edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [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]=>2 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>2 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>2 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>2 [4,3,1,2]=>2 [4,3,2,1]=>3 [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]=>2 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [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]=>2 [1,4,3,2,5]=>2 [1,4,3,5,2]=>2 [1,4,5,2,3]=>2 [1,4,5,3,2]=>2 [1,5,2,3,4]=>1 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>2 [1,5,4,2,3]=>2 [1,5,4,3,2]=>3 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>2 [2,1,5,3,4]=>2 [2,1,5,4,3]=>3 [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]=>2 [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]=>3 [2,5,3,1,4]=>2 [2,5,3,4,1]=>2 [2,5,4,1,3]=>3 [2,5,4,3,1]=>3 [3,1,2,4,5]=>1 [3,1,2,5,4]=>2 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>3 [3,2,1,4,5]=>2 [3,2,1,5,4]=>3 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>3 [3,2,5,4,1]=>3 [3,4,1,2,5]=>2 [3,4,1,5,2]=>2 [3,4,2,1,5]=>2 [3,4,2,5,1]=>2 [3,4,5,1,2]=>2 [3,4,5,2,1]=>2 [3,5,1,2,4]=>2 [3,5,1,4,2]=>3 [3,5,2,1,4]=>3 [3,5,2,4,1]=>3 [3,5,4,1,2]=>3 [3,5,4,2,1]=>3 [4,1,2,3,5]=>1 [4,1,2,5,3]=>2 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>3 [4,2,1,3,5]=>2 [4,2,1,5,3]=>3 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>3 [4,2,5,3,1]=>3 [4,3,1,2,5]=>2 [4,3,1,5,2]=>3 [4,3,2,1,5]=>3 [4,3,2,5,1]=>3 [4,3,5,1,2]=>3 [4,3,5,2,1]=>3 [4,5,1,2,3]=>2 [4,5,1,3,2]=>3 [4,5,2,1,3]=>3 [4,5,2,3,1]=>3 [4,5,3,1,2]=>3 [4,5,3,2,1]=>3 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>2 [5,1,4,2,3]=>2 [5,1,4,3,2]=>3 [5,2,1,3,4]=>2 [5,2,1,4,3]=>3 [5,2,3,1,4]=>2 [5,2,3,4,1]=>2 [5,2,4,1,3]=>3 [5,2,4,3,1]=>3 [5,3,1,2,4]=>2 [5,3,1,4,2]=>3 [5,3,2,1,4]=>3 [5,3,2,4,1]=>3 [5,3,4,1,2]=>3 [5,3,4,2,1]=>3 [5,4,1,2,3]=>2 [5,4,1,3,2]=>3 [5,4,2,1,3]=>3 [5,4,2,3,1]=>3 [5,4,3,1,2]=>3 [5,4,3,2,1]=>4 [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]=>2 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [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]=>2 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>2 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>2 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>2 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>3 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>2 [1,3,2,6,5,4]=>3 [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]=>3 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>2 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>3 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>3 [1,4,3,5,2,6]=>2 [1,4,3,5,6,2]=>2 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>3 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>2 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>2 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>2 [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]=>3 [1,4,6,5,3,2]=>3 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>3 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>2 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>3 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>3 [1,5,4,6,3,2]=>3 [1,5,6,2,3,4]=>2 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>3 [1,5,6,3,4,2]=>3 [1,5,6,4,2,3]=>3 [1,5,6,4,3,2]=>3 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>2 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>2 [1,6,2,5,3,4]=>2 [1,6,2,5,4,3]=>3 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>3 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>3 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>3 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>3 [1,6,5,3,4,2]=>3 [1,6,5,4,2,3]=>3 [1,6,5,4,3,2]=>4 [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]=>3 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>2 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>3 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>2 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>4 [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]=>3 [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]=>2 [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]=>3 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>3 [2,4,1,3,5,6]=>2 [2,4,1,3,6,5]=>3 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>2 [2,4,1,6,3,5]=>3 [2,4,1,6,5,3]=>3 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>3 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>3 [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]=>3 [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]=>3 [2,5,1,3,4,6]=>2 [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]=>3 [2,5,1,6,4,3]=>3 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>3 [2,5,3,4,1,6]=>2 [2,5,3,4,6,1]=>2 [2,5,3,6,1,4]=>3 [2,5,3,6,4,1]=>3 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>3 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>3 [2,5,6,4,3,1]=>3 [2,6,1,3,4,5]=>2 [2,6,1,3,5,4]=>3 [2,6,1,4,3,5]=>3 [2,6,1,4,5,3]=>3 [2,6,1,5,3,4]=>3 [2,6,1,5,4,3]=>4 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>3 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>2 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>3 [2,6,4,3,1,5]=>3 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>3 [2,6,5,1,4,3]=>4 [2,6,5,3,1,4]=>3 [2,6,5,3,4,1]=>3 [2,6,5,4,1,3]=>4 [2,6,5,4,3,1]=>4 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>2 [3,1,2,5,6,4]=>2 [3,1,2,6,4,5]=>2 [3,1,2,6,5,4]=>3 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>2 [3,1,4,6,2,5]=>3 [3,1,4,6,5,2]=>3 [3,1,5,2,4,6]=>2 [3,1,5,2,6,4]=>3 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>3 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>3 [3,1,6,2,4,5]=>2 [3,1,6,2,5,4]=>3 [3,1,6,4,2,5]=>3 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>4 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>3 [3,2,1,5,4,6]=>3 [3,2,1,5,6,4]=>3 [3,2,1,6,4,5]=>3 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>2 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>2 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>3 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>3 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>3 [3,2,5,6,1,4]=>3 [3,2,5,6,4,1]=>3 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>4 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>4 [3,2,6,5,4,1]=>4 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>2 [3,4,1,6,2,5]=>3 [3,4,1,6,5,2]=>3 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>2 [3,4,2,5,6,1]=>2 [3,4,2,6,1,5]=>3 [3,4,2,6,5,1]=>3 [3,4,5,1,2,6]=>2 [3,4,5,1,6,2]=>2 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>2 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>2 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>3 [3,4,6,2,5,1]=>3 [3,4,6,5,1,2]=>3 [3,4,6,5,2,1]=>3 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>3 [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]=>3 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>3 [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]=>3 [3,5,4,1,2,6]=>3 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>3 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>3 [3,5,6,1,2,4]=>3 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>3 [3,5,6,2,4,1]=>3 [3,5,6,4,1,2]=>3 [3,5,6,4,2,1]=>3 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>3 [3,6,1,4,2,5]=>3 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>4 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>4 [3,6,2,4,1,5]=>3 [3,6,2,4,5,1]=>3 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>4 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>3 [3,6,4,2,1,5]=>3 [3,6,4,2,5,1]=>3 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>3 [3,6,5,1,4,2]=>4 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>4 [3,6,5,4,1,2]=>4 [3,6,5,4,2,1]=>4 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>2 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>3 [4,1,3,2,5,6]=>2 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>3 [4,1,3,6,5,2]=>3 [4,1,5,2,3,6]=>2 [4,1,5,2,6,3]=>3 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>3 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>3 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>3 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>2 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>3 [4,2,1,6,3,5]=>3 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>3 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>3 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>3 [4,2,5,6,1,3]=>3 [4,2,5,6,3,1]=>3 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>4 [4,2,6,3,1,5]=>3 [4,2,6,3,5,1]=>3 [4,2,6,5,1,3]=>4 [4,2,6,5,3,1]=>4 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>3 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>4 [4,3,2,1,5,6]=>3 [4,3,2,1,6,5]=>4 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>3 [4,3,2,6,1,5]=>4 [4,3,2,6,5,1]=>4 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>3 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>4 [4,3,6,2,1,5]=>4 [4,3,6,2,5,1]=>4 [4,3,6,5,1,2]=>4 [4,3,6,5,2,1]=>4 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>3 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>3 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>3 [4,5,2,1,6,3]=>3 [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]=>3 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>3 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>3 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>3 [4,5,6,2,1,3]=>3 [4,5,6,2,3,1]=>3 [4,5,6,3,1,2]=>3 [4,5,6,3,2,1]=>3 [4,6,1,2,3,5]=>2 [4,6,1,2,5,3]=>3 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>3 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>4 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>4 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>4 [4,6,3,1,2,5]=>3 [4,6,3,1,5,2]=>4 [4,6,3,2,1,5]=>4 [4,6,3,2,5,1]=>4 [4,6,3,5,1,2]=>4 [4,6,3,5,2,1]=>4 [4,6,5,1,2,3]=>3 [4,6,5,1,3,2]=>4 [4,6,5,2,1,3]=>4 [4,6,5,2,3,1]=>4 [4,6,5,3,1,2]=>4 [4,6,5,3,2,1]=>4 [5,1,2,3,4,6]=>1 [5,1,2,3,6,4]=>2 [5,1,2,4,3,6]=>2 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>2 [5,1,2,6,4,3]=>3 [5,1,3,2,4,6]=>2 [5,1,3,2,6,4]=>3 [5,1,3,4,2,6]=>2 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>3 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>3 [5,1,4,3,6,2]=>3 [5,1,4,6,2,3]=>3 [5,1,4,6,3,2]=>3 [5,1,6,2,3,4]=>2 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>3 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>3 [5,1,6,4,3,2]=>4 [5,2,1,3,4,6]=>2 [5,2,1,3,6,4]=>3 [5,2,1,4,3,6]=>3 [5,2,1,4,6,3]=>3 [5,2,1,6,3,4]=>3 [5,2,1,6,4,3]=>4 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>3 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>3 [5,2,3,6,4,1]=>3 [5,2,4,1,3,6]=>3 [5,2,4,1,6,3]=>3 [5,2,4,3,1,6]=>3 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>3 [5,2,4,6,3,1]=>3 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>4 [5,2,6,3,1,4]=>3 [5,2,6,3,4,1]=>3 [5,2,6,4,1,3]=>4 [5,2,6,4,3,1]=>4 [5,3,1,2,4,6]=>2 [5,3,1,2,6,4]=>3 [5,3,1,4,2,6]=>3 [5,3,1,4,6,2]=>3 [5,3,1,6,2,4]=>3 [5,3,1,6,4,2]=>4 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>4 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>3 [5,3,2,6,1,4]=>4 [5,3,2,6,4,1]=>4 [5,3,4,1,2,6]=>3 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>3 [5,3,4,2,6,1]=>3 [5,3,4,6,1,2]=>3 [5,3,4,6,2,1]=>3 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>4 [5,3,6,2,1,4]=>4 [5,3,6,2,4,1]=>4 [5,3,6,4,1,2]=>4 [5,3,6,4,2,1]=>4 [5,4,1,2,3,6]=>2 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>3 [5,4,1,3,6,2]=>3 [5,4,1,6,2,3]=>3 [5,4,1,6,3,2]=>4 [5,4,2,1,3,6]=>3 [5,4,2,1,6,3]=>4 [5,4,2,3,1,6]=>3 [5,4,2,3,6,1]=>3 [5,4,2,6,1,3]=>4 [5,4,2,6,3,1]=>4 [5,4,3,1,2,6]=>3 [5,4,3,1,6,2]=>4 [5,4,3,2,1,6]=>4 [5,4,3,2,6,1]=>4 [5,4,3,6,1,2]=>4 [5,4,3,6,2,1]=>4 [5,4,6,1,2,3]=>3 [5,4,6,1,3,2]=>4 [5,4,6,2,1,3]=>4 [5,4,6,2,3,1]=>4 [5,4,6,3,1,2]=>4 [5,4,6,3,2,1]=>4 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>3 [5,6,1,3,2,4]=>3 [5,6,1,3,4,2]=>3 [5,6,1,4,2,3]=>3 [5,6,1,4,3,2]=>4 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>4 [5,6,2,3,1,4]=>3 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>4 [5,6,2,4,3,1]=>4 [5,6,3,1,2,4]=>3 [5,6,3,1,4,2]=>4 [5,6,3,2,1,4]=>4 [5,6,3,2,4,1]=>4 [5,6,3,4,1,2]=>4 [5,6,3,4,2,1]=>4 [5,6,4,1,2,3]=>3 [5,6,4,1,3,2]=>4 [5,6,4,2,1,3]=>4 [5,6,4,2,3,1]=>4 [5,6,4,3,1,2]=>4 [5,6,4,3,2,1]=>4 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>2 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>2 [6,1,2,5,4,3]=>3 [6,1,3,2,4,5]=>2 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>3 [6,1,3,5,4,2]=>3 [6,1,4,2,3,5]=>2 [6,1,4,2,5,3]=>3 [6,1,4,3,2,5]=>3 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>3 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>3 [6,1,5,3,2,4]=>3 [6,1,5,3,4,2]=>3 [6,1,5,4,2,3]=>3 [6,1,5,4,3,2]=>4 [6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>3 [6,2,1,4,3,5]=>3 [6,2,1,4,5,3]=>3 [6,2,1,5,3,4]=>3 [6,2,1,5,4,3]=>4 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>2 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>3 [6,2,3,5,4,1]=>3 [6,2,4,1,3,5]=>3 [6,2,4,1,5,3]=>3 [6,2,4,3,1,5]=>3 [6,2,4,3,5,1]=>3 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>3 [6,2,5,1,4,3]=>4 [6,2,5,3,1,4]=>3 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>4 [6,2,5,4,3,1]=>4 [6,3,1,2,4,5]=>2 [6,3,1,2,5,4]=>3 [6,3,1,4,2,5]=>3 [6,3,1,4,5,2]=>3 [6,3,1,5,2,4]=>3 [6,3,1,5,4,2]=>4 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>4 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>3 [6,3,2,5,1,4]=>4 [6,3,2,5,4,1]=>4 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>3 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>3 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>4 [6,3,5,2,1,4]=>4 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>4 [6,3,5,4,2,1]=>4 [6,4,1,2,3,5]=>2 [6,4,1,2,5,3]=>3 [6,4,1,3,2,5]=>3 [6,4,1,3,5,2]=>3 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>4 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>4 [6,4,2,3,1,5]=>3 [6,4,2,3,5,1]=>3 [6,4,2,5,1,3]=>4 [6,4,2,5,3,1]=>4 [6,4,3,1,2,5]=>3 [6,4,3,1,5,2]=>4 [6,4,3,2,1,5]=>4 [6,4,3,2,5,1]=>4 [6,4,3,5,1,2]=>4 [6,4,3,5,2,1]=>4 [6,4,5,1,2,3]=>3 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>4 [6,4,5,3,1,2]=>4 [6,4,5,3,2,1]=>4 [6,5,1,2,3,4]=>2 [6,5,1,2,4,3]=>3 [6,5,1,3,2,4]=>3 [6,5,1,3,4,2]=>3 [6,5,1,4,2,3]=>3 [6,5,1,4,3,2]=>4 [6,5,2,1,3,4]=>3 [6,5,2,1,4,3]=>4 [6,5,2,3,1,4]=>3 [6,5,2,3,4,1]=>3 [6,5,2,4,1,3]=>4 [6,5,2,4,3,1]=>4 [6,5,3,1,2,4]=>3 [6,5,3,1,4,2]=>4 [6,5,3,2,1,4]=>4 [6,5,3,2,4,1]=>4 [6,5,3,4,1,2]=>4 [6,5,3,4,2,1]=>4 [6,5,4,1,2,3]=>3 [6,5,4,1,3,2]=>4 [6,5,4,2,1,3]=>4 [6,5,4,2,3,1]=>4 [6,5,4,3,1,2]=>4 [6,5,4,3,2,1]=>5 [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]=>2 [1,2,3,5,4,6,7]=>1 [1,2,3,5,4,7,6]=>2 [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]=>2 [1,2,3,6,5,4,7]=>2 [1,2,3,6,5,7,4]=>2 [1,2,3,6,7,4,5]=>2 [1,2,3,6,7,5,4]=>2 [1,2,3,7,4,5,6]=>1 [1,2,3,7,4,6,5]=>2 [1,2,3,7,5,4,6]=>2 [1,2,3,7,5,6,4]=>2 [1,2,3,7,6,4,5]=>2 [1,2,3,7,6,5,4]=>3 [1,2,4,3,5,6,7]=>1 [1,2,4,3,5,7,6]=>2 [1,2,4,3,6,5,7]=>2 [1,2,4,3,6,7,5]=>2 [1,2,4,3,7,5,6]=>2 [1,2,4,3,7,6,5]=>3 [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]=>3 [1,2,4,7,5,3,6]=>2 [1,2,4,7,5,6,3]=>2 [1,2,4,7,6,3,5]=>3 [1,2,4,7,6,5,3]=>3 [1,2,5,3,4,6,7]=>1 [1,2,5,3,4,7,6]=>2 [1,2,5,3,6,4,7]=>2 [1,2,5,3,6,7,4]=>2 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>3 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>3 [1,2,5,4,6,3,7]=>2 [1,2,5,4,6,7,3]=>2 [1,2,5,4,7,3,6]=>3 [1,2,5,4,7,6,3]=>3 [1,2,5,6,3,4,7]=>2 [1,2,5,6,3,7,4]=>2 [1,2,5,6,4,3,7]=>2 [1,2,5,6,4,7,3]=>2 [1,2,5,6,7,3,4]=>2 [1,2,5,6,7,4,3]=>2 [1,2,5,7,3,4,6]=>2 [1,2,5,7,3,6,4]=>3 [1,2,5,7,4,3,6]=>3 [1,2,5,7,4,6,3]=>3 [1,2,5,7,6,3,4]=>3 [1,2,5,7,6,4,3]=>3 [1,2,6,3,4,5,7]=>1 [1,2,6,3,4,7,5]=>2 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>2 [1,2,6,3,7,5,4]=>3 [1,2,6,4,3,5,7]=>2 [1,2,6,4,3,7,5]=>3 [1,2,6,4,5,3,7]=>2 [1,2,6,4,5,7,3]=>2 [1,2,6,4,7,3,5]=>3 [1,2,6,4,7,5,3]=>3 [1,2,6,5,3,4,7]=>2 [1,2,6,5,3,7,4]=>3 [1,2,6,5,4,3,7]=>3 [1,2,6,5,4,7,3]=>3 [1,2,6,5,7,3,4]=>3 [1,2,6,5,7,4,3]=>3 [1,2,6,7,3,4,5]=>2 [1,2,6,7,3,5,4]=>3 [1,2,6,7,4,3,5]=>3 [1,2,6,7,4,5,3]=>3 [1,2,6,7,5,3,4]=>3 [1,2,6,7,5,4,3]=>3 [1,2,7,3,4,5,6]=>1 [1,2,7,3,4,6,5]=>2 [1,2,7,3,5,4,6]=>2 [1,2,7,3,5,6,4]=>2 [1,2,7,3,6,4,5]=>2 [1,2,7,3,6,5,4]=>3 [1,2,7,4,3,5,6]=>2 [1,2,7,4,3,6,5]=>3 [1,2,7,4,5,3,6]=>2 [1,2,7,4,5,6,3]=>2 [1,2,7,4,6,3,5]=>3 [1,2,7,4,6,5,3]=>3 [1,2,7,5,3,4,6]=>2 [1,2,7,5,3,6,4]=>3 [1,2,7,5,4,3,6]=>3 [1,2,7,5,4,6,3]=>3 [1,2,7,5,6,3,4]=>3 [1,2,7,5,6,4,3]=>3 [1,2,7,6,3,4,5]=>2 [1,2,7,6,3,5,4]=>3 [1,2,7,6,4,3,5]=>3 [1,2,7,6,4,5,3]=>3 [1,2,7,6,5,3,4]=>3 [1,2,7,6,5,4,3]=>4 [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]=>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]=>2 [1,3,2,5,7,4,6]=>3 [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]=>3 [1,3,2,6,7,5,4]=>3 [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]=>3 [1,3,2,7,6,4,5]=>3 [1,3,2,7,6,5,4]=>4 [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]=>3 [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]=>3 [1,3,4,7,5,2,6]=>2 [1,3,4,7,5,6,2]=>2 [1,3,4,7,6,2,5]=>3 [1,3,4,7,6,5,2]=>3 [1,3,5,2,4,6,7]=>2 [1,3,5,2,4,7,6]=>3 [1,3,5,2,6,4,7]=>2 [1,3,5,2,6,7,4]=>2 [1,3,5,2,7,4,6]=>3 [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]=>2 [1,3,5,4,6,7,2]=>2 [1,3,5,4,7,2,6]=>3 [1,3,5,4,7,6,2]=>3 [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]=>3 [1,3,6,2,5,4,7]=>3 [1,3,6,2,5,7,4]=>3 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>3 [1,3,6,4,2,5,7]=>2 [1,3,6,4,2,7,5]=>3 [1,3,6,4,5,2,7]=>2 [1,3,6,4,5,7,2]=>2 [1,3,6,4,7,2,5]=>3 [1,3,6,4,7,5,2]=>3 [1,3,6,5,2,4,7]=>3 [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]=>3 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>3 [1,3,6,7,2,5,4]=>3 [1,3,6,7,4,2,5]=>3 [1,3,6,7,4,5,2]=>3 [1,3,6,7,5,2,4]=>3 [1,3,6,7,5,4,2]=>3 [1,3,7,2,4,5,6]=>2 [1,3,7,2,4,6,5]=>3 [1,3,7,2,5,4,6]=>3 [1,3,7,2,5,6,4]=>3 [1,3,7,2,6,4,5]=>3 [1,3,7,2,6,5,4]=>4 [1,3,7,4,2,5,6]=>2 [1,3,7,4,2,6,5]=>3 [1,3,7,4,5,2,6]=>2 [1,3,7,4,5,6,2]=>2 [1,3,7,4,6,2,5]=>3 [1,3,7,4,6,5,2]=>3 [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]=>3 [1,3,7,6,2,5,4]=>4 [1,3,7,6,4,2,5]=>3 [1,3,7,6,4,5,2]=>3 [1,3,7,6,5,2,4]=>4 [1,3,7,6,5,4,2]=>4 [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]=>2 [1,4,2,3,7,5,6]=>2 [1,4,2,3,7,6,5]=>3 [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]=>2 [1,4,2,5,7,3,6]=>3 [1,4,2,5,7,6,3]=>3 [1,4,2,6,3,5,7]=>2 [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]=>3 [1,4,2,6,7,5,3]=>3 [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]=>3 [1,4,2,7,6,3,5]=>3 [1,4,2,7,6,5,3]=>4 [1,4,3,2,5,6,7]=>2 [1,4,3,2,5,7,6]=>3 [1,4,3,2,6,5,7]=>3 [1,4,3,2,6,7,5]=>3 [1,4,3,2,7,5,6]=>3 [1,4,3,2,7,6,5]=>4 [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]=>2 [1,4,3,5,7,2,6]=>3 [1,4,3,5,7,6,2]=>3 [1,4,3,6,2,5,7]=>3 [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]=>3 [1,4,3,6,7,5,2]=>3 [1,4,3,7,2,5,6]=>3 [1,4,3,7,2,6,5]=>4 [1,4,3,7,5,2,6]=>3 [1,4,3,7,5,6,2]=>3 [1,4,3,7,6,2,5]=>4 [1,4,3,7,6,5,2]=>4 [1,4,5,2,3,6,7]=>2 [1,4,5,2,3,7,6]=>3 [1,4,5,2,6,3,7]=>2 [1,4,5,2,6,7,3]=>2 [1,4,5,2,7,3,6]=>3 [1,4,5,2,7,6,3]=>3 [1,4,5,3,2,6,7]=>2 [1,4,5,3,2,7,6]=>3 [1,4,5,3,6,2,7]=>2 [1,4,5,3,6,7,2]=>2 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>3 [1,4,5,6,2,3,7]=>2 [1,4,5,6,2,7,3]=>2 [1,4,5,6,3,2,7]=>2 [1,4,5,6,3,7,2]=>2 [1,4,5,6,7,2,3]=>2 [1,4,5,6,7,3,2]=>2 [1,4,5,7,2,3,6]=>3 [1,4,5,7,2,6,3]=>3 [1,4,5,7,3,2,6]=>3 [1,4,5,7,3,6,2]=>3 [1,4,5,7,6,2,3]=>3 [1,4,5,7,6,3,2]=>3 [1,4,6,2,3,5,7]=>2 [1,4,6,2,3,7,5]=>3 [1,4,6,2,5,3,7]=>3 [1,4,6,2,5,7,3]=>3 [1,4,6,2,7,3,5]=>3 [1,4,6,2,7,5,3]=>3 [1,4,6,3,2,5,7]=>3 [1,4,6,3,2,7,5]=>3 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>3 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>3 [1,4,6,5,2,3,7]=>3 [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 Ulam distance of a permutation to the identity permutation.
This is, for a permutation $\pi$ of $n$, given by $n$ minus the length of the longest increasing subsequence of $\pi^{-1}$.
In other words, this statistic plus St000062The length of the longest increasing subsequence of the permutation. equals $n$.
References
[1] Chatterjee, S., Diaconis, P. A central limit theorem for a new statistic on permutations arXiv:1608.01666
Code
def statistic(pi):
    return len(pi) - pi.inverse().longest_increasing_subsequence_length()
Created
May 31, 2017 at 10:48 by Christian Stump
Updated
May 31, 2017 at 13:52 by Martin Rubey