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]=>2 [2,4,1,3]=>1 [2,4,3,1]=>3 [3,1,2,4]=>1 [3,1,4,2]=>3 [3,2,1,4]=>2 [3,2,4,1]=>3 [3,4,1,2]=>2 [3,4,2,1]=>3 [4,1,2,3]=>2 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>3 [4,3,1,2]=>3 [4,3,2,1]=>4 [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]=>2 [1,3,5,2,4]=>1 [1,3,5,4,2]=>3 [1,4,2,3,5]=>1 [1,4,2,5,3]=>3 [1,4,3,2,5]=>2 [1,4,3,5,2]=>3 [1,4,5,2,3]=>2 [1,4,5,3,2]=>3 [1,5,2,3,4]=>2 [1,5,2,4,3]=>3 [1,5,3,2,4]=>3 [1,5,3,4,2]=>3 [1,5,4,2,3]=>3 [1,5,4,3,2]=>4 [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]=>2 [2,3,4,5,1]=>2 [2,3,5,1,4]=>2 [2,3,5,4,1]=>3 [2,4,1,3,5]=>1 [2,4,1,5,3]=>3 [2,4,3,1,5]=>3 [2,4,3,5,1]=>3 [2,4,5,1,3]=>3 [2,4,5,3,1]=>3 [2,5,1,3,4]=>2 [2,5,1,4,3]=>3 [2,5,3,1,4]=>4 [2,5,3,4,1]=>3 [2,5,4,1,3]=>4 [2,5,4,3,1]=>4 [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]=>3 [3,1,5,4,2]=>3 [3,2,1,4,5]=>2 [3,2,1,5,4]=>3 [3,2,4,1,5]=>3 [3,2,4,5,1]=>3 [3,2,5,1,4]=>3 [3,2,5,4,1]=>4 [3,4,1,2,5]=>2 [3,4,1,5,2]=>3 [3,4,2,1,5]=>3 [3,4,2,5,1]=>3 [3,4,5,1,2]=>3 [3,4,5,2,1]=>4 [3,5,1,2,4]=>3 [3,5,1,4,2]=>3 [3,5,2,1,4]=>4 [3,5,2,4,1]=>3 [3,5,4,1,2]=>4 [3,5,4,2,1]=>5 [4,1,2,3,5]=>2 [4,1,2,5,3]=>2 [4,1,3,2,5]=>3 [4,1,3,5,2]=>2 [4,1,5,2,3]=>3 [4,1,5,3,2]=>4 [4,2,1,3,5]=>3 [4,2,1,5,3]=>3 [4,2,3,1,5]=>3 [4,2,3,5,1]=>3 [4,2,5,1,3]=>3 [4,2,5,3,1]=>5 [4,3,1,2,5]=>3 [4,3,1,5,2]=>4 [4,3,2,1,5]=>4 [4,3,2,5,1]=>4 [4,3,5,1,2]=>4 [4,3,5,2,1]=>5 [4,5,1,2,3]=>3 [4,5,1,3,2]=>4 [4,5,2,1,3]=>4 [4,5,2,3,1]=>4 [4,5,3,1,2]=>4 [4,5,3,2,1]=>5 [5,1,2,3,4]=>2 [5,1,2,4,3]=>3 [5,1,3,2,4]=>3 [5,1,3,4,2]=>3 [5,1,4,2,3]=>3 [5,1,4,3,2]=>4 [5,2,1,3,4]=>3 [5,2,1,4,3]=>4 [5,2,3,1,4]=>3 [5,2,3,4,1]=>4 [5,2,4,1,3]=>3 [5,2,4,3,1]=>5 [5,3,1,2,4]=>3 [5,3,1,4,2]=>5 [5,3,2,1,4]=>4 [5,3,2,4,1]=>5 [5,3,4,1,2]=>4 [5,3,4,2,1]=>5 [5,4,1,2,3]=>4 [5,4,1,3,2]=>5 [5,4,2,1,3]=>5 [5,4,2,3,1]=>5 [5,4,3,1,2]=>5 [5,4,3,2,1]=>6 [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]=>2 [1,2,4,6,3,5]=>1 [1,2,4,6,5,3]=>3 [1,2,5,3,4,6]=>1 [1,2,5,3,6,4]=>3 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>3 [1,2,5,6,3,4]=>2 [1,2,5,6,4,3]=>3 [1,2,6,3,4,5]=>2 [1,2,6,3,5,4]=>3 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>3 [1,2,6,5,3,4]=>3 [1,2,6,5,4,3]=>4 [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]=>2 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>2 [1,3,4,6,5,2]=>3 [1,3,5,2,4,6]=>1 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>3 [1,3,5,6,2,4]=>3 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>2 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>4 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>4 [1,3,6,5,4,2]=>4 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>2 [1,4,2,5,3,6]=>3 [1,4,2,5,6,3]=>2 [1,4,2,6,3,5]=>3 [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]=>3 [1,4,3,5,6,2]=>3 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>4 [1,4,5,2,3,6]=>2 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>3 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>4 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>4 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>4 [1,4,6,5,3,2]=>5 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>2 [1,5,2,6,3,4]=>3 [1,5,2,6,4,3]=>4 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>3 [1,5,3,4,2,6]=>3 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>5 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>4 [1,5,4,3,2,6]=>4 [1,5,4,3,6,2]=>4 [1,5,4,6,2,3]=>4 [1,5,4,6,3,2]=>5 [1,5,6,2,3,4]=>3 [1,5,6,2,4,3]=>4 [1,5,6,3,2,4]=>4 [1,5,6,3,4,2]=>4 [1,5,6,4,2,3]=>4 [1,5,6,4,3,2]=>5 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>3 [1,6,2,4,3,5]=>3 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>3 [1,6,2,5,4,3]=>4 [1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>4 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>4 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>5 [1,6,4,2,3,5]=>3 [1,6,4,2,5,3]=>5 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>5 [1,6,4,5,2,3]=>4 [1,6,4,5,3,2]=>5 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>5 [1,6,5,3,2,4]=>5 [1,6,5,3,4,2]=>5 [1,6,5,4,2,3]=>5 [1,6,5,4,3,2]=>6 [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]=>3 [2,1,4,6,3,5]=>2 [2,1,4,6,5,3]=>4 [2,1,5,3,4,6]=>2 [2,1,5,3,6,4]=>4 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>4 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>4 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>4 [2,1,6,4,3,5]=>4 [2,1,6,4,5,3]=>4 [2,1,6,5,3,4]=>4 [2,1,6,5,4,3]=>5 [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]=>2 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>2 [2,3,4,5,6,1]=>3 [2,3,4,6,1,5]=>2 [2,3,4,6,5,1]=>4 [2,3,5,1,4,6]=>2 [2,3,5,1,6,4]=>4 [2,3,5,4,1,6]=>3 [2,3,5,4,6,1]=>4 [2,3,5,6,1,4]=>3 [2,3,5,6,4,1]=>4 [2,3,6,1,4,5]=>3 [2,3,6,1,5,4]=>4 [2,3,6,4,1,5]=>4 [2,3,6,4,5,1]=>4 [2,3,6,5,1,4]=>4 [2,3,6,5,4,1]=>5 [2,4,1,3,5,6]=>1 [2,4,1,3,6,5]=>2 [2,4,1,5,3,6]=>3 [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]=>3 [2,4,3,1,6,5]=>4 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>4 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>5 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>4 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>4 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>5 [2,4,6,1,3,5]=>4 [2,4,6,1,5,3]=>4 [2,4,6,3,1,5]=>4 [2,4,6,3,5,1]=>4 [2,4,6,5,1,3]=>4 [2,4,6,5,3,1]=>6 [2,5,1,3,4,6]=>2 [2,5,1,3,6,4]=>2 [2,5,1,4,3,6]=>3 [2,5,1,4,6,3]=>2 [2,5,1,6,3,4]=>3 [2,5,1,6,4,3]=>4 [2,5,3,1,4,6]=>4 [2,5,3,1,6,4]=>4 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>4 [2,5,3,6,1,4]=>3 [2,5,3,6,4,1]=>6 [2,5,4,1,3,6]=>4 [2,5,4,1,6,3]=>5 [2,5,4,3,1,6]=>4 [2,5,4,3,6,1]=>5 [2,5,4,6,1,3]=>4 [2,5,4,6,3,1]=>6 [2,5,6,1,3,4]=>4 [2,5,6,1,4,3]=>5 [2,5,6,3,1,4]=>4 [2,5,6,3,4,1]=>5 [2,5,6,4,1,3]=>4 [2,5,6,4,3,1]=>6 [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]=>4 [2,6,3,1,5,4]=>5 [2,6,3,4,1,5]=>3 [2,6,3,4,5,1]=>5 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>6 [2,6,4,1,3,5]=>4 [2,6,4,1,5,3]=>6 [2,6,4,3,1,5]=>4 [2,6,4,3,5,1]=>6 [2,6,4,5,1,3]=>4 [2,6,4,5,3,1]=>6 [2,6,5,1,3,4]=>5 [2,6,5,1,4,3]=>6 [2,6,5,3,1,4]=>5 [2,6,5,3,4,1]=>6 [2,6,5,4,1,3]=>5 [2,6,5,4,3,1]=>7 [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]=>3 [3,1,4,2,6,5]=>4 [3,1,4,5,2,6]=>2 [3,1,4,5,6,2]=>4 [3,1,4,6,2,5]=>2 [3,1,4,6,5,2]=>5 [3,1,5,2,4,6]=>3 [3,1,5,2,6,4]=>5 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>5 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>5 [3,1,6,2,4,5]=>4 [3,1,6,2,5,4]=>5 [3,1,6,4,2,5]=>4 [3,1,6,4,5,2]=>5 [3,1,6,5,2,4]=>4 [3,1,6,5,4,2]=>6 [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]=>3 [3,2,4,1,6,5]=>4 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>4 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>5 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>5 [3,2,5,4,1,6]=>4 [3,2,5,4,6,1]=>5 [3,2,5,6,1,4]=>4 [3,2,5,6,4,1]=>5 [3,2,6,1,4,5]=>4 [3,2,6,1,5,4]=>5 [3,2,6,4,1,5]=>5 [3,2,6,4,5,1]=>5 [3,2,6,5,1,4]=>5 [3,2,6,5,4,1]=>6 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>3 [3,4,1,5,6,2]=>3 [3,4,1,6,2,5]=>3 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>3 [3,4,2,1,6,5]=>4 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>4 [3,4,2,6,1,5]=>3 [3,4,2,6,5,1]=>5 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>5 [3,4,5,2,1,6]=>4 [3,4,5,2,6,1]=>5 [3,4,5,6,1,2]=>4 [3,4,5,6,2,1]=>5 [3,4,6,1,2,5]=>4 [3,4,6,1,5,2]=>5 [3,4,6,2,1,5]=>5 [3,4,6,2,5,1]=>5 [3,4,6,5,1,2]=>5 [3,4,6,5,2,1]=>6 [3,5,1,2,4,6]=>3 [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]=>5 [3,5,2,1,4,6]=>4 [3,5,2,1,6,4]=>4 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>4 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>6 [3,5,4,1,2,6]=>4 [3,5,4,1,6,2]=>6 [3,5,4,2,1,6]=>5 [3,5,4,2,6,1]=>6 [3,5,4,6,1,2]=>5 [3,5,4,6,2,1]=>6 [3,5,6,1,2,4]=>4 [3,5,6,1,4,2]=>6 [3,5,6,2,1,4]=>5 [3,5,6,2,4,1]=>6 [3,5,6,4,1,2]=>5 [3,5,6,4,2,1]=>6 [3,6,1,2,4,5]=>3 [3,6,1,2,5,4]=>4 [3,6,1,4,2,5]=>3 [3,6,1,4,5,2]=>4 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>5 [3,6,2,1,4,5]=>4 [3,6,2,1,5,4]=>5 [3,6,2,4,1,5]=>3 [3,6,2,4,5,1]=>5 [3,6,2,5,1,4]=>3 [3,6,2,5,4,1]=>6 [3,6,4,1,2,5]=>4 [3,6,4,1,5,2]=>7 [3,6,4,2,1,5]=>5 [3,6,4,2,5,1]=>7 [3,6,4,5,1,2]=>5 [3,6,4,5,2,1]=>6 [3,6,5,1,2,4]=>5 [3,6,5,1,4,2]=>7 [3,6,5,2,1,4]=>6 [3,6,5,2,4,1]=>7 [3,6,5,4,1,2]=>6 [3,6,5,4,2,1]=>7 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>3 [4,1,2,5,3,6]=>2 [4,1,2,5,6,3]=>3 [4,1,2,6,3,5]=>2 [4,1,2,6,5,3]=>4 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>4 [4,1,3,5,2,6]=>2 [4,1,3,5,6,2]=>4 [4,1,3,6,2,5]=>2 [4,1,3,6,5,2]=>5 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>6 [4,1,5,3,2,6]=>4 [4,1,5,3,6,2]=>6 [4,1,5,6,2,3]=>4 [4,1,5,6,3,2]=>5 [4,1,6,2,3,5]=>4 [4,1,6,2,5,3]=>6 [4,1,6,3,2,5]=>5 [4,1,6,3,5,2]=>6 [4,1,6,5,2,3]=>5 [4,1,6,5,3,2]=>6 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>4 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>4 [4,2,1,6,3,5]=>3 [4,2,1,6,5,3]=>5 [4,2,3,1,5,6]=>3 [4,2,3,1,6,5]=>4 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>4 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>5 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>6 [4,2,5,3,1,6]=>5 [4,2,5,3,6,1]=>6 [4,2,5,6,1,3]=>5 [4,2,5,6,3,1]=>5 [4,2,6,1,3,5]=>4 [4,2,6,1,5,3]=>6 [4,2,6,3,1,5]=>6 [4,2,6,3,5,1]=>6 [4,2,6,5,1,3]=>6 [4,2,6,5,3,1]=>6 [4,3,1,2,5,6]=>3 [4,3,1,2,6,5]=>4 [4,3,1,5,2,6]=>4 [4,3,1,5,6,2]=>4 [4,3,1,6,2,5]=>4 [4,3,1,6,5,2]=>5 [4,3,2,1,5,6]=>4 [4,3,2,1,6,5]=>5 [4,3,2,5,1,6]=>4 [4,3,2,5,6,1]=>5 [4,3,2,6,1,5]=>4 [4,3,2,6,5,1]=>6 [4,3,5,1,2,6]=>4 [4,3,5,1,6,2]=>6 [4,3,5,2,1,6]=>5 [4,3,5,2,6,1]=>6 [4,3,5,6,1,2]=>5 [4,3,5,6,2,1]=>6 [4,3,6,1,2,5]=>5 [4,3,6,1,5,2]=>6 [4,3,6,2,1,5]=>6 [4,3,6,2,5,1]=>6 [4,3,6,5,1,2]=>6 [4,3,6,5,2,1]=>7 [4,5,1,2,3,6]=>3 [4,5,1,2,6,3]=>4 [4,5,1,3,2,6]=>4 [4,5,1,3,6,2]=>4 [4,5,1,6,2,3]=>4 [4,5,1,6,3,2]=>5 [4,5,2,1,3,6]=>4 [4,5,2,1,6,3]=>5 [4,5,2,3,1,6]=>4 [4,5,2,3,6,1]=>5 [4,5,2,6,1,3]=>4 [4,5,2,6,3,1]=>6 [4,5,3,1,2,6]=>4 [4,5,3,1,6,2]=>6 [4,5,3,2,1,6]=>5 [4,5,3,2,6,1]=>6 [4,5,3,6,1,2]=>5 [4,5,3,6,2,1]=>6 [4,5,6,1,2,3]=>5 [4,5,6,1,3,2]=>6 [4,5,6,2,1,3]=>6 [4,5,6,2,3,1]=>6 [4,5,6,3,1,2]=>6 [4,5,6,3,2,1]=>7 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>5 [4,6,1,3,2,5]=>4 [4,6,1,3,5,2]=>5 [4,6,1,5,2,3]=>4 [4,6,1,5,3,2]=>5 [4,6,2,1,3,5]=>4 [4,6,2,1,5,3]=>6 [4,6,2,3,1,5]=>4 [4,6,2,3,5,1]=>6 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>6 [4,6,3,1,2,5]=>4 [4,6,3,1,5,2]=>7 [4,6,3,2,1,5]=>5 [4,6,3,2,5,1]=>7 [4,6,3,5,1,2]=>5 [4,6,3,5,2,1]=>6 [4,6,5,1,2,3]=>6 [4,6,5,1,3,2]=>7 [4,6,5,2,1,3]=>7 [4,6,5,2,3,1]=>7 [4,6,5,3,1,2]=>7 [4,6,5,3,2,1]=>8 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>4 [5,1,2,4,3,6]=>3 [5,1,2,4,6,3]=>4 [5,1,2,6,3,4]=>3 [5,1,2,6,4,3]=>4 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>5 [5,1,3,4,2,6]=>3 [5,1,3,4,6,2]=>5 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>5 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>6 [5,1,4,3,2,6]=>4 [5,1,4,3,6,2]=>6 [5,1,4,6,2,3]=>4 [5,1,4,6,3,2]=>5 [5,1,6,2,3,4]=>5 [5,1,6,2,4,3]=>6 [5,1,6,3,2,4]=>6 [5,1,6,3,4,2]=>6 [5,1,6,4,2,3]=>6 [5,1,6,4,3,2]=>7 [5,2,1,3,4,6]=>3 [5,2,1,3,6,4]=>5 [5,2,1,4,3,6]=>4 [5,2,1,4,6,3]=>5 [5,2,1,6,3,4]=>4 [5,2,1,6,4,3]=>5 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>5 [5,2,3,4,1,6]=>4 [5,2,3,4,6,1]=>5 [5,2,3,6,1,4]=>4 [5,2,3,6,4,1]=>5 [5,2,4,1,3,6]=>3 [5,2,4,1,6,3]=>6 [5,2,4,3,1,6]=>5 [5,2,4,3,6,1]=>6 [5,2,4,6,1,3]=>5 [5,2,4,6,3,1]=>5 [5,2,6,1,3,4]=>5 [5,2,6,1,4,3]=>6 [5,2,6,3,1,4]=>7 [5,2,6,3,4,1]=>6 [5,2,6,4,1,3]=>7 [5,2,6,4,3,1]=>7 [5,3,1,2,4,6]=>3 [5,3,1,2,6,4]=>5 [5,3,1,4,2,6]=>5 [5,3,1,4,6,2]=>5 [5,3,1,6,2,4]=>5 [5,3,1,6,4,2]=>5 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>6 [5,3,2,4,1,6]=>5 [5,3,2,4,6,1]=>6 [5,3,2,6,1,4]=>5 [5,3,2,6,4,1]=>6 [5,3,4,1,2,6]=>4 [5,3,4,1,6,2]=>6 [5,3,4,2,1,6]=>5 [5,3,4,2,6,1]=>6 [5,3,4,6,1,2]=>5 [5,3,4,6,2,1]=>6 [5,3,6,1,2,4]=>6 [5,3,6,1,4,2]=>6 [5,3,6,2,1,4]=>7 [5,3,6,2,4,1]=>6 [5,3,6,4,1,2]=>7 [5,3,6,4,2,1]=>8 [5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>5 [5,4,1,3,2,6]=>5 [5,4,1,3,6,2]=>5 [5,4,1,6,2,3]=>5 [5,4,1,6,3,2]=>6 [5,4,2,1,3,6]=>5 [5,4,2,1,6,3]=>6 [5,4,2,3,1,6]=>5 [5,4,2,3,6,1]=>6 [5,4,2,6,1,3]=>5 [5,4,2,6,3,1]=>7 [5,4,3,1,2,6]=>5 [5,4,3,1,6,2]=>7 [5,4,3,2,1,6]=>6 [5,4,3,2,6,1]=>7 [5,4,3,6,1,2]=>6 [5,4,3,6,2,1]=>7 [5,4,6,1,2,3]=>6 [5,4,6,1,3,2]=>7 [5,4,6,2,1,3]=>7 [5,4,6,2,3,1]=>7 [5,4,6,3,1,2]=>7 [5,4,6,3,2,1]=>8 [5,6,1,2,3,4]=>4 [5,6,1,2,4,3]=>5 [5,6,1,3,2,4]=>5 [5,6,1,3,4,2]=>5 [5,6,1,4,2,3]=>5 [5,6,1,4,3,2]=>6 [5,6,2,1,3,4]=>5 [5,6,2,1,4,3]=>6 [5,6,2,3,1,4]=>5 [5,6,2,3,4,1]=>6 [5,6,2,4,1,3]=>5 [5,6,2,4,3,1]=>7 [5,6,3,1,2,4]=>5 [5,6,3,1,4,2]=>7 [5,6,3,2,1,4]=>6 [5,6,3,2,4,1]=>7 [5,6,3,4,1,2]=>6 [5,6,3,4,2,1]=>7 [5,6,4,1,2,3]=>6 [5,6,4,1,3,2]=>7 [5,6,4,2,1,3]=>7 [5,6,4,2,3,1]=>7 [5,6,4,3,1,2]=>7 [5,6,4,3,2,1]=>8 [6,1,2,3,4,5]=>3 [6,1,2,3,5,4]=>4 [6,1,2,4,3,5]=>4 [6,1,2,4,5,3]=>4 [6,1,2,5,3,4]=>4 [6,1,2,5,4,3]=>5 [6,1,3,2,4,5]=>4 [6,1,3,2,5,4]=>5 [6,1,3,4,2,5]=>4 [6,1,3,4,5,2]=>5 [6,1,3,5,2,4]=>4 [6,1,3,5,4,2]=>6 [6,1,4,2,3,5]=>4 [6,1,4,2,5,3]=>6 [6,1,4,3,2,5]=>5 [6,1,4,3,5,2]=>6 [6,1,4,5,2,3]=>5 [6,1,4,5,3,2]=>6 [6,1,5,2,3,4]=>5 [6,1,5,2,4,3]=>6 [6,1,5,3,2,4]=>6 [6,1,5,3,4,2]=>6 [6,1,5,4,2,3]=>6 [6,1,5,4,3,2]=>7 [6,2,1,3,4,5]=>4 [6,2,1,3,5,4]=>5 [6,2,1,4,3,5]=>5 [6,2,1,4,5,3]=>5 [6,2,1,5,3,4]=>5 [6,2,1,5,4,3]=>6 [6,2,3,1,4,5]=>4 [6,2,3,1,5,4]=>5 [6,2,3,4,1,5]=>5 [6,2,3,4,5,1]=>5 [6,2,3,5,1,4]=>5 [6,2,3,5,4,1]=>6 [6,2,4,1,3,5]=>4 [6,2,4,1,5,3]=>6 [6,2,4,3,1,5]=>6 [6,2,4,3,5,1]=>6 [6,2,4,5,1,3]=>6 [6,2,4,5,3,1]=>6 [6,2,5,1,3,4]=>5 [6,2,5,1,4,3]=>6 [6,2,5,3,1,4]=>7 [6,2,5,3,4,1]=>6 [6,2,5,4,1,3]=>7 [6,2,5,4,3,1]=>7 [6,3,1,2,4,5]=>4 [6,3,1,2,5,4]=>5 [6,3,1,4,2,5]=>6 [6,3,1,4,5,2]=>5 [6,3,1,5,2,4]=>6 [6,3,1,5,4,2]=>6 [6,3,2,1,4,5]=>5 [6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>6 [6,3,2,4,5,1]=>6 [6,3,2,5,1,4]=>6 [6,3,2,5,4,1]=>7 [6,3,4,1,2,5]=>5 [6,3,4,1,5,2]=>6 [6,3,4,2,1,5]=>6 [6,3,4,2,5,1]=>6 [6,3,4,5,1,2]=>6 [6,3,4,5,2,1]=>7 [6,3,5,1,2,4]=>6 [6,3,5,1,4,2]=>6 [6,3,5,2,1,4]=>7 [6,3,5,2,4,1]=>6 [6,3,5,4,1,2]=>7 [6,3,5,4,2,1]=>8 [6,4,1,2,3,5]=>5 [6,4,1,2,5,3]=>5 [6,4,1,3,2,5]=>6 [6,4,1,3,5,2]=>5 [6,4,1,5,2,3]=>6 [6,4,1,5,3,2]=>7 [6,4,2,1,3,5]=>6 [6,4,2,1,5,3]=>6 [6,4,2,3,1,5]=>6 [6,4,2,3,5,1]=>6 [6,4,2,5,1,3]=>6 [6,4,2,5,3,1]=>8 [6,4,3,1,2,5]=>6 [6,4,3,1,5,2]=>7 [6,4,3,2,1,5]=>7 [6,4,3,2,5,1]=>7 [6,4,3,5,1,2]=>7 [6,4,3,5,2,1]=>8 [6,4,5,1,2,3]=>6 [6,4,5,1,3,2]=>7 [6,4,5,2,1,3]=>7 [6,4,5,2,3,1]=>7 [6,4,5,3,1,2]=>7 [6,4,5,3,2,1]=>8 [6,5,1,2,3,4]=>5 [6,5,1,2,4,3]=>6 [6,5,1,3,2,4]=>6 [6,5,1,3,4,2]=>6 [6,5,1,4,2,3]=>6 [6,5,1,4,3,2]=>7 [6,5,2,1,3,4]=>6 [6,5,2,1,4,3]=>7 [6,5,2,3,1,4]=>6 [6,5,2,3,4,1]=>7 [6,5,2,4,1,3]=>6 [6,5,2,4,3,1]=>8 [6,5,3,1,2,4]=>6 [6,5,3,1,4,2]=>8 [6,5,3,2,1,4]=>7 [6,5,3,2,4,1]=>8 [6,5,3,4,1,2]=>7 [6,5,3,4,2,1]=>8 [6,5,4,1,2,3]=>7 [6,5,4,1,3,2]=>8 [6,5,4,2,1,3]=>8 [6,5,4,2,3,1]=>8 [6,5,4,3,1,2]=>8 [6,5,4,3,2,1]=>9 [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]=>2 [1,2,3,5,7,4,6]=>1 [1,2,3,5,7,6,4]=>3 [1,2,3,6,4,5,7]=>1 [1,2,3,6,4,7,5]=>3 [1,2,3,6,5,4,7]=>2 [1,2,3,6,5,7,4]=>3 [1,2,3,6,7,4,5]=>2 [1,2,3,6,7,5,4]=>3 [1,2,3,7,4,5,6]=>2 [1,2,3,7,4,6,5]=>3 [1,2,3,7,5,4,6]=>3 [1,2,3,7,5,6,4]=>3 [1,2,3,7,6,4,5]=>3 [1,2,3,7,6,5,4]=>4 [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]=>2 [1,2,4,5,6,7,3]=>2 [1,2,4,5,7,3,6]=>2 [1,2,4,5,7,6,3]=>3 [1,2,4,6,3,5,7]=>1 [1,2,4,6,3,7,5]=>3 [1,2,4,6,5,3,7]=>3 [1,2,4,6,5,7,3]=>3 [1,2,4,6,7,3,5]=>3 [1,2,4,6,7,5,3]=>3 [1,2,4,7,3,5,6]=>2 [1,2,4,7,3,6,5]=>3 [1,2,4,7,5,3,6]=>4 [1,2,4,7,5,6,3]=>3 [1,2,4,7,6,3,5]=>4 [1,2,4,7,6,5,3]=>4 [1,2,5,3,4,6,7]=>1 [1,2,5,3,4,7,6]=>2 [1,2,5,3,6,4,7]=>3 [1,2,5,3,6,7,4]=>2 [1,2,5,3,7,4,6]=>3 [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]=>3 [1,2,5,4,6,7,3]=>3 [1,2,5,4,7,3,6]=>3 [1,2,5,4,7,6,3]=>4 [1,2,5,6,3,4,7]=>2 [1,2,5,6,3,7,4]=>3 [1,2,5,6,4,3,7]=>3 [1,2,5,6,4,7,3]=>3 [1,2,5,6,7,3,4]=>3 [1,2,5,6,7,4,3]=>4 [1,2,5,7,3,4,6]=>3 [1,2,5,7,3,6,4]=>3 [1,2,5,7,4,3,6]=>4 [1,2,5,7,4,6,3]=>3 [1,2,5,7,6,3,4]=>4 [1,2,5,7,6,4,3]=>5 [1,2,6,3,4,5,7]=>2 [1,2,6,3,4,7,5]=>2 [1,2,6,3,5,4,7]=>3 [1,2,6,3,5,7,4]=>2 [1,2,6,3,7,4,5]=>3 [1,2,6,3,7,5,4]=>4 [1,2,6,4,3,5,7]=>3 [1,2,6,4,3,7,5]=>3 [1,2,6,4,5,3,7]=>3 [1,2,6,4,5,7,3]=>3 [1,2,6,4,7,3,5]=>3 [1,2,6,4,7,5,3]=>5 [1,2,6,5,3,4,7]=>3 [1,2,6,5,3,7,4]=>4 [1,2,6,5,4,3,7]=>4 [1,2,6,5,4,7,3]=>4 [1,2,6,5,7,3,4]=>4 [1,2,6,5,7,4,3]=>5 [1,2,6,7,3,4,5]=>3 [1,2,6,7,3,5,4]=>4 [1,2,6,7,4,3,5]=>4 [1,2,6,7,4,5,3]=>4 [1,2,6,7,5,3,4]=>4 [1,2,6,7,5,4,3]=>5 [1,2,7,3,4,5,6]=>2 [1,2,7,3,4,6,5]=>3 [1,2,7,3,5,4,6]=>3 [1,2,7,3,5,6,4]=>3 [1,2,7,3,6,4,5]=>3 [1,2,7,3,6,5,4]=>4 [1,2,7,4,3,5,6]=>3 [1,2,7,4,3,6,5]=>4 [1,2,7,4,5,3,6]=>3 [1,2,7,4,5,6,3]=>4 [1,2,7,4,6,3,5]=>3 [1,2,7,4,6,5,3]=>5 [1,2,7,5,3,4,6]=>3 [1,2,7,5,3,6,4]=>5 [1,2,7,5,4,3,6]=>4 [1,2,7,5,4,6,3]=>5 [1,2,7,5,6,3,4]=>4 [1,2,7,5,6,4,3]=>5 [1,2,7,6,3,4,5]=>4 [1,2,7,6,3,5,4]=>5 [1,2,7,6,4,3,5]=>5 [1,2,7,6,4,5,3]=>5 [1,2,7,6,5,3,4]=>5 [1,2,7,6,5,4,3]=>6 [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]=>3 [1,3,2,5,7,4,6]=>2 [1,3,2,5,7,6,4]=>4 [1,3,2,6,4,5,7]=>2 [1,3,2,6,4,7,5]=>4 [1,3,2,6,5,4,7]=>3 [1,3,2,6,5,7,4]=>4 [1,3,2,6,7,4,5]=>3 [1,3,2,6,7,5,4]=>4 [1,3,2,7,4,5,6]=>3 [1,3,2,7,4,6,5]=>4 [1,3,2,7,5,4,6]=>4 [1,3,2,7,5,6,4]=>4 [1,3,2,7,6,4,5]=>4 [1,3,2,7,6,5,4]=>5 [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]=>2 [1,3,4,5,2,7,6]=>3 [1,3,4,5,6,2,7]=>2 [1,3,4,5,6,7,2]=>3 [1,3,4,5,7,2,6]=>2 [1,3,4,5,7,6,2]=>4 [1,3,4,6,2,5,7]=>2 [1,3,4,6,2,7,5]=>4 [1,3,4,6,5,2,7]=>3 [1,3,4,6,5,7,2]=>4 [1,3,4,6,7,2,5]=>3 [1,3,4,6,7,5,2]=>4 [1,3,4,7,2,5,6]=>3 [1,3,4,7,2,6,5]=>4 [1,3,4,7,5,2,6]=>4 [1,3,4,7,5,6,2]=>4 [1,3,4,7,6,2,5]=>4 [1,3,4,7,6,5,2]=>5 [1,3,5,2,4,6,7]=>1 [1,3,5,2,4,7,6]=>2 [1,3,5,2,6,4,7]=>3 [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]=>3 [1,3,5,4,2,7,6]=>4 [1,3,5,4,6,2,7]=>3 [1,3,5,4,6,7,2]=>4 [1,3,5,4,7,2,6]=>3 [1,3,5,4,7,6,2]=>5 [1,3,5,6,2,4,7]=>3 [1,3,5,6,2,7,4]=>4 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>4 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>5 [1,3,5,7,2,4,6]=>4 [1,3,5,7,2,6,4]=>4 [1,3,5,7,4,2,6]=>4 [1,3,5,7,4,6,2]=>4 [1,3,5,7,6,2,4]=>4 [1,3,5,7,6,4,2]=>6 [1,3,6,2,4,5,7]=>2 [1,3,6,2,4,7,5]=>2 [1,3,6,2,5,4,7]=>3 [1,3,6,2,5,7,4]=>2 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>4 [1,3,6,4,2,5,7]=>4 [1,3,6,4,2,7,5]=>4 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>4 [1,3,6,4,7,2,5]=>3 [1,3,6,4,7,5,2]=>6 [1,3,6,5,2,4,7]=>4 [1,3,6,5,2,7,4]=>5 [1,3,6,5,4,2,7]=>4 [1,3,6,5,4,7,2]=>5 [1,3,6,5,7,2,4]=>4 [1,3,6,5,7,4,2]=>6 [1,3,6,7,2,4,5]=>4 [1,3,6,7,2,5,4]=>5 [1,3,6,7,4,2,5]=>4 [1,3,6,7,4,5,2]=>5 [1,3,6,7,5,2,4]=>4 [1,3,6,7,5,4,2]=>6 [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]=>4 [1,3,7,4,2,6,5]=>5 [1,3,7,4,5,2,6]=>3 [1,3,7,4,5,6,2]=>5 [1,3,7,4,6,2,5]=>3 [1,3,7,4,6,5,2]=>6 [1,3,7,5,2,4,6]=>4 [1,3,7,5,2,6,4]=>6 [1,3,7,5,4,2,6]=>4 [1,3,7,5,4,6,2]=>6 [1,3,7,5,6,2,4]=>4 [1,3,7,5,6,4,2]=>6 [1,3,7,6,2,4,5]=>5 [1,3,7,6,2,5,4]=>6 [1,3,7,6,4,2,5]=>5 [1,3,7,6,4,5,2]=>6 [1,3,7,6,5,2,4]=>5 [1,3,7,6,5,4,2]=>7 [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]=>3 [1,4,2,5,3,7,6]=>4 [1,4,2,5,6,3,7]=>2 [1,4,2,5,6,7,3]=>4 [1,4,2,5,7,3,6]=>2 [1,4,2,5,7,6,3]=>5 [1,4,2,6,3,5,7]=>3 [1,4,2,6,3,7,5]=>5 [1,4,2,6,5,3,7]=>3 [1,4,2,6,5,7,3]=>5 [1,4,2,6,7,3,5]=>3 [1,4,2,6,7,5,3]=>5 [1,4,2,7,3,5,6]=>4 [1,4,2,7,3,6,5]=>5 [1,4,2,7,5,3,6]=>4 [1,4,2,7,5,6,3]=>5 [1,4,2,7,6,3,5]=>4 [1,4,2,7,6,5,3]=>6 [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]=>3 [1,4,3,5,2,7,6]=>4 [1,4,3,5,6,2,7]=>3 [1,4,3,5,6,7,2]=>4 [1,4,3,5,7,2,6]=>3 [1,4,3,5,7,6,2]=>5 [1,4,3,6,2,5,7]=>3 [1,4,3,6,2,7,5]=>5 [1,4,3,6,5,2,7]=>4 [1,4,3,6,5,7,2]=>5 [1,4,3,6,7,2,5]=>4 [1,4,3,6,7,5,2]=>5 [1,4,3,7,2,5,6]=>4 [1,4,3,7,2,6,5]=>5 [1,4,3,7,5,2,6]=>5 [1,4,3,7,5,6,2]=>5 [1,4,3,7,6,2,5]=>5 [1,4,3,7,6,5,2]=>6 [1,4,5,2,3,6,7]=>2 [1,4,5,2,3,7,6]=>3 [1,4,5,2,6,3,7]=>3 [1,4,5,2,6,7,3]=>3 [1,4,5,2,7,3,6]=>3 [1,4,5,2,7,6,3]=>4 [1,4,5,3,2,6,7]=>3 [1,4,5,3,2,7,6]=>4 [1,4,5,3,6,2,7]=>3 [1,4,5,3,6,7,2]=>4 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>5 [1,4,5,6,2,3,7]=>3 [1,4,5,6,2,7,3]=>5 [1,4,5,6,3,2,7]=>4 [1,4,5,6,3,7,2]=>5 [1,4,5,6,7,2,3]=>4 [1,4,5,6,7,3,2]=>5 [1,4,5,7,2,3,6]=>4 [1,4,5,7,2,6,3]=>5 [1,4,5,7,3,2,6]=>5 [1,4,5,7,3,6,2]=>5 [1,4,5,7,6,2,3]=>5 [1,4,5,7,6,3,2]=>6 [1,4,6,2,3,5,7]=>3 [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]=>5 [1,4,6,3,2,5,7]=>4 [1,4,6,3,2,7,5]=>4 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>4 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>6 [1,4,6,5,2,3,7]=>4 [1,4,6,5,2,7,3]=>6 [1,4,6,5,3,2,7]=>5 [1,4,6,5,3,7,2]=>6
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Description
The number of odd inversions of a permutation.
An inversion $i < j$ of a permutation is odd if $i \not\equiv j\ (\operatorname{mod} 2)$. See St000538The number of even inversions of a permutation. for even inversions.
References
[1] Klopsch, B., Voll, C. Igusa-type functions associated to finite formed spaces and their functional equations MathSciNet:2500892 arXiv:math/0603565
[2] Brenti, F., Carnevale, A. Odd length for even hyperoctahedral groups and signed generating functions arXiv:1606.01751
[3] Brenti, F., Carnevale, A. Odd length in Weyl groups arXiv:1709.03320
Code
def statistic(pi):
    return sum(1 for i,j in pi.inversions() if is_odd(j-i))

Created
Jun 22, 2016 at 12:32 by Christian Stump
Updated
Nov 06, 2017 at 21:57 by Martin Rubey