edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>1 [2,1]=>1 [1,2,3]=>2 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [1,2,3,4]=>3 [1,2,4,3]=>1 [1,3,2,4]=>2 [1,3,4,2]=>1 [1,4,2,3]=>2 [1,4,3,2]=>1 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>2 [2,3,4,1]=>1 [2,4,1,3]=>2 [2,4,3,1]=>1 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>1 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>1 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>1 [4,2,3,1]=>2 [4,3,1,2]=>1 [4,3,2,1]=>3 [1,2,3,4,5]=>4 [1,2,3,5,4]=>1 [1,2,4,3,5]=>2 [1,2,4,5,3]=>1 [1,2,5,3,4]=>2 [1,2,5,4,3]=>1 [1,3,2,4,5]=>2 [1,3,2,5,4]=>3 [1,3,4,2,5]=>2 [1,3,4,5,2]=>1 [1,3,5,2,4]=>2 [1,3,5,4,2]=>1 [1,4,2,3,5]=>2 [1,4,2,5,3]=>3 [1,4,3,2,5]=>2 [1,4,3,5,2]=>1 [1,4,5,2,3]=>2 [1,4,5,3,2]=>1 [1,5,2,3,4]=>2 [1,5,2,4,3]=>3 [1,5,3,2,4]=>2 [1,5,3,4,2]=>1 [1,5,4,2,3]=>2 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>3 [2,1,4,5,3]=>2 [2,1,5,3,4]=>1 [2,1,5,4,3]=>2 [2,3,1,4,5]=>2 [2,3,1,5,4]=>1 [2,3,4,1,5]=>2 [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]=>1 [2,4,3,1,5]=>2 [2,4,3,5,1]=>1 [2,4,5,1,3]=>2 [2,4,5,3,1]=>1 [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]=>2 [2,5,4,3,1]=>1 [3,1,2,4,5]=>1 [3,1,2,5,4]=>2 [3,1,4,2,5]=>3 [3,1,4,5,2]=>2 [3,1,5,2,4]=>1 [3,1,5,4,2]=>2 [3,2,1,4,5]=>1 [3,2,1,5,4]=>2 [3,2,4,1,5]=>3 [3,2,4,5,1]=>2 [3,2,5,1,4]=>1 [3,2,5,4,1]=>2 [3,4,1,2,5]=>2 [3,4,1,5,2]=>1 [3,4,2,1,5]=>2 [3,4,2,5,1]=>3 [3,4,5,1,2]=>2 [3,4,5,2,1]=>1 [3,5,1,2,4]=>2 [3,5,1,4,2]=>1 [3,5,2,1,4]=>2 [3,5,2,4,1]=>3 [3,5,4,1,2]=>2 [3,5,4,2,1]=>1 [4,1,2,3,5]=>1 [4,1,2,5,3]=>2 [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]=>1 [4,2,1,5,3]=>2 [4,2,3,1,5]=>1 [4,2,3,5,1]=>2 [4,2,5,1,3]=>1 [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]=>2 [4,3,5,1,2]=>1 [4,3,5,2,1]=>2 [4,5,1,2,3]=>2 [4,5,1,3,2]=>1 [4,5,2,1,3]=>2 [4,5,2,3,1]=>3 [4,5,3,1,2]=>2 [4,5,3,2,1]=>1 [5,1,2,3,4]=>1 [5,1,2,4,3]=>2 [5,1,3,2,4]=>1 [5,1,3,4,2]=>2 [5,1,4,2,3]=>3 [5,1,4,3,2]=>2 [5,2,1,3,4]=>1 [5,2,1,4,3]=>2 [5,2,3,1,4]=>1 [5,2,3,4,1]=>2 [5,2,4,1,3]=>3 [5,2,4,3,1]=>2 [5,3,1,2,4]=>1 [5,3,1,4,2]=>2 [5,3,2,1,4]=>1 [5,3,2,4,1]=>2 [5,3,4,1,2]=>3 [5,3,4,2,1]=>2 [5,4,1,2,3]=>1 [5,4,1,3,2]=>2 [5,4,2,1,3]=>1 [5,4,2,3,1]=>2 [5,4,3,1,2]=>1 [5,4,3,2,1]=>4 [1,2,3,4,5,6]=>5 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>2 [1,2,3,5,6,4]=>1 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>1 [1,2,4,3,5,6]=>3 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>2 [1,2,4,5,6,3]=>1 [1,2,4,6,3,5]=>2 [1,2,4,6,5,3]=>1 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>1 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>1 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>1 [1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>1 [1,2,6,4,3,5]=>2 [1,2,6,4,5,3]=>1 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>1 [1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>4 [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]=>3 [1,3,4,2,6,5]=>1 [1,3,4,5,2,6]=>2 [1,3,4,5,6,2]=>1 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>1 [1,3,5,2,4,6]=>3 [1,3,5,2,6,4]=>1 [1,3,5,4,2,6]=>2 [1,3,5,4,6,2]=>1 [1,3,5,6,2,4]=>2 [1,3,5,6,4,2]=>1 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>1 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>1 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>1 [1,4,2,3,5,6]=>2 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>4 [1,4,2,5,6,3]=>1 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>1 [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]=>1 [1,4,3,6,2,5]=>2 [1,4,3,6,5,2]=>1 [1,4,5,2,3,6]=>3 [1,4,5,2,6,3]=>1 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>1 [1,4,5,6,2,3]=>2 [1,4,5,6,3,2]=>1 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>1 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>1 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>1 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>1 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>1 [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]=>1 [1,5,3,6,2,4]=>2 [1,5,3,6,4,2]=>1 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>2 [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]=>3 [1,5,6,2,4,3]=>1 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>1 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>1 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>2 [1,6,2,4,5,3]=>1 [1,6,2,5,3,4]=>4 [1,6,2,5,4,3]=>1 [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]=>1 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>1 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>2 [1,6,4,3,5,2]=>1 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>1 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>2 [1,6,5,3,4,2]=>1 [1,6,5,4,2,3]=>2 [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]=>3 [2,1,3,5,6,4]=>2 [2,1,3,6,4,5]=>1 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>4 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>1 [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]=>3 [2,1,5,4,6,3]=>2 [2,1,5,6,3,4]=>1 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>2 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>2 [2,3,1,4,5,6]=>2 [2,3,1,4,6,5]=>1 [2,3,1,5,4,6]=>2 [2,3,1,5,6,4]=>3 [2,3,1,6,4,5]=>2 [2,3,1,6,5,4]=>1 [2,3,4,1,5,6]=>3 [2,3,4,1,6,5]=>1 [2,3,4,5,1,6]=>2 [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]=>3 [2,3,5,1,6,4]=>1 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>1 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>1 [2,3,6,1,4,5]=>3 [2,3,6,1,5,4]=>1 [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]=>1 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>2 [2,4,1,6,5,3]=>1 [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]=>1 [2,4,3,6,1,5]=>2 [2,4,3,6,5,1]=>1 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>1 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>1 [2,4,5,6,1,3]=>2 [2,4,5,6,3,1]=>1 [2,4,6,1,3,5]=>3 [2,4,6,1,5,3]=>1 [2,4,6,3,1,5]=>2 [2,4,6,3,5,1]=>1 [2,4,6,5,1,3]=>2 [2,4,6,5,3,1]=>1 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>1 [2,5,1,4,3,6]=>2 [2,5,1,4,6,3]=>3 [2,5,1,6,3,4]=>2 [2,5,1,6,4,3]=>1 [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]=>1 [2,5,3,6,1,4]=>2 [2,5,3,6,4,1]=>1 [2,5,4,1,3,6]=>2 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>1 [2,5,4,6,1,3]=>2 [2,5,4,6,3,1]=>1 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>1 [2,5,6,3,1,4]=>2 [2,5,6,3,4,1]=>1 [2,5,6,4,1,3]=>2 [2,5,6,4,3,1]=>1 [2,6,1,3,4,5]=>2 [2,6,1,3,5,4]=>1 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>3 [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]=>3 [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]=>3 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>1 [2,6,4,5,1,3]=>2 [2,6,4,5,3,1]=>1 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>3 [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]=>1 [3,1,2,4,6,5]=>2 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>2 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>2 [3,1,4,2,5,6]=>1 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>2 [3,1,4,6,2,5]=>1 [3,1,4,6,5,2]=>2 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>4 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>2 [3,1,5,6,2,4]=>1 [3,1,5,6,4,2]=>2 [3,1,6,2,4,5]=>1 [3,1,6,2,5,4]=>2 [3,1,6,4,2,5]=>3 [3,1,6,4,5,2]=>2 [3,1,6,5,2,4]=>1 [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]=>2 [3,2,1,6,4,5]=>1 [3,2,1,6,5,4]=>3 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>2 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>1 [3,2,4,6,5,1]=>2 [3,2,5,1,4,6]=>1 [3,2,5,1,6,4]=>2 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>2 [3,2,5,6,1,4]=>1 [3,2,5,6,4,1]=>2 [3,2,6,1,4,5]=>1 [3,2,6,1,5,4]=>2 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>2 [3,2,6,5,1,4]=>1 [3,2,6,5,4,1]=>2 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>1 [3,4,1,5,2,6]=>2 [3,4,1,5,6,2]=>3 [3,4,1,6,2,5]=>2 [3,4,1,6,5,2]=>1 [3,4,2,1,5,6]=>2 [3,4,2,1,6,5]=>1 [3,4,2,5,1,6]=>4 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>2 [3,4,2,6,5,1]=>1 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>1 [3,4,5,2,1,6]=>2 [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]=>3 [3,4,6,1,5,2]=>1 [3,4,6,2,1,5]=>2 [3,4,6,2,5,1]=>1 [3,4,6,5,1,2]=>2 [3,4,6,5,2,1]=>1 [3,5,1,2,4,6]=>2 [3,5,1,2,6,4]=>1 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>3 [3,5,1,6,2,4]=>2 [3,5,1,6,4,2]=>1 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>1 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>3 [3,5,2,6,1,4]=>2 [3,5,2,6,4,1]=>1 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>1 [3,5,4,6,1,2]=>2 [3,5,4,6,2,1]=>1 [3,5,6,1,2,4]=>3 [3,5,6,1,4,2]=>1 [3,5,6,2,1,4]=>2 [3,5,6,2,4,1]=>1 [3,5,6,4,1,2]=>2 [3,5,6,4,2,1]=>1 [3,6,1,2,4,5]=>2 [3,6,1,2,5,4]=>1 [3,6,1,4,2,5]=>2 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>2 [3,6,1,5,4,2]=>1 [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]=>3 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>1 [3,6,4,1,2,5]=>2 [3,6,4,1,5,2]=>3 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>1 [3,6,4,5,1,2]=>2 [3,6,4,5,2,1]=>1 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>3 [3,6,5,2,1,4]=>2 [3,6,5,2,4,1]=>1 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>1 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>1 [4,1,2,5,6,3]=>2 [4,1,2,6,3,5]=>3 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>2 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>2 [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]=>4 [4,1,5,3,2,6]=>3 [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]=>1 [4,1,6,2,5,3]=>2 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>1 [4,1,6,5,3,2]=>2 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>2 [4,2,1,5,3,6]=>1 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>1 [4,2,1,6,5,3]=>3 [4,2,3,1,5,6]=>1 [4,2,3,1,6,5]=>2 [4,2,3,5,1,6]=>1 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>2 [4,2,5,1,3,6]=>1 [4,2,5,1,6,3]=>2 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>2 [4,2,5,6,1,3]=>1 [4,2,5,6,3,1]=>2 [4,2,6,1,3,5]=>1 [4,2,6,1,5,3]=>2 [4,2,6,3,1,5]=>3 [4,2,6,3,5,1]=>2 [4,2,6,5,1,3]=>1 [4,2,6,5,3,1]=>2 [4,3,1,2,5,6]=>1 [4,3,1,2,6,5]=>2 [4,3,1,5,2,6]=>1 [4,3,1,5,6,2]=>2 [4,3,1,6,2,5]=>1 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>2 [4,3,2,5,1,6]=>1 [4,3,2,5,6,1]=>2 [4,3,2,6,1,5]=>1 [4,3,2,6,5,1]=>3 [4,3,5,1,2,6]=>1 [4,3,5,1,6,2]=>2 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>4 [4,3,5,6,1,2]=>1 [4,3,5,6,2,1]=>2 [4,3,6,1,2,5]=>1 [4,3,6,1,5,2]=>2 [4,3,6,2,1,5]=>3 [4,3,6,2,5,1]=>2 [4,3,6,5,1,2]=>1 [4,3,6,5,2,1]=>2 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>1 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>2 [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]=>2 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>2 [4,5,2,6,3,1]=>1 [4,5,3,1,2,6]=>2 [4,5,3,1,6,2]=>1 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>2 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>1 [4,5,6,2,1,3]=>2 [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]=>1 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>3 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>1 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>1 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>1 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>1 [4,6,3,2,1,5]=>2 [4,6,3,2,5,1]=>3 [4,6,3,5,1,2]=>2 [4,6,3,5,2,1]=>1 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>2 [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]=>2 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>3 [5,1,2,6,4,3]=>2 [5,1,3,2,4,6]=>1 [5,1,3,2,6,4]=>2 [5,1,3,4,2,6]=>1 [5,1,3,4,6,2]=>2 [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]=>1 [5,1,4,3,6,2]=>2 [5,1,4,6,2,3]=>3 [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]=>3 [5,1,6,3,4,2]=>2 [5,1,6,4,2,3]=>1 [5,1,6,4,3,2]=>2 [5,2,1,3,4,6]=>1 [5,2,1,3,6,4]=>2 [5,2,1,4,3,6]=>1 [5,2,1,4,6,3]=>2 [5,2,1,6,3,4]=>1 [5,2,1,6,4,3]=>3 [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]=>2 [5,2,3,6,1,4]=>3 [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]=>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]=>3 [5,2,6,3,4,1]=>2 [5,2,6,4,1,3]=>1 [5,2,6,4,3,1]=>2 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>2 [5,3,1,4,2,6]=>1 [5,3,1,4,6,2]=>2 [5,3,1,6,2,4]=>1 [5,3,1,6,4,2]=>3 [5,3,2,1,4,6]=>1 [5,3,2,1,6,4]=>2 [5,3,2,4,1,6]=>1 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>1 [5,3,2,6,4,1]=>3 [5,3,4,1,2,6]=>1 [5,3,4,1,6,2]=>2 [5,3,4,2,1,6]=>1 [5,3,4,2,6,1]=>2 [5,3,4,6,1,2]=>3 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>1 [5,3,6,1,4,2]=>2 [5,3,6,2,1,4]=>3 [5,3,6,2,4,1]=>2 [5,3,6,4,1,2]=>1 [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]=>1 [5,4,1,6,3,2]=>3 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>2 [5,4,2,3,1,6]=>1 [5,4,2,3,6,1]=>2 [5,4,2,6,1,3]=>1 [5,4,2,6,3,1]=>3 [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]=>2 [5,4,3,6,1,2]=>1 [5,4,3,6,2,1]=>3 [5,4,6,1,2,3]=>1 [5,4,6,1,3,2]=>2 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>2 [5,4,6,3,1,2]=>1 [5,4,6,3,2,1]=>2 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>1 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>3 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>1 [5,6,2,3,1,4]=>2 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>2 [5,6,2,4,3,1]=>1 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>1 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>4 [5,6,3,4,2,1]=>1 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>1 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>3 [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]=>2 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>3 [6,1,2,5,4,3]=>2 [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]=>2 [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]=>1 [6,1,4,3,5,2]=>2 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>2 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>4 [6,1,5,3,2,4]=>1 [6,1,5,3,4,2]=>2 [6,1,5,4,2,3]=>3 [6,1,5,4,3,2]=>2 [6,2,1,3,4,5]=>1 [6,2,1,3,5,4]=>2 [6,2,1,4,3,5]=>1 [6,2,1,4,5,3]=>2 [6,2,1,5,3,4]=>1 [6,2,1,5,4,3]=>3 [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]=>2 [6,2,3,5,1,4]=>3 [6,2,3,5,4,1]=>2 [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]=>2 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>1 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>1 [6,2,5,3,4,1]=>2 [6,2,5,4,1,3]=>3 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>1 [6,3,1,2,5,4]=>2 [6,3,1,4,2,5]=>1 [6,3,1,4,5,2]=>2 [6,3,1,5,2,4]=>1 [6,3,1,5,4,2]=>3 [6,3,2,1,4,5]=>1 [6,3,2,1,5,4]=>2 [6,3,2,4,1,5]=>1 [6,3,2,4,5,1]=>2 [6,3,2,5,1,4]=>1 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>1 [6,3,4,1,5,2]=>2 [6,3,4,2,1,5]=>1 [6,3,4,2,5,1]=>2 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>1 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>1 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>3 [6,3,5,4,2,1]=>2 [6,4,1,2,3,5]=>1 [6,4,1,2,5,3]=>2 [6,4,1,3,2,5]=>1 [6,4,1,3,5,2]=>2 [6,4,1,5,2,3]=>1 [6,4,1,5,3,2]=>3 [6,4,2,1,3,5]=>1 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>1 [6,4,2,3,5,1]=>2 [6,4,2,5,1,3]=>1 [6,4,2,5,3,1]=>3 [6,4,3,1,2,5]=>1 [6,4,3,1,5,2]=>2 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>2 [6,4,3,5,1,2]=>1 [6,4,3,5,2,1]=>3 [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]=>4 [6,4,5,3,1,2]=>3 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>2 [6,5,1,3,2,4]=>1 [6,5,1,3,4,2]=>2 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>3 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>2 [6,5,2,3,1,4]=>1 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>1 [6,5,2,4,3,1]=>3 [6,5,3,1,2,4]=>1 [6,5,3,1,4,2]=>2 [6,5,3,2,1,4]=>1 [6,5,3,2,4,1]=>2 [6,5,3,4,1,2]=>1 [6,5,3,4,2,1]=>3 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>2 [6,5,4,2,1,3]=>1 [6,5,4,2,3,1]=>2 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>5 [1,2,3,4,5,6,7]=>6 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>2 [1,2,3,6,4,7,5]=>1 [1,2,6,3,4,7,5]=>4 [1,3,2,4,5,6,7]=>2 [1,3,7,2,4,5,6]=>3 [1,3,7,6,5,4,2]=>1 [1,4,6,7,2,3,5]=>3 [1,4,6,7,5,3,2]=>1 [1,4,7,2,3,5,6]=>3 [1,4,7,6,5,3,2]=>1 [1,5,2,3,4,7,6]=>3 [1,5,2,7,3,4,6]=>2 [1,5,4,7,6,3,2]=>1 [1,5,6,2,7,3,4]=>2 [1,5,6,4,7,3,2]=>1 [1,5,6,7,2,3,4]=>3 [1,5,6,7,4,3,2]=>1 [1,5,7,2,3,4,6]=>3 [1,5,7,6,4,3,2]=>1 [1,6,2,3,4,7,5]=>3 [1,6,2,3,7,4,5]=>4 [1,6,2,7,3,4,5]=>2 [1,6,5,4,3,7,2]=>1 [1,6,5,4,7,3,2]=>1 [1,6,5,7,4,3,2]=>1 [1,6,7,2,3,4,5]=>3 [1,6,7,5,4,3,2]=>1 [1,7,2,3,4,5,6]=>2 [1,7,3,5,6,4,2]=>1 [1,7,3,6,5,4,2]=>1 [1,7,4,3,6,5,2]=>1 [1,7,4,5,3,6,2]=>1 [1,7,4,5,6,3,2]=>1 [1,7,4,6,5,3,2]=>1 [1,7,5,4,3,6,2]=>1 [1,7,5,4,6,3,2]=>1 [1,7,6,4,5,3,2]=>1 [1,7,6,5,4,3,2]=>1 [2,1,3,4,5,6,7]=>1 [2,1,3,4,7,5,6]=>1 [2,1,3,7,4,5,6]=>1 [2,1,6,3,4,5,7]=>1 [2,1,7,3,4,5,6]=>1 [2,1,7,6,5,4,3]=>2 [2,3,1,4,5,6,7]=>2 [2,3,4,1,5,6,7]=>3 [2,3,4,1,5,7,6]=>1 [2,3,4,5,1,6,7]=>3 [2,3,4,5,1,7,6]=>1 [2,3,4,5,6,1,7]=>2 [2,3,4,5,6,7,1]=>1 [2,3,4,5,7,1,6]=>2 [2,3,4,6,1,7,5]=>1 [2,3,4,6,7,1,5]=>2 [2,3,4,7,1,5,6]=>3 [2,3,5,6,7,1,4]=>2 [2,4,1,3,5,6,7]=>2 [2,5,1,3,4,6,7]=>2 [2,5,7,1,3,4,6]=>3 [2,6,1,3,4,5,7]=>2 [2,6,1,7,3,4,5]=>2 [2,6,5,4,3,1,7]=>2 [2,6,7,1,3,4,5]=>3 [2,7,1,3,4,5,6]=>2 [3,1,2,4,5,6,7]=>1 [3,1,2,4,5,7,6]=>2 [3,2,1,4,5,6,7]=>1 [3,2,4,5,6,7,1]=>2 [3,4,1,2,5,6,7]=>2 [3,4,2,5,6,7,1]=>3 [3,4,5,2,6,7,1]=>4 [3,4,5,6,2,7,1]=>1 [3,4,5,6,7,1,2]=>2 [3,5,6,1,2,4,7]=>3 [3,5,6,4,2,1,7]=>2 [3,6,1,2,4,5,7]=>2 [3,6,5,4,2,1,7]=>2 [4,1,2,3,5,6,7]=>1 [4,1,2,3,5,7,6]=>2 [4,1,6,2,3,5,7]=>1 [4,2,3,5,6,7,1]=>2 [4,2,5,1,3,6,7]=>1 [4,3,2,1,5,6,7]=>1 [4,3,2,5,6,7,1]=>2 [4,3,5,2,6,7,1]=>2 [4,3,6,5,2,1,7]=>3 [4,5,1,6,2,3,7]=>2 [4,5,2,3,6,7,1]=>3 [4,5,3,6,2,1,7]=>2 [4,5,6,1,2,3,7]=>3 [4,5,6,3,2,1,7]=>2 [4,6,1,2,3,5,7]=>2 [4,6,1,2,3,7,5]=>1 [4,6,5,3,2,1,7]=>2 [5,1,2,3,4,6,7]=>1 [5,1,2,3,4,7,6]=>2 [5,1,2,3,6,4,7]=>1 [5,1,2,3,6,7,4]=>2 [5,1,2,3,7,4,6]=>3 [5,1,2,6,3,4,7]=>4 [5,1,6,2,3,4,7]=>1 [5,1,6,2,3,7,4]=>2 [5,2,3,4,6,7,1]=>2 [5,2,6,7,1,3,4]=>1 [5,3,2,4,6,7,1]=>2 [5,3,2,6,1,4,7]=>1 [5,3,6,7,1,2,4]=>1 [5,4,3,2,1,6,7]=>1 [5,4,3,2,1,7,6]=>2 [5,4,3,2,6,1,7]=>1 [5,4,3,6,2,1,7]=>4 [5,4,6,3,2,1,7]=>3 [5,4,6,7,1,2,3]=>1 [5,6,1,2,3,4,7]=>2 [5,6,1,2,3,7,4]=>1 [5,6,3,4,1,2,7]=>2 [5,6,4,3,2,1,7]=>2 [5,6,7,1,2,3,4]=>3 [6,1,2,3,4,5,7]=>1 [6,1,2,3,4,7,5]=>2 [6,1,2,3,7,4,5]=>3 [6,1,2,7,3,4,5]=>1 [6,2,3,4,5,7,1]=>2 [6,2,4,5,3,1,7]=>1 [6,2,5,4,3,1,7]=>1 [6,3,2,5,4,1,7]=>1 [6,3,4,2,5,1,7]=>1 [6,3,4,5,2,1,7]=>1 [6,3,4,7,1,2,5]=>1 [6,3,5,4,2,1,7]=>1 [6,4,3,2,5,1,7]=>1 [6,4,3,2,7,1,5]=>1 [6,4,3,5,2,1,7]=>1 [6,4,5,7,1,2,3]=>1 [6,4,7,2,5,1,3]=>1 [6,4,7,3,5,1,2]=>1 [6,5,3,4,2,1,7]=>1 [6,5,4,3,2,1,7]=>1 [6,5,7,3,4,1,2]=>1 [6,7,1,2,3,4,5]=>2 [6,7,3,4,1,2,5]=>2 [6,7,4,5,1,2,3]=>2 [7,1,2,3,4,5,6]=>1 [7,2,1,3,4,5,6]=>1 [7,2,3,1,4,5,6]=>1 [7,2,3,4,1,5,6]=>1 [7,2,3,4,5,1,6]=>1 [7,3,1,2,4,5,6]=>1 [7,3,2,1,4,5,6]=>1 [7,3,2,4,1,5,6]=>1 [7,3,4,1,2,5,6]=>1 [7,4,1,2,3,5,6]=>1 [7,4,2,1,3,5,6]=>1 [7,4,5,6,1,2,3]=>4 [7,5,1,2,3,4,6]=>1 [7,5,6,1,2,3,4]=>1 [7,5,6,3,4,1,2]=>5 [7,6,1,2,3,4,5]=>1 [7,6,4,5,1,2,3]=>1 [7,6,5,1,2,3,4]=>1 [7,6,5,3,4,1,2]=>1 [7,6,5,4,1,2,3]=>1 [7,6,5,4,3,1,2]=>1 [7,6,5,4,3,2,1]=>6 [8,7,6,5,4,3,2,1]=>7 [7,6,8,5,4,3,2,1]=>2 [7,8,5,6,4,3,2,1]=>1 [7,8,6,4,5,3,2,1]=>1 [8,6,7,4,5,3,2,1]=>2 [7,6,5,4,8,3,2,1]=>4 [6,5,7,4,8,3,2,1]=>2 [7,8,6,5,3,4,2,1]=>4 [8,6,7,5,3,4,2,1]=>5 [8,7,5,6,3,4,2,1]=>3 [6,7,8,3,4,5,2,1]=>1 [7,8,6,5,4,2,3,1]=>3 [8,6,7,5,4,2,3,1]=>4 [8,7,5,6,4,2,3,1]=>5 [8,7,6,4,5,2,3,1]=>2 [8,6,5,7,3,2,4,1]=>5 [6,7,8,5,2,3,4,1]=>4 [8,5,6,7,2,3,4,1]=>5 [7,8,3,2,4,5,6,1]=>3 [7,6,5,4,3,2,8,1]=>2 [6,5,7,4,3,2,8,1]=>4 [6,5,4,3,7,2,8,1]=>2 [5,4,6,3,7,2,8,1]=>6 [3,4,5,2,6,7,8,1]=>4 [5,2,3,4,6,7,8,1]=>2 [4,3,2,5,6,7,8,1]=>2 [3,4,2,5,6,7,8,1]=>3 [4,2,3,5,6,7,8,1]=>2 [3,2,4,5,6,7,8,1]=>2 [2,3,4,5,6,7,8,1]=>1 [8,7,6,5,4,3,1,2]=>1 [7,8,6,5,4,3,1,2]=>2 [8,6,7,5,4,3,1,2]=>3 [8,7,5,6,4,3,1,2]=>4 [8,7,6,4,5,3,1,2]=>1 [8,7,6,5,3,4,1,2]=>1 [8,7,5,6,3,4,1,2]=>1 [7,8,5,6,3,4,1,2]=>6 [5,6,7,8,3,4,1,2]=>2 [7,8,3,4,5,6,1,2]=>4 [3,4,5,6,7,8,1,2]=>2 [8,7,6,5,4,2,1,3]=>1 [7,6,8,5,4,2,1,3]=>3 [8,7,6,5,4,1,2,3]=>1 [6,7,8,5,4,1,2,3]=>3 [8,5,6,7,4,1,2,3]=>4 [8,7,6,4,5,1,2,3]=>1 [8,6,7,4,5,1,2,3]=>1 [8,7,4,5,6,1,2,3]=>1 [7,8,4,5,6,1,2,3]=>5 [6,7,4,5,8,1,2,3]=>2 [7,6,5,8,3,2,1,4]=>4 [7,5,6,8,2,3,1,4]=>1 [6,7,5,8,3,1,2,4]=>2 [6,5,7,8,2,1,3,4]=>4 [8,7,6,5,1,2,3,4]=>1 [8,7,5,6,1,2,3,4]=>1 [7,8,5,6,1,2,3,4]=>2 [8,5,6,7,1,2,3,4]=>1 [5,6,7,8,1,2,3,4]=>4 [8,7,6,4,3,2,1,5]=>1 [8,7,6,4,2,1,3,5]=>1 [8,7,6,1,2,3,4,5]=>1 [8,6,7,1,2,3,4,5]=>1 [6,7,8,1,2,3,4,5]=>3 [7,8,5,4,2,1,3,6]=>2 [7,8,5,4,1,2,3,6]=>2 [8,7,1,2,3,4,5,6]=>1 [7,8,1,2,3,4,5,6]=>2 [8,6,5,4,3,2,1,7]=>1 [8,6,5,4,3,1,2,7]=>1 [8,5,6,3,4,1,2,7]=>1 [8,6,5,4,2,1,3,7]=>1 [8,6,4,3,2,1,5,7]=>1 [8,6,4,2,1,3,5,7]=>1 [8,2,3,4,1,5,6,7]=>1 [8,4,1,2,3,5,6,7]=>1 [8,3,2,1,4,5,6,7]=>1 [8,2,3,1,4,5,6,7]=>1 [8,3,1,2,4,5,6,7]=>1 [8,2,1,3,4,5,6,7]=>1 [8,1,2,3,4,5,6,7]=>1 [7,6,5,4,3,2,1,8]=>1 [6,7,5,4,3,2,1,8]=>2 [6,5,7,4,3,2,1,8]=>3 [5,6,7,4,3,2,1,8]=>2 [7,6,4,5,3,2,1,8]=>1 [6,5,4,7,3,2,1,8]=>4 [7,5,6,3,4,2,1,8]=>1 [7,6,4,3,5,2,1,8]=>1 [7,6,3,4,5,2,1,8]=>1 [7,5,4,3,6,2,1,8]=>1 [6,7,5,4,2,3,1,8]=>2 [6,5,7,3,2,4,1,8]=>3 [5,6,7,2,3,4,1,8]=>2 [2,3,4,5,6,7,1,8]=>2 [5,6,7,1,2,3,4,8]=>3 [6,7,1,2,3,4,5,8]=>2 [7,1,2,3,4,5,6,8]=>1 [6,5,4,3,2,1,7,8]=>1 [2,3,4,5,6,1,7,8]=>3 [5,6,3,4,1,2,7,8]=>2 [4,5,6,1,2,3,7,8]=>3 [6,1,2,3,4,5,7,8]=>1 [5,4,3,2,1,6,7,8]=>1 [2,3,4,5,1,6,7,8]=>4 [5,1,2,3,4,6,7,8]=>1 [4,3,2,1,5,6,7,8]=>1 [3,4,1,2,5,6,7,8]=>2 [3,2,1,4,5,6,7,8]=>1 [2,1,3,4,5,6,7,8]=>1 [1,2,3,4,5,6,7,8]=>7 [6,5,8,7,4,3,2,1]=>2 [3,5,8,7,6,4,2,1]=>1 [4,3,6,5,8,7,2,1]=>2 [2,6,8,7,5,4,3,1]=>1 [2,3,5,6,8,7,4,1]=>1 [3,2,6,5,4,8,7,1]=>2 [4,3,6,5,7,2,8,1]=>2 [3,2,6,5,7,4,8,1]=>2 [4,3,5,2,7,6,8,1]=>4 [3,2,5,4,7,6,8,1]=>2 [1,8,7,6,5,4,3,2]=>1 [1,7,8,6,5,4,3,2]=>1 [1,6,8,7,5,4,3,2]=>1 [1,7,6,8,5,4,3,2]=>1 [1,6,7,8,5,4,3,2]=>1 [1,5,8,7,6,4,3,2]=>1 [1,7,6,5,8,4,3,2]=>1 [1,3,5,7,8,6,4,2]=>1 [1,4,3,8,7,6,5,2]=>1 [1,6,5,4,3,8,7,2]=>1 [1,4,3,6,5,8,7,2]=>1 [2,1,8,7,6,5,4,3]=>2 [2,1,6,5,7,4,8,3]=>2 [2,1,5,4,7,6,8,3]=>2 [1,2,6,7,8,5,4,3]=>1 [3,2,1,8,7,6,5,4]=>3 [3,2,1,6,5,8,7,4]=>3 [1,2,3,5,6,7,8,4]=>1 [4,3,2,1,8,7,6,5]=>4 [3,4,2,1,7,8,6,5]=>4 [2,4,3,1,6,8,7,5]=>4 [2,4,3,1,7,6,8,5]=>1 [3,2,4,1,6,8,7,5]=>2 [3,2,4,1,7,6,8,5]=>4 [2,3,4,1,6,7,8,5]=>4 [2,1,4,3,8,7,6,5]=>2 [2,1,4,3,6,8,7,5]=>2 [2,1,4,3,7,6,8,5]=>2 [5,4,3,2,1,8,7,6]=>3 [3,2,5,4,1,8,7,6]=>2 [3,2,1,4,5,8,7,6]=>3 [2,3,1,4,5,7,8,6]=>3 [6,5,4,3,2,1,8,7]=>2 [4,3,5,2,6,1,8,7]=>2 [3,2,5,4,6,1,8,7]=>4 [2,3,4,5,6,1,8,7]=>1 [2,1,6,5,4,3,8,7]=>4 [2,1,4,6,5,3,8,7]=>2 [2,1,5,4,6,3,8,7]=>4 [4,3,2,1,6,5,8,7]=>2 [2,4,3,1,6,5,8,7]=>3 [3,2,4,1,6,5,8,7]=>2 [2,1,4,3,6,5,8,7]=>6 [2,1,3,4,5,6,8,7]=>2 [1,2,3,4,5,6,8,7]=>1 [5,7,6,4,3,2,1,8]=>2 [4,7,6,5,3,2,1,8]=>2 [3,2,7,6,5,4,1,8]=>3 [5,4,3,2,7,6,1,8]=>1 [3,2,5,4,7,6,1,8]=>3 [1,4,3,2,7,6,5,8]=>5 [1,3,4,2,6,7,5,8]=>5 [1,3,2,5,4,7,6,8]=>6 [1,2,3,5,4,7,6,8]=>2 [1,3,2,4,5,7,6,8]=>4 [1,2,3,4,5,7,6,8]=>2 [1,2,4,3,6,5,7,8]=>3 [1,3,2,5,4,6,7,8]=>2 [1,2,3,5,4,6,7,8]=>4 [1,3,2,4,5,6,7,8]=>2 [1,8,4,7,6,5,3,2]=>1 [1,8,5,4,7,6,3,2]=>1 [1,8,7,4,5,6,3,2]=>1 [1,8,7,4,6,5,3,2]=>1 [1,8,6,5,4,7,3,2]=>1 [1,8,7,5,4,6,3,2]=>1 [1,8,7,5,6,4,3,2]=>1 [2,1,4,5,8,6,7,3]=>2 [2,1,8,5,4,7,6,3]=>2 [2,3,4,8,5,6,7,1]=>1 [2,3,6,4,5,1,8,7]=>1 [2,3,7,4,5,6,8,1]=>1 [2,8,4,3,5,7,6,1]=>1 [4,2,3,1,8,6,7,5]=>4 [8,2,7,4,6,5,3,1]=>2 [4,3,2,7,5,6,8,1]=>2 [4,3,2,8,5,7,6,1]=>3 [6,3,2,5,4,1,8,7]=>2 [8,3,2,5,4,7,6,1]=>3 [8,3,2,7,6,5,4,1]=>3 [8,3,7,4,6,5,2,1]=>2 [7,3,6,5,4,2,1,8]=>1 [7,4,3,6,5,2,1,8]=>1 [7,6,3,5,4,2,1,8]=>1 [8,5,4,3,2,7,6,1]=>3 [8,7,4,3,6,5,2,1]=>4 [2,4,6,8,1,3,5,7]=>4 [2,4,6,1,7,3,8,5]=>1 [2,1,4,3,7,5,8,6]=>2 [2,4,1,3,7,5,8,6]=>1 [2,1,4,3,7,8,5,6]=>1 [2,4,7,8,1,3,5,6]=>4 [2,1,4,3,8,5,6,7]=>1 [2,4,5,6,7,1,8,3]=>1 [2,1,5,3,6,4,8,7]=>4 [2,1,5,6,3,4,8,7]=>2 [2,5,6,8,1,3,4,7]=>4 [2,1,5,3,7,4,8,6]=>2 [2,5,1,7,3,4,8,6]=>1 [2,1,5,7,3,8,4,6]=>1 [2,5,7,8,1,3,4,6]=>4 [2,3,5,6,1,7,8,4]=>1 [2,1,6,3,7,4,8,5]=>2 [2,6,7,1,3,4,8,5]=>1 [2,1,6,7,8,3,4,5]=>1 [2,6,7,8,1,3,4,5]=>4 [2,1,6,3,4,7,8,5]=>2 [2,1,6,3,4,5,8,7]=>2 [2,6,1,3,4,5,7,8]=>2 [2,7,8,1,3,4,5,6]=>3 [2,7,1,3,4,5,6,8]=>2 [2,3,4,5,7,8,1,6]=>2 [2,1,8,3,4,5,6,7]=>1 [2,8,1,3,4,5,6,7]=>2 [2,1,3,8,4,5,6,7]=>1 [2,3,4,5,6,8,1,7]=>2 [3,1,4,2,6,5,8,7]=>2 [3,4,1,2,6,5,8,7]=>1 [3,1,4,2,6,8,5,7]=>1 [3,4,6,8,1,2,5,7]=>4 [3,1,4,2,7,5,8,6]=>4 [3,4,1,2,7,8,5,6]=>4 [3,4,7,8,1,2,5,6]=>4 [3,1,5,2,6,4,8,7]=>2 [3,5,1,6,2,4,8,7]=>1 [3,1,5,6,2,8,4,7]=>1 [3,5,6,8,1,2,4,7]=>4 [3,1,5,2,7,4,8,6]=>6 [3,5,1,7,2,8,4,6]=>2 [3,5,7,8,1,2,4,6]=>4 [1,3,2,5,4,8,6,7]=>2 [1,3,5,8,2,4,6,7]=>4 [1,3,5,6,2,7,4,8]=>2 [3,1,6,2,7,4,8,5]=>4 [3,6,7,1,2,8,4,5]=>2 [3,6,1,7,8,2,4,5]=>2 [3,6,7,8,1,2,4,5]=>4 [1,3,2,6,4,7,5,8]=>4 [3,1,2,6,7,4,8,5]=>2 [1,3,2,6,4,8,5,7]=>2 [1,3,2,6,4,5,7,8]=>2 [1,3,2,7,4,8,5,6]=>2 [1,3,2,7,4,5,6,8]=>2 [1,3,2,8,4,5,6,7]=>2 [3,1,2,4,5,8,6,7]=>3 [1,3,2,4,5,8,6,7]=>2 [4,1,5,2,6,3,8,7]=>2 [4,5,6,1,2,3,8,7]=>1 [4,1,5,6,8,2,3,7]=>1 [4,5,6,8,1,2,3,7]=>4 [4,1,5,2,7,3,8,6]=>4 [4,1,5,2,7,8,3,6]=>1 [4,5,7,1,2,8,3,6]=>2 [4,5,1,7,8,2,3,6]=>2 [4,5,7,8,1,2,3,6]=>4 [1,4,2,5,3,7,6,8]=>4 [1,4,2,5,3,8,6,7]=>2 [1,4,2,5,3,6,7,8]=>2 [1,4,5,6,7,2,3,8]=>3 [4,1,6,2,7,3,8,5]=>6 [4,6,7,1,8,2,3,5]=>3 [4,6,7,8,1,2,3,5]=>4 [1,4,2,6,3,7,5,8]=>6 [1,4,2,6,7,8,3,5]=>2 [1,4,2,6,3,8,5,7]=>2 [4,1,2,3,6,5,8,7]=>2 [1,4,2,6,3,5,7,8]=>2 [1,4,2,7,3,8,5,6]=>2 [4,7,1,2,3,5,6,8]=>2 [1,4,2,7,3,5,6,8]=>2 [1,4,2,3,7,5,6,8]=>5 [1,4,2,3,5,7,6,8]=>2 [1,4,2,8,3,5,6,7]=>2 [4,1,2,3,8,5,6,7]=>4 [1,4,2,3,5,8,6,7]=>4 [1,4,2,3,5,6,7,8]=>2 [5,1,6,2,7,3,8,4]=>6 [1,5,2,6,3,7,4,8]=>6 [1,5,2,6,3,8,4,7]=>2 [1,5,2,6,3,4,7,8]=>2 [1,2,5,6,3,4,7,8]=>4 [1,5,2,7,3,8,4,6]=>2 [5,7,1,2,3,4,6,8]=>2 [1,5,2,7,3,4,6,8]=>2 [1,5,2,3,4,7,6,8]=>2 [5,1,2,8,3,4,6,7]=>1 [1,5,2,8,3,4,6,7]=>2 [1,5,8,2,3,4,6,7]=>3 [1,5,2,3,4,8,6,7]=>4 [1,2,3,5,4,8,6,7]=>2 [5,1,2,3,4,6,8,7]=>2 [1,5,2,3,4,6,7,8]=>2 [1,6,2,7,3,8,4,5]=>2 [1,6,7,8,2,3,4,5]=>4 [6,7,1,2,3,4,8,5]=>1 [6,1,7,2,3,4,5,8]=>1 [6,1,2,7,3,4,5,8]=>1 [1,6,2,7,3,4,5,8]=>2 [1,6,7,2,3,4,5,8]=>3 [1,6,2,3,4,7,5,8]=>2 [1,2,3,6,4,7,5,8]=>2 [6,1,8,2,3,4,5,7]=>1 [1,6,2,8,3,4,5,7]=>2 [1,6,8,2,3,4,5,7]=>3 [1,6,2,3,4,8,5,7]=>4 [1,2,3,6,4,8,5,7]=>2 [6,1,2,3,4,5,8,7]=>2 [1,6,2,3,4,5,7,8]=>2 [1,2,3,6,4,5,7,8]=>4 [1,7,2,8,3,4,5,6]=>2 [1,7,8,2,3,4,5,6]=>3 [1,7,2,3,8,4,5,6]=>2 [7,1,2,3,4,8,5,6]=>3 [1,7,2,3,4,8,5,6]=>4 [1,2,3,7,4,8,5,6]=>2 [7,1,2,3,4,5,8,6]=>2 [1,7,2,3,4,5,8,6]=>3 [1,2,7,3,4,5,8,6]=>4 [1,7,2,3,4,5,6,8]=>2 [1,2,3,7,4,5,6,8]=>4 [1,8,2,3,4,5,6,7]=>2 [1,2,3,8,4,5,6,7]=>4 [1,2,3,4,5,8,6,7]=>2 [5,3,2,6,1,4,8,7]=>2 [7,3,2,5,4,8,1,6]=>1 [8,4,5,2,3,7,6,1]=>2 [7,4,5,2,3,8,1,6]=>3 [6,4,5,2,3,1,8,7]=>2 [5,4,6,2,1,3,8,7]=>2 [3,6,1,5,4,2,8,7]=>1 [4,6,5,1,3,2,8,7]=>3 [5,6,4,3,1,2,8,7]=>1 [7,5,4,3,2,8,1,6]=>1 [8,6,4,3,7,2,5,1]=>2 [7,6,4,3,8,2,1,5]=>1 [6,7,4,3,8,1,2,5]=>2 [5,7,4,3,1,8,2,6]=>2 [4,7,5,1,3,8,2,6]=>2 [3,7,1,5,4,8,2,6]=>4 [2,1,7,5,4,8,3,6]=>1 [3,8,1,5,4,7,6,2]=>1 [4,8,5,1,3,7,6,2]=>4 [5,8,4,3,1,7,6,2]=>1 [6,8,4,3,7,1,5,2]=>1 [7,8,4,3,6,5,1,2]=>2 [6,8,5,7,3,1,4,2]=>1 [5,8,6,7,1,3,4,2]=>1 [4,8,6,1,7,3,5,2]=>1 [3,8,1,6,7,4,5,2]=>3 [2,1,8,6,7,4,5,3]=>2 [2,1,7,6,8,4,3,5]=>3 [3,7,1,6,8,4,2,5]=>2 [4,7,6,1,8,3,2,5]=>2 [5,7,6,8,1,3,2,4]=>4 [5,4,7,2,1,8,3,6]=>1 [6,4,7,2,8,1,3,5]=>1 [7,4,6,2,8,3,1,5]=>1 [8,4,6,2,7,3,5,1]=>4 [8,3,2,6,7,4,5,1]=>2 [7,3,2,6,8,4,1,5]=>4 [6,3,2,7,8,1,4,5]=>1 [5,3,2,7,1,8,4,6]=>1 [4,3,2,1,7,8,5,6]=>1 [3,4,1,2,8,7,6,5]=>1 [5,3,2,8,1,7,6,4]=>3 [6,3,2,8,7,1,5,4]=>2 [7,3,2,8,6,5,1,4]=>1 [8,4,7,2,6,5,3,1]=>2 [7,4,8,2,6,5,1,3]=>1 [6,4,8,2,7,1,5,3]=>2 [5,4,8,2,1,7,6,3]=>2 [4,5,8,1,2,7,6,3]=>1 [3,5,1,8,2,7,6,4]=>1 [2,1,5,8,3,7,6,4]=>2 [2,1,6,8,7,3,5,4]=>2 [3,6,1,8,7,2,5,4]=>1 [4,6,8,1,7,2,5,3]=>1 [5,6,8,7,1,2,4,3]=>4 [6,5,8,7,2,1,4,3]=>4 [7,5,8,6,2,4,1,3]=>1 [8,5,7,6,2,4,3,1]=>5 [5,7,8,6,1,4,2,3]=>2 [4,7,8,1,6,5,2,3]=>2 [3,7,1,8,6,5,2,4]=>2 [2,1,7,8,6,5,3,4]=>1 [3,8,1,7,6,5,4,2]=>1 [4,8,7,1,6,5,3,2]=>1 [5,8,7,6,1,4,3,2]=>4 [6,8,7,5,4,1,3,2]=>3 [4,2,5,1,3,6,7,8]=>1 [5,2,6,7,1,3,4,8]=>1 [3,2,7,8,1,4,5,6]=>1 [5,3,2,6,1,4,7,8]=>1 [7,4,3,8,1,2,5,6]=>1 [4,7,3,6,8,1,2,5]=>2 [6,7,3,4,8,1,2,5]=>2 [5,4,2,7,8,1,3,6]=>1 [6,4,7,2,5,1,3,8]=>1 [6,4,3,2,7,1,5,8]=>1 [5,4,3,2,8,1,6,7]=>1 [7,5,3,8,2,6,1,4]=>1 [8,5,4,7,2,6,1,3]=>1 [8,5,4,7,3,6,1,2]=>1 [8,1,2,7,6,3,4,5]=>4 [8,1,4,2,6,3,5,7]=>1 [8,3,1,2,4,7,5,6]=>1 [8,3,1,5,6,2,4,7]=>1 [6,3,8,1,2,7,4,5]=>1 [7,8,4,1,6,2,3,5]=>2 [8,3,4,1,6,7,2,5]=>3 [2,7,6,5,1,3,8,4]=>3 [8,3,6,5,1,7,2,4]=>3 [4,6,7,3,8,5,1,2]=>2 [3,5,2,7,1,8,6,4]=>1 [4,6,7,2,8,1,5,3]=>1 [5,6,7,8,2,1,4,3]=>1 [6,5,8,7,3,4,1,2]=>1 [3,6,7,4,5,8,1,2]=>2 [2,6,7,4,5,1,8,3]=>1 [1,6,7,4,5,2,3,8]=>3 [1,5,4,7,6,2,3,8]=>2 [2,5,4,7,6,1,8,3]=>3 [3,5,4,7,6,8,1,2]=>2 [4,5,3,7,8,6,1,2]=>2 [5,4,3,8,7,6,1,2]=>1 [6,4,8,3,7,5,1,2]=>1 [6,3,8,4,5,7,1,2]=>1 [5,3,4,8,6,7,1,2]=>3 [4,3,5,6,8,7,1,2]=>1 [3,2,5,6,1,8,7,4]=>2 [4,2,5,6,8,1,7,3]=>2 [5,2,4,8,6,1,7,3]=>2 [6,2,8,4,5,1,7,3]=>4 [7,8,2,4,5,1,6,3]=>1 [7,8,1,4,5,2,3,6]=>2 [6,1,8,4,5,2,3,7]=>1 [5,1,4,8,6,2,3,7]=>4 [4,1,3,2,8,6,5,7]=>1 [5,1,3,8,2,6,4,7]=>1 [6,1,8,3,2,5,4,7]=>3 [7,8,1,3,2,5,4,6]=>2 [7,8,2,3,1,5,6,4]=>3 [6,2,8,3,1,5,7,4]=>2 [5,2,3,8,1,6,7,4]=>2 [6,3,8,2,1,7,5,4]=>2 [7,8,3,2,1,6,5,4]=>1 [7,8,4,2,6,1,5,3]=>1 [5,4,2,8,7,1,6,3]=>2 [4,5,2,7,8,1,6,3]=>1 [2,5,3,7,1,6,8,4]=>1 [1,5,3,7,2,6,4,8]=>4 [1,6,7,3,2,5,4,8]=>2 [2,6,7,3,1,5,8,4]=>4 [3,6,7,2,1,8,5,4]=>1 [7,8,5,6,2,1,4,3]=>1 [6,5,8,7,1,2,3,4]=>1 [5,4,1,8,7,2,3,6]=>1 [6,4,8,1,7,2,3,5]=>1 [7,8,3,1,2,6,4,5]=>2 [5,3,1,8,2,7,4,6]=>1 [4,3,1,2,8,7,5,6]=>4 [4,2,1,3,8,5,7,6]=>2 [5,2,1,8,3,4,7,6]=>2 [6,2,8,1,3,4,7,5]=>2 [7,8,2,1,3,4,6,5]=>1 [6,3,1,5,2,4,8,7]=>2 [2,1,8,5,3,7,4,6]=>1 [8,2,6,1,4,3,7,5]=>2 [4,7,1,5,8,3,2,6]=>2 [8,6,1,3,4,2,5,7]=>1 [8,1,2,4,5,6,3,7]=>1 [8,2,5,1,3,6,4,7]=>1 [4,1,5,3,7,2,8,6]=>4 [5,2,7,1,3,8,4,6]=>1 [5,3,1,7,8,2,4,6]=>1 [1,7,3,4,2,5,8,6]=>3 [4,7,2,1,3,5,8,6]=>1 [4,5,2,3,7,6,1,8]=>2 [6,4,3,7,2,5,1,8]=>1 [8,4,3,6,5,1,2,7]=>1 [1,5,6,3,4,8,7,2]=>1 [4,6,2,7,3,5,1,8]=>4 [3,2,6,7,4,5,1,8]=>3 [4,7,2,6,5,3,1,8]=>2 [5,7,6,2,4,3,1,8]=>2 [1,7,5,4,8,3,6,2]=>1 [8,7,5,4,1,3,2,6]=>1 [6,8,5,4,2,1,3,7]=>2 [5,8,6,2,4,1,3,7]=>2 [4,8,2,6,5,1,3,7]=>2 [3,2,8,6,5,1,4,7]=>1 [4,1,2,6,5,8,7,3]=>2 [5,1,6,2,4,8,7,3]=>2 [6,1,5,4,2,8,7,3]=>2 [7,1,5,4,8,2,6,3]=>4 [8,1,5,4,7,6,2,3]=>3 [1,8,6,7,4,5,3,2]=>1 [8,1,6,7,4,5,2,3]=>3 [7,1,6,8,4,2,5,3]=>2 [6,1,7,8,2,4,5,3]=>2 [5,1,7,2,8,4,6,3]=>2 [4,1,2,7,8,5,6,3]=>2 [3,2,1,7,8,5,6,4]=>2 [3,2,8,7,1,5,4,6]=>3 [4,8,2,7,1,5,3,6]=>2 [5,8,7,2,1,4,3,6]=>2 [6,8,7,1,2,4,3,5]=>2 [7,8,6,1,4,2,3,5]=>2 [8,7,6,1,4,3,2,5]=>1 [1,7,6,8,4,3,5,2]=>1 [1,6,7,8,3,4,5,2]=>1 [8,6,7,1,3,4,2,5]=>1 [7,6,8,1,3,2,4,5]=>1 [5,7,8,2,1,3,4,6]=>3 [4,7,2,8,1,3,5,6]=>2 [3,2,6,8,4,1,5,7]=>4 [4,6,2,8,3,1,5,7]=>2 [5,6,8,2,3,1,4,7]=>3 [6,5,8,3,2,1,4,7]=>1 [7,5,8,3,1,2,4,6]=>1 [8,5,7,3,1,4,2,6]=>1 [1,5,7,3,8,4,6,2]=>1 [1,4,3,7,8,5,6,2]=>1 [8,4,3,7,1,5,2,6]=>1 [6,4,3,8,2,1,5,7]=>1 [4,5,2,3,8,1,6,7]=>2 [3,2,5,4,8,1,6,7]=>1 [4,5,2,3,1,8,7,6]=>1 [6,4,3,1,2,8,7,5]=>3 [7,4,3,1,8,2,6,5]=>2 [8,4,3,1,7,6,2,5]=>1 [1,5,8,3,7,6,4,2]=>1 [8,5,1,3,7,6,2,4]=>4 [7,5,1,3,8,2,6,4]=>2 [6,5,1,3,2,8,7,4]=>3 [5,6,1,2,3,8,7,4]=>1 [4,6,2,1,3,8,7,5]=>1 [3,2,6,1,4,8,7,5]=>2 [3,2,7,1,8,4,6,5]=>2 [4,7,2,1,8,3,6,5]=>1 [5,7,1,2,8,3,6,4]=>1 [6,7,1,8,2,3,5,4]=>1 [7,6,1,8,3,2,5,4]=>2 [8,6,1,7,3,5,2,4]=>1 [1,6,8,7,3,5,4,2]=>1 [1,7,8,6,5,3,4,2]=>1 [8,7,1,6,5,3,2,4]=>1 [7,8,1,6,5,2,3,4]=>2 [6,8,1,7,2,5,3,4]=>2 [5,8,1,2,7,6,3,4]=>2 [4,8,2,1,7,6,3,5]=>2 [3,2,8,1,7,6,4,5]=>1 [4,1,2,8,7,6,5,3]=>2 [5,1,8,2,7,6,4,3]=>2 [6,1,8,7,2,5,4,3]=>2 [7,1,8,6,5,2,4,3]=>2 [8,1,7,6,5,4,2,3]=>3 [1,4,3,8,7,5,6,2]=>1 [4,1,2,8,7,5,6,3]=>2 [3,2,5,1,6,4,8,7]=>2 [3,2,5,4,7,1,8,6]=>2 [4,2,5,3,7,6,8,1]=>2 [4,2,5,3,7,1,8,6]=>4 [4,2,5,3,6,1,8,7]=>2 [4,2,5,1,6,3,8,7]=>2 [3,1,5,4,6,2,8,7]=>4 [4,1,5,3,6,2,8,7]=>2 [4,3,5,1,6,2,8,7]=>2 [4,3,5,2,7,1,8,6]=>2 [4,3,6,2,7,5,8,1]=>4 [4,3,6,2,7,1,8,5]=>2 [4,3,6,1,7,2,8,5]=>2 [4,3,5,1,7,2,8,6]=>2 [3,1,5,4,7,2,8,6]=>2 [2,1,5,4,7,3,8,6]=>2 [3,1,5,4,7,6,8,2]=>2 [4,1,5,3,7,6,8,2]=>2 [4,3,5,1,7,6,8,2]=>4 [4,3,6,1,7,5,8,2]=>4 [4,3,6,5,7,1,8,2]=>2 [5,3,6,4,7,2,8,1]=>2 [5,3,6,4,7,1,8,2]=>4 [5,3,6,1,7,4,8,2]=>4 [5,1,6,3,7,4,8,2]=>2 [4,1,6,3,7,5,8,2]=>2 [3,1,6,4,7,5,8,2]=>2 [2,1,6,4,7,5,8,3]=>2 [2,1,6,4,7,3,8,5]=>2 [3,1,6,4,7,2,8,5]=>2 [4,1,6,3,7,2,8,5]=>4 [5,1,6,3,7,2,8,4]=>4 [5,3,6,1,7,2,8,4]=>2 [5,3,6,2,7,1,8,4]=>2 [5,3,6,2,7,4,8,1]=>4 [5,2,6,3,7,4,8,1]=>2 [5,2,6,3,7,1,8,4]=>4 [5,2,6,1,7,3,8,4]=>2 [4,2,5,1,7,3,8,6]=>2 [4,2,6,1,7,3,8,5]=>2 [4,2,6,3,7,1,8,5]=>4 [4,2,6,3,7,5,8,1]=>2 [3,2,6,4,7,5,8,1]=>2 [3,2,6,4,7,1,8,5]=>2 [3,2,6,1,7,4,8,5]=>2 [3,2,5,1,7,4,8,6]=>2 [3,2,4,1,7,5,8,6]=>2 [3,1,4,2,7,6,8,5]=>2 [3,2,5,1,7,6,8,4]=>4 [3,2,6,1,7,5,8,4]=>4 [3,2,6,5,7,1,8,4]=>2 [4,2,6,5,7,3,8,1]=>2 [4,2,6,5,7,1,8,3]=>2 [4,2,6,1,7,5,8,3]=>4 [4,2,5,1,7,6,8,3]=>4 [4,1,5,2,7,6,8,3]=>2 [3,1,5,2,7,6,8,4]=>2 [2,1,5,3,7,6,8,4]=>2 [2,1,6,3,7,5,8,4]=>2 [3,1,6,2,7,5,8,4]=>2 [4,1,6,2,7,5,8,3]=>2 [5,1,6,2,7,4,8,3]=>2 [5,2,6,1,7,4,8,3]=>4 [5,2,6,4,7,1,8,3]=>4 [5,2,6,4,7,3,8,1]=>2 [5,4,6,2,7,3,8,1]=>4 [5,4,6,2,7,1,8,3]=>2 [5,4,6,1,7,2,8,3]=>2 [5,1,6,4,7,2,8,3]=>4 [4,1,6,5,7,2,8,3]=>2 [3,1,6,5,7,2,8,4]=>2 [2,1,6,5,7,3,8,4]=>2 [3,1,6,5,7,4,8,2]=>2 [4,1,6,5,7,3,8,2]=>2 [5,1,6,4,7,3,8,2]=>2 [5,4,6,1,7,3,8,2]=>4 [5,4,6,3,7,1,8,2]=>2 [8,3,5,2,1,6,4,7]=>1 [8,6,3,5,2,4,1,7]=>1 [3,7,5,2,4,1,8,6]=>3 [8,3,7,5,2,4,6,1]=>2 [8,2,4,5,7,3,6,1]=>2 [2,4,5,7,3,1,8,6]=>1 [8,2,4,6,5,3,1,7]=>1 [8,2,5,4,6,1,3,7]=>1 [8,6,3,5,1,4,2,7]=>1 [8,6,1,4,5,3,2,7]=>1 [8,1,5,6,4,3,2,7]=>1 [5,7,4,3,2,1,8,6]=>1 [8,5,7,4,3,2,6,1]=>2 [4,6,8,3,2,7,5,1]=>1 [4,7,6,3,2,8,1,5]=>2 [1,4,6,7,3,2,8,5]=>1 [5,4,7,3,1,8,2,6]=>1 [1,7,4,5,3,2,8,6]=>3 [3,7,5,1,4,2,8,6]=>3 [5,7,4,2,1,3,8,6]=>1 [8,5,7,4,2,1,6,3]=>2 [8,3,7,5,1,4,6,2]=>2 [8,4,1,7,5,3,6,2]=>2 [4,6,3,8,7,1,5,2]=>1 [1,7,4,8,6,3,5,2]=>1 [8,4,7,6,3,5,2,1]=>2 [3,6,5,8,7,4,1,2]=>2 [3,1,5,8,6,7,4,2]=>2 [4,8,1,6,7,3,5,2]=>3 [3,6,4,1,8,7,5,2]=>1 [8,2,6,1,4,7,5,3]=>2 [2,7,6,8,1,4,3,5]=>4 [3,7,1,6,4,8,2,5]=>4 [1,7,3,5,6,8,2,4]=>2 [1,3,6,7,5,8,2,4]=>2 [3,7,6,5,8,2,1,4]=>2 [3,6,8,5,7,2,4,1]=>1 [2,3,5,7,6,8,1,4]=>2 [2,1,6,5,7,8,3,4]=>1 [4,2,7,6,8,3,1,5]=>3 [4,2,6,8,7,3,5,1]=>2 [3,8,2,4,6,7,5,1]=>1 [3,7,2,6,4,8,1,5]=>4 [3,2,6,1,4,7,8,5]=>2 [5,3,7,2,1,8,4,6]=>1 [4,7,3,2,1,5,8,6]=>1 [8,7,6,1,3,4,2,5]=>1 [8,5,7,3,2,1,6,4]=>2 [8,3,6,7,2,1,5,4]=>2 [3,7,8,6,2,1,5,4]=>1 [8,7,6,3,5,2,4,1]=>2 [2,7,4,8,1,6,5,3]=>1 [4,6,8,2,1,7,5,3]=>1 [8,4,1,5,7,2,6,3]=>2 [8,5,3,7,1,6,2,4]=>1 [8,5,7,2,1,3,6,4]=>2 [8,2,6,7,1,3,5,4]=>2 [8,3,6,1,7,5,2,4]=>3 [4,6,1,8,7,2,5,3]=>1 [8,1,2,5,6,7,4,3]=>2 [8,2,6,5,7,4,1,3]=>3 [2,1,7,8,5,6,4,3]=>2 [8,2,5,7,6,4,3,1]=>2 [2,7,6,8,5,4,1,3]=>2 [1,7,2,5,8,6,4,3]=>1 [1,7,4,8,2,6,5,3]=>1 [3,7,8,1,6,5,2,4]=>2 [2,7,8,6,1,3,5,4]=>1 [8,7,6,3,5,1,4,2]=>2 [8,4,7,6,5,1,3,2]=>4 [8,7,1,5,6,4,3,2]=>3 [8,1,6,7,5,4,3,2]=>2 [5,4,3,6,1,2,8,7]=>2 [2,7,6,4,5,8,1,3]=>2 [5,7,3,6,1,8,2,4]=>2 [2,1,7,6,5,8,3,4]=>1 [6,4,3,5,8,1,7,2]=>2 [7,3,5,4,8,6,1,2]=>3 [5,4,3,2,7,1,8,6]=>2 [4,3,6,2,8,7,5,1]=>2 [4,3,7,6,2,1,8,5]=>4 [6,4,3,1,7,2,8,5]=>2 [4,3,7,1,8,6,5,2]=>2 [5,3,8,7,6,4,2,1]=>2 [7,5,3,1,8,6,4,2]=>4 [1,8,6,5,3,7,4,2]=>1 [6,1,7,5,3,2,8,4]=>2 [7,6,5,3,2,1,8,4]=>2 [6,5,3,2,8,7,4,1]=>4 [5,2,6,3,8,7,4,1]=>2 [5,2,7,6,3,1,8,4]=>4 [6,5,2,1,7,3,8,4]=>2 [5,2,7,1,8,6,4,3]=>2 [6,2,8,7,5,4,3,1]=>2 [7,6,2,1,8,5,4,3]=>4 [6,1,7,2,8,5,4,3]=>2 [7,1,8,6,5,4,3,2]=>2 [4,5,2,6,3,1,8,7]=>1 [6,5,2,1,4,3,8,7]=>2 [6,5,2,7,4,8,3,1]=>3 [8,5,2,7,4,1,6,3]=>5 [8,3,7,5,2,1,6,4]=>2 [6,3,7,5,2,8,4,1]=>5 [3,1,6,5,4,2,8,7]=>4 [5,6,3,2,4,1,8,7]=>1 [3,6,2,4,1,5,8,7]=>1 [2,6,1,3,5,4,8,7]=>1 [6,7,2,3,4,8,5,1]=>1 [8,7,2,3,4,1,6,5]=>2 [5,1,7,3,8,4,6,2]=>2 [2,5,7,3,8,6,4,1]=>1 [7,6,1,3,5,8,4,2]=>3 [3,6,7,4,1,8,5,2]=>1 [5,6,3,7,4,8,1,2]=>2 [2,1,6,7,4,8,5,3]=>2 [2,1,8,7,4,3,6,5]=>4 [5,8,3,7,4,2,6,1]=>3 [3,8,7,4,1,2,6,5]=>3 [7,8,1,3,5,2,6,4]=>1 [5,8,7,3,2,6,1,4]=>2 [2,8,6,3,1,5,7,4]=>1 [8,1,6,3,2,5,4,7]=>1 [2,8,4,1,6,3,7,5]=>3 [4,8,1,2,7,6,3,5]=>2 [3,8,4,2,5,7,1,6]=>2 [6,8,3,5,2,7,4,1]=>1 [2,1,5,3,8,7,6,4]=>2 [6,5,3,2,8,7,1,4]=>1 [7,5,2,4,8,1,6,3]=>2 [3,4,2,8,5,7,6,1]=>1 [2,4,1,8,7,6,5,3]=>1 [8,4,2,1,7,5,3,6]=>1 [4,3,1,8,6,7,5,2]=>3 [3,1,4,8,6,5,7,2]=>2 [7,1,6,5,4,8,2,3]=>3 [3,7,5,6,8,4,2,1]=>1 [5,7,1,6,8,2,4,3]=>1 [8,6,2,5,1,7,4,3]=>3 [5,6,2,1,8,7,3,4]=>2 [4,6,2,5,8,3,7,1]=>3 [7,5,2,6,3,8,1,4]=>1 [4,1,2,3,6,8,7,5]=>2 [2,4,3,1,8,5,6,7]=>2 [7,5,2,8,3,4,6,1]=>2 [5,6,2,8,4,3,1,7]=>2 [4,7,2,8,1,5,3,6]=>2 [8,7,2,1,4,5,6,3]=>2 [3,6,8,7,1,5,4,2]=>1 [5,7,8,6,3,4,1,2]=>2 [7,1,8,5,4,3,6,2]=>2 [2,7,8,4,5,3,6,1]=>1 [5,7,3,8,1,4,6,2]=>3 [2,1,7,8,5,4,6,3]=>2 [2,1,5,8,4,6,3,7]=>3 [6,5,3,8,4,1,2,7]=>1 [7,5,8,4,3,6,2,1]=>5 [2,4,8,3,5,6,1,7]=>2 [4,1,8,3,6,5,2,7]=>3 [3,4,8,1,7,2,5,6]=>3 [8,4,1,3,7,2,6,5]=>2 [3,1,8,2,4,7,6,5]=>2 [2,3,8,1,4,6,7,5]=>1 [4,3,8,2,5,1,7,6]=>2 [6,3,8,4,2,5,7,1]=>2 [7,4,3,8,2,5,1,6]=>1 [2,1,4,8,3,5,7,6]=>2 [6,8,2,4,3,5,1,7]=>2 [4,8,2,3,5,1,6,7]=>2 [3,8,2,1,4,6,5,7]=>2 [2,8,1,3,4,5,7,6]=>1 [7,1,6,8,4,3,2,5]=>1 [7,1,6,5,8,3,2,4]=>1 [3,7,6,1,4,8,2,5]=>2 [2,7,8,4,1,6,5,3]=>1 [3,6,4,5,7,2,8,1]=>1 [1,8,2,7,3,4,5,6]=>2 [3,2,1,5,8,4,6,7]=>1 [5,4,3,2,1,8,6,7]=>1 [1,8,2,4,3,5,6,7]=>2 [1,7,2,4,3,5,6,8]=>2 [1,6,2,4,3,5,7,8]=>2 [1,5,2,4,3,6,7,8]=>2 [1,6,2,5,3,4,7,8]=>2 [1,7,2,5,3,4,6,8]=>2 [1,8,2,5,3,4,6,7]=>2 [1,8,2,6,3,4,5,7]=>2 [1,7,2,6,3,4,5,8]=>2 [1,8,2,7,3,5,4,6]=>2 [1,7,2,8,3,5,4,6]=>4 [1,6,2,8,3,5,4,7]=>4 [1,5,2,8,3,6,4,7]=>4 [1,4,2,8,3,6,5,7]=>4 [1,3,2,8,4,6,5,7]=>4 [1,2,3,8,4,6,5,7]=>2 [1,2,3,7,4,6,5,8]=>2 [1,3,2,7,4,6,5,8]=>4 [1,4,2,7,3,6,5,8]=>4 [1,5,2,7,3,6,4,8]=>4 [1,6,2,7,3,5,4,8]=>4 [1,7,2,6,3,5,4,8]=>2 [1,8,2,6,3,5,4,7]=>2 [1,8,2,5,3,6,4,7]=>2 [1,7,2,5,3,6,4,8]=>2 [1,6,2,5,3,7,4,8]=>2 [1,5,2,4,3,7,6,8]=>2 [1,6,2,4,3,7,5,8]=>2 [1,7,2,4,3,6,5,8]=>2 [1,8,2,4,3,6,5,7]=>2 [1,8,2,3,4,6,5,7]=>2 [1,7,2,3,4,6,5,8]=>2 [1,8,2,3,4,7,5,6]=>4 [1,8,2,4,3,7,5,6]=>4 [1,7,2,4,3,8,5,6]=>4 [1,6,2,4,3,8,5,7]=>4 [1,5,2,4,3,8,6,7]=>4 [1,6,2,5,3,8,4,7]=>4 [1,7,2,5,3,8,4,6]=>4 [1,8,2,5,3,7,4,6]=>4 [1,8,2,6,3,7,4,5]=>4 [1,7,2,6,3,8,4,5]=>4 [1,2,3,8,4,7,5,6]=>2 [1,3,2,8,4,7,5,6]=>2 [1,4,2,8,3,7,5,6]=>2 [1,5,2,8,3,7,4,6]=>2 [1,6,2,8,3,7,4,5]=>2 [1,7,2,8,3,6,4,5]=>2 [1,8,2,7,3,6,4,5]=>6 [6,7,8,1,4,3,2,5]=>2 [2,8,4,1,6,7,5,3]=>1 [4,8,5,7,1,6,2,3]=>4 [8,7,6,5,2,1,4,3]=>2 [8,3,1,5,4,7,2,6]=>1 [8,7,6,5,1,4,2,3]=>1 [7,5,1,3,8,4,2,6]=>1 [7,6,1,4,8,3,2,5]=>1 [7,1,3,5,8,2,4,6]=>4 [7,5,3,6,4,2,8,1]=>2 [8,2,6,3,4,7,5,1]=>2 [7,2,6,3,5,4,8,1]=>2 [6,2,7,4,3,5,8,1]=>2 [3,7,6,4,5,2,8,1]=>1 [2,7,6,5,3,4,8,1]=>1 [8,6,5,4,2,7,3,1]=>3 [6,5,8,4,2,7,3,1]=>2 [1,8,6,3,7,5,2,4]=>2 [8,7,5,2,6,4,3,1]=>4 [8,7,1,6,2,5,4,3]=>3 [1,7,2,8,5,3,4,6]=>2 [7,6,1,8,4,3,2,5]=>4 [8,6,1,7,4,2,5,3]=>5 [8,1,2,7,3,4,6,5]=>5 [7,1,2,8,3,5,4,6]=>1 [8,2,6,1,7,3,5,4]=>2 [4,7,5,6,8,3,2,1]=>1 [8,6,4,7,5,3,2,1]=>3 [5,4,8,1,7,2,6,3]=>2 [2,3,8,7,4,5,6,1]=>1 [7,2,8,6,4,3,5,1]=>2 [8,2,7,6,3,5,4,1]=>2 [8,1,7,6,5,2,4,3]=>4 [7,1,8,6,5,3,2,4]=>3 [1,2,8,7,6,3,4,5]=>3 [3,8,7,6,4,5,2,1]=>1 [2,8,7,6,5,3,4,1]=>1 [1,8,7,6,5,4,2,3]=>2 [3,8,6,7,1,5,2,4]=>4 [5,4,7,1,3,8,2,6]=>1 [5,6,2,1,4,8,3,7]=>2 [2,1,8,4,7,5,6,3]=>2 [4,1,3,2,8,5,6,7]=>1 [3,2,1,4,8,5,6,7]=>1 [1,8,4,2,5,3,6,7]=>2 [8,1,5,3,2,4,6,7]=>1 [3,8,1,5,2,4,6,7]=>2 [1,6,7,2,8,4,3,5]=>2 [6,7,1,4,2,8,3,5]=>2 [6,3,7,1,4,8,2,5]=>1 [3,7,8,1,5,2,4,6]=>3 [7,1,2,8,5,3,4,6]=>4 [1,7,2,8,4,5,3,6]=>2 [1,2,7,5,8,3,4,6]=>3 [2,8,1,7,4,3,6,5]=>1 [4,2,6,5,8,3,7,1]=>2 [5,2,4,7,3,6,8,1]=>2 [5,1,2,4,8,3,6,7]=>4 [4,3,6,1,5,8,2,7]=>1 [2,6,1,4,5,8,3,7]=>4 [2,5,3,4,1,8,6,7]=>4 [4,3,5,2,1,8,6,7]=>1 [3,1,6,7,5,8,2,4]=>1 [2,8,1,7,5,6,3,4]=>2 [5,3,6,8,4,7,2,1]=>2 [3,7,2,5,4,8,6,1]=>1 [8,4,2,5,7,3,6,1]=>2 [4,7,2,5,8,3,6,1]=>3 [5,2,6,8,4,3,7,1]=>2 [3,1,6,5,4,8,2,7]=>1 [4,1,6,5,8,3,2,7]=>3 [5,1,6,8,4,3,2,7]=>3 [8,5,4,7,6,3,2,1]=>3 [5,7,1,8,4,3,2,6]=>2 [2,7,1,5,4,3,8,6]=>1 [8,2,1,5,4,3,7,6]=>2 [8,4,1,5,7,3,2,6]=>4 [8,5,6,7,1,3,2,4]=>1 [8,4,6,1,7,3,2,5]=>1 [8,3,6,1,4,7,2,5]=>3 [2,7,6,1,4,3,8,5]=>3 [6,7,8,5,1,3,2,4]=>2 [5,7,6,8,2,3,4,1]=>1 [5,7,2,8,4,3,6,1]=>3 [6,7,8,2,4,3,5,1]=>1 [4,7,6,2,8,3,5,1]=>1 [8,3,6,2,4,7,5,1]=>2 [3,7,6,2,4,8,5,1]=>4 [5,7,3,8,4,6,2,1]=>1 [4,7,3,5,8,6,2,1]=>1 [8,7,2,1,4,3,6,5]=>2 [8,7,3,1,4,6,2,5]=>1 [8,7,6,3,2,5,4,1]=>3 [8,7,3,5,1,6,2,4]=>1 [8,7,2,5,1,3,6,4]=>2 [8,2,6,5,1,3,7,4]=>2 [8,4,6,5,7,1,2,3]=>1 [5,7,6,8,4,1,2,3]=>2 [4,7,6,5,8,1,2,3]=>2 [3,7,6,5,1,8,2,4]=>2 [2,6,5,7,3,4,8,1]=>1 [1,6,4,7,5,8,2,3]=>2 [8,5,3,6,2,7,4,1]=>3 [1,3,7,4,6,8,2,5]=>2 [4,7,5,6,3,2,8,1]=>1 [1,7,6,5,4,8,2,3]=>2 [8,1,6,5,7,2,4,3]=>4 [1,2,7,6,8,3,4,5]=>3 [6,1,7,5,3,8,2,4]=>1 [2,1,7,5,6,8,3,4]=>1 [5,4,1,7,6,8,2,3]=>1 [4,8,5,6,2,7,3,1]=>1 [3,8,6,4,2,7,5,1]=>1 [7,8,5,2,4,6,3,1]=>4 [2,8,6,3,7,4,5,1]=>1 [7,8,1,6,2,4,5,3]=>3 [6,8,1,4,7,2,5,3]=>1 [3,8,4,1,7,2,6,5]=>3 [5,4,7,1,8,3,2,6]=>3 [3,7,4,1,8,5,2,6]=>2 [6,7,1,4,8,3,2,5]=>2 [2,7,1,8,4,5,3,6]=>4 [6,1,2,8,4,3,5,7]=>1 [6,5,1,4,3,8,2,7]=>1 [1,6,2,5,8,3,4,7]=>2 [8,5,1,3,7,2,6,4]=>2 [8,4,2,1,7,3,6,5]=>2 [7,4,2,1,8,5,3,6]=>1 [1,5,4,2,8,3,6,7]=>2 [6,4,3,1,5,8,2,7]=>1 [3,7,6,8,4,5,2,1]=>1 [2,7,6,8,5,3,4,1]=>1 [1,7,6,8,5,4,2,3]=>2 [1,4,8,6,7,5,2,3]=>2 [2,4,8,6,7,3,5,1]=>1 [7,3,8,5,4,6,2,1]=>2 [3,4,8,5,6,7,2,1]=>1 [6,3,5,8,4,7,2,1]=>2 [5,4,3,8,6,7,2,1]=>3 [5,4,2,8,7,3,6,1]=>2 [6,2,5,8,7,3,4,1]=>2 [3,2,8,5,7,4,6,1]=>2 [1,3,8,7,5,6,2,4]=>2 [2,1,8,7,4,6,3,5]=>1 [3,1,8,5,7,6,2,4]=>1 [6,1,5,8,7,4,2,3]=>3 [5,4,1,8,7,6,2,3]=>1 [5,8,6,7,4,3,2,1]=>1 [4,8,7,5,6,3,2,1]=>1 [2,8,3,1,5,4,6,7]=>2 [2,5,3,4,7,1,8,6]=>3 [2,4,8,3,5,7,6,1]=>1 [4,2,5,3,1,8,6,7]=>1 [4,2,1,8,5,3,6,7]=>1 [5,4,1,3,8,2,6,7]=>1 [5,1,4,8,3,2,6,7]=>1 [1,5,8,4,3,2,6,7]=>3 [1,8,5,4,3,2,6,7]=>2 [1,7,4,3,8,5,2,6]=>2 [1,5,7,3,8,4,2,6]=>2 [5,1,4,7,8,3,2,6]=>1 [4,8,1,5,7,3,6,2]=>3 [8,1,5,3,7,4,6,2]=>2 [3,8,4,7,6,5,2,1]=>1 [1,6,8,5,3,7,4,2]=>1 [6,8,1,7,4,3,5,2]=>3 [6,4,8,1,7,3,5,2]=>2 [6,4,8,7,1,5,2,3]=>1 [7,6,4,1,3,8,2,5]=>1 [1,7,5,6,3,2,8,4]=>3 [4,2,1,7,8,5,3,6]=>1 [2,7,4,6,3,1,8,5]=>3 [2,6,8,4,3,7,5,1]=>1 [6,2,4,8,3,7,5,1]=>2 [7,2,6,3,4,1,8,5]=>2 [2,6,7,3,1,4,8,5]=>1 [2,7,1,8,3,5,4,6]=>2 [2,1,7,3,5,8,4,6]=>1 [8,7,1,3,6,2,4,5]=>1 [8,2,1,7,3,5,6,4]=>2 [7,8,2,6,3,1,5,4]=>1 [8,7,2,6,3,5,4,1]=>3 [1,2,8,7,4,5,6,3]=>1 [8,3,7,1,5,6,2,4]=>3 [8,6,1,2,7,5,3,4]=>4 [8,1,6,2,7,4,5,3]=>2 [1,8,5,2,6,7,4,3]=>1 [5,2,1,8,6,7,4,3]=>3 [2,8,5,7,6,4,3,1]=>1 [1,7,8,5,2,6,4,3]=>1 [7,8,1,6,4,2,5,3]=>1 [7,8,6,1,5,3,2,4]=>2 [7,3,8,6,1,5,2,4]=>1 [8,7,6,1,5,3,4,2]=>2 [8,7,1,6,4,5,3,2]=>3 [8,1,7,5,6,4,3,2]=>2 [1,8,6,7,5,4,3,2]=>1 [9,1,2,3,4,5,6,7,8]=>1 [8,1,2,3,4,5,6,9,7]=>2 [2,9,1,3,4,5,6,7,8]=>2 [9,3,1,2,4,5,6,7,8]=>1 [8,9,1,2,3,4,5,6,7]=>2 [9,7,8,1,2,3,4,5,6]=>1 [2,3,4,5,6,7,9,1,8]=>2 [2,3,4,5,6,7,8,9,1]=>1 [2,3,4,5,6,7,8,1,9]=>2 [2,3,4,5,6,7,1,8,9]=>3 [1,2,3,4,5,6,7,9,8]=>1 [2,1,3,4,5,6,7,8,9]=>1 [1,8,2,3,4,5,6,9,7]=>3 [7,1,2,3,4,5,6,9,8]=>2 [2,1,9,3,4,5,6,7,8]=>1 [2,8,1,3,4,5,6,7,9]=>2 [1,2,3,4,5,6,7,8,9]=>8 [3,2,4,5,6,7,8,9,1]=>2 [9,8,7,6,5,4,3,2,1]=>8 [8,7,6,5,4,3,2,1,9]=>1 [1,9,8,7,6,5,4,3,2]=>1 [8,7,6,4,5,3,2,1,9]=>1 [1,9,8,7,5,6,4,3,2]=>1 [8,7,5,4,6,3,2,1,9]=>1 [8,7,4,6,5,3,2,1,9]=>1 [1,9,8,6,5,7,4,3,2]=>1 [1,9,8,5,7,6,4,3,2]=>1 [9,2,1,3,4,5,6,7,8]=>1 [9,2,3,1,4,5,6,7,8]=>1 [4,2,3,5,6,7,8,9,1]=>2 [3,4,2,5,6,7,8,9,1]=>3 [9,8,1,2,3,4,5,6,7]=>1 [7,8,9,1,2,3,4,5,6]=>3 [9,8,7,1,2,3,4,5,6]=>1 [6,7,8,9,1,2,3,4,5]=>4 [9,6,7,8,1,2,3,4,5]=>1 [8,9,6,7,1,2,3,4,5]=>2 [9,8,6,7,1,2,3,4,5]=>1 [9,8,7,6,1,2,3,4,5]=>1 [9,5,6,7,8,1,2,3,4]=>5 [8,9,5,6,7,1,2,3,4]=>2 [9,8,5,6,7,1,2,3,4]=>1 [9,7,8,5,6,1,2,3,4]=>1 [9,8,7,5,6,1,2,3,4]=>1 [9,8,7,6,5,1,2,3,4]=>1 [7,8,9,4,5,6,1,2,3]=>6 [9,7,8,4,5,6,1,2,3]=>1 [9,8,7,4,5,6,1,2,3]=>1 [8,9,6,7,4,5,1,2,3]=>2 [9,8,6,7,4,5,1,2,3]=>1 [9,8,7,6,4,5,1,2,3]=>1 [9,8,7,6,5,4,1,2,3]=>1 [9,7,8,5,6,3,4,1,2]=>7 [9,8,7,5,6,3,4,1,2]=>1 [9,8,7,6,5,3,4,1,2]=>1 [9,8,7,6,5,4,3,1,2]=>1 [7,8,6,5,4,3,2,1,9]=>2 [1,8,9,7,6,5,4,3,2]=>1 [7,6,8,5,4,3,2,1,9]=>3 [6,8,7,5,4,3,2,1,9]=>2 [1,8,7,9,6,5,4,3,2]=>1 [1,7,9,8,6,5,4,3,2]=>1 [8,1,2,3,4,5,6,7,9]=>1 [1,9,2,3,4,5,6,7,8]=>2 [7,8,1,2,3,4,5,6,9]=>2 [1,8,9,2,3,4,5,6,7]=>3 [7,1,8,2,3,4,5,6,9]=>1 [6,8,1,2,3,4,5,7,9]=>2 [1,8,2,9,3,4,5,6,7]=>2 [1,7,9,2,3,4,5,6,8]=>3 [7,1,2,3,4,5,6,8,9]=>1 [3,4,1,2,5,6,7,8,9]=>2 [3,2,1,4,5,6,7,8,9]=>1 [4,5,6,1,2,3,7,8,9]=>3 [4,2,5,1,3,6,7,8,9]=>1 [4,3,2,1,5,6,7,8,9]=>1 [5,6,7,8,1,2,3,4,9]=>4 [5,2,6,7,1,3,4,8,9]=>1 [5,6,3,4,1,2,7,8,9]=>2 [5,3,2,6,1,4,7,8,9]=>1 [5,4,3,2,1,6,7,8,9]=>1 [6,2,7,8,9,1,3,4,5]=>1 [6,7,3,4,8,1,2,5,9]=>2 [6,3,2,7,8,1,4,5,9]=>1 [6,4,7,2,5,1,3,8,9]=>1 [6,4,3,2,7,1,5,8,9]=>1 [6,5,4,3,2,1,7,8,9]=>1 [7,4,8,2,5,9,1,3,6]=>1 [7,4,3,2,8,9,1,5,6]=>1 [7,8,5,6,3,4,1,2,9]=>2 [7,5,3,8,2,6,1,4,9]=>1 [7,5,4,3,2,8,1,6,9]=>1 [7,6,5,4,3,2,1,8,9]=>1 [8,6,9,4,7,2,5,1,3]=>1 [8,6,4,3,9,2,7,1,5]=>1 [8,6,5,4,3,2,9,1,7]=>1 [2,1,4,3,6,5,8,7,10,9]=>8 [4,3,2,1,6,5,8,7,10,9]=>2 [6,3,2,5,4,1,8,7,10,9]=>2 [8,3,2,5,4,7,6,1,10,9]=>2 [10,3,2,5,4,7,6,9,8,1]=>3 [2,1,6,5,4,3,8,7,10,9]=>4 [6,5,4,3,2,1,8,7,10,9]=>2 [8,5,4,3,2,7,6,1,10,9]=>2 [10,5,4,3,2,7,6,9,8,1]=>3 [2,1,8,5,4,7,6,3,10,9]=>4 [8,7,4,3,6,5,2,1,10,9]=>2 [10,7,4,3,6,5,2,9,8,1]=>3 [2,1,10,5,4,7,6,9,8,3]=>2 [10,9,4,3,6,5,8,7,2,1]=>4 [8,9,5,6,3,4,10,1,2,7]=>2 [2,1,4,3,8,7,6,5,10,9]=>4 [4,3,2,1,8,7,6,5,10,9]=>6 [8,3,2,7,6,5,4,1,10,9]=>2 [10,3,2,7,6,5,4,9,8,1]=>3 [2,1,8,7,6,5,4,3,10,9]=>4 [8,7,6,5,4,3,2,1,10,9]=>2 [9,7,6,5,4,3,2,10,1,8]=>1 [10,7,6,5,4,3,2,9,8,1]=>3 [2,1,10,7,6,5,4,9,8,3]=>2 [10,9,6,5,4,3,8,7,2,1]=>4 [2,1,4,3,10,7,6,9,8,5]=>2 [4,3,2,1,10,7,6,9,8,5]=>3 [10,3,2,9,6,5,8,7,4,1]=>3 [2,1,10,9,6,5,8,7,4,3]=>2 [10,9,8,5,4,7,6,3,2,1]=>5 [6,7,8,9,10,1,2,3,4,5]=>5 [7,3,2,8,9,10,1,4,5,6]=>1 [8,5,4,3,2,9,10,1,6,7]=>1 [2,1,4,3,6,5,10,9,8,7]=>2 [4,3,2,1,6,5,10,9,8,7]=>4 [6,3,2,5,4,1,10,9,8,7]=>3 [10,3,2,5,4,9,8,7,6,1]=>3 [2,1,6,5,4,3,10,9,8,7]=>6 [6,5,4,3,2,1,10,9,8,7]=>4 [10,5,4,3,2,9,8,7,6,1]=>5 [2,1,10,5,4,9,8,7,6,3]=>2 [10,9,4,3,8,7,6,5,2,1]=>4 [9,7,5,10,3,8,2,6,1,4]=>1 [2,1,4,3,10,9,8,7,6,5]=>2 [4,3,2,1,10,9,8,7,6,5]=>4 [10,3,2,9,8,7,6,5,4,1]=>3 [2,1,10,9,8,7,6,5,4,3]=>2 [10,9,8,7,6,5,4,3,2,1]=>9 [2,3,4,5,6,7,8,9,10,1]=>1 [2,3,4,5,6,7,8,9,1,10]=>2 [10,8,9,5,6,7,1,2,3,4]=>1 [10,8,9,4,5,6,1,2,3,7]=>1 [10,7,8,5,6,9,1,2,3,4]=>1 [10,7,8,4,5,9,1,2,3,6]=>1 [10,6,7,4,5,8,1,2,3,9]=>1 [10,7,8,3,4,9,1,2,5,6]=>1 [10,6,7,3,4,8,1,2,5,9]=>1 [9,8,10,5,6,7,1,2,3,4]=>1 [9,8,10,4,5,6,1,2,3,7]=>1 [9,7,10,5,6,8,1,2,3,4]=>1 [9,7,10,4,5,8,1,2,3,6]=>1 [9,6,10,4,5,7,1,2,3,8]=>1 [9,7,10,3,4,8,1,2,5,6]=>1 [9,6,10,3,4,7,1,2,5,8]=>1 [8,7,9,5,6,10,1,2,3,4]=>1 [8,7,9,4,5,10,1,2,3,6]=>1 [8,6,9,4,5,10,1,2,3,7]=>1 [7,6,8,4,5,9,1,2,3,10]=>1 [8,7,9,3,4,10,1,2,5,6]=>1 [8,6,9,3,4,10,1,2,5,7]=>1 [7,6,8,3,4,9,1,2,5,10]=>1 [9,6,10,5,7,8,1,2,3,4]=>1 [9,6,10,4,7,8,1,2,3,5]=>1 [9,5,10,4,6,7,1,2,3,8]=>1 [9,6,10,3,7,8,1,2,4,5]=>1 [9,5,10,3,6,7,1,2,4,8]=>1 [8,6,9,5,7,10,1,2,3,4]=>1 [8,6,9,4,7,10,1,2,3,5]=>1 [8,5,9,4,6,10,1,2,3,7]=>1 [7,5,8,4,6,9,1,2,3,10]=>1 [8,6,9,3,7,10,1,2,4,5]=>1 [8,5,9,3,6,10,1,2,4,7]=>1 [7,5,8,3,6,9,1,2,4,10]=>1 [8,4,9,3,5,10,1,2,6,7]=>1 [7,4,8,3,5,9,1,2,6,10]=>1 [9,6,10,2,7,8,1,3,4,5]=>1 [9,5,10,2,6,7,1,3,4,8]=>1 [8,6,9,2,7,10,1,3,4,5]=>1 [8,5,9,2,6,10,1,3,4,7]=>1 [7,5,8,2,6,9,1,3,4,10]=>1 [8,4,9,2,5,10,1,3,6,7]=>1 [7,4,8,2,5,9,1,3,6,10]=>1 [1,2,3,4,5,6,7,8,10,9]=>1 [2,1,3,4,5,6,7,8,9,10]=>1 [9,1,2,3,4,5,6,7,10,8]=>2 [2,10,1,3,4,5,6,7,8,9]=>2 [1,2,3,4,5,6,7,8,9,10]=>9 [9,8,7,6,5,4,3,2,1,10]=>1 [10,1,2,3,4,5,6,7,8,9]=>1 [10,9,1,2,3,4,5,6,7,8]=>1 [1,10,9,8,7,6,5,4,3,2]=>1 [9,8,7,5,6,4,3,2,1,10]=>1 [1,10,9,8,6,7,5,4,3,2]=>1 [10,2,1,3,4,5,6,7,8,9]=>1 [3,2,4,5,6,7,8,9,10,1]=>2 [2,4,6,8,10,1,3,5,7,9]=>5 [2,4,6,9,10,1,3,5,7,8]=>5 [2,4,7,8,10,1,3,5,6,9]=>5 [2,4,7,9,10,1,3,5,6,8]=>5 [2,4,8,9,10,1,3,5,6,7]=>5 [2,5,6,8,10,1,3,4,7,9]=>5 [2,5,6,9,10,1,3,4,7,8]=>5 [2,5,7,8,10,1,3,4,6,9]=>5 [2,5,7,9,10,1,3,4,6,8]=>5 [2,5,8,9,10,1,3,4,6,7]=>5 [2,6,7,8,10,1,3,4,5,9]=>5 [2,6,7,9,10,1,3,4,5,8]=>5 [2,6,8,9,10,1,3,4,5,7]=>5 [2,7,8,9,10,1,3,4,5,6]=>5 [3,4,6,8,10,1,2,5,7,9]=>5 [3,4,6,9,10,1,2,5,7,8]=>5 [3,4,7,8,10,1,2,5,6,9]=>5 [3,4,7,9,10,1,2,5,6,8]=>5 [3,4,8,9,10,1,2,5,6,7]=>5 [3,5,6,8,10,1,2,4,7,9]=>5 [3,5,6,9,10,1,2,4,7,8]=>5 [3,5,7,8,10,1,2,4,6,9]=>5 [3,5,7,9,10,1,2,4,6,8]=>5 [3,5,8,9,10,1,2,4,6,7]=>5 [3,6,7,8,10,1,2,4,5,9]=>5 [3,6,7,9,10,1,2,4,5,8]=>5 [3,6,8,9,10,1,2,4,5,7]=>5 [3,7,8,9,10,1,2,4,5,6]=>5 [4,5,6,8,10,1,2,3,7,9]=>5 [4,5,6,9,10,1,2,3,7,8]=>5 [4,5,7,8,10,1,2,3,6,9]=>5 [4,5,7,9,10,1,2,3,6,8]=>5 [4,5,8,9,10,1,2,3,6,7]=>5 [4,6,7,8,10,1,2,3,5,9]=>5 [4,6,7,9,10,1,2,3,5,8]=>5 [4,6,8,9,10,1,2,3,5,7]=>5 [4,7,8,9,10,1,2,3,5,6]=>5 [5,6,7,8,10,1,2,3,4,9]=>5 [5,6,7,9,10,1,2,3,4,8]=>5 [5,6,8,9,10,1,2,3,4,7]=>5 [5,7,8,9,10,1,2,3,4,6]=>5 [9,10,1,2,3,4,5,6,7,8]=>2 [8,9,10,1,2,3,4,5,6,7]=>3 [10,8,9,1,2,3,4,5,6,7]=>1 [10,9,8,1,2,3,4,5,6,7]=>1 [7,8,9,10,1,2,3,4,5,6]=>4 [10,7,8,9,1,2,3,4,5,6]=>1 [9,10,7,8,1,2,3,4,5,6]=>2 [10,9,7,8,1,2,3,4,5,6]=>1 [10,9,8,7,1,2,3,4,5,6]=>1 [10,6,7,8,9,1,2,3,4,5]=>1 [9,10,6,7,8,1,2,3,4,5]=>2 [10,9,6,7,8,1,2,3,4,5]=>1 [10,8,9,6,7,1,2,3,4,5]=>1 [10,9,8,6,7,1,2,3,4,5]=>1 [10,9,8,7,6,1,2,3,4,5]=>1 [9,10,5,6,7,8,1,2,3,4]=>6 [10,9,5,6,7,8,1,2,3,4]=>1 [8,9,10,5,6,7,1,2,3,4]=>3 [10,9,8,5,6,7,1,2,3,4]=>1 [9,10,7,8,5,6,1,2,3,4]=>2 [10,9,7,8,5,6,1,2,3,4]=>1 [10,9,8,7,5,6,1,2,3,4]=>1 [10,9,8,7,6,5,1,2,3,4]=>1 [10,7,8,9,4,5,6,1,2,3]=>7 [9,10,7,8,4,5,6,1,2,3]=>2 [10,9,7,8,4,5,6,1,2,3]=>1 [10,9,8,7,4,5,6,1,2,3]=>1 [10,8,9,6,7,4,5,1,2,3]=>1 [10,9,8,6,7,4,5,1,2,3]=>1 [10,9,8,7,6,4,5,1,2,3]=>1 [10,9,8,7,6,5,4,1,2,3]=>1 [9,10,7,8,5,6,3,4,1,2]=>8 [10,9,7,8,5,6,3,4,1,2]=>1 [10,9,8,7,5,6,3,4,1,2]=>1 [10,9,8,7,6,5,3,4,1,2]=>1 [10,9,8,7,6,5,4,3,1,2]=>1 [8,9,7,6,5,4,3,2,1,10]=>2 [1,9,10,8,7,6,5,4,3,2]=>1 [9,1,2,3,4,5,6,7,8,10]=>1 [1,10,2,3,4,5,6,7,8,9]=>2 [8,9,1,2,3,4,5,6,7,10]=>2 [1,9,10,2,3,4,5,6,7,8]=>3 [3,4,1,2,5,6,7,8,9,10]=>2 [3,2,1,4,5,6,7,8,9,10]=>1 [4,5,6,1,2,3,7,8,9,10]=>3 [4,2,5,1,3,6,7,8,9,10]=>1 [4,3,2,1,5,6,7,8,9,10]=>1 [5,6,7,8,1,2,3,4,9,10]=>4 [5,2,6,7,1,3,4,8,9,10]=>1 [5,6,3,4,1,2,7,8,9,10]=>2 [5,3,2,6,1,4,7,8,9,10]=>1 [5,4,3,2,1,6,7,8,9,10]=>1 [6,2,7,8,9,1,3,4,5,10]=>1 [6,7,3,4,8,1,2,5,9,10]=>2 [6,3,2,7,8,1,4,5,9,10]=>1 [6,4,7,2,5,1,3,8,9,10]=>1 [6,4,3,2,7,1,5,8,9,10]=>1 [6,5,4,3,2,1,7,8,9,10]=>1 [7,8,3,4,9,10,1,2,5,6]=>2 [7,8,9,4,5,6,1,2,3,10]=>3 [7,4,3,2,8,9,1,5,6,10]=>1 [7,8,5,6,3,4,1,2,9,10]=>2 [7,5,3,8,2,6,1,4,9,10]=>1 [7,5,4,3,2,8,1,6,9,10]=>1 [7,6,5,4,3,2,1,8,9,10]=>1 [8,5,9,10,2,6,7,1,3,4]=>1 [8,5,3,9,2,6,10,1,4,7]=>1 [8,6,9,4,7,2,5,1,3,10]=>1 [8,6,4,3,9,2,7,1,5,10]=>1 [8,6,5,4,3,2,9,1,7,10]=>1 [8,7,6,5,4,3,2,1,9,10]=>1 [9,7,5,4,3,10,2,8,1,6]=>1 [1,2,3,4,5,6,7,8,9,11,10]=>1 [2,1,3,4,5,6,7,8,9,10,11]=>1 [11,1,2,3,4,5,6,7,8,9,10]=>1 [10,9,8,7,6,5,4,3,2,1,11]=>1 [1,11,10,9,8,7,6,5,4,3,2]=>1 [2,3,4,5,6,7,8,9,10,11,1]=>1 [10,1,2,3,4,5,6,7,8,9,11]=>1 [1,11,2,3,4,5,6,7,8,9,10]=>2 [2,1,4,3,6,5,8,7,10,9,12,11]=>10 [2,1,4,3,6,5,8,7,12,11,10,9]=>2 [2,1,4,3,6,5,10,9,8,7,12,11]=>4 [2,1,4,3,6,5,12,9,8,11,10,7]=>2 [2,1,4,3,6,5,12,11,10,9,8,7]=>2 [2,1,4,3,8,7,6,5,10,9,12,11]=>6 [2,1,4,3,8,7,6,5,12,11,10,9]=>2 [2,1,4,3,10,7,6,9,8,5,12,11]=>4 [2,1,4,3,12,7,6,9,8,11,10,5]=>2 [2,1,4,3,12,7,6,11,10,9,8,5]=>2 [2,1,4,3,10,9,8,7,6,5,12,11]=>4 [2,1,4,3,12,9,8,7,6,11,10,5]=>2 [2,1,4,3,12,11,8,7,10,9,6,5]=>2 [2,1,4,3,12,11,10,9,8,7,6,5]=>2 [2,1,6,5,4,3,8,7,10,9,12,11]=>4 [2,1,6,5,4,3,8,7,12,11,10,9]=>6 [2,1,6,5,4,3,10,9,8,7,12,11]=>8 [2,1,6,5,4,3,12,9,8,11,10,7]=>2 [2,1,6,5,4,3,12,11,10,9,8,7]=>2 [2,1,8,5,4,7,6,3,10,9,12,11]=>4 [2,1,8,5,4,7,6,3,12,11,10,9]=>2 [2,1,10,5,4,7,6,9,8,3,12,11]=>4 [2,1,12,5,4,7,6,9,8,11,10,3]=>2 [2,1,12,5,4,7,6,11,10,9,8,3]=>2 [2,1,10,5,4,9,8,7,6,3,12,11]=>4 [2,1,12,5,4,9,8,7,6,11,10,3]=>2 [2,1,12,5,4,11,8,7,10,9,6,3]=>2 [2,1,12,5,4,11,10,9,8,7,6,3]=>2 [2,1,8,7,6,5,4,3,10,9,12,11]=>4 [2,1,8,7,6,5,4,3,12,11,10,9]=>6 [2,1,10,7,6,5,4,9,8,3,12,11]=>4 [2,1,12,7,6,5,4,9,8,11,10,3]=>2 [2,1,12,7,6,5,4,11,10,9,8,3]=>2 [2,1,10,9,6,5,8,7,4,3,12,11]=>4 [2,1,12,9,6,5,8,7,4,11,10,3]=>2 [2,1,12,11,6,5,8,7,10,9,4,3]=>2 [2,1,12,11,6,5,10,9,8,7,4,3]=>2 [2,1,10,9,8,7,6,5,4,3,12,11]=>4 [2,1,12,9,8,7,6,5,4,11,10,3]=>2 [2,1,12,11,8,7,6,5,10,9,4,3]=>2 [2,1,12,11,10,7,6,9,8,5,4,3]=>2 [2,1,12,11,10,9,8,7,6,5,4,3]=>2 [4,3,2,1,6,5,8,7,10,9,12,11]=>2 [4,3,2,1,6,5,8,7,12,11,10,9]=>4 [4,3,2,1,6,5,10,9,8,7,12,11]=>6 [4,3,2,1,6,5,12,9,8,11,10,7]=>3 [4,3,2,1,6,5,12,11,10,9,8,7]=>4 [4,3,2,1,8,7,6,5,10,9,12,11]=>2 [4,3,2,1,8,7,6,5,12,11,10,9]=>8 [4,3,2,1,10,7,6,9,8,5,12,11]=>2 [4,3,2,1,12,7,6,9,8,11,10,5]=>3 [4,3,2,1,12,7,6,11,10,9,8,5]=>4 [4,3,2,1,10,9,8,7,6,5,12,11]=>6 [4,3,2,1,12,9,8,7,6,11,10,5]=>3 [4,3,2,1,12,11,8,7,10,9,6,5]=>4 [4,3,2,1,12,11,10,9,8,7,6,5]=>4 [6,3,2,5,4,1,8,7,10,9,12,11]=>2 [6,3,2,5,4,1,8,7,12,11,10,9]=>3 [6,3,2,5,4,1,10,9,8,7,12,11]=>2 [6,3,2,5,4,1,12,9,8,11,10,7]=>6 [6,3,2,5,4,1,12,11,10,9,8,7]=>3 [8,3,2,5,4,7,6,1,10,9,12,11]=>2 [8,3,2,5,4,7,6,1,12,11,10,9]=>3 [10,3,2,5,4,7,6,9,8,1,12,11]=>2 [12,3,2,5,4,7,6,9,8,11,10,1]=>3 [12,3,2,5,4,7,6,11,10,9,8,1]=>3 [10,3,2,5,4,9,8,7,6,1,12,11]=>2 [12,3,2,5,4,9,8,7,6,11,10,1]=>3 [12,3,2,5,4,11,8,7,10,9,6,1]=>3 [12,3,2,5,4,11,10,9,8,7,6,1]=>3 [8,3,2,7,6,5,4,1,10,9,12,11]=>2 [8,3,2,7,6,5,4,1,12,11,10,9]=>3 [10,3,2,7,6,5,4,9,8,1,12,11]=>2 [12,3,2,7,6,5,4,9,8,11,10,1]=>3 [12,3,2,7,6,5,4,11,10,9,8,1]=>3 [10,3,2,9,6,5,8,7,4,1,12,11]=>2 [12,3,2,9,6,5,8,7,4,11,10,1]=>3 [12,3,2,11,6,5,8,7,10,9,4,1]=>3 [12,3,2,11,6,5,10,9,8,7,4,1]=>3 [10,3,2,9,8,7,6,5,4,1,12,11]=>2 [12,3,2,9,8,7,6,5,4,11,10,1]=>3 [12,3,2,11,8,7,6,5,10,9,4,1]=>3 [12,3,2,11,10,7,6,9,8,5,4,1]=>3 [12,3,2,11,10,9,8,7,6,5,4,1]=>3 [6,5,4,3,2,1,8,7,10,9,12,11]=>2 [6,5,4,3,2,1,8,7,12,11,10,9]=>4 [6,5,4,3,2,1,10,9,8,7,12,11]=>2 [6,5,4,3,2,1,12,9,8,11,10,7]=>3 [6,5,4,3,2,1,12,11,10,9,8,7]=>6 [8,5,4,3,2,7,6,1,10,9,12,11]=>2 [8,5,4,3,2,7,6,1,12,11,10,9]=>4 [10,5,4,3,2,7,6,9,8,1,12,11]=>2 [12,5,4,3,2,7,6,9,8,11,10,1]=>3 [12,5,4,3,2,7,6,11,10,9,8,1]=>5 [10,5,4,3,2,9,8,7,6,1,12,11]=>2 [12,5,4,3,2,9,8,7,6,11,10,1]=>3 [12,5,4,3,2,11,8,7,10,9,6,1]=>4 [12,5,4,3,2,11,10,9,8,7,6,1]=>5 [8,7,4,3,6,5,2,1,10,9,12,11]=>2 [8,7,4,3,6,5,2,1,12,11,10,9]=>4 [10,7,4,3,6,5,2,9,8,1,12,11]=>2 [12,7,4,3,6,5,2,9,8,11,10,1]=>3 [12,7,4,3,6,5,2,11,10,9,8,1]=>4 [10,9,4,3,6,5,8,7,2,1,12,11]=>2 [12,9,4,3,6,5,8,7,2,11,10,1]=>3 [12,11,4,3,6,5,8,7,10,9,2,1]=>4 [12,11,4,3,6,5,10,9,8,7,2,1]=>4 [10,9,4,3,8,7,6,5,2,1,12,11]=>2 [12,9,4,3,8,7,6,5,2,11,10,1]=>3 [12,11,4,3,8,7,6,5,10,9,2,1]=>4 [12,11,4,3,10,7,6,9,8,5,2,1]=>4 [12,11,4,3,10,9,8,7,6,5,2,1]=>4 [8,7,6,5,4,3,2,1,10,9,12,11]=>2 [8,7,6,5,4,3,2,1,12,11,10,9]=>4 [10,7,6,5,4,3,2,9,8,1,12,11]=>2 [12,7,6,5,4,3,2,9,8,11,10,1]=>3 [12,7,6,5,4,3,2,11,10,9,8,1]=>5 [10,9,6,5,4,3,8,7,2,1,12,11]=>2 [12,9,6,5,4,3,8,7,2,11,10,1]=>3 [12,11,6,5,4,3,8,7,10,9,2,1]=>4 [12,11,6,5,4,3,10,9,8,7,2,1]=>6 [10,9,8,5,4,7,6,3,2,1,12,11]=>2 [12,9,8,5,4,7,6,3,2,11,10,1]=>3 [12,11,8,5,4,7,6,3,10,9,2,1]=>4 [12,11,10,5,4,7,6,9,8,3,2,1]=>5 [12,11,10,5,4,9,8,7,6,3,2,1]=>5 [10,9,8,7,6,5,4,3,2,1,12,11]=>2 [12,9,8,7,6,5,4,3,2,11,10,1]=>3 [12,11,8,7,6,5,4,3,10,9,2,1]=>4 [12,11,10,7,6,5,4,9,8,3,2,1]=>5 [12,11,10,9,6,5,8,7,4,3,2,1]=>6 [12,11,10,9,8,7,6,5,4,3,2,1]=>11 [2,4,6,8,10,12,1,3,5,7,9,11]=>6 [2,4,6,8,11,12,1,3,5,7,9,10]=>6 [2,4,6,9,10,12,1,3,5,7,8,11]=>6 [2,4,6,9,11,12,1,3,5,7,8,10]=>6 [2,4,6,10,11,12,1,3,5,7,8,9]=>6 [2,4,7,8,10,12,1,3,5,6,9,11]=>6 [2,4,7,8,11,12,1,3,5,6,9,10]=>6 [2,4,7,9,10,12,1,3,5,6,8,11]=>6 [2,4,7,9,11,12,1,3,5,6,8,10]=>6 [2,4,7,10,11,12,1,3,5,6,8,9]=>6 [2,4,8,9,10,12,1,3,5,6,7,11]=>6 [2,4,8,9,11,12,1,3,5,6,7,10]=>6 [2,4,8,10,11,12,1,3,5,6,7,9]=>6 [2,4,9,10,11,12,1,3,5,6,7,8]=>6 [2,5,6,8,10,12,1,3,4,7,9,11]=>6 [2,5,6,8,11,12,1,3,4,7,9,10]=>6 [2,5,6,9,10,12,1,3,4,7,8,11]=>6 [2,5,6,9,11,12,1,3,4,7,8,10]=>6 [2,5,6,10,11,12,1,3,4,7,8,9]=>6 [2,5,7,8,10,12,1,3,4,6,9,11]=>6 [2,5,7,8,11,12,1,3,4,6,9,10]=>6 [2,5,7,9,10,12,1,3,4,6,8,11]=>6 [2,5,7,9,11,12,1,3,4,6,8,10]=>6 [2,5,7,10,11,12,1,3,4,6,8,9]=>6 [2,5,8,9,10,12,1,3,4,6,7,11]=>6 [2,5,8,9,11,12,1,3,4,6,7,10]=>6 [2,5,8,10,11,12,1,3,4,6,7,9]=>6 [2,5,9,10,11,12,1,3,4,6,7,8]=>6 [2,6,7,8,10,12,1,3,4,5,9,11]=>6 [2,6,7,8,11,12,1,3,4,5,9,10]=>6 [2,6,7,9,10,12,1,3,4,5,8,11]=>6 [2,6,7,9,11,12,1,3,4,5,8,10]=>6 [2,6,7,10,11,12,1,3,4,5,8,9]=>6 [2,6,8,9,10,12,1,3,4,5,7,11]=>6 [2,6,8,9,11,12,1,3,4,5,7,10]=>6 [2,6,8,10,11,12,1,3,4,5,7,9]=>6 [2,6,9,10,11,12,1,3,4,5,7,8]=>6 [2,7,8,9,10,12,1,3,4,5,6,11]=>6 [2,7,8,9,11,12,1,3,4,5,6,10]=>6 [2,7,8,10,11,12,1,3,4,5,6,9]=>6 [2,7,9,10,11,12,1,3,4,5,6,8]=>6 [2,8,9,10,11,12,1,3,4,5,6,7]=>6 [3,4,6,8,10,12,1,2,5,7,9,11]=>6 [3,4,6,8,11,12,1,2,5,7,9,10]=>6 [3,4,6,9,10,12,1,2,5,7,8,11]=>6 [3,4,6,9,11,12,1,2,5,7,8,10]=>6 [3,4,6,10,11,12,1,2,5,7,8,9]=>6 [3,4,7,8,10,12,1,2,5,6,9,11]=>6 [3,4,7,8,11,12,1,2,5,6,9,10]=>6 [3,4,7,9,10,12,1,2,5,6,8,11]=>6 [3,4,7,9,11,12,1,2,5,6,8,10]=>6 [3,4,7,10,11,12,1,2,5,6,8,9]=>6 [3,4,8,9,10,12,1,2,5,6,7,11]=>6 [3,4,8,9,11,12,1,2,5,6,7,10]=>6 [3,4,8,10,11,12,1,2,5,6,7,9]=>6 [3,4,9,10,11,12,1,2,5,6,7,8]=>6 [3,5,6,8,10,12,1,2,4,7,9,11]=>6 [3,5,6,8,11,12,1,2,4,7,9,10]=>6 [3,5,6,9,10,12,1,2,4,7,8,11]=>6 [3,5,6,9,11,12,1,2,4,7,8,10]=>6 [3,5,6,10,11,12,1,2,4,7,8,9]=>6 [3,5,7,8,10,12,1,2,4,6,9,11]=>6 [3,5,7,8,11,12,1,2,4,6,9,10]=>6 [3,5,7,9,10,12,1,2,4,6,8,11]=>6 [3,5,7,9,11,12,1,2,4,6,8,10]=>6 [3,5,7,10,11,12,1,2,4,6,8,9]=>6 [3,5,8,9,10,12,1,2,4,6,7,11]=>6 [3,5,8,9,11,12,1,2,4,6,7,10]=>6 [3,5,8,10,11,12,1,2,4,6,7,9]=>6 [3,5,9,10,11,12,1,2,4,6,7,8]=>6 [3,6,7,8,10,12,1,2,4,5,9,11]=>6 [3,6,7,8,11,12,1,2,4,5,9,10]=>6 [3,6,7,9,10,12,1,2,4,5,8,11]=>6 [3,6,7,9,11,12,1,2,4,5,8,10]=>6 [3,6,7,10,11,12,1,2,4,5,8,9]=>6 [3,6,8,9,10,12,1,2,4,5,7,11]=>6 [3,6,8,9,11,12,1,2,4,5,7,10]=>6 [3,6,8,10,11,12,1,2,4,5,7,9]=>6 [3,6,9,10,11,12,1,2,4,5,7,8]=>6 [3,7,8,9,10,12,1,2,4,5,6,11]=>6 [3,7,8,9,11,12,1,2,4,5,6,10]=>6 [3,7,8,10,11,12,1,2,4,5,6,9]=>6 [3,7,9,10,11,12,1,2,4,5,6,8]=>6 [3,8,9,10,11,12,1,2,4,5,6,7]=>6 [4,5,6,8,10,12,1,2,3,7,9,11]=>6 [4,5,6,8,11,12,1,2,3,7,9,10]=>6 [4,5,6,9,10,12,1,2,3,7,8,11]=>6 [4,5,6,9,11,12,1,2,3,7,8,10]=>6 [4,5,6,10,11,12,1,2,3,7,8,9]=>6 [4,5,7,8,10,12,1,2,3,6,9,11]=>6 [4,5,7,8,11,12,1,2,3,6,9,10]=>6 [4,5,7,9,10,12,1,2,3,6,8,11]=>6 [4,5,7,9,11,12,1,2,3,6,8,10]=>6 [4,5,7,10,11,12,1,2,3,6,8,9]=>6 [4,5,8,9,10,12,1,2,3,6,7,11]=>6 [4,5,8,9,11,12,1,2,3,6,7,10]=>6 [4,5,8,10,11,12,1,2,3,6,7,9]=>6 [4,5,9,10,11,12,1,2,3,6,7,8]=>6 [4,6,7,8,10,12,1,2,3,5,9,11]=>6 [4,6,7,8,11,12,1,2,3,5,9,10]=>6 [4,6,7,9,10,12,1,2,3,5,8,11]=>6 [4,6,7,9,11,12,1,2,3,5,8,10]=>6 [4,6,7,10,11,12,1,2,3,5,8,9]=>6 [4,6,8,9,10,12,1,2,3,5,7,11]=>6 [4,6,8,9,11,12,1,2,3,5,7,10]=>6 [4,6,8,10,11,12,1,2,3,5,7,9]=>6 [4,6,9,10,11,12,1,2,3,5,7,8]=>6 [4,7,8,9,10,12,1,2,3,5,6,11]=>6 [4,7,8,9,11,12,1,2,3,5,6,10]=>6 [4,7,8,10,11,12,1,2,3,5,6,9]=>6 [4,7,9,10,11,12,1,2,3,5,6,8]=>6 [4,8,9,10,11,12,1,2,3,5,6,7]=>6 [5,6,7,8,10,12,1,2,3,4,9,11]=>6 [5,6,7,8,11,12,1,2,3,4,9,10]=>6 [5,6,7,9,10,12,1,2,3,4,8,11]=>6 [5,6,7,9,11,12,1,2,3,4,8,10]=>6 [5,6,7,10,11,12,1,2,3,4,8,9]=>6 [5,6,8,9,10,12,1,2,3,4,7,11]=>6 [5,6,8,9,11,12,1,2,3,4,7,10]=>6 [5,6,8,10,11,12,1,2,3,4,7,9]=>6 [5,6,9,10,11,12,1,2,3,4,7,8]=>6 [5,7,8,9,10,12,1,2,3,4,6,11]=>6 [5,7,8,9,11,12,1,2,3,4,6,10]=>6 [5,7,8,10,11,12,1,2,3,4,6,9]=>6 [5,7,9,10,11,12,1,2,3,4,6,8]=>6 [5,8,9,10,11,12,1,2,3,4,6,7]=>6 [6,7,8,9,10,12,1,2,3,4,5,11]=>6 [6,7,8,9,11,12,1,2,3,4,5,10]=>6 [6,7,8,10,11,12,1,2,3,4,5,9]=>6 [6,7,9,10,11,12,1,2,3,4,5,8]=>6 [6,8,9,10,11,12,1,2,3,4,5,7]=>6 [7,8,9,10,11,12,1,2,3,4,5,6]=>6
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Description
The length of the exterior of a permutation.
The exterior of a permutation is the longest proper prefix that is also a suffix, when viewed as a pattern. In other words, the length of the exterior of a permutation $\sigma$ of length $n$ is the largest $i < n$ such that the first $i$ entries of $\sigma$ are in the same relative order as the last $i$ entries of $\sigma$.
References
[1] Elizalde, S., McNamara, P. R. W. The structure of the consecutive pattern poset arXiv:1508.05963 DOI:10.1093/imrn/rnw293
Code
from sage.combinat.permutation import to_standard
def statistic(x):
    """
    sage: R. = PolynomialRing(ZZ)
    sage: [sum(q^statistic(x) for x in Permutations(n)) for n in range(2,9)]
    [2*q,
     2*q^2 + 4*q,
     2*q^3 + 10*q^2 + 12*q,
     2*q^4 + 12*q^3 + 58*q^2 + 48*q,
     2*q^5 + 14*q^4 + 118*q^3 + 306*q^2 + 280*q,
     2*q^6 + 16*q^5 + 150*q^4 + 822*q^3 + 2186*q^2 + 1864*q,
     2*q^7 + 18*q^6 + 186*q^5 + 1660*q^4 + 6580*q^3 + 17034*q^2 + 14840*q]
    """
    n = len(x)
    for i in range(n-1, 0, -1):
        if to_standard(x[:i]) == to_standard(x[n-i:]):
            return i
Created
Nov 19, 2017 at 21:22 by Sergi Elizalde
Updated
Dec 25, 2017 at 17:37 by Martin Rubey