edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>2 [2,1]=>2 [1,2,3]=>3 [1,3,2]=>3 [2,1,3]=>3 [2,3,1]=>3 [3,1,2]=>3 [3,2,1]=>3 [1,2,3,4]=>5 [1,2,4,3]=>5 [1,3,2,4]=>5 [1,3,4,2]=>3 [1,4,2,3]=>3 [1,4,3,2]=>3 [2,1,3,4]=>5 [2,1,4,3]=>5 [2,3,1,4]=>3 [2,3,4,1]=>3 [2,4,1,3]=>1 [2,4,3,1]=>3 [3,1,2,4]=>3 [3,1,4,2]=>1 [3,2,1,4]=>3 [3,2,4,1]=>3 [3,4,1,2]=>5 [3,4,2,1]=>5 [4,1,2,3]=>3 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>5 [4,3,1,2]=>5 [4,3,2,1]=>5 [1,2,3,4,5]=>8 [1,2,3,5,4]=>8 [1,2,4,3,5]=>8 [1,2,4,5,3]=>6 [1,2,5,3,4]=>6 [1,2,5,4,3]=>6 [1,3,2,4,5]=>8 [1,3,2,5,4]=>8 [1,3,4,2,5]=>3 [1,3,4,5,2]=>3 [1,3,5,2,4]=>1 [1,3,5,4,2]=>3 [1,4,2,3,5]=>3 [1,4,2,5,3]=>1 [1,4,3,2,5]=>3 [1,4,3,5,2]=>3 [1,4,5,2,3]=>5 [1,4,5,3,2]=>5 [1,5,2,3,4]=>3 [1,5,2,4,3]=>3 [1,5,3,2,4]=>3 [1,5,3,4,2]=>5 [1,5,4,2,3]=>5 [1,5,4,3,2]=>5 [2,1,3,4,5]=>8 [2,1,3,5,4]=>8 [2,1,4,3,5]=>8 [2,1,4,5,3]=>6 [2,1,5,3,4]=>6 [2,1,5,4,3]=>6 [2,3,1,4,5]=>6 [2,3,1,5,4]=>6 [2,3,4,1,5]=>3 [2,3,4,5,1]=>5 [2,3,5,1,4]=>2 [2,3,5,4,1]=>5 [2,4,1,3,5]=>1 [2,4,1,5,3]=>1 [2,4,3,1,5]=>3 [2,4,3,5,1]=>5 [2,4,5,1,3]=>2 [2,4,5,3,1]=>3 [2,5,1,3,4]=>2 [2,5,1,4,3]=>2 [2,5,3,1,4]=>1 [2,5,3,4,1]=>3 [2,5,4,1,3]=>2 [2,5,4,3,1]=>3 [3,1,2,4,5]=>6 [3,1,2,5,4]=>6 [3,1,4,2,5]=>1 [3,1,4,5,2]=>2 [3,1,5,2,4]=>1 [3,1,5,4,2]=>2 [3,2,1,4,5]=>6 [3,2,1,5,4]=>6 [3,2,4,1,5]=>3 [3,2,4,5,1]=>5 [3,2,5,1,4]=>2 [3,2,5,4,1]=>5 [3,4,1,2,5]=>5 [3,4,1,5,2]=>2 [3,4,2,1,5]=>5 [3,4,2,5,1]=>3 [3,4,5,1,2]=>6 [3,4,5,2,1]=>6 [3,5,1,2,4]=>2 [3,5,1,4,2]=>1 [3,5,2,1,4]=>2 [3,5,2,4,1]=>1 [3,5,4,1,2]=>6 [3,5,4,2,1]=>6 [4,1,2,3,5]=>3 [4,1,2,5,3]=>2 [4,1,3,2,5]=>3 [4,1,3,5,2]=>1 [4,1,5,2,3]=>2 [4,1,5,3,2]=>2 [4,2,1,3,5]=>3 [4,2,1,5,3]=>2 [4,2,3,1,5]=>5 [4,2,3,5,1]=>3 [4,2,5,1,3]=>1 [4,2,5,3,1]=>1 [4,3,1,2,5]=>5 [4,3,1,5,2]=>2 [4,3,2,1,5]=>5 [4,3,2,5,1]=>3 [4,3,5,1,2]=>6 [4,3,5,2,1]=>6 [4,5,1,2,3]=>6 [4,5,1,3,2]=>6 [4,5,2,1,3]=>6 [4,5,2,3,1]=>8 [4,5,3,1,2]=>8 [4,5,3,2,1]=>8 [5,1,2,3,4]=>5 [5,1,2,4,3]=>5 [5,1,3,2,4]=>5 [5,1,3,4,2]=>3 [5,1,4,2,3]=>3 [5,1,4,3,2]=>3 [5,2,1,3,4]=>5 [5,2,1,4,3]=>5 [5,2,3,1,4]=>3 [5,2,3,4,1]=>3 [5,2,4,1,3]=>1 [5,2,4,3,1]=>3 [5,3,1,2,4]=>3 [5,3,1,4,2]=>1 [5,3,2,1,4]=>3 [5,3,2,4,1]=>3 [5,3,4,1,2]=>8 [5,3,4,2,1]=>8 [5,4,1,2,3]=>6 [5,4,1,3,2]=>6 [5,4,2,1,3]=>6 [5,4,2,3,1]=>8 [5,4,3,1,2]=>8 [5,4,3,2,1]=>8 [1,2,3,4,5,6]=>13 [1,2,3,4,6,5]=>13 [1,2,3,5,4,6]=>13 [1,2,3,5,6,4]=>9 [1,2,3,6,4,5]=>9 [1,2,3,6,5,4]=>9 [1,2,4,3,5,6]=>13 [1,2,4,3,6,5]=>13 [1,2,4,5,3,6]=>6 [1,2,4,5,6,3]=>6 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>6 [1,2,5,3,4,6]=>6 [1,2,5,3,6,4]=>2 [1,2,5,4,3,6]=>6 [1,2,5,4,6,3]=>6 [1,2,5,6,3,4]=>10 [1,2,5,6,4,3]=>10 [1,2,6,3,4,5]=>6 [1,2,6,3,5,4]=>6 [1,2,6,4,3,5]=>6 [1,2,6,4,5,3]=>10 [1,2,6,5,3,4]=>10 [1,2,6,5,4,3]=>10 [1,3,2,4,5,6]=>13 [1,3,2,4,6,5]=>13 [1,3,2,5,4,6]=>13 [1,3,2,5,6,4]=>9 [1,3,2,6,4,5]=>9 [1,3,2,6,5,4]=>9 [1,3,4,2,5,6]=>6 [1,3,4,2,6,5]=>6 [1,3,4,5,2,6]=>3 [1,3,4,5,6,2]=>5 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>5 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>5 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>1 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>6 [1,4,2,3,6,5]=>6 [1,4,2,5,3,6]=>1 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>1 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>6 [1,4,3,2,6,5]=>6 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>5 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>5 [1,4,5,2,3,6]=>5 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>5 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>6 [1,4,5,6,3,2]=>6 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>6 [1,4,6,5,3,2]=>6 [1,5,2,3,4,6]=>3 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>2 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>2 [1,5,3,4,2,6]=>5 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>1 [1,5,4,2,3,6]=>5 [1,5,4,2,6,3]=>2 [1,5,4,3,2,6]=>5 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>6 [1,5,4,6,3,2]=>6 [1,5,6,2,3,4]=>6 [1,5,6,2,4,3]=>6 [1,5,6,3,2,4]=>6 [1,5,6,3,4,2]=>8 [1,5,6,4,2,3]=>8 [1,5,6,4,3,2]=>8 [1,6,2,3,4,5]=>5 [1,6,2,3,5,4]=>5 [1,6,2,4,3,5]=>5 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>3 [1,6,3,2,4,5]=>5 [1,6,3,2,5,4]=>5 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>3 [1,6,3,5,2,4]=>1 [1,6,3,5,4,2]=>3 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>3 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>8 [1,6,4,5,3,2]=>8 [1,6,5,2,3,4]=>6 [1,6,5,2,4,3]=>6 [1,6,5,3,2,4]=>6 [1,6,5,3,4,2]=>8 [1,6,5,4,2,3]=>8 [1,6,5,4,3,2]=>8 [2,1,3,4,5,6]=>13 [2,1,3,4,6,5]=>13 [2,1,3,5,4,6]=>13 [2,1,3,5,6,4]=>9 [2,1,3,6,4,5]=>9 [2,1,3,6,5,4]=>9 [2,1,4,3,5,6]=>13 [2,1,4,3,6,5]=>13 [2,1,4,5,3,6]=>6 [2,1,4,5,6,3]=>6 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>6 [2,1,5,3,4,6]=>6 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>6 [2,1,5,4,6,3]=>6 [2,1,5,6,3,4]=>10 [2,1,5,6,4,3]=>10 [2,1,6,3,4,5]=>6 [2,1,6,3,5,4]=>6 [2,1,6,4,3,5]=>6 [2,1,6,4,5,3]=>10 [2,1,6,5,3,4]=>10 [2,1,6,5,4,3]=>10 [2,3,1,4,5,6]=>9 [2,3,1,4,6,5]=>9 [2,3,1,5,4,6]=>9 [2,3,1,5,6,4]=>9 [2,3,1,6,4,5]=>9 [2,3,1,6,5,4]=>9 [2,3,4,1,5,6]=>6 [2,3,4,1,6,5]=>6 [2,3,4,5,1,6]=>5 [2,3,4,5,6,1]=>8 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>8 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>5 [2,3,5,4,6,1]=>8 [2,3,5,6,1,4]=>4 [2,3,5,6,4,1]=>6 [2,3,6,1,4,5]=>4 [2,3,6,1,5,4]=>4 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>6 [2,3,6,5,1,4]=>4 [2,3,6,5,4,1]=>6 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>1 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>1 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>6 [2,4,3,1,6,5]=>6 [2,4,3,5,1,6]=>5 [2,4,3,5,6,1]=>8 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>8 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>3 [2,4,6,1,3,5]=>1 [2,4,6,1,5,3]=>1 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>1 [2,4,6,5,1,3]=>3 [2,4,6,5,3,1]=>3 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>1 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>1 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>2 [2,5,3,1,4,6]=>1 [2,5,3,1,6,4]=>1 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>3 [2,5,3,6,1,4]=>1 [2,5,3,6,4,1]=>1 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>2 [2,5,4,3,1,6]=>3 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>4 [2,5,6,1,4,3]=>4 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>5 [2,5,6,4,1,3]=>3 [2,5,6,4,3,1]=>5 [2,6,1,3,4,5]=>3 [2,6,1,3,5,4]=>3 [2,6,1,4,3,5]=>3 [2,6,1,4,5,3]=>3 [2,6,1,5,3,4]=>3 [2,6,1,5,4,3]=>3 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>2 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>3 [2,6,3,5,1,4]=>1 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>1 [2,6,4,1,5,3]=>1 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>5 [2,6,5,1,3,4]=>4 [2,6,5,1,4,3]=>4 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>5 [2,6,5,4,1,3]=>3 [2,6,5,4,3,1]=>5 [3,1,2,4,5,6]=>9 [3,1,2,4,6,5]=>9 [3,1,2,5,4,6]=>9 [3,1,2,5,6,4]=>9 [3,1,2,6,4,5]=>9 [3,1,2,6,5,4]=>9 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>1 [3,1,4,6,5,2]=>3 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>1 [3,1,5,4,2,6]=>2 [3,1,5,4,6,2]=>3 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>3 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>1 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>3 [3,2,1,4,5,6]=>9 [3,2,1,4,6,5]=>9 [3,2,1,5,4,6]=>9 [3,2,1,5,6,4]=>9 [3,2,1,6,4,5]=>9 [3,2,1,6,5,4]=>9 [3,2,4,1,5,6]=>6 [3,2,4,1,6,5]=>6 [3,2,4,5,1,6]=>5 [3,2,4,5,6,1]=>8 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>8 [3,2,5,1,4,6]=>2 [3,2,5,1,6,4]=>2 [3,2,5,4,1,6]=>5 [3,2,5,4,6,1]=>8 [3,2,5,6,1,4]=>4 [3,2,5,6,4,1]=>6 [3,2,6,1,4,5]=>4 [3,2,6,1,5,4]=>4 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>6 [3,2,6,5,1,4]=>4 [3,2,6,5,4,1]=>6 [3,4,1,2,5,6]=>10 [3,4,1,2,6,5]=>10 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>4 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>10 [3,4,2,1,6,5]=>10 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>6 [3,4,2,6,1,5]=>3 [3,4,2,6,5,1]=>6 [3,4,5,1,2,6]=>6 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>6 [3,4,5,2,6,1]=>3 [3,4,5,6,1,2]=>10 [3,4,5,6,2,1]=>10 [3,4,6,1,2,5]=>4 [3,4,6,1,5,2]=>2 [3,4,6,2,1,5]=>4 [3,4,6,2,5,1]=>2 [3,4,6,5,1,2]=>10 [3,4,6,5,2,1]=>10 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>1 [3,5,1,6,4,2]=>1 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>2 [3,5,2,4,1,6]=>1 [3,5,2,4,6,1]=>1 [3,5,2,6,1,4]=>1 [3,5,2,6,4,1]=>1 [3,5,4,1,2,6]=>6 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>6 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>10 [3,5,4,6,2,1]=>10 [3,5,6,1,2,4]=>4 [3,5,6,1,4,2]=>2 [3,5,6,2,1,4]=>4 [3,5,6,2,4,1]=>2 [3,5,6,4,1,2]=>6 [3,5,6,4,2,1]=>6 [3,6,1,2,4,5]=>4 [3,6,1,2,5,4]=>4 [3,6,1,4,2,5]=>1 [3,6,1,4,5,2]=>2 [3,6,1,5,2,4]=>1 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>4 [3,6,2,1,5,4]=>4 [3,6,2,4,1,5]=>1 [3,6,2,4,5,1]=>2 [3,6,2,5,1,4]=>1 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>2 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>1 [3,6,4,5,1,2]=>6 [3,6,4,5,2,1]=>6 [3,6,5,1,2,4]=>4 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>2 [3,6,5,4,1,2]=>6 [3,6,5,4,2,1]=>6 [4,1,2,3,5,6]=>6 [4,1,2,3,6,5]=>6 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>4 [4,1,3,2,5,6]=>6 [4,1,3,2,6,5]=>6 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>1 [4,1,3,6,5,2]=>2 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>1 [4,1,5,6,2,3]=>4 [4,1,5,6,3,2]=>4 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>1 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>1 [4,1,6,5,2,3]=>4 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>6 [4,2,1,3,6,5]=>6 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>4 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>10 [4,2,3,1,6,5]=>10 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>6 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>6 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>1 [4,2,5,3,1,6]=>1 [4,2,5,3,6,1]=>1 [4,2,5,6,1,3]=>2 [4,2,5,6,3,1]=>2 [4,2,6,1,3,5]=>1 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>1 [4,2,6,3,5,1]=>1 [4,2,6,5,1,3]=>2 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>10 [4,3,1,2,6,5]=>10 [4,3,1,5,2,6]=>2 [4,3,1,5,6,2]=>4 [4,3,1,6,2,5]=>2 [4,3,1,6,5,2]=>4 [4,3,2,1,5,6]=>10 [4,3,2,1,6,5]=>10 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>6 [4,3,2,6,1,5]=>3 [4,3,2,6,5,1]=>6 [4,3,5,1,2,6]=>6 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>6 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>10 [4,3,5,6,2,1]=>10 [4,3,6,1,2,5]=>4 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>4 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>10 [4,3,6,5,2,1]=>10 [4,5,1,2,3,6]=>6 [4,5,1,2,6,3]=>4 [4,5,1,3,2,6]=>6 [4,5,1,3,6,2]=>2 [4,5,1,6,2,3]=>4 [4,5,1,6,3,2]=>4 [4,5,2,1,3,6]=>6 [4,5,2,1,6,3]=>4 [4,5,2,3,1,6]=>8 [4,5,2,3,6,1]=>5 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>2 [4,5,3,1,2,6]=>8 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>8 [4,5,3,2,6,1]=>5 [4,5,3,6,1,2]=>6 [4,5,3,6,2,1]=>6 [4,5,6,1,2,3]=>9 [4,5,6,1,3,2]=>9 [4,5,6,2,1,3]=>9 [4,5,6,2,3,1]=>9 [4,5,6,3,1,2]=>9 [4,5,6,3,2,1]=>9 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>2 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>1 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>2 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>2 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>2 [4,6,2,5,1,3]=>1 [4,6,2,5,3,1]=>1 [4,6,3,1,2,5]=>3 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>3 [4,6,3,2,5,1]=>2 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>2 [4,6,5,1,2,3]=>9 [4,6,5,1,3,2]=>9 [4,6,5,2,1,3]=>9 [4,6,5,2,3,1]=>9 [4,6,5,3,1,2]=>9 [4,6,5,3,2,1]=>9 [5,1,2,3,4,6]=>5 [5,1,2,3,6,4]=>3 [5,1,2,4,3,6]=>5 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>4 [5,1,2,6,4,3]=>4 [5,1,3,2,4,6]=>5 [5,1,3,2,6,4]=>3 [5,1,3,4,2,6]=>3 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>1 [5,1,3,6,4,2]=>1 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>3 [5,1,4,3,6,2]=>2 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>2 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>3 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>3 [5,1,6,4,3,2]=>3 [5,2,1,3,4,6]=>5 [5,2,1,3,6,4]=>3 [5,2,1,4,3,6]=>5 [5,2,1,4,6,3]=>2 [5,2,1,6,3,4]=>4 [5,2,1,6,4,3]=>4 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>3 [5,2,3,4,1,6]=>3 [5,2,3,4,6,1]=>3 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>2 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>1 [5,2,4,3,1,6]=>3 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>1 [5,2,4,6,3,1]=>1 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>2 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>3 [5,3,1,2,6,4]=>3 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>1 [5,3,1,6,2,4]=>1 [5,3,1,6,4,2]=>1 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>3 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>3 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>8 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>8 [5,3,4,2,6,1]=>5 [5,3,4,6,1,2]=>6 [5,3,4,6,2,1]=>6 [5,3,6,1,2,4]=>2 [5,3,6,1,4,2]=>1 [5,3,6,2,1,4]=>2 [5,3,6,2,4,1]=>1 [5,3,6,4,1,2]=>2 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>6 [5,4,1,2,6,3]=>4 [5,4,1,3,2,6]=>6 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>4 [5,4,1,6,3,2]=>4 [5,4,2,1,3,6]=>6 [5,4,2,1,6,3]=>4 [5,4,2,3,1,6]=>8 [5,4,2,3,6,1]=>5 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>2 [5,4,3,1,2,6]=>8 [5,4,3,1,6,2]=>3 [5,4,3,2,1,6]=>8 [5,4,3,2,6,1]=>5 [5,4,3,6,1,2]=>6 [5,4,3,6,2,1]=>6 [5,4,6,1,2,3]=>9 [5,4,6,1,3,2]=>9 [5,4,6,2,1,3]=>9 [5,4,6,2,3,1]=>9 [5,4,6,3,1,2]=>9 [5,4,6,3,2,1]=>9 [5,6,1,2,3,4]=>10 [5,6,1,2,4,3]=>10 [5,6,1,3,2,4]=>10 [5,6,1,3,4,2]=>6 [5,6,1,4,2,3]=>6 [5,6,1,4,3,2]=>6 [5,6,2,1,3,4]=>10 [5,6,2,1,4,3]=>10 [5,6,2,3,1,4]=>6 [5,6,2,3,4,1]=>6 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>6 [5,6,3,1,2,4]=>6 [5,6,3,1,4,2]=>2 [5,6,3,2,1,4]=>6 [5,6,3,2,4,1]=>6 [5,6,3,4,1,2]=>13 [5,6,3,4,2,1]=>13 [5,6,4,1,2,3]=>9 [5,6,4,1,3,2]=>9 [5,6,4,2,1,3]=>9 [5,6,4,2,3,1]=>13 [5,6,4,3,1,2]=>13 [5,6,4,3,2,1]=>13 [6,1,2,3,4,5]=>8 [6,1,2,3,5,4]=>8 [6,1,2,4,3,5]=>8 [6,1,2,4,5,3]=>6 [6,1,2,5,3,4]=>6 [6,1,2,5,4,3]=>6 [6,1,3,2,4,5]=>8 [6,1,3,2,5,4]=>8 [6,1,3,4,2,5]=>3 [6,1,3,4,5,2]=>3 [6,1,3,5,2,4]=>1 [6,1,3,5,4,2]=>3 [6,1,4,2,3,5]=>3 [6,1,4,2,5,3]=>1 [6,1,4,3,2,5]=>3 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>5 [6,1,4,5,3,2]=>5 [6,1,5,2,3,4]=>3 [6,1,5,2,4,3]=>3 [6,1,5,3,2,4]=>3 [6,1,5,3,4,2]=>5 [6,1,5,4,2,3]=>5 [6,1,5,4,3,2]=>5 [6,2,1,3,4,5]=>8 [6,2,1,3,5,4]=>8 [6,2,1,4,3,5]=>8 [6,2,1,4,5,3]=>6 [6,2,1,5,3,4]=>6 [6,2,1,5,4,3]=>6 [6,2,3,1,4,5]=>6 [6,2,3,1,5,4]=>6 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>5 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>5 [6,2,4,1,3,5]=>1 [6,2,4,1,5,3]=>1 [6,2,4,3,1,5]=>3 [6,2,4,3,5,1]=>5 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>1 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>3 [6,3,1,2,4,5]=>6 [6,3,1,2,5,4]=>6 [6,3,1,4,2,5]=>1 [6,3,1,4,5,2]=>2 [6,3,1,5,2,4]=>1 [6,3,1,5,4,2]=>2 [6,3,2,1,4,5]=>6 [6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>5 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>5 [6,3,4,1,2,5]=>5 [6,3,4,1,5,2]=>2 [6,3,4,2,1,5]=>5 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>6 [6,3,4,5,2,1]=>6 [6,3,5,1,2,4]=>2 [6,3,5,1,4,2]=>1 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>1 [6,3,5,4,1,2]=>6 [6,3,5,4,2,1]=>6 [6,4,1,2,3,5]=>3 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>3 [6,4,1,3,5,2]=>1 [6,4,1,5,2,3]=>2 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>5 [6,4,2,3,5,1]=>3 [6,4,2,5,1,3]=>1 [6,4,2,5,3,1]=>1 [6,4,3,1,2,5]=>5 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>3 [6,4,3,5,1,2]=>6 [6,4,3,5,2,1]=>6 [6,4,5,1,2,3]=>9 [6,4,5,1,3,2]=>9 [6,4,5,2,1,3]=>9 [6,4,5,2,3,1]=>13 [6,4,5,3,1,2]=>13 [6,4,5,3,2,1]=>13 [6,5,1,2,3,4]=>10 [6,5,1,2,4,3]=>10 [6,5,1,3,2,4]=>10 [6,5,1,3,4,2]=>6 [6,5,1,4,2,3]=>6 [6,5,1,4,3,2]=>6 [6,5,2,1,3,4]=>10 [6,5,2,1,4,3]=>10 [6,5,2,3,1,4]=>6 [6,5,2,3,4,1]=>6 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>6 [6,5,3,1,2,4]=>6 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>6 [6,5,3,2,4,1]=>6 [6,5,3,4,1,2]=>13 [6,5,3,4,2,1]=>13 [6,5,4,1,2,3]=>9 [6,5,4,1,3,2]=>9 [6,5,4,2,1,3]=>9 [6,5,4,2,3,1]=>13 [6,5,4,3,1,2]=>13 [6,5,4,3,2,1]=>13 [1,2,3,4,5,6,7]=>21 [1,2,3,4,5,7,6]=>21 [1,2,3,4,6,5,7]=>21 [1,2,3,4,6,7,5]=>15 [1,2,3,4,7,5,6]=>15 [1,2,3,4,7,6,5]=>15 [1,2,3,5,4,6,7]=>21 [1,2,3,5,4,7,6]=>21 [1,2,3,5,6,4,7]=>9 [1,2,3,5,6,7,4]=>9 [1,2,3,5,7,4,6]=>3 [1,2,3,5,7,6,4]=>9 [1,2,3,6,4,5,7]=>9 [1,2,3,6,4,7,5]=>3 [1,2,3,6,5,4,7]=>9 [1,2,3,6,5,7,4]=>9 [1,2,3,6,7,4,5]=>15 [1,2,3,6,7,5,4]=>15 [1,2,3,7,4,5,6]=>9 [1,2,3,7,4,6,5]=>9 [1,2,3,7,5,4,6]=>9 [1,2,3,7,5,6,4]=>15 [1,2,3,7,6,4,5]=>15 [1,2,3,7,6,5,4]=>15 [1,2,4,3,5,6,7]=>21 [1,2,4,3,5,7,6]=>21 [1,2,4,3,6,5,7]=>21 [1,2,4,3,6,7,5]=>15 [1,2,4,3,7,5,6]=>15 [1,2,4,3,7,6,5]=>15 [1,2,4,5,3,6,7]=>12 [1,2,4,5,3,7,6]=>12 [1,2,4,5,6,3,7]=>6 [1,2,4,5,6,7,3]=>10 [1,2,4,5,7,3,6]=>4 [1,2,4,5,7,6,3]=>10 [1,2,4,6,3,5,7]=>2 [1,2,4,6,3,7,5]=>2 [1,2,4,6,5,3,7]=>6 [1,2,4,6,5,7,3]=>10 [1,2,4,6,7,3,5]=>4 [1,2,4,6,7,5,3]=>6 [1,2,4,7,3,5,6]=>4 [1,2,4,7,3,6,5]=>4 [1,2,4,7,5,3,6]=>2 [1,2,4,7,5,6,3]=>6 [1,2,4,7,6,3,5]=>4 [1,2,4,7,6,5,3]=>6 [1,2,5,3,4,6,7]=>12 [1,2,5,3,4,7,6]=>12 [1,2,5,3,6,4,7]=>2 [1,2,5,3,6,7,4]=>4 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>4 [1,2,5,4,3,6,7]=>12 [1,2,5,4,3,7,6]=>12 [1,2,5,4,6,3,7]=>6 [1,2,5,4,6,7,3]=>10 [1,2,5,4,7,3,6]=>4 [1,2,5,4,7,6,3]=>10 [1,2,5,6,3,4,7]=>10 [1,2,5,6,3,7,4]=>4 [1,2,5,6,4,3,7]=>10 [1,2,5,6,4,7,3]=>6 [1,2,5,6,7,3,4]=>12 [1,2,5,6,7,4,3]=>12 [1,2,5,7,3,4,6]=>4 [1,2,5,7,3,6,4]=>2 [1,2,5,7,4,3,6]=>4 [1,2,5,7,4,6,3]=>2 [1,2,5,7,6,3,4]=>12 [1,2,5,7,6,4,3]=>12 [1,2,6,3,4,5,7]=>6 [1,2,6,3,4,7,5]=>4 [1,2,6,3,5,4,7]=>6 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>4 [1,2,6,3,7,5,4]=>4 [1,2,6,4,3,5,7]=>6 [1,2,6,4,3,7,5]=>4 [1,2,6,4,5,3,7]=>10 [1,2,6,4,5,7,3]=>6 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>2 [1,2,6,5,3,4,7]=>10 [1,2,6,5,3,7,4]=>4 [1,2,6,5,4,3,7]=>10 [1,2,6,5,4,7,3]=>6 [1,2,6,5,7,3,4]=>12 [1,2,6,5,7,4,3]=>12 [1,2,6,7,3,4,5]=>12 [1,2,6,7,3,5,4]=>12 [1,2,6,7,4,3,5]=>12 [1,2,6,7,4,5,3]=>16 [1,2,6,7,5,3,4]=>16 [1,2,6,7,5,4,3]=>16 [1,2,7,3,4,5,6]=>10 [1,2,7,3,4,6,5]=>10 [1,2,7,3,5,4,6]=>10 [1,2,7,3,5,6,4]=>6 [1,2,7,3,6,4,5]=>6 [1,2,7,3,6,5,4]=>6 [1,2,7,4,3,5,6]=>10 [1,2,7,4,3,6,5]=>10 [1,2,7,4,5,3,6]=>6 [1,2,7,4,5,6,3]=>6 [1,2,7,4,6,3,5]=>2 [1,2,7,4,6,5,3]=>6 [1,2,7,5,3,4,6]=>6 [1,2,7,5,3,6,4]=>2 [1,2,7,5,4,3,6]=>6 [1,2,7,5,4,6,3]=>6 [1,2,7,5,6,3,4]=>16 [1,2,7,5,6,4,3]=>16 [1,2,7,6,3,4,5]=>12 [1,2,7,6,3,5,4]=>12 [1,2,7,6,4,3,5]=>12 [1,2,7,6,4,5,3]=>16 [1,2,7,6,5,3,4]=>16 [1,2,7,6,5,4,3]=>16 [1,3,2,4,5,6,7]=>21 [1,3,2,4,5,7,6]=>21 [1,3,2,4,6,5,7]=>21 [1,3,2,4,6,7,5]=>15 [1,3,2,4,7,5,6]=>15 [1,3,2,4,7,6,5]=>15 [1,3,2,5,4,6,7]=>21 [1,3,2,5,4,7,6]=>21 [1,3,2,5,6,4,7]=>9 [1,3,2,5,6,7,4]=>9 [1,3,2,5,7,4,6]=>3 [1,3,2,5,7,6,4]=>9 [1,3,2,6,4,5,7]=>9 [1,3,2,6,4,7,5]=>3 [1,3,2,6,5,4,7]=>9 [1,3,2,6,5,7,4]=>9 [1,3,2,6,7,4,5]=>15 [1,3,2,6,7,5,4]=>15 [1,3,2,7,4,5,6]=>9 [1,3,2,7,4,6,5]=>9 [1,3,2,7,5,4,6]=>9 [1,3,2,7,5,6,4]=>15 [1,3,2,7,6,4,5]=>15 [1,3,2,7,6,5,4]=>15 [1,3,4,2,5,6,7]=>9 [1,3,4,2,5,7,6]=>9 [1,3,4,2,6,5,7]=>9 [1,3,4,2,6,7,5]=>9 [1,3,4,2,7,5,6]=>9 [1,3,4,2,7,6,5]=>9 [1,3,4,5,2,6,7]=>6 [1,3,4,5,2,7,6]=>6 [1,3,4,5,6,2,7]=>5 [1,3,4,5,6,7,2]=>8 [1,3,4,5,7,2,6]=>3 [1,3,4,5,7,6,2]=>8 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>2 [1,3,4,6,5,2,7]=>5 [1,3,4,6,5,7,2]=>8 [1,3,4,6,7,2,5]=>4 [1,3,4,6,7,5,2]=>6 [1,3,4,7,2,5,6]=>4 [1,3,4,7,2,6,5]=>4 [1,3,4,7,5,2,6]=>2 [1,3,4,7,5,6,2]=>6 [1,3,4,7,6,2,5]=>4 [1,3,4,7,6,5,2]=>6 [1,3,5,2,4,6,7]=>2 [1,3,5,2,4,7,6]=>2 [1,3,5,2,6,4,7]=>1 [1,3,5,2,6,7,4]=>2 [1,3,5,2,7,4,6]=>1 [1,3,5,2,7,6,4]=>2 [1,3,5,4,2,6,7]=>6 [1,3,5,4,2,7,6]=>6 [1,3,5,4,6,2,7]=>5 [1,3,5,4,6,7,2]=>8 [1,3,5,4,7,2,6]=>3 [1,3,5,4,7,6,2]=>8 [1,3,5,6,2,4,7]=>2 [1,3,5,6,2,7,4]=>2 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>3 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>3 [1,3,5,7,2,4,6]=>1 [1,3,5,7,2,6,4]=>1 [1,3,5,7,4,2,6]=>1 [1,3,5,7,4,6,2]=>1 [1,3,5,7,6,2,4]=>3 [1,3,5,7,6,4,2]=>3 [1,3,6,2,4,5,7]=>2 [1,3,6,2,4,7,5]=>1 [1,3,6,2,5,4,7]=>2 [1,3,6,2,5,7,4]=>1 [1,3,6,2,7,4,5]=>2 [1,3,6,2,7,5,4]=>2 [1,3,6,4,2,5,7]=>1 [1,3,6,4,2,7,5]=>1 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>3 [1,3,6,4,7,2,5]=>1 [1,3,6,4,7,5,2]=>1 [1,3,6,5,2,4,7]=>2 [1,3,6,5,2,7,4]=>2 [1,3,6,5,4,2,7]=>3 [1,3,6,5,4,7,2]=>3 [1,3,6,5,7,2,4]=>3 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>4 [1,3,6,7,2,5,4]=>4 [1,3,6,7,4,2,5]=>2 [1,3,6,7,4,5,2]=>5 [1,3,6,7,5,2,4]=>3 [1,3,6,7,5,4,2]=>5 [1,3,7,2,4,5,6]=>3 [1,3,7,2,4,6,5]=>3 [1,3,7,2,5,4,6]=>3 [1,3,7,2,5,6,4]=>3 [1,3,7,2,6,4,5]=>3 [1,3,7,2,6,5,4]=>3 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>2 [1,3,7,4,5,2,6]=>2 [1,3,7,4,5,6,2]=>3 [1,3,7,4,6,2,5]=>1 [1,3,7,4,6,5,2]=>3 [1,3,7,5,2,4,6]=>1 [1,3,7,5,2,6,4]=>1 [1,3,7,5,4,2,6]=>2 [1,3,7,5,4,6,2]=>3 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>5 [1,3,7,6,2,4,5]=>4 [1,3,7,6,2,5,4]=>4 [1,3,7,6,4,2,5]=>2 [1,3,7,6,4,5,2]=>5 [1,3,7,6,5,2,4]=>3 [1,3,7,6,5,4,2]=>5 [1,4,2,3,5,6,7]=>9 [1,4,2,3,5,7,6]=>9 [1,4,2,3,6,5,7]=>9 [1,4,2,3,6,7,5]=>9 [1,4,2,3,7,5,6]=>9 [1,4,2,3,7,6,5]=>9 [1,4,2,5,3,6,7]=>2 [1,4,2,5,3,7,6]=>2 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>3 [1,4,2,5,7,3,6]=>1 [1,4,2,5,7,6,3]=>3 [1,4,2,6,3,5,7]=>1 [1,4,2,6,3,7,5]=>1 [1,4,2,6,5,3,7]=>2 [1,4,2,6,5,7,3]=>3 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>3 [1,4,2,7,3,5,6]=>2 [1,4,2,7,3,6,5]=>2 [1,4,2,7,5,3,6]=>1 [1,4,2,7,5,6,3]=>3 [1,4,2,7,6,3,5]=>2 [1,4,2,7,6,5,3]=>3 [1,4,3,2,5,6,7]=>9 [1,4,3,2,5,7,6]=>9 [1,4,3,2,6,5,7]=>9 [1,4,3,2,6,7,5]=>9 [1,4,3,2,7,5,6]=>9 [1,4,3,2,7,6,5]=>9 [1,4,3,5,2,6,7]=>6 [1,4,3,5,2,7,6]=>6 [1,4,3,5,6,2,7]=>5 [1,4,3,5,6,7,2]=>8 [1,4,3,5,7,2,6]=>3 [1,4,3,5,7,6,2]=>8 [1,4,3,6,2,5,7]=>2 [1,4,3,6,2,7,5]=>2 [1,4,3,6,5,2,7]=>5 [1,4,3,6,5,7,2]=>8 [1,4,3,6,7,2,5]=>4 [1,4,3,6,7,5,2]=>6 [1,4,3,7,2,5,6]=>4 [1,4,3,7,2,6,5]=>4 [1,4,3,7,5,2,6]=>2 [1,4,3,7,5,6,2]=>6 [1,4,3,7,6,2,5]=>4 [1,4,3,7,6,5,2]=>6 [1,4,5,2,3,6,7]=>10 [1,4,5,2,3,7,6]=>10 [1,4,5,2,6,3,7]=>2 [1,4,5,2,6,7,3]=>4 [1,4,5,2,7,3,6]=>2 [1,4,5,2,7,6,3]=>4 [1,4,5,3,2,6,7]=>10 [1,4,5,3,2,7,6]=>10 [1,4,5,3,6,2,7]=>3 [1,4,5,3,6,7,2]=>6 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>6 [1,4,5,6,2,3,7]=>6 [1,4,5,6,2,7,3]=>3 [1,4,5,6,3,2,7]=>6 [1,4,5,6,3,7,2]=>3 [1,4,5,6,7,2,3]=>10 [1,4,5,6,7,3,2]=>10 [1,4,5,7,2,3,6]=>4 [1,4,5,7,2,6,3]=>2 [1,4,5,7,3,2,6]=>4 [1,4,5,7,3,6,2]=>2 [1,4,5,7,6,2,3]=>10 [1,4,5,7,6,3,2]=>10 [1,4,6,2,3,5,7]=>2 [1,4,6,2,3,7,5]=>2 [1,4,6,2,5,3,7]=>1 [1,4,6,2,5,7,3]=>1 [1,4,6,2,7,3,5]=>1 [1,4,6,2,7,5,3]=>1 [1,4,6,3,2,5,7]=>2 [1,4,6,3,2,7,5]=>2 [1,4,6,3,5,2,7]=>1 [1,4,6,3,5,7,2]=>1 [1,4,6,3,7,2,5]=>1 [1,4,6,3,7,5,2]=>1 [1,4,6,5,2,3,7]=>6 [1,4,6,5,2,7,3]=>3 [1,4,6,5,3,2,7]=>6 [1,4,6,5,3,7,2]=>3
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Description
The number of permutations obtained by switching adjacencies or successions.
For a permutation $\pi$, this statistic is the size of its equivalence class of the equivalence relation generated by the interchange of any two adjacent elements $\pi_i$ and $\pi_{i+1}$ such that $|\pi_i - \pi_{i+1}| = 1$.
References
[1] Stanley, R. P. An equivalence relation on the symmetric group and multiplicity-free flag $h$-vectors MathSciNet:3029438 arXiv:1208.3540
[2] Amdeberhan, T. "flavored" equivalence classes of permutations MathOverflow:256673
Code
def statistic(pi):
    def children(a):
        for i in range(len(a)-1):
            d = a[i] - a[i+1]
            if d == 1 or d == -1:
                yield Permutation(a[:i] + [a[i+1], a[i]] + a[i+2:])

    return len([1 for pi in RecursivelyEnumeratedSet([Permutation(pi)], children)])

Created
Apr 05, 2016 at 17:34 by Jiang Zeng
Updated
May 10, 2019 at 17:36 by Henning Ulfarsson