edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>0 [2,1]=>0 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>0 [3,1,2]=>0 [3,2,1]=>0 [1,2,3,4]=>0 [1,2,4,3]=>0 [1,3,2,4]=>2 [1,3,4,2]=>0 [1,4,2,3]=>1 [1,4,3,2]=>1 [2,1,3,4]=>0 [2,1,4,3]=>1 [2,3,1,4]=>1 [2,3,4,1]=>0 [2,4,1,3]=>2 [2,4,3,1]=>1 [3,1,2,4]=>0 [3,1,4,2]=>1 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>0 [3,4,2,1]=>0 [4,1,2,3]=>0 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>0 [4,3,1,2]=>0 [4,3,2,1]=>0 [1,2,3,4,5]=>0 [1,2,3,5,4]=>0 [1,2,4,3,5]=>1 [1,2,4,5,3]=>0 [1,2,5,3,4]=>0 [1,2,5,4,3]=>0 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>1 [1,3,4,5,2]=>0 [1,3,5,2,4]=>3 [1,3,5,4,2]=>2 [1,4,2,3,5]=>1 [1,4,2,5,3]=>2 [1,4,3,2,5]=>2 [1,4,3,5,2]=>2 [1,4,5,2,3]=>0 [1,4,5,3,2]=>0 [1,5,2,3,4]=>1 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>1 [1,5,4,2,3]=>1 [1,5,4,3,2]=>1 [2,1,3,4,5]=>0 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>0 [2,1,5,3,4]=>1 [2,1,5,4,3]=>1 [2,3,1,4,5]=>0 [2,3,1,5,4]=>1 [2,3,4,1,5]=>1 [2,3,4,5,1]=>0 [2,3,5,1,4]=>1 [2,3,5,4,1]=>0 [2,4,1,3,5]=>3 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>1 [2,4,5,3,1]=>0 [2,5,1,3,4]=>1 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>1 [2,5,4,1,3]=>2 [2,5,4,3,1]=>1 [3,1,2,4,5]=>0 [3,1,2,5,4]=>0 [3,1,4,2,5]=>2 [3,1,4,5,2]=>0 [3,1,5,2,4]=>2 [3,1,5,4,2]=>1 [3,2,1,4,5]=>0 [3,2,1,5,4]=>1 [3,2,4,1,5]=>2 [3,2,4,5,1]=>0 [3,2,5,1,4]=>2 [3,2,5,4,1]=>1 [3,4,1,2,5]=>0 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>0 [3,4,5,2,1]=>0 [3,5,1,2,4]=>1 [3,5,1,4,2]=>2 [3,5,2,1,4]=>2 [3,5,2,4,1]=>2 [3,5,4,1,2]=>1 [3,5,4,2,1]=>1 [4,1,2,3,5]=>0 [4,1,2,5,3]=>0 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>1 [4,1,5,3,2]=>1 [4,2,1,3,5]=>2 [4,2,1,5,3]=>1 [4,2,3,1,5]=>1 [4,2,3,5,1]=>0 [4,2,5,1,3]=>2 [4,2,5,3,1]=>1 [4,3,1,2,5]=>0 [4,3,1,5,2]=>1 [4,3,2,1,5]=>1 [4,3,2,5,1]=>1 [4,3,5,1,2]=>1 [4,3,5,2,1]=>1 [4,5,1,2,3]=>0 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>0 [4,5,3,1,2]=>0 [4,5,3,2,1]=>0 [5,1,2,3,4]=>0 [5,1,2,4,3]=>0 [5,1,3,2,4]=>2 [5,1,3,4,2]=>0 [5,1,4,2,3]=>1 [5,1,4,3,2]=>1 [5,2,1,3,4]=>0 [5,2,1,4,3]=>1 [5,2,3,1,4]=>1 [5,2,3,4,1]=>0 [5,2,4,1,3]=>2 [5,2,4,3,1]=>1 [5,3,1,2,4]=>0 [5,3,1,4,2]=>1 [5,3,2,1,4]=>1 [5,3,2,4,1]=>1 [5,3,4,1,2]=>0 [5,3,4,2,1]=>0 [5,4,1,2,3]=>0 [5,4,1,3,2]=>1 [5,4,2,1,3]=>1 [5,4,2,3,1]=>0 [5,4,3,1,2]=>0 [5,4,3,2,1]=>0 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>0 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>0 [1,2,3,6,4,5]=>0 [1,2,3,6,5,4]=>0 [1,2,4,3,5,6]=>0 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>1 [1,2,4,5,6,3]=>0 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>1 [1,2,5,3,4,6]=>0 [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]=>0 [1,2,5,6,4,3]=>0 [1,2,6,3,4,5]=>0 [1,2,6,3,5,4]=>1 [1,2,6,4,3,5]=>1 [1,2,6,4,5,3]=>0 [1,2,6,5,3,4]=>0 [1,2,6,5,4,3]=>0 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>3 [1,3,2,5,6,4]=>1 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>0 [1,3,4,2,6,5]=>1 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>0 [1,3,4,6,2,5]=>1 [1,3,4,6,5,2]=>0 [1,3,5,2,4,6]=>4 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>3 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>1 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>3 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>2 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>1 [1,4,2,5,3,6]=>3 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>3 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>1 [1,4,3,2,6,5]=>2 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>1 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>2 [1,4,5,2,3,6]=>0 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>0 [1,4,5,6,3,2]=>0 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>2 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>3 [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]=>2 [1,5,3,4,6,2]=>1 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>2 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>2 [1,5,4,3,2,6]=>2 [1,5,4,3,6,2]=>2 [1,5,4,6,2,3]=>2 [1,5,4,6,3,2]=>2 [1,5,6,2,3,4]=>0 [1,5,6,2,4,3]=>1 [1,5,6,3,2,4]=>1 [1,5,6,3,4,2]=>0 [1,5,6,4,2,3]=>0 [1,5,6,4,3,2]=>0 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>1 [1,6,2,4,3,5]=>3 [1,6,2,4,5,3]=>1 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>2 [1,6,3,2,4,5]=>1 [1,6,3,2,5,4]=>2 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>1 [1,6,3,5,2,4]=>3 [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]=>2 [1,6,4,3,5,2]=>2 [1,6,4,5,2,3]=>1 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>2 [1,6,5,3,2,4]=>2 [1,6,5,3,4,2]=>1 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>0 [2,1,3,4,6,5]=>0 [2,1,3,5,4,6]=>3 [2,1,3,5,6,4]=>1 [2,1,3,6,4,5]=>2 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>2 [2,1,4,5,3,6]=>1 [2,1,4,5,6,3]=>0 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>1 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>2 [2,1,5,4,6,3]=>2 [2,1,5,6,3,4]=>0 [2,1,5,6,4,3]=>0 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>1 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>0 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>0 [2,3,1,6,4,5]=>1 [2,3,1,6,5,4]=>1 [2,3,4,1,5,6]=>0 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>1 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>2 [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]=>1 [2,3,5,6,4,1]=>0 [2,3,6,1,4,5]=>0 [2,3,6,1,5,4]=>1 [2,3,6,4,1,5]=>1 [2,3,6,4,5,1]=>0 [2,3,6,5,1,4]=>1 [2,3,6,5,4,1]=>0 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>3 [2,4,1,5,3,6]=>3 [2,4,1,5,6,3]=>1 [2,4,1,6,3,5]=>3 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>1 [2,4,3,1,6,5]=>2 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>1 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>2 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>1 [2,4,5,3,1,6]=>1 [2,4,5,3,6,1]=>1 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>0 [2,4,6,1,3,5]=>4 [2,4,6,1,5,3]=>3 [2,4,6,3,1,5]=>3 [2,4,6,3,5,1]=>3 [2,4,6,5,1,3]=>3 [2,4,6,5,3,1]=>2 [2,5,1,3,4,6]=>1 [2,5,1,3,6,4]=>3 [2,5,1,4,3,6]=>3 [2,5,1,4,6,3]=>3 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>2 [2,5,3,1,4,6]=>3 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>1 [2,5,3,6,1,4]=>3 [2,5,3,6,4,1]=>2 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>2 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>2 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>2 [2,5,6,1,3,4]=>0 [2,5,6,1,4,3]=>1 [2,5,6,3,1,4]=>1 [2,5,6,3,4,1]=>0 [2,5,6,4,1,3]=>1 [2,5,6,4,3,1]=>0 [2,6,1,3,4,5]=>1 [2,6,1,3,5,4]=>3 [2,6,1,4,3,5]=>3 [2,6,1,4,5,3]=>1 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>2 [2,6,3,1,4,5]=>1 [2,6,3,1,5,4]=>2 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>1 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>2 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>2 [2,6,4,5,1,3]=>2 [2,6,4,5,3,1]=>1 [2,6,5,1,3,4]=>1 [2,6,5,1,4,3]=>2 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>1 [2,6,5,4,1,3]=>2 [2,6,5,4,3,1]=>1 [3,1,2,4,5,6]=>0 [3,1,2,4,6,5]=>1 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>0 [3,1,2,6,4,5]=>0 [3,1,2,6,5,4]=>0 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>1 [3,1,4,5,6,2]=>0 [3,1,4,6,2,5]=>3 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>3 [3,1,5,2,6,4]=>2 [3,1,5,4,2,6]=>2 [3,1,5,4,6,2]=>2 [3,1,5,6,2,4]=>1 [3,1,5,6,4,2]=>0 [3,1,6,2,4,5]=>1 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>1 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>1 [3,2,1,4,5,6]=>0 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>0 [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]=>2 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>0 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>2 [3,2,5,4,1,6]=>2 [3,2,5,4,6,1]=>2 [3,2,5,6,1,4]=>1 [3,2,5,6,4,1]=>0 [3,2,6,1,4,5]=>1 [3,2,6,1,5,4]=>2 [3,2,6,4,1,5]=>2 [3,2,6,4,5,1]=>1 [3,2,6,5,1,4]=>2 [3,2,6,5,4,1]=>1 [3,4,1,2,5,6]=>0 [3,4,1,2,6,5]=>0 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>0 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>1 [3,4,2,1,5,6]=>0 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>0 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>1 [3,4,5,1,2,6]=>0 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>1 [3,4,5,6,1,2]=>0 [3,4,5,6,2,1]=>0 [3,4,6,1,2,5]=>0 [3,4,6,1,5,2]=>1 [3,4,6,2,1,5]=>1 [3,4,6,2,5,1]=>1 [3,4,6,5,1,2]=>0 [3,4,6,5,2,1]=>0 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>1 [3,5,1,4,2,6]=>3 [3,5,1,4,6,2]=>3 [3,5,1,6,2,4]=>3 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>2 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>3 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>2 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>2 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>2 [3,5,4,6,1,2]=>2 [3,5,4,6,2,1]=>2 [3,5,6,1,2,4]=>0 [3,5,6,1,4,2]=>1 [3,5,6,2,1,4]=>1 [3,5,6,2,4,1]=>1 [3,5,6,4,1,2]=>0 [3,5,6,4,2,1]=>0 [3,6,1,2,4,5]=>1 [3,6,1,2,5,4]=>1 [3,6,1,4,2,5]=>3 [3,6,1,4,5,2]=>1 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>1 [3,6,2,1,5,4]=>2 [3,6,2,4,1,5]=>3 [3,6,2,4,5,1]=>1 [3,6,2,5,1,4]=>3 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>1 [3,6,4,1,5,2]=>2 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>2 [3,6,4,5,1,2]=>1 [3,6,4,5,2,1]=>1 [3,6,5,1,2,4]=>1 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>2 [3,6,5,2,4,1]=>2 [3,6,5,4,1,2]=>1 [3,6,5,4,2,1]=>1 [4,1,2,3,5,6]=>0 [4,1,2,3,6,5]=>0 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>0 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>0 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>2 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>3 [4,1,3,6,5,2]=>2 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>2 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>2 [4,1,5,6,2,3]=>0 [4,1,5,6,3,2]=>0 [4,1,6,2,3,5]=>1 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>1 [4,1,6,5,3,2]=>1 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>0 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>1 [4,2,3,1,5,6]=>0 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>0 [4,2,3,6,1,5]=>1 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>3 [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]=>1 [4,2,5,6,3,1]=>0 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>2 [4,2,6,3,1,5]=>2 [4,2,6,3,5,1]=>2 [4,2,6,5,1,3]=>2 [4,2,6,5,3,1]=>1 [4,3,1,2,5,6]=>0 [4,3,1,2,6,5]=>0 [4,3,1,5,2,6]=>2 [4,3,1,5,6,2]=>0 [4,3,1,6,2,5]=>2 [4,3,1,6,5,2]=>1 [4,3,2,1,5,6]=>0 [4,3,2,1,6,5]=>1 [4,3,2,5,1,6]=>2 [4,3,2,5,6,1]=>0 [4,3,2,6,1,5]=>2 [4,3,2,6,5,1]=>1 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>2 [4,3,5,2,1,6]=>2 [4,3,5,2,6,1]=>2 [4,3,5,6,1,2]=>0 [4,3,5,6,2,1]=>0 [4,3,6,1,2,5]=>1 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>2 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>1 [4,3,6,5,2,1]=>1 [4,5,1,2,3,6]=>0 [4,5,1,2,6,3]=>0 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>2 [4,5,1,6,2,3]=>1 [4,5,1,6,3,2]=>1 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>1 [4,5,2,3,1,6]=>1 [4,5,2,3,6,1]=>0 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>1 [4,5,3,1,2,6]=>0 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>1 [4,5,3,6,1,2]=>1 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>0 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>0 [4,5,6,3,1,2]=>0 [4,5,6,3,2,1]=>0 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>1 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>3 [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]=>2 [4,6,2,3,5,1]=>1 [4,6,2,5,1,3]=>3 [4,6,2,5,3,1]=>2 [4,6,3,1,2,5]=>1 [4,6,3,1,5,2]=>2 [4,6,3,2,1,5]=>2 [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]=>1 [4,6,5,1,3,2]=>2 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>1 [4,6,5,3,1,2]=>1 [4,6,5,3,2,1]=>1 [5,1,2,3,4,6]=>0 [5,1,2,3,6,4]=>0 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>0 [5,1,2,6,4,3]=>0 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>0 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>2 [5,1,4,3,2,6]=>2 [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]=>1 [5,1,6,2,4,3]=>2 [5,1,6,3,2,4]=>2 [5,1,6,3,4,2]=>1 [5,1,6,4,2,3]=>1 [5,1,6,4,3,2]=>1 [5,2,1,3,4,6]=>0 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>2 [5,2,1,4,6,3]=>2 [5,2,1,6,3,4]=>1 [5,2,1,6,4,3]=>1 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>1 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>0 [5,2,3,6,1,4]=>1 [5,2,3,6,4,1]=>0 [5,2,4,1,3,6]=>3 [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]=>3 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>1 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>2 [5,2,6,3,4,1]=>1 [5,2,6,4,1,3]=>2 [5,2,6,4,3,1]=>1 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>0 [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]=>1 [5,3,2,1,4,6]=>2 [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]=>1 [5,3,4,1,2,6]=>0 [5,3,4,1,6,2]=>1 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>1 [5,3,4,6,1,2]=>0 [5,3,4,6,2,1]=>0 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>2 [5,3,6,2,1,4]=>2 [5,3,6,2,4,1]=>2 [5,3,6,4,1,2]=>1 [5,3,6,4,2,1]=>1 [5,4,1,2,3,6]=>0 [5,4,1,2,6,3]=>0 [5,4,1,3,2,6]=>2 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>1 [5,4,1,6,3,2]=>1 [5,4,2,1,3,6]=>2 [5,4,2,1,6,3]=>1 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>0 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>1 [5,4,3,1,2,6]=>0 [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]=>1 [5,4,3,6,2,1]=>1 [5,4,6,1,2,3]=>1 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>2 [5,4,6,2,3,1]=>1 [5,4,6,3,1,2]=>1 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>0 [5,6,1,2,4,3]=>0 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>0 [5,6,1,4,2,3]=>1 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>0 [5,6,2,1,4,3]=>1 [5,6,2,3,1,4]=>1 [5,6,2,3,4,1]=>0 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>1 [5,6,3,1,2,4]=>0 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>1 [5,6,3,4,1,2]=>0 [5,6,3,4,2,1]=>0 [5,6,4,1,2,3]=>0 [5,6,4,1,3,2]=>1 [5,6,4,2,1,3]=>1 [5,6,4,2,3,1]=>0 [5,6,4,3,1,2]=>0 [5,6,4,3,2,1]=>0 [6,1,2,3,4,5]=>0 [6,1,2,3,5,4]=>0 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>0 [6,1,2,5,3,4]=>0 [6,1,2,5,4,3]=>0 [6,1,3,2,4,5]=>1 [6,1,3,2,5,4]=>2 [6,1,3,4,2,5]=>1 [6,1,3,4,5,2]=>0 [6,1,3,5,2,4]=>3 [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]=>2 [6,1,4,3,5,2]=>2 [6,1,4,5,2,3]=>0 [6,1,4,5,3,2]=>0 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>2 [6,1,5,3,2,4]=>2 [6,1,5,3,4,2]=>1 [6,1,5,4,2,3]=>1 [6,1,5,4,3,2]=>1 [6,2,1,3,4,5]=>0 [6,2,1,3,5,4]=>2 [6,2,1,4,3,5]=>2 [6,2,1,4,5,3]=>0 [6,2,1,5,3,4]=>1 [6,2,1,5,4,3]=>1 [6,2,3,1,4,5]=>0 [6,2,3,1,5,4]=>1 [6,2,3,4,1,5]=>1 [6,2,3,4,5,1]=>0 [6,2,3,5,1,4]=>1 [6,2,3,5,4,1]=>0 [6,2,4,1,3,5]=>3 [6,2,4,1,5,3]=>2 [6,2,4,3,1,5]=>2 [6,2,4,3,5,1]=>2 [6,2,4,5,1,3]=>1 [6,2,4,5,3,1]=>0 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>1 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>1 [6,3,1,2,4,5]=>0 [6,3,1,2,5,4]=>0 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>0 [6,3,1,5,2,4]=>2 [6,3,1,5,4,2]=>1 [6,3,2,1,4,5]=>0 [6,3,2,1,5,4]=>1 [6,3,2,4,1,5]=>2 [6,3,2,4,5,1]=>0 [6,3,2,5,1,4]=>2 [6,3,2,5,4,1]=>1 [6,3,4,1,2,5]=>0 [6,3,4,1,5,2]=>1 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>1 [6,3,4,5,1,2]=>0 [6,3,4,5,2,1]=>0 [6,3,5,1,2,4]=>1 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>2 [6,3,5,4,1,2]=>1 [6,3,5,4,2,1]=>1 [6,4,1,2,3,5]=>0 [6,4,1,2,5,3]=>0 [6,4,1,3,2,5]=>2 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>1 [6,4,2,1,3,5]=>2 [6,4,2,1,5,3]=>1 [6,4,2,3,1,5]=>1 [6,4,2,3,5,1]=>0 [6,4,2,5,1,3]=>2 [6,4,2,5,3,1]=>1 [6,4,3,1,2,5]=>0 [6,4,3,1,5,2]=>1 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>1 [6,4,3,5,1,2]=>1 [6,4,3,5,2,1]=>1 [6,4,5,1,2,3]=>0 [6,4,5,1,3,2]=>1 [6,4,5,2,1,3]=>1 [6,4,5,2,3,1]=>0 [6,4,5,3,1,2]=>0 [6,4,5,3,2,1]=>0 [6,5,1,2,3,4]=>0 [6,5,1,2,4,3]=>0 [6,5,1,3,2,4]=>2 [6,5,1,3,4,2]=>0 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>1 [6,5,2,1,3,4]=>0 [6,5,2,1,4,3]=>1 [6,5,2,3,1,4]=>1 [6,5,2,3,4,1]=>0 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>1 [6,5,3,1,2,4]=>0 [6,5,3,1,4,2]=>1 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>1 [6,5,3,4,1,2]=>0 [6,5,3,4,2,1]=>0 [6,5,4,1,2,3]=>0 [6,5,4,1,3,2]=>1 [6,5,4,2,1,3]=>1 [6,5,4,2,3,1]=>0 [6,5,4,3,1,2]=>0 [6,5,4,3,2,1]=>0 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>0 [1,2,3,4,6,5,7]=>1 [1,2,3,4,6,7,5]=>0 [1,2,3,4,7,5,6]=>0 [1,2,3,4,7,6,5]=>0 [1,2,3,5,4,6,7]=>0 [1,2,3,5,4,7,6]=>1 [1,2,3,5,6,4,7]=>1 [1,2,3,5,6,7,4]=>0 [1,2,3,5,7,4,6]=>2 [1,2,3,5,7,6,4]=>1 [1,2,3,6,4,5,7]=>0 [1,2,3,6,4,7,5]=>1 [1,2,3,6,5,4,7]=>1 [1,2,3,6,5,7,4]=>1 [1,2,3,6,7,4,5]=>0 [1,2,3,6,7,5,4]=>0 [1,2,3,7,4,5,6]=>0 [1,2,3,7,4,6,5]=>1 [1,2,3,7,5,4,6]=>1 [1,2,3,7,5,6,4]=>0 [1,2,3,7,6,4,5]=>0 [1,2,3,7,6,5,4]=>0 [1,2,4,3,5,6,7]=>0 [1,2,4,3,5,7,6]=>2 [1,2,4,3,6,5,7]=>2 [1,2,4,3,6,7,5]=>0 [1,2,4,3,7,5,6]=>1 [1,2,4,3,7,6,5]=>1 [1,2,4,5,3,6,7]=>0 [1,2,4,5,3,7,6]=>1 [1,2,4,5,6,3,7]=>1 [1,2,4,5,6,7,3]=>0 [1,2,4,5,7,3,6]=>1 [1,2,4,5,7,6,3]=>0 [1,2,4,6,3,5,7]=>3 [1,2,4,6,3,7,5]=>2 [1,2,4,6,5,3,7]=>2 [1,2,4,6,5,7,3]=>2 [1,2,4,6,7,3,5]=>1 [1,2,4,6,7,5,3]=>0 [1,2,4,7,3,5,6]=>1 [1,2,4,7,3,6,5]=>2 [1,2,4,7,5,3,6]=>2 [1,2,4,7,5,6,3]=>1 [1,2,4,7,6,3,5]=>2 [1,2,4,7,6,5,3]=>1 [1,2,5,3,4,6,7]=>0 [1,2,5,3,4,7,6]=>0 [1,2,5,3,6,4,7]=>2 [1,2,5,3,6,7,4]=>0 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>1 [1,2,5,4,3,6,7]=>0 [1,2,5,4,3,7,6]=>1 [1,2,5,4,6,3,7]=>2 [1,2,5,4,6,7,3]=>0 [1,2,5,4,7,3,6]=>2 [1,2,5,4,7,6,3]=>1 [1,2,5,6,3,4,7]=>0 [1,2,5,6,3,7,4]=>1 [1,2,5,6,4,3,7]=>1 [1,2,5,6,4,7,3]=>1 [1,2,5,6,7,3,4]=>0 [1,2,5,6,7,4,3]=>0 [1,2,5,7,3,4,6]=>1 [1,2,5,7,3,6,4]=>2 [1,2,5,7,4,3,6]=>2 [1,2,5,7,4,6,3]=>2 [1,2,5,7,6,3,4]=>1 [1,2,5,7,6,4,3]=>1 [1,2,6,3,4,5,7]=>0 [1,2,6,3,4,7,5]=>0 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>1 [1,2,6,3,7,5,4]=>1 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>1 [1,2,6,4,5,3,7]=>1 [1,2,6,4,5,7,3]=>0 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>1 [1,2,6,5,3,4,7]=>0 [1,2,6,5,3,7,4]=>1 [1,2,6,5,4,3,7]=>1 [1,2,6,5,4,7,3]=>1 [1,2,6,5,7,3,4]=>1 [1,2,6,5,7,4,3]=>1 [1,2,6,7,3,4,5]=>0 [1,2,6,7,3,5,4]=>1 [1,2,6,7,4,3,5]=>1 [1,2,6,7,4,5,3]=>0 [1,2,6,7,5,3,4]=>0 [1,2,6,7,5,4,3]=>0 [1,2,7,3,4,5,6]=>0 [1,2,7,3,4,6,5]=>0 [1,2,7,3,5,4,6]=>2 [1,2,7,3,5,6,4]=>0 [1,2,7,3,6,4,5]=>1 [1,2,7,3,6,5,4]=>1 [1,2,7,4,3,5,6]=>0 [1,2,7,4,3,6,5]=>1 [1,2,7,4,5,3,6]=>1 [1,2,7,4,5,6,3]=>0 [1,2,7,4,6,3,5]=>2 [1,2,7,4,6,5,3]=>1 [1,2,7,5,3,4,6]=>0 [1,2,7,5,3,6,4]=>1 [1,2,7,5,4,3,6]=>1 [1,2,7,5,4,6,3]=>1 [1,2,7,5,6,3,4]=>0 [1,2,7,5,6,4,3]=>0 [1,2,7,6,3,4,5]=>0 [1,2,7,6,3,5,4]=>1 [1,2,7,6,4,3,5]=>1 [1,2,7,6,4,5,3]=>0 [1,2,7,6,5,3,4]=>0 [1,2,7,6,5,4,3]=>0 [1,3,2,4,5,6,7]=>1 [1,3,2,4,5,7,6]=>1 [1,3,2,4,6,5,7]=>4 [1,3,2,4,6,7,5]=>2 [1,3,2,4,7,5,6]=>3 [1,3,2,4,7,6,5]=>3 [1,3,2,5,4,6,7]=>2 [1,3,2,5,4,7,6]=>3 [1,3,2,5,6,4,7]=>2 [1,3,2,5,6,7,4]=>1 [1,3,2,5,7,4,6]=>4 [1,3,2,5,7,6,4]=>3 [1,3,2,6,4,5,7]=>2 [1,3,2,6,4,7,5]=>3 [1,3,2,6,5,4,7]=>3 [1,3,2,6,5,7,4]=>3 [1,3,2,6,7,4,5]=>1 [1,3,2,6,7,5,4]=>1 [1,3,2,7,4,5,6]=>2 [1,3,2,7,4,6,5]=>3 [1,3,2,7,5,4,6]=>3 [1,3,2,7,5,6,4]=>2 [1,3,2,7,6,4,5]=>2 [1,3,2,7,6,5,4]=>2 [1,3,4,2,5,6,7]=>0 [1,3,4,2,5,7,6]=>2 [1,3,4,2,6,5,7]=>2 [1,3,4,2,6,7,5]=>0 [1,3,4,2,7,5,6]=>1 [1,3,4,2,7,6,5]=>1 [1,3,4,5,2,6,7]=>0 [1,3,4,5,2,7,6]=>1 [1,3,4,5,6,2,7]=>1 [1,3,4,5,6,7,2]=>0 [1,3,4,5,7,2,6]=>1 [1,3,4,5,7,6,2]=>0 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>1 [1,3,4,6,5,2,7]=>1 [1,3,4,6,5,7,2]=>1 [1,3,4,6,7,2,5]=>1 [1,3,4,6,7,5,2]=>0 [1,3,4,7,2,5,6]=>0 [1,3,4,7,2,6,5]=>1 [1,3,4,7,5,2,6]=>1 [1,3,4,7,5,6,2]=>0 [1,3,4,7,6,2,5]=>1 [1,3,4,7,6,5,2]=>0 [1,3,5,2,4,6,7]=>3 [1,3,5,2,4,7,6]=>4 [1,3,5,2,6,4,7]=>4 [1,3,5,2,6,7,4]=>2 [1,3,5,2,7,4,6]=>4 [1,3,5,2,7,6,4]=>3 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>3 [1,3,5,4,6,2,7]=>4 [1,3,5,4,6,7,2]=>2 [1,3,5,4,7,2,6]=>4 [1,3,5,4,7,6,2]=>3 [1,3,5,6,2,4,7]=>3 [1,3,5,6,2,7,4]=>2 [1,3,5,6,4,2,7]=>2 [1,3,5,6,4,7,2]=>2 [1,3,5,6,7,2,4]=>2 [1,3,5,6,7,4,2]=>1 [1,3,5,7,2,4,6]=>5 [1,3,5,7,2,6,4]=>4 [1,3,5,7,4,2,6]=>4 [1,3,5,7,4,6,2]=>4 [1,3,5,7,6,2,4]=>4 [1,3,5,7,6,4,2]=>3 [1,3,6,2,4,5,7]=>2 [1,3,6,2,4,7,5]=>4 [1,3,6,2,5,4,7]=>4 [1,3,6,2,5,7,4]=>4 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>3 [1,3,6,4,2,5,7]=>4 [1,3,6,4,2,7,5]=>3 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>2 [1,3,6,4,7,2,5]=>4 [1,3,6,4,7,5,2]=>3 [1,3,6,5,2,4,7]=>4 [1,3,6,5,2,7,4]=>3 [1,3,6,5,4,2,7]=>3 [1,3,6,5,4,7,2]=>3 [1,3,6,5,7,2,4]=>4 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>1 [1,3,6,7,2,5,4]=>2 [1,3,6,7,4,2,5]=>2 [1,3,6,7,4,5,2]=>1 [1,3,6,7,5,2,4]=>2 [1,3,6,7,5,4,2]=>1 [1,3,7,2,4,5,6]=>2 [1,3,7,2,4,6,5]=>4 [1,3,7,2,5,4,6]=>4 [1,3,7,2,5,6,4]=>2 [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]=>3 [1,3,7,4,5,2,6]=>3 [1,3,7,4,5,6,2]=>2 [1,3,7,4,6,2,5]=>4 [1,3,7,4,6,5,2]=>3 [1,3,7,5,2,4,6]=>4 [1,3,7,5,2,6,4]=>3 [1,3,7,5,4,2,6]=>3 [1,3,7,5,4,6,2]=>3 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>2 [1,3,7,6,2,4,5]=>2 [1,3,7,6,2,5,4]=>3 [1,3,7,6,4,2,5]=>3 [1,3,7,6,4,5,2]=>2 [1,3,7,6,5,2,4]=>3 [1,3,7,6,5,4,2]=>2 [1,4,2,3,5,6,7]=>1 [1,4,2,3,5,7,6]=>2 [1,4,2,3,6,5,7]=>2 [1,4,2,3,6,7,5]=>1 [1,4,2,3,7,5,6]=>1 [1,4,2,3,7,6,5]=>1 [1,4,2,5,3,6,7]=>2 [1,4,2,5,3,7,6]=>3 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>1 [1,4,2,5,7,3,6]=>4 [1,4,2,5,7,6,3]=>3 [1,4,2,6,3,5,7]=>4 [1,4,2,6,3,7,5]=>3 [1,4,2,6,5,3,7]=>3 [1,4,2,6,5,7,3]=>3 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>1 [1,4,2,7,3,5,6]=>2 [1,4,2,7,3,6,5]=>3 [1,4,2,7,5,3,6]=>3 [1,4,2,7,5,6,3]=>2 [1,4,2,7,6,3,5]=>3 [1,4,2,7,6,5,3]=>2 [1,4,3,2,5,6,7]=>1 [1,4,3,2,5,7,6]=>3 [1,4,3,2,6,5,7]=>3 [1,4,3,2,6,7,5]=>1 [1,4,3,2,7,5,6]=>2 [1,4,3,2,7,6,5]=>2 [1,4,3,5,2,6,7]=>2 [1,4,3,5,2,7,6]=>3 [1,4,3,5,6,2,7]=>2 [1,4,3,5,6,7,2]=>1 [1,4,3,5,7,2,6]=>4 [1,4,3,5,7,6,2]=>3 [1,4,3,6,2,5,7]=>4 [1,4,3,6,2,7,5]=>3 [1,4,3,6,5,2,7]=>3 [1,4,3,6,5,7,2]=>3 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>1 [1,4,3,7,2,5,6]=>2 [1,4,3,7,2,6,5]=>3 [1,4,3,7,5,2,6]=>3 [1,4,3,7,5,6,2]=>2 [1,4,3,7,6,2,5]=>3 [1,4,3,7,6,5,2]=>2 [1,4,5,2,3,6,7]=>0 [1,4,5,2,3,7,6]=>0 [1,4,5,2,6,3,7]=>2 [1,4,5,2,6,7,3]=>0 [1,4,5,2,7,3,6]=>2 [1,4,5,2,7,6,3]=>1 [1,4,5,3,2,6,7]=>0 [1,4,5,3,2,7,6]=>1 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>0 [1,4,5,3,7,2,6]=>2 [1,4,5,3,7,6,2]=>1 [1,4,5,6,2,3,7]=>0 [1,4,5,6,2,7,3]=>1 [1,4,5,6,3,2,7]=>1 [1,4,5,6,3,7,2]=>1 [1,4,5,6,7,2,3]=>0 [1,4,5,6,7,3,2]=>0 [1,4,5,7,2,3,6]=>0 [1,4,5,7,2,6,3]=>1 [1,4,5,7,3,2,6]=>1 [1,4,5,7,3,6,2]=>1 [1,4,5,7,6,2,3]=>0 [1,4,5,7,6,3,2]=>0 [1,4,6,2,3,5,7]=>3 [1,4,6,2,3,7,5]=>2 [1,4,6,2,5,3,7]=>4 [1,4,6,2,5,7,3]=>4 [1,4,6,2,7,3,5]=>4 [1,4,6,2,7,5,3]=>3 [1,4,6,3,2,5,7]=>4 [1,4,6,3,2,7,5]=>3 [1,4,6,3,5,2,7]=>4 [1,4,6,3,5,7,2]=>4 [1,4,6,3,7,2,5]=>4 [1,4,6,3,7,5,2]=>3 [1,4,6,5,2,3,7]=>2 [1,4,6,5,2,7,3]=>3 [1,4,6,5,3,2,7]=>3 [1,4,6,5,3,7,2]=>3
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Description
The number of right floats of a permutation.
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right float is a large ascent not consecutive to any raft of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
References
[1] Billey, S. C., Konvalinka, M., Petersen, T. K., Slofstra, W., Tenner, B. E. Parabolic double cosets in Coxeter groups arXiv:1612.00736
Code
def statistic(pi):
    rafts = [[]]
    for i in range(len(pi)-1):
        if pi[i+1] == pi[i]+1:
            rafts[-1].append(i)
        else:
            rafts.append([])
    rafts = sum(rafts,[])
    return sum(1 for i in range(len(pi)-1)
               if pi[i+1] > pi[i]+1 and i-1 not in rafts and i+1 not in rafts)
Created
Dec 05, 2016 at 12:37 by Christian Stump
Updated
Nov 03, 2017 at 00:20 by Martin Rubey