135 [5,1,3,6,2,4]=>264 [5,1,3,6,4,2]=>264 [5,1,4,2,3,6]=>264 [5,1,4,2,6,3]=>265 [5,1,4,3,2,6]=>264 [5,1,4,3,6,2]=>265 [5,1,4,6,2,3]=>265 [5,1,4,6,3,2]=>265 [5,1,6,2,3,4]=>265 [5,1,6,2,4,3]=>265 [5,1,6,3,2,4]=>265 [5,1,6,3,4,2]=>265 [5,1,6,4,2,3]=>264 [5,1,6,4,3,2]=>264 [5,2,1,3,4,6]=>135 [5,2,1,3,6,4]=>264 [5,2,1,4,3,6]=>40 [5,2,1,4,6,3]=>135 [5,2,1,6,3,4]=>264 [5,2,1,6,4,3]=>264 [5,2,3,1,4,6]=>40 [5,2,3,1,6,4]=>135 [5,2,3,4,1,6]=>15 [5,2,3,4,6,1]=>40 [5,2,3,6,1,4]=>135 [5,2,3,6,4,1]=>135 [5,2,4,1,3,6]=>135 [5,2,4,1,6,3]=>264 [5,2,4,3,1,6]=>135 [5,2,4,3,6,1]=>264 [5,2,4,6,1,3]=>264 [5,2,4,6,3,1]=>264 [5,2,6,1,3,4]=>264 [5,2,6,1,4,3]=>264 [5,2,6,3,1,4]=>264 [5,2,6,3,4,1]=>264 [5,2,6,4,1,3]=>135 [5,2,6,4,3,1]=>135 [5,3,1,2,4,6]=>264 [5,3,1,2,6,4]=>265 [5,3,1,4,2,6]=>135 [5,3,1,4,6,2]=>264 [5,3,1,6,2,4]=>265 [5,3,1,6,4,2]=>265 [5,3,2,1,4,6]=>264 [5,3,2,1,6,4]=>265 [5,3,2,4,1,6]=>135 [5,3,2,4,6,1]=>264 [5,3,2,6,1,4]=>265 [5,3,2,6,4,1]=>265 [5,3,4,1,2,6]=>264 [5,3,4,1,6,2]=>265 [5,3,4,2,1,6]=>264 [5,3,4,2,6,1]=>265 [5,3,4,6,1,2]=>265 [5,3,4,6,2,1]=>265 [5,3,6,1,2,4]=>265 [5,3,6,1,4,2]=>265 [5,3,6,2,1,4]=>265 [5,3,6,2,4,1]=>265 [5,3,6,4,1,2]=>264 [5,3,6,4,2,1]=>264 [5,4,1,2,3,6]=>264 [5,4,1,2,6,3]=>265 [5,4,1,3,2,6]=>264 [5,4,1,3,6,2]=>265 [5,4,1,6,2,3]=>265 [5,4,1,6,3,2]=>265 [5,4,2,1,3,6]=>264 [5,4,2,1,6,3]=>265 [5,4,2,3,1,6]=>264 [5,4,2,3,6,1]=>265 [5,4,2,6,1,3]=>265 [5,4,2,6,3,1]=>265 [5,4,3,1,2,6]=>135 [5,4,3,1,6,2]=>264 [5,4,3,2,1,6]=>135 [5,4,3,2,6,1]=>264 [5,4,3,6,1,2]=>264 [5,4,3,6,2,1]=>264 [5,4,6,1,2,3]=>265 [5,4,6,1,3,2]=>265 [5,4,6,2,1,3]=>265 [5,4,6,2,3,1]=>265 [5,4,6,3,1,2]=>265 [5,4,6,3,2,1]=>265 [5,6,1,2,3,4]=>265 [5,6,1,2,4,3]=>265 [5,6,1,3,2,4]=>265 [5,6,1,3,4,2]=>265 [5,6,1,4,2,3]=>264 [5,6,1,4,3,2]=>264 [5,6,2,1,3,4]=>265 [5,6,2,1,4,3]=>265 [5,6,2,3,1,4]=>265 [5,6,2,3,4,1]=>265 [5,6,2,4,1,3]=>264 [5,6,2,4,3,1]=>264 [5,6,3,1,2,4]=>264 [5,6,3,1,4,2]=>264 [5,6,3,2,1,4]=>264 [5,6,3,2,4,1]=>264 [5,6,3,4,1,2]=>135 [5,6,3,4,2,1]=>135 [5,6,4,1,2,3]=>265 [5,6,4,1,3,2]=>265 [5,6,4,2,1,3]=>265 [5,6,4,2,3,1]=>265 [5,6,4,3,1,2]=>265 [5,6,4,3,2,1]=>265 [6,1,2,3,4,5]=>265 [6,1,2,3,5,4]=>264 [6,1,2,4,3,5]=>264 [6,1,2,4,5,3]=>135 [6,1,2,5,3,4]=>265 [6,1,2,5,4,3]=>265 [6,1,3,2,4,5]=>264 [6,1,3,2,5,4]=>135 [6,1,3,4,2,5]=>135 [6,1,3,4,5,2]=>40 [6,1,3,5,2,4]=>264 [6,1,3,5,4,2]=>264 [6,1,4,2,3,5]=>265 [6,1,4,2,5,3]=>264 [6,1,4,3,2,5]=>265 [6,1,4,3,5,2]=>264 [6,1,4,5,2,3]=>265 [6,1,4,5,3,2]=>265 [6,1,5,2,3,4]=>265 [6,1,5,2,4,3]=>265 [6,1,5,3,2,4]=>265 [6,1,5,3,4,2]=>265 [6,1,5,4,2,3]=>264 [6,1,5,4,3,2]=>264 [6,2,1,3,4,5]=>264 [6,2,1,3,5,4]=>135 [6,2,1,4,3,5]=>135 [6,2,1,4,5,3]=>40 [6,2,1,5,3,4]=>264 [6,2,1,5,4,3]=>264 [6,2,3,1,4,5]=>135 [6,2,3,1,5,4]=>40 [6,2,3,4,1,5]=>40 [6,2,3,4,5,1]=>15 [6,2,3,5,1,4]=>135 [6,2,3,5,4,1]=>135 [6,2,4,1,3,5]=>264 [6,2,4,1,5,3]=>135 [6,2,4,3,1,5]=>264 [6,2,4,3,5,1]=>135 [6,2,4,5,1,3]=>264 [6,2,4,5,3,1]=>264 [6,2,5,1,3,4]=>264 [6,2,5,1,4,3]=>264 [6,2,5,3,1,4]=>264 [6,2,5,3,4,1]=>264 [6,2,5,4,1,3]=>135 [6,2,5,4,3,1]=>135 [6,3,1,2,4,5]=>265 [6,3,1,2,5,4]=>264 [6,3,1,4,2,5]=>264 [6,3,1,4,5,2]=>135 [6,3,1,5,2,4]=>265 [6,3,1,5,4,2]=>265 [6,3,2,1,4,5]=>265 [6,3,2,1,5,4]=>264 [6,3,2,4,1,5]=>264 [6,3,2,4,5,1]=>135 [6,3,2,5,1,4]=>265 [6,3,2,5,4,1]=>265 [6,3,4,1,2,5]=>265 [6,3,4,1,5,2]=>264 [6,3,4,2,1,5]=>265 [6,3,4,2,5,1]=>264 [6,3,4,5,1,2]=>265 [6,3,4,5,2,1]=>265 [6,3,5,1,2,4]=>265 [6,3,5,1,4,2]=>265 [6,3,5,2,1,4]=>265 [6,3,5,2,4,1]=>265 [6,3,5,4,1,2]=>264 [6,3,5,4,2,1]=>264 [6,4,1,2,3,5]=>265 [6,4,1,2,5,3]=>264 [6,4,1,3,2,5]=>265 [6,4,1,3,5,2]=>264 [6,4,1,5,2,3]=>265 [6,4,1,5,3,2]=>265 [6,4,2,1,3,5]=>265 [6,4,2,1,5,3]=>264 [6,4,2,3,1,5]=>265 [6,4,2,3,5,1]=>264 [6,4,2,5,1,3]=>265 [6,4,2,5,3,1]=>265 [6,4,3,1,2,5]=>264 [6,4,3,1,5,2]=>135 [6,4,3,2,1,5]=>264 [6,4,3,2,5,1]=>135 [6,4,3,5,1,2]=>264 [6,4,3,5,2,1]=>264 [6,4,5,1,2,3]=>265 [6,4,5,1,3,2]=>265 [6,4,5,2,1,3]=>265 [6,4,5,2,3,1]=>265 [6,4,5,3,1,2]=>265 [6,4,5,3,2,1]=>265 [6,5,1,2,3,4]=>265 [6,5,1,2,4,3]=>265 [6,5,1,3,2,4]=>265 [6,5,1,3,4,2]=>265 [6,5,1,4,2,3]=>264 [6,5,1,4,3,2]=>264 [6,5,2,1,3,4]=>265 [6,5,2,1,4,3]=>265 [6,5,2,3,1,4]=>265 [6,5,2,3,4,1]=>265 [6,5,2,4,1,3]=>264 [6,5,2,4,3,1]=>264 [6,5,3,1,2,4]=>264 [6,5,3,1,4,2]=>264 [6,5,3,2,1,4]=>264 [6,5,3,2,4,1]=>264 [6,5,3,4,1,2]=>135 [6,5,3,4,2,1]=>135 [6,5,4,1,2,3]=>265 [6,5,4,1,3,2]=>265 [6,5,4,2,1,3]=>265 [6,5,4,2,3,1]=>265 [6,5,4,3,1,2]=>265 [6,5,4,3,2,1]=>265 [1,2,3,4,5,6,7]=>1 [1,2,3,4,5,7,6]=>21 [1,2,3,4,6,5,7]=>21 [1,2,3,4,6,7,5]=>70 [1,2,3,4,7,5,6]=>70 [1,2,3,4,7,6,5]=>21 [1,2,3,5,4,6,7]=>21 [1,2,3,5,4,7,6]=>315 [1,2,3,5,6,4,7]=>70 [1,2,3,5,6,7,4]=>315 [1,2,3,5,7,4,6]=>315 [1,2,3,5,7,6,4]=>70 [1,2,3,6,4,5,7]=>70 [1,2,3,6,4,7,5]=>315 [1,2,3,6,5,4,7]=>21 [1,2,3,6,5,7,4]=>70 [1,2,3,6,7,4,5]=>315 [1,2,3,6,7,5,4]=>315 [1,2,3,7,4,5,6]=>315 [1,2,3,7,4,6,5]=>70 [1,2,3,7,5,4,6]=>70 [1,2,3,7,5,6,4]=>21 [1,2,3,7,6,4,5]=>315 [1,2,3,7,6,5,4]=>315 [1,2,4,3,5,6,7]=>21 [1,2,4,3,5,7,6]=>315 [1,2,4,3,6,5,7]=>315 [1,2,4,3,6,7,5]=>924 [1,2,4,3,7,5,6]=>924 [1,2,4,3,7,6,5]=>315 [1,2,4,5,3,6,7]=>70 [1,2,4,5,3,7,6]=>924 [1,2,4,5,6,3,7]=>315 [1,2,4,5,6,7,3]=>924 [1,2,4,5,7,3,6]=>924 [1,2,4,5,7,6,3]=>315 [1,2,4,6,3,5,7]=>315 [1,2,4,6,3,7,5]=>924 [1,2,4,6,5,3,7]=>70 [1,2,4,6,5,7,3]=>315 [1,2,4,6,7,3,5]=>924 [1,2,4,6,7,5,3]=>924 [1,2,4,7,3,5,6]=>924 [1,2,4,7,3,6,5]=>315 [1,2,4,7,5,3,6]=>315 [1,2,4,7,5,6,3]=>70 [1,2,4,7,6,3,5]=>924 [1,2,4,7,6,5,3]=>924 [1,2,5,3,4,6,7]=>70 [1,2,5,3,4,7,6]=>924 [1,2,5,3,6,4,7]=>315 [1,2,5,3,6,7,4]=>924 [1,2,5,3,7,4,6]=>924 [1,2,5,3,7,6,4]=>315 [1,2,5,4,3,6,7]=>21 [1,2,5,4,3,7,6]=>315 [1,2,5,4,6,3,7]=>70 [1,2,5,4,6,7,3]=>315 [1,2,5,4,7,3,6]=>315 [1,2,5,4,7,6,3]=>70 [1,2,5,6,3,4,7]=>315 [1,2,5,6,3,7,4]=>924 [1,2,5,6,4,3,7]=>315 [1,2,5,6,4,7,3]=>924 [1,2,5,6,7,3,4]=>924 [1,2,5,6,7,4,3]=>924 [1,2,5,7,3,4,6]=>924 [1,2,5,7,3,6,4]=>315 [1,2,5,7,4,3,6]=>924 [1,2,5,7,4,6,3]=>315 [1,2,5,7,6,3,4]=>924 [1,2,5,7,6,4,3]=>924 [1,2,6,3,4,5,7]=>315 [1,2,6,3,4,7,5]=>924 [1,2,6,3,5,4,7]=>70 [1,2,6,3,5,7,4]=>315 [1,2,6,3,7,4,5]=>924 [1,2,6,3,7,5,4]=>924 [1,2,6,4,3,5,7]=>70 [1,2,6,4,3,7,5]=>315 [1,2,6,4,5,3,7]=>21 [1,2,6,4,5,7,3]=>70 [1,2,6,4,7,3,5]=>315 [1,2,6,4,7,5,3]=>315 [1,2,6,5,3,4,7]=>315 [1,2,6,5,3,7,4]=>924 [1,2,6,5,4,3,7]=>315 [1,2,6,5,4,7,3]=>924 [1,2,6,5,7,3,4]=>924 [1,2,6,5,7,4,3]=>924 [1,2,6,7,3,4,5]=>924 [1,2,6,7,3,5,4]=>924 [1,2,6,7,4,3,5]=>924 [1,2,6,7,4,5,3]=>924 [1,2,6,7,5,3,4]=>315 [1,2,6,7,5,4,3]=>315 [1,2,7,3,4,5,6]=>924 [1,2,7,3,4,6,5]=>315 [1,2,7,3,5,4,6]=>315 [1,2,7,3,5,6,4]=>70 [1,2,7,3,6,4,5]=>924 [1,2,7,3,6,5,4]=>924 [1,2,7,4,3,5,6]=>315 [1,2,7,4,3,6,5]=>70 [1,2,7,4,5,3,6]=>70 [1,2,7,4,5,6,3]=>21 [1,2,7,4,6,3,5]=>315 [1,2,7,4,6,5,3]=>315 [1,2,7,5,3,4,6]=>924 [1,2,7,5,3,6,4]=>315 [1,2,7,5,4,3,6]=>924 [1,2,7,5,4,6,3]=>315 [1,2,7,5,6,3,4]=>924 [1,2,7,5,6,4,3]=>924 [1,2,7,6,3,4,5]=>924 [1,2,7,6,3,5,4]=>924 [1,2,7,6,4,3,5]=>924 [1,2,7,6,4,5,3]=>924 [1,2,7,6,5,3,4]=>315 [1,2,7,6,5,4,3]=>315 [1,3,2,4,5,6,7]=>21 [1,3,2,4,5,7,6]=>315 [1,3,2,4,6,5,7]=>315 [1,3,2,4,6,7,5]=>924 [1,3,2,4,7,5,6]=>924 [1,3,2,4,7,6,5]=>315 [1,3,2,5,4,6,7]=>315 [1,3,2,5,4,7,6]=>1855 [1,3,2,5,6,4,7]=>924 [1,3,2,5,6,7,4]=>1855 [1,3,2,5,7,4,6]=>1855 [1,3,2,5,7,6,4]=>924 [1,3,2,6,4,5,7]=>924 [1,3,2,6,4,7,5]=>1855 [1,3,2,6,5,4,7]=>315 [1,3,2,6,5,7,4]=>924 [1,3,2,6,7,4,5]=>1855 [1,3,2,6,7,5,4]=>1855 [1,3,2,7,4,5,6]=>1855 [1,3,2,7,4,6,5]=>924 [1,3,2,7,5,4,6]=>924 [1,3,2,7,5,6,4]=>315 [1,3,2,7,6,4,5]=>1855 [1,3,2,7,6,5,4]=>1855 [1,3,4,2,5,6,7]=>70 [1,3,4,2,5,7,6]=>924 [1,3,4,2,6,5,7]=>924 [1,3,4,2,6,7,5]=>1855 [1,3,4,2,7,5,6]=>1855 [1,3,4,2,7,6,5]=>924 [1,3,4,5,2,6,7]=>315 [1,3,4,5,2,7,6]=>1855 [1,3,4,5,6,2,7]=>924 [1,3,4,5,6,7,2]=>1855 [1,3,4,5,7,2,6]=>1855 [1,3,4,5,7,6,2]=>924 [1,3,4,6,2,5,7]=>924 [1,3,4,6,2,7,5]=>1855 [1,3,4,6,5,2,7]=>315 [1,3,4,6,5,7,2]=>924 [1,3,4,6,7,2,5]=>1855 [1,3,4,6,7,5,2]=>1855 [1,3,4,7,2,5,6]=>1855 [1,3,4,7,2,6,5]=>924 [1,3,4,7,5,2,6]=>924 [1,3,4,7,5,6,2]=>315 [1,3,4,7,6,2,5]=>1855 [1,3,4,7,6,5,2]=>1855 [1,3,5,2,4,6,7]=>315 [1,3,5,2,4,7,6]=>1855 [1,3,5,2,6,4,7]=>924 [1,3,5,2,6,7,4]=>1855 [1,3,5,2,7,4,6]=>1855 [1,3,5,2,7,6,4]=>924 [1,3,5,4,2,6,7]=>70 [1,3,5,4,2,7,6]=>924 [1,3,5,4,6,2,7]=>315 [1,3,5,4,6,7,2]=>924 [1,3,5,4,7,2,6]=>924 [1,3,5,4,7,6,2]=>315 [1,3,5,6,2,4,7]=>924 [1,3,5,6,2,7,4]=>1855 [1,3,5,6,4,2,7]=>924 [1,3,5,6,4,7,2]=>1855 [1,3,5,6,7,2,4]=>1855 [1,3,5,6,7,4,2]=>1855 [1,3,5,7,2,4,6]=>1855 [1,3,5,7,2,6,4]=>924 [1,3,5,7,4,2,6]=>1855 [1,3,5,7,4,6,2]=>924 [1,3,5,7,6,2,4]=>1855 [1,3,5,7,6,4,2]=>1855 [1,3,6,2,4,5,7]=>924 [1,3,6,2,4,7,5]=>1855 [1,3,6,2,5,4,7]=>315 [1,3,6,2,5,7,4]=>924 [1,3,6,2,7,4,5]=>1855 [1,3,6,2,7,5,4]=>1855 [1,3,6,4,2,5,7]=>315 [1,3,6,4,2,7,5]=>924 [1,3,6,4,5,2,7]=>70 [1,3,6,4,5,7,2]=>315 [1,3,6,4,7,2,5]=>924 [1,3,6,4,7,5,2]=>924 [1,3,6,5,2,4,7]=>924 [1,3,6,5,2,7,4]=>1855 [1,3,6,5,4,2,7]=>924 [1,3,6,5,4,7,2]=>1855 [1,3,6,5,7,2,4]=>1855 [1,3,6,5,7,4,2]=>1855 [1,3,6,7,2,4,5]=>1855 [1,3,6,7,2,5,4]=>1855 [1,3,6,7,4,2,5]=>1855 [1,3,6,7,4,5,2]=>1855 [1,3,6,7,5,2,4]=>924 [1,3,6,7,5,4,2]=>924 [1,3,7,2,4,5,6]=>1855 [1,3,7,2,4,6,5]=>924 [1,3,7,2,5,4,6]=>924 [1,3,7,2,5,6,4]=>315 [1,3,7,2,6,4,5]=>1855 [1,3,7,2,6,5,4]=>1855 [1,3,7,4,2,5,6]=>924 [1,3,7,4,2,6,5]=>315 [1,3,7,4,5,2,6]=>315 [1,3,7,4,5,6,2]=>70 [1,3,7,4,6,2,5]=>924 [1,3,7,4,6,5,2]=>924 [1,3,7,5,2,4,6]=>1855 [1,3,7,5,2,6,4]=>924 [1,3,7,5,4,2,6]=>1855 [1,3,7,5,4,6,2]=>924 [1,3,7,5,6,2,4]=>1855 [1,3,7,5,6,4,2]=>1855 [1,3,7,6,2,4,5]=>1855 [1,3,7,6,2,5,4]=>1855 [1,3,7,6,4,2,5]=>1855 [1,3,7,6,4,5,2]=>1855 [1,3,7,6,5,2,4]=>924 [1,3,7,6,5,4,2]=>924 [1,4,2,3,5,6,7]=>70 [1,4,2,3,5,7,6]=>924 [1,4,2,3,6,5,7]=>924 [1,4,2,3,6,7,5]=>1855 [1,4,2,3,7,5,6]=>1855 [1,4,2,3,7,6,5]=>924 [1,4,2,5,3,6,7]=>315 [1,4,2,5,3,7,6]=>1855 [1,4,2,5,6,3,7]=>924 [1,4,2,5,6,7,3]=>1855 [1,4,2,5,7,3,6]=>1855 [1,4,2,5,7,6,3]=>924 [1,4,2,6,3,5,7]=>924 [1,4,2,6,3,7,5]=>1855 [1,4,2,6,5,3,7]=>315 [1,4,2,6,5,7,3]=>924 [1,4,2,6,7,3,5]=>1855 [1,4,2,6,7,5,3]=>1855 [1,4,2,7,3,5,6]=>1855 [1,4,2,7,3,6,5]=>924 [1,4,2,7,5,3,6]=>924 [1,4,2,7,5,6,3]=>315 [1,4,2,7,6,3,5]=>1855 [1,4,2,7,6,5,3]=>1855 [1,4,3,2,5,6,7]=>21 [1,4,3,2,5,7,6]=>315 [1,4,3,2,6,5,7]=>315 [1,4,3,2,6,7,5]=>924 [1,4,3,2,7,5,6]=>924 [1,4,3,2,7,6,5]=>315 [1,4,3,5,2,6,7]=>70 [1,4,3,5,2,7,6]=>924 [1,4,3,5,6,2,7]=>315 [1,4,3,5,6,7,2]=>924 [1,4,3,5,7,2,6]=>924 [1,4,3,5,7,6,2]=>315 [1,4,3,6,2,5,7]=>315 [1,4,3,6,2,7,5]=>924 [1,4,3,6,5,2,7]=>70 [1,4,3,6,5,7,2]=>315 [1,4,3,6,7,2,5]=>924 [1,4,3,6,7,5,2]=>924 [1,4,3,7,2,5,6]=>924 [1,4,3,7,2,6,5]=>315 [1,4,3,7,5,2,6]=>315 [1,4,3,7,5,6,2]=>70 [1,4,3,7,6,2,5]=>924 [1,4,3,7,6,5,2]=>924 [1,4,5,2,3,6,7]=>315 [1,4,5,2,3,7,6]=>1855 [1,4,5,2,6,3,7]=>924 [1,4,5,2,6,7,3]=>1855 [1,4,5,2,7,3,6]=>1855 [1,4,5,2,7,6,3]=>924 [1,4,5,3,2,6,7]=>315 [1,4,5,3,2,7,6]=>1855 [1,4,5,3,6,2,7]=>924 [1,4,5,3,6,7,2]=>1855 [1,4,5,3,7,2,6]=>1855 [1,4,5,3,7,6,2]=>924 [1,4,5,6,2,3,7]=>924 [1,4,5,6,2,7,3]=>1855 [1,4,5,6,3,2,7]=>924 [1,4,5,6,3,7,2]=>1855 [1,4,5,6,7,2,3]=>1855 [1,4,5,6,7,3,2]=>1855 [1,4,5,7,2,3,6]=>1855 [1,4,5,7,2,6,3]=>924 [1,4,5,7,3,2,6]=>1855 [1,4,5,7,3,6,2]=>924 [1,4,5,7,6,2,3]=>1855 [1,4,5,7,6,3,2]=>1855 [1,4,6,2,3,5,7]=>924 [1,4,6,2,3,7,5]=>1855 [1,4,6,2,5,3,7]=>315 [1,4,6,2,5,7,3]=>924 [1,4,6,2,7,3,5]=>1855 [1,4,6,2,7,5,3]=>1855 [1,4,6,3,2,5,7]=>924 [1,4,6,3,2,7,5]=>1855 [1,4,6,3,5,2,7]=>315 [1,4,6,3,5,7,2]=>924 [1,4,6,3,7,2,5]=>1855 [1,4,6,3,7,5,2]=>1855 [1,4,6,5,2,3,7]=>924 [1,4,6,5,2,7,3]=>1855 [1,4,6,5,3,2,7]=>924
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Description
The number of permutations such that the product with the permutation has the same number of fixed points.
More formally, given a permutation $\pi$, this is the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same number of fixed points.
Note that the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same cycle type is the size of the conjugacy class of $\pi$, St000690The size of the conjugacy class of a permutation..
References
[1] balli Number of Permutations? MathOverflow:144899
Code
def statistic(pi):
    m = pi.number_of_fixed_points()
    return sum(1 for tau in Permutations(pi.size()) if (pi*tau).number_of_fixed_points() == m)

Created
Apr 09, 2020 at 18:37 by Martin Rubey
Updated
Apr 09, 2020 at 18:37 by Martin Rubey