edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>1 [1,2,3,4]=>2 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>2 [1,4,2,3]=>2 [1,4,3,2]=>1 [2,1,3,4]=>2 [2,1,4,3]=>2 [2,3,1,4]=>2 [2,3,4,1]=>1 [2,4,1,3]=>2 [2,4,3,1]=>2 [3,1,2,4]=>2 [3,1,4,2]=>2 [3,2,1,4]=>1 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>2 [4,1,2,3]=>1 [4,1,3,2]=>2 [4,2,1,3]=>2 [4,2,3,1]=>2 [4,3,1,2]=>2 [4,3,2,1]=>2 [1,2,3,4,5]=>2 [1,2,3,5,4]=>2 [1,2,4,3,5]=>2 [1,2,4,5,3]=>2 [1,2,5,3,4]=>2 [1,2,5,4,3]=>2 [1,3,2,4,5]=>2 [1,3,2,5,4]=>2 [1,3,4,2,5]=>2 [1,3,4,5,2]=>2 [1,3,5,2,4]=>2 [1,3,5,4,2]=>2 [1,4,2,3,5]=>2 [1,4,2,5,3]=>2 [1,4,3,2,5]=>2 [1,4,3,5,2]=>2 [1,4,5,2,3]=>2 [1,4,5,3,2]=>2 [1,5,2,3,4]=>2 [1,5,2,4,3]=>2 [1,5,3,2,4]=>2 [1,5,3,4,2]=>2 [1,5,4,2,3]=>2 [1,5,4,3,2]=>2 [2,1,3,4,5]=>2 [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]=>2 [2,3,1,4,5]=>2 [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]=>2 [2,4,1,3,5]=>2 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>2 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,4,3]=>2 [2,5,3,1,4]=>2 [2,5,3,4,1]=>2 [2,5,4,1,3]=>2 [2,5,4,3,1]=>2 [3,1,2,4,5]=>2 [3,1,2,5,4]=>2 [3,1,4,2,5]=>2 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,4,2]=>2 [3,2,1,4,5]=>2 [3,2,1,5,4]=>2 [3,2,4,1,5]=>2 [3,2,4,5,1]=>2 [3,2,5,1,4]=>2 [3,2,5,4,1]=>2 [3,4,1,2,5]=>2 [3,4,1,5,2]=>2 [3,4,2,1,5]=>2 [3,4,2,5,1]=>2 [3,4,5,1,2]=>2 [3,4,5,2,1]=>2 [3,5,1,2,4]=>2 [3,5,1,4,2]=>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]=>2 [4,1,2,5,3]=>2 [4,1,3,2,5]=>2 [4,1,3,5,2]=>2 [4,1,5,2,3]=>2 [4,1,5,3,2]=>2 [4,2,1,3,5]=>2 [4,2,1,5,3]=>2 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>2 [4,2,5,3,1]=>2 [4,3,1,2,5]=>2 [4,3,1,5,2]=>2 [4,3,2,1,5]=>2 [4,3,2,5,1]=>2 [4,3,5,1,2]=>2 [4,3,5,2,1]=>2 [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]=>2 [5,1,2,4,3]=>2 [5,1,3,2,4]=>2 [5,1,3,4,2]=>2 [5,1,4,2,3]=>2 [5,1,4,3,2]=>2 [5,2,1,3,4]=>2 [5,2,1,4,3]=>2 [5,2,3,1,4]=>2 [5,2,3,4,1]=>2 [5,2,4,1,3]=>2 [5,2,4,3,1]=>2 [5,3,1,2,4]=>2 [5,3,1,4,2]=>2 [5,3,2,1,4]=>2 [5,3,2,4,1]=>2 [5,3,4,1,2]=>2 [5,3,4,2,1]=>2 [5,4,1,2,3]=>2 [5,4,1,3,2]=>2 [5,4,2,1,3]=>2 [5,4,2,3,1]=>2 [5,4,3,1,2]=>2 [5,4,3,2,1]=>2 [1,2,3,4,5,6]=>3 [1,2,3,4,6,5]=>3 [1,2,3,5,4,6]=>3 [1,2,3,5,6,4]=>3 [1,2,3,6,4,5]=>3 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>3 [1,2,4,3,6,5]=>3 [1,2,4,5,3,6]=>3 [1,2,4,5,6,3]=>3 [1,2,4,6,3,5]=>3 [1,2,4,6,5,3]=>3 [1,2,5,3,4,6]=>3 [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]=>3 [1,2,5,6,4,3]=>3 [1,2,6,3,4,5]=>3 [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]=>3 [1,3,2,4,5,6]=>3 [1,3,2,4,6,5]=>3 [1,3,2,5,4,6]=>3 [1,3,2,5,6,4]=>3 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>2 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>3 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>3 [1,3,5,2,4,6]=>3 [1,3,5,2,6,4]=>3 [1,3,5,4,2,6]=>2 [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]=>3 [1,3,6,2,5,4]=>3 [1,3,6,4,2,5]=>3 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>3 [1,3,6,5,4,2]=>3 [1,4,2,3,5,6]=>3 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>3 [1,4,2,5,6,3]=>3 [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]=>2 [1,4,3,5,6,2]=>3 [1,4,3,6,2,5]=>3 [1,4,3,6,5,2]=>3 [1,4,5,2,3,6]=>3 [1,4,5,2,6,3]=>3 [1,4,5,3,2,6]=>2 [1,4,5,3,6,2]=>3 [1,4,5,6,2,3]=>3 [1,4,5,6,3,2]=>3 [1,4,6,2,3,5]=>3 [1,4,6,2,5,3]=>3 [1,4,6,3,2,5]=>3 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>3 [1,4,6,5,3,2]=>3 [1,5,2,3,4,6]=>3 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>3 [1,5,2,6,3,4]=>3 [1,5,2,6,4,3]=>3 [1,5,3,2,4,6]=>2 [1,5,3,2,6,4]=>3 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>3 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>2 [1,5,4,2,6,3]=>3 [1,5,4,3,2,6]=>2 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>3 [1,5,4,6,3,2]=>3 [1,5,6,2,3,4]=>3 [1,5,6,2,4,3]=>3 [1,5,6,3,2,4]=>3 [1,5,6,3,4,2]=>3 [1,5,6,4,2,3]=>3 [1,5,6,4,3,2]=>3 [1,6,2,3,4,5]=>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]=>3 [1,6,3,2,4,5]=>2 [1,6,3,2,5,4]=>3 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>3 [1,6,3,5,2,4]=>3 [1,6,3,5,4,2]=>3 [1,6,4,2,3,5]=>2 [1,6,4,2,5,3]=>3 [1,6,4,3,2,5]=>2 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>3 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>3 [1,6,5,3,2,4]=>2 [1,6,5,3,4,2]=>3 [1,6,5,4,2,3]=>2 [1,6,5,4,3,2]=>2 [2,1,3,4,5,6]=>3 [2,1,3,4,6,5]=>3 [2,1,3,5,4,6]=>3 [2,1,3,5,6,4]=>3 [2,1,3,6,4,5]=>3 [2,1,3,6,5,4]=>2 [2,1,4,3,5,6]=>3 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>3 [2,1,4,5,6,3]=>2 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>3 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>3 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>3 [2,1,5,6,3,4]=>3 [2,1,5,6,4,3]=>3 [2,1,6,3,4,5]=>3 [2,1,6,3,5,4]=>3 [2,1,6,4,3,5]=>3 [2,1,6,4,5,3]=>3 [2,1,6,5,3,4]=>3 [2,1,6,5,4,3]=>3 [2,3,1,4,5,6]=>3 [2,3,1,4,6,5]=>3 [2,3,1,5,4,6]=>3 [2,3,1,5,6,4]=>3 [2,3,1,6,4,5]=>3 [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]=>2 [2,3,4,5,6,1]=>2 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>3 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>3 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>3 [2,3,5,6,1,4]=>3 [2,3,5,6,4,1]=>3 [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]=>3 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>3 [2,4,1,3,5,6]=>3 [2,4,1,3,6,5]=>3 [2,4,1,5,3,6]=>3 [2,4,1,5,6,3]=>3 [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]=>3 [2,4,3,5,1,6]=>3 [2,4,3,5,6,1]=>3 [2,4,3,6,1,5]=>3 [2,4,3,6,5,1]=>3 [2,4,5,1,3,6]=>3 [2,4,5,1,6,3]=>3 [2,4,5,3,1,6]=>2 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>3 [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]=>3 [2,5,1,3,6,4]=>3 [2,5,1,4,3,6]=>3 [2,5,1,4,6,3]=>3 [2,5,1,6,3,4]=>3 [2,5,1,6,4,3]=>3 [2,5,3,1,4,6]=>3 [2,5,3,1,6,4]=>3 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>3 [2,5,3,6,1,4]=>3 [2,5,3,6,4,1]=>3 [2,5,4,1,3,6]=>3 [2,5,4,1,6,3]=>3 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>3 [2,5,4,6,1,3]=>3 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>3 [2,5,6,1,4,3]=>3 [2,5,6,3,1,4]=>3 [2,5,6,3,4,1]=>3 [2,5,6,4,1,3]=>3 [2,5,6,4,3,1]=>3 [2,6,1,3,4,5]=>3 [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]=>3 [2,6,3,1,4,5]=>3 [2,6,3,1,5,4]=>3 [2,6,3,4,1,5]=>3 [2,6,3,4,5,1]=>3 [2,6,3,5,1,4]=>3 [2,6,3,5,4,1]=>3 [2,6,4,1,3,5]=>3 [2,6,4,1,5,3]=>3 [2,6,4,3,1,5]=>2 [2,6,4,3,5,1]=>3 [2,6,4,5,1,3]=>3 [2,6,4,5,3,1]=>3 [2,6,5,1,3,4]=>2 [2,6,5,1,4,3]=>3 [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]=>3 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>3 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>2 [3,1,4,2,5,6]=>3 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>3 [3,1,4,5,6,2]=>2 [3,1,4,6,2,5]=>3 [3,1,4,6,5,2]=>3 [3,1,5,2,4,6]=>3 [3,1,5,2,6,4]=>3 [3,1,5,4,2,6]=>3 [3,1,5,4,6,2]=>3 [3,1,5,6,2,4]=>3 [3,1,5,6,4,2]=>3 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>3 [3,1,6,4,2,5]=>3 [3,1,6,4,5,2]=>3 [3,1,6,5,2,4]=>3 [3,1,6,5,4,2]=>3 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>2 [3,2,1,5,4,6]=>2 [3,2,1,5,6,4]=>2 [3,2,1,6,4,5]=>2 [3,2,1,6,5,4]=>3 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>3 [3,2,4,5,1,6]=>3 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>3 [3,2,4,6,5,1]=>3 [3,2,5,1,4,6]=>3 [3,2,5,1,6,4]=>3 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>3 [3,2,5,6,1,4]=>3 [3,2,5,6,4,1]=>3 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>3 [3,2,6,4,1,5]=>3 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>3 [3,2,6,5,4,1]=>3 [3,4,1,2,5,6]=>3 [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]=>3 [3,4,2,1,5,6]=>3 [3,4,2,1,6,5]=>3 [3,4,2,5,1,6]=>3 [3,4,2,5,6,1]=>3 [3,4,2,6,1,5]=>3 [3,4,2,6,5,1]=>3 [3,4,5,1,2,6]=>3 [3,4,5,1,6,2]=>3 [3,4,5,2,1,6]=>2 [3,4,5,2,6,1]=>3 [3,4,5,6,1,2]=>3 [3,4,5,6,2,1]=>3 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>3 [3,4,6,2,1,5]=>2 [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]=>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]=>3 [3,5,2,1,4,6]=>3 [3,5,2,1,6,4]=>3 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>3 [3,5,2,6,1,4]=>3 [3,5,2,6,4,1]=>3 [3,5,4,1,2,6]=>3 [3,5,4,1,6,2]=>3 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>3 [3,5,4,6,1,2]=>3 [3,5,4,6,2,1]=>3 [3,5,6,1,2,4]=>3 [3,5,6,1,4,2]=>3 [3,5,6,2,1,4]=>2 [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]=>3 [3,6,1,2,5,4]=>3 [3,6,1,4,2,5]=>3 [3,6,1,4,5,2]=>3 [3,6,1,5,2,4]=>3 [3,6,1,5,4,2]=>3 [3,6,2,1,4,5]=>3 [3,6,2,1,5,4]=>3 [3,6,2,4,1,5]=>3 [3,6,2,4,5,1]=>3 [3,6,2,5,1,4]=>3 [3,6,2,5,4,1]=>3 [3,6,4,1,2,5]=>3 [3,6,4,1,5,2]=>3 [3,6,4,2,1,5]=>2 [3,6,4,2,5,1]=>3 [3,6,4,5,1,2]=>3 [3,6,4,5,2,1]=>3 [3,6,5,1,2,4]=>2 [3,6,5,1,4,2]=>3 [3,6,5,2,1,4]=>3 [3,6,5,2,4,1]=>3 [3,6,5,4,1,2]=>2 [3,6,5,4,2,1]=>3 [4,1,2,3,5,6]=>3 [4,1,2,3,6,5]=>2 [4,1,2,5,3,6]=>3 [4,1,2,5,6,3]=>3 [4,1,2,6,3,5]=>3 [4,1,2,6,5,3]=>2 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>3 [4,1,3,5,2,6]=>3 [4,1,3,5,6,2]=>2 [4,1,3,6,2,5]=>3 [4,1,3,6,5,2]=>3 [4,1,5,2,3,6]=>3 [4,1,5,2,6,3]=>3 [4,1,5,3,2,6]=>3 [4,1,5,3,6,2]=>3 [4,1,5,6,2,3]=>3 [4,1,5,6,3,2]=>3 [4,1,6,2,3,5]=>3 [4,1,6,2,5,3]=>3 [4,1,6,3,2,5]=>3 [4,1,6,3,5,2]=>3 [4,1,6,5,2,3]=>3 [4,1,6,5,3,2]=>3 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>3 [4,2,1,5,6,3]=>2 [4,2,1,6,3,5]=>3 [4,2,1,6,5,3]=>3 [4,2,3,1,5,6]=>3 [4,2,3,1,6,5]=>3 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>3 [4,2,3,6,5,1]=>3 [4,2,5,1,3,6]=>3 [4,2,5,1,6,3]=>3 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>3 [4,2,5,6,1,3]=>3 [4,2,5,6,3,1]=>3 [4,2,6,1,3,5]=>3 [4,2,6,1,5,3]=>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]=>3 [4,3,1,2,6,5]=>3 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>2 [4,3,1,6,2,5]=>3 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>3 [4,3,2,1,6,5]=>3 [4,3,2,5,1,6]=>3 [4,3,2,5,6,1]=>2 [4,3,2,6,1,5]=>3 [4,3,2,6,5,1]=>3 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>3 [4,3,5,2,1,6]=>3 [4,3,5,2,6,1]=>3 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>3 [4,3,6,1,2,5]=>3 [4,3,6,1,5,2]=>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]=>3 [4,5,1,2,6,3]=>3 [4,5,1,3,2,6]=>3 [4,5,1,3,6,2]=>3 [4,5,1,6,2,3]=>3 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>3 [4,5,2,1,6,3]=>3 [4,5,2,3,1,6]=>3 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>3 [4,5,2,6,3,1]=>3 [4,5,3,1,2,6]=>3 [4,5,3,1,6,2]=>3 [4,5,3,2,1,6]=>2 [4,5,3,2,6,1]=>3 [4,5,3,6,1,2]=>3 [4,5,3,6,2,1]=>3 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>2 [4,5,6,2,3,1]=>2 [4,5,6,3,1,2]=>2 [4,5,6,3,2,1]=>2 [4,6,1,2,3,5]=>3 [4,6,1,2,5,3]=>3 [4,6,1,3,2,5]=>3 [4,6,1,3,5,2]=>3 [4,6,1,5,2,3]=>3 [4,6,1,5,3,2]=>3 [4,6,2,1,3,5]=>3 [4,6,2,1,5,3]=>3 [4,6,2,3,1,5]=>3 [4,6,2,3,5,1]=>3 [4,6,2,5,1,3]=>3 [4,6,2,5,3,1]=>3 [4,6,3,1,2,5]=>3 [4,6,3,1,5,2]=>3 [4,6,3,2,1,5]=>2 [4,6,3,2,5,1]=>3 [4,6,3,5,1,2]=>3 [4,6,3,5,2,1]=>3 [4,6,5,1,2,3]=>2 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>3 [4,6,5,2,3,1]=>3 [4,6,5,3,1,2]=>3 [4,6,5,3,2,1]=>3 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>2 [5,1,2,4,3,6]=>3 [5,1,2,4,6,3]=>2 [5,1,2,6,3,4]=>3 [5,1,2,6,4,3]=>2 [5,1,3,2,4,6]=>3 [5,1,3,2,6,4]=>3 [5,1,3,4,2,6]=>3 [5,1,3,4,6,2]=>2 [5,1,3,6,2,4]=>3 [5,1,3,6,4,2]=>3 [5,1,4,2,3,6]=>3 [5,1,4,2,6,3]=>3 [5,1,4,3,2,6]=>3 [5,1,4,3,6,2]=>3 [5,1,4,6,2,3]=>3 [5,1,4,6,3,2]=>3 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>3 [5,1,6,3,2,4]=>3 [5,1,6,3,4,2]=>3 [5,1,6,4,2,3]=>3 [5,1,6,4,3,2]=>3 [5,2,1,3,4,6]=>3 [5,2,1,3,6,4]=>3 [5,2,1,4,3,6]=>3 [5,2,1,4,6,3]=>3 [5,2,1,6,3,4]=>3 [5,2,1,6,4,3]=>3 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>3 [5,2,3,4,1,6]=>3 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>3 [5,2,3,6,4,1]=>3 [5,2,4,1,3,6]=>3 [5,2,4,1,6,3]=>3 [5,2,4,3,1,6]=>3 [5,2,4,3,6,1]=>3 [5,2,4,6,1,3]=>3 [5,2,4,6,3,1]=>3 [5,2,6,1,3,4]=>3 [5,2,6,1,4,3]=>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]=>3 [5,3,1,2,6,4]=>3 [5,3,1,4,2,6]=>3 [5,3,1,4,6,2]=>3 [5,3,1,6,2,4]=>3 [5,3,1,6,4,2]=>3 [5,3,2,1,4,6]=>3 [5,3,2,1,6,4]=>3 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>2 [5,3,2,6,1,4]=>3 [5,3,2,6,4,1]=>3 [5,3,4,1,2,6]=>3 [5,3,4,1,6,2]=>3 [5,3,4,2,1,6]=>3 [5,3,4,2,6,1]=>3 [5,3,4,6,1,2]=>3 [5,3,4,6,2,1]=>3 [5,3,6,1,2,4]=>3 [5,3,6,1,4,2]=>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]=>3 [5,4,1,2,6,3]=>3 [5,4,1,3,2,6]=>3 [5,4,1,3,6,2]=>3 [5,4,1,6,2,3]=>3 [5,4,1,6,3,2]=>3 [5,4,2,1,3,6]=>3 [5,4,2,1,6,3]=>3 [5,4,2,3,1,6]=>3 [5,4,2,3,6,1]=>2 [5,4,2,6,1,3]=>3 [5,4,2,6,3,1]=>3 [5,4,3,1,2,6]=>3 [5,4,3,1,6,2]=>3 [5,4,3,2,1,6]=>2 [5,4,3,2,6,1]=>2 [5,4,3,6,1,2]=>3 [5,4,3,6,2,1]=>3 [5,4,6,1,2,3]=>2 [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]=>3 [5,6,1,2,4,3]=>3 [5,6,1,3,2,4]=>3 [5,6,1,3,4,2]=>3 [5,6,1,4,2,3]=>3 [5,6,1,4,3,2]=>3 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>3 [5,6,2,3,1,4]=>3 [5,6,2,3,4,1]=>3 [5,6,2,4,1,3]=>3 [5,6,2,4,3,1]=>3 [5,6,3,1,2,4]=>3 [5,6,3,1,4,2]=>3 [5,6,3,2,1,4]=>2 [5,6,3,2,4,1]=>3 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>3 [5,6,4,1,2,3]=>2 [5,6,4,1,3,2]=>3 [5,6,4,2,1,3]=>3 [5,6,4,2,3,1]=>3 [5,6,4,3,1,2]=>3 [5,6,4,3,2,1]=>3 [6,1,2,3,4,5]=>2 [6,1,2,3,5,4]=>2 [6,1,2,4,3,5]=>3 [6,1,2,4,5,3]=>2 [6,1,2,5,3,4]=>3 [6,1,2,5,4,3]=>2 [6,1,3,2,4,5]=>3 [6,1,3,2,5,4]=>3 [6,1,3,4,2,5]=>3 [6,1,3,4,5,2]=>2 [6,1,3,5,2,4]=>3 [6,1,3,5,4,2]=>2 [6,1,4,2,3,5]=>3 [6,1,4,2,5,3]=>3 [6,1,4,3,2,5]=>3 [6,1,4,3,5,2]=>3 [6,1,4,5,2,3]=>3 [6,1,4,5,3,2]=>2 [6,1,5,2,3,4]=>3 [6,1,5,2,4,3]=>3 [6,1,5,3,2,4]=>3 [6,1,5,3,4,2]=>3 [6,1,5,4,2,3]=>3 [6,1,5,4,3,2]=>2 [6,2,1,3,4,5]=>3 [6,2,1,3,5,4]=>3 [6,2,1,4,3,5]=>3 [6,2,1,4,5,3]=>3 [6,2,1,5,3,4]=>3 [6,2,1,5,4,3]=>3 [6,2,3,1,4,5]=>3 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>3 [6,2,3,5,4,1]=>2 [6,2,4,1,3,5]=>3 [6,2,4,1,5,3]=>3 [6,2,4,3,1,5]=>3 [6,2,4,3,5,1]=>2 [6,2,4,5,1,3]=>3 [6,2,4,5,3,1]=>2 [6,2,5,1,3,4]=>3 [6,2,5,1,4,3]=>3 [6,2,5,3,1,4]=>3 [6,2,5,3,4,1]=>2 [6,2,5,4,1,3]=>3 [6,2,5,4,3,1]=>3 [6,3,1,2,4,5]=>3 [6,3,1,2,5,4]=>3 [6,3,1,4,2,5]=>3 [6,3,1,4,5,2]=>3 [6,3,1,5,2,4]=>3 [6,3,1,5,4,2]=>3 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>3 [6,3,2,4,1,5]=>3 [6,3,2,4,5,1]=>2 [6,3,2,5,1,4]=>3 [6,3,2,5,4,1]=>3 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>3 [6,3,4,2,1,5]=>3 [6,3,4,2,5,1]=>2 [6,3,4,5,1,2]=>3 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>3 [6,3,5,1,4,2]=>3 [6,3,5,2,1,4]=>3 [6,3,5,2,4,1]=>3 [6,3,5,4,1,2]=>3 [6,3,5,4,2,1]=>3 [6,4,1,2,3,5]=>3 [6,4,1,2,5,3]=>3 [6,4,1,3,2,5]=>3 [6,4,1,3,5,2]=>3 [6,4,1,5,2,3]=>3 [6,4,1,5,3,2]=>3 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>3 [6,4,2,3,1,5]=>3 [6,4,2,3,5,1]=>2 [6,4,2,5,1,3]=>3 [6,4,2,5,3,1]=>3 [6,4,3,1,2,5]=>3 [6,4,3,1,5,2]=>3 [6,4,3,2,1,5]=>2 [6,4,3,2,5,1]=>3 [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]=>3 [6,4,5,2,1,3]=>3 [6,4,5,2,3,1]=>3 [6,4,5,3,1,2]=>3 [6,4,5,3,2,1]=>3 [6,5,1,2,3,4]=>3 [6,5,1,2,4,3]=>3 [6,5,1,3,2,4]=>3 [6,5,1,3,4,2]=>3 [6,5,1,4,2,3]=>3 [6,5,1,4,3,2]=>3 [6,5,2,1,3,4]=>3 [6,5,2,1,4,3]=>3 [6,5,2,3,1,4]=>3 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>3 [6,5,2,4,3,1]=>3 [6,5,3,1,2,4]=>3 [6,5,3,1,4,2]=>3 [6,5,3,2,1,4]=>3 [6,5,3,2,4,1]=>3 [6,5,3,4,1,2]=>3 [6,5,3,4,2,1]=>3 [6,5,4,1,2,3]=>2 [6,5,4,1,3,2]=>3 [6,5,4,2,1,3]=>3 [6,5,4,2,3,1]=>3 [6,5,4,3,1,2]=>3 [6,5,4,3,2,1]=>3 [1,2,3,4,5,6,7]=>3 [1,2,3,4,5,7,6]=>3 [1,2,3,4,6,5,7]=>3 [1,2,3,4,6,7,5]=>3 [1,2,3,4,7,5,6]=>3 [1,2,3,4,7,6,5]=>3 [1,2,3,5,4,6,7]=>3 [1,2,3,5,4,7,6]=>3 [1,2,3,5,6,4,7]=>3 [1,2,3,5,6,7,4]=>3 [1,2,3,5,7,4,6]=>3 [1,2,3,5,7,6,4]=>3 [1,2,3,6,4,5,7]=>3 [1,2,3,6,4,7,5]=>3 [1,2,3,6,5,4,7]=>3 [1,2,3,6,5,7,4]=>3 [1,2,3,6,7,4,5]=>3 [1,2,3,6,7,5,4]=>3 [1,2,3,7,4,5,6]=>3 [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]=>3 [1,2,4,3,5,6,7]=>3 [1,2,4,3,5,7,6]=>3 [1,2,4,3,6,5,7]=>3 [1,2,4,3,6,7,5]=>3 [1,2,4,3,7,5,6]=>3 [1,2,4,3,7,6,5]=>3 [1,2,4,5,3,6,7]=>3 [1,2,4,5,3,7,6]=>3 [1,2,4,5,6,3,7]=>3 [1,2,4,5,6,7,3]=>3 [1,2,4,5,7,3,6]=>3 [1,2,4,5,7,6,3]=>3 [1,2,4,6,3,5,7]=>3 [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]=>3 [1,2,4,7,3,6,5]=>3 [1,2,4,7,5,3,6]=>3 [1,2,4,7,5,6,3]=>3 [1,2,4,7,6,3,5]=>3 [1,2,4,7,6,5,3]=>3 [1,2,5,3,4,6,7]=>3 [1,2,5,3,4,7,6]=>3 [1,2,5,3,6,4,7]=>3 [1,2,5,3,6,7,4]=>3 [1,2,5,3,7,4,6]=>3 [1,2,5,3,7,6,4]=>3 [1,2,5,4,3,6,7]=>3 [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]=>3 [1,2,5,6,3,4,7]=>3 [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]=>3 [1,2,5,7,3,4,6]=>3 [1,2,5,7,3,6,4]=>3 [1,2,5,7,4,3,6]=>3 [1,2,5,7,4,6,3]=>3 [1,2,5,7,6,3,4]=>3 [1,2,5,7,6,4,3]=>3 [1,2,6,3,4,5,7]=>3 [1,2,6,3,4,7,5]=>3 [1,2,6,3,5,4,7]=>3 [1,2,6,3,5,7,4]=>3 [1,2,6,3,7,4,5]=>3 [1,2,6,3,7,5,4]=>3 [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]=>3 [1,2,6,5,3,4,7]=>3 [1,2,6,5,3,7,4]=>3 [1,2,6,5,4,3,7]=>3 [1,2,6,5,4,7,3]=>3 [1,2,6,5,7,3,4]=>3 [1,2,6,5,7,4,3]=>3 [1,2,6,7,3,4,5]=>3 [1,2,6,7,3,5,4]=>3 [1,2,6,7,4,3,5]=>3 [1,2,6,7,4,5,3]=>3 [1,2,6,7,5,3,4]=>3 [1,2,6,7,5,4,3]=>3 [1,2,7,3,4,5,6]=>3 [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]=>3 [1,2,7,4,3,5,6]=>3 [1,2,7,4,3,6,5]=>3 [1,2,7,4,5,3,6]=>3 [1,2,7,4,5,6,3]=>3 [1,2,7,4,6,3,5]=>3 [1,2,7,4,6,5,3]=>3 [1,2,7,5,3,4,6]=>3 [1,2,7,5,3,6,4]=>3 [1,2,7,5,4,3,6]=>3 [1,2,7,5,4,6,3]=>3 [1,2,7,5,6,3,4]=>3 [1,2,7,5,6,4,3]=>3 [1,2,7,6,3,4,5]=>3 [1,2,7,6,3,5,4]=>3 [1,2,7,6,4,3,5]=>3 [1,2,7,6,4,5,3]=>3 [1,2,7,6,5,3,4]=>3 [1,2,7,6,5,4,3]=>3 [1,3,2,4,5,6,7]=>3 [1,3,2,4,5,7,6]=>3 [1,3,2,4,6,5,7]=>3 [1,3,2,4,6,7,5]=>3 [1,3,2,4,7,5,6]=>3 [1,3,2,4,7,6,5]=>3 [1,3,2,5,4,6,7]=>3 [1,3,2,5,4,7,6]=>3 [1,3,2,5,6,4,7]=>3 [1,3,2,5,6,7,4]=>3 [1,3,2,5,7,4,6]=>3 [1,3,2,5,7,6,4]=>3 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>3 [1,3,2,6,5,4,7]=>3 [1,3,2,6,5,7,4]=>3 [1,3,2,6,7,4,5]=>3 [1,3,2,6,7,5,4]=>3 [1,3,2,7,4,5,6]=>3 [1,3,2,7,4,6,5]=>3 [1,3,2,7,5,4,6]=>3 [1,3,2,7,5,6,4]=>3 [1,3,2,7,6,4,5]=>3 [1,3,2,7,6,5,4]=>3 [1,3,4,2,5,6,7]=>3 [1,3,4,2,5,7,6]=>3 [1,3,4,2,6,5,7]=>3 [1,3,4,2,6,7,5]=>3 [1,3,4,2,7,5,6]=>3 [1,3,4,2,7,6,5]=>3 [1,3,4,5,2,6,7]=>3 [1,3,4,5,2,7,6]=>3 [1,3,4,5,6,2,7]=>3 [1,3,4,5,6,7,2]=>3 [1,3,4,5,7,2,6]=>3 [1,3,4,5,7,6,2]=>3 [1,3,4,6,2,5,7]=>3 [1,3,4,6,2,7,5]=>3 [1,3,4,6,5,2,7]=>3 [1,3,4,6,5,7,2]=>3 [1,3,4,6,7,2,5]=>3 [1,3,4,6,7,5,2]=>3 [1,3,4,7,2,5,6]=>3 [1,3,4,7,2,6,5]=>3 [1,3,4,7,5,2,6]=>3 [1,3,4,7,5,6,2]=>3 [1,3,4,7,6,2,5]=>3 [1,3,4,7,6,5,2]=>3 [1,3,5,2,4,6,7]=>3 [1,3,5,2,4,7,6]=>3 [1,3,5,2,6,4,7]=>3 [1,3,5,2,6,7,4]=>3 [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]=>3 [1,3,5,4,6,2,7]=>3 [1,3,5,4,6,7,2]=>3 [1,3,5,4,7,2,6]=>3 [1,3,5,4,7,6,2]=>3 [1,3,5,6,2,4,7]=>3 [1,3,5,6,2,7,4]=>3 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>3 [1,3,5,6,7,2,4]=>3 [1,3,5,6,7,4,2]=>3 [1,3,5,7,2,4,6]=>3 [1,3,5,7,2,6,4]=>3 [1,3,5,7,4,2,6]=>3 [1,3,5,7,4,6,2]=>3 [1,3,5,7,6,2,4]=>3 [1,3,5,7,6,4,2]=>3 [1,3,6,2,4,5,7]=>3 [1,3,6,2,4,7,5]=>3 [1,3,6,2,5,4,7]=>3 [1,3,6,2,5,7,4]=>3 [1,3,6,2,7,4,5]=>3 [1,3,6,2,7,5,4]=>3 [1,3,6,4,2,5,7]=>3 [1,3,6,4,2,7,5]=>3 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>3 [1,3,6,4,7,2,5]=>3 [1,3,6,4,7,5,2]=>3 [1,3,6,5,2,4,7]=>3 [1,3,6,5,2,7,4]=>3 [1,3,6,5,4,2,7]=>3 [1,3,6,5,4,7,2]=>3 [1,3,6,5,7,2,4]=>3 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>3 [1,3,6,7,2,5,4]=>3 [1,3,6,7,4,2,5]=>3 [1,3,6,7,4,5,2]=>3 [1,3,6,7,5,2,4]=>3 [1,3,6,7,5,4,2]=>3 [1,3,7,2,4,5,6]=>3 [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]=>3 [1,3,7,4,2,5,6]=>3 [1,3,7,4,2,6,5]=>3 [1,3,7,4,5,2,6]=>3 [1,3,7,4,5,6,2]=>3 [1,3,7,4,6,2,5]=>3 [1,3,7,4,6,5,2]=>3 [1,3,7,5,2,4,6]=>3 [1,3,7,5,2,6,4]=>3 [1,3,7,5,4,2,6]=>3 [1,3,7,5,4,6,2]=>3 [1,3,7,5,6,2,4]=>3 [1,3,7,5,6,4,2]=>3 [1,3,7,6,2,4,5]=>3 [1,3,7,6,2,5,4]=>3 [1,3,7,6,4,2,5]=>3 [1,3,7,6,4,5,2]=>3 [1,3,7,6,5,2,4]=>3 [1,3,7,6,5,4,2]=>3 [1,4,2,3,5,6,7]=>3 [1,4,2,3,5,7,6]=>3 [1,4,2,3,6,5,7]=>3 [1,4,2,3,6,7,5]=>3 [1,4,2,3,7,5,6]=>3 [1,4,2,3,7,6,5]=>3 [1,4,2,5,3,6,7]=>3 [1,4,2,5,3,7,6]=>3 [1,4,2,5,6,3,7]=>3 [1,4,2,5,6,7,3]=>3 [1,4,2,5,7,3,6]=>3 [1,4,2,5,7,6,3]=>3 [1,4,2,6,3,5,7]=>3 [1,4,2,6,3,7,5]=>3 [1,4,2,6,5,3,7]=>3 [1,4,2,6,5,7,3]=>3 [1,4,2,6,7,3,5]=>3 [1,4,2,6,7,5,3]=>3 [1,4,2,7,3,5,6]=>3 [1,4,2,7,3,6,5]=>3 [1,4,2,7,5,3,6]=>3 [1,4,2,7,5,6,3]=>3 [1,4,2,7,6,3,5]=>3 [1,4,2,7,6,5,3]=>3 [1,4,3,2,5,6,7]=>3 [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]=>3 [1,4,3,5,2,6,7]=>3 [1,4,3,5,2,7,6]=>3 [1,4,3,5,6,2,7]=>3 [1,4,3,5,6,7,2]=>3 [1,4,3,5,7,2,6]=>3 [1,4,3,5,7,6,2]=>3 [1,4,3,6,2,5,7]=>3 [1,4,3,6,2,7,5]=>3 [1,4,3,6,5,2,7]=>3 [1,4,3,6,5,7,2]=>3 [1,4,3,6,7,2,5]=>3 [1,4,3,6,7,5,2]=>3 [1,4,3,7,2,5,6]=>3 [1,4,3,7,2,6,5]=>3 [1,4,3,7,5,2,6]=>3 [1,4,3,7,5,6,2]=>3 [1,4,3,7,6,2,5]=>3 [1,4,3,7,6,5,2]=>3 [1,4,5,2,3,6,7]=>3 [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]=>3 [1,4,5,3,2,6,7]=>3 [1,4,5,3,2,7,6]=>3 [1,4,5,3,6,2,7]=>3 [1,4,5,3,6,7,2]=>3 [1,4,5,3,7,2,6]=>3 [1,4,5,3,7,6,2]=>3 [1,4,5,6,2,3,7]=>3 [1,4,5,6,2,7,3]=>3 [1,4,5,6,3,2,7]=>3 [1,4,5,6,3,7,2]=>3 [1,4,5,6,7,2,3]=>3 [1,4,5,6,7,3,2]=>3 [1,4,5,7,2,3,6]=>3 [1,4,5,7,2,6,3]=>3 [1,4,5,7,3,2,6]=>3 [1,4,5,7,3,6,2]=>3 [1,4,5,7,6,2,3]=>3 [1,4,5,7,6,3,2]=>3 [1,4,6,2,3,5,7]=>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]=>3 [1,4,6,3,2,5,7]=>3 [1,4,6,3,2,7,5]=>3 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>3 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>3 [1,4,6,5,2,3,7]=>3 [1,4,6,5,2,7,3]=>3 [1,4,6,5,3,2,7]=>3
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Description
The maximal size of a pair of weak twins for a permutation.
A pair of weak twins in a permutation is a pair of two disjoint subsequences of the same length with the same descent pattern. More formally, a pair of weak twins of size $k$ for a permutation $\pi$ of length $n$ are two disjoint lists $1 \leq i_1 < \dots < i_k \leq n$ and $1 \leq j_1 < \dots < j_k \leq n$ such that $\pi(i_a) < \pi(i_{a+1})$ if and only if $\pi(j_a) < \pi(j_{a+1})$ for all $1 \leq a < k$.
References
[1] Dudek, A., Grytczuk, Jarosław, Ruciński, A. On weak twins and up-and-down sub-permutations arXiv:2012.11451
Code
def statistic(pi):
    n = len(pi)
    pairs = [[set([i]), set([j])] for j in range(n) for i in range(j)]
    m = 0
    while pairs:
        m += 1
        new_pairs = []
        for A,B in pairs:
            a = max(A)
            b = max(B)
            for i in range(a+1,n):
                for j in range(b+1,n):
                    Anew = A.union([i])
                    Bnew = B.union([j])
                    if i not in Bnew and j not in Anew and (pi[a] > pi[i]) == (pi[b] > pi[j]):
                        new_pairs.append( [Anew,Bnew] )
        pairs = new_pairs
    return m
Created
Jan 08, 2021 at 12:18 by Christian Stump
Updated
Jan 08, 2021 at 12:59 by Martin Rubey