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]=>1 [3,1,2]=>1 [3,2,1]=>0 [1,2,3,4]=>0 [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]=>1 [3,4,2,1]=>1 [4,1,2,3]=>1 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>1 [4,3,1,2]=>1 [4,3,2,1]=>0 [1,2,3,4,5]=>0 [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]=>2 [1,3,5,4,2]=>2 [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]=>1 [1,4,5,3,2]=>1 [1,5,2,3,4]=>1 [1,5,2,4,3]=>1 [1,5,3,2,4]=>2 [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]=>2 [2,1,4,3,5]=>1 [2,1,4,5,3]=>1 [2,1,5,3,4]=>2 [2,1,5,4,3]=>1 [2,3,1,4,5]=>1 [2,3,1,5,4]=>2 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>2 [2,3,5,4,1]=>1 [2,4,1,3,5]=>2 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>2 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,4,3]=>1 [2,5,3,1,4]=>2 [2,5,3,4,1]=>1 [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]=>2 [3,1,5,4,2]=>2 [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]=>1 [3,4,1,5,2]=>1 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>1 [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]=>1 [3,5,4,1,2]=>1 [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]=>2 [4,1,5,2,3]=>1 [4,1,5,3,2]=>2 [4,2,1,3,5]=>2 [4,2,1,5,3]=>2 [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]=>2 [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]=>1 [4,5,1,3,2]=>2 [4,5,2,1,3]=>1 [4,5,2,3,1]=>1 [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]=>2 [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]=>1 [5,2,3,4,1]=>1 [5,2,4,1,3]=>1 [5,2,4,3,1]=>1 [5,3,1,2,4]=>2 [5,3,1,4,2]=>2 [5,3,2,1,4]=>1 [5,3,2,4,1]=>1 [5,3,4,1,2]=>1 [5,3,4,2,1]=>1 [5,4,1,2,3]=>1 [5,4,1,3,2]=>1 [5,4,2,1,3]=>1 [5,4,2,3,1]=>1 [5,4,3,1,2]=>1 [5,4,3,2,1]=>0 [1,2,3,4,5,6]=>0 [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]=>2 [1,2,4,6,5,3]=>2 [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]=>1 [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]=>2 [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]=>2 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>1 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>1 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>1 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>2 [1,3,5,2,4,6]=>2 [1,3,5,2,6,4]=>2 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>2 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>2 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>2 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>2 [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]=>1 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>2 [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]=>2 [1,4,3,6,5,2]=>2 [1,4,5,2,3,6]=>1 [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]=>1 [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]=>2 [1,4,6,3,5,2]=>2 [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]=>1 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>1 [1,5,2,6,4,3]=>2 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>2 [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]=>2 [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]=>1 [1,5,6,2,4,3]=>2 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>2 [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]=>2 [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]=>2 [1,6,3,2,5,4]=>2 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>2 [1,6,4,2,3,5]=>2 [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]=>2 [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]=>2 [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]=>2 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>2 [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]=>1 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>2 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>2 [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]=>2 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>2 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>2 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>2 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>2 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>2 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>2 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>1 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>2 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>2 [2,3,6,1,4,5]=>2 [2,3,6,1,5,4]=>2 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>1 [2,3,6,5,1,4]=>2 [2,3,6,5,4,1]=>1 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>2 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>2 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>2 [2,4,5,1,3,6]=>2 [2,4,5,1,6,3]=>2 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>2 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>2 [2,4,6,1,3,5]=>2 [2,4,6,1,5,3]=>2 [2,4,6,3,1,5]=>2 [2,4,6,3,5,1]=>2 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>2 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>2 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>2 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>2 [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]=>2 [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]=>2 [2,5,4,6,3,1]=>2 [2,5,6,1,3,4]=>2 [2,5,6,1,4,3]=>2 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>2 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>2 [2,6,1,3,4,5]=>2 [2,6,1,3,5,4]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>1 [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]=>1 [2,6,3,5,1,4]=>2 [2,6,3,5,4,1]=>1 [2,6,4,1,3,5]=>2 [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]=>2 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>1 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>1 [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]=>2 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>1 [3,1,2,6,4,5]=>2 [3,1,2,6,5,4]=>1 [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]=>1 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>2 [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]=>2 [3,1,5,6,4,2]=>2 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>2 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>1 [3,2,1,5,6,4]=>1 [3,2,1,6,4,5]=>2 [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]=>1 [3,2,4,6,1,5]=>2 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>2 [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]=>2 [3,2,5,6,4,1]=>2 [3,2,6,1,4,5]=>2 [3,2,6,1,5,4]=>1 [3,2,6,4,1,5]=>2 [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]=>1 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>1 [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]=>2 [3,4,2,5,1,6]=>1 [3,4,2,5,6,1]=>1 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>2 [3,4,5,1,2,6]=>1 [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]=>1 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>2 [3,4,6,1,5,2]=>2 [3,4,6,2,1,5]=>2 [3,4,6,2,5,1]=>2 [3,4,6,5,1,2]=>1 [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]=>2 [3,5,1,6,4,2]=>2 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>2 [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]=>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]=>2 [3,5,6,1,4,2]=>2 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>2 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>2 [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]=>2 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>1 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>2 [3,6,2,5,1,4]=>1 [3,6,2,5,4,1]=>1 [3,6,4,1,2,5]=>2 [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]=>2 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>1 [3,6,5,2,4,1]=>1 [3,6,5,4,1,2]=>1 [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]=>2 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>2 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>2 [4,1,5,3,6,2]=>2 [4,1,5,6,2,3]=>1 [4,1,5,6,3,2]=>2 [4,1,6,2,3,5]=>2 [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]=>2 [4,1,6,5,3,2]=>2 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>2 [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]=>2 [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]=>2 [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]=>2 [4,3,1,5,6,2]=>2 [4,3,1,6,2,5]=>2 [4,3,1,6,5,2]=>2 [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]=>2 [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]=>1 [4,3,6,5,1,2]=>2 [4,3,6,5,2,1]=>1 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>1 [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]=>2 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>2 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>2 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>2 [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]=>2 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>1 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>2 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>2 [4,6,1,5,2,3]=>2 [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]=>2 [4,6,2,3,5,1]=>2 [4,6,2,5,1,3]=>2 [4,6,2,5,3,1]=>2 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>2 [4,6,3,2,1,5]=>1 [4,6,3,2,5,1]=>1 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>1 [4,6,5,1,2,3]=>1 [4,6,5,1,3,2]=>2 [4,6,5,2,1,3]=>1 [4,6,5,2,3,1]=>1 [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]=>2 [5,1,2,6,3,4]=>1 [5,1,2,6,4,3]=>2 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>2 [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]=>2 [5,1,4,3,2,6]=>1 [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]=>2 [5,1,6,4,2,3]=>2 [5,1,6,4,3,2]=>2 [5,2,1,3,4,6]=>2 [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]=>2 [5,2,1,6,4,3]=>2 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>2 [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]=>2 [5,2,4,6,3,1]=>2 [5,2,6,1,3,4]=>2 [5,2,6,1,4,3]=>2 [5,2,6,3,1,4]=>2 [5,2,6,3,4,1]=>2 [5,2,6,4,1,3]=>2 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>2 [5,3,1,2,6,4]=>2 [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]=>2 [5,3,2,1,6,4]=>2 [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]=>2 [5,3,4,1,6,2]=>2 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>2 [5,3,4,6,1,2]=>2 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>2 [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]=>2 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>2 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>2 [5,4,1,6,3,2]=>2 [5,4,2,1,3,6]=>2 [5,4,2,1,6,3]=>2 [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]=>2 [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]=>2 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>2 [5,4,6,2,3,1]=>2 [5,4,6,3,1,2]=>2 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>1 [5,6,1,2,4,3]=>2 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>2 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>2 [5,6,2,1,3,4]=>1 [5,6,2,1,4,3]=>2 [5,6,2,3,1,4]=>1 [5,6,2,3,4,1]=>1 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>2 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>2 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>1 [5,6,3,4,1,2]=>2 [5,6,3,4,2,1]=>1 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>2 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>2 [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]=>2 [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]=>2 [6,1,3,2,5,4]=>2 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>2 [6,1,3,5,4,2]=>2 [6,1,4,2,3,5]=>2 [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]=>2 [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]=>2 [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]=>2 [6,2,1,4,3,5]=>2 [6,2,1,4,5,3]=>2 [6,2,1,5,3,4]=>2 [6,2,1,5,4,3]=>1 [6,2,3,1,4,5]=>1 [6,2,3,1,5,4]=>2 [6,2,3,4,1,5]=>1 [6,2,3,4,5,1]=>1 [6,2,3,5,1,4]=>2 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>2 [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]=>2 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>1 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>1 [6,2,5,4,1,3]=>1 [6,2,5,4,3,1]=>1 [6,3,1,2,4,5]=>2 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>2 [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]=>1 [6,3,2,4,5,1]=>1 [6,3,2,5,1,4]=>1 [6,3,2,5,4,1]=>1 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>2 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>1 [6,3,4,5,1,2]=>1 [6,3,4,5,2,1]=>1 [6,3,5,1,2,4]=>2 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>1 [6,3,5,2,4,1]=>1 [6,3,5,4,1,2]=>1 [6,3,5,4,2,1]=>1 [6,4,1,2,3,5]=>2 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>2 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>2 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>2 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>2 [6,4,2,3,5,1]=>2 [6,4,2,5,1,3]=>2 [6,4,2,5,3,1]=>2 [6,4,3,1,2,5]=>2 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>1 [6,4,3,5,1,2]=>2 [6,4,3,5,2,1]=>1 [6,4,5,1,2,3]=>1 [6,4,5,1,3,2]=>2 [6,4,5,2,1,3]=>1 [6,4,5,2,3,1]=>1 [6,4,5,3,1,2]=>2 [6,4,5,3,2,1]=>1 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>1 [6,5,1,3,2,4]=>2 [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]=>1 [6,5,2,3,4,1]=>1 [6,5,2,4,1,3]=>1 [6,5,2,4,3,1]=>1 [6,5,3,1,2,4]=>2 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>1 [6,5,3,4,1,2]=>1 [6,5,3,4,2,1]=>1 [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]=>1 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>0 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,4,6,7,5]=>1 [1,2,3,4,7,5,6]=>1 [1,2,3,4,7,6,5]=>1 [1,2,3,5,4,6,7]=>1 [1,2,3,5,4,7,6]=>1 [1,2,3,5,6,4,7]=>1 [1,2,3,5,6,7,4]=>1 [1,2,3,5,7,4,6]=>2 [1,2,3,5,7,6,4]=>2 [1,2,3,6,4,5,7]=>1 [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]=>1 [1,2,3,6,7,5,4]=>1 [1,2,3,7,4,5,6]=>1 [1,2,3,7,4,6,5]=>1 [1,2,3,7,5,4,6]=>2 [1,2,3,7,5,6,4]=>2 [1,2,3,7,6,4,5]=>1 [1,2,3,7,6,5,4]=>1 [1,2,4,3,5,6,7]=>1 [1,2,4,3,5,7,6]=>2 [1,2,4,3,6,5,7]=>1 [1,2,4,3,6,7,5]=>1 [1,2,4,3,7,5,6]=>2 [1,2,4,3,7,6,5]=>1 [1,2,4,5,3,6,7]=>1 [1,2,4,5,3,7,6]=>2 [1,2,4,5,6,3,7]=>1 [1,2,4,5,6,7,3]=>1 [1,2,4,5,7,3,6]=>2 [1,2,4,5,7,6,3]=>2 [1,2,4,6,3,5,7]=>2 [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]=>2 [1,2,4,6,7,5,3]=>2 [1,2,4,7,3,5,6]=>2 [1,2,4,7,3,6,5]=>2 [1,2,4,7,5,3,6]=>2 [1,2,4,7,5,6,3]=>2 [1,2,4,7,6,3,5]=>2 [1,2,4,7,6,5,3]=>2 [1,2,5,3,4,6,7]=>1 [1,2,5,3,4,7,6]=>1 [1,2,5,3,6,4,7]=>1 [1,2,5,3,6,7,4]=>1 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>2 [1,2,5,4,3,6,7]=>1 [1,2,5,4,3,7,6]=>1 [1,2,5,4,6,3,7]=>1 [1,2,5,4,6,7,3]=>1 [1,2,5,4,7,3,6]=>2 [1,2,5,4,7,6,3]=>2 [1,2,5,6,3,4,7]=>1 [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]=>1 [1,2,5,6,7,4,3]=>1 [1,2,5,7,3,4,6]=>2 [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]=>2 [1,2,5,7,6,4,3]=>2 [1,2,6,3,4,5,7]=>1 [1,2,6,3,4,7,5]=>1 [1,2,6,3,5,4,7]=>1 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>1 [1,2,6,3,7,5,4]=>2 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>2 [1,2,6,4,5,3,7]=>2 [1,2,6,4,5,7,3]=>2 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>2 [1,2,6,5,3,4,7]=>1 [1,2,6,5,3,7,4]=>2 [1,2,6,5,4,3,7]=>1 [1,2,6,5,4,7,3]=>1 [1,2,6,5,7,3,4]=>2 [1,2,6,5,7,4,3]=>1 [1,2,6,7,3,4,5]=>1 [1,2,6,7,3,5,4]=>2 [1,2,6,7,4,3,5]=>2 [1,2,6,7,4,5,3]=>2 [1,2,6,7,5,3,4]=>2 [1,2,6,7,5,4,3]=>1 [1,2,7,3,4,5,6]=>1 [1,2,7,3,4,6,5]=>1 [1,2,7,3,5,4,6]=>2 [1,2,7,3,5,6,4]=>2 [1,2,7,3,6,4,5]=>1 [1,2,7,3,6,5,4]=>1 [1,2,7,4,3,5,6]=>2 [1,2,7,4,3,6,5]=>2 [1,2,7,4,5,3,6]=>2 [1,2,7,4,5,6,3]=>2 [1,2,7,4,6,3,5]=>2 [1,2,7,4,6,5,3]=>2 [1,2,7,5,3,4,6]=>2 [1,2,7,5,3,6,4]=>2 [1,2,7,5,4,3,6]=>2 [1,2,7,5,4,6,3]=>2 [1,2,7,5,6,3,4]=>2 [1,2,7,5,6,4,3]=>2 [1,2,7,6,3,4,5]=>1 [1,2,7,6,3,5,4]=>1 [1,2,7,6,4,3,5]=>2 [1,2,7,6,4,5,3]=>2 [1,2,7,6,5,3,4]=>1 [1,2,7,6,5,4,3]=>1 [1,3,2,4,5,6,7]=>1 [1,3,2,4,5,7,6]=>2 [1,3,2,4,6,5,7]=>2 [1,3,2,4,6,7,5]=>2 [1,3,2,4,7,5,6]=>2 [1,3,2,4,7,6,5]=>2 [1,3,2,5,4,6,7]=>1 [1,3,2,5,4,7,6]=>2 [1,3,2,5,6,4,7]=>1 [1,3,2,5,6,7,4]=>1 [1,3,2,5,7,4,6]=>2 [1,3,2,5,7,6,4]=>2 [1,3,2,6,4,5,7]=>2 [1,3,2,6,4,7,5]=>2 [1,3,2,6,5,4,7]=>1 [1,3,2,6,5,7,4]=>2 [1,3,2,6,7,4,5]=>2 [1,3,2,6,7,5,4]=>2 [1,3,2,7,4,5,6]=>2 [1,3,2,7,4,6,5]=>2 [1,3,2,7,5,4,6]=>2 [1,3,2,7,5,6,4]=>2 [1,3,2,7,6,4,5]=>2 [1,3,2,7,6,5,4]=>1 [1,3,4,2,5,6,7]=>1 [1,3,4,2,5,7,6]=>2 [1,3,4,2,6,5,7]=>2 [1,3,4,2,6,7,5]=>2 [1,3,4,2,7,5,6]=>2 [1,3,4,2,7,6,5]=>2 [1,3,4,5,2,6,7]=>1 [1,3,4,5,2,7,6]=>2 [1,3,4,5,6,2,7]=>1 [1,3,4,5,6,7,2]=>1 [1,3,4,5,7,2,6]=>2 [1,3,4,5,7,6,2]=>2 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>2 [1,3,4,6,5,2,7]=>2 [1,3,4,6,5,7,2]=>2 [1,3,4,6,7,2,5]=>2 [1,3,4,6,7,5,2]=>2 [1,3,4,7,2,5,6]=>2 [1,3,4,7,2,6,5]=>2 [1,3,4,7,5,2,6]=>2 [1,3,4,7,5,6,2]=>2 [1,3,4,7,6,2,5]=>2 [1,3,4,7,6,5,2]=>2 [1,3,5,2,4,6,7]=>2 [1,3,5,2,4,7,6]=>2 [1,3,5,2,6,4,7]=>2 [1,3,5,2,6,7,4]=>2 [1,3,5,2,7,4,6]=>2 [1,3,5,2,7,6,4]=>2 [1,3,5,4,2,6,7]=>2 [1,3,5,4,2,7,6]=>2 [1,3,5,4,6,2,7]=>2 [1,3,5,4,6,7,2]=>2 [1,3,5,4,7,2,6]=>2 [1,3,5,4,7,6,2]=>2 [1,3,5,6,2,4,7]=>2 [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]=>2 [1,3,5,7,2,4,6]=>3 [1,3,5,7,2,6,4]=>3 [1,3,5,7,4,2,6]=>3 [1,3,5,7,4,6,2]=>3 [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]=>2 [1,3,6,2,5,4,7]=>2 [1,3,6,2,5,7,4]=>2 [1,3,6,2,7,4,5]=>2 [1,3,6,2,7,5,4]=>2 [1,3,6,4,2,5,7]=>2 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>2 [1,3,6,4,5,7,2]=>2 [1,3,6,4,7,2,5]=>2 [1,3,6,4,7,5,2]=>2 [1,3,6,5,2,4,7]=>2 [1,3,6,5,2,7,4]=>2 [1,3,6,5,4,2,7]=>2 [1,3,6,5,4,7,2]=>2 [1,3,6,5,7,2,4]=>2 [1,3,6,5,7,4,2]=>2 [1,3,6,7,2,4,5]=>2 [1,3,6,7,2,5,4]=>2 [1,3,6,7,4,2,5]=>2 [1,3,6,7,4,5,2]=>2 [1,3,6,7,5,2,4]=>2 [1,3,6,7,5,4,2]=>2 [1,3,7,2,4,5,6]=>2 [1,3,7,2,4,6,5]=>2 [1,3,7,2,5,4,6]=>2 [1,3,7,2,5,6,4]=>2 [1,3,7,2,6,4,5]=>2 [1,3,7,2,6,5,4]=>2 [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]=>2 [1,3,7,4,6,2,5]=>2 [1,3,7,4,6,5,2]=>2 [1,3,7,5,2,4,6]=>3 [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]=>3 [1,3,7,6,2,4,5]=>2 [1,3,7,6,2,5,4]=>2 [1,3,7,6,4,2,5]=>2 [1,3,7,6,4,5,2]=>2 [1,3,7,6,5,2,4]=>2 [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]=>1 [1,4,2,3,6,7,5]=>1 [1,4,2,3,7,5,6]=>2 [1,4,2,3,7,6,5]=>1 [1,4,2,5,3,6,7]=>1 [1,4,2,5,3,7,6]=>2 [1,4,2,5,6,3,7]=>1 [1,4,2,5,6,7,3]=>1 [1,4,2,5,7,3,6]=>2 [1,4,2,5,7,6,3]=>2 [1,4,2,6,3,5,7]=>2 [1,4,2,6,3,7,5]=>2 [1,4,2,6,5,3,7]=>2 [1,4,2,6,5,7,3]=>2 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>2 [1,4,2,7,3,5,6]=>2 [1,4,2,7,3,6,5]=>2 [1,4,2,7,5,3,6]=>2 [1,4,2,7,5,6,3]=>2 [1,4,2,7,6,3,5]=>2 [1,4,2,7,6,5,3]=>2 [1,4,3,2,5,6,7]=>1 [1,4,3,2,5,7,6]=>2 [1,4,3,2,6,5,7]=>1 [1,4,3,2,6,7,5]=>1 [1,4,3,2,7,5,6]=>2 [1,4,3,2,7,6,5]=>1 [1,4,3,5,2,6,7]=>1 [1,4,3,5,2,7,6]=>2 [1,4,3,5,6,2,7]=>1 [1,4,3,5,6,7,2]=>1 [1,4,3,5,7,2,6]=>2 [1,4,3,5,7,6,2]=>2 [1,4,3,6,2,5,7]=>2 [1,4,3,6,2,7,5]=>2 [1,4,3,6,5,2,7]=>2 [1,4,3,6,5,7,2]=>2 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>2 [1,4,3,7,2,5,6]=>2 [1,4,3,7,2,6,5]=>2 [1,4,3,7,5,2,6]=>2 [1,4,3,7,5,6,2]=>2 [1,4,3,7,6,2,5]=>2 [1,4,3,7,6,5,2]=>2 [1,4,5,2,3,6,7]=>1 [1,4,5,2,3,7,6]=>2 [1,4,5,2,6,3,7]=>1 [1,4,5,2,6,7,3]=>1 [1,4,5,2,7,3,6]=>2 [1,4,5,2,7,6,3]=>2 [1,4,5,3,2,6,7]=>1 [1,4,5,3,2,7,6]=>2 [1,4,5,3,6,2,7]=>1 [1,4,5,3,6,7,2]=>1 [1,4,5,3,7,2,6]=>2 [1,4,5,3,7,6,2]=>2 [1,4,5,6,2,3,7]=>1 [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]=>1 [1,4,5,6,7,3,2]=>1 [1,4,5,7,2,3,6]=>2 [1,4,5,7,2,6,3]=>2 [1,4,5,7,3,2,6]=>2 [1,4,5,7,3,6,2]=>2 [1,4,5,7,6,2,3]=>2 [1,4,5,7,6,3,2]=>2 [1,4,6,2,3,5,7]=>2 [1,4,6,2,3,7,5]=>2 [1,4,6,2,5,3,7]=>2 [1,4,6,2,5,7,3]=>2 [1,4,6,2,7,3,5]=>2 [1,4,6,2,7,5,3]=>2 [1,4,6,3,2,5,7]=>2 [1,4,6,3,2,7,5]=>2 [1,4,6,3,5,2,7]=>2 [1,4,6,3,5,7,2]=>2 [1,4,6,3,7,2,5]=>2 [1,4,6,3,7,5,2]=>2 [1,4,6,5,2,3,7]=>2 [1,4,6,5,2,7,3]=>2 [1,4,6,5,3,2,7]=>2
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Description
The holeyness of a permutation.
For $S\subset [n]:=\{1,2,\dots,n\}$ let $\delta(S)$ be the number of elements $m\in S$ such that $m+1\notin S$.
For a permutation $\pi$ of $[n]$ the holeyness of $\pi$ is $$\max_{S\subset [n]} (\delta(\pi(S))-\delta(S)).$$
References
[1] Helfgott, H. A. How rare are unholey permutations? MathOverflow:340179
Code
def delta(S): return sum(1 for m in S if m + 1 not in S)

def statistic(pi):
    n = len(pi)
    m = 0
    for S in subsets(range(1, n+1)):
        h_pi = delta([pi(s) for s in S])
        h_S = delta(S)
        m = max(m, h_pi-h_S)

    return m
Created
Sep 09, 2019 at 07:41 by Martin Rubey
Updated
Sep 09, 2019 at 07:41 by Martin Rubey