edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>2 [2,1]=>2 [1,2,3]=>3 [1,3,2]=>2 [2,1,3]=>3 [2,3,1]=>3 [3,1,2]=>2 [3,2,1]=>3 [1,2,3,4]=>4 [1,2,4,3]=>3 [1,3,2,4]=>3 [1,3,4,2]=>3 [1,4,2,3]=>3 [1,4,3,2]=>3 [2,1,3,4]=>4 [2,1,4,3]=>3 [2,3,1,4]=>4 [2,3,4,1]=>4 [2,4,1,3]=>3 [2,4,3,1]=>3 [3,1,2,4]=>3 [3,1,4,2]=>3 [3,2,1,4]=>4 [3,2,4,1]=>4 [3,4,1,2]=>3 [3,4,2,1]=>4 [4,1,2,3]=>3 [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]=>5 [1,2,3,5,4]=>4 [1,2,4,3,5]=>4 [1,2,4,5,3]=>4 [1,2,5,3,4]=>4 [1,2,5,4,3]=>3 [1,3,2,4,5]=>4 [1,3,2,5,4]=>3 [1,3,4,2,5]=>4 [1,3,4,5,2]=>4 [1,3,5,2,4]=>3 [1,3,5,4,2]=>3 [1,4,2,3,5]=>4 [1,4,2,5,3]=>3 [1,4,3,2,5]=>4 [1,4,3,5,2]=>4 [1,4,5,2,3]=>3 [1,4,5,3,2]=>4 [1,5,2,3,4]=>4 [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]=>5 [2,1,3,5,4]=>4 [2,1,4,3,5]=>4 [2,1,4,5,3]=>4 [2,1,5,3,4]=>4 [2,1,5,4,3]=>3 [2,3,1,4,5]=>5 [2,3,1,5,4]=>4 [2,3,4,1,5]=>5 [2,3,4,5,1]=>5 [2,3,5,1,4]=>4 [2,3,5,4,1]=>4 [2,4,1,3,5]=>4 [2,4,1,5,3]=>4 [2,4,3,1,5]=>4 [2,4,3,5,1]=>4 [2,4,5,1,3]=>4 [2,4,5,3,1]=>4 [2,5,1,3,4]=>4 [2,5,1,4,3]=>3 [2,5,3,1,4]=>4 [2,5,3,4,1]=>4 [2,5,4,1,3]=>3 [2,5,4,3,1]=>4 [3,1,2,4,5]=>4 [3,1,2,5,4]=>3 [3,1,4,2,5]=>4 [3,1,4,5,2]=>4 [3,1,5,2,4]=>3 [3,1,5,4,2]=>3 [3,2,1,4,5]=>5 [3,2,1,5,4]=>4 [3,2,4,1,5]=>5 [3,2,4,5,1]=>5 [3,2,5,1,4]=>4 [3,2,5,4,1]=>4 [3,4,1,2,5]=>4 [3,4,1,5,2]=>4 [3,4,2,1,5]=>5 [3,4,2,5,1]=>5 [3,4,5,1,2]=>4 [3,4,5,2,1]=>5 [3,5,1,2,4]=>3 [3,5,1,4,2]=>3 [3,5,2,1,4]=>4 [3,5,2,4,1]=>4 [3,5,4,1,2]=>3 [3,5,4,2,1]=>4 [4,1,2,3,5]=>4 [4,1,2,5,3]=>3 [4,1,3,2,5]=>4 [4,1,3,5,2]=>4 [4,1,5,2,3]=>3 [4,1,5,3,2]=>4 [4,2,1,3,5]=>4 [4,2,1,5,3]=>4 [4,2,3,1,5]=>4 [4,2,3,5,1]=>4 [4,2,5,1,3]=>4 [4,2,5,3,1]=>4 [4,3,1,2,5]=>4 [4,3,1,5,2]=>4 [4,3,2,1,5]=>5 [4,3,2,5,1]=>5 [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]=>4 [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]=>4 [5,2,1,4,3]=>3 [5,2,3,1,4]=>4 [5,2,3,4,1]=>4 [5,2,4,1,3]=>3 [5,2,4,3,1]=>4 [5,3,1,2,4]=>3 [5,3,1,4,2]=>3 [5,3,2,1,4]=>4 [5,3,2,4,1]=>4 [5,3,4,1,2]=>3 [5,3,4,2,1]=>4 [5,4,1,2,3]=>3 [5,4,1,3,2]=>4 [5,4,2,1,3]=>4 [5,4,2,3,1]=>4 [5,4,3,1,2]=>4 [5,4,3,2,1]=>5 [1,2,3,4,5,6]=>6 [1,2,3,4,6,5]=>5 [1,2,3,5,4,6]=>5 [1,2,3,5,6,4]=>5 [1,2,3,6,4,5]=>5 [1,2,3,6,5,4]=>4 [1,2,4,3,5,6]=>5 [1,2,4,3,6,5]=>4 [1,2,4,5,3,6]=>5 [1,2,4,5,6,3]=>5 [1,2,4,6,3,5]=>4 [1,2,4,6,5,3]=>4 [1,2,5,3,4,6]=>5 [1,2,5,3,6,4]=>4 [1,2,5,4,3,6]=>4 [1,2,5,4,6,3]=>4 [1,2,5,6,3,4]=>4 [1,2,5,6,4,3]=>4 [1,2,6,3,4,5]=>5 [1,2,6,3,5,4]=>4 [1,2,6,4,3,5]=>4 [1,2,6,4,5,3]=>4 [1,2,6,5,3,4]=>4 [1,2,6,5,4,3]=>4 [1,3,2,4,5,6]=>5 [1,3,2,4,6,5]=>4 [1,3,2,5,4,6]=>4 [1,3,2,5,6,4]=>4 [1,3,2,6,4,5]=>4 [1,3,2,6,5,4]=>3 [1,3,4,2,5,6]=>5 [1,3,4,2,6,5]=>4 [1,3,4,5,2,6]=>5 [1,3,4,5,6,2]=>5 [1,3,4,6,2,5]=>4 [1,3,4,6,5,2]=>4 [1,3,5,2,4,6]=>4 [1,3,5,2,6,4]=>4 [1,3,5,4,2,6]=>4 [1,3,5,4,6,2]=>4 [1,3,5,6,2,4]=>4 [1,3,5,6,4,2]=>4 [1,3,6,2,4,5]=>4 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>4 [1,3,6,4,5,2]=>4 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>4 [1,4,2,3,5,6]=>5 [1,4,2,3,6,5]=>4 [1,4,2,5,3,6]=>4 [1,4,2,5,6,3]=>4 [1,4,2,6,3,5]=>4 [1,4,2,6,5,3]=>3 [1,4,3,2,5,6]=>5 [1,4,3,2,6,5]=>4 [1,4,3,5,2,6]=>5 [1,4,3,5,6,2]=>5 [1,4,3,6,2,5]=>4 [1,4,3,6,5,2]=>4 [1,4,5,2,3,6]=>4 [1,4,5,2,6,3]=>4 [1,4,5,3,2,6]=>5 [1,4,5,3,6,2]=>5 [1,4,5,6,2,3]=>4 [1,4,5,6,3,2]=>5 [1,4,6,2,3,5]=>4 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>4 [1,4,6,3,5,2]=>4 [1,4,6,5,2,3]=>3 [1,4,6,5,3,2]=>4 [1,5,2,3,4,6]=>5 [1,5,2,3,6,4]=>4 [1,5,2,4,3,6]=>4 [1,5,2,4,6,3]=>4 [1,5,2,6,3,4]=>4 [1,5,2,6,4,3]=>4 [1,5,3,2,4,6]=>4 [1,5,3,2,6,4]=>4 [1,5,3,4,2,6]=>4 [1,5,3,4,6,2]=>4 [1,5,3,6,2,4]=>4 [1,5,3,6,4,2]=>4 [1,5,4,2,3,6]=>4 [1,5,4,2,6,3]=>4 [1,5,4,3,2,6]=>5 [1,5,4,3,6,2]=>5 [1,5,4,6,2,3]=>4 [1,5,4,6,3,2]=>5 [1,5,6,2,3,4]=>4 [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]=>5 [1,6,2,3,5,4]=>4 [1,6,2,4,3,5]=>4 [1,6,2,4,5,3]=>4 [1,6,2,5,3,4]=>4 [1,6,2,5,4,3]=>4 [1,6,3,2,4,5]=>4 [1,6,3,2,5,4]=>3 [1,6,3,4,2,5]=>4 [1,6,3,4,5,2]=>4 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>4 [1,6,4,2,3,5]=>4 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>4 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>4 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>4 [1,6,5,3,2,4]=>4 [1,6,5,3,4,2]=>4 [1,6,5,4,2,3]=>4 [1,6,5,4,3,2]=>5 [2,1,3,4,5,6]=>6 [2,1,3,4,6,5]=>5 [2,1,3,5,4,6]=>5 [2,1,3,5,6,4]=>5 [2,1,3,6,4,5]=>5 [2,1,3,6,5,4]=>4 [2,1,4,3,5,6]=>5 [2,1,4,3,6,5]=>4 [2,1,4,5,3,6]=>5 [2,1,4,5,6,3]=>5 [2,1,4,6,3,5]=>4 [2,1,4,6,5,3]=>4 [2,1,5,3,4,6]=>5 [2,1,5,3,6,4]=>4 [2,1,5,4,3,6]=>4 [2,1,5,4,6,3]=>4 [2,1,5,6,3,4]=>4 [2,1,5,6,4,3]=>4 [2,1,6,3,4,5]=>5 [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]=>4 [2,3,1,4,5,6]=>6 [2,3,1,4,6,5]=>5 [2,3,1,5,4,6]=>5 [2,3,1,5,6,4]=>5 [2,3,1,6,4,5]=>5 [2,3,1,6,5,4]=>4 [2,3,4,1,5,6]=>6 [2,3,4,1,6,5]=>5 [2,3,4,5,1,6]=>6 [2,3,4,5,6,1]=>6 [2,3,4,6,1,5]=>5 [2,3,4,6,5,1]=>5 [2,3,5,1,4,6]=>5 [2,3,5,1,6,4]=>5 [2,3,5,4,1,6]=>5 [2,3,5,4,6,1]=>5 [2,3,5,6,1,4]=>5 [2,3,5,6,4,1]=>5 [2,3,6,1,4,5]=>5 [2,3,6,1,5,4]=>4 [2,3,6,4,1,5]=>5 [2,3,6,4,5,1]=>5 [2,3,6,5,1,4]=>4 [2,3,6,5,4,1]=>4 [2,4,1,3,5,6]=>5 [2,4,1,3,6,5]=>4 [2,4,1,5,3,6]=>5 [2,4,1,5,6,3]=>5 [2,4,1,6,3,5]=>4 [2,4,1,6,5,3]=>4 [2,4,3,1,5,6]=>5 [2,4,3,1,6,5]=>4 [2,4,3,5,1,6]=>5 [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]=>5 [2,4,5,1,6,3]=>5 [2,4,5,3,1,6]=>5 [2,4,5,3,6,1]=>5 [2,4,5,6,1,3]=>5 [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]=>4 [2,5,1,3,4,6]=>5 [2,5,1,3,6,4]=>4 [2,5,1,4,3,6]=>4 [2,5,1,4,6,3]=>4 [2,5,1,6,3,4]=>4 [2,5,1,6,4,3]=>4 [2,5,3,1,4,6]=>5 [2,5,3,1,6,4]=>4 [2,5,3,4,1,6]=>5 [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]=>4 [2,5,4,1,6,3]=>4 [2,5,4,3,1,6]=>5 [2,5,4,3,6,1]=>5 [2,5,4,6,1,3]=>4 [2,5,4,6,3,1]=>5 [2,5,6,1,3,4]=>4 [2,5,6,1,4,3]=>4 [2,5,6,3,1,4]=>4 [2,5,6,3,4,1]=>4 [2,5,6,4,1,3]=>4 [2,5,6,4,3,1]=>5 [2,6,1,3,4,5]=>5 [2,6,1,3,5,4]=>4 [2,6,1,4,3,5]=>4 [2,6,1,4,5,3]=>4 [2,6,1,5,3,4]=>4 [2,6,1,5,4,3]=>4 [2,6,3,1,4,5]=>5 [2,6,3,1,5,4]=>4 [2,6,3,4,1,5]=>5 [2,6,3,4,5,1]=>5 [2,6,3,5,1,4]=>4 [2,6,3,5,4,1]=>4 [2,6,4,1,3,5]=>4 [2,6,4,1,5,3]=>4 [2,6,4,3,1,5]=>4 [2,6,4,3,5,1]=>4 [2,6,4,5,1,3]=>4 [2,6,4,5,3,1]=>4 [2,6,5,1,3,4]=>4 [2,6,5,1,4,3]=>4 [2,6,5,3,1,4]=>4 [2,6,5,3,4,1]=>4 [2,6,5,4,1,3]=>4 [2,6,5,4,3,1]=>5 [3,1,2,4,5,6]=>5 [3,1,2,4,6,5]=>4 [3,1,2,5,4,6]=>4 [3,1,2,5,6,4]=>4 [3,1,2,6,4,5]=>4 [3,1,2,6,5,4]=>3 [3,1,4,2,5,6]=>5 [3,1,4,2,6,5]=>4 [3,1,4,5,2,6]=>5 [3,1,4,5,6,2]=>5 [3,1,4,6,2,5]=>4 [3,1,4,6,5,2]=>4 [3,1,5,2,4,6]=>4 [3,1,5,2,6,4]=>4 [3,1,5,4,2,6]=>4 [3,1,5,4,6,2]=>4 [3,1,5,6,2,4]=>4 [3,1,5,6,4,2]=>4 [3,1,6,2,4,5]=>4 [3,1,6,2,5,4]=>3 [3,1,6,4,2,5]=>4 [3,1,6,4,5,2]=>4 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>4 [3,2,1,4,5,6]=>6 [3,2,1,4,6,5]=>5 [3,2,1,5,4,6]=>5 [3,2,1,5,6,4]=>5 [3,2,1,6,4,5]=>5 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>6 [3,2,4,1,6,5]=>5 [3,2,4,5,1,6]=>6 [3,2,4,5,6,1]=>6 [3,2,4,6,1,5]=>5 [3,2,4,6,5,1]=>5 [3,2,5,1,4,6]=>5 [3,2,5,1,6,4]=>5 [3,2,5,4,1,6]=>5 [3,2,5,4,6,1]=>5 [3,2,5,6,1,4]=>5 [3,2,5,6,4,1]=>5 [3,2,6,1,4,5]=>5 [3,2,6,1,5,4]=>4 [3,2,6,4,1,5]=>5 [3,2,6,4,5,1]=>5 [3,2,6,5,1,4]=>4 [3,2,6,5,4,1]=>4 [3,4,1,2,5,6]=>5 [3,4,1,2,6,5]=>4 [3,4,1,5,2,6]=>5 [3,4,1,5,6,2]=>5 [3,4,1,6,2,5]=>4 [3,4,1,6,5,2]=>4 [3,4,2,1,5,6]=>6 [3,4,2,1,6,5]=>5 [3,4,2,5,1,6]=>6 [3,4,2,5,6,1]=>6 [3,4,2,6,1,5]=>5 [3,4,2,6,5,1]=>5 [3,4,5,1,2,6]=>5 [3,4,5,1,6,2]=>5 [3,4,5,2,1,6]=>6 [3,4,5,2,6,1]=>6 [3,4,5,6,1,2]=>5 [3,4,5,6,2,1]=>6 [3,4,6,1,2,5]=>4 [3,4,6,1,5,2]=>4 [3,4,6,2,1,5]=>5 [3,4,6,2,5,1]=>5 [3,4,6,5,1,2]=>4 [3,4,6,5,2,1]=>5 [3,5,1,2,4,6]=>4 [3,5,1,2,6,4]=>4 [3,5,1,4,2,6]=>4 [3,5,1,4,6,2]=>4 [3,5,1,6,2,4]=>4 [3,5,1,6,4,2]=>4 [3,5,2,1,4,6]=>5 [3,5,2,1,6,4]=>5 [3,5,2,4,1,6]=>5 [3,5,2,4,6,1]=>5 [3,5,2,6,1,4]=>5 [3,5,2,6,4,1]=>5 [3,5,4,1,2,6]=>4 [3,5,4,1,6,2]=>4 [3,5,4,2,1,6]=>5 [3,5,4,2,6,1]=>5 [3,5,4,6,1,2]=>4 [3,5,4,6,2,1]=>5 [3,5,6,1,2,4]=>4 [3,5,6,1,4,2]=>4 [3,5,6,2,1,4]=>5 [3,5,6,2,4,1]=>5 [3,5,6,4,1,2]=>4 [3,5,6,4,2,1]=>5 [3,6,1,2,4,5]=>4 [3,6,1,2,5,4]=>3 [3,6,1,4,2,5]=>4 [3,6,1,4,5,2]=>4 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>4 [3,6,2,1,4,5]=>5 [3,6,2,1,5,4]=>4 [3,6,2,4,1,5]=>5 [3,6,2,4,5,1]=>5 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>4 [3,6,4,1,2,5]=>4 [3,6,4,1,5,2]=>4 [3,6,4,2,1,5]=>5 [3,6,4,2,5,1]=>5 [3,6,4,5,1,2]=>4 [3,6,4,5,2,1]=>5 [3,6,5,1,2,4]=>3 [3,6,5,1,4,2]=>4 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>4 [3,6,5,4,1,2]=>4 [3,6,5,4,2,1]=>5 [4,1,2,3,5,6]=>5 [4,1,2,3,6,5]=>4 [4,1,2,5,3,6]=>4 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>4 [4,1,2,6,5,3]=>3 [4,1,3,2,5,6]=>5 [4,1,3,2,6,5]=>4 [4,1,3,5,2,6]=>5 [4,1,3,5,6,2]=>5 [4,1,3,6,2,5]=>4 [4,1,3,6,5,2]=>4 [4,1,5,2,3,6]=>4 [4,1,5,2,6,3]=>4 [4,1,5,3,2,6]=>5 [4,1,5,3,6,2]=>5 [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]=>3 [4,1,6,3,2,5]=>4 [4,1,6,3,5,2]=>4 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>5 [4,2,1,3,6,5]=>4 [4,2,1,5,3,6]=>5 [4,2,1,5,6,3]=>5 [4,2,1,6,3,5]=>4 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>5 [4,2,3,1,6,5]=>4 [4,2,3,5,1,6]=>5 [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]=>5 [4,2,5,1,6,3]=>5 [4,2,5,3,1,6]=>5 [4,2,5,3,6,1]=>5 [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]=>4 [4,2,6,3,1,5]=>4 [4,2,6,3,5,1]=>4 [4,2,6,5,1,3]=>4 [4,2,6,5,3,1]=>4 [4,3,1,2,5,6]=>5 [4,3,1,2,6,5]=>4 [4,3,1,5,2,6]=>5 [4,3,1,5,6,2]=>5 [4,3,1,6,2,5]=>4 [4,3,1,6,5,2]=>4 [4,3,2,1,5,6]=>6 [4,3,2,1,6,5]=>5 [4,3,2,5,1,6]=>6 [4,3,2,5,6,1]=>6 [4,3,2,6,1,5]=>5 [4,3,2,6,5,1]=>5 [4,3,5,1,2,6]=>5 [4,3,5,1,6,2]=>5 [4,3,5,2,1,6]=>6 [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]=>4 [4,3,6,1,5,2]=>4 [4,3,6,2,1,5]=>5 [4,3,6,2,5,1]=>5 [4,3,6,5,1,2]=>4 [4,3,6,5,2,1]=>5 [4,5,1,2,3,6]=>4 [4,5,1,2,6,3]=>4 [4,5,1,3,2,6]=>5 [4,5,1,3,6,2]=>5 [4,5,1,6,2,3]=>4 [4,5,1,6,3,2]=>5 [4,5,2,1,3,6]=>5 [4,5,2,1,6,3]=>5 [4,5,2,3,1,6]=>5 [4,5,2,3,6,1]=>5 [4,5,2,6,1,3]=>5 [4,5,2,6,3,1]=>5 [4,5,3,1,2,6]=>5 [4,5,3,1,6,2]=>5 [4,5,3,2,1,6]=>6 [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]=>4 [4,5,6,1,3,2]=>5 [4,5,6,2,1,3]=>5 [4,5,6,2,3,1]=>5 [4,5,6,3,1,2]=>5 [4,5,6,3,2,1]=>6 [4,6,1,2,3,5]=>4 [4,6,1,2,5,3]=>3 [4,6,1,3,2,5]=>4 [4,6,1,3,5,2]=>4 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>4 [4,6,2,1,3,5]=>4 [4,6,2,1,5,3]=>4 [4,6,2,3,1,5]=>4 [4,6,2,3,5,1]=>4 [4,6,2,5,1,3]=>4 [4,6,2,5,3,1]=>4 [4,6,3,1,2,5]=>4 [4,6,3,1,5,2]=>4 [4,6,3,2,1,5]=>5 [4,6,3,2,5,1]=>5 [4,6,3,5,1,2]=>4 [4,6,3,5,2,1]=>5 [4,6,5,1,2,3]=>3 [4,6,5,1,3,2]=>4 [4,6,5,2,1,3]=>4 [4,6,5,2,3,1]=>4 [4,6,5,3,1,2]=>4 [4,6,5,3,2,1]=>5 [5,1,2,3,4,6]=>5 [5,1,2,3,6,4]=>4 [5,1,2,4,3,6]=>4 [5,1,2,4,6,3]=>4 [5,1,2,6,3,4]=>4 [5,1,2,6,4,3]=>4 [5,1,3,2,4,6]=>4 [5,1,3,2,6,4]=>4 [5,1,3,4,2,6]=>4 [5,1,3,4,6,2]=>4 [5,1,3,6,2,4]=>4 [5,1,3,6,4,2]=>4 [5,1,4,2,3,6]=>4 [5,1,4,2,6,3]=>4 [5,1,4,3,2,6]=>5 [5,1,4,3,6,2]=>5 [5,1,4,6,2,3]=>4 [5,1,4,6,3,2]=>5 [5,1,6,2,3,4]=>4 [5,1,6,2,4,3]=>4 [5,1,6,3,2,4]=>4 [5,1,6,3,4,2]=>4 [5,1,6,4,2,3]=>4 [5,1,6,4,3,2]=>5 [5,2,1,3,4,6]=>5 [5,2,1,3,6,4]=>4 [5,2,1,4,3,6]=>4 [5,2,1,4,6,3]=>4 [5,2,1,6,3,4]=>4 [5,2,1,6,4,3]=>4 [5,2,3,1,4,6]=>5 [5,2,3,1,6,4]=>4 [5,2,3,4,1,6]=>5 [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]=>4 [5,2,4,1,6,3]=>4 [5,2,4,3,1,6]=>5 [5,2,4,3,6,1]=>5 [5,2,4,6,1,3]=>4 [5,2,4,6,3,1]=>5 [5,2,6,1,3,4]=>4 [5,2,6,1,4,3]=>4 [5,2,6,3,1,4]=>4 [5,2,6,3,4,1]=>4 [5,2,6,4,1,3]=>4 [5,2,6,4,3,1]=>5 [5,3,1,2,4,6]=>4 [5,3,1,2,6,4]=>4 [5,3,1,4,2,6]=>4 [5,3,1,4,6,2]=>4 [5,3,1,6,2,4]=>4 [5,3,1,6,4,2]=>4 [5,3,2,1,4,6]=>5 [5,3,2,1,6,4]=>5 [5,3,2,4,1,6]=>5 [5,3,2,4,6,1]=>5 [5,3,2,6,1,4]=>5 [5,3,2,6,4,1]=>5 [5,3,4,1,2,6]=>4 [5,3,4,1,6,2]=>4 [5,3,4,2,1,6]=>5 [5,3,4,2,6,1]=>5 [5,3,4,6,1,2]=>4 [5,3,4,6,2,1]=>5 [5,3,6,1,2,4]=>4 [5,3,6,1,4,2]=>4 [5,3,6,2,1,4]=>5 [5,3,6,2,4,1]=>5 [5,3,6,4,1,2]=>4 [5,3,6,4,2,1]=>5 [5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>4 [5,4,1,3,2,6]=>5 [5,4,1,3,6,2]=>5 [5,4,1,6,2,3]=>4 [5,4,1,6,3,2]=>5 [5,4,2,1,3,6]=>5 [5,4,2,1,6,3]=>5 [5,4,2,3,1,6]=>5 [5,4,2,3,6,1]=>5 [5,4,2,6,1,3]=>5 [5,4,2,6,3,1]=>5 [5,4,3,1,2,6]=>5 [5,4,3,1,6,2]=>5 [5,4,3,2,1,6]=>6 [5,4,3,2,6,1]=>6 [5,4,3,6,1,2]=>5 [5,4,3,6,2,1]=>6 [5,4,6,1,2,3]=>4 [5,4,6,1,3,2]=>5 [5,4,6,2,1,3]=>5 [5,4,6,2,3,1]=>5 [5,4,6,3,1,2]=>5 [5,4,6,3,2,1]=>6 [5,6,1,2,3,4]=>4 [5,6,1,2,4,3]=>4 [5,6,1,3,2,4]=>4 [5,6,1,3,4,2]=>4 [5,6,1,4,2,3]=>4 [5,6,1,4,3,2]=>5 [5,6,2,1,3,4]=>4 [5,6,2,1,4,3]=>4 [5,6,2,3,1,4]=>4 [5,6,2,3,4,1]=>4 [5,6,2,4,1,3]=>4 [5,6,2,4,3,1]=>5 [5,6,3,1,2,4]=>4 [5,6,3,1,4,2]=>4 [5,6,3,2,1,4]=>5 [5,6,3,2,4,1]=>5 [5,6,3,4,1,2]=>4 [5,6,3,4,2,1]=>5 [5,6,4,1,2,3]=>4 [5,6,4,1,3,2]=>5 [5,6,4,2,1,3]=>5 [5,6,4,2,3,1]=>5 [5,6,4,3,1,2]=>5 [5,6,4,3,2,1]=>6 [6,1,2,3,4,5]=>5 [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]=>4 [6,1,3,2,4,5]=>4 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>4 [6,1,3,4,5,2]=>4 [6,1,3,5,2,4]=>3 [6,1,3,5,4,2]=>4 [6,1,4,2,3,5]=>4 [6,1,4,2,5,3]=>3 [6,1,4,3,2,5]=>4 [6,1,4,3,5,2]=>4 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>4 [6,1,5,2,3,4]=>4 [6,1,5,2,4,3]=>4 [6,1,5,3,2,4]=>4 [6,1,5,3,4,2]=>4 [6,1,5,4,2,3]=>4 [6,1,5,4,3,2]=>5 [6,2,1,3,4,5]=>5 [6,2,1,3,5,4]=>4 [6,2,1,4,3,5]=>4 [6,2,1,4,5,3]=>4 [6,2,1,5,3,4]=>4 [6,2,1,5,4,3]=>4 [6,2,3,1,4,5]=>5 [6,2,3,1,5,4]=>4 [6,2,3,4,1,5]=>5 [6,2,3,4,5,1]=>5 [6,2,3,5,1,4]=>4 [6,2,3,5,4,1]=>4 [6,2,4,1,3,5]=>4 [6,2,4,1,5,3]=>4 [6,2,4,3,1,5]=>4 [6,2,4,3,5,1]=>4 [6,2,4,5,1,3]=>4 [6,2,4,5,3,1]=>4 [6,2,5,1,3,4]=>4 [6,2,5,1,4,3]=>4 [6,2,5,3,1,4]=>4 [6,2,5,3,4,1]=>4 [6,2,5,4,1,3]=>4 [6,2,5,4,3,1]=>5 [6,3,1,2,4,5]=>4 [6,3,1,2,5,4]=>3 [6,3,1,4,2,5]=>4 [6,3,1,4,5,2]=>4 [6,3,1,5,2,4]=>3 [6,3,1,5,4,2]=>4 [6,3,2,1,4,5]=>5 [6,3,2,1,5,4]=>4 [6,3,2,4,1,5]=>5 [6,3,2,4,5,1]=>5 [6,3,2,5,1,4]=>4 [6,3,2,5,4,1]=>4 [6,3,4,1,2,5]=>4 [6,3,4,1,5,2]=>4 [6,3,4,2,1,5]=>5 [6,3,4,2,5,1]=>5 [6,3,4,5,1,2]=>4 [6,3,4,5,2,1]=>5 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>4 [6,3,5,2,1,4]=>4 [6,3,5,2,4,1]=>4 [6,3,5,4,1,2]=>4 [6,3,5,4,2,1]=>5 [6,4,1,2,3,5]=>4 [6,4,1,2,5,3]=>3 [6,4,1,3,2,5]=>4 [6,4,1,3,5,2]=>4 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>4 [6,4,2,1,3,5]=>4 [6,4,2,1,5,3]=>4 [6,4,2,3,1,5]=>4 [6,4,2,3,5,1]=>4 [6,4,2,5,1,3]=>4 [6,4,2,5,3,1]=>4 [6,4,3,1,2,5]=>4 [6,4,3,1,5,2]=>4 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>5 [6,4,3,5,1,2]=>4 [6,4,3,5,2,1]=>5 [6,4,5,1,2,3]=>3 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>4 [6,4,5,3,1,2]=>4 [6,4,5,3,2,1]=>5 [6,5,1,2,3,4]=>4 [6,5,1,2,4,3]=>4 [6,5,1,3,2,4]=>4 [6,5,1,3,4,2]=>4 [6,5,1,4,2,3]=>4 [6,5,1,4,3,2]=>5 [6,5,2,1,3,4]=>4 [6,5,2,1,4,3]=>4 [6,5,2,3,1,4]=>4 [6,5,2,3,4,1]=>4 [6,5,2,4,1,3]=>4 [6,5,2,4,3,1]=>5 [6,5,3,1,2,4]=>4 [6,5,3,1,4,2]=>4 [6,5,3,2,1,4]=>5 [6,5,3,2,4,1]=>5 [6,5,3,4,1,2]=>4 [6,5,3,4,2,1]=>5 [6,5,4,1,2,3]=>4 [6,5,4,1,3,2]=>5 [6,5,4,2,1,3]=>5 [6,5,4,2,3,1]=>5 [6,5,4,3,1,2]=>5 [6,5,4,3,2,1]=>6 [1,2,3,4,5,6,7]=>7 [1,2,3,4,5,7,6]=>6 [1,2,3,4,6,5,7]=>6 [1,2,3,4,6,7,5]=>6 [1,2,3,4,7,5,6]=>6 [1,2,3,4,7,6,5]=>5 [1,2,3,5,4,6,7]=>6 [1,2,3,5,4,7,6]=>5 [1,2,3,5,6,4,7]=>6 [1,2,3,5,6,7,4]=>6 [1,2,3,5,7,4,6]=>5 [1,2,3,5,7,6,4]=>5 [1,2,3,6,4,5,7]=>6 [1,2,3,6,4,7,5]=>5 [1,2,3,6,5,4,7]=>5 [1,2,3,6,5,7,4]=>5 [1,2,3,6,7,4,5]=>5 [1,2,3,6,7,5,4]=>5 [1,2,3,7,4,5,6]=>6 [1,2,3,7,4,6,5]=>5 [1,2,3,7,5,4,6]=>5 [1,2,3,7,5,6,4]=>5 [1,2,3,7,6,4,5]=>5 [1,2,3,7,6,5,4]=>4 [1,2,4,3,5,6,7]=>6 [1,2,4,3,5,7,6]=>5 [1,2,4,3,6,5,7]=>5 [1,2,4,3,6,7,5]=>5 [1,2,4,3,7,5,6]=>5 [1,2,4,3,7,6,5]=>4 [1,2,4,5,3,6,7]=>6 [1,2,4,5,3,7,6]=>5 [1,2,4,5,6,3,7]=>6 [1,2,4,5,6,7,3]=>6 [1,2,4,5,7,3,6]=>5 [1,2,4,5,7,6,3]=>5 [1,2,4,6,3,5,7]=>5 [1,2,4,6,3,7,5]=>5 [1,2,4,6,5,3,7]=>5 [1,2,4,6,5,7,3]=>5 [1,2,4,6,7,3,5]=>5 [1,2,4,6,7,5,3]=>5 [1,2,4,7,3,5,6]=>5 [1,2,4,7,3,6,5]=>4 [1,2,4,7,5,3,6]=>5 [1,2,4,7,5,6,3]=>5 [1,2,4,7,6,3,5]=>4 [1,2,4,7,6,5,3]=>4 [1,2,5,3,4,6,7]=>6 [1,2,5,3,4,7,6]=>5 [1,2,5,3,6,4,7]=>5 [1,2,5,3,6,7,4]=>5 [1,2,5,3,7,4,6]=>5 [1,2,5,3,7,6,4]=>4 [1,2,5,4,3,6,7]=>5 [1,2,5,4,3,7,6]=>4 [1,2,5,4,6,3,7]=>5 [1,2,5,4,6,7,3]=>5 [1,2,5,4,7,3,6]=>4 [1,2,5,4,7,6,3]=>4 [1,2,5,6,3,4,7]=>5 [1,2,5,6,3,7,4]=>5 [1,2,5,6,4,3,7]=>5 [1,2,5,6,4,7,3]=>5 [1,2,5,6,7,3,4]=>5 [1,2,5,6,7,4,3]=>5 [1,2,5,7,3,4,6]=>5 [1,2,5,7,3,6,4]=>4 [1,2,5,7,4,3,6]=>4 [1,2,5,7,4,6,3]=>4 [1,2,5,7,6,3,4]=>4 [1,2,5,7,6,4,3]=>4 [1,2,6,3,4,5,7]=>6 [1,2,6,3,4,7,5]=>5 [1,2,6,3,5,4,7]=>5 [1,2,6,3,5,7,4]=>5 [1,2,6,3,7,4,5]=>5 [1,2,6,3,7,5,4]=>4 [1,2,6,4,3,5,7]=>5 [1,2,6,4,3,7,5]=>4 [1,2,6,4,5,3,7]=>5 [1,2,6,4,5,7,3]=>5 [1,2,6,4,7,3,5]=>4 [1,2,6,4,7,5,3]=>4 [1,2,6,5,3,4,7]=>5 [1,2,6,5,3,7,4]=>4 [1,2,6,5,4,3,7]=>5 [1,2,6,5,4,7,3]=>5 [1,2,6,5,7,3,4]=>4 [1,2,6,5,7,4,3]=>5 [1,2,6,7,3,4,5]=>5 [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]=>6 [1,2,7,3,4,6,5]=>5 [1,2,7,3,5,4,6]=>5 [1,2,7,3,5,6,4]=>5 [1,2,7,3,6,4,5]=>5 [1,2,7,3,6,5,4]=>4 [1,2,7,4,3,5,6]=>5 [1,2,7,4,3,6,5]=>4 [1,2,7,4,5,3,6]=>5 [1,2,7,4,5,6,3]=>5 [1,2,7,4,6,3,5]=>4 [1,2,7,4,6,5,3]=>4 [1,2,7,5,3,4,6]=>5 [1,2,7,5,3,6,4]=>4 [1,2,7,5,4,3,6]=>4 [1,2,7,5,4,6,3]=>4 [1,2,7,5,6,3,4]=>4 [1,2,7,5,6,4,3]=>4 [1,2,7,6,3,4,5]=>5 [1,2,7,6,3,5,4]=>4 [1,2,7,6,4,3,5]=>4 [1,2,7,6,4,5,3]=>4 [1,2,7,6,5,3,4]=>4 [1,2,7,6,5,4,3]=>5 [1,3,2,4,5,6,7]=>6 [1,3,2,4,5,7,6]=>5 [1,3,2,4,6,5,7]=>5 [1,3,2,4,6,7,5]=>5 [1,3,2,4,7,5,6]=>5 [1,3,2,4,7,6,5]=>4 [1,3,2,5,4,6,7]=>5 [1,3,2,5,4,7,6]=>4 [1,3,2,5,6,4,7]=>5 [1,3,2,5,6,7,4]=>5 [1,3,2,5,7,4,6]=>4 [1,3,2,5,7,6,4]=>4 [1,3,2,6,4,5,7]=>5 [1,3,2,6,4,7,5]=>4 [1,3,2,6,5,4,7]=>4 [1,3,2,6,5,7,4]=>4 [1,3,2,6,7,4,5]=>4 [1,3,2,6,7,5,4]=>4 [1,3,2,7,4,5,6]=>5 [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]=>4 [1,3,4,2,5,6,7]=>6 [1,3,4,2,5,7,6]=>5 [1,3,4,2,6,5,7]=>5 [1,3,4,2,6,7,5]=>5 [1,3,4,2,7,5,6]=>5 [1,3,4,2,7,6,5]=>4 [1,3,4,5,2,6,7]=>6 [1,3,4,5,2,7,6]=>5 [1,3,4,5,6,2,7]=>6 [1,3,4,5,6,7,2]=>6 [1,3,4,5,7,2,6]=>5 [1,3,4,5,7,6,2]=>5 [1,3,4,6,2,5,7]=>5 [1,3,4,6,2,7,5]=>5 [1,3,4,6,5,2,7]=>5 [1,3,4,6,5,7,2]=>5 [1,3,4,6,7,2,5]=>5 [1,3,4,6,7,5,2]=>5 [1,3,4,7,2,5,6]=>5 [1,3,4,7,2,6,5]=>4 [1,3,4,7,5,2,6]=>5 [1,3,4,7,5,6,2]=>5 [1,3,4,7,6,2,5]=>4 [1,3,4,7,6,5,2]=>4 [1,3,5,2,4,6,7]=>5 [1,3,5,2,4,7,6]=>4 [1,3,5,2,6,4,7]=>5 [1,3,5,2,6,7,4]=>5 [1,3,5,2,7,4,6]=>4 [1,3,5,2,7,6,4]=>4 [1,3,5,4,2,6,7]=>5 [1,3,5,4,2,7,6]=>4 [1,3,5,4,6,2,7]=>5 [1,3,5,4,6,7,2]=>5 [1,3,5,4,7,2,6]=>4 [1,3,5,4,7,6,2]=>4 [1,3,5,6,2,4,7]=>5 [1,3,5,6,2,7,4]=>5 [1,3,5,6,4,2,7]=>5 [1,3,5,6,4,7,2]=>5 [1,3,5,6,7,2,4]=>5 [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]=>4 [1,3,6,2,4,5,7]=>5 [1,3,6,2,4,7,5]=>4 [1,3,6,2,5,4,7]=>4 [1,3,6,2,5,7,4]=>4 [1,3,6,2,7,4,5]=>4 [1,3,6,2,7,5,4]=>4 [1,3,6,4,2,5,7]=>5 [1,3,6,4,2,7,5]=>4 [1,3,6,4,5,2,7]=>5 [1,3,6,4,5,7,2]=>5 [1,3,6,4,7,2,5]=>4 [1,3,6,4,7,5,2]=>4 [1,3,6,5,2,4,7]=>4 [1,3,6,5,2,7,4]=>4 [1,3,6,5,4,2,7]=>5 [1,3,6,5,4,7,2]=>5 [1,3,6,5,7,2,4]=>4 [1,3,6,5,7,4,2]=>5 [1,3,6,7,2,4,5]=>4 [1,3,6,7,2,5,4]=>4 [1,3,6,7,4,2,5]=>4 [1,3,6,7,4,5,2]=>4 [1,3,6,7,5,2,4]=>4 [1,3,6,7,5,4,2]=>5 [1,3,7,2,4,5,6]=>5 [1,3,7,2,4,6,5]=>4 [1,3,7,2,5,4,6]=>4 [1,3,7,2,5,6,4]=>4 [1,3,7,2,6,4,5]=>4 [1,3,7,2,6,5,4]=>4 [1,3,7,4,2,5,6]=>5 [1,3,7,4,2,6,5]=>4 [1,3,7,4,5,2,6]=>5 [1,3,7,4,5,6,2]=>5 [1,3,7,4,6,2,5]=>4 [1,3,7,4,6,5,2]=>4 [1,3,7,5,2,4,6]=>4 [1,3,7,5,2,6,4]=>4 [1,3,7,5,4,2,6]=>4 [1,3,7,5,4,6,2]=>4 [1,3,7,5,6,2,4]=>4 [1,3,7,5,6,4,2]=>4 [1,3,7,6,2,4,5]=>4 [1,3,7,6,2,5,4]=>4 [1,3,7,6,4,2,5]=>4 [1,3,7,6,4,5,2]=>4 [1,3,7,6,5,2,4]=>4 [1,3,7,6,5,4,2]=>5 [1,4,2,3,5,6,7]=>6 [1,4,2,3,5,7,6]=>5 [1,4,2,3,6,5,7]=>5 [1,4,2,3,6,7,5]=>5 [1,4,2,3,7,5,6]=>5 [1,4,2,3,7,6,5]=>4 [1,4,2,5,3,6,7]=>5 [1,4,2,5,3,7,6]=>4 [1,4,2,5,6,3,7]=>5 [1,4,2,5,6,7,3]=>5 [1,4,2,5,7,3,6]=>4 [1,4,2,5,7,6,3]=>4 [1,4,2,6,3,5,7]=>5 [1,4,2,6,3,7,5]=>4 [1,4,2,6,5,3,7]=>4 [1,4,2,6,5,7,3]=>4 [1,4,2,6,7,3,5]=>4 [1,4,2,6,7,5,3]=>4 [1,4,2,7,3,5,6]=>5 [1,4,2,7,3,6,5]=>4 [1,4,2,7,5,3,6]=>4 [1,4,2,7,5,6,3]=>4 [1,4,2,7,6,3,5]=>4 [1,4,2,7,6,5,3]=>4 [1,4,3,2,5,6,7]=>6 [1,4,3,2,5,7,6]=>5 [1,4,3,2,6,5,7]=>5 [1,4,3,2,6,7,5]=>5 [1,4,3,2,7,5,6]=>5 [1,4,3,2,7,6,5]=>4 [1,4,3,5,2,6,7]=>6 [1,4,3,5,2,7,6]=>5 [1,4,3,5,6,2,7]=>6 [1,4,3,5,6,7,2]=>6 [1,4,3,5,7,2,6]=>5 [1,4,3,5,7,6,2]=>5 [1,4,3,6,2,5,7]=>5 [1,4,3,6,2,7,5]=>5 [1,4,3,6,5,2,7]=>5 [1,4,3,6,5,7,2]=>5 [1,4,3,6,7,2,5]=>5 [1,4,3,6,7,5,2]=>5 [1,4,3,7,2,5,6]=>5 [1,4,3,7,2,6,5]=>4 [1,4,3,7,5,2,6]=>5 [1,4,3,7,5,6,2]=>5 [1,4,3,7,6,2,5]=>4 [1,4,3,7,6,5,2]=>4 [1,4,5,2,3,6,7]=>5 [1,4,5,2,3,7,6]=>4 [1,4,5,2,6,3,7]=>5 [1,4,5,2,6,7,3]=>5 [1,4,5,2,7,3,6]=>4 [1,4,5,2,7,6,3]=>4 [1,4,5,3,2,6,7]=>6 [1,4,5,3,2,7,6]=>5 [1,4,5,3,6,2,7]=>6 [1,4,5,3,6,7,2]=>6 [1,4,5,3,7,2,6]=>5 [1,4,5,3,7,6,2]=>5 [1,4,5,6,2,3,7]=>5 [1,4,5,6,2,7,3]=>5 [1,4,5,6,3,2,7]=>6 [1,4,5,6,3,7,2]=>6 [1,4,5,6,7,2,3]=>5 [1,4,5,6,7,3,2]=>6 [1,4,5,7,2,3,6]=>4 [1,4,5,7,2,6,3]=>4 [1,4,5,7,3,2,6]=>5 [1,4,5,7,3,6,2]=>5 [1,4,5,7,6,2,3]=>4 [1,4,5,7,6,3,2]=>5 [1,4,6,2,3,5,7]=>5 [1,4,6,2,3,7,5]=>4 [1,4,6,2,5,3,7]=>4 [1,4,6,2,5,7,3]=>4 [1,4,6,2,7,3,5]=>4 [1,4,6,2,7,5,3]=>4 [1,4,6,3,2,5,7]=>5 [1,4,6,3,2,7,5]=>5 [1,4,6,3,5,2,7]=>5 [1,4,6,3,5,7,2]=>5 [1,4,6,3,7,2,5]=>5 [1,4,6,3,7,5,2]=>5 [1,4,6,5,2,3,7]=>4 [1,4,6,5,2,7,3]=>4 [1,4,6,5,3,2,7]=>5 [1,4,6,5,3,7,2]=>5
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Description
The length of the first row of the shifted shape of a permutation.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the length of the first row of $P$ and $Q$.
References
[1] Sagan, B. E. Shifted tableaux, Schur $Q$-functions, and a conjecture of R. Stanley MathSciNet:0883894
[2] Worley, D. R. A THEORY OF SHIFTED YOUNG TABLEAUX MathSciNet:2941073
[3] Haiman, M. D. On mixed insertion, symmetry, and shifted Young tableaux MathSciNet:0989194
Code
def statistic(pi):
    return GrowthDiagram.rules.ShiftedShapes()(pi).P_chain()[-1][0]

Created
Jun 25, 2017 at 20:09 by Martin Rubey
Updated
Feb 09, 2021 at 14:57 by Martin Rubey