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]=>0 [2,1,3]=>0 [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]=>0 [1,3,4,2]=>0 [1,4,2,3]=>0 [1,4,3,2]=>0 [2,1,3,4]=>0 [2,1,4,3]=>0 [2,3,1,4]=>0 [2,3,4,1]=>0 [2,4,1,3]=>0 [2,4,3,1]=>0 [3,1,2,4]=>0 [3,1,4,2]=>0 [3,2,1,4]=>0 [3,2,4,1]=>0 [3,4,1,2]=>1 [3,4,2,1]=>0 [4,1,2,3]=>0 [4,1,3,2]=>0 [4,2,1,3]=>0 [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]=>0 [1,2,4,5,3]=>0 [1,2,5,3,4]=>0 [1,2,5,4,3]=>0 [1,3,2,4,5]=>0 [1,3,2,5,4]=>0 [1,3,4,2,5]=>0 [1,3,4,5,2]=>0 [1,3,5,2,4]=>0 [1,3,5,4,2]=>0 [1,4,2,3,5]=>0 [1,4,2,5,3]=>0 [1,4,3,2,5]=>0 [1,4,3,5,2]=>0 [1,4,5,2,3]=>1 [1,4,5,3,2]=>0 [1,5,2,3,4]=>0 [1,5,2,4,3]=>0 [1,5,3,2,4]=>0 [1,5,3,4,2]=>0 [1,5,4,2,3]=>0 [1,5,4,3,2]=>0 [2,1,3,4,5]=>0 [2,1,3,5,4]=>0 [2,1,4,3,5]=>0 [2,1,4,5,3]=>0 [2,1,5,3,4]=>0 [2,1,5,4,3]=>0 [2,3,1,4,5]=>0 [2,3,1,5,4]=>0 [2,3,4,1,5]=>0 [2,3,4,5,1]=>0 [2,3,5,1,4]=>0 [2,3,5,4,1]=>0 [2,4,1,3,5]=>0 [2,4,1,5,3]=>0 [2,4,3,1,5]=>0 [2,4,3,5,1]=>0 [2,4,5,1,3]=>1 [2,4,5,3,1]=>0 [2,5,1,3,4]=>0 [2,5,1,4,3]=>0 [2,5,3,1,4]=>0 [2,5,3,4,1]=>0 [2,5,4,1,3]=>0 [2,5,4,3,1]=>0 [3,1,2,4,5]=>0 [3,1,2,5,4]=>0 [3,1,4,2,5]=>0 [3,1,4,5,2]=>0 [3,1,5,2,4]=>0 [3,1,5,4,2]=>0 [3,2,1,4,5]=>0 [3,2,1,5,4]=>0 [3,2,4,1,5]=>0 [3,2,4,5,1]=>0 [3,2,5,1,4]=>0 [3,2,5,4,1]=>0 [3,4,1,2,5]=>1 [3,4,1,5,2]=>1 [3,4,2,1,5]=>0 [3,4,2,5,1]=>0 [3,4,5,1,2]=>1 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,4,2]=>1 [3,5,2,1,4]=>0 [3,5,2,4,1]=>0 [3,5,4,1,2]=>1 [3,5,4,2,1]=>0 [4,1,2,3,5]=>0 [4,1,2,5,3]=>0 [4,1,3,2,5]=>0 [4,1,3,5,2]=>0 [4,1,5,2,3]=>1 [4,1,5,3,2]=>0 [4,2,1,3,5]=>0 [4,2,1,5,3]=>0 [4,2,3,1,5]=>0 [4,2,3,5,1]=>0 [4,2,5,1,3]=>1 [4,2,5,3,1]=>0 [4,3,1,2,5]=>0 [4,3,1,5,2]=>0 [4,3,2,1,5]=>0 [4,3,2,5,1]=>0 [4,3,5,1,2]=>1 [4,3,5,2,1]=>0 [4,5,1,2,3]=>1 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>0 [4,5,3,1,2]=>1 [4,5,3,2,1]=>0 [5,1,2,3,4]=>0 [5,1,2,4,3]=>0 [5,1,3,2,4]=>0 [5,1,3,4,2]=>0 [5,1,4,2,3]=>0 [5,1,4,3,2]=>0 [5,2,1,3,4]=>0 [5,2,1,4,3]=>0 [5,2,3,1,4]=>0 [5,2,3,4,1]=>0 [5,2,4,1,3]=>0 [5,2,4,3,1]=>0 [5,3,1,2,4]=>0 [5,3,1,4,2]=>0 [5,3,2,1,4]=>0 [5,3,2,4,1]=>0 [5,3,4,1,2]=>0 [5,3,4,2,1]=>0 [5,4,1,2,3]=>1 [5,4,1,3,2]=>0 [5,4,2,1,3]=>0 [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]=>0 [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]=>0 [1,2,4,5,3,6]=>0 [1,2,4,5,6,3]=>0 [1,2,4,6,3,5]=>0 [1,2,4,6,5,3]=>0 [1,2,5,3,4,6]=>0 [1,2,5,3,6,4]=>0 [1,2,5,4,3,6]=>0 [1,2,5,4,6,3]=>0 [1,2,5,6,3,4]=>1 [1,2,5,6,4,3]=>0 [1,2,6,3,4,5]=>0 [1,2,6,3,5,4]=>0 [1,2,6,4,3,5]=>0 [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]=>0 [1,3,2,4,6,5]=>0 [1,3,2,5,4,6]=>0 [1,3,2,5,6,4]=>0 [1,3,2,6,4,5]=>0 [1,3,2,6,5,4]=>0 [1,3,4,2,5,6]=>0 [1,3,4,2,6,5]=>0 [1,3,4,5,2,6]=>0 [1,3,4,5,6,2]=>0 [1,3,4,6,2,5]=>0 [1,3,4,6,5,2]=>0 [1,3,5,2,4,6]=>0 [1,3,5,2,6,4]=>0 [1,3,5,4,2,6]=>0 [1,3,5,4,6,2]=>0 [1,3,5,6,2,4]=>1 [1,3,5,6,4,2]=>0 [1,3,6,2,4,5]=>0 [1,3,6,2,5,4]=>0 [1,3,6,4,2,5]=>0 [1,3,6,4,5,2]=>0 [1,3,6,5,2,4]=>0 [1,3,6,5,4,2]=>0 [1,4,2,3,5,6]=>0 [1,4,2,3,6,5]=>0 [1,4,2,5,3,6]=>0 [1,4,2,5,6,3]=>0 [1,4,2,6,3,5]=>0 [1,4,2,6,5,3]=>0 [1,4,3,2,5,6]=>0 [1,4,3,2,6,5]=>0 [1,4,3,5,2,6]=>0 [1,4,3,5,6,2]=>0 [1,4,3,6,2,5]=>0 [1,4,3,6,5,2]=>0 [1,4,5,2,3,6]=>1 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>0 [1,4,5,3,6,2]=>0 [1,4,5,6,2,3]=>1 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>1 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>0 [1,4,6,3,5,2]=>0 [1,4,6,5,2,3]=>1 [1,4,6,5,3,2]=>0 [1,5,2,3,4,6]=>0 [1,5,2,3,6,4]=>0 [1,5,2,4,3,6]=>0 [1,5,2,4,6,3]=>0 [1,5,2,6,3,4]=>1 [1,5,2,6,4,3]=>0 [1,5,3,2,4,6]=>0 [1,5,3,2,6,4]=>0 [1,5,3,4,2,6]=>0 [1,5,3,4,6,2]=>0 [1,5,3,6,2,4]=>1 [1,5,3,6,4,2]=>0 [1,5,4,2,3,6]=>0 [1,5,4,2,6,3]=>0 [1,5,4,3,2,6]=>0 [1,5,4,3,6,2]=>0 [1,5,4,6,2,3]=>1 [1,5,4,6,3,2]=>0 [1,5,6,2,3,4]=>1 [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]=>1 [1,5,6,4,3,2]=>0 [1,6,2,3,4,5]=>0 [1,6,2,3,5,4]=>0 [1,6,2,4,3,5]=>0 [1,6,2,4,5,3]=>0 [1,6,2,5,3,4]=>0 [1,6,2,5,4,3]=>0 [1,6,3,2,4,5]=>0 [1,6,3,2,5,4]=>0 [1,6,3,4,2,5]=>0 [1,6,3,4,5,2]=>0 [1,6,3,5,2,4]=>0 [1,6,3,5,4,2]=>0 [1,6,4,2,3,5]=>0 [1,6,4,2,5,3]=>0 [1,6,4,3,2,5]=>0 [1,6,4,3,5,2]=>0 [1,6,4,5,2,3]=>0 [1,6,4,5,3,2]=>0 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>0 [1,6,5,3,2,4]=>0 [1,6,5,3,4,2]=>0 [1,6,5,4,2,3]=>0 [1,6,5,4,3,2]=>0 [2,1,3,4,5,6]=>0 [2,1,3,4,6,5]=>0 [2,1,3,5,4,6]=>0 [2,1,3,5,6,4]=>0 [2,1,3,6,4,5]=>0 [2,1,3,6,5,4]=>0 [2,1,4,3,5,6]=>0 [2,1,4,3,6,5]=>0 [2,1,4,5,3,6]=>0 [2,1,4,5,6,3]=>0 [2,1,4,6,3,5]=>0 [2,1,4,6,5,3]=>0 [2,1,5,3,4,6]=>0 [2,1,5,3,6,4]=>0 [2,1,5,4,3,6]=>0 [2,1,5,4,6,3]=>0 [2,1,5,6,3,4]=>1 [2,1,5,6,4,3]=>0 [2,1,6,3,4,5]=>0 [2,1,6,3,5,4]=>0 [2,1,6,4,3,5]=>0 [2,1,6,4,5,3]=>0 [2,1,6,5,3,4]=>0 [2,1,6,5,4,3]=>0 [2,3,1,4,5,6]=>0 [2,3,1,4,6,5]=>0 [2,3,1,5,4,6]=>0 [2,3,1,5,6,4]=>0 [2,3,1,6,4,5]=>0 [2,3,1,6,5,4]=>0 [2,3,4,1,5,6]=>0 [2,3,4,1,6,5]=>0 [2,3,4,5,1,6]=>0 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>0 [2,3,4,6,5,1]=>0 [2,3,5,1,4,6]=>0 [2,3,5,1,6,4]=>0 [2,3,5,4,1,6]=>0 [2,3,5,4,6,1]=>0 [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]=>0 [2,3,6,4,1,5]=>0 [2,3,6,4,5,1]=>0 [2,3,6,5,1,4]=>0 [2,3,6,5,4,1]=>0 [2,4,1,3,5,6]=>0 [2,4,1,3,6,5]=>0 [2,4,1,5,3,6]=>0 [2,4,1,5,6,3]=>0 [2,4,1,6,3,5]=>0 [2,4,1,6,5,3]=>0 [2,4,3,1,5,6]=>0 [2,4,3,1,6,5]=>0 [2,4,3,5,1,6]=>0 [2,4,3,5,6,1]=>0 [2,4,3,6,1,5]=>0 [2,4,3,6,5,1]=>0 [2,4,5,1,3,6]=>1 [2,4,5,1,6,3]=>1 [2,4,5,3,1,6]=>0 [2,4,5,3,6,1]=>0 [2,4,5,6,1,3]=>1 [2,4,5,6,3,1]=>1 [2,4,6,1,3,5]=>1 [2,4,6,1,5,3]=>1 [2,4,6,3,1,5]=>0 [2,4,6,3,5,1]=>0 [2,4,6,5,1,3]=>1 [2,4,6,5,3,1]=>0 [2,5,1,3,4,6]=>0 [2,5,1,3,6,4]=>0 [2,5,1,4,3,6]=>0 [2,5,1,4,6,3]=>0 [2,5,1,6,3,4]=>1 [2,5,1,6,4,3]=>0 [2,5,3,1,4,6]=>0 [2,5,3,1,6,4]=>0 [2,5,3,4,1,6]=>0 [2,5,3,4,6,1]=>0 [2,5,3,6,1,4]=>1 [2,5,3,6,4,1]=>0 [2,5,4,1,3,6]=>0 [2,5,4,1,6,3]=>0 [2,5,4,3,1,6]=>0 [2,5,4,3,6,1]=>0 [2,5,4,6,1,3]=>1 [2,5,4,6,3,1]=>0 [2,5,6,1,3,4]=>1 [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]=>0 [2,6,1,3,5,4]=>0 [2,6,1,4,3,5]=>0 [2,6,1,4,5,3]=>0 [2,6,1,5,3,4]=>0 [2,6,1,5,4,3]=>0 [2,6,3,1,4,5]=>0 [2,6,3,1,5,4]=>0 [2,6,3,4,1,5]=>0 [2,6,3,4,5,1]=>0 [2,6,3,5,1,4]=>0 [2,6,3,5,4,1]=>0 [2,6,4,1,3,5]=>0 [2,6,4,1,5,3]=>0 [2,6,4,3,1,5]=>0 [2,6,4,3,5,1]=>0 [2,6,4,5,1,3]=>0 [2,6,4,5,3,1]=>0 [2,6,5,1,3,4]=>1 [2,6,5,1,4,3]=>0 [2,6,5,3,1,4]=>0 [2,6,5,3,4,1]=>0 [2,6,5,4,1,3]=>0 [2,6,5,4,3,1]=>0 [3,1,2,4,5,6]=>0 [3,1,2,4,6,5]=>0 [3,1,2,5,4,6]=>0 [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]=>0 [3,1,4,2,6,5]=>0 [3,1,4,5,2,6]=>0 [3,1,4,5,6,2]=>0 [3,1,4,6,2,5]=>0 [3,1,4,6,5,2]=>0 [3,1,5,2,4,6]=>0 [3,1,5,2,6,4]=>0 [3,1,5,4,2,6]=>0 [3,1,5,4,6,2]=>0 [3,1,5,6,2,4]=>1 [3,1,5,6,4,2]=>0 [3,1,6,2,4,5]=>0 [3,1,6,2,5,4]=>0 [3,1,6,4,2,5]=>0 [3,1,6,4,5,2]=>0 [3,1,6,5,2,4]=>0 [3,1,6,5,4,2]=>0 [3,2,1,4,5,6]=>0 [3,2,1,4,6,5]=>0 [3,2,1,5,4,6]=>0 [3,2,1,5,6,4]=>0 [3,2,1,6,4,5]=>0 [3,2,1,6,5,4]=>0 [3,2,4,1,5,6]=>0 [3,2,4,1,6,5]=>0 [3,2,4,5,1,6]=>0 [3,2,4,5,6,1]=>0 [3,2,4,6,1,5]=>0 [3,2,4,6,5,1]=>0 [3,2,5,1,4,6]=>0 [3,2,5,1,6,4]=>0 [3,2,5,4,1,6]=>0 [3,2,5,4,6,1]=>0 [3,2,5,6,1,4]=>1 [3,2,5,6,4,1]=>0 [3,2,6,1,4,5]=>0 [3,2,6,1,5,4]=>0 [3,2,6,4,1,5]=>0 [3,2,6,4,5,1]=>0 [3,2,6,5,1,4]=>0 [3,2,6,5,4,1]=>0 [3,4,1,2,5,6]=>1 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>1 [3,4,1,5,6,2]=>1 [3,4,1,6,2,5]=>1 [3,4,1,6,5,2]=>1 [3,4,2,1,5,6]=>0 [3,4,2,1,6,5]=>0 [3,4,2,5,1,6]=>0 [3,4,2,5,6,1]=>0 [3,4,2,6,1,5]=>0 [3,4,2,6,5,1]=>0 [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]=>2 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>1 [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]=>1 [3,4,6,5,2,1]=>1 [3,5,1,2,4,6]=>1 [3,5,1,2,6,4]=>1 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>1 [3,5,2,1,4,6]=>0 [3,5,2,1,6,4]=>0 [3,5,2,4,1,6]=>0 [3,5,2,4,6,1]=>0 [3,5,2,6,1,4]=>1 [3,5,2,6,4,1]=>0 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>1 [3,5,4,2,1,6]=>0 [3,5,4,2,6,1]=>0 [3,5,4,6,1,2]=>1 [3,5,4,6,2,1]=>1 [3,5,6,1,2,4]=>2 [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]=>1 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>1 [3,6,1,2,5,4]=>1 [3,6,1,4,2,5]=>1 [3,6,1,4,5,2]=>1 [3,6,1,5,2,4]=>1 [3,6,1,5,4,2]=>1 [3,6,2,1,4,5]=>0 [3,6,2,1,5,4]=>0 [3,6,2,4,1,5]=>0 [3,6,2,4,5,1]=>0 [3,6,2,5,1,4]=>0 [3,6,2,5,4,1]=>0 [3,6,4,1,2,5]=>1 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>0 [3,6,4,2,5,1]=>0 [3,6,4,5,1,2]=>1 [3,6,4,5,2,1]=>0 [3,6,5,1,2,4]=>1 [3,6,5,1,4,2]=>1 [3,6,5,2,1,4]=>1 [3,6,5,2,4,1]=>0 [3,6,5,4,1,2]=>1 [3,6,5,4,2,1]=>0 [4,1,2,3,5,6]=>0 [4,1,2,3,6,5]=>0 [4,1,2,5,3,6]=>0 [4,1,2,5,6,3]=>0 [4,1,2,6,3,5]=>0 [4,1,2,6,5,3]=>0 [4,1,3,2,5,6]=>0 [4,1,3,2,6,5]=>0 [4,1,3,5,2,6]=>0 [4,1,3,5,6,2]=>0 [4,1,3,6,2,5]=>0 [4,1,3,6,5,2]=>0 [4,1,5,2,3,6]=>1 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>0 [4,1,5,3,6,2]=>0 [4,1,5,6,2,3]=>1 [4,1,5,6,3,2]=>1 [4,1,6,2,3,5]=>1 [4,1,6,2,5,3]=>1 [4,1,6,3,2,5]=>0 [4,1,6,3,5,2]=>0 [4,1,6,5,2,3]=>1 [4,1,6,5,3,2]=>0 [4,2,1,3,5,6]=>0 [4,2,1,3,6,5]=>0 [4,2,1,5,3,6]=>0 [4,2,1,5,6,3]=>0 [4,2,1,6,3,5]=>0 [4,2,1,6,5,3]=>0 [4,2,3,1,5,6]=>0 [4,2,3,1,6,5]=>0 [4,2,3,5,1,6]=>0 [4,2,3,5,6,1]=>0 [4,2,3,6,1,5]=>0 [4,2,3,6,5,1]=>0 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>1 [4,2,5,3,1,6]=>0 [4,2,5,3,6,1]=>0 [4,2,5,6,1,3]=>1 [4,2,5,6,3,1]=>1 [4,2,6,1,3,5]=>1 [4,2,6,1,5,3]=>1 [4,2,6,3,1,5]=>0 [4,2,6,3,5,1]=>0 [4,2,6,5,1,3]=>1 [4,2,6,5,3,1]=>0 [4,3,1,2,5,6]=>0 [4,3,1,2,6,5]=>0 [4,3,1,5,2,6]=>0 [4,3,1,5,6,2]=>0 [4,3,1,6,2,5]=>0 [4,3,1,6,5,2]=>0 [4,3,2,1,5,6]=>0 [4,3,2,1,6,5]=>0 [4,3,2,5,1,6]=>0 [4,3,2,5,6,1]=>0 [4,3,2,6,1,5]=>0 [4,3,2,6,5,1]=>0 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>1 [4,3,5,2,1,6]=>0 [4,3,5,2,6,1]=>0 [4,3,5,6,1,2]=>1 [4,3,5,6,2,1]=>1 [4,3,6,1,2,5]=>1 [4,3,6,1,5,2]=>1 [4,3,6,2,1,5]=>0 [4,3,6,2,5,1]=>0 [4,3,6,5,1,2]=>1 [4,3,6,5,2,1]=>0 [4,5,1,2,3,6]=>1 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>1 [4,5,1,3,6,2]=>1 [4,5,1,6,2,3]=>2 [4,5,1,6,3,2]=>1 [4,5,2,1,3,6]=>1 [4,5,2,1,6,3]=>1 [4,5,2,3,1,6]=>0 [4,5,2,3,6,1]=>0 [4,5,2,6,1,3]=>1 [4,5,2,6,3,1]=>1 [4,5,3,1,2,6]=>1 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>0 [4,5,3,2,6,1]=>0 [4,5,3,6,1,2]=>1 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>1 [4,5,6,3,1,2]=>1 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>1 [4,6,1,2,5,3]=>1 [4,6,1,3,2,5]=>1 [4,6,1,3,5,2]=>1 [4,6,1,5,2,3]=>1 [4,6,1,5,3,2]=>1 [4,6,2,1,3,5]=>1 [4,6,2,1,5,3]=>1 [4,6,2,3,1,5]=>0 [4,6,2,3,5,1]=>0 [4,6,2,5,1,3]=>1 [4,6,2,5,3,1]=>0 [4,6,3,1,2,5]=>1 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>0 [4,6,3,2,5,1]=>0 [4,6,3,5,1,2]=>1 [4,6,3,5,2,1]=>0 [4,6,5,1,2,3]=>2 [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]=>1 [4,6,5,3,2,1]=>0 [5,1,2,3,4,6]=>0 [5,1,2,3,6,4]=>0 [5,1,2,4,3,6]=>0 [5,1,2,4,6,3]=>0 [5,1,2,6,3,4]=>1 [5,1,2,6,4,3]=>0 [5,1,3,2,4,6]=>0 [5,1,3,2,6,4]=>0 [5,1,3,4,2,6]=>0 [5,1,3,4,6,2]=>0 [5,1,3,6,2,4]=>1 [5,1,3,6,4,2]=>0 [5,1,4,2,3,6]=>0 [5,1,4,2,6,3]=>0 [5,1,4,3,2,6]=>0 [5,1,4,3,6,2]=>0 [5,1,4,6,2,3]=>1 [5,1,4,6,3,2]=>0 [5,1,6,2,3,4]=>1 [5,1,6,2,4,3]=>1 [5,1,6,3,2,4]=>1 [5,1,6,3,4,2]=>0 [5,1,6,4,2,3]=>1 [5,1,6,4,3,2]=>0 [5,2,1,3,4,6]=>0 [5,2,1,3,6,4]=>0 [5,2,1,4,3,6]=>0 [5,2,1,4,6,3]=>0 [5,2,1,6,3,4]=>1 [5,2,1,6,4,3]=>0 [5,2,3,1,4,6]=>0 [5,2,3,1,6,4]=>0 [5,2,3,4,1,6]=>0 [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]=>0 [5,2,4,1,6,3]=>0 [5,2,4,3,1,6]=>0 [5,2,4,3,6,1]=>0 [5,2,4,6,1,3]=>1 [5,2,4,6,3,1]=>0 [5,2,6,1,3,4]=>1 [5,2,6,1,4,3]=>1 [5,2,6,3,1,4]=>1 [5,2,6,3,4,1]=>0 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>0 [5,3,1,2,4,6]=>0 [5,3,1,2,6,4]=>0 [5,3,1,4,2,6]=>0 [5,3,1,4,6,2]=>0 [5,3,1,6,2,4]=>1 [5,3,1,6,4,2]=>0 [5,3,2,1,4,6]=>0 [5,3,2,1,6,4]=>0 [5,3,2,4,1,6]=>0 [5,3,2,4,6,1]=>0 [5,3,2,6,1,4]=>1 [5,3,2,6,4,1]=>0 [5,3,4,1,2,6]=>0 [5,3,4,1,6,2]=>0 [5,3,4,2,1,6]=>0 [5,3,4,2,6,1]=>0 [5,3,4,6,1,2]=>1 [5,3,4,6,2,1]=>0 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>1 [5,3,6,2,1,4]=>1 [5,3,6,2,4,1]=>0 [5,3,6,4,1,2]=>1 [5,3,6,4,2,1]=>0 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>1 [5,4,1,3,2,6]=>0 [5,4,1,3,6,2]=>0 [5,4,1,6,2,3]=>1 [5,4,1,6,3,2]=>1 [5,4,2,1,3,6]=>0 [5,4,2,1,6,3]=>0 [5,4,2,3,1,6]=>0 [5,4,2,3,6,1]=>0 [5,4,2,6,1,3]=>1 [5,4,2,6,3,1]=>0 [5,4,3,1,2,6]=>0 [5,4,3,1,6,2]=>0 [5,4,3,2,1,6]=>0 [5,4,3,2,6,1]=>0 [5,4,3,6,1,2]=>1 [5,4,3,6,2,1]=>0 [5,4,6,1,2,3]=>2 [5,4,6,1,3,2]=>1 [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]=>0 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>1 [5,6,1,3,4,2]=>1 [5,6,1,4,2,3]=>1 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>1 [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]=>1 [5,6,2,4,3,1]=>0 [5,6,3,1,2,4]=>1 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>0 [5,6,3,4,1,2]=>1 [5,6,3,4,2,1]=>0 [5,6,4,1,2,3]=>1 [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]=>1 [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]=>0 [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]=>0 [6,1,3,2,5,4]=>0 [6,1,3,4,2,5]=>0 [6,1,3,4,5,2]=>0 [6,1,3,5,2,4]=>0 [6,1,3,5,4,2]=>0 [6,1,4,2,3,5]=>0 [6,1,4,2,5,3]=>0 [6,1,4,3,2,5]=>0 [6,1,4,3,5,2]=>0 [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]=>0 [6,1,5,3,2,4]=>0 [6,1,5,3,4,2]=>0 [6,1,5,4,2,3]=>0 [6,1,5,4,3,2]=>0 [6,2,1,3,4,5]=>0 [6,2,1,3,5,4]=>0 [6,2,1,4,3,5]=>0 [6,2,1,4,5,3]=>0 [6,2,1,5,3,4]=>0 [6,2,1,5,4,3]=>0 [6,2,3,1,4,5]=>0 [6,2,3,1,5,4]=>0 [6,2,3,4,1,5]=>0 [6,2,3,4,5,1]=>0 [6,2,3,5,1,4]=>0 [6,2,3,5,4,1]=>0 [6,2,4,1,3,5]=>0 [6,2,4,1,5,3]=>0 [6,2,4,3,1,5]=>0 [6,2,4,3,5,1]=>0 [6,2,4,5,1,3]=>0 [6,2,4,5,3,1]=>0 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>0 [6,2,5,3,1,4]=>0 [6,2,5,3,4,1]=>0 [6,2,5,4,1,3]=>0 [6,2,5,4,3,1]=>0 [6,3,1,2,4,5]=>0 [6,3,1,2,5,4]=>0 [6,3,1,4,2,5]=>0 [6,3,1,4,5,2]=>0 [6,3,1,5,2,4]=>0 [6,3,1,5,4,2]=>0 [6,3,2,1,4,5]=>0 [6,3,2,1,5,4]=>0 [6,3,2,4,1,5]=>0 [6,3,2,4,5,1]=>0 [6,3,2,5,1,4]=>0 [6,3,2,5,4,1]=>0 [6,3,4,1,2,5]=>0 [6,3,4,1,5,2]=>0 [6,3,4,2,1,5]=>0 [6,3,4,2,5,1]=>0 [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]=>0 [6,3,5,2,1,4]=>0 [6,3,5,2,4,1]=>0 [6,3,5,4,1,2]=>0 [6,3,5,4,2,1]=>0 [6,4,1,2,3,5]=>1 [6,4,1,2,5,3]=>1 [6,4,1,3,2,5]=>0 [6,4,1,3,5,2]=>0 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>0 [6,4,2,1,3,5]=>0 [6,4,2,1,5,3]=>0 [6,4,2,3,1,5]=>0 [6,4,2,3,5,1]=>0 [6,4,2,5,1,3]=>0 [6,4,2,5,3,1]=>0 [6,4,3,1,2,5]=>0 [6,4,3,1,5,2]=>0 [6,4,3,2,1,5]=>0 [6,4,3,2,5,1]=>0 [6,4,3,5,1,2]=>0 [6,4,3,5,2,1]=>0 [6,4,5,1,2,3]=>1 [6,4,5,1,3,2]=>1 [6,4,5,2,1,3]=>1 [6,4,5,2,3,1]=>1 [6,4,5,3,1,2]=>0 [6,4,5,3,2,1]=>0 [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]=>0 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>0 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>0 [6,5,2,3,1,4]=>0 [6,5,2,3,4,1]=>0 [6,5,2,4,1,3]=>0 [6,5,2,4,3,1]=>0 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>0 [6,5,3,2,1,4]=>0 [6,5,3,2,4,1]=>0 [6,5,3,4,1,2]=>0 [6,5,3,4,2,1]=>0 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>0 [6,5,4,2,1,3]=>0 [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]=>0 [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]=>0 [1,2,3,5,6,4,7]=>0 [1,2,3,5,6,7,4]=>0 [1,2,3,5,7,4,6]=>0 [1,2,3,5,7,6,4]=>0 [1,2,3,6,4,5,7]=>0 [1,2,3,6,4,7,5]=>0 [1,2,3,6,5,4,7]=>0 [1,2,3,6,5,7,4]=>0 [1,2,3,6,7,4,5]=>1 [1,2,3,6,7,5,4]=>0 [1,2,3,7,4,5,6]=>0 [1,2,3,7,4,6,5]=>0 [1,2,3,7,5,4,6]=>0 [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]=>0 [1,2,4,3,6,5,7]=>0 [1,2,4,3,6,7,5]=>0 [1,2,4,3,7,5,6]=>0 [1,2,4,3,7,6,5]=>0 [1,2,4,5,3,6,7]=>0 [1,2,4,5,3,7,6]=>0 [1,2,4,5,6,3,7]=>0 [1,2,4,5,6,7,3]=>0 [1,2,4,5,7,3,6]=>0 [1,2,4,5,7,6,3]=>0 [1,2,4,6,3,5,7]=>0 [1,2,4,6,3,7,5]=>0 [1,2,4,6,5,3,7]=>0 [1,2,4,6,5,7,3]=>0 [1,2,4,6,7,3,5]=>1 [1,2,4,6,7,5,3]=>0 [1,2,4,7,3,5,6]=>0 [1,2,4,7,3,6,5]=>0 [1,2,4,7,5,3,6]=>0 [1,2,4,7,5,6,3]=>0 [1,2,4,7,6,3,5]=>0 [1,2,4,7,6,5,3]=>0 [1,2,5,3,4,6,7]=>0 [1,2,5,3,4,7,6]=>0 [1,2,5,3,6,4,7]=>0 [1,2,5,3,6,7,4]=>0 [1,2,5,3,7,4,6]=>0 [1,2,5,3,7,6,4]=>0 [1,2,5,4,3,6,7]=>0 [1,2,5,4,3,7,6]=>0 [1,2,5,4,6,3,7]=>0 [1,2,5,4,6,7,3]=>0 [1,2,5,4,7,3,6]=>0 [1,2,5,4,7,6,3]=>0 [1,2,5,6,3,4,7]=>1 [1,2,5,6,3,7,4]=>1 [1,2,5,6,4,3,7]=>0 [1,2,5,6,4,7,3]=>0 [1,2,5,6,7,3,4]=>1 [1,2,5,6,7,4,3]=>1 [1,2,5,7,3,4,6]=>1 [1,2,5,7,3,6,4]=>1 [1,2,5,7,4,3,6]=>0 [1,2,5,7,4,6,3]=>0 [1,2,5,7,6,3,4]=>1 [1,2,5,7,6,4,3]=>0 [1,2,6,3,4,5,7]=>0 [1,2,6,3,4,7,5]=>0 [1,2,6,3,5,4,7]=>0 [1,2,6,3,5,7,4]=>0 [1,2,6,3,7,4,5]=>1 [1,2,6,3,7,5,4]=>0 [1,2,6,4,3,5,7]=>0 [1,2,6,4,3,7,5]=>0 [1,2,6,4,5,3,7]=>0 [1,2,6,4,5,7,3]=>0 [1,2,6,4,7,3,5]=>1 [1,2,6,4,7,5,3]=>0 [1,2,6,5,3,4,7]=>0 [1,2,6,5,3,7,4]=>0 [1,2,6,5,4,3,7]=>0 [1,2,6,5,4,7,3]=>0 [1,2,6,5,7,3,4]=>1 [1,2,6,5,7,4,3]=>0 [1,2,6,7,3,4,5]=>1 [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]=>1 [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]=>0 [1,2,7,3,5,6,4]=>0 [1,2,7,3,6,4,5]=>0 [1,2,7,3,6,5,4]=>0 [1,2,7,4,3,5,6]=>0 [1,2,7,4,3,6,5]=>0 [1,2,7,4,5,3,6]=>0 [1,2,7,4,5,6,3]=>0 [1,2,7,4,6,3,5]=>0 [1,2,7,4,6,5,3]=>0 [1,2,7,5,3,4,6]=>0 [1,2,7,5,3,6,4]=>0 [1,2,7,5,4,3,6]=>0 [1,2,7,5,4,6,3]=>0 [1,2,7,5,6,3,4]=>0 [1,2,7,5,6,4,3]=>0 [1,2,7,6,3,4,5]=>1 [1,2,7,6,3,5,4]=>0 [1,2,7,6,4,3,5]=>0 [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]=>0 [1,3,2,4,5,7,6]=>0 [1,3,2,4,6,5,7]=>0 [1,3,2,4,6,7,5]=>0 [1,3,2,4,7,5,6]=>0 [1,3,2,4,7,6,5]=>0 [1,3,2,5,4,6,7]=>0 [1,3,2,5,4,7,6]=>0 [1,3,2,5,6,4,7]=>0 [1,3,2,5,6,7,4]=>0 [1,3,2,5,7,4,6]=>0 [1,3,2,5,7,6,4]=>0 [1,3,2,6,4,5,7]=>0 [1,3,2,6,4,7,5]=>0 [1,3,2,6,5,4,7]=>0 [1,3,2,6,5,7,4]=>0 [1,3,2,6,7,4,5]=>1 [1,3,2,6,7,5,4]=>0 [1,3,2,7,4,5,6]=>0 [1,3,2,7,4,6,5]=>0 [1,3,2,7,5,4,6]=>0 [1,3,2,7,5,6,4]=>0 [1,3,2,7,6,4,5]=>0 [1,3,2,7,6,5,4]=>0 [1,3,4,2,5,6,7]=>0 [1,3,4,2,5,7,6]=>0 [1,3,4,2,6,5,7]=>0 [1,3,4,2,6,7,5]=>0 [1,3,4,2,7,5,6]=>0 [1,3,4,2,7,6,5]=>0 [1,3,4,5,2,6,7]=>0 [1,3,4,5,2,7,6]=>0 [1,3,4,5,6,2,7]=>0 [1,3,4,5,6,7,2]=>0 [1,3,4,5,7,2,6]=>0 [1,3,4,5,7,6,2]=>0 [1,3,4,6,2,5,7]=>0 [1,3,4,6,2,7,5]=>0 [1,3,4,6,5,2,7]=>0 [1,3,4,6,5,7,2]=>0 [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]=>0 [1,3,4,7,5,2,6]=>0 [1,3,4,7,5,6,2]=>0 [1,3,4,7,6,2,5]=>0 [1,3,4,7,6,5,2]=>0 [1,3,5,2,4,6,7]=>0 [1,3,5,2,4,7,6]=>0 [1,3,5,2,6,4,7]=>0 [1,3,5,2,6,7,4]=>0 [1,3,5,2,7,4,6]=>0 [1,3,5,2,7,6,4]=>0 [1,3,5,4,2,6,7]=>0 [1,3,5,4,2,7,6]=>0 [1,3,5,4,6,2,7]=>0 [1,3,5,4,6,7,2]=>0 [1,3,5,4,7,2,6]=>0 [1,3,5,4,7,6,2]=>0 [1,3,5,6,2,4,7]=>1 [1,3,5,6,2,7,4]=>1 [1,3,5,6,4,2,7]=>0 [1,3,5,6,4,7,2]=>0 [1,3,5,6,7,2,4]=>1 [1,3,5,6,7,4,2]=>1 [1,3,5,7,2,4,6]=>1 [1,3,5,7,2,6,4]=>1 [1,3,5,7,4,2,6]=>0 [1,3,5,7,4,6,2]=>0 [1,3,5,7,6,2,4]=>1 [1,3,5,7,6,4,2]=>0 [1,3,6,2,4,5,7]=>0 [1,3,6,2,4,7,5]=>0 [1,3,6,2,5,4,7]=>0 [1,3,6,2,5,7,4]=>0 [1,3,6,2,7,4,5]=>1 [1,3,6,2,7,5,4]=>0 [1,3,6,4,2,5,7]=>0 [1,3,6,4,2,7,5]=>0 [1,3,6,4,5,2,7]=>0 [1,3,6,4,5,7,2]=>0 [1,3,6,4,7,2,5]=>1 [1,3,6,4,7,5,2]=>0 [1,3,6,5,2,4,7]=>0 [1,3,6,5,2,7,4]=>0 [1,3,6,5,4,2,7]=>0 [1,3,6,5,4,7,2]=>0 [1,3,6,5,7,2,4]=>1 [1,3,6,5,7,4,2]=>0 [1,3,6,7,2,4,5]=>1 [1,3,6,7,2,5,4]=>1 [1,3,6,7,4,2,5]=>1 [1,3,6,7,4,5,2]=>0 [1,3,6,7,5,2,4]=>1 [1,3,6,7,5,4,2]=>0 [1,3,7,2,4,5,6]=>0 [1,3,7,2,4,6,5]=>0 [1,3,7,2,5,4,6]=>0 [1,3,7,2,5,6,4]=>0 [1,3,7,2,6,4,5]=>0 [1,3,7,2,6,5,4]=>0 [1,3,7,4,2,5,6]=>0 [1,3,7,4,2,6,5]=>0 [1,3,7,4,5,2,6]=>0 [1,3,7,4,5,6,2]=>0 [1,3,7,4,6,2,5]=>0 [1,3,7,4,6,5,2]=>0 [1,3,7,5,2,4,6]=>0 [1,3,7,5,2,6,4]=>0 [1,3,7,5,4,2,6]=>0 [1,3,7,5,4,6,2]=>0 [1,3,7,5,6,2,4]=>0 [1,3,7,5,6,4,2]=>0 [1,3,7,6,2,4,5]=>1 [1,3,7,6,2,5,4]=>0 [1,3,7,6,4,2,5]=>0 [1,3,7,6,4,5,2]=>0 [1,3,7,6,5,2,4]=>0 [1,3,7,6,5,4,2]=>0 [1,4,2,3,5,6,7]=>0 [1,4,2,3,5,7,6]=>0 [1,4,2,3,6,5,7]=>0 [1,4,2,3,6,7,5]=>0 [1,4,2,3,7,5,6]=>0 [1,4,2,3,7,6,5]=>0 [1,4,2,5,3,6,7]=>0 [1,4,2,5,3,7,6]=>0 [1,4,2,5,6,3,7]=>0 [1,4,2,5,6,7,3]=>0 [1,4,2,5,7,3,6]=>0 [1,4,2,5,7,6,3]=>0 [1,4,2,6,3,5,7]=>0 [1,4,2,6,3,7,5]=>0 [1,4,2,6,5,3,7]=>0 [1,4,2,6,5,7,3]=>0 [1,4,2,6,7,3,5]=>1 [1,4,2,6,7,5,3]=>0 [1,4,2,7,3,5,6]=>0 [1,4,2,7,3,6,5]=>0 [1,4,2,7,5,3,6]=>0 [1,4,2,7,5,6,3]=>0 [1,4,2,7,6,3,5]=>0 [1,4,2,7,6,5,3]=>0 [1,4,3,2,5,6,7]=>0 [1,4,3,2,5,7,6]=>0 [1,4,3,2,6,5,7]=>0 [1,4,3,2,6,7,5]=>0 [1,4,3,2,7,5,6]=>0 [1,4,3,2,7,6,5]=>0 [1,4,3,5,2,6,7]=>0 [1,4,3,5,2,7,6]=>0 [1,4,3,5,6,2,7]=>0 [1,4,3,5,6,7,2]=>0 [1,4,3,5,7,2,6]=>0 [1,4,3,5,7,6,2]=>0 [1,4,3,6,2,5,7]=>0 [1,4,3,6,2,7,5]=>0 [1,4,3,6,5,2,7]=>0 [1,4,3,6,5,7,2]=>0 [1,4,3,6,7,2,5]=>1 [1,4,3,6,7,5,2]=>0 [1,4,3,7,2,5,6]=>0 [1,4,3,7,2,6,5]=>0 [1,4,3,7,5,2,6]=>0 [1,4,3,7,5,6,2]=>0 [1,4,3,7,6,2,5]=>0 [1,4,3,7,6,5,2]=>0 [1,4,5,2,3,6,7]=>1 [1,4,5,2,3,7,6]=>1 [1,4,5,2,6,3,7]=>1 [1,4,5,2,6,7,3]=>1 [1,4,5,2,7,3,6]=>1 [1,4,5,2,7,6,3]=>1 [1,4,5,3,2,6,7]=>0 [1,4,5,3,2,7,6]=>0 [1,4,5,3,6,2,7]=>0 [1,4,5,3,6,7,2]=>0 [1,4,5,3,7,2,6]=>0 [1,4,5,3,7,6,2]=>0 [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]=>2 [1,4,5,6,7,3,2]=>1 [1,4,5,7,2,3,6]=>1 [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]=>1 [1,4,5,7,6,3,2]=>1 [1,4,6,2,3,5,7]=>1 [1,4,6,2,3,7,5]=>1 [1,4,6,2,5,3,7]=>1 [1,4,6,2,5,7,3]=>1 [1,4,6,2,7,3,5]=>2 [1,4,6,2,7,5,3]=>1 [1,4,6,3,2,5,7]=>0 [1,4,6,3,2,7,5]=>0 [1,4,6,3,5,2,7]=>0 [1,4,6,3,5,7,2]=>0 [1,4,6,3,7,2,5]=>1 [1,4,6,3,7,5,2]=>0 [1,4,6,5,2,3,7]=>1 [1,4,6,5,2,7,3]=>1 [1,4,6,5,3,2,7]=>0
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Description
Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation.
Let $\pi$ be a permutation. Its total displacement St000830The total displacement of a permutation. is $D(\pi) = \sum_i |\pi(i) - i|$, and its absolute length St000216The absolute length of a permutation. is the minimal number $T(\pi)$ of transpositions whose product is $\pi$. Finally, let $I(\pi)$ be the number of inversions St000018The number of inversions of a permutation. of $\pi$.
This statistic equals $\left(D(\pi)-T(\pi)-I(\pi)\right)/2$.
Diaconis and Graham [1] proved that this statistic is always nonnegative.
References
[1] Diaconis, P., Graham, R. L. Spearman's footrule as a measure of disarray MathSciNet:0652736
[2] (bad identifier) MathOverflow:449361
Code
def statistic(pi):
    return (sum(abs(e - i) for i, e in enumerate(pi, 1)) - pi.number_of_inversions() - pi.absolute_length())/2

Created
Jun 22, 2023 at 22:48 by Martin Rubey
Updated
Jun 22, 2023 at 22:48 by Martin Rubey