edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>0 [2,1]=>0 [1,2,3]=>0 [1,3,2]=>0 [2,1,3]=>0 [2,3,1]=>1 [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]=>1 [1,4,2,3]=>0 [1,4,3,2]=>0 [2,1,3,4]=>0 [2,1,4,3]=>0 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>1 [2,4,3,1]=>1 [3,1,2,4]=>0 [3,1,4,2]=>1 [3,2,1,4]=>0 [3,2,4,1]=>1 [3,4,1,2]=>1 [3,4,2,1]=>1 [4,1,2,3]=>0 [4,1,3,2]=>0 [4,2,1,3]=>0 [4,2,3,1]=>1 [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]=>1 [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]=>1 [1,3,4,5,2]=>1 [1,3,5,2,4]=>1 [1,3,5,4,2]=>1 [1,4,2,3,5]=>0 [1,4,2,5,3]=>1 [1,4,3,2,5]=>0 [1,4,3,5,2]=>1 [1,4,5,2,3]=>1 [1,4,5,3,2]=>1 [1,5,2,3,4]=>0 [1,5,2,4,3]=>0 [1,5,3,2,4]=>0 [1,5,3,4,2]=>1 [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]=>1 [2,1,5,3,4]=>0 [2,1,5,4,3]=>0 [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]=>2 [2,4,3,1,5]=>1 [2,4,3,5,1]=>1 [2,4,5,1,3]=>2 [2,4,5,3,1]=>2 [2,5,1,3,4]=>1 [2,5,1,4,3]=>1 [2,5,3,1,4]=>1 [2,5,3,4,1]=>1 [2,5,4,1,3]=>1 [2,5,4,3,1]=>1 [3,1,2,4,5]=>0 [3,1,2,5,4]=>0 [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]=>0 [3,2,1,5,4]=>0 [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]=>2 [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]=>1 [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]=>1 [4,1,3,2,5]=>0 [4,1,3,5,2]=>1 [4,1,5,2,3]=>1 [4,1,5,3,2]=>1 [4,2,1,3,5]=>0 [4,2,1,5,3]=>1 [4,2,3,1,5]=>1 [4,2,3,5,1]=>1 [4,2,5,1,3]=>2 [4,2,5,3,1]=>2 [4,3,1,2,5]=>0 [4,3,1,5,2]=>1 [4,3,2,1,5]=>0 [4,3,2,5,1]=>1 [4,3,5,1,2]=>1 [4,3,5,2,1]=>1 [4,5,1,2,3]=>1 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>2 [4,5,3,1,2]=>1 [4,5,3,2,1]=>1 [5,1,2,3,4]=>0 [5,1,2,4,3]=>0 [5,1,3,2,4]=>0 [5,1,3,4,2]=>1 [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]=>1 [5,2,3,4,1]=>1 [5,2,4,1,3]=>1 [5,2,4,3,1]=>1 [5,3,1,2,4]=>0 [5,3,1,4,2]=>1 [5,3,2,1,4]=>0 [5,3,2,4,1]=>1 [5,3,4,1,2]=>1 [5,3,4,2,1]=>1 [5,4,1,2,3]=>0 [5,4,1,3,2]=>0 [5,4,2,1,3]=>0 [5,4,2,3,1]=>1 [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]=>1 [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]=>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]=>0 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>0 [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]=>0 [1,2,6,3,5,4]=>0 [1,2,6,4,3,5]=>0 [1,2,6,4,5,3]=>1 [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]=>1 [1,3,2,6,4,5]=>0 [1,3,2,6,5,4]=>0 [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]=>2 [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]=>2 [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]=>1 [1,3,6,5,2,4]=>1 [1,3,6,5,4,2]=>1 [1,4,2,3,5,6]=>0 [1,4,2,3,6,5]=>0 [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]=>0 [1,4,3,2,6,5]=>0 [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]=>1 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>1 [1,4,5,3,6,2]=>2 [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]=>1 [1,4,6,3,5,2]=>2 [1,4,6,5,2,3]=>1 [1,4,6,5,3,2]=>1 [1,5,2,3,4,6]=>0 [1,5,2,3,6,4]=>1 [1,5,2,4,3,6]=>0 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>1 [1,5,2,6,4,3]=>1 [1,5,3,2,4,6]=>0 [1,5,3,2,6,4]=>1 [1,5,3,4,2,6]=>1 [1,5,3,4,6,2]=>1 [1,5,3,6,2,4]=>2 [1,5,3,6,4,2]=>2 [1,5,4,2,3,6]=>0 [1,5,4,2,6,3]=>1 [1,5,4,3,2,6]=>0 [1,5,4,3,6,2]=>1 [1,5,4,6,2,3]=>1 [1,5,4,6,3,2]=>1 [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]=>2 [1,5,6,4,2,3]=>1 [1,5,6,4,3,2]=>1 [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]=>1 [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]=>1 [1,6,3,4,5,2]=>1 [1,6,3,5,2,4]=>1 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>0 [1,6,4,2,5,3]=>1 [1,6,4,3,2,5]=>0 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>1 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>0 [1,6,5,2,4,3]=>0 [1,6,5,3,2,4]=>0 [1,6,5,3,4,2]=>1 [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]=>1 [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]=>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]=>0 [2,1,5,3,6,4]=>1 [2,1,5,4,3,6]=>0 [2,1,5,4,6,3]=>1 [2,1,5,6,3,4]=>1 [2,1,5,6,4,3]=>1 [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]=>1 [2,1,6,5,3,4]=>0 [2,1,6,5,4,3]=>0 [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]=>2 [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]=>2 [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]=>2 [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]=>1 [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]=>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]=>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]=>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]=>1 [2,5,1,3,6,4]=>2 [2,5,1,4,3,6]=>1 [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]=>1 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>1 [2,5,3,4,6,1]=>1 [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]=>2 [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]=>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]=>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]=>1 [2,6,3,4,5,1]=>1 [2,6,3,5,1,4]=>1 [2,6,3,5,4,1]=>1 [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]=>1 [2,6,4,5,1,3]=>2 [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]=>1 [2,6,5,4,1,3]=>1 [2,6,5,4,3,1]=>1 [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]=>1 [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]=>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]=>2 [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]=>2 [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]=>1 [3,1,6,5,2,4]=>1 [3,1,6,5,4,2]=>1 [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]=>1 [3,2,1,6,4,5]=>0 [3,2,1,6,5,4]=>0 [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]=>2 [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]=>2 [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]=>1 [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]=>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]=>1 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>2 [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]=>2 [3,4,5,6,1,2]=>1 [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]=>2 [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]=>2 [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]=>2 [3,5,2,1,4,6]=>1 [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]=>3 [3,5,2,6,4,1]=>3 [3,5,4,1,2,6]=>1 [3,5,4,1,6,2]=>1 [3,5,4,2,1,6]=>1 [3,5,4,2,6,1]=>2 [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]=>2 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>2 [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]=>1 [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]=>2 [3,6,2,5,4,1]=>2 [3,6,4,1,2,5]=>1 [3,6,4,1,5,2]=>1 [3,6,4,2,1,5]=>1 [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]=>1 [3,6,5,2,1,4]=>1 [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]=>1 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>1 [4,1,3,2,5,6]=>0 [4,1,3,2,6,5]=>0 [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]=>1 [4,1,5,2,6,3]=>1 [4,1,5,3,2,6]=>1 [4,1,5,3,6,2]=>2 [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]=>1 [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]=>0 [4,2,1,3,6,5]=>0 [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]=>1 [4,2,3,1,6,5]=>1 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>1 [4,2,3,6,1,5]=>1 [4,2,3,6,5,1]=>1 [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]=>0 [4,3,1,2,6,5]=>0 [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]=>0 [4,3,2,1,6,5]=>0 [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]=>1 [4,3,5,1,6,2]=>1 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>2 [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]=>1 [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]=>1 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>1 [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]=>1 [4,5,2,1,6,3]=>1 [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]=>1 [4,5,3,1,6,2]=>2 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>2 [4,5,3,6,1,2]=>2 [4,5,3,6,2,1]=>2 [4,5,6,1,2,3]=>1 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>1 [4,5,6,2,3,1]=>2 [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]=>2 [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]=>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]=>1 [4,6,3,1,5,2]=>2 [4,6,3,2,1,5]=>1 [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]=>1 [4,6,5,2,1,3]=>1 [4,6,5,2,3,1]=>2 [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]=>1 [5,1,2,4,3,6]=>0 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>1 [5,1,2,6,4,3]=>1 [5,1,3,2,4,6]=>0 [5,1,3,2,6,4]=>1 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>1 [5,1,3,6,2,4]=>2 [5,1,3,6,4,2]=>2 [5,1,4,2,3,6]=>0 [5,1,4,2,6,3]=>1 [5,1,4,3,2,6]=>0 [5,1,4,3,6,2]=>1 [5,1,4,6,2,3]=>1 [5,1,4,6,3,2]=>1 [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]=>2 [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]=>1 [5,2,1,4,3,6]=>0 [5,2,1,4,6,3]=>1 [5,2,1,6,3,4]=>1 [5,2,1,6,4,3]=>1 [5,2,3,1,4,6]=>1 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>1 [5,2,3,4,6,1]=>1 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>2 [5,2,4,1,3,6]=>1 [5,2,4,1,6,3]=>2 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>1 [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]=>0 [5,3,1,2,6,4]=>1 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>1 [5,3,1,6,2,4]=>2 [5,3,1,6,4,2]=>2 [5,3,2,1,4,6]=>0 [5,3,2,1,6,4]=>1 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>1 [5,3,2,6,1,4]=>2 [5,3,2,6,4,1]=>2 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>1 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>2 [5,3,4,6,1,2]=>1 [5,3,4,6,2,1]=>1 [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]=>3 [5,3,6,4,1,2]=>2 [5,3,6,4,2,1]=>2 [5,4,1,2,3,6]=>0 [5,4,1,2,6,3]=>1 [5,4,1,3,2,6]=>0 [5,4,1,3,6,2]=>1 [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]=>1 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>1 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>2 [5,4,3,1,2,6]=>0 [5,4,3,1,6,2]=>1 [5,4,3,2,1,6]=>0 [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]=>1 [5,4,6,2,1,3]=>1 [5,4,6,2,3,1]=>2 [5,4,6,3,1,2]=>1 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>1 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>1 [5,6,1,3,4,2]=>2 [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]=>2 [5,6,2,3,4,1]=>2 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>2 [5,6,3,1,2,4]=>1 [5,6,3,1,4,2]=>2 [5,6,3,2,1,4]=>1 [5,6,3,2,4,1]=>2 [5,6,3,4,1,2]=>2 [5,6,3,4,2,1]=>2 [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]=>2 [5,6,4,3,1,2]=>1 [5,6,4,3,2,1]=>1 [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]=>1 [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]=>1 [6,1,3,4,5,2]=>1 [6,1,3,5,2,4]=>1 [6,1,3,5,4,2]=>1 [6,1,4,2,3,5]=>0 [6,1,4,2,5,3]=>1 [6,1,4,3,2,5]=>0 [6,1,4,3,5,2]=>1 [6,1,4,5,2,3]=>1 [6,1,4,5,3,2]=>1 [6,1,5,2,3,4]=>0 [6,1,5,2,4,3]=>0 [6,1,5,3,2,4]=>0 [6,1,5,3,4,2]=>1 [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]=>1 [6,2,1,5,3,4]=>0 [6,2,1,5,4,3]=>0 [6,2,3,1,4,5]=>1 [6,2,3,1,5,4]=>1 [6,2,3,4,1,5]=>1 [6,2,3,4,5,1]=>1 [6,2,3,5,1,4]=>1 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>1 [6,2,4,1,5,3]=>2 [6,2,4,3,1,5]=>1 [6,2,4,3,5,1]=>1 [6,2,4,5,1,3]=>2 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>1 [6,2,5,3,1,4]=>1 [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]=>0 [6,3,1,2,5,4]=>0 [6,3,1,4,2,5]=>1 [6,3,1,4,5,2]=>1 [6,3,1,5,2,4]=>1 [6,3,1,5,4,2]=>1 [6,3,2,1,4,5]=>0 [6,3,2,1,5,4]=>0 [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]=>1 [6,3,4,1,5,2]=>1 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>2 [6,3,4,5,1,2]=>1 [6,3,4,5,2,1]=>1 [6,3,5,1,2,4]=>1 [6,3,5,1,4,2]=>1 [6,3,5,2,1,4]=>1 [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]=>1 [6,4,1,3,2,5]=>0 [6,4,1,3,5,2]=>1 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>1 [6,4,2,1,3,5]=>0 [6,4,2,1,5,3]=>1 [6,4,2,3,1,5]=>1 [6,4,2,3,5,1]=>1 [6,4,2,5,1,3]=>2 [6,4,2,5,3,1]=>2 [6,4,3,1,2,5]=>0 [6,4,3,1,5,2]=>1 [6,4,3,2,1,5]=>0 [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]=>1 [6,4,5,1,3,2]=>1 [6,4,5,2,1,3]=>1 [6,4,5,2,3,1]=>2 [6,4,5,3,1,2]=>1 [6,4,5,3,2,1]=>1 [6,5,1,2,3,4]=>0 [6,5,1,2,4,3]=>0 [6,5,1,3,2,4]=>0 [6,5,1,3,4,2]=>1 [6,5,1,4,2,3]=>0 [6,5,1,4,3,2]=>0 [6,5,2,1,3,4]=>0 [6,5,2,1,4,3]=>0 [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]=>0 [6,5,3,1,4,2]=>1 [6,5,3,2,1,4]=>0 [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]=>0 [6,5,4,1,3,2]=>0 [6,5,4,2,1,3]=>0 [6,5,4,2,3,1]=>1 [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]=>1 [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]=>1 [1,2,3,5,6,7,4]=>1 [1,2,3,5,7,4,6]=>1 [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]=>0 [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]=>0 [1,2,3,7,4,6,5]=>0 [1,2,3,7,5,4,6]=>0 [1,2,3,7,5,6,4]=>1 [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]=>1 [1,2,4,3,7,5,6]=>0 [1,2,4,3,7,6,5]=>0 [1,2,4,5,3,6,7]=>1 [1,2,4,5,3,7,6]=>1 [1,2,4,5,6,3,7]=>1 [1,2,4,5,6,7,3]=>1 [1,2,4,5,7,3,6]=>1 [1,2,4,5,7,6,3]=>1 [1,2,4,6,3,5,7]=>1 [1,2,4,6,3,7,5]=>2 [1,2,4,6,5,3,7]=>1 [1,2,4,6,5,7,3]=>1 [1,2,4,6,7,3,5]=>2 [1,2,4,6,7,5,3]=>2 [1,2,4,7,3,5,6]=>1 [1,2,4,7,3,6,5]=>1 [1,2,4,7,5,3,6]=>1 [1,2,4,7,5,6,3]=>1 [1,2,4,7,6,3,5]=>1 [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]=>1 [1,2,5,3,6,7,4]=>1 [1,2,5,3,7,4,6]=>1 [1,2,5,3,7,6,4]=>1 [1,2,5,4,3,6,7]=>0 [1,2,5,4,3,7,6]=>0 [1,2,5,4,6,3,7]=>1 [1,2,5,4,6,7,3]=>1 [1,2,5,4,7,3,6]=>1 [1,2,5,4,7,6,3]=>1 [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]=>2 [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]=>1 [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]=>1 [1,2,6,3,5,4,7]=>0 [1,2,6,3,5,7,4]=>1 [1,2,6,3,7,4,5]=>1 [1,2,6,3,7,5,4]=>1 [1,2,6,4,3,5,7]=>0 [1,2,6,4,3,7,5]=>1 [1,2,6,4,5,3,7]=>1 [1,2,6,4,5,7,3]=>1 [1,2,6,4,7,3,5]=>2 [1,2,6,4,7,5,3]=>2 [1,2,6,5,3,4,7]=>0 [1,2,6,5,3,7,4]=>1 [1,2,6,5,4,3,7]=>0 [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]=>1 [1,2,6,7,3,5,4]=>1 [1,2,6,7,4,3,5]=>1 [1,2,6,7,4,5,3]=>2 [1,2,6,7,5,3,4]=>1 [1,2,6,7,5,4,3]=>1 [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]=>1 [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]=>1 [1,2,7,4,5,6,3]=>1 [1,2,7,4,6,3,5]=>1 [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]=>0 [1,2,7,5,4,6,3]=>1 [1,2,7,5,6,3,4]=>1 [1,2,7,5,6,4,3]=>1 [1,2,7,6,3,4,5]=>0 [1,2,7,6,3,5,4]=>0 [1,2,7,6,4,3,5]=>0 [1,2,7,6,4,5,3]=>1 [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]=>1 [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]=>1 [1,3,2,5,6,7,4]=>1 [1,3,2,5,7,4,6]=>1 [1,3,2,5,7,6,4]=>1 [1,3,2,6,4,5,7]=>0 [1,3,2,6,4,7,5]=>1 [1,3,2,6,5,4,7]=>0 [1,3,2,6,5,7,4]=>1 [1,3,2,6,7,4,5]=>1 [1,3,2,6,7,5,4]=>1 [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]=>1 [1,3,2,7,6,4,5]=>0 [1,3,2,7,6,5,4]=>0 [1,3,4,2,5,6,7]=>1 [1,3,4,2,5,7,6]=>1 [1,3,4,2,6,5,7]=>1 [1,3,4,2,6,7,5]=>2 [1,3,4,2,7,5,6]=>1 [1,3,4,2,7,6,5]=>1 [1,3,4,5,2,6,7]=>1 [1,3,4,5,2,7,6]=>1 [1,3,4,5,6,2,7]=>1 [1,3,4,5,6,7,2]=>1 [1,3,4,5,7,2,6]=>1 [1,3,4,5,7,6,2]=>1 [1,3,4,6,2,5,7]=>1 [1,3,4,6,2,7,5]=>2 [1,3,4,6,5,2,7]=>1 [1,3,4,6,5,7,2]=>1 [1,3,4,6,7,2,5]=>2 [1,3,4,6,7,5,2]=>2 [1,3,4,7,2,5,6]=>1 [1,3,4,7,2,6,5]=>1 [1,3,4,7,5,2,6]=>1 [1,3,4,7,5,6,2]=>1 [1,3,4,7,6,2,5]=>1 [1,3,4,7,6,5,2]=>1 [1,3,5,2,4,6,7]=>1 [1,3,5,2,4,7,6]=>1 [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]=>1 [1,3,5,4,2,7,6]=>1 [1,3,5,4,6,2,7]=>1 [1,3,5,4,6,7,2]=>1 [1,3,5,4,7,2,6]=>1 [1,3,5,4,7,6,2]=>1 [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]=>2 [1,3,5,7,2,6,4]=>2 [1,3,5,7,4,2,6]=>2 [1,3,5,7,4,6,2]=>2 [1,3,5,7,6,2,4]=>2 [1,3,5,7,6,4,2]=>2 [1,3,6,2,4,5,7]=>1 [1,3,6,2,4,7,5]=>2 [1,3,6,2,5,4,7]=>1 [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]=>1 [1,3,6,4,2,7,5]=>2 [1,3,6,4,5,2,7]=>1 [1,3,6,4,5,7,2]=>1 [1,3,6,4,7,2,5]=>2 [1,3,6,4,7,5,2]=>2 [1,3,6,5,2,4,7]=>1 [1,3,6,5,2,7,4]=>2 [1,3,6,5,4,2,7]=>1 [1,3,6,5,4,7,2]=>1 [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]=>1 [1,3,7,2,4,6,5]=>1 [1,3,7,2,5,4,6]=>1 [1,3,7,2,5,6,4]=>2 [1,3,7,2,6,4,5]=>1 [1,3,7,2,6,5,4]=>1 [1,3,7,4,2,5,6]=>1 [1,3,7,4,2,6,5]=>1 [1,3,7,4,5,2,6]=>1 [1,3,7,4,5,6,2]=>1 [1,3,7,4,6,2,5]=>1 [1,3,7,4,6,5,2]=>1 [1,3,7,5,2,4,6]=>1 [1,3,7,5,2,6,4]=>2 [1,3,7,5,4,2,6]=>1 [1,3,7,5,4,6,2]=>1 [1,3,7,5,6,2,4]=>2 [1,3,7,5,6,4,2]=>2 [1,3,7,6,2,4,5]=>1 [1,3,7,6,2,5,4]=>1 [1,3,7,6,4,2,5]=>1 [1,3,7,6,4,5,2]=>1 [1,3,7,6,5,2,4]=>1 [1,3,7,6,5,4,2]=>1 [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]=>1 [1,4,2,3,7,5,6]=>0 [1,4,2,3,7,6,5]=>0 [1,4,2,5,3,6,7]=>1 [1,4,2,5,3,7,6]=>1 [1,4,2,5,6,3,7]=>1 [1,4,2,5,6,7,3]=>1 [1,4,2,5,7,3,6]=>1 [1,4,2,5,7,6,3]=>1 [1,4,2,6,3,5,7]=>1 [1,4,2,6,3,7,5]=>2 [1,4,2,6,5,3,7]=>1 [1,4,2,6,5,7,3]=>1 [1,4,2,6,7,3,5]=>2 [1,4,2,6,7,5,3]=>2 [1,4,2,7,3,5,6]=>1 [1,4,2,7,3,6,5]=>1 [1,4,2,7,5,3,6]=>1 [1,4,2,7,5,6,3]=>1 [1,4,2,7,6,3,5]=>1 [1,4,2,7,6,5,3]=>1 [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]=>1 [1,4,3,2,7,5,6]=>0 [1,4,3,2,7,6,5]=>0 [1,4,3,5,2,6,7]=>1 [1,4,3,5,2,7,6]=>1 [1,4,3,5,6,2,7]=>1 [1,4,3,5,6,7,2]=>1 [1,4,3,5,7,2,6]=>1 [1,4,3,5,7,6,2]=>1 [1,4,3,6,2,5,7]=>1 [1,4,3,6,2,7,5]=>2 [1,4,3,6,5,2,7]=>1 [1,4,3,6,5,7,2]=>1 [1,4,3,6,7,2,5]=>2 [1,4,3,6,7,5,2]=>2 [1,4,3,7,2,5,6]=>1 [1,4,3,7,2,6,5]=>1 [1,4,3,7,5,2,6]=>1 [1,4,3,7,5,6,2]=>1 [1,4,3,7,6,2,5]=>1 [1,4,3,7,6,5,2]=>1 [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]=>1 [1,4,5,3,2,7,6]=>1 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>2 [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]=>2 [1,4,5,6,7,2,3]=>1 [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]=>2 [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]=>2 [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]=>2 [1,4,6,3,2,5,7]=>1 [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]=>3 [1,4,6,3,7,5,2]=>3 [1,4,6,5,2,3,7]=>1 [1,4,6,5,2,7,3]=>1 [1,4,6,5,3,2,7]=>1 [1,4,6,5,3,7,2]=>2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The tier of a permutation.
This is the number of elements $i$ such that $[i+1,k,i]$ is an occurrence of the pattern $[2,3,1]$. For example, $[3,5,6,1,2,4]$ has tier $2$, with witnesses $[3,5,2]$ (or $[3,6,2]$) and $[5,6,4]$.
According to [1], this is the number of passes minus one needed to sort the permutation using a single stack. The generating function for this statistic appears as OEIS:A122890 and OEIS:A158830 in the form of triangles read by rows, see [sec. 4, 1].
References
[1] Mansour, T., Skogman, H., Smith, R. Passing through a stack $k$ times arXiv:1704.04288
Code
def statistic(pi):
    pi = Permutation(pi)
    return len(set([p[0] for p in pi.pattern_positions([2,3,1]) if pi[p[0]] == pi[p[2]] +1]))
Created
Apr 17, 2017 at 11:47 by Martin Rubey
Updated
Nov 06, 2017 at 21:24 by Martin Rubey