edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>1 [1,2,3,4]=>1 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>1 [1,4,2,3]=>1 [1,4,3,2]=>1 [2,1,3,4]=>1 [2,1,4,3]=>1 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>1 [2,4,3,1]=>1 [3,1,2,4]=>1 [3,1,4,2]=>1 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>2 [3,4,2,1]=>1 [4,1,2,3]=>1 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>2 [4,3,1,2]=>1 [4,3,2,1]=>1 [1,2,3,4,5]=>1 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>1 [1,2,5,3,4]=>1 [1,2,5,4,3]=>1 [1,3,2,4,5]=>1 [1,3,2,5,4]=>1 [1,3,4,2,5]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>1 [1,4,2,3,5]=>1 [1,4,2,5,3]=>1 [1,4,3,2,5]=>1 [1,4,3,5,2]=>1 [1,4,5,2,3]=>2 [1,4,5,3,2]=>1 [1,5,2,3,4]=>1 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>2 [1,5,4,2,3]=>1 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>1 [2,1,5,3,4]=>1 [2,1,5,4,3]=>1 [2,3,1,4,5]=>1 [2,3,1,5,4]=>1 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>1 [2,3,5,4,1]=>1 [2,4,1,3,5]=>1 [2,4,1,5,3]=>1 [2,4,3,1,5]=>1 [2,4,3,5,1]=>1 [2,4,5,1,3]=>2 [2,4,5,3,1]=>1 [2,5,1,3,4]=>1 [2,5,1,4,3]=>1 [2,5,3,1,4]=>1 [2,5,3,4,1]=>2 [2,5,4,1,3]=>1 [2,5,4,3,1]=>1 [3,1,2,4,5]=>1 [3,1,2,5,4]=>1 [3,1,4,2,5]=>1 [3,1,4,5,2]=>1 [3,1,5,2,4]=>1 [3,1,5,4,2]=>1 [3,2,1,4,5]=>1 [3,2,1,5,4]=>1 [3,2,4,1,5]=>1 [3,2,4,5,1]=>1 [3,2,5,1,4]=>1 [3,2,5,4,1]=>1 [3,4,1,2,5]=>2 [3,4,1,5,2]=>2 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>3 [3,4,5,2,1]=>1 [3,5,1,2,4]=>2 [3,5,1,4,2]=>2 [3,5,2,1,4]=>1 [3,5,2,4,1]=>2 [3,5,4,1,2]=>2 [3,5,4,2,1]=>1 [4,1,2,3,5]=>1 [4,1,2,5,3]=>1 [4,1,3,2,5]=>1 [4,1,3,5,2]=>1 [4,1,5,2,3]=>2 [4,1,5,3,2]=>1 [4,2,1,3,5]=>1 [4,2,1,5,3]=>1 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>2 [4,2,5,3,1]=>2 [4,3,1,2,5]=>1 [4,3,1,5,2]=>1 [4,3,2,1,5]=>1 [4,3,2,5,1]=>1 [4,3,5,1,2]=>2 [4,3,5,2,1]=>1 [4,5,1,2,3]=>3 [4,5,1,3,2]=>2 [4,5,2,1,3]=>2 [4,5,2,3,1]=>3 [4,5,3,1,2]=>2 [4,5,3,2,1]=>1 [5,1,2,3,4]=>1 [5,1,2,4,3]=>1 [5,1,3,2,4]=>1 [5,1,3,4,2]=>2 [5,1,4,2,3]=>1 [5,1,4,3,2]=>1 [5,2,1,3,4]=>1 [5,2,1,4,3]=>1 [5,2,3,1,4]=>2 [5,2,3,4,1]=>4 [5,2,4,1,3]=>2 [5,2,4,3,1]=>2 [5,3,1,2,4]=>1 [5,3,1,4,2]=>2 [5,3,2,1,4]=>1 [5,3,2,4,1]=>2 [5,3,4,1,2]=>3 [5,3,4,2,1]=>2 [5,4,1,2,3]=>1 [5,4,1,3,2]=>1 [5,4,2,1,3]=>1 [5,4,2,3,1]=>2 [5,4,3,1,2]=>1 [5,4,3,2,1]=>1 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>1 [1,2,3,6,5,4]=>1 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>1 [1,2,4,6,5,3]=>1 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>1 [1,2,5,4,6,3]=>1 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>1 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>1 [1,2,6,4,3,5]=>1 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>1 [1,2,6,5,4,3]=>1 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>1 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>1 [1,3,2,6,4,5]=>1 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>1 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>1 [1,3,4,6,5,2]=>1 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>1 [1,3,5,4,6,2]=>1 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>1 [1,3,6,2,4,5]=>1 [1,3,6,2,5,4]=>1 [1,3,6,4,2,5]=>1 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>1 [1,3,6,5,4,2]=>1 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>1 [1,4,2,5,3,6]=>1 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>1 [1,4,2,6,5,3]=>1 [1,4,3,2,5,6]=>1 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>1 [1,4,3,5,6,2]=>1 [1,4,3,6,2,5]=>1 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>2 [1,4,6,3,2,5]=>1 [1,4,6,3,5,2]=>2 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>1 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>1 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>1 [1,5,3,2,4,6]=>1 [1,5,3,2,6,4]=>1 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>2 [1,5,3,6,4,2]=>2 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>1 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>1 [1,5,4,6,2,3]=>2 [1,5,4,6,3,2]=>1 [1,5,6,2,3,4]=>3 [1,5,6,2,4,3]=>2 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>3 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>1 [1,6,2,4,3,5]=>1 [1,6,2,4,5,3]=>2 [1,6,2,5,3,4]=>1 [1,6,2,5,4,3]=>1 [1,6,3,2,4,5]=>1 [1,6,3,2,5,4]=>1 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>4 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>2 [1,6,4,2,3,5]=>1 [1,6,4,2,5,3]=>2 [1,6,4,3,2,5]=>1 [1,6,4,3,5,2]=>2 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>2 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>1 [1,6,5,3,2,4]=>1 [1,6,5,3,4,2]=>2 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>1 [2,1,3,6,4,5]=>1 [2,1,3,6,5,4]=>1 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>1 [2,1,4,5,3,6]=>1 [2,1,4,5,6,3]=>1 [2,1,4,6,3,5]=>1 [2,1,4,6,5,3]=>1 [2,1,5,3,4,6]=>1 [2,1,5,3,6,4]=>1 [2,1,5,4,3,6]=>1 [2,1,5,4,6,3]=>1 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>1 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>1 [2,1,6,4,3,5]=>1 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>1 [2,3,1,5,4,6]=>1 [2,3,1,5,6,4]=>1 [2,3,1,6,4,5]=>1 [2,3,1,6,5,4]=>1 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>1 [2,3,4,6,5,1]=>1 [2,3,5,1,4,6]=>1 [2,3,5,1,6,4]=>1 [2,3,5,4,1,6]=>1 [2,3,5,4,6,1]=>1 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>1 [2,3,6,1,4,5]=>1 [2,3,6,1,5,4]=>1 [2,3,6,4,1,5]=>1 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>1 [2,3,6,5,4,1]=>1 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>1 [2,4,1,5,3,6]=>1 [2,4,1,5,6,3]=>1 [2,4,1,6,3,5]=>1 [2,4,1,6,5,3]=>1 [2,4,3,1,5,6]=>1 [2,4,3,1,6,5]=>1 [2,4,3,5,1,6]=>1 [2,4,3,5,6,1]=>1 [2,4,3,6,1,5]=>1 [2,4,3,6,5,1]=>1 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>1 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>1 [2,4,6,1,3,5]=>2 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>1 [2,4,6,3,5,1]=>2 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>1 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>1 [2,5,1,4,3,6]=>1 [2,5,1,4,6,3]=>1 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>1 [2,5,3,1,4,6]=>1 [2,5,3,1,6,4]=>1 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>2 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>2 [2,5,4,1,3,6]=>1 [2,5,4,1,6,3]=>1 [2,5,4,3,1,6]=>1 [2,5,4,3,6,1]=>1 [2,5,4,6,1,3]=>2 [2,5,4,6,3,1]=>1 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>2 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>1 [2,6,1,3,4,5]=>1 [2,6,1,3,5,4]=>1 [2,6,1,4,3,5]=>1 [2,6,1,4,5,3]=>2 [2,6,1,5,3,4]=>1 [2,6,1,5,4,3]=>1 [2,6,3,1,4,5]=>1 [2,6,3,1,5,4]=>1 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>4 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>2 [2,6,4,1,3,5]=>1 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>1 [2,6,4,3,5,1]=>2 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>2 [2,6,5,1,3,4]=>1 [2,6,5,1,4,3]=>1 [2,6,5,3,1,4]=>1 [2,6,5,3,4,1]=>2 [2,6,5,4,1,3]=>1 [2,6,5,4,3,1]=>1 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>1 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>1 [3,1,2,6,5,4]=>1 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>1 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>1 [3,1,4,6,2,5]=>1 [3,1,4,6,5,2]=>1 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>1 [3,1,5,4,2,6]=>1 [3,1,5,4,6,2]=>1 [3,1,5,6,2,4]=>2 [3,1,5,6,4,2]=>1 [3,1,6,2,4,5]=>1 [3,1,6,2,5,4]=>1 [3,1,6,4,2,5]=>1 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>1 [3,1,6,5,4,2]=>1 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>1 [3,2,1,5,4,6]=>1 [3,2,1,5,6,4]=>1 [3,2,1,6,4,5]=>1 [3,2,1,6,5,4]=>1 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>1 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>1 [3,2,4,6,1,5]=>1 [3,2,4,6,5,1]=>1 [3,2,5,1,4,6]=>1 [3,2,5,1,6,4]=>1 [3,2,5,4,1,6]=>1 [3,2,5,4,6,1]=>1 [3,2,5,6,1,4]=>2 [3,2,5,6,4,1]=>1 [3,2,6,1,4,5]=>1 [3,2,6,1,5,4]=>1 [3,2,6,4,1,5]=>1 [3,2,6,4,5,1]=>2 [3,2,6,5,1,4]=>1 [3,2,6,5,4,1]=>1 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>2 [3,4,2,1,5,6]=>1 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>1 [3,4,2,5,6,1]=>1 [3,4,2,6,1,5]=>1 [3,4,2,6,5,1]=>1 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>1 [3,4,5,6,1,2]=>5 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>1 [3,4,6,2,5,1]=>2 [3,4,6,5,1,2]=>3 [3,4,6,5,2,1]=>1 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>2 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>2 [3,5,1,6,2,4]=>4 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>1 [3,5,2,1,6,4]=>1 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>2 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>2 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>2 [3,5,4,2,1,6]=>1 [3,5,4,2,6,1]=>1 [3,5,4,6,1,2]=>4 [3,5,4,6,2,1]=>1 [3,5,6,1,2,4]=>5 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>3 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>2 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>4 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>1 [3,6,2,1,5,4]=>1 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>4 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>2 [3,6,4,1,5,2]=>4 [3,6,4,2,1,5]=>1 [3,6,4,2,5,1]=>2 [3,6,4,5,1,2]=>6 [3,6,4,5,2,1]=>2 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>1 [3,6,5,2,4,1]=>2 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>1 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>1 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>1 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>1 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>1 [4,1,3,6,5,2]=>1 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>2 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>1 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>1 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>1 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>2 [4,1,6,5,3,2]=>1 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>1 [4,2,1,5,3,6]=>1 [4,2,1,5,6,3]=>1 [4,2,1,6,3,5]=>1 [4,2,1,6,5,3]=>1 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>2 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>2 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>2 [4,2,5,3,1,6]=>2 [4,2,5,3,6,1]=>2 [4,2,5,6,1,3]=>3 [4,2,5,6,3,1]=>2 [4,2,6,1,3,5]=>2 [4,2,6,1,5,3]=>2 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>4 [4,2,6,5,1,3]=>2 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>1 [4,3,1,2,6,5]=>1 [4,3,1,5,2,6]=>1 [4,3,1,5,6,2]=>1 [4,3,1,6,2,5]=>1 [4,3,1,6,5,2]=>1 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>1 [4,3,2,5,1,6]=>1 [4,3,2,5,6,1]=>1 [4,3,2,6,1,5]=>1 [4,3,2,6,5,1]=>1 [4,3,5,1,2,6]=>2 [4,3,5,1,6,2]=>2 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>1 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>1 [4,3,6,1,2,5]=>2 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>1 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>1 [4,5,1,2,3,6]=>3 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>2 [4,5,1,6,2,3]=>5 [4,5,1,6,3,2]=>2 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>2 [4,5,2,3,1,6]=>3 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>3 [4,5,2,6,3,1]=>3 [4,5,3,1,2,6]=>2 [4,5,3,1,6,2]=>2 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>1 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>10 [4,5,6,1,3,2]=>4 [4,5,6,2,1,3]=>4 [4,5,6,2,3,1]=>6 [4,5,6,3,1,2]=>3 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>3 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>4 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>2 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>2 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>6 [4,6,2,5,1,3]=>3 [4,6,2,5,3,1]=>3 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>3 [4,6,3,2,1,5]=>1 [4,6,3,2,5,1]=>2 [4,6,3,5,1,2]=>4 [4,6,3,5,2,1]=>2 [4,6,5,1,2,3]=>4 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>4 [4,6,5,3,1,2]=>2 [4,6,5,3,2,1]=>1 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>1 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>1 [5,1,3,2,4,6]=>1 [5,1,3,2,6,4]=>1 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>1 [5,1,4,3,6,2]=>1 [5,1,4,6,2,3]=>2 [5,1,4,6,3,2]=>1 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>2 [5,1,6,3,2,4]=>2 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>2 [5,1,6,4,3,2]=>1 [5,2,1,3,4,6]=>1 [5,2,1,3,6,4]=>1 [5,2,1,4,3,6]=>1 [5,2,1,4,6,3]=>1 [5,2,1,6,3,4]=>2 [5,2,1,6,4,3]=>1 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>4 [5,2,3,4,6,1]=>4 [5,2,3,6,1,4]=>4 [5,2,3,6,4,1]=>4 [5,2,4,1,3,6]=>2 [5,2,4,1,6,3]=>2 [5,2,4,3,1,6]=>2 [5,2,4,3,6,1]=>2 [5,2,4,6,1,3]=>4 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>4 [5,2,6,3,4,1]=>6 [5,2,6,4,1,3]=>3 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>1 [5,3,1,4,2,6]=>2 [5,3,1,4,6,2]=>2 [5,3,1,6,2,4]=>2 [5,3,1,6,4,2]=>2 [5,3,2,1,4,6]=>1 [5,3,2,1,6,4]=>1 [5,3,2,4,1,6]=>2 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>3 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>2 [5,3,4,6,1,2]=>6 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>3 [5,3,6,2,1,4]=>2 [5,3,6,2,4,1]=>3 [5,3,6,4,1,2]=>4 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>1 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>1 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>1 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>1 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>2 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>2 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>1 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>1 [5,4,3,6,1,2]=>2 [5,4,3,6,2,1]=>1 [5,4,6,1,2,3]=>4 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>4 [5,4,6,3,1,2]=>2 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>5 [5,6,1,2,4,3]=>3 [5,6,1,3,2,4]=>4 [5,6,1,3,4,2]=>6 [5,6,1,4,2,3]=>3 [5,6,1,4,3,2]=>2 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>2 [5,6,2,3,1,4]=>6 [5,6,2,3,4,1]=>9 [5,6,2,4,1,3]=>4 [5,6,2,4,3,1]=>3 [5,6,3,1,2,4]=>3 [5,6,3,1,4,2]=>4 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>8 [5,6,3,4,2,1]=>4 [5,6,4,1,2,3]=>3 [5,6,4,1,3,2]=>2 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>3 [5,6,4,3,1,2]=>2 [5,6,4,3,2,1]=>1 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>1 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>1 [6,1,2,5,4,3]=>1 [6,1,3,2,4,5]=>1 [6,1,3,2,5,4]=>1 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>4 [6,1,3,5,2,4]=>2 [6,1,3,5,4,2]=>2 [6,1,4,2,3,5]=>1 [6,1,4,2,5,3]=>2 [6,1,4,3,2,5]=>1 [6,1,4,3,5,2]=>2 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>2 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>1 [6,1,5,3,2,4]=>1 [6,1,5,3,4,2]=>2 [6,1,5,4,2,3]=>1 [6,1,5,4,3,2]=>1 [6,2,1,3,4,5]=>1 [6,2,1,3,5,4]=>1 [6,2,1,4,3,5]=>1 [6,2,1,4,5,3]=>2 [6,2,1,5,3,4]=>1 [6,2,1,5,4,3]=>1 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>2 [6,2,3,4,1,5]=>4 [6,2,3,4,5,1]=>8 [6,2,3,5,1,4]=>4 [6,2,3,5,4,1]=>4 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>4 [6,2,4,3,1,5]=>2 [6,2,4,3,5,1]=>4 [6,2,4,5,1,3]=>6 [6,2,4,5,3,1]=>4 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>4 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>1 [6,3,1,2,5,4]=>1 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>4 [6,3,1,5,2,4]=>2 [6,3,1,5,4,2]=>2 [6,3,2,1,4,5]=>1 [6,3,2,1,5,4]=>1 [6,3,2,4,1,5]=>2 [6,3,2,4,5,1]=>4 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>6 [6,3,4,2,1,5]=>2 [6,3,4,2,5,1]=>4 [6,3,4,5,1,2]=>9 [6,3,4,5,2,1]=>4 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>3 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>3 [6,3,5,4,2,1]=>2 [6,4,1,2,3,5]=>1 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>1 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>1 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>2 [6,4,2,3,5,1]=>4 [6,4,2,5,1,3]=>3 [6,4,2,5,3,1]=>4 [6,4,3,1,2,5]=>1 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>2 [6,4,3,5,1,2]=>3 [6,4,3,5,2,1]=>2 [6,4,5,1,2,3]=>6 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>8 [6,4,5,3,1,2]=>3 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>1 [6,5,1,3,2,4]=>1 [6,5,1,3,4,2]=>2 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>1 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>1 [6,5,2,3,1,4]=>2 [6,5,2,3,4,1]=>4 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>2 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>2 [6,5,3,4,1,2]=>4 [6,5,3,4,2,1]=>3 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>1 [6,5,4,2,1,3]=>1 [6,5,4,2,3,1]=>2 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>1 [1,2,3,4,5,6,7]=>1 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,6,4,7,5]=>1 [1,2,6,3,4,7,5]=>1 [1,3,2,4,5,6,7]=>1 [1,3,7,2,4,5,6]=>1 [1,3,7,6,5,4,2]=>1 [1,4,6,7,2,3,5]=>5 [1,4,6,7,5,3,2]=>1 [1,4,7,2,3,5,6]=>2 [1,4,7,6,5,3,2]=>1 [1,5,2,3,4,7,6]=>1 [1,5,2,7,3,4,6]=>2 [1,5,4,7,6,3,2]=>1 [1,5,6,2,7,3,4]=>5 [1,5,6,4,7,3,2]=>1 [1,5,6,7,2,3,4]=>10 [1,5,6,7,4,3,2]=>1 [1,5,7,2,3,4,6]=>3 [1,5,7,6,4,3,2]=>1 [1,6,2,3,4,7,5]=>1 [1,6,2,3,7,4,5]=>2 [1,6,2,7,3,4,5]=>3 [1,6,5,4,3,7,2]=>1 [1,6,5,4,7,3,2]=>1 [1,6,5,7,4,3,2]=>1 [1,6,7,2,3,4,5]=>5 [1,6,7,5,4,3,2]=>1 [1,7,2,3,4,5,6]=>1 [1,7,3,5,6,4,2]=>4 [1,7,3,6,5,4,2]=>2 [1,7,4,3,6,5,2]=>3 [1,7,4,5,3,6,2]=>4 [1,7,4,5,6,3,2]=>4 [1,7,4,6,5,3,2]=>2 [1,7,5,4,3,6,2]=>2 [1,7,5,4,6,3,2]=>2 [1,7,6,4,5,3,2]=>3 [1,7,6,5,4,3,2]=>1 [2,1,3,4,5,6,7]=>1 [2,1,3,4,7,5,6]=>1 [2,1,3,7,4,5,6]=>1 [2,1,6,3,4,5,7]=>1 [2,1,7,3,4,5,6]=>1 [2,1,7,6,5,4,3]=>1 [2,3,1,4,5,6,7]=>1 [2,3,4,1,5,6,7]=>1 [2,3,4,1,5,7,6]=>1 [2,3,4,5,1,6,7]=>1 [2,3,4,5,1,7,6]=>1 [2,3,4,5,6,1,7]=>1 [2,3,4,5,6,7,1]=>1 [2,3,4,5,7,1,6]=>1 [2,3,4,6,1,7,5]=>1 [2,3,4,6,7,1,5]=>2 [2,3,4,7,1,5,6]=>1 [2,3,5,6,7,1,4]=>3 [2,4,1,3,5,6,7]=>1 [2,5,1,3,4,6,7]=>1 [2,5,7,1,3,4,6]=>3 [2,6,1,3,4,5,7]=>1 [2,6,1,7,3,4,5]=>3 [2,6,5,4,3,1,7]=>1 [2,6,7,1,3,4,5]=>5 [2,7,1,3,4,5,6]=>1 [3,1,2,4,5,6,7]=>1 [3,1,2,4,5,7,6]=>1 [3,2,1,4,5,6,7]=>1 [3,2,4,5,6,7,1]=>1 [3,4,1,2,5,6,7]=>2 [3,4,2,5,6,7,1]=>1 [3,4,5,2,6,7,1]=>1 [3,4,5,6,2,7,1]=>1 [3,4,5,6,7,1,2]=>8 [3,5,6,1,2,4,7]=>5 [3,5,6,4,2,1,7]=>1 [3,6,1,2,4,5,7]=>2 [3,6,5,4,2,1,7]=>1 [4,1,2,3,5,6,7]=>1 [4,1,2,3,5,7,6]=>1 [4,1,6,2,3,5,7]=>2 [4,2,3,5,6,7,1]=>2 [4,2,5,1,3,6,7]=>2 [4,3,2,1,5,6,7]=>1 [4,3,2,5,6,7,1]=>1 [4,3,5,2,6,7,1]=>1 [4,3,6,5,2,1,7]=>1 [4,5,1,6,2,3,7]=>5 [4,5,2,3,6,7,1]=>3 [4,5,3,6,2,1,7]=>1 [4,5,6,1,2,3,7]=>10 [4,5,6,3,2,1,7]=>1 [4,6,1,2,3,5,7]=>3 [4,6,1,2,3,7,5]=>3 [4,6,5,3,2,1,7]=>1 [5,1,2,3,4,6,7]=>1 [5,1,2,3,4,7,6]=>1 [5,1,2,3,6,4,7]=>1 [5,1,2,3,6,7,4]=>1 [5,1,2,3,7,4,6]=>1 [5,1,2,6,3,4,7]=>2 [5,1,6,2,3,4,7]=>3 [5,1,6,2,3,7,4]=>3 [5,2,3,4,6,7,1]=>4 [5,2,6,7,1,3,4]=>10 [5,3,2,4,6,7,1]=>2 [5,3,2,6,1,4,7]=>2 [5,3,6,7,1,2,4]=>10 [5,4,3,2,1,6,7]=>1 [5,4,3,2,1,7,6]=>1 [5,4,3,2,6,1,7]=>1 [5,4,3,6,2,1,7]=>1 [5,4,6,3,2,1,7]=>1 [5,4,6,7,1,2,3]=>12 [5,6,1,2,3,4,7]=>5 [5,6,1,2,3,7,4]=>5 [5,6,3,4,1,2,7]=>8 [5,6,4,3,2,1,7]=>1 [5,6,7,1,2,3,4]=>26 [6,1,2,3,4,5,7]=>1 [6,1,2,3,4,7,5]=>1 [6,1,2,3,7,4,5]=>2 [6,1,2,7,3,4,5]=>3 [6,2,3,4,5,7,1]=>8 [6,2,4,5,3,1,7]=>4 [6,2,5,4,3,1,7]=>2 [6,3,2,5,4,1,7]=>3 [6,3,4,2,5,1,7]=>4 [6,3,4,5,2,1,7]=>4 [6,3,4,7,1,2,5]=>9 [6,3,5,4,2,1,7]=>2 [6,4,3,2,5,1,7]=>2 [6,4,3,2,7,1,5]=>2 [6,4,3,5,2,1,7]=>2 [6,4,5,7,1,2,3]=>20 [6,4,7,2,5,1,3]=>8 [6,4,7,3,5,1,2]=>8 [6,5,3,4,2,1,7]=>3 [6,5,4,3,2,1,7]=>1 [6,5,7,3,4,1,2]=>10 [6,7,1,2,3,4,5]=>8 [6,7,3,4,1,2,5]=>14 [6,7,4,5,1,2,3]=>17 [7,1,2,3,4,5,6]=>1 [7,2,1,3,4,5,6]=>1 [7,2,3,1,4,5,6]=>2 [7,2,3,4,1,5,6]=>4 [7,2,3,4,5,1,6]=>8 [7,3,1,2,4,5,6]=>1 [7,3,2,1,4,5,6]=>1 [7,3,2,4,1,5,6]=>2 [7,3,4,1,2,5,6]=>3 [7,4,1,2,3,5,6]=>1 [7,4,2,1,3,5,6]=>1 [7,4,5,6,1,2,3]=>31 [7,5,1,2,3,4,6]=>1 [7,5,6,1,2,3,4]=>11 [7,5,6,3,4,1,2]=>17 [7,6,1,2,3,4,5]=>1 [7,6,4,5,1,2,3]=>7 [7,6,5,1,2,3,4]=>1 [7,6,5,3,4,1,2]=>4 [7,6,5,4,1,2,3]=>1 [7,6,5,4,3,1,2]=>1 [7,6,5,4,3,2,1]=>1 [8,7,6,5,4,3,2,1]=>1 [7,6,8,5,4,3,2,1]=>1 [7,8,5,6,4,3,2,1]=>4 [7,8,6,4,5,3,2,1]=>5 [8,6,7,4,5,3,2,1]=>12 [7,6,5,4,8,3,2,1]=>1 [6,5,7,4,8,3,2,1]=>1 [7,8,6,5,3,4,2,1]=>4 [8,6,7,5,3,4,2,1]=>10 [8,7,5,6,3,4,2,1]=>18 [6,7,8,3,4,5,2,1]=>49 [7,8,6,5,4,2,3,1]=>3 [8,6,7,5,4,2,3,1]=>8 [8,7,5,6,4,2,3,1]=>10 [8,7,6,4,5,2,3,1]=>12 [8,6,5,7,3,2,4,1]=>10 [6,7,8,5,2,3,4,1]=>31 [8,5,6,7,2,3,4,1]=>198 [7,8,3,2,4,5,6,1]=>27 [7,6,5,4,3,2,8,1]=>1 [6,5,7,4,3,2,8,1]=>1 [6,5,4,3,7,2,8,1]=>1 [5,4,6,3,7,2,8,1]=>1 [3,4,5,2,6,7,8,1]=>1 [5,2,3,4,6,7,8,1]=>4 [4,3,2,5,6,7,8,1]=>1 [3,4,2,5,6,7,8,1]=>1 [4,2,3,5,6,7,8,1]=>2 [3,2,4,5,6,7,8,1]=>1 [2,3,4,5,6,7,8,1]=>1 [8,7,6,5,4,3,1,2]=>1 [7,8,6,5,4,3,1,2]=>2 [8,6,7,5,4,3,1,2]=>3 [8,7,5,6,4,3,1,2]=>4 [8,7,6,4,5,3,1,2]=>5 [8,7,6,5,3,4,1,2]=>4 [8,7,5,6,3,4,1,2]=>28 [7,8,5,6,3,4,1,2]=>56 [5,6,7,8,3,4,1,2]=>42 [7,8,3,4,5,6,1,2]=>239 [3,4,5,6,7,8,1,2]=>13 [8,7,6,5,4,2,1,3]=>1 [7,6,8,5,4,2,1,3]=>3 [8,7,6,5,4,1,2,3]=>1 [6,7,8,5,4,1,2,3]=>10 [8,5,6,7,4,1,2,3]=>31 [8,7,6,4,5,1,2,3]=>8 [8,6,7,4,5,1,2,3]=>48 [8,7,4,5,6,1,2,3]=>49 [7,8,4,5,6,1,2,3]=>166 [6,7,4,5,8,1,2,3]=>62 [7,6,5,8,3,2,1,4]=>4 [7,5,6,8,2,3,1,4]=>72 [6,7,5,8,3,1,2,4]=>13 [6,5,7,8,2,1,3,4]=>24 [8,7,6,5,1,2,3,4]=>1 [8,7,5,6,1,2,3,4]=>14 [7,8,5,6,1,2,3,4]=>42 [8,5,6,7,1,2,3,4]=>114 [5,6,7,8,1,2,3,4]=>145 [8,7,6,4,3,2,1,5]=>1 [8,7,6,4,2,1,3,5]=>1 [8,7,6,1,2,3,4,5]=>1 [8,6,7,1,2,3,4,5]=>20 [6,7,8,1,2,3,4,5]=>73 [7,8,5,4,2,1,3,6]=>3 [7,8,5,4,1,2,3,6]=>5 [8,7,1,2,3,4,5,6]=>1 [7,8,1,2,3,4,5,6]=>13 [8,6,5,4,3,2,1,7]=>1 [8,6,5,4,3,1,2,7]=>1 [8,5,6,3,4,1,2,7]=>17 [8,6,5,4,2,1,3,7]=>1 [8,6,4,3,2,1,5,7]=>1 [8,6,4,2,1,3,5,7]=>1 [8,2,3,4,1,5,6,7]=>4 [8,4,1,2,3,5,6,7]=>1 [8,3,2,1,4,5,6,7]=>1 [8,2,3,1,4,5,6,7]=>2 [8,3,1,2,4,5,6,7]=>1 [8,2,1,3,4,5,6,7]=>1 [8,1,2,3,4,5,6,7]=>1 [7,6,5,4,3,2,1,8]=>1 [6,7,5,4,3,2,1,8]=>1 [6,5,7,4,3,2,1,8]=>1 [5,6,7,4,3,2,1,8]=>1 [7,6,4,5,3,2,1,8]=>3 [6,5,4,7,3,2,1,8]=>1 [7,5,6,3,4,2,1,8]=>10 [7,6,4,3,5,2,1,8]=>3 [7,6,3,4,5,2,1,8]=>9 [7,5,4,3,6,2,1,8]=>2 [6,7,5,4,2,3,1,8]=>3 [6,5,7,3,2,4,1,8]=>4 [5,6,7,2,3,4,1,8]=>31 [2,3,4,5,6,7,1,8]=>1 [5,6,7,1,2,3,4,8]=>26 [6,7,1,2,3,4,5,8]=>8 [7,1,2,3,4,5,6,8]=>1 [6,5,4,3,2,1,7,8]=>1 [2,3,4,5,6,1,7,8]=>1 [5,6,3,4,1,2,7,8]=>8 [4,5,6,1,2,3,7,8]=>10 [6,1,2,3,4,5,7,8]=>1 [5,4,3,2,1,6,7,8]=>1 [2,3,4,5,1,6,7,8]=>1 [5,1,2,3,4,6,7,8]=>1 [4,3,2,1,5,6,7,8]=>1 [3,4,1,2,5,6,7,8]=>2 [3,2,1,4,5,6,7,8]=>1 [2,1,3,4,5,6,7,8]=>1 [1,2,3,4,5,6,7,8]=>1 [6,5,8,7,4,3,2,1]=>1 [3,5,8,7,6,4,2,1]=>1 [4,3,6,5,8,7,2,1]=>1 [2,6,8,7,5,4,3,1]=>1 [2,3,5,6,8,7,4,1]=>1 [3,2,6,5,4,8,7,1]=>1 [4,3,6,5,7,2,8,1]=>1 [3,2,6,5,7,4,8,1]=>1 [4,3,5,2,7,6,8,1]=>1 [3,2,5,4,7,6,8,1]=>1 [1,8,7,6,5,4,3,2]=>1 [1,7,8,6,5,4,3,2]=>1 [1,6,8,7,5,4,3,2]=>1 [1,7,6,8,5,4,3,2]=>1 [1,6,7,8,5,4,3,2]=>1 [1,5,8,7,6,4,3,2]=>1 [1,7,6,5,8,4,3,2]=>1 [1,3,5,7,8,6,4,2]=>1 [1,4,3,8,7,6,5,2]=>1 [1,6,5,4,3,8,7,2]=>1 [1,4,3,6,5,8,7,2]=>1 [2,1,8,7,6,5,4,3]=>1 [2,1,6,5,7,4,8,3]=>1 [2,1,5,4,7,6,8,3]=>1 [1,2,6,7,8,5,4,3]=>1 [3,2,1,8,7,6,5,4]=>1 [3,2,1,6,5,8,7,4]=>1 [1,2,3,5,6,7,8,4]=>1 [4,3,2,1,8,7,6,5]=>1 [3,4,2,1,7,8,6,5]=>1 [2,4,3,1,6,8,7,5]=>1 [2,4,3,1,7,6,8,5]=>1 [3,2,4,1,6,8,7,5]=>1 [3,2,4,1,7,6,8,5]=>1 [2,3,4,1,6,7,8,5]=>1 [2,1,4,3,8,7,6,5]=>1 [2,1,4,3,6,8,7,5]=>1 [2,1,4,3,7,6,8,5]=>1 [5,4,3,2,1,8,7,6]=>1 [3,2,5,4,1,8,7,6]=>1 [3,2,1,4,5,8,7,6]=>1 [2,3,1,4,5,7,8,6]=>1 [6,5,4,3,2,1,8,7]=>1 [4,3,5,2,6,1,8,7]=>1 [3,2,5,4,6,1,8,7]=>1 [2,3,4,5,6,1,8,7]=>1 [2,1,6,5,4,3,8,7]=>1 [2,1,4,6,5,3,8,7]=>1 [2,1,5,4,6,3,8,7]=>1 [4,3,2,1,6,5,8,7]=>1 [2,4,3,1,6,5,8,7]=>1 [3,2,4,1,6,5,8,7]=>1 [2,1,4,3,6,5,8,7]=>1 [2,1,3,4,5,6,8,7]=>1 [1,2,3,4,5,6,8,7]=>1 [5,7,6,4,3,2,1,8]=>1 [4,7,6,5,3,2,1,8]=>1 [3,2,7,6,5,4,1,8]=>1 [5,4,3,2,7,6,1,8]=>1 [3,2,5,4,7,6,1,8]=>1 [1,4,3,2,7,6,5,8]=>1 [1,3,4,2,6,7,5,8]=>1 [1,3,2,5,4,7,6,8]=>1 [1,2,3,5,4,7,6,8]=>1 [1,3,2,4,5,7,6,8]=>1 [1,2,3,4,5,7,6,8]=>1 [1,2,4,3,6,5,7,8]=>1 [1,3,2,5,4,6,7,8]=>1 [1,2,3,5,4,6,7,8]=>1 [1,3,2,4,5,6,7,8]=>1 [1,8,4,7,6,5,3,2]=>2 [1,8,5,4,7,6,3,2]=>3 [1,8,7,4,5,6,3,2]=>9 [1,8,7,4,6,5,3,2]=>3 [1,8,6,5,4,7,3,2]=>2 [1,8,7,5,4,6,3,2]=>3 [1,8,7,5,6,4,3,2]=>3 [2,1,4,5,8,6,7,3]=>2 [2,1,8,5,4,7,6,3]=>3 [2,3,4,8,5,6,7,1]=>4 [2,3,6,4,5,1,8,7]=>2 [2,3,7,4,5,6,8,1]=>4 [2,8,4,3,5,7,6,1]=>5 [4,2,3,1,8,6,7,5]=>4 [8,2,7,4,6,5,3,1]=>6 [4,3,2,7,5,6,8,1]=>2 [4,3,2,8,5,7,6,1]=>2 [6,3,2,5,4,1,8,7]=>3 [8,3,2,5,4,7,6,1]=>9 [8,3,2,7,6,5,4,1]=>3 [8,3,7,4,6,5,2,1]=>6 [7,3,6,5,4,2,1,8]=>2 [7,4,3,6,5,2,1,8]=>3 [7,6,3,5,4,2,1,8]=>3 [8,5,4,3,2,7,6,1]=>3 [8,7,4,3,6,5,2,1]=>6 [2,4,6,8,1,3,5,7]=>5 [2,4,6,1,7,3,8,5]=>4 [2,1,4,3,7,5,8,6]=>1 [2,4,1,3,7,5,8,6]=>1 [2,1,4,3,7,8,5,6]=>2 [2,4,7,8,1,3,5,6]=>8 [2,1,4,3,8,5,6,7]=>1 [2,4,5,6,7,1,8,3]=>5 [2,1,5,3,6,4,8,7]=>1 [2,1,5,6,3,4,8,7]=>2 [2,5,6,8,1,3,4,7]=>10 [2,1,5,3,7,4,8,6]=>1 [2,5,1,7,3,4,8,6]=>2 [2,1,5,7,3,8,4,6]=>4 [2,5,7,8,1,3,4,6]=>16 [2,3,5,6,1,7,8,4]=>2 [2,1,6,3,7,4,8,5]=>2 [2,6,7,1,3,4,8,5]=>5 [2,1,6,7,8,3,4,5]=>10 [2,6,7,8,1,3,4,5]=>26 [2,1,6,3,4,7,8,5]=>1 [2,1,6,3,4,5,8,7]=>1 [2,6,1,3,4,5,7,8]=>1 [2,7,8,1,3,4,5,6]=>8 [2,7,1,3,4,5,6,8]=>1 [2,3,4,5,7,8,1,6]=>2 [2,1,8,3,4,5,6,7]=>1 [2,8,1,3,4,5,6,7]=>1 [2,1,3,8,4,5,6,7]=>1 [2,3,4,5,6,8,1,7]=>1 [3,1,4,2,6,5,8,7]=>1 [3,4,1,2,6,5,8,7]=>2 [3,1,4,2,6,8,5,7]=>1 [3,4,6,8,1,2,5,7]=>8 [3,1,4,2,7,5,8,6]=>1 [3,4,1,2,7,8,5,6]=>4 [3,4,7,8,1,2,5,6]=>13 [3,1,5,2,6,4,8,7]=>1 [3,5,1,6,2,4,8,7]=>4 [3,1,5,6,2,8,4,7]=>2 [3,5,6,8,1,2,4,7]=>16 [3,1,5,2,7,4,8,6]=>1 [3,5,1,7,2,8,4,6]=>8 [3,5,7,8,1,2,4,6]=>26 [1,3,2,5,4,8,6,7]=>1 [1,3,5,8,2,4,6,7]=>2 [1,3,5,6,2,7,4,8]=>2 [3,1,6,2,7,4,8,5]=>2 [3,6,7,1,2,8,4,5]=>13 [3,6,1,7,8,2,4,5]=>20 [3,6,7,8,1,2,4,5]=>43 [1,3,2,6,4,7,5,8]=>1 [3,1,2,6,7,4,8,5]=>2 [1,3,2,6,4,8,5,7]=>1 [1,3,2,6,4,5,7,8]=>1 [1,3,2,7,4,8,5,6]=>2 [1,3,2,7,4,5,6,8]=>1 [1,3,2,8,4,5,6,7]=>1 [3,1,2,4,5,8,6,7]=>1 [1,3,2,4,5,8,6,7]=>1 [4,1,5,2,6,3,8,7]=>2 [4,5,6,1,2,3,8,7]=>10 [4,1,5,6,8,2,3,7]=>5 [4,5,6,8,1,2,3,7]=>26 [4,1,5,2,7,3,8,6]=>2 [4,1,5,2,7,8,3,6]=>4 [4,5,7,1,2,8,3,6]=>20 [4,5,1,7,8,2,3,6]=>13 [4,5,7,8,1,2,3,6]=>43 [1,4,2,5,3,7,6,8]=>1 [1,4,2,5,3,8,6,7]=>1 [1,4,2,5,3,6,7,8]=>1 [1,4,5,6,7,2,3,8]=>5 [4,1,6,2,7,3,8,5]=>4 [4,6,7,1,8,2,3,5]=>51 [4,6,7,8,1,2,3,5]=>73 [1,4,2,6,3,7,5,8]=>1 [1,4,2,6,7,8,3,5]=>3 [1,4,2,6,3,8,5,7]=>1 [4,1,2,3,6,5,8,7]=>1 [1,4,2,6,3,5,7,8]=>1 [1,4,2,7,3,8,5,6]=>2 [4,7,1,2,3,5,6,8]=>3 [1,4,2,7,3,5,6,8]=>1 [1,4,2,3,7,5,6,8]=>1 [1,4,2,3,5,7,6,8]=>1 [1,4,2,8,3,5,6,7]=>1 [4,1,2,3,8,5,6,7]=>1 [1,4,2,3,5,8,6,7]=>1 [1,4,2,3,5,6,7,8]=>1 [5,1,6,2,7,3,8,4]=>5 [1,5,2,6,3,7,4,8]=>2 [1,5,2,6,3,8,4,7]=>2 [1,5,2,6,3,4,7,8]=>2 [1,2,5,6,3,4,7,8]=>2 [1,5,2,7,3,8,4,6]=>4 [5,7,1,2,3,4,6,8]=>5 [1,5,2,7,3,4,6,8]=>2 [1,5,2,3,4,7,6,8]=>1 [5,1,2,8,3,4,6,7]=>2 [1,5,2,8,3,4,6,7]=>2 [1,5,8,2,3,4,6,7]=>3 [1,5,2,3,4,8,6,7]=>1 [1,2,3,5,4,8,6,7]=>1 [5,1,2,3,4,6,8,7]=>1 [1,5,2,3,4,6,7,8]=>1 [1,6,2,7,3,8,4,5]=>5 [1,6,7,8,2,3,4,5]=>26 [6,7,1,2,3,4,8,5]=>8 [6,1,7,2,3,4,5,8]=>5 [6,1,2,7,3,4,5,8]=>3 [1,6,2,7,3,4,5,8]=>3 [1,6,7,2,3,4,5,8]=>5 [1,6,2,3,4,7,5,8]=>1 [1,2,3,6,4,7,5,8]=>1 [6,1,8,2,3,4,5,7]=>5 [1,6,2,8,3,4,5,7]=>3 [1,6,8,2,3,4,5,7]=>5 [1,6,2,3,4,8,5,7]=>1 [1,2,3,6,4,8,5,7]=>1 [6,1,2,3,4,5,8,7]=>1 [1,6,2,3,4,5,7,8]=>1 [1,2,3,6,4,5,7,8]=>1 [1,7,2,8,3,4,5,6]=>5 [1,7,8,2,3,4,5,6]=>8 [1,7,2,3,8,4,5,6]=>3 [7,1,2,3,4,8,5,6]=>2 [1,7,2,3,4,8,5,6]=>2 [1,2,3,7,4,8,5,6]=>2 [7,1,2,3,4,5,8,6]=>1 [1,7,2,3,4,5,8,6]=>1 [1,2,7,3,4,5,8,6]=>1 [1,7,2,3,4,5,6,8]=>1 [1,2,3,7,4,5,6,8]=>1 [1,8,2,3,4,5,6,7]=>1 [1,2,3,8,4,5,6,7]=>1 [1,2,3,4,5,8,6,7]=>1 [5,3,2,6,1,4,8,7]=>2 [7,3,2,5,4,8,1,6]=>6 [8,4,5,2,3,7,6,1]=>24 [7,4,5,2,3,8,1,6]=>16 [6,4,5,2,3,1,8,7]=>8 [5,4,6,2,1,3,8,7]=>3 [3,6,1,5,4,2,8,7]=>2 [4,6,5,1,3,2,8,7]=>3 [5,6,4,3,1,2,8,7]=>2 [7,5,4,3,2,8,1,6]=>2 [8,6,4,3,7,2,5,1]=>8 [7,6,4,3,8,2,1,5]=>3 [6,7,4,3,8,1,2,5]=>10 [5,7,4,3,1,8,2,6]=>4 [4,7,5,1,3,8,2,6]=>6 [3,7,1,5,4,8,2,6]=>4 [2,1,7,5,4,8,3,6]=>2 [3,8,1,5,4,7,6,2]=>6 [4,8,5,1,3,7,6,2]=>9 [5,8,4,3,1,7,6,2]=>4 [6,8,4,3,7,1,5,2]=>10 [7,8,4,3,6,5,1,2]=>18 [6,8,5,7,3,1,4,2]=>18 [5,8,6,7,1,3,4,2]=>72 [4,8,6,1,7,3,5,2]=>24 [3,8,1,6,7,4,5,2]=>16 [2,1,8,6,7,4,5,3]=>8 [2,1,7,6,8,4,3,5]=>3 [3,7,1,6,8,4,2,5]=>6 [4,7,6,1,8,3,2,5]=>9 [5,7,6,8,1,3,2,4]=>26 [5,4,7,2,1,8,3,6]=>6 [6,4,7,2,8,1,3,5]=>14 [7,4,6,2,8,3,1,5]=>24 [8,4,6,2,7,3,5,1]=>63 [8,3,2,6,7,4,5,1]=>24 [7,3,2,6,8,4,1,5]=>9 [6,3,2,7,8,1,4,5]=>10 [5,3,2,7,1,8,4,6]=>4 [4,3,2,1,7,8,5,6]=>2 [3,4,1,2,8,7,6,5]=>2 [5,3,2,8,1,7,6,4]=>2 [6,3,2,8,7,1,5,4]=>3 [7,3,2,8,6,5,1,4]=>4 [8,4,7,2,6,5,3,1]=>8 [7,4,8,2,6,5,1,3]=>10 [6,4,8,2,7,1,5,3]=>8 [5,4,8,2,1,7,6,3]=>3 [4,5,8,1,2,7,6,3]=>10 [3,5,1,8,2,7,6,4]=>4 [2,1,5,8,3,7,6,4]=>2 [2,1,6,8,7,3,5,4]=>3 [3,6,1,8,7,2,5,4]=>6 [4,6,8,1,7,2,5,3]=>14 [5,6,8,7,1,2,4,3]=>24 [6,5,8,7,2,1,4,3]=>6 [7,5,8,6,2,4,1,3]=>18 [8,5,7,6,2,4,3,1]=>10 [5,7,8,6,1,4,2,3]=>13 [4,7,8,1,6,5,2,3]=>10 [3,7,1,8,6,5,2,4]=>4 [2,1,7,8,6,5,3,4]=>2 [3,8,1,7,6,5,4,2]=>2 [4,8,7,1,6,5,3,2]=>3 [5,8,7,6,1,4,3,2]=>4 [6,8,7,5,4,1,3,2]=>3 [4,2,5,1,3,6,7,8]=>2 [5,2,6,7,1,3,4,8]=>10 [3,2,7,8,1,4,5,6]=>5 [5,3,2,6,1,4,7,8]=>2 [7,4,3,8,1,2,5,6]=>5 [4,7,3,6,8,1,2,5]=>16 [6,7,3,4,8,1,2,5]=>44 [5,4,2,7,8,1,3,6]=>5 [6,4,7,2,5,1,3,8]=>8 [6,4,3,2,7,1,5,8]=>2 [5,4,3,2,8,1,6,7]=>1 [7,5,3,8,2,6,1,4]=>8 [8,5,4,7,2,6,1,3]=>10 [8,5,4,7,3,6,1,2]=>10 [2,1,4,3,6,5,8,7,10,9]=>1 [4,3,2,1,6,5,8,7,10,9]=>1 [6,3,2,5,4,1,8,7,10,9]=>3 [8,3,2,5,4,7,6,1,10,9]=>9 [10,3,2,5,4,7,6,9,8,1]=>27 [2,1,6,5,4,3,8,7,10,9]=>1 [6,5,4,3,2,1,8,7,10,9]=>1 [8,5,4,3,2,7,6,1,10,9]=>3 [10,5,4,3,2,7,6,9,8,1]=>9 [2,1,8,5,4,7,6,3,10,9]=>3 [8,7,4,3,6,5,2,1,10,9]=>6 [10,7,4,3,6,5,2,9,8,1]=>18 [2,1,10,5,4,7,6,9,8,3]=>9 [10,9,4,3,6,5,8,7,2,1]=>36 [8,9,5,6,3,4,10,1,2,7]=>320 [2,1,4,3,8,7,6,5,10,9]=>1 [4,3,2,1,8,7,6,5,10,9]=>1 [8,3,2,7,6,5,4,1,10,9]=>3 [10,3,2,7,6,5,4,9,8,1]=>9 [2,1,8,7,6,5,4,3,10,9]=>1 [8,7,6,5,4,3,2,1,10,9]=>1 [9,7,6,5,4,3,2,10,1,8]=>2 [10,7,6,5,4,3,2,9,8,1]=>3 [2,1,10,7,6,5,4,9,8,3]=>3 [10,9,6,5,4,3,8,7,2,1]=>6 [2,1,4,3,10,7,6,9,8,5]=>3 [4,3,2,1,10,7,6,9,8,5]=>3 [10,3,2,9,6,5,8,7,4,1]=>18 [2,1,10,9,6,5,8,7,4,3]=>6 [10,9,8,5,4,7,6,3,2,1]=>10 [6,7,8,9,10,1,2,3,4,5]=>6307 [7,3,2,8,9,10,1,4,5,6]=>147 [8,5,4,3,2,9,10,1,6,7]=>10 [2,1,4,3,6,5,10,9,8,7]=>1 [4,3,2,1,6,5,10,9,8,7]=>1 [6,3,2,5,4,1,10,9,8,7]=>3 [10,3,2,5,4,9,8,7,6,1]=>9 [2,1,6,5,4,3,10,9,8,7]=>1 [6,5,4,3,2,1,10,9,8,7]=>1 [10,5,4,3,2,9,8,7,6,1]=>5 [2,1,10,5,4,9,8,7,6,3]=>3 [10,9,4,3,8,7,6,5,2,1]=>6 [9,7,5,10,3,8,2,6,1,4]=>56 [2,1,4,3,10,9,8,7,6,5]=>1 [4,3,2,1,10,9,8,7,6,5]=>1 [10,3,2,9,8,7,6,5,4,1]=>3 [2,1,10,9,8,7,6,5,4,3]=>1 [10,9,8,7,6,5,4,3,2,1]=>1 [10,8,9,5,6,7,1,2,3,4]=>2902 [10,8,9,4,5,6,1,2,3,7]=>1166 [10,7,8,5,6,9,1,2,3,4]=>1334 [10,6,7,4,5,8,1,2,3,9]=>262 [10,7,8,3,4,9,1,2,5,6]=>662 [10,6,7,3,4,8,1,2,5,9]=>181 [9,8,10,5,6,7,1,2,3,4]=>1664 [9,8,10,4,5,6,1,2,3,7]=>806 [8,7,9,5,6,10,1,2,3,4]=>484 [7,6,8,4,5,9,1,2,3,10]=>96 [8,7,9,3,4,10,1,2,5,6]=>260 [7,6,8,3,4,9,1,2,5,10]=>68 [9,6,10,5,7,8,1,2,3,4]=>928 [9,5,10,4,6,7,1,2,3,8]=>348 [8,6,9,5,7,10,1,2,3,4]=>340 [7,5,8,4,6,9,1,2,3,10]=>72 [8,4,9,3,5,10,1,2,6,7]=>120 [7,4,8,3,5,9,1,2,6,10]=>44 [9,6,10,2,7,8,1,3,4,5]=>735 [9,5,10,2,6,7,1,3,4,8]=>301 [8,6,9,2,7,10,1,3,4,5]=>268 [7,5,8,2,6,9,1,3,4,10]=>62 [8,4,9,2,5,10,1,3,6,7]=>120 [7,4,8,2,5,9,1,3,6,10]=>44 [2,4,6,8,10,1,3,5,7,9]=>26 [2,4,6,9,10,1,3,5,7,8]=>42 [2,4,7,8,10,1,3,5,6,9]=>43 [2,4,7,9,10,1,3,5,6,8]=>71 [2,4,8,9,10,1,3,5,6,7]=>120 [2,5,6,8,10,1,3,4,7,9]=>43 [2,5,6,9,10,1,3,4,7,8]=>69 [2,5,7,8,10,1,3,4,6,9]=>73 [2,5,7,9,10,1,3,4,6,8]=>120 [2,5,8,9,10,1,3,4,6,7]=>202 [2,6,7,8,10,1,3,4,5,9]=>145 [2,6,7,9,10,1,3,4,5,8]=>238 [2,6,8,9,10,1,3,4,5,7]=>394 [2,7,8,9,10,1,3,4,5,6]=>673 [3,4,6,8,10,1,2,5,7,9]=>42 [3,4,6,9,10,1,2,5,7,8]=>68 [3,4,7,8,10,1,2,5,6,9]=>69 [3,4,7,9,10,1,2,5,6,8]=>114 [3,4,8,9,10,1,2,5,6,7]=>193 [3,5,6,8,10,1,2,4,7,9]=>71 [3,5,6,9,10,1,2,4,7,8]=>114 [3,5,7,8,10,1,2,4,6,9]=>120 [3,5,7,9,10,1,2,4,6,8]=>197 [3,5,8,9,10,1,2,4,6,7]=>334 [3,6,7,8,10,1,2,4,5,9]=>238 [3,6,7,9,10,1,2,4,5,8]=>390 [3,6,8,9,10,1,2,4,5,7]=>652 [3,7,8,9,10,1,2,4,5,6]=>1114 [4,5,6,8,10,1,2,3,7,9]=>120 [4,5,6,9,10,1,2,3,7,8]=>193 [4,5,7,8,10,1,2,3,6,9]=>202 [4,5,7,9,10,1,2,3,6,8]=>334 [4,5,8,9,10,1,2,3,6,7]=>566 [4,6,7,8,10,1,2,3,5,9]=>394 [4,6,7,9,10,1,2,3,5,8]=>652 [4,6,8,9,10,1,2,3,5,7]=>1084 [4,7,8,9,10,1,2,3,5,6]=>1872 [5,6,7,8,10,1,2,3,4,9]=>673 [5,6,7,9,10,1,2,3,4,8]=>1114 [5,6,8,9,10,1,2,3,4,7]=>1872 [5,7,8,9,10,1,2,3,4,6]=>3206 [2,1,12,11,10,9,8,7,6,5,4,3]=>1 [10,9,8,7,6,5,4,3,2,1,12,11]=>1 [2,8,9,10,11,12,1,3,4,5,6,7]=>51312 [6,7,8,9,10,12,1,2,3,4,5,11]=>51312
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Description
The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation.
These are multiplicities of Verma modules.
References
[1] Kazhdan, D., Lusztig, G. Representations of Coxeter groups and Hecke algebras MathSciNet:0560412
[2] Björner, A., Brenti, F. Combinatorics of Coxeter groups MathSciNet:2133266
[3] Humphreys, J. E. Reflection groups and Coxeter groups MathSciNet:1066460
[4] Number of permutations w in S_n whose Kazhdan-Lusztig polynomial evaluated at q=1 is less than or equal to 2; P_id,w(1) <= 2. OEIS:A224255
[5] Number of permutations w in S_n whose Kazhdan-Lusztig polynomial P_id,w(1) <= 3. OEIS:A224316
[6] Woo, A. Permutations with Kazhdan-Lusztig polynomial $P_{id,w}(q)=1+q^h$ MathSciNet:2515773
Code
# takes a long time!
def statistic(x):
    if x.size() == 1:
        return 1
    G = WeylGroup(['A',x.size()-1])
    R.=LaurentPolynomialRing(QQ)
    KL=KazhdanLusztigPolynomial(G,q)
    w = G.from_reduced_word(x.reduced_word())
    return KL.P(1,w).substitute({q:1})

# alternative, with coxeter3 installed:
def statistic_alt(x):
    if x.size() == 1:
        return 1
    G = CoxeterGroup(['A',x.size()-1], implementation="coxeter3")
    R. = PolynomialRing(QQ)
    P = G.kazhdan_lusztig_polynomial([],x.reduced_word())
    return P.substitute({q:1})
Created
Feb 14, 2013 at 00:43 by Sara Billey
Updated
Dec 28, 2017 at 20:18 by Martin Rubey