edit this statistic or download as text // json
Identifier
Values
=>
[]=>0 [1]=>0 [1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>2 [3,1,2]=>1 [3,2,1]=>1 [1,2,3,4]=>0 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>2 [1,4,2,3]=>1 [1,4,3,2]=>1 [2,1,3,4]=>1 [2,1,4,3]=>1 [2,3,1,4]=>2 [2,3,4,1]=>3 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>1 [3,1,4,2]=>2 [3,2,1,4]=>1 [3,2,4,1]=>3 [3,4,1,2]=>2 [3,4,2,1]=>2 [4,1,2,3]=>1 [4,1,3,2]=>1 [4,2,1,3]=>1 [4,2,3,1]=>2 [4,3,1,2]=>1 [4,3,2,1]=>1 [1,2,3,4,5]=>0 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>2 [1,2,5,3,4]=>1 [1,2,5,4,3]=>1 [1,3,2,4,5]=>1 [1,3,2,5,4]=>1 [1,3,4,2,5]=>2 [1,3,4,5,2]=>3 [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]=>1 [1,4,3,5,2]=>3 [1,4,5,2,3]=>2 [1,4,5,3,2]=>2 [1,5,2,3,4]=>1 [1,5,2,4,3]=>1 [1,5,3,2,4]=>1 [1,5,3,4,2]=>2 [1,5,4,2,3]=>1 [1,5,4,3,2]=>1 [2,1,3,4,5]=>1 [2,1,3,5,4]=>1 [2,1,4,3,5]=>1 [2,1,4,5,3]=>2 [2,1,5,3,4]=>1 [2,1,5,4,3]=>1 [2,3,1,4,5]=>2 [2,3,1,5,4]=>2 [2,3,4,1,5]=>3 [2,3,4,5,1]=>4 [2,3,5,1,4]=>3 [2,3,5,4,1]=>3 [2,4,1,3,5]=>2 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>4 [2,4,5,1,3]=>3 [2,4,5,3,1]=>3 [2,5,1,3,4]=>2 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>3 [2,5,4,1,3]=>2 [2,5,4,3,1]=>2 [3,1,2,4,5]=>1 [3,1,2,5,4]=>1 [3,1,4,2,5]=>2 [3,1,4,5,2]=>3 [3,1,5,2,4]=>2 [3,1,5,4,2]=>2 [3,2,1,4,5]=>1 [3,2,1,5,4]=>1 [3,2,4,1,5]=>3 [3,2,4,5,1]=>4 [3,2,5,1,4]=>3 [3,2,5,4,1]=>3 [3,4,1,2,5]=>2 [3,4,1,5,2]=>3 [3,4,2,1,5]=>2 [3,4,2,5,1]=>4 [3,4,5,1,2]=>3 [3,4,5,2,1]=>3 [3,5,1,2,4]=>2 [3,5,1,4,2]=>2 [3,5,2,1,4]=>2 [3,5,2,4,1]=>2 [3,5,4,1,2]=>2 [3,5,4,2,1]=>2 [4,1,2,3,5]=>1 [4,1,2,5,3]=>2 [4,1,3,2,5]=>1 [4,1,3,5,2]=>3 [4,1,5,2,3]=>2 [4,1,5,3,2]=>2 [4,2,1,3,5]=>1 [4,2,1,5,3]=>2 [4,2,3,1,5]=>2 [4,2,3,5,1]=>4 [4,2,5,1,3]=>3 [4,2,5,3,1]=>3 [4,3,1,2,5]=>1 [4,3,1,5,2]=>3 [4,3,2,1,5]=>1 [4,3,2,5,1]=>4 [4,3,5,1,2]=>3 [4,3,5,2,1]=>3 [4,5,1,2,3]=>2 [4,5,1,3,2]=>2 [4,5,2,1,3]=>2 [4,5,2,3,1]=>2 [4,5,3,1,2]=>2 [4,5,3,2,1]=>2 [5,1,2,3,4]=>1 [5,1,2,4,3]=>1 [5,1,3,2,4]=>1 [5,1,3,4,2]=>2 [5,1,4,2,3]=>1 [5,1,4,3,2]=>1 [5,2,1,3,4]=>1 [5,2,1,4,3]=>1 [5,2,3,1,4]=>2 [5,2,3,4,1]=>3 [5,2,4,1,3]=>2 [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]=>3 [5,3,4,1,2]=>2 [5,3,4,2,1]=>2 [5,4,1,2,3]=>1 [5,4,1,3,2]=>1 [5,4,2,1,3]=>1 [5,4,2,3,1]=>2 [5,4,3,1,2]=>1 [5,4,3,2,1]=>1 [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]=>2 [1,2,3,6,4,5]=>1 [1,2,3,6,5,4]=>1 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>1 [1,2,4,5,3,6]=>2 [1,2,4,5,6,3]=>3 [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]=>1 [1,2,5,4,6,3]=>3 [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]=>1 [1,2,6,4,3,5]=>1 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>1 [1,2,6,5,4,3]=>1 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>1 [1,3,2,5,4,6]=>1 [1,3,2,5,6,4]=>2 [1,3,2,6,4,5]=>1 [1,3,2,6,5,4]=>1 [1,3,4,2,5,6]=>2 [1,3,4,2,6,5]=>2 [1,3,4,5,2,6]=>3 [1,3,4,5,6,2]=>4 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>3 [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]=>4 [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]=>2 [1,3,6,4,2,5]=>2 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>2 [1,3,6,5,4,2]=>2 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>1 [1,4,2,5,3,6]=>2 [1,4,2,5,6,3]=>3 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>2 [1,4,3,2,5,6]=>1 [1,4,3,2,6,5]=>1 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>4 [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]=>3 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>4 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>3 [1,4,6,2,3,5]=>2 [1,4,6,2,5,3]=>2 [1,4,6,3,2,5]=>2 [1,4,6,3,5,2]=>2 [1,4,6,5,2,3]=>2 [1,4,6,5,3,2]=>2 [1,5,2,3,4,6]=>1 [1,5,2,3,6,4]=>2 [1,5,2,4,3,6]=>1 [1,5,2,4,6,3]=>3 [1,5,2,6,3,4]=>2 [1,5,2,6,4,3]=>2 [1,5,3,2,4,6]=>1 [1,5,3,2,6,4]=>2 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>4 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>1 [1,5,4,3,6,2]=>4 [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]=>2 [1,5,6,3,2,4]=>2 [1,5,6,3,4,2]=>2 [1,5,6,4,2,3]=>2 [1,5,6,4,3,2]=>2 [1,6,2,3,4,5]=>1 [1,6,2,3,5,4]=>1 [1,6,2,4,3,5]=>1 [1,6,2,4,5,3]=>2 [1,6,2,5,3,4]=>1 [1,6,2,5,4,3]=>1 [1,6,3,2,4,5]=>1 [1,6,3,2,5,4]=>1 [1,6,3,4,2,5]=>2 [1,6,3,4,5,2]=>3 [1,6,3,5,2,4]=>2 [1,6,3,5,4,2]=>2 [1,6,4,2,3,5]=>1 [1,6,4,2,5,3]=>2 [1,6,4,3,2,5]=>1 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>2 [1,6,4,5,3,2]=>2 [1,6,5,2,3,4]=>1 [1,6,5,2,4,3]=>1 [1,6,5,3,2,4]=>1 [1,6,5,3,4,2]=>2 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>1 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>1 [2,1,3,5,4,6]=>1 [2,1,3,5,6,4]=>2 [2,1,3,6,4,5]=>1 [2,1,3,6,5,4]=>1 [2,1,4,3,5,6]=>1 [2,1,4,3,6,5]=>1 [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]=>2 [2,1,5,3,4,6]=>1 [2,1,5,3,6,4]=>2 [2,1,5,4,3,6]=>1 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>2 [2,1,5,6,4,3]=>2 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>1 [2,1,6,4,3,5]=>1 [2,1,6,4,5,3]=>2 [2,1,6,5,3,4]=>1 [2,1,6,5,4,3]=>1 [2,3,1,4,5,6]=>2 [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]=>2 [2,3,4,1,5,6]=>3 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>4 [2,3,4,5,6,1]=>5 [2,3,4,6,1,5]=>4 [2,3,4,6,5,1]=>4 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>3 [2,3,5,4,6,1]=>5 [2,3,5,6,1,4]=>4 [2,3,5,6,4,1]=>4 [2,3,6,1,4,5]=>3 [2,3,6,1,5,4]=>3 [2,3,6,4,1,5]=>3 [2,3,6,4,5,1]=>4 [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]=>2 [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]=>2 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>2 [2,4,3,5,1,6]=>4 [2,4,3,5,6,1]=>5 [2,4,3,6,1,5]=>4 [2,4,3,6,5,1]=>4 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>3 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>5 [2,4,5,6,1,3]=>4 [2,4,5,6,3,1]=>4 [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]=>2 [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]=>2 [2,5,3,1,4,6]=>2 [2,5,3,1,6,4]=>2 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>5 [2,5,3,6,1,4]=>4 [2,5,3,6,4,1]=>4 [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]=>5 [2,5,4,6,1,3]=>4 [2,5,4,6,3,1]=>4 [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]=>2 [2,6,1,4,3,5]=>2 [2,6,1,4,5,3]=>2 [2,6,1,5,3,4]=>2 [2,6,1,5,4,3]=>2 [2,6,3,1,4,5]=>2 [2,6,3,1,5,4]=>2 [2,6,3,4,1,5]=>3 [2,6,3,4,5,1]=>4 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>2 [2,6,4,1,5,3]=>2 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>4 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>2 [2,6,5,3,1,4]=>2 [2,6,5,3,4,1]=>3 [2,6,5,4,1,3]=>2 [2,6,5,4,3,1]=>2 [3,1,2,4,5,6]=>1 [3,1,2,4,6,5]=>1 [3,1,2,5,4,6]=>1 [3,1,2,5,6,4]=>2 [3,1,2,6,4,5]=>1 [3,1,2,6,5,4]=>1 [3,1,4,2,5,6]=>2 [3,1,4,2,6,5]=>2 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>4 [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]=>2 [3,1,5,4,2,6]=>2 [3,1,5,4,6,2]=>4 [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]=>2 [3,1,6,4,2,5]=>2 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>2 [3,1,6,5,4,2]=>2 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>1 [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]=>1 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>4 [3,2,4,5,6,1]=>5 [3,2,4,6,1,5]=>4 [3,2,4,6,5,1]=>4 [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]=>5 [3,2,5,6,1,4]=>4 [3,2,5,6,4,1]=>4 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>3 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>4 [3,2,6,5,1,4]=>3 [3,2,6,5,4,1]=>3 [3,4,1,2,5,6]=>2 [3,4,1,2,6,5]=>2 [3,4,1,5,2,6]=>3 [3,4,1,5,6,2]=>4 [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]=>2 [3,4,2,5,1,6]=>4 [3,4,2,5,6,1]=>5 [3,4,2,6,1,5]=>4 [3,4,2,6,5,1]=>4 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>4 [3,4,5,2,1,6]=>3 [3,4,5,2,6,1]=>5 [3,4,5,6,1,2]=>4 [3,4,5,6,2,1]=>4 [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]=>2 [3,5,1,4,2,6]=>2 [3,5,1,4,6,2]=>4 [3,5,1,6,2,4]=>3 [3,5,1,6,4,2]=>3 [3,5,2,1,4,6]=>2 [3,5,2,1,6,4]=>2 [3,5,2,4,1,6]=>2 [3,5,2,4,6,1]=>5 [3,5,2,6,1,4]=>4 [3,5,2,6,4,1]=>4 [3,5,4,1,2,6]=>2 [3,5,4,1,6,2]=>4 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>5 [3,5,4,6,1,2]=>4 [3,5,4,6,2,1]=>4 [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]=>2 [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]=>2 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>2 [3,6,2,4,1,5]=>2 [3,6,2,4,5,1]=>4 [3,6,2,5,1,4]=>2 [3,6,2,5,4,1]=>2 [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]=>4 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>2 [3,6,5,2,1,4]=>2 [3,6,5,2,4,1]=>2 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>2 [4,1,2,3,5,6]=>1 [4,1,2,3,6,5]=>1 [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]=>2 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>1 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>4 [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]=>2 [4,1,5,3,6,2]=>4 [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]=>2 [4,1,6,3,2,5]=>2 [4,1,6,3,5,2]=>2 [4,1,6,5,2,3]=>2 [4,1,6,5,3,2]=>2 [4,2,1,3,5,6]=>1 [4,2,1,3,6,5]=>1 [4,2,1,5,3,6]=>2 [4,2,1,5,6,3]=>3 [4,2,1,6,3,5]=>2 [4,2,1,6,5,3]=>2 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>2 [4,2,3,5,1,6]=>4 [4,2,3,5,6,1]=>5 [4,2,3,6,1,5]=>4 [4,2,3,6,5,1]=>4 [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]=>5 [4,2,5,6,1,3]=>4 [4,2,5,6,3,1]=>4 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>3 [4,2,6,3,1,5]=>3 [4,2,6,3,5,1]=>3 [4,2,6,5,1,3]=>3 [4,2,6,5,3,1]=>3 [4,3,1,2,5,6]=>1 [4,3,1,2,6,5]=>1 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>4 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>1 [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]=>4 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>4 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>5 [4,3,5,6,1,2]=>4 [4,3,5,6,2,1]=>4 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>3 [4,3,6,2,1,5]=>3 [4,3,6,2,5,1]=>3 [4,3,6,5,1,2]=>3 [4,3,6,5,2,1]=>3 [4,5,1,2,3,6]=>2 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>2 [4,5,1,3,6,2]=>4 [4,5,1,6,2,3]=>3 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>2 [4,5,2,1,6,3]=>3 [4,5,2,3,1,6]=>2 [4,5,2,3,6,1]=>5 [4,5,2,6,1,3]=>4 [4,5,2,6,3,1]=>4 [4,5,3,1,2,6]=>2 [4,5,3,1,6,2]=>4 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>5 [4,5,3,6,1,2]=>4 [4,5,3,6,2,1]=>4 [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]=>2 [4,6,1,3,2,5]=>2 [4,6,1,3,5,2]=>2 [4,6,1,5,2,3]=>2 [4,6,1,5,3,2]=>2 [4,6,2,1,3,5]=>2 [4,6,2,1,5,3]=>2 [4,6,2,3,1,5]=>2 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>2 [4,6,2,5,3,1]=>2 [4,6,3,1,2,5]=>2 [4,6,3,1,5,2]=>2 [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]=>2 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>2 [4,6,5,2,1,3]=>2 [4,6,5,2,3,1]=>2 [4,6,5,3,1,2]=>2 [4,6,5,3,2,1]=>2 [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]=>3 [5,1,2,6,3,4]=>2 [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]=>2 [5,1,3,4,6,2]=>4 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>3 [5,1,4,2,3,6]=>1 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>1 [5,1,4,3,6,2]=>4 [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]=>2 [5,1,6,3,2,4]=>2 [5,1,6,3,4,2]=>2 [5,1,6,4,2,3]=>2 [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]=>3 [5,2,1,6,3,4]=>2 [5,2,1,6,4,3]=>2 [5,2,3,1,4,6]=>2 [5,2,3,1,6,4]=>2 [5,2,3,4,1,6]=>3 [5,2,3,4,6,1]=>5 [5,2,3,6,1,4]=>4 [5,2,3,6,4,1]=>4 [5,2,4,1,3,6]=>2 [5,2,4,1,6,3]=>3 [5,2,4,3,1,6]=>2 [5,2,4,3,6,1]=>5 [5,2,4,6,1,3]=>4 [5,2,4,6,3,1]=>4 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>3 [5,2,6,3,1,4]=>3 [5,2,6,3,4,1]=>3 [5,2,6,4,1,3]=>3 [5,2,6,4,3,1]=>3 [5,3,1,2,4,6]=>1 [5,3,1,2,6,4]=>2 [5,3,1,4,2,6]=>2 [5,3,1,4,6,2]=>4 [5,3,1,6,2,4]=>3 [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]=>3 [5,3,2,4,6,1]=>5 [5,3,2,6,1,4]=>4 [5,3,2,6,4,1]=>4 [5,3,4,1,2,6]=>2 [5,3,4,1,6,2]=>4 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>5 [5,3,4,6,1,2]=>4 [5,3,4,6,2,1]=>4 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>3 [5,3,6,2,1,4]=>3 [5,3,6,2,4,1]=>3 [5,3,6,4,1,2]=>3 [5,3,6,4,2,1]=>3 [5,4,1,2,3,6]=>1 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>1 [5,4,1,3,6,2]=>4 [5,4,1,6,2,3]=>3 [5,4,1,6,3,2]=>3 [5,4,2,1,3,6]=>1 [5,4,2,1,6,3]=>3 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>5 [5,4,2,6,1,3]=>4 [5,4,2,6,3,1]=>4 [5,4,3,1,2,6]=>1 [5,4,3,1,6,2]=>4 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>5 [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]=>3 [5,4,6,2,1,3]=>3 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>3 [5,4,6,3,2,1]=>3 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>2 [5,6,1,3,2,4]=>2 [5,6,1,3,4,2]=>2 [5,6,1,4,2,3]=>2 [5,6,1,4,3,2]=>2 [5,6,2,1,3,4]=>2 [5,6,2,1,4,3]=>2 [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]=>2 [5,6,3,1,2,4]=>2 [5,6,3,1,4,2]=>2 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>2 [5,6,3,4,2,1]=>2 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>2 [5,6,4,2,1,3]=>2 [5,6,4,2,3,1]=>2 [5,6,4,3,1,2]=>2 [5,6,4,3,2,1]=>2 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>1 [6,1,2,4,3,5]=>1 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>1 [6,1,2,5,4,3]=>1 [6,1,3,2,4,5]=>1 [6,1,3,2,5,4]=>1 [6,1,3,4,2,5]=>2 [6,1,3,4,5,2]=>3 [6,1,3,5,2,4]=>2 [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]=>3 [6,1,4,5,2,3]=>2 [6,1,4,5,3,2]=>2 [6,1,5,2,3,4]=>1 [6,1,5,2,4,3]=>1 [6,1,5,3,2,4]=>1 [6,1,5,3,4,2]=>2 [6,1,5,4,2,3]=>1 [6,1,5,4,3,2]=>1 [6,2,1,3,4,5]=>1 [6,2,1,3,5,4]=>1 [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]=>1 [6,2,3,1,4,5]=>2 [6,2,3,1,5,4]=>2 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>4 [6,2,3,5,1,4]=>3 [6,2,3,5,4,1]=>3 [6,2,4,1,3,5]=>2 [6,2,4,1,5,3]=>2 [6,2,4,3,1,5]=>2 [6,2,4,3,5,1]=>4 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>3 [6,2,5,1,3,4]=>2 [6,2,5,1,4,3]=>2 [6,2,5,3,1,4]=>2 [6,2,5,3,4,1]=>3 [6,2,5,4,1,3]=>2 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>1 [6,3,1,2,5,4]=>1 [6,3,1,4,2,5]=>2 [6,3,1,4,5,2]=>3 [6,3,1,5,2,4]=>2 [6,3,1,5,4,2]=>2 [6,3,2,1,4,5]=>1 [6,3,2,1,5,4]=>1 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>4 [6,3,2,5,1,4]=>3 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>2 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>2 [6,3,4,2,5,1]=>4 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>3 [6,3,5,1,2,4]=>2 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>2 [6,3,5,2,4,1]=>2 [6,3,5,4,1,2]=>2 [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]=>3 [6,4,1,5,2,3]=>2 [6,4,1,5,3,2]=>2 [6,4,2,1,3,5]=>1 [6,4,2,1,5,3]=>2 [6,4,2,3,1,5]=>2 [6,4,2,3,5,1]=>4 [6,4,2,5,1,3]=>3 [6,4,2,5,3,1]=>3 [6,4,3,1,2,5]=>1 [6,4,3,1,5,2]=>3 [6,4,3,2,1,5]=>1 [6,4,3,2,5,1]=>4 [6,4,3,5,1,2]=>3 [6,4,3,5,2,1]=>3 [6,4,5,1,2,3]=>2 [6,4,5,1,3,2]=>2 [6,4,5,2,1,3]=>2 [6,4,5,2,3,1]=>2 [6,4,5,3,1,2]=>2 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>1 [6,5,1,2,4,3]=>1 [6,5,1,3,2,4]=>1 [6,5,1,3,4,2]=>2 [6,5,1,4,2,3]=>1 [6,5,1,4,3,2]=>1 [6,5,2,1,3,4]=>1 [6,5,2,1,4,3]=>1 [6,5,2,3,1,4]=>2 [6,5,2,3,4,1]=>3 [6,5,2,4,1,3]=>2 [6,5,2,4,3,1]=>2 [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]=>3 [6,5,3,4,1,2]=>2 [6,5,3,4,2,1]=>2 [6,5,4,1,2,3]=>1 [6,5,4,1,3,2]=>1 [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]=>1 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,6,4,7,5]=>2 [1,2,6,3,4,7,5]=>2 [1,3,2,4,5,6,7]=>1 [1,3,7,2,4,5,6]=>2 [1,3,7,6,5,4,2]=>2 [1,4,6,7,2,3,5]=>3 [1,4,6,7,5,3,2]=>3 [1,4,7,2,3,5,6]=>2 [1,4,7,6,5,3,2]=>2 [1,5,2,3,4,7,6]=>1 [1,5,2,7,3,4,6]=>2 [1,5,4,7,6,3,2]=>3 [1,5,6,2,7,3,4]=>3 [1,5,6,4,7,3,2]=>4 [1,5,6,7,2,3,4]=>3 [1,5,6,7,4,3,2]=>3 [1,5,7,2,3,4,6]=>2 [1,5,7,6,4,3,2]=>2 [1,6,2,3,4,7,5]=>2 [1,6,2,3,7,4,5]=>2 [1,6,2,7,3,4,5]=>2 [1,6,5,4,3,7,2]=>5 [1,6,5,4,7,3,2]=>4 [1,6,5,7,4,3,2]=>3 [1,6,7,2,3,4,5]=>2 [1,6,7,5,4,3,2]=>2 [1,7,2,3,4,5,6]=>1 [1,7,3,5,6,4,2]=>3 [1,7,3,6,5,4,2]=>2 [1,7,4,3,6,5,2]=>3 [1,7,4,5,3,6,2]=>4 [1,7,4,5,6,3,2]=>3 [1,7,4,6,5,3,2]=>2 [1,7,5,4,3,6,2]=>4 [1,7,5,4,6,3,2]=>3 [1,7,6,4,5,3,2]=>2 [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]=>1 [2,3,1,4,5,6,7]=>2 [2,3,4,1,5,6,7]=>3 [2,3,4,1,5,7,6]=>3 [2,3,4,5,1,6,7]=>4 [2,3,4,5,1,7,6]=>4 [2,3,4,5,6,1,7]=>5 [2,3,4,5,6,7,1]=>6 [2,3,4,5,7,1,6]=>5 [2,3,4,6,1,7,5]=>4 [2,3,4,6,7,1,5]=>5 [2,3,4,7,1,5,6]=>4 [2,3,5,6,7,1,4]=>5 [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]=>1 [3,2,1,4,5,6,7]=>1 [3,2,4,5,6,7,1]=>6 [3,4,1,2,5,6,7]=>2 [3,4,2,5,6,7,1]=>6 [3,4,5,2,6,7,1]=>6 [3,4,5,6,2,7,1]=>6 [3,4,5,6,7,1,2]=>5 [3,5,6,1,2,4,7]=>3 [3,5,6,4,2,1,7]=>3 [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]=>1 [4,1,6,2,3,5,7]=>2 [4,2,3,5,6,7,1]=>6 [4,2,5,1,3,6,7]=>3 [4,3,2,1,5,6,7]=>1 [4,3,2,5,6,7,1]=>6 [4,3,5,2,6,7,1]=>6 [4,3,6,5,2,1,7]=>3 [4,5,1,6,2,3,7]=>3 [4,5,2,3,6,7,1]=>6 [4,5,3,6,2,1,7]=>4 [4,5,6,1,2,3,7]=>3 [4,5,6,3,2,1,7]=>3 [4,6,1,2,3,5,7]=>2 [4,6,1,2,3,7,5]=>2 [4,6,5,3,2,1,7]=>2 [5,1,2,3,4,6,7]=>1 [5,1,2,3,4,7,6]=>1 [5,1,2,3,6,4,7]=>2 [5,1,2,3,6,7,4]=>3 [5,1,2,3,7,4,6]=>2 [5,1,2,6,3,4,7]=>2 [5,1,6,2,3,4,7]=>2 [5,1,6,2,3,7,4]=>3 [5,2,3,4,6,7,1]=>6 [5,2,6,7,1,3,4]=>4 [5,3,2,4,6,7,1]=>6 [5,3,2,6,1,4,7]=>4 [5,3,6,7,1,2,4]=>4 [5,4,3,2,1,6,7]=>1 [5,4,3,2,1,7,6]=>1 [5,4,3,2,6,1,7]=>5 [5,4,3,6,2,1,7]=>4 [5,4,6,3,2,1,7]=>3 [5,4,6,7,1,2,3]=>4 [5,6,1,2,3,4,7]=>2 [5,6,1,2,3,7,4]=>3 [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]=>2 [6,1,2,7,3,4,5]=>2 [6,2,3,4,5,7,1]=>6 [6,2,4,5,3,1,7]=>3 [6,2,5,4,3,1,7]=>2 [6,3,2,5,4,1,7]=>3 [6,3,4,2,5,1,7]=>4 [6,3,4,5,2,1,7]=>3 [6,3,4,7,1,2,5]=>4 [6,3,5,4,2,1,7]=>2 [6,4,3,2,5,1,7]=>4 [6,4,3,2,7,1,5]=>5 [6,4,3,5,2,1,7]=>3 [6,4,5,7,1,2,3]=>4 [6,4,7,2,5,1,3]=>3 [6,4,7,3,5,1,2]=>3 [6,5,3,4,2,1,7]=>2 [6,5,4,3,2,1,7]=>1 [6,5,7,3,4,1,2]=>3 [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]=>2 [7,2,3,4,1,5,6]=>3 [7,2,3,4,5,1,6]=>4 [7,3,1,2,4,5,6]=>1 [7,3,2,1,4,5,6]=>1 [7,3,2,4,1,5,6]=>3 [7,3,4,1,2,5,6]=>2 [7,4,1,2,3,5,6]=>1 [7,4,2,1,3,5,6]=>1 [7,4,5,6,1,2,3]=>3 [7,5,1,2,3,4,6]=>1 [7,5,6,1,2,3,4]=>2 [7,5,6,3,4,1,2]=>2 [7,6,1,2,3,4,5]=>1 [7,6,4,5,1,2,3]=>2 [7,6,5,1,2,3,4]=>1 [7,6,5,3,4,1,2]=>2 [7,6,5,4,1,2,3]=>1 [7,6,5,4,3,1,2]=>1 [7,6,5,4,3,2,1]=>1 [8,7,6,5,4,3,2,1]=>1 [7,6,8,5,4,3,2,1]=>3 [7,8,5,6,4,3,2,1]=>2 [7,8,6,4,5,3,2,1]=>2 [8,6,7,4,5,3,2,1]=>2 [7,6,5,4,8,3,2,1]=>5 [6,5,7,4,8,3,2,1]=>5 [7,8,6,5,3,4,2,1]=>2 [8,6,7,5,3,4,2,1]=>2 [8,7,5,6,3,4,2,1]=>2 [6,7,8,3,4,5,2,1]=>3 [7,8,6,5,4,2,3,1]=>2 [8,6,7,5,4,2,3,1]=>2 [8,7,5,6,4,2,3,1]=>2 [8,7,6,4,5,2,3,1]=>2 [8,6,5,7,3,2,4,1]=>3 [6,7,8,5,2,3,4,1]=>3 [8,5,6,7,2,3,4,1]=>3 [7,8,3,2,4,5,6,1]=>5 [7,6,5,4,3,2,8,1]=>7 [6,5,7,4,3,2,8,1]=>7 [6,5,4,3,7,2,8,1]=>7 [5,4,6,3,7,2,8,1]=>7 [3,4,5,2,6,7,8,1]=>7 [5,2,3,4,6,7,8,1]=>7 [4,3,2,5,6,7,8,1]=>7 [3,4,2,5,6,7,8,1]=>7 [4,2,3,5,6,7,8,1]=>7 [3,2,4,5,6,7,8,1]=>7 [2,3,4,5,6,7,8,1]=>7 [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]=>2 [8,7,5,6,4,3,1,2]=>2 [8,7,6,4,5,3,1,2]=>2 [8,7,6,5,3,4,1,2]=>2 [8,7,5,6,3,4,1,2]=>2 [7,8,5,6,3,4,1,2]=>2 [5,6,7,8,3,4,1,2]=>4 [7,8,3,4,5,6,1,2]=>4 [3,4,5,6,7,8,1,2]=>6 [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]=>3 [8,7,6,4,5,1,2,3]=>2 [8,6,7,4,5,1,2,3]=>2 [8,7,4,5,6,1,2,3]=>3 [7,8,4,5,6,1,2,3]=>3 [6,7,4,5,8,1,2,3]=>5 [7,6,5,8,3,2,1,4]=>4 [7,5,6,8,2,3,1,4]=>4 [6,7,5,8,3,1,2,4]=>4 [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]=>2 [7,8,5,6,1,2,3,4]=>2 [8,5,6,7,1,2,3,4]=>3 [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]=>2 [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]=>2 [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]=>3 [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]=>2 [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]=>3 [7,6,4,5,3,2,1,8]=>2 [6,5,4,7,3,2,1,8]=>4 [7,5,6,3,4,2,1,8]=>2 [7,6,4,3,5,2,1,8]=>3 [7,6,3,4,5,2,1,8]=>3 [7,5,4,3,6,2,1,8]=>4 [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]=>3 [2,3,4,5,6,7,1,8]=>6 [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]=>5 [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]=>0 [6,5,8,7,4,3,2,1]=>3 [3,5,8,7,6,4,2,1]=>3 [4,3,6,5,8,7,2,1]=>5 [2,6,8,7,5,4,3,1]=>3 [2,3,5,6,8,7,4,1]=>5 [3,2,6,5,4,8,7,1]=>6 [4,3,6,5,7,2,8,1]=>7 [3,2,6,5,7,4,8,1]=>7 [4,3,5,2,7,6,8,1]=>7 [3,2,5,4,7,6,8,1]=>7 [1,8,7,6,5,4,3,2]=>1 [1,7,8,6,5,4,3,2]=>2 [1,6,8,7,5,4,3,2]=>2 [1,7,6,8,5,4,3,2]=>3 [1,6,7,8,5,4,3,2]=>3 [1,5,8,7,6,4,3,2]=>2 [1,7,6,5,8,4,3,2]=>4 [1,3,5,7,8,6,4,2]=>4 [1,4,3,8,7,6,5,2]=>3 [1,6,5,4,3,8,7,2]=>5 [1,4,3,6,5,8,7,2]=>5 [2,1,8,7,6,5,4,3]=>1 [2,1,6,5,7,4,8,3]=>5 [2,1,5,4,7,6,8,3]=>5 [1,2,6,7,8,5,4,3]=>3 [3,2,1,8,7,6,5,4]=>1 [3,2,1,6,5,8,7,4]=>3 [1,2,3,5,6,7,8,4]=>4 [4,3,2,1,8,7,6,5]=>1 [3,4,2,1,7,8,6,5]=>2 [2,4,3,1,6,8,7,5]=>2 [2,4,3,1,7,6,8,5]=>3 [3,2,4,1,6,8,7,5]=>3 [3,2,4,1,7,6,8,5]=>3 [2,3,4,1,6,7,8,5]=>3 [2,1,4,3,8,7,6,5]=>1 [2,1,4,3,6,8,7,5]=>2 [2,1,4,3,7,6,8,5]=>3 [5,4,3,2,1,8,7,6]=>1 [3,2,5,4,1,8,7,6]=>3 [3,2,1,4,5,8,7,6]=>1 [2,3,1,4,5,7,8,6]=>2 [6,5,4,3,2,1,8,7]=>1 [4,3,5,2,6,1,8,7]=>5 [3,2,5,4,6,1,8,7]=>5 [2,3,4,5,6,1,8,7]=>5 [2,1,6,5,4,3,8,7]=>1 [2,1,4,6,5,3,8,7]=>2 [2,1,5,4,6,3,8,7]=>3 [4,3,2,1,6,5,8,7]=>1 [2,4,3,1,6,5,8,7]=>2 [3,2,4,1,6,5,8,7]=>3 [2,1,4,3,6,5,8,7]=>1 [2,1,3,4,5,6,8,7]=>1 [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]=>5 [3,2,5,4,7,6,1,8]=>5 [1,4,3,2,7,6,5,8]=>1 [1,3,4,2,6,7,5,8]=>2 [1,3,2,5,4,7,6,8]=>1 [1,2,3,5,4,7,6,8]=>1 [1,3,2,4,5,7,6,8]=>1 [1,2,3,4,5,7,6,8]=>1 [1,2,4,3,6,5,7,8]=>1 [1,3,2,5,4,6,7,8]=>1 [1,2,3,5,4,6,7,8]=>1 [1,3,2,4,5,6,7,8]=>1 [1,8,4,7,6,5,3,2]=>2 [1,8,5,4,7,6,3,2]=>3 [1,8,7,4,5,6,3,2]=>3 [1,8,7,4,6,5,3,2]=>2 [1,8,6,5,4,7,3,2]=>4 [1,8,7,5,4,6,3,2]=>3 [1,8,7,5,6,4,3,2]=>2 [2,1,4,5,8,6,7,3]=>4 [2,1,8,5,4,7,6,3]=>3 [2,3,4,8,5,6,7,1]=>6 [2,3,6,4,5,1,8,7]=>4 [2,3,7,4,5,6,8,1]=>7 [2,8,4,3,5,7,6,1]=>5 [4,2,3,1,8,6,7,5]=>2 [8,2,7,4,6,5,3,1]=>3 [4,3,2,7,5,6,8,1]=>7 [4,3,2,8,5,7,6,1]=>5 [6,3,2,5,4,1,8,7]=>3 [8,3,2,5,4,7,6,1]=>5 [8,3,2,7,6,5,4,1]=>3 [8,3,7,4,6,5,2,1]=>3 [7,3,6,5,4,2,1,8]=>2 [7,4,3,6,5,2,1,8]=>3 [7,6,3,5,4,2,1,8]=>2 [8,5,4,3,2,7,6,1]=>5 [8,7,4,3,6,5,2,1]=>3 [2,4,6,8,1,3,5,7]=>4 [2,4,6,1,7,3,8,5]=>3 [2,1,4,3,7,5,8,6]=>2 [2,4,1,3,7,5,8,6]=>2 [2,1,4,3,7,8,5,6]=>2 [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]=>5 [2,1,5,3,6,4,8,7]=>2 [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]=>2 [2,1,5,7,3,8,4,6]=>3 [2,5,7,8,1,3,4,6]=>4 [2,3,5,6,1,7,8,4]=>4 [2,1,6,3,7,4,8,5]=>3 [2,6,7,1,3,4,8,5]=>3 [2,1,6,7,8,3,4,5]=>3 [2,6,7,8,1,3,4,5]=>4 [2,1,6,3,4,7,8,5]=>3 [2,1,6,3,4,5,8,7]=>1 [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]=>6 [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]=>6 [3,1,4,2,6,5,8,7]=>2 [3,4,1,2,6,5,8,7]=>2 [3,1,4,2,6,8,5,7]=>2 [3,4,6,8,1,2,5,7]=>4 [3,1,4,2,7,5,8,6]=>2 [3,4,1,2,7,8,5,6]=>2 [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]=>3 [3,1,5,6,2,8,4,7]=>3 [3,5,6,8,1,2,4,7]=>4 [3,1,5,2,7,4,8,6]=>2 [3,5,1,7,2,8,4,6]=>3 [3,5,7,8,1,2,4,6]=>4 [1,3,2,5,4,8,6,7]=>1 [1,3,5,8,2,4,6,7]=>3 [1,3,5,6,2,7,4,8]=>3 [3,1,6,2,7,4,8,5]=>3 [3,6,7,1,2,8,4,5]=>3 [3,6,1,7,8,2,4,5]=>4 [3,6,7,8,1,2,4,5]=>4 [1,3,2,6,4,7,5,8]=>2 [3,1,2,6,7,4,8,5]=>3 [1,3,2,6,4,8,5,7]=>2 [1,3,2,6,4,5,7,8]=>1 [1,3,2,7,4,8,5,6]=>2 [1,3,2,7,4,5,6,8]=>1 [1,3,2,8,4,5,6,7]=>1 [3,1,2,4,5,8,6,7]=>1 [1,3,2,4,5,8,6,7]=>1 [4,1,5,2,6,3,8,7]=>3 [4,5,6,1,2,3,8,7]=>3 [4,1,5,6,8,2,3,7]=>4 [4,5,6,8,1,2,3,7]=>4 [4,1,5,2,7,3,8,6]=>3 [4,1,5,2,7,8,3,6]=>4 [4,5,7,1,2,8,3,6]=>4 [4,5,1,7,8,2,3,6]=>4 [4,5,7,8,1,2,3,6]=>4 [1,4,2,5,3,7,6,8]=>2 [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]=>4 [4,1,6,2,7,3,8,5]=>3 [4,6,7,1,8,2,3,5]=>4 [4,6,7,8,1,2,3,5]=>4 [1,4,2,6,3,7,5,8]=>2 [1,4,2,6,7,8,3,5]=>4 [1,4,2,6,3,8,5,7]=>2 [4,1,2,3,6,5,8,7]=>1 [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]=>1 [1,4,2,3,5,7,6,8]=>1 [1,4,2,8,3,5,6,7]=>2 [4,1,2,3,8,5,6,7]=>1 [1,4,2,3,5,8,6,7]=>1 [1,4,2,3,5,6,7,8]=>1 [5,1,6,2,7,3,8,4]=>4 [1,5,2,6,3,7,4,8]=>3 [1,5,2,6,3,8,4,7]=>3 [1,5,2,6,3,4,7,8]=>2 [1,2,5,6,3,4,7,8]=>2 [1,5,2,7,3,8,4,6]=>3 [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]=>1 [5,1,2,8,3,4,6,7]=>2 [1,5,2,8,3,4,6,7]=>2 [1,5,8,2,3,4,6,7]=>2 [1,5,2,3,4,8,6,7]=>1 [1,2,3,5,4,8,6,7]=>1 [5,1,2,3,4,6,8,7]=>1 [1,5,2,3,4,6,7,8]=>1 [1,6,2,7,3,8,4,5]=>3 [1,6,7,8,2,3,4,5]=>3 [6,7,1,2,3,4,8,5]=>3 [6,1,7,2,3,4,5,8]=>2 [6,1,2,7,3,4,5,8]=>2 [1,6,2,7,3,4,5,8]=>2 [1,6,7,2,3,4,5,8]=>2 [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]=>2 [1,6,2,8,3,4,5,7]=>2 [1,6,8,2,3,4,5,7]=>2 [1,6,2,3,4,8,5,7]=>2 [1,2,3,6,4,8,5,7]=>2 [6,1,2,3,4,5,8,7]=>1 [1,6,2,3,4,5,7,8]=>1 [1,2,3,6,4,5,7,8]=>1 [1,7,2,8,3,4,5,6]=>2 [1,7,8,2,3,4,5,6]=>2 [1,7,2,3,8,4,5,6]=>2 [7,1,2,3,4,8,5,6]=>2 [1,7,2,3,4,8,5,6]=>2 [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]=>2 [1,2,7,3,4,5,8,6]=>2 [1,7,2,3,4,5,6,8]=>1 [1,2,3,7,4,5,6,8]=>1 [1,8,2,3,4,5,6,7]=>1 [1,2,3,8,4,5,6,7]=>1 [1,2,3,4,5,8,6,7]=>1 [5,3,2,6,1,4,8,7]=>4 [7,3,2,5,4,8,1,6]=>6 [8,4,5,2,3,7,6,1]=>5 [7,4,5,2,3,8,1,6]=>6 [6,4,5,2,3,1,8,7]=>2 [5,4,6,2,1,3,8,7]=>3 [3,6,1,5,4,2,8,7]=>2 [4,6,5,1,3,2,8,7]=>2 [5,6,4,3,1,2,8,7]=>2 [7,5,4,3,2,8,1,6]=>6 [8,6,4,3,7,2,5,1]=>4 [7,6,4,3,8,2,1,5]=>5 [6,7,4,3,8,1,2,5]=>5 [5,7,4,3,1,8,2,6]=>5 [4,7,5,1,3,8,2,6]=>5 [3,7,1,5,4,8,2,6]=>5 [2,1,7,5,4,8,3,6]=>4 [3,8,1,5,4,7,6,2]=>4 [4,8,5,1,3,7,6,2]=>4 [5,8,4,3,1,7,6,2]=>3 [6,8,4,3,7,1,5,2]=>3 [7,8,4,3,6,5,1,2]=>3 [6,8,5,7,3,1,4,2]=>2 [5,8,6,7,1,3,4,2]=>3 [4,8,6,1,7,3,5,2]=>3 [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]=>4 [4,7,6,1,8,3,2,5]=>4 [5,7,6,8,1,3,2,4]=>4 [5,4,7,2,1,8,3,6]=>4 [6,4,7,2,8,1,3,5]=>5 [7,4,6,2,8,3,1,5]=>5 [8,4,6,2,7,3,5,1]=>4 [8,3,2,6,7,4,5,1]=>4 [7,3,2,6,8,4,1,5]=>5 [6,3,2,7,8,1,4,5]=>5 [5,3,2,7,1,8,4,6]=>4 [4,3,2,1,7,8,5,6]=>2 [3,4,1,2,8,7,6,5]=>2 [5,3,2,8,1,7,6,4]=>4 [6,3,2,8,7,1,5,4]=>4 [7,3,2,8,6,5,1,4]=>4 [8,4,7,2,6,5,3,1]=>2 [7,4,8,2,6,5,1,3]=>3 [6,4,8,2,7,1,5,3]=>3 [5,4,8,2,1,7,6,3]=>3 [4,5,8,1,2,7,6,3]=>3 [3,5,1,8,2,7,6,4]=>3 [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]=>3 [4,6,8,1,7,2,5,3]=>3 [5,6,8,7,1,2,4,3]=>3 [6,5,8,7,2,1,4,3]=>3 [7,5,8,6,2,4,1,3]=>3 [8,5,7,6,2,4,3,1]=>2 [5,7,8,6,1,4,2,3]=>3 [4,7,8,1,6,5,2,3]=>3 [3,7,1,8,6,5,2,4]=>3 [2,1,7,8,6,5,3,4]=>2 [3,8,1,7,6,5,4,2]=>2 [4,8,7,1,6,5,3,2]=>2 [5,8,7,6,1,4,3,2]=>2 [6,8,7,5,4,1,3,2]=>2 [4,2,5,1,3,6,7,8]=>3 [5,2,6,7,1,3,4,8]=>4 [3,2,7,8,1,4,5,6]=>4 [5,3,2,6,1,4,7,8]=>4 [7,4,3,8,1,2,5,6]=>4 [4,7,3,6,8,1,2,5]=>5 [6,7,3,4,8,1,2,5]=>5 [5,4,2,7,8,1,3,6]=>5 [6,4,7,2,5,1,3,8]=>3 [6,4,3,2,7,1,5,8]=>5 [5,4,3,2,8,1,6,7]=>5 [7,5,3,8,2,6,1,4]=>4 [8,5,4,7,2,6,1,3]=>3 [8,5,4,7,3,6,1,2]=>3 [8,1,2,7,6,3,4,5]=>1 [8,1,4,2,6,3,5,7]=>2 [8,3,1,2,4,7,5,6]=>1 [8,3,1,5,6,2,4,7]=>3 [6,3,8,1,2,7,4,5]=>3 [7,8,4,1,6,2,3,5]=>2 [8,3,4,1,6,7,2,5]=>4 [2,7,6,5,1,3,8,4]=>4 [8,3,6,5,1,7,2,4]=>4 [4,6,7,3,8,5,1,2]=>5 [3,5,2,7,1,8,6,4]=>4 [4,6,7,2,8,1,5,3]=>5 [5,6,7,8,2,1,4,3]=>4 [6,5,8,7,3,4,1,2]=>3 [3,6,7,4,5,8,1,2]=>6 [2,6,7,4,5,1,8,3]=>5 [1,6,7,4,5,2,3,8]=>2 [1,5,4,7,6,2,3,8]=>3 [2,5,4,7,6,1,8,3]=>5 [3,5,4,7,6,8,1,2]=>6 [4,5,3,7,8,6,1,2]=>5 [5,4,3,8,7,6,1,2]=>4 [6,4,8,3,7,5,1,2]=>3 [6,3,8,4,5,7,1,2]=>4 [5,3,4,8,6,7,1,2]=>5 [4,3,5,6,8,7,1,2]=>5 [3,2,5,6,1,8,7,4]=>4 [4,2,5,6,8,1,7,3]=>5 [5,2,4,8,6,1,7,3]=>4 [6,2,8,4,5,1,7,3]=>3 [7,8,2,4,5,1,6,3]=>3 [7,8,1,4,5,2,3,6]=>2 [6,1,8,4,5,2,3,7]=>2 [5,1,4,8,6,2,3,7]=>3 [4,1,3,2,8,6,5,7]=>1 [5,1,3,8,2,6,4,7]=>3 [6,1,8,3,2,5,4,7]=>2 [7,8,1,3,2,5,4,6]=>2 [7,8,2,3,1,5,6,4]=>2 [6,2,8,3,1,5,7,4]=>3 [5,2,3,8,1,6,7,4]=>4 [6,3,8,2,1,7,5,4]=>3 [7,8,3,2,1,6,5,4]=>2 [7,8,4,2,6,1,5,3]=>3 [5,4,2,8,7,1,6,3]=>4 [4,5,2,7,8,1,6,3]=>5 [2,5,3,7,1,6,8,4]=>4 [1,5,3,7,2,6,4,8]=>3 [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]=>3 [7,8,5,6,2,1,4,3]=>2 [6,5,8,7,1,2,3,4]=>3 [5,4,1,8,7,2,3,6]=>3 [6,4,8,1,7,2,3,5]=>3 [7,8,3,1,2,6,4,5]=>2 [5,3,1,8,2,7,4,6]=>3 [4,3,1,2,8,7,5,6]=>1 [4,2,1,3,8,5,7,6]=>1 [5,2,1,8,3,4,7,6]=>2 [6,2,8,1,3,4,7,5]=>3 [7,8,2,1,3,4,6,5]=>2 [6,3,1,5,2,4,8,7]=>2 [2,1,8,5,3,7,4,6]=>2 [8,2,6,1,4,3,7,5]=>2 [4,7,1,5,8,3,2,6]=>4 [8,6,1,3,4,2,5,7]=>2 [8,1,2,4,5,6,3,7]=>3 [8,2,5,1,3,6,4,7]=>2 [4,1,5,3,7,2,8,6]=>4 [5,2,7,1,3,8,4,6]=>3 [5,3,1,7,8,2,4,6]=>4 [1,7,3,4,2,5,8,6]=>2 [4,7,2,1,3,5,8,6]=>2 [4,5,2,3,7,6,1,8]=>5 [6,4,3,7,2,5,1,8]=>4 [8,4,3,6,5,1,2,7]=>3 [1,5,6,3,4,8,7,2]=>5 [4,6,2,7,3,5,1,8]=>4 [3,2,6,7,4,5,1,8]=>4 [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]=>4 [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]=>3 [4,1,2,6,5,8,7,3]=>4 [5,1,6,2,4,8,7,3]=>4 [6,1,5,4,2,8,7,3]=>4 [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]=>2 [8,1,6,7,4,5,2,3]=>2 [7,1,6,8,4,2,5,3]=>3 [6,1,7,8,2,4,5,3]=>3 [5,1,7,2,8,4,6,3]=>3 [4,1,2,7,8,5,6,3]=>3 [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]=>3 [1,6,7,8,3,4,5,2]=>3 [8,6,7,1,3,4,2,5]=>2 [7,6,8,1,3,2,4,5]=>3 [5,7,8,2,1,3,4,6]=>3 [4,7,2,8,1,3,5,6]=>4 [3,2,6,8,4,1,5,7]=>4 [4,6,2,8,3,1,5,7]=>4 [5,6,8,2,3,1,4,7]=>3 [6,5,8,3,2,1,4,7]=>3 [7,5,8,3,1,2,4,6]=>3 [8,5,7,3,1,4,2,6]=>2 [1,5,7,3,8,4,6,2]=>4 [1,4,3,7,8,5,6,2]=>4 [8,4,3,7,1,5,2,6]=>3 [6,4,3,8,2,1,5,7]=>4 [4,5,2,3,8,1,6,7]=>5 [3,2,5,4,8,1,6,7]=>5 [4,5,2,3,1,8,7,6]=>2 [6,4,3,1,2,8,7,5]=>2 [7,4,3,1,8,2,6,5]=>4 [8,4,3,1,7,6,2,5]=>3 [1,5,8,3,7,6,4,2]=>2 [8,5,1,3,7,6,2,4]=>3 [7,5,1,3,8,2,6,4]=>4 [6,5,1,3,2,8,7,4]=>3 [5,6,1,2,3,8,7,4]=>3 [4,6,2,1,3,8,7,5]=>2 [3,2,6,1,4,8,7,5]=>3 [3,2,7,1,8,4,6,5]=>3 [4,7,2,1,8,3,6,5]=>3 [5,7,1,2,8,3,6,4]=>3 [6,7,1,8,2,3,5,4]=>3 [7,6,1,8,3,2,5,4]=>3 [8,6,1,7,3,5,2,4]=>2 [1,6,8,7,3,5,4,2]=>2 [1,7,8,6,5,3,4,2]=>2 [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]=>3 [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]=>1 [1,4,3,8,7,5,6,2]=>4 [4,1,2,8,7,5,6,3]=>3 [3,2,5,1,6,4,8,7]=>3 [3,2,5,4,7,1,8,6]=>5 [4,2,5,3,7,6,8,1]=>7 [4,2,5,3,7,1,8,6]=>5 [4,2,5,3,6,1,8,7]=>5 [4,2,5,1,6,3,8,7]=>3 [3,1,5,4,6,2,8,7]=>4 [4,1,5,3,6,2,8,7]=>4 [4,3,5,1,6,2,8,7]=>4 [4,3,5,2,7,1,8,6]=>5 [4,3,6,2,7,5,8,1]=>7 [4,3,6,2,7,1,8,5]=>5 [4,3,6,1,7,2,8,5]=>4 [4,3,5,1,7,2,8,6]=>4 [3,1,5,4,7,2,8,6]=>4 [2,1,5,4,7,3,8,6]=>3 [3,1,5,4,7,6,8,2]=>6 [4,1,5,3,7,6,8,2]=>6 [4,3,5,1,7,6,8,2]=>6 [4,3,6,1,7,5,8,2]=>6 [4,3,6,5,7,1,8,2]=>6 [5,3,6,4,7,2,8,1]=>7 [5,3,6,4,7,1,8,2]=>6 [5,3,6,1,7,4,8,2]=>6 [5,1,6,3,7,4,8,2]=>6 [4,1,6,3,7,5,8,2]=>6 [3,1,6,4,7,5,8,2]=>6 [2,1,6,4,7,5,8,3]=>5 [2,1,6,4,7,3,8,5]=>3 [3,1,6,4,7,2,8,5]=>4 [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]=>4 [5,3,6,2,7,1,8,4]=>5 [5,3,6,2,7,4,8,1]=>7 [5,2,6,3,7,4,8,1]=>7 [5,2,6,3,7,1,8,4]=>5 [5,2,6,1,7,3,8,4]=>4 [4,2,5,1,7,3,8,6]=>3 [4,2,6,1,7,3,8,5]=>3 [4,2,6,3,7,1,8,5]=>5 [4,2,6,3,7,5,8,1]=>7 [3,2,6,4,7,5,8,1]=>7 [3,2,6,4,7,1,8,5]=>5 [3,2,6,1,7,4,8,5]=>3 [3,2,5,1,7,4,8,6]=>3 [3,2,4,1,7,5,8,6]=>3 [3,1,4,2,7,6,8,5]=>3 [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]=>5 [4,2,6,5,7,3,8,1]=>7 [4,2,6,5,7,1,8,3]=>5 [4,2,6,1,7,5,8,3]=>5 [4,2,5,1,7,6,8,3]=>5 [4,1,5,2,7,6,8,3]=>5 [3,1,5,2,7,6,8,4]=>4 [2,1,5,3,7,6,8,4]=>4 [2,1,6,3,7,5,8,4]=>4 [3,1,6,2,7,5,8,4]=>4 [4,1,6,2,7,5,8,3]=>5 [5,1,6,2,7,4,8,3]=>5 [5,2,6,1,7,4,8,3]=>5 [5,2,6,4,7,1,8,3]=>5 [5,2,6,4,7,3,8,1]=>7 [5,4,6,2,7,3,8,1]=>7 [5,4,6,2,7,1,8,3]=>5 [5,4,6,1,7,2,8,3]=>5 [5,1,6,4,7,2,8,3]=>5 [4,1,6,5,7,2,8,3]=>5 [3,1,6,5,7,2,8,4]=>4 [2,1,6,5,7,3,8,4]=>4 [3,1,6,5,7,4,8,2]=>6 [4,1,6,5,7,3,8,2]=>6 [5,1,6,4,7,3,8,2]=>6 [5,4,6,1,7,3,8,2]=>6 [5,4,6,3,7,1,8,2]=>6 [8,3,5,2,1,6,4,7]=>2 [8,6,3,5,2,4,1,7]=>2 [3,7,5,2,4,1,8,6]=>2 [8,3,7,5,2,4,6,1]=>5 [8,2,4,5,7,3,6,1]=>4 [2,4,5,7,3,1,8,6]=>4 [8,2,4,6,5,3,1,7]=>3 [8,2,5,4,6,1,3,7]=>4 [8,6,3,5,1,4,2,7]=>2 [8,6,1,4,5,3,2,7]=>2 [8,1,5,6,4,3,2,7]=>2 [5,7,4,3,2,1,8,6]=>2 [8,5,7,4,3,2,6,1]=>4 [4,6,8,3,2,7,5,1]=>3 [4,7,6,3,2,8,1,5]=>6 [1,4,6,7,3,2,8,5]=>3 [5,4,7,3,1,8,2,6]=>5 [1,7,4,5,3,2,8,6]=>2 [3,7,5,1,4,2,8,6]=>2 [5,7,4,2,1,3,8,6]=>2 [8,5,7,4,2,1,6,3]=>2 [8,3,7,5,1,4,6,2]=>4 [8,4,1,7,5,3,6,2]=>4 [4,6,3,8,7,1,5,2]=>4 [1,7,4,8,6,3,5,2]=>3 [8,4,7,6,3,5,2,1]=>2 [3,6,5,8,7,4,1,2]=>4 [3,1,5,8,6,7,4,2]=>4 [4,8,1,6,7,3,5,2]=>3 [3,6,4,1,8,7,5,2]=>4 [8,2,6,1,4,7,5,3]=>3 [2,7,6,8,1,4,3,5]=>4 [3,7,1,6,4,8,2,5]=>5 [1,7,3,5,6,8,2,4]=>5 [1,3,6,7,5,8,2,4]=>5 [3,7,6,5,8,2,1,4]=>5 [3,6,8,5,7,2,4,1]=>3 [2,3,5,7,6,8,1,4]=>6 [2,1,6,5,7,8,3,4]=>4 [4,2,7,6,8,3,1,5]=>5 [4,2,6,8,7,3,5,1]=>4 [3,8,2,4,6,7,5,1]=>5 [3,7,2,6,4,8,1,5]=>6 [3,2,6,1,4,7,8,5]=>3 [5,3,7,2,1,8,4,6]=>3 [4,7,3,2,1,5,8,6]=>2 [8,7,6,1,3,4,2,5]=>2 [8,5,7,3,2,1,6,4]=>2 [8,3,6,7,2,1,5,4]=>3 [3,7,8,6,2,1,5,4]=>3 [8,7,6,3,5,2,4,1]=>2 [2,7,4,8,1,6,5,3]=>4 [4,6,8,2,1,7,5,3]=>3 [8,4,1,5,7,2,6,3]=>3 [8,5,3,7,1,6,2,4]=>3 [8,5,7,2,1,3,6,4]=>2 [8,2,6,7,1,3,5,4]=>3 [8,3,6,1,7,5,2,4]=>3 [4,6,1,8,7,2,5,3]=>3 [8,1,2,5,6,7,4,3]=>3 [8,2,6,5,7,4,1,3]=>4 [2,1,7,8,5,6,4,3]=>2 [8,2,5,7,6,4,3,1]=>3 [2,7,6,8,5,4,1,3]=>4 [1,7,2,5,8,6,4,3]=>3 [1,7,4,8,2,6,5,3]=>3 [3,7,8,1,6,5,2,4]=>3 [2,7,8,6,1,3,5,4]=>3 [8,7,6,3,5,1,4,2]=>2 [8,4,7,6,5,1,3,2]=>2 [8,7,1,5,6,4,3,2]=>2 [8,1,6,7,5,4,3,2]=>2 [5,4,3,6,1,2,8,7]=>4 [2,7,6,4,5,8,1,3]=>6 [5,7,3,6,1,8,2,4]=>5 [2,1,7,6,5,8,3,4]=>4 [6,4,3,5,8,1,7,2]=>5 [7,3,5,4,8,6,1,2]=>5 [5,4,3,2,7,1,8,6]=>5 [4,3,6,2,8,7,5,1]=>5 [4,3,7,6,2,1,8,5]=>3 [6,4,3,1,7,2,8,5]=>4 [4,3,7,1,8,6,5,2]=>4 [5,3,8,7,6,4,2,1]=>3 [7,5,3,1,8,6,4,2]=>4 [1,8,6,5,3,7,4,2]=>4 [6,1,7,5,3,2,8,4]=>4 [7,6,5,3,2,1,8,4]=>4 [6,5,3,2,8,7,4,1]=>5 [5,2,6,3,8,7,4,1]=>5 [5,2,7,6,3,1,8,4]=>4 [6,5,2,1,7,3,8,4]=>4 [5,2,7,1,8,6,4,3]=>3 [6,2,8,7,5,4,3,1]=>3 [7,6,2,1,8,5,4,3]=>3 [6,1,7,2,8,5,4,3]=>3 [7,1,8,6,5,4,3,2]=>2 [4,5,2,6,3,1,8,7]=>4 [6,5,2,1,4,3,8,7]=>1 [6,5,2,7,4,8,3,1]=>6 [8,5,2,7,4,1,6,3]=>3 [8,3,7,5,2,1,6,4]=>2 [6,3,7,5,2,8,4,1]=>6 [3,1,6,5,4,2,8,7]=>2 [5,6,3,2,4,1,8,7]=>3 [3,6,2,4,1,5,8,7]=>2 [2,6,1,3,5,4,8,7]=>2 [6,7,2,3,4,8,5,1]=>6 [8,7,2,3,4,1,6,5]=>3 [5,1,7,3,8,4,6,2]=>4 [2,5,7,3,8,6,4,1]=>5 [7,6,1,3,5,8,4,2]=>5 [3,6,7,4,1,8,5,2]=>5 [5,6,3,7,4,8,1,2]=>6 [2,1,6,7,4,8,5,3]=>4 [2,1,8,7,4,3,6,5]=>1 [5,8,3,7,4,2,6,1]=>4 [3,8,7,4,1,2,6,5]=>2 [7,8,1,3,5,2,6,4]=>2 [5,8,7,3,2,6,1,4]=>3 [2,8,6,3,1,5,7,4]=>3 [8,1,6,3,2,5,4,7]=>1 [2,8,4,1,6,3,7,5]=>2 [4,8,1,2,7,6,3,5]=>2 [3,8,4,2,5,7,1,6]=>5 [6,8,3,5,2,7,4,1]=>4 [2,1,5,3,8,7,6,4]=>2 [6,5,3,2,8,7,1,4]=>5 [7,5,2,4,8,1,6,3]=>5 [3,4,2,8,5,7,6,1]=>5 [2,4,1,8,7,6,5,3]=>2 [8,4,2,1,7,5,3,6]=>2 [4,3,1,8,6,7,5,2]=>4 [3,1,4,8,6,5,7,2]=>5 [7,1,6,5,4,8,2,3]=>5 [3,7,5,6,8,4,2,1]=>5 [5,7,1,6,8,2,4,3]=>4 [8,6,2,5,1,7,4,3]=>3 [5,6,2,1,8,7,3,4]=>3 [4,6,2,5,8,3,7,1]=>5 [7,5,2,6,3,8,1,4]=>6 [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]=>4 [5,6,2,8,4,3,1,7]=>4 [4,7,2,8,1,5,3,6]=>4 [8,7,2,1,4,5,6,3]=>3 [3,6,8,7,1,5,4,2]=>3 [5,7,8,6,3,4,1,2]=>3 [7,1,8,5,4,3,6,2]=>4 [2,7,8,4,5,3,6,1]=>5 [5,7,3,8,1,4,6,2]=>4 [2,1,7,8,5,4,6,3]=>3 [2,1,5,8,4,6,3,7]=>2 [6,5,3,8,4,1,2,7]=>4 [7,5,8,4,3,6,2,1]=>3 [2,4,8,3,5,6,1,7]=>5 [4,1,8,3,6,5,2,7]=>2 [3,4,8,1,7,2,5,6]=>3 [8,4,1,3,7,2,6,5]=>3 [3,1,8,2,4,7,6,5]=>2 [2,3,8,1,4,6,7,5]=>3 [4,3,8,2,5,1,7,6]=>3 [6,3,8,4,2,5,7,1]=>5 [7,4,3,8,2,5,1,6]=>4 [2,1,4,8,3,5,7,6]=>2 [6,8,2,4,3,5,1,7]=>4 [4,8,2,3,5,1,6,7]=>3 [3,8,2,1,4,6,5,7]=>2 [2,8,1,3,4,5,7,6]=>2 [7,1,6,8,4,3,2,5]=>3 [7,1,6,5,8,3,2,4]=>4 [3,7,6,1,4,8,2,5]=>5 [2,7,8,4,1,6,5,3]=>3 [3,6,4,5,7,2,8,1]=>7 [1,8,2,7,3,4,5,6]=>1 [3,2,1,5,8,4,6,7]=>2 [5,4,3,2,1,8,6,7]=>1 [1,8,2,4,3,5,6,7]=>1 [1,7,2,4,3,5,6,8]=>1 [1,6,2,4,3,5,7,8]=>1 [1,5,2,4,3,6,7,8]=>1 [1,6,2,5,3,4,7,8]=>1 [1,7,2,5,3,4,6,8]=>1 [1,8,2,5,3,4,6,7]=>1 [1,8,2,6,3,4,5,7]=>1 [1,7,2,6,3,4,5,8]=>1 [1,8,2,7,3,5,4,6]=>1 [1,7,2,8,3,5,4,6]=>2 [1,6,2,8,3,5,4,7]=>2 [1,5,2,8,3,6,4,7]=>2 [1,4,2,8,3,6,5,7]=>2 [1,3,2,8,4,6,5,7]=>1 [1,2,3,8,4,6,5,7]=>1 [1,2,3,7,4,6,5,8]=>1 [1,3,2,7,4,6,5,8]=>1 [1,4,2,7,3,6,5,8]=>2 [1,5,2,7,3,6,4,8]=>2 [1,6,2,7,3,5,4,8]=>2 [1,7,2,6,3,5,4,8]=>1 [1,8,2,6,3,5,4,7]=>1 [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]=>3 [1,5,2,4,3,7,6,8]=>1 [1,6,2,4,3,7,5,8]=>2 [1,7,2,4,3,6,5,8]=>1 [1,8,2,4,3,6,5,7]=>1 [1,8,2,3,4,6,5,7]=>1 [1,7,2,3,4,6,5,8]=>1 [1,8,2,3,4,7,5,6]=>1 [1,8,2,4,3,7,5,6]=>1 [1,7,2,4,3,8,5,6]=>2 [1,6,2,4,3,8,5,7]=>2 [1,5,2,4,3,8,6,7]=>1 [1,6,2,5,3,8,4,7]=>3 [1,7,2,5,3,8,4,6]=>3 [1,8,2,5,3,7,4,6]=>2 [1,8,2,6,3,7,4,5]=>2 [1,7,2,6,3,8,4,5]=>3 [1,2,3,8,4,7,5,6]=>1 [1,3,2,8,4,7,5,6]=>1 [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]=>1 [6,7,8,1,4,3,2,5]=>3 [2,8,4,1,6,7,5,3]=>3 [4,8,5,7,1,6,2,3]=>3 [8,7,6,5,2,1,4,3]=>1 [8,3,1,5,4,7,2,6]=>4 [8,7,6,5,1,4,2,3]=>1 [7,5,1,3,8,4,2,6]=>4 [7,6,1,4,8,3,2,5]=>4 [7,1,3,5,8,2,4,6]=>4 [7,5,3,6,4,2,8,1]=>7 [8,2,6,3,4,7,5,1]=>5 [7,2,6,3,5,4,8,1]=>7 [6,2,7,4,3,5,8,1]=>7 [3,7,6,4,5,2,8,1]=>7 [2,7,6,5,3,4,8,1]=>7 [8,6,5,4,2,7,3,1]=>5 [6,5,8,4,2,7,3,1]=>3 [1,8,6,3,7,5,2,4]=>3 [8,7,5,2,6,4,3,1]=>3 [8,7,1,6,2,5,4,3]=>1 [1,7,2,8,5,3,4,6]=>2 [7,6,1,8,4,3,2,5]=>3 [8,6,1,7,4,2,5,3]=>2 [8,1,2,7,3,4,6,5]=>1 [7,1,2,8,3,5,4,6]=>2 [8,2,6,1,7,3,5,4]=>2 [4,7,5,6,8,3,2,1]=>5 [8,6,4,7,5,3,2,1]=>3 [5,4,8,1,7,2,6,3]=>3 [2,3,8,7,4,5,6,1]=>5 [7,2,8,6,4,3,5,1]=>4 [8,2,7,6,3,5,4,1]=>3 [8,1,7,6,5,2,4,3]=>1 [7,1,8,6,5,3,2,4]=>2 [1,2,8,7,6,3,4,5]=>1 [3,8,7,6,4,5,2,1]=>3 [2,8,7,6,5,3,4,1]=>3 [1,8,7,6,5,4,2,3]=>1 [3,8,6,7,1,5,2,4]=>3 [5,4,7,1,3,8,2,6]=>5 [5,6,2,1,4,8,3,7]=>4 [2,1,8,4,7,5,6,3]=>3 [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]=>3 [6,7,1,4,2,8,3,5]=>4 [6,3,7,1,4,8,2,5]=>5 [3,7,8,1,5,2,4,6]=>3 [7,1,2,8,5,3,4,6]=>2 [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]=>2 [4,2,6,5,8,3,7,1]=>5 [5,2,4,7,3,6,8,1]=>7 [5,1,2,4,8,3,6,7]=>3 [4,3,6,1,5,8,2,7]=>5 [2,6,1,4,5,8,3,7]=>4 [2,5,3,4,1,8,6,7]=>3 [4,3,5,2,1,8,6,7]=>3 [3,1,6,7,5,8,2,4]=>5 [2,8,1,7,5,6,3,4]=>2 [5,3,6,8,4,7,2,1]=>4 [3,7,2,5,4,8,6,1]=>6 [8,4,2,5,7,3,6,1]=>4 [4,7,2,5,8,3,6,1]=>5 [5,2,6,8,4,3,7,1]=>4 [3,1,6,5,4,8,2,7]=>5 [4,1,6,5,8,3,2,7]=>4 [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]=>3 [2,7,1,5,4,3,8,6]=>2 [8,2,1,5,4,3,7,6]=>1 [8,4,1,5,7,3,2,6]=>3 [8,5,6,7,1,3,2,4]=>3 [8,4,6,1,7,3,2,5]=>3 [8,3,6,1,4,7,2,5]=>4 [2,7,6,1,4,3,8,5]=>3 [6,7,8,5,1,3,2,4]=>3 [5,7,6,8,2,3,4,1]=>4 [5,7,2,8,4,3,6,1]=>4 [6,7,8,2,4,3,5,1]=>4 [4,7,6,2,8,3,5,1]=>5 [8,3,6,2,4,7,5,1]=>5 [3,7,6,2,4,8,5,1]=>6 [5,7,3,8,4,6,2,1]=>4 [4,7,3,5,8,6,2,1]=>5 [8,7,2,1,4,3,6,5]=>1 [8,7,3,1,4,6,2,5]=>3 [8,7,6,3,2,5,4,1]=>3 [8,7,3,5,1,6,2,4]=>3 [8,7,2,5,1,3,6,4]=>2 [8,2,6,5,1,3,7,4]=>3 [8,4,6,5,7,1,2,3]=>4 [5,7,6,8,4,1,2,3]=>4 [4,7,6,5,8,1,2,3]=>5 [3,7,6,5,1,8,2,4]=>5 [2,6,5,7,3,4,8,1]=>7 [1,6,4,7,5,8,2,3]=>5 [8,5,3,6,2,7,4,1]=>5 [1,3,7,4,6,8,2,5]=>5 [4,7,5,6,3,2,8,1]=>7 [1,7,6,5,4,8,2,3]=>5 [8,1,6,5,7,2,4,3]=>3 [1,2,7,6,8,3,4,5]=>3 [6,1,7,5,3,8,2,4]=>5 [2,1,7,5,6,8,3,4]=>4 [5,4,1,7,6,8,2,3]=>5 [4,8,5,6,2,7,3,1]=>5 [3,8,6,4,2,7,5,1]=>5 [7,8,5,2,4,6,3,1]=>4 [2,8,6,3,7,4,5,1]=>4 [7,8,1,6,2,4,5,3]=>2 [6,8,1,4,7,2,5,3]=>2 [3,8,4,1,7,2,6,5]=>3 [5,4,7,1,8,3,2,6]=>4 [3,7,4,1,8,5,2,6]=>4 [6,7,1,4,8,3,2,5]=>4 [2,7,1,8,4,5,3,6]=>2 [6,1,2,8,4,3,5,7]=>2 [6,5,1,4,3,8,2,7]=>5 [1,6,2,5,8,3,4,7]=>3 [8,5,1,3,7,2,6,4]=>3 [8,4,2,1,7,3,6,5]=>2 [7,4,2,1,8,5,3,6]=>3 [1,5,4,2,8,3,6,7]=>3 [6,4,3,1,5,8,2,7]=>5 [3,7,6,8,4,5,2,1]=>4 [2,7,6,8,5,3,4,1]=>4 [1,7,6,8,5,4,2,3]=>3 [1,4,8,6,7,5,2,3]=>3 [2,4,8,6,7,3,5,1]=>4 [7,3,8,5,4,6,2,1]=>4 [3,4,8,5,6,7,2,1]=>5 [6,3,5,8,4,7,2,1]=>4 [5,4,3,8,6,7,2,1]=>5 [5,4,2,8,7,3,6,1]=>4 [6,2,5,8,7,3,4,1]=>4 [3,2,8,5,7,4,6,1]=>4 [1,3,8,7,5,6,2,4]=>3 [2,1,8,7,4,6,3,5]=>2 [3,1,8,5,7,6,2,4]=>3 [6,1,5,8,7,4,2,3]=>3 [5,4,1,8,7,6,2,3]=>3 [5,8,6,7,4,3,2,1]=>3 [4,8,7,5,6,3,2,1]=>3 [2,8,3,1,5,4,6,7]=>2 [2,5,3,4,7,1,8,6]=>5 [2,4,8,3,5,7,6,1]=>5 [4,2,5,3,1,8,6,7]=>3 [4,2,1,8,5,3,6,7]=>2 [5,4,1,3,8,2,6,7]=>4 [5,1,4,8,3,2,6,7]=>3 [1,5,8,4,3,2,6,7]=>2 [1,8,5,4,3,2,6,7]=>1 [1,7,4,3,8,5,2,6]=>4 [1,5,7,3,8,4,2,6]=>4 [5,1,4,7,8,3,2,6]=>4 [4,8,1,5,7,3,6,2]=>3 [8,1,5,3,7,4,6,2]=>3 [3,8,4,7,6,5,2,1]=>3 [1,6,8,5,3,7,4,2]=>3 [6,8,1,7,4,3,5,2]=>3 [6,4,8,1,7,3,5,2]=>3 [6,4,8,7,1,5,2,3]=>3 [7,6,4,1,3,8,2,5]=>5 [1,7,5,6,3,2,8,4]=>4 [4,2,1,7,8,5,3,6]=>3 [2,7,4,6,3,1,8,5]=>3 [2,6,8,4,3,7,5,1]=>4 [6,2,4,8,3,7,5,1]=>4 [7,2,6,3,4,1,8,5]=>3 [2,6,7,3,1,4,8,5]=>3 [2,7,1,8,3,5,4,6]=>2 [2,1,7,3,5,8,4,6]=>3 [8,7,1,3,6,2,4,5]=>2 [8,2,1,7,3,5,6,4]=>2 [7,8,2,6,3,1,5,4]=>2 [8,7,2,6,3,5,4,1]=>3 [1,2,8,7,4,5,6,3]=>3 [8,3,7,1,5,6,2,4]=>3 [8,6,1,2,7,5,3,4]=>2 [8,1,6,2,7,4,5,3]=>2 [1,8,5,2,6,7,4,3]=>3 [5,2,1,8,6,7,4,3]=>3 [2,8,5,7,6,4,3,1]=>3 [1,7,8,5,2,6,4,3]=>2 [7,8,1,6,4,2,5,3]=>2 [7,8,6,1,5,3,2,4]=>2 [7,3,8,6,1,5,2,4]=>3 [8,7,6,1,5,3,4,2]=>2 [8,7,1,6,4,5,3,2]=>2 [8,1,7,5,6,4,3,2]=>2 [1,8,6,7,5,4,3,2]=>2 [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]=>2 [2,3,4,5,6,7,9,1,8]=>7 [2,3,4,5,6,7,8,9,1]=>8 [2,3,4,5,6,7,8,1,9]=>7 [2,3,4,5,6,7,1,8,9]=>6 [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]=>2 [7,1,2,3,4,5,6,9,8]=>1 [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]=>0 [3,2,4,5,6,7,8,9,1]=>8 [9,8,7,6,5,4,3,2,1]=>1 [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]=>2 [1,9,8,7,5,6,4,3,2]=>2 [8,7,5,4,6,3,2,1,9]=>3 [8,7,4,6,5,3,2,1,9]=>2 [1,9,8,6,5,7,4,3,2]=>3 [1,9,8,5,7,6,4,3,2]=>2 [9,2,1,3,4,5,6,7,8]=>1 [9,2,3,1,4,5,6,7,8]=>2 [4,2,3,5,6,7,8,9,1]=>8 [3,4,2,5,6,7,8,9,1]=>8 [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]=>3 [8,9,6,7,1,2,3,4,5]=>2 [9,8,6,7,1,2,3,4,5]=>2 [9,8,7,6,1,2,3,4,5]=>1 [9,5,6,7,8,1,2,3,4]=>4 [8,9,5,6,7,1,2,3,4]=>3 [9,8,5,6,7,1,2,3,4]=>3 [9,7,8,5,6,1,2,3,4]=>2 [9,8,7,5,6,1,2,3,4]=>2 [9,8,7,6,5,1,2,3,4]=>1 [7,8,9,4,5,6,1,2,3]=>3 [9,7,8,4,5,6,1,2,3]=>3 [9,8,7,4,5,6,1,2,3]=>3 [8,9,6,7,4,5,1,2,3]=>2 [9,8,6,7,4,5,1,2,3]=>2 [9,8,7,6,4,5,1,2,3]=>2 [9,8,7,6,5,4,1,2,3]=>1 [9,7,8,5,6,3,4,1,2]=>2 [9,8,7,5,6,3,4,1,2]=>2 [9,8,7,6,5,3,4,1,2]=>2 [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]=>2 [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]=>3 [1,7,9,8,6,5,4,3,2]=>2 [8,1,2,3,4,5,6,7,9]=>1 [1,9,2,3,4,5,6,7,8]=>1 [7,8,1,2,3,4,5,6,9]=>2 [1,8,9,2,3,4,5,6,7]=>2 [7,1,8,2,3,4,5,6,9]=>2 [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]=>2 [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]=>3 [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]=>4 [5,6,3,4,1,2,7,8,9]=>2 [5,3,2,6,1,4,7,8,9]=>4 [5,4,3,2,1,6,7,8,9]=>1 [6,2,7,8,9,1,3,4,5]=>5 [6,7,3,4,8,1,2,5,9]=>5 [6,3,2,7,8,1,4,5,9]=>5 [6,4,7,2,5,1,3,8,9]=>3 [6,4,3,2,7,1,5,8,9]=>5 [6,5,4,3,2,1,7,8,9]=>1 [7,4,8,2,5,9,1,3,6]=>6 [7,4,3,2,8,9,1,5,6]=>6 [7,8,5,6,3,4,1,2,9]=>2 [7,5,3,8,2,6,1,4,9]=>4 [7,5,4,3,2,8,1,6,9]=>6 [7,6,5,4,3,2,1,8,9]=>1 [8,6,9,4,7,2,5,1,3]=>3 [8,6,4,3,9,2,7,1,5]=>5 [8,6,5,4,3,2,9,1,7]=>7 [2,1,4,3,6,5,8,7,10,9]=>1 [4,3,2,1,6,5,8,7,10,9]=>1 [6,3,2,5,4,1,8,7,10,9]=>3 [8,3,2,5,4,7,6,1,10,9]=>5 [10,3,2,5,4,7,6,9,8,1]=>7 [2,1,6,5,4,3,8,7,10,9]=>1 [6,5,4,3,2,1,8,7,10,9]=>1 [8,5,4,3,2,7,6,1,10,9]=>5 [10,5,4,3,2,7,6,9,8,1]=>7 [2,1,8,5,4,7,6,3,10,9]=>3 [8,7,4,3,6,5,2,1,10,9]=>3 [10,7,4,3,6,5,2,9,8,1]=>7 [2,1,10,5,4,7,6,9,8,3]=>5 [10,9,4,3,6,5,8,7,2,1]=>5 [8,9,5,6,3,4,10,1,2,7]=>7 [2,1,4,3,8,7,6,5,10,9]=>1 [4,3,2,1,8,7,6,5,10,9]=>1 [8,3,2,7,6,5,4,1,10,9]=>3 [10,3,2,7,6,5,4,9,8,1]=>7 [2,1,8,7,6,5,4,3,10,9]=>1 [8,7,6,5,4,3,2,1,10,9]=>1 [9,7,6,5,4,3,2,10,1,8]=>8 [10,7,6,5,4,3,2,9,8,1]=>7 [2,1,10,7,6,5,4,9,8,3]=>5 [10,9,6,5,4,3,8,7,2,1]=>5 [2,1,4,3,10,7,6,9,8,5]=>3 [4,3,2,1,10,7,6,9,8,5]=>3 [10,3,2,9,6,5,8,7,4,1]=>5 [2,1,10,9,6,5,8,7,4,3]=>3 [10,9,8,5,4,7,6,3,2,1]=>3 [6,7,8,9,10,1,2,3,4,5]=>5 [7,3,2,8,9,10,1,4,5,6]=>6 [8,5,4,3,2,9,10,1,6,7]=>7 [2,1,4,3,6,5,10,9,8,7]=>1 [4,3,2,1,6,5,10,9,8,7]=>1 [6,3,2,5,4,1,10,9,8,7]=>3 [10,3,2,5,4,9,8,7,6,1]=>5 [2,1,6,5,4,3,10,9,8,7]=>1 [6,5,4,3,2,1,10,9,8,7]=>1 [10,5,4,3,2,9,8,7,6,1]=>5 [2,1,10,5,4,9,8,7,6,3]=>3 [10,9,4,3,8,7,6,5,2,1]=>3 [9,7,5,10,3,8,2,6,1,4]=>4 [2,1,4,3,10,9,8,7,6,5]=>1 [4,3,2,1,10,9,8,7,6,5]=>1 [10,3,2,9,8,7,6,5,4,1]=>3 [2,1,10,9,8,7,6,5,4,3]=>1 [10,9,8,7,6,5,4,3,2,1]=>1 [2,3,4,5,6,7,8,9,10,1]=>9 [2,3,4,5,6,7,8,9,1,10]=>8 [10,8,9,5,6,7,1,2,3,4]=>3 [10,8,9,4,5,6,1,2,3,7]=>3 [10,7,8,5,6,9,1,2,3,4]=>5 [10,7,8,4,5,9,1,2,3,6]=>5 [10,6,7,4,5,8,1,2,3,9]=>5 [10,7,8,3,4,9,1,2,5,6]=>5 [10,6,7,3,4,8,1,2,5,9]=>5 [9,8,10,5,6,7,1,2,3,4]=>3 [9,8,10,4,5,6,1,2,3,7]=>3 [9,7,10,5,6,8,1,2,3,4]=>3 [9,7,10,4,5,8,1,2,3,6]=>3 [9,6,10,4,5,7,1,2,3,8]=>3 [9,7,10,3,4,8,1,2,5,6]=>3 [9,6,10,3,4,7,1,2,5,8]=>3 [8,7,9,5,6,10,1,2,3,4]=>6 [8,7,9,4,5,10,1,2,3,6]=>6 [8,6,9,4,5,10,1,2,3,7]=>6 [7,6,8,4,5,9,1,2,3,10]=>6 [8,7,9,3,4,10,1,2,5,6]=>6 [8,6,9,3,4,10,1,2,5,7]=>6 [7,6,8,3,4,9,1,2,5,10]=>6 [9,6,10,5,7,8,1,2,3,4]=>3 [9,6,10,4,7,8,1,2,3,5]=>3 [9,5,10,4,6,7,1,2,3,8]=>3 [9,6,10,3,7,8,1,2,4,5]=>3 [9,5,10,3,6,7,1,2,4,8]=>3 [8,6,9,5,7,10,1,2,3,4]=>6 [8,6,9,4,7,10,1,2,3,5]=>6 [8,5,9,4,6,10,1,2,3,7]=>6 [7,5,8,4,6,9,1,2,3,10]=>6 [8,6,9,3,7,10,1,2,4,5]=>6 [8,5,9,3,6,10,1,2,4,7]=>6 [7,5,8,3,6,9,1,2,4,10]=>6 [8,4,9,3,5,10,1,2,6,7]=>6 [7,4,8,3,5,9,1,2,6,10]=>6 [9,6,10,2,7,8,1,3,4,5]=>3 [9,5,10,2,6,7,1,3,4,8]=>3 [8,6,9,2,7,10,1,3,4,5]=>6 [8,5,9,2,6,10,1,3,4,7]=>6 [7,5,8,2,6,9,1,3,4,10]=>6 [8,4,9,2,5,10,1,3,6,7]=>6 [7,4,8,2,5,9,1,3,6,10]=>6 [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]=>0 [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]=>2 [1,10,9,8,6,7,5,4,3,2]=>2 [10,2,1,3,4,5,6,7,8,9]=>1 [3,2,4,5,6,7,8,9,10,1]=>9 [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]=>2 [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]=>3 [9,10,7,8,1,2,3,4,5,6]=>2 [10,9,7,8,1,2,3,4,5,6]=>2 [10,9,8,7,1,2,3,4,5,6]=>1 [10,6,7,8,9,1,2,3,4,5]=>4 [9,10,6,7,8,1,2,3,4,5]=>3 [10,9,6,7,8,1,2,3,4,5]=>3 [10,8,9,6,7,1,2,3,4,5]=>2 [10,9,8,6,7,1,2,3,4,5]=>2 [10,9,8,7,6,1,2,3,4,5]=>1 [9,10,5,6,7,8,1,2,3,4]=>4 [10,9,5,6,7,8,1,2,3,4]=>4 [8,9,10,5,6,7,1,2,3,4]=>3 [10,9,8,5,6,7,1,2,3,4]=>3 [9,10,7,8,5,6,1,2,3,4]=>2 [10,9,7,8,5,6,1,2,3,4]=>2 [10,9,8,7,5,6,1,2,3,4]=>2 [10,9,8,7,6,5,1,2,3,4]=>1 [10,7,8,9,4,5,6,1,2,3]=>3 [9,10,7,8,4,5,6,1,2,3]=>3 [10,9,7,8,4,5,6,1,2,3]=>3 [10,9,8,7,4,5,6,1,2,3]=>3 [10,8,9,6,7,4,5,1,2,3]=>2 [10,9,8,6,7,4,5,1,2,3]=>2 [10,9,8,7,6,4,5,1,2,3]=>2 [10,9,8,7,6,5,4,1,2,3]=>1 [9,10,7,8,5,6,3,4,1,2]=>2 [10,9,7,8,5,6,3,4,1,2]=>2 [10,9,8,7,5,6,3,4,1,2]=>2 [10,9,8,7,6,5,3,4,1,2]=>2 [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]=>2 [9,1,2,3,4,5,6,7,8,10]=>1 [1,10,2,3,4,5,6,7,8,9]=>1 [8,9,1,2,3,4,5,6,7,10]=>2 [1,9,10,2,3,4,5,6,7,8]=>2 [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]=>3 [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]=>4 [5,6,3,4,1,2,7,8,9,10]=>2 [5,3,2,6,1,4,7,8,9,10]=>4 [5,4,3,2,1,6,7,8,9,10]=>1 [6,2,7,8,9,1,3,4,5,10]=>5 [6,7,3,4,8,1,2,5,9,10]=>5 [6,3,2,7,8,1,4,5,9,10]=>5 [6,4,7,2,5,1,3,8,9,10]=>3 [6,4,3,2,7,1,5,8,9,10]=>5 [6,5,4,3,2,1,7,8,9,10]=>1 [7,8,3,4,9,10,1,2,5,6]=>6 [7,8,9,4,5,6,1,2,3,10]=>3 [7,4,3,2,8,9,1,5,6,10]=>6 [7,8,5,6,3,4,1,2,9,10]=>2 [7,5,3,8,2,6,1,4,9,10]=>4 [7,5,4,3,2,8,1,6,9,10]=>6 [7,6,5,4,3,2,1,8,9,10]=>1 [8,5,9,10,2,6,7,1,3,4]=>4 [8,5,3,9,2,6,10,1,4,7]=>7 [8,6,9,4,7,2,5,1,3,10]=>3 [8,6,4,3,9,2,7,1,5,10]=>5 [8,6,5,4,3,2,9,1,7,10]=>7 [8,7,6,5,4,3,2,1,9,10]=>1 [9,7,5,4,3,10,2,8,1,6]=>6 [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]=>10 [10,1,2,3,4,5,6,7,8,9,11]=>1 [1,11,2,3,4,5,6,7,8,9,10]=>1 [2,1,4,3,6,5,8,7,10,9,12,11]=>1 [2,1,4,3,6,5,8,7,12,11,10,9]=>1 [2,1,4,3,6,5,10,9,8,7,12,11]=>1 [2,1,4,3,6,5,12,9,8,11,10,7]=>3 [2,1,4,3,6,5,12,11,10,9,8,7]=>1 [2,1,4,3,8,7,6,5,10,9,12,11]=>1 [2,1,4,3,8,7,6,5,12,11,10,9]=>1 [2,1,4,3,10,7,6,9,8,5,12,11]=>3 [2,1,4,3,12,7,6,9,8,11,10,5]=>5 [2,1,4,3,12,7,6,11,10,9,8,5]=>3 [2,1,4,3,10,9,8,7,6,5,12,11]=>1 [2,1,4,3,12,9,8,7,6,11,10,5]=>5 [2,1,4,3,12,11,8,7,10,9,6,5]=>3 [2,1,4,3,12,11,10,9,8,7,6,5]=>1 [2,1,6,5,4,3,8,7,10,9,12,11]=>1 [2,1,6,5,4,3,8,7,12,11,10,9]=>1 [2,1,6,5,4,3,10,9,8,7,12,11]=>1 [2,1,6,5,4,3,12,9,8,11,10,7]=>3 [2,1,6,5,4,3,12,11,10,9,8,7]=>1 [2,1,8,5,4,7,6,3,10,9,12,11]=>3 [2,1,8,5,4,7,6,3,12,11,10,9]=>3 [2,1,10,5,4,7,6,9,8,3,12,11]=>5 [2,1,12,5,4,7,6,9,8,11,10,3]=>7 [2,1,12,5,4,7,6,11,10,9,8,3]=>5 [2,1,10,5,4,9,8,7,6,3,12,11]=>3 [2,1,12,5,4,9,8,7,6,11,10,3]=>7 [2,1,12,5,4,11,8,7,10,9,6,3]=>5 [2,1,12,5,4,11,10,9,8,7,6,3]=>3 [2,1,8,7,6,5,4,3,10,9,12,11]=>1 [2,1,8,7,6,5,4,3,12,11,10,9]=>1 [2,1,10,7,6,5,4,9,8,3,12,11]=>5 [2,1,12,7,6,5,4,9,8,11,10,3]=>7 [2,1,12,7,6,5,4,11,10,9,8,3]=>5 [2,1,10,9,6,5,8,7,4,3,12,11]=>3 [2,1,12,9,6,5,8,7,4,11,10,3]=>7 [2,1,12,11,6,5,8,7,10,9,4,3]=>5 [2,1,12,11,6,5,10,9,8,7,4,3]=>3 [2,1,10,9,8,7,6,5,4,3,12,11]=>1 [2,1,12,9,8,7,6,5,4,11,10,3]=>7 [2,1,12,11,8,7,6,5,10,9,4,3]=>5 [2,1,12,11,10,7,6,9,8,5,4,3]=>3 [2,1,12,11,10,9,8,7,6,5,4,3]=>1 [4,3,2,1,6,5,8,7,10,9,12,11]=>1 [4,3,2,1,6,5,8,7,12,11,10,9]=>1 [4,3,2,1,6,5,10,9,8,7,12,11]=>1 [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]=>1 [4,3,2,1,8,7,6,5,10,9,12,11]=>1 [4,3,2,1,8,7,6,5,12,11,10,9]=>1 [4,3,2,1,10,7,6,9,8,5,12,11]=>3 [4,3,2,1,12,7,6,9,8,11,10,5]=>5 [4,3,2,1,12,7,6,11,10,9,8,5]=>3 [4,3,2,1,10,9,8,7,6,5,12,11]=>1 [4,3,2,1,12,9,8,7,6,11,10,5]=>5 [4,3,2,1,12,11,8,7,10,9,6,5]=>3 [4,3,2,1,12,11,10,9,8,7,6,5]=>1 [6,3,2,5,4,1,8,7,10,9,12,11]=>3 [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]=>3 [6,3,2,5,4,1,12,9,8,11,10,7]=>3 [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]=>5 [8,3,2,5,4,7,6,1,12,11,10,9]=>5 [10,3,2,5,4,7,6,9,8,1,12,11]=>7 [12,3,2,5,4,7,6,9,8,11,10,1]=>9 [12,3,2,5,4,7,6,11,10,9,8,1]=>7 [10,3,2,5,4,9,8,7,6,1,12,11]=>5 [12,3,2,5,4,9,8,7,6,11,10,1]=>9 [12,3,2,5,4,11,8,7,10,9,6,1]=>7 [12,3,2,5,4,11,10,9,8,7,6,1]=>5 [8,3,2,7,6,5,4,1,10,9,12,11]=>3 [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]=>7 [12,3,2,7,6,5,4,9,8,11,10,1]=>9 [12,3,2,7,6,5,4,11,10,9,8,1]=>7 [10,3,2,9,6,5,8,7,4,1,12,11]=>5 [12,3,2,9,6,5,8,7,4,11,10,1]=>9 [12,3,2,11,6,5,8,7,10,9,4,1]=>7 [12,3,2,11,6,5,10,9,8,7,4,1]=>5 [10,3,2,9,8,7,6,5,4,1,12,11]=>3 [12,3,2,9,8,7,6,5,4,11,10,1]=>9 [12,3,2,11,8,7,6,5,10,9,4,1]=>7 [12,3,2,11,10,7,6,9,8,5,4,1]=>5 [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]=>1 [6,5,4,3,2,1,8,7,12,11,10,9]=>1 [6,5,4,3,2,1,10,9,8,7,12,11]=>1 [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]=>1 [8,5,4,3,2,7,6,1,10,9,12,11]=>5 [8,5,4,3,2,7,6,1,12,11,10,9]=>5 [10,5,4,3,2,7,6,9,8,1,12,11]=>7 [12,5,4,3,2,7,6,9,8,11,10,1]=>9 [12,5,4,3,2,7,6,11,10,9,8,1]=>7 [10,5,4,3,2,9,8,7,6,1,12,11]=>5 [12,5,4,3,2,9,8,7,6,11,10,1]=>9 [12,5,4,3,2,11,8,7,10,9,6,1]=>7 [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]=>3 [8,7,4,3,6,5,2,1,12,11,10,9]=>3 [10,7,4,3,6,5,2,9,8,1,12,11]=>7 [12,7,4,3,6,5,2,9,8,11,10,1]=>9 [12,7,4,3,6,5,2,11,10,9,8,1]=>7 [10,9,4,3,6,5,8,7,2,1,12,11]=>5 [12,9,4,3,6,5,8,7,2,11,10,1]=>9 [12,11,4,3,6,5,8,7,10,9,2,1]=>7 [12,11,4,3,6,5,10,9,8,7,2,1]=>5 [10,9,4,3,8,7,6,5,2,1,12,11]=>3 [12,9,4,3,8,7,6,5,2,11,10,1]=>9 [12,11,4,3,8,7,6,5,10,9,2,1]=>7 [12,11,4,3,10,7,6,9,8,5,2,1]=>5 [12,11,4,3,10,9,8,7,6,5,2,1]=>3 [8,7,6,5,4,3,2,1,10,9,12,11]=>1 [8,7,6,5,4,3,2,1,12,11,10,9]=>1 [10,7,6,5,4,3,2,9,8,1,12,11]=>7 [12,7,6,5,4,3,2,9,8,11,10,1]=>9 [12,7,6,5,4,3,2,11,10,9,8,1]=>7 [10,9,6,5,4,3,8,7,2,1,12,11]=>5 [12,9,6,5,4,3,8,7,2,11,10,1]=>9 [12,11,6,5,4,3,8,7,10,9,2,1]=>7 [12,11,6,5,4,3,10,9,8,7,2,1]=>5 [10,9,8,5,4,7,6,3,2,1,12,11]=>3 [12,9,8,5,4,7,6,3,2,11,10,1]=>9 [12,11,8,5,4,7,6,3,10,9,2,1]=>7 [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]=>3 [10,9,8,7,6,5,4,3,2,1,12,11]=>1 [12,9,8,7,6,5,4,3,2,11,10,1]=>9 [12,11,8,7,6,5,4,3,10,9,2,1]=>7 [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]=>3 [12,11,10,9,8,7,6,5,4,3,2,1]=>1 [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 number of stack-sorts needed to sort a permutation.
A permutation is (West) $t$-stack sortable if it is sortable using $t$ stacks in series.
Let $W_t(n,k)$ be the number of permutations of size $n$
with $k$ descents which are $t$-stack sortable. Then the polynomials $W_{n,t}(x) = \sum_{k=0}^n W_t(n,k)x^k$
are symmetric and unimodal.
We have $W_{n,1}(x) = A_n(x)$, the Eulerian polynomials. One can show that $W_{n,1}(x)$ and $W_{n,2}(x)$ are real-rooted.
Precisely the permutations that avoid the pattern $231$ have statistic at most $1$, see [3]. These are counted by $\frac{1}{n+1}\binom{2n}{n}$ (OEIS:A000108). Precisely the permutations that avoid the pattern $2341$ and the barred pattern $3\bar 5241$ have statistic at most $2$, see [4]. These are counted by $\frac{2(3n)!}{(n+1)!(2n+1)!}$ (OEIS:A000139).
References
[1] Bóna, Miklós A survey of stack-sorting disciplines MathSciNet:2028290
[2] Úlfarsson, H. Describing West-3-stack-sortable permutations with permutation patterns arXiv:1110.1219
[3] Knuth, D. E. The art of computer programming. Volume 3 MathSciNet:0445948
[4] Zeilberger, D. A proof of Julian West's conjecture that the number of two-stack-sortable permutations of length $n$ is $2(3n)!/((n+1)!(2n+1)!)$ MathSciNet:1168135
Code
def stack_sort(x):
    stack = []
    result = []
    for e in x:
        while stack and e > stack[-1]:
            result += [stack.pop()]
        stack.append(e)
    while stack:
        result += [stack.pop()]
    return Permutation(result)

def statistic(x):
    i = 0
    id = Permutations(x.size()).identity()
    while x != id:
        x = stack_sort(x)
        i += 1
    return i
Created
Aug 05, 2012 at 10:27 by Per Alexandersson
Updated
Jan 17, 2018 at 08:56 by Martin Rubey