Identifier
- St001550: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,2,3,4]=>0
[1,2,4,3]=>0
[1,3,2,4]=>0
[1,3,4,2]=>0
[1,4,2,3]=>0
[1,4,3,2]=>0
[2,1,3,4]=>0
[2,1,4,3]=>0
[2,3,1,4]=>0
[2,3,4,1]=>0
[2,4,1,3]=>0
[2,4,3,1]=>0
[3,1,2,4]=>0
[3,1,4,2]=>0
[3,2,1,4]=>0
[3,2,4,1]=>0
[3,4,1,2]=>0
[3,4,2,1]=>0
[4,1,2,3]=>0
[4,1,3,2]=>0
[4,2,1,3]=>0
[4,2,3,1]=>0
[4,3,1,2]=>0
[4,3,2,1]=>0
[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
[1,2,4,3,5]=>0
[1,2,4,5,3]=>0
[1,2,5,3,4]=>0
[1,2,5,4,3]=>0
[1,3,2,4,5]=>0
[1,3,2,5,4]=>0
[1,3,4,2,5]=>0
[1,3,4,5,2]=>0
[1,3,5,2,4]=>0
[1,3,5,4,2]=>0
[1,4,2,3,5]=>0
[1,4,2,5,3]=>0
[1,4,3,2,5]=>0
[1,4,3,5,2]=>0
[1,4,5,2,3]=>0
[1,4,5,3,2]=>0
[1,5,2,3,4]=>0
[1,5,2,4,3]=>0
[1,5,3,2,4]=>0
[1,5,3,4,2]=>0
[1,5,4,2,3]=>0
[1,5,4,3,2]=>0
[2,1,3,4,5]=>0
[2,1,3,5,4]=>0
[2,1,4,3,5]=>0
[2,1,4,5,3]=>0
[2,1,5,3,4]=>0
[2,1,5,4,3]=>0
[2,3,1,4,5]=>0
[2,3,1,5,4]=>0
[2,3,4,1,5]=>0
[2,3,4,5,1]=>0
[2,3,5,1,4]=>0
[2,3,5,4,1]=>0
[2,4,1,3,5]=>0
[2,4,1,5,3]=>0
[2,4,3,1,5]=>0
[2,4,3,5,1]=>0
[2,4,5,1,3]=>0
[2,4,5,3,1]=>0
[2,5,1,3,4]=>0
[2,5,1,4,3]=>0
[2,5,3,1,4]=>0
[2,5,3,4,1]=>0
[2,5,4,1,3]=>0
[2,5,4,3,1]=>0
[3,1,2,4,5]=>0
[3,1,2,5,4]=>0
[3,1,4,2,5]=>0
[3,1,4,5,2]=>0
[3,1,5,2,4]=>0
[3,1,5,4,2]=>0
[3,2,1,4,5]=>0
[3,2,1,5,4]=>0
[3,2,4,1,5]=>0
[3,2,4,5,1]=>0
[3,2,5,1,4]=>0
[3,2,5,4,1]=>0
[3,4,1,2,5]=>0
[3,4,1,5,2]=>0
[3,4,2,1,5]=>0
[3,4,2,5,1]=>0
[3,4,5,1,2]=>0
[3,4,5,2,1]=>0
[3,5,1,2,4]=>0
[3,5,1,4,2]=>0
[3,5,2,1,4]=>0
[3,5,2,4,1]=>0
[3,5,4,1,2]=>1
[3,5,4,2,1]=>1
[4,1,2,3,5]=>0
[4,1,2,5,3]=>0
[4,1,3,2,5]=>0
[4,1,3,5,2]=>0
[4,1,5,2,3]=>0
[4,1,5,3,2]=>0
[4,2,1,3,5]=>0
[4,2,1,5,3]=>0
[4,2,3,1,5]=>0
[4,2,3,5,1]=>0
[4,2,5,1,3]=>0
[4,2,5,3,1]=>0
[4,3,1,2,5]=>0
[4,3,1,5,2]=>0
[4,3,2,1,5]=>0
[4,3,2,5,1]=>0
[4,3,5,1,2]=>0
[4,3,5,2,1]=>0
[4,5,1,2,3]=>0
[4,5,1,3,2]=>0
[4,5,2,1,3]=>0
[4,5,2,3,1]=>0
[4,5,3,1,2]=>0
[4,5,3,2,1]=>0
[5,1,2,3,4]=>0
[5,1,2,4,3]=>0
[5,1,3,2,4]=>0
[5,1,3,4,2]=>0
[5,1,4,2,3]=>0
[5,1,4,3,2]=>0
[5,2,1,3,4]=>0
[5,2,1,4,3]=>0
[5,2,3,1,4]=>0
[5,2,3,4,1]=>0
[5,2,4,1,3]=>0
[5,2,4,3,1]=>0
[5,3,1,2,4]=>0
[5,3,1,4,2]=>0
[5,3,2,1,4]=>0
[5,3,2,4,1]=>0
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>0
[5,4,1,3,2]=>0
[5,4,2,1,3]=>0
[5,4,2,3,1]=>0
[5,4,3,1,2]=>0
[5,4,3,2,1]=>0
[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
[1,2,3,5,6,4]=>0
[1,2,3,6,4,5]=>0
[1,2,3,6,5,4]=>0
[1,2,4,3,5,6]=>0
[1,2,4,3,6,5]=>0
[1,2,4,5,3,6]=>0
[1,2,4,5,6,3]=>0
[1,2,4,6,3,5]=>0
[1,2,4,6,5,3]=>0
[1,2,5,3,4,6]=>0
[1,2,5,3,6,4]=>0
[1,2,5,4,3,6]=>0
[1,2,5,4,6,3]=>0
[1,2,5,6,3,4]=>0
[1,2,5,6,4,3]=>0
[1,2,6,3,4,5]=>0
[1,2,6,3,5,4]=>0
[1,2,6,4,3,5]=>0
[1,2,6,4,5,3]=>0
[1,2,6,5,3,4]=>0
[1,2,6,5,4,3]=>0
[1,3,2,4,5,6]=>0
[1,3,2,4,6,5]=>0
[1,3,2,5,4,6]=>0
[1,3,2,5,6,4]=>0
[1,3,2,6,4,5]=>0
[1,3,2,6,5,4]=>0
[1,3,4,2,5,6]=>0
[1,3,4,2,6,5]=>0
[1,3,4,5,2,6]=>0
[1,3,4,5,6,2]=>0
[1,3,4,6,2,5]=>0
[1,3,4,6,5,2]=>0
[1,3,5,2,4,6]=>0
[1,3,5,2,6,4]=>0
[1,3,5,4,2,6]=>0
[1,3,5,4,6,2]=>0
[1,3,5,6,2,4]=>0
[1,3,5,6,4,2]=>0
[1,3,6,2,4,5]=>0
[1,3,6,2,5,4]=>0
[1,3,6,4,2,5]=>0
[1,3,6,4,5,2]=>0
[1,3,6,5,2,4]=>0
[1,3,6,5,4,2]=>0
[1,4,2,3,5,6]=>0
[1,4,2,3,6,5]=>0
[1,4,2,5,3,6]=>0
[1,4,2,5,6,3]=>0
[1,4,2,6,3,5]=>0
[1,4,2,6,5,3]=>0
[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
[1,4,3,5,2,6]=>0
[1,4,3,5,6,2]=>0
[1,4,3,6,2,5]=>0
[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>0
[1,4,5,2,6,3]=>0
[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
[1,4,5,6,2,3]=>0
[1,4,5,6,3,2]=>0
[1,4,6,2,3,5]=>0
[1,4,6,2,5,3]=>0
[1,4,6,3,2,5]=>0
[1,4,6,3,5,2]=>0
[1,4,6,5,2,3]=>1
[1,4,6,5,3,2]=>1
[1,5,2,3,4,6]=>0
[1,5,2,3,6,4]=>0
[1,5,2,4,3,6]=>0
[1,5,2,4,6,3]=>0
[1,5,2,6,3,4]=>0
[1,5,2,6,4,3]=>0
[1,5,3,2,4,6]=>0
[1,5,3,2,6,4]=>0
[1,5,3,4,2,6]=>0
[1,5,3,4,6,2]=>0
[1,5,3,6,2,4]=>0
[1,5,3,6,4,2]=>0
[1,5,4,2,3,6]=>0
[1,5,4,2,6,3]=>0
[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,2,3]=>0
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>0
[1,5,6,2,4,3]=>0
[1,5,6,3,2,4]=>0
[1,5,6,3,4,2]=>0
[1,5,6,4,2,3]=>0
[1,5,6,4,3,2]=>0
[1,6,2,3,4,5]=>0
[1,6,2,3,5,4]=>0
[1,6,2,4,3,5]=>0
[1,6,2,4,5,3]=>0
[1,6,2,5,3,4]=>0
[1,6,2,5,4,3]=>0
[1,6,3,2,4,5]=>0
[1,6,3,2,5,4]=>0
[1,6,3,4,2,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,2,4]=>0
[1,6,3,5,4,2]=>0
[1,6,4,2,3,5]=>0
[1,6,4,2,5,3]=>0
[1,6,4,3,2,5]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,2,3]=>1
[1,6,4,5,3,2]=>1
[1,6,5,2,3,4]=>0
[1,6,5,2,4,3]=>0
[1,6,5,3,2,4]=>0
[1,6,5,3,4,2]=>0
[1,6,5,4,2,3]=>0
[1,6,5,4,3,2]=>0
[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>0
[2,1,3,5,4,6]=>0
[2,1,3,5,6,4]=>0
[2,1,3,6,4,5]=>0
[2,1,3,6,5,4]=>0
[2,1,4,3,5,6]=>0
[2,1,4,3,6,5]=>0
[2,1,4,5,3,6]=>0
[2,1,4,5,6,3]=>0
[2,1,4,6,3,5]=>0
[2,1,4,6,5,3]=>0
[2,1,5,3,4,6]=>0
[2,1,5,3,6,4]=>0
[2,1,5,4,3,6]=>0
[2,1,5,4,6,3]=>0
[2,1,5,6,3,4]=>0
[2,1,5,6,4,3]=>0
[2,1,6,3,4,5]=>0
[2,1,6,3,5,4]=>0
[2,1,6,4,3,5]=>0
[2,1,6,4,5,3]=>0
[2,1,6,5,3,4]=>0
[2,1,6,5,4,3]=>0
[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>0
[2,3,1,5,4,6]=>0
[2,3,1,5,6,4]=>0
[2,3,1,6,4,5]=>0
[2,3,1,6,5,4]=>0
[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>0
[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>0
[2,3,4,6,1,5]=>0
[2,3,4,6,5,1]=>0
[2,3,5,1,4,6]=>0
[2,3,5,1,6,4]=>0
[2,3,5,4,1,6]=>0
[2,3,5,4,6,1]=>0
[2,3,5,6,1,4]=>0
[2,3,5,6,4,1]=>0
[2,3,6,1,4,5]=>0
[2,3,6,1,5,4]=>0
[2,3,6,4,1,5]=>0
[2,3,6,4,5,1]=>0
[2,3,6,5,1,4]=>0
[2,3,6,5,4,1]=>0
[2,4,1,3,5,6]=>0
[2,4,1,3,6,5]=>0
[2,4,1,5,3,6]=>0
[2,4,1,5,6,3]=>0
[2,4,1,6,3,5]=>0
[2,4,1,6,5,3]=>0
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,1,5]=>0
[2,4,3,6,5,1]=>0
[2,4,5,1,3,6]=>0
[2,4,5,1,6,3]=>0
[2,4,5,3,1,6]=>0
[2,4,5,3,6,1]=>0
[2,4,5,6,1,3]=>0
[2,4,5,6,3,1]=>0
[2,4,6,1,3,5]=>0
[2,4,6,1,5,3]=>0
[2,4,6,3,1,5]=>0
[2,4,6,3,5,1]=>0
[2,4,6,5,1,3]=>1
[2,4,6,5,3,1]=>1
[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
[2,5,1,4,3,6]=>0
[2,5,1,4,6,3]=>0
[2,5,1,6,3,4]=>0
[2,5,1,6,4,3]=>0
[2,5,3,1,4,6]=>0
[2,5,3,1,6,4]=>0
[2,5,3,4,1,6]=>0
[2,5,3,4,6,1]=>0
[2,5,3,6,1,4]=>0
[2,5,3,6,4,1]=>0
[2,5,4,1,3,6]=>0
[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>0
[2,5,4,3,6,1]=>0
[2,5,4,6,1,3]=>0
[2,5,4,6,3,1]=>0
[2,5,6,1,3,4]=>0
[2,5,6,1,4,3]=>0
[2,5,6,3,1,4]=>0
[2,5,6,3,4,1]=>0
[2,5,6,4,1,3]=>0
[2,5,6,4,3,1]=>0
[2,6,1,3,4,5]=>0
[2,6,1,3,5,4]=>0
[2,6,1,4,3,5]=>0
[2,6,1,4,5,3]=>0
[2,6,1,5,3,4]=>0
[2,6,1,5,4,3]=>0
[2,6,3,1,4,5]=>0
[2,6,3,1,5,4]=>0
[2,6,3,4,1,5]=>0
[2,6,3,4,5,1]=>0
[2,6,3,5,1,4]=>0
[2,6,3,5,4,1]=>0
[2,6,4,1,3,5]=>0
[2,6,4,1,5,3]=>0
[2,6,4,3,1,5]=>0
[2,6,4,3,5,1]=>0
[2,6,4,5,1,3]=>1
[2,6,4,5,3,1]=>1
[2,6,5,1,3,4]=>0
[2,6,5,1,4,3]=>0
[2,6,5,3,1,4]=>0
[2,6,5,3,4,1]=>0
[2,6,5,4,1,3]=>0
[2,6,5,4,3,1]=>0
[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>0
[3,1,2,5,4,6]=>0
[3,1,2,5,6,4]=>0
[3,1,2,6,4,5]=>0
[3,1,2,6,5,4]=>0
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
[3,1,4,6,2,5]=>0
[3,1,4,6,5,2]=>0
[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,4,2,6]=>0
[3,1,5,4,6,2]=>0
[3,1,5,6,2,4]=>0
[3,1,5,6,4,2]=>0
[3,1,6,2,4,5]=>0
[3,1,6,2,5,4]=>0
[3,1,6,4,2,5]=>0
[3,1,6,4,5,2]=>0
[3,1,6,5,2,4]=>0
[3,1,6,5,4,2]=>0
[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>0
[3,2,1,5,4,6]=>0
[3,2,1,5,6,4]=>0
[3,2,1,6,4,5]=>0
[3,2,1,6,5,4]=>0
[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>0
[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>0
[3,2,4,6,1,5]=>0
[3,2,4,6,5,1]=>0
[3,2,5,1,4,6]=>0
[3,2,5,1,6,4]=>0
[3,2,5,4,1,6]=>0
[3,2,5,4,6,1]=>0
[3,2,5,6,1,4]=>0
[3,2,5,6,4,1]=>0
[3,2,6,1,4,5]=>0
[3,2,6,1,5,4]=>0
[3,2,6,4,1,5]=>0
[3,2,6,4,5,1]=>0
[3,2,6,5,1,4]=>0
[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>0
[3,4,1,5,2,6]=>0
[3,4,1,5,6,2]=>0
[3,4,1,6,2,5]=>0
[3,4,1,6,5,2]=>0
[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>0
[3,4,2,6,1,5]=>0
[3,4,2,6,5,1]=>0
[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>0
[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>0
[3,4,5,6,1,2]=>0
[3,4,5,6,2,1]=>0
[3,4,6,1,2,5]=>0
[3,4,6,1,5,2]=>0
[3,4,6,2,1,5]=>0
[3,4,6,2,5,1]=>0
[3,4,6,5,1,2]=>1
[3,4,6,5,2,1]=>1
[3,5,1,2,4,6]=>0
[3,5,1,2,6,4]=>0
[3,5,1,4,2,6]=>0
[3,5,1,4,6,2]=>0
[3,5,1,6,2,4]=>0
[3,5,1,6,4,2]=>0
[3,5,2,1,4,6]=>0
[3,5,2,1,6,4]=>0
[3,5,2,4,1,6]=>0
[3,5,2,4,6,1]=>0
[3,5,2,6,1,4]=>0
[3,5,2,6,4,1]=>0
[3,5,4,1,2,6]=>1
[3,5,4,1,6,2]=>1
[3,5,4,2,1,6]=>1
[3,5,4,2,6,1]=>1
[3,5,4,6,1,2]=>1
[3,5,4,6,2,1]=>1
[3,5,6,1,2,4]=>0
[3,5,6,1,4,2]=>0
[3,5,6,2,1,4]=>0
[3,5,6,2,4,1]=>0
[3,5,6,4,1,2]=>0
[3,5,6,4,2,1]=>0
[3,6,1,2,4,5]=>0
[3,6,1,2,5,4]=>0
[3,6,1,4,2,5]=>0
[3,6,1,4,5,2]=>0
[3,6,1,5,2,4]=>0
[3,6,1,5,4,2]=>0
[3,6,2,1,4,5]=>0
[3,6,2,1,5,4]=>0
[3,6,2,4,1,5]=>0
[3,6,2,4,5,1]=>0
[3,6,2,5,1,4]=>0
[3,6,2,5,4,1]=>0
[3,6,4,1,2,5]=>1
[3,6,4,1,5,2]=>1
[3,6,4,2,1,5]=>1
[3,6,4,2,5,1]=>1
[3,6,4,5,1,2]=>2
[3,6,4,5,2,1]=>2
[3,6,5,1,2,4]=>1
[3,6,5,1,4,2]=>1
[3,6,5,2,1,4]=>1
[3,6,5,2,4,1]=>1
[3,6,5,4,1,2]=>1
[3,6,5,4,2,1]=>1
[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>0
[4,1,2,5,3,6]=>0
[4,1,2,5,6,3]=>0
[4,1,2,6,3,5]=>0
[4,1,2,6,5,3]=>0
[4,1,3,2,5,6]=>0
[4,1,3,2,6,5]=>0
[4,1,3,5,2,6]=>0
[4,1,3,5,6,2]=>0
[4,1,3,6,2,5]=>0
[4,1,3,6,5,2]=>0
[4,1,5,2,3,6]=>0
[4,1,5,2,6,3]=>0
[4,1,5,3,2,6]=>0
[4,1,5,3,6,2]=>0
[4,1,5,6,2,3]=>0
[4,1,5,6,3,2]=>0
[4,1,6,2,3,5]=>0
[4,1,6,2,5,3]=>0
[4,1,6,3,2,5]=>0
[4,1,6,3,5,2]=>0
[4,1,6,5,2,3]=>1
[4,1,6,5,3,2]=>1
[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>0
[4,2,1,5,3,6]=>0
[4,2,1,5,6,3]=>0
[4,2,1,6,3,5]=>0
[4,2,1,6,5,3]=>0
[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>0
[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>0
[4,2,3,6,1,5]=>0
[4,2,3,6,5,1]=>0
[4,2,5,1,3,6]=>0
[4,2,5,1,6,3]=>0
[4,2,5,3,1,6]=>0
[4,2,5,3,6,1]=>0
[4,2,5,6,1,3]=>0
[4,2,5,6,3,1]=>0
[4,2,6,1,3,5]=>0
[4,2,6,1,5,3]=>0
[4,2,6,3,1,5]=>0
[4,2,6,3,5,1]=>0
[4,2,6,5,1,3]=>1
[4,2,6,5,3,1]=>1
[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>0
[4,3,1,5,2,6]=>0
[4,3,1,5,6,2]=>0
[4,3,1,6,2,5]=>0
[4,3,1,6,5,2]=>0
[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>0
[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>0
[4,3,2,6,1,5]=>0
[4,3,2,6,5,1]=>0
[4,3,5,1,2,6]=>0
[4,3,5,1,6,2]=>0
[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>0
[4,3,5,6,1,2]=>0
[4,3,5,6,2,1]=>0
[4,3,6,1,2,5]=>0
[4,3,6,1,5,2]=>0
[4,3,6,2,1,5]=>0
[4,3,6,2,5,1]=>0
[4,3,6,5,1,2]=>1
[4,3,6,5,2,1]=>1
[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>0
[4,5,1,3,2,6]=>0
[4,5,1,3,6,2]=>0
[4,5,1,6,2,3]=>0
[4,5,1,6,3,2]=>0
[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>0
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>0
[4,5,2,6,1,3]=>0
[4,5,2,6,3,1]=>0
[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>0
[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>0
[4,5,3,6,1,2]=>0
[4,5,3,6,2,1]=>0
[4,5,6,1,2,3]=>0
[4,5,6,1,3,2]=>0
[4,5,6,2,1,3]=>0
[4,5,6,2,3,1]=>0
[4,5,6,3,1,2]=>0
[4,5,6,3,2,1]=>0
[4,6,1,2,3,5]=>0
[4,6,1,2,5,3]=>0
[4,6,1,3,2,5]=>0
[4,6,1,3,5,2]=>0
[4,6,1,5,2,3]=>1
[4,6,1,5,3,2]=>1
[4,6,2,1,3,5]=>0
[4,6,2,1,5,3]=>0
[4,6,2,3,1,5]=>0
[4,6,2,3,5,1]=>0
[4,6,2,5,1,3]=>1
[4,6,2,5,3,1]=>1
[4,6,3,1,2,5]=>0
[4,6,3,1,5,2]=>0
[4,6,3,2,1,5]=>0
[4,6,3,2,5,1]=>0
[4,6,3,5,1,2]=>1
[4,6,3,5,2,1]=>1
[4,6,5,1,2,3]=>0
[4,6,5,1,3,2]=>0
[4,6,5,2,1,3]=>0
[4,6,5,2,3,1]=>0
[4,6,5,3,1,2]=>0
[4,6,5,3,2,1]=>0
[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>0
[5,1,2,4,3,6]=>0
[5,1,2,4,6,3]=>0
[5,1,2,6,3,4]=>0
[5,1,2,6,4,3]=>0
[5,1,3,2,4,6]=>0
[5,1,3,2,6,4]=>0
[5,1,3,4,2,6]=>0
[5,1,3,4,6,2]=>0
[5,1,3,6,2,4]=>0
[5,1,3,6,4,2]=>0
[5,1,4,2,3,6]=>0
[5,1,4,2,6,3]=>0
[5,1,4,3,2,6]=>0
[5,1,4,3,6,2]=>0
[5,1,4,6,2,3]=>0
[5,1,4,6,3,2]=>0
[5,1,6,2,3,4]=>0
[5,1,6,2,4,3]=>0
[5,1,6,3,2,4]=>0
[5,1,6,3,4,2]=>0
[5,1,6,4,2,3]=>0
[5,1,6,4,3,2]=>0
[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>0
[5,2,1,4,3,6]=>0
[5,2,1,4,6,3]=>0
[5,2,1,6,3,4]=>0
[5,2,1,6,4,3]=>0
[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>0
[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>0
[5,2,3,6,1,4]=>0
[5,2,3,6,4,1]=>0
[5,2,4,1,3,6]=>0
[5,2,4,1,6,3]=>0
[5,2,4,3,1,6]=>0
[5,2,4,3,6,1]=>0
[5,2,4,6,1,3]=>0
[5,2,4,6,3,1]=>0
[5,2,6,1,3,4]=>0
[5,2,6,1,4,3]=>0
[5,2,6,3,1,4]=>0
[5,2,6,3,4,1]=>0
[5,2,6,4,1,3]=>0
[5,2,6,4,3,1]=>0
[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>0
[5,3,1,4,2,6]=>0
[5,3,1,4,6,2]=>0
[5,3,1,6,2,4]=>0
[5,3,1,6,4,2]=>0
[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>0
[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>0
[5,3,2,6,1,4]=>0
[5,3,2,6,4,1]=>0
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>1
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>0
[5,3,6,1,4,2]=>0
[5,3,6,2,1,4]=>0
[5,3,6,2,4,1]=>0
[5,3,6,4,1,2]=>0
[5,3,6,4,2,1]=>0
[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>0
[5,4,1,3,2,6]=>0
[5,4,1,3,6,2]=>0
[5,4,1,6,2,3]=>0
[5,4,1,6,3,2]=>0
[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>0
[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>0
[5,4,2,6,1,3]=>0
[5,4,2,6,3,1]=>0
[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>0
[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>0
[5,4,3,6,1,2]=>0
[5,4,3,6,2,1]=>0
[5,4,6,1,2,3]=>0
[5,4,6,1,3,2]=>0
[5,4,6,2,1,3]=>0
[5,4,6,2,3,1]=>0
[5,4,6,3,1,2]=>0
[5,4,6,3,2,1]=>0
[5,6,1,2,3,4]=>0
[5,6,1,2,4,3]=>0
[5,6,1,3,2,4]=>0
[5,6,1,3,4,2]=>0
[5,6,1,4,2,3]=>0
[5,6,1,4,3,2]=>0
[5,6,2,1,3,4]=>0
[5,6,2,1,4,3]=>0
[5,6,2,3,1,4]=>0
[5,6,2,3,4,1]=>0
[5,6,2,4,1,3]=>0
[5,6,2,4,3,1]=>0
[5,6,3,1,2,4]=>0
[5,6,3,1,4,2]=>0
[5,6,3,2,1,4]=>0
[5,6,3,2,4,1]=>0
[5,6,3,4,1,2]=>0
[5,6,3,4,2,1]=>0
[5,6,4,1,2,3]=>0
[5,6,4,1,3,2]=>0
[5,6,4,2,1,3]=>0
[5,6,4,2,3,1]=>0
[5,6,4,3,1,2]=>0
[5,6,4,3,2,1]=>0
[6,1,2,3,4,5]=>0
[6,1,2,3,5,4]=>0
[6,1,2,4,3,5]=>0
[6,1,2,4,5,3]=>0
[6,1,2,5,3,4]=>0
[6,1,2,5,4,3]=>0
[6,1,3,2,4,5]=>0
[6,1,3,2,5,4]=>0
[6,1,3,4,2,5]=>0
[6,1,3,4,5,2]=>0
[6,1,3,5,2,4]=>0
[6,1,3,5,4,2]=>0
[6,1,4,2,3,5]=>0
[6,1,4,2,5,3]=>0
[6,1,4,3,2,5]=>0
[6,1,4,3,5,2]=>0
[6,1,4,5,2,3]=>1
[6,1,4,5,3,2]=>1
[6,1,5,2,3,4]=>0
[6,1,5,2,4,3]=>0
[6,1,5,3,2,4]=>0
[6,1,5,3,4,2]=>0
[6,1,5,4,2,3]=>0
[6,1,5,4,3,2]=>0
[6,2,1,3,4,5]=>0
[6,2,1,3,5,4]=>0
[6,2,1,4,3,5]=>0
[6,2,1,4,5,3]=>0
[6,2,1,5,3,4]=>0
[6,2,1,5,4,3]=>0
[6,2,3,1,4,5]=>0
[6,2,3,1,5,4]=>0
[6,2,3,4,1,5]=>0
[6,2,3,4,5,1]=>0
[6,2,3,5,1,4]=>0
[6,2,3,5,4,1]=>0
[6,2,4,1,3,5]=>0
[6,2,4,1,5,3]=>0
[6,2,4,3,1,5]=>0
[6,2,4,3,5,1]=>0
[6,2,4,5,1,3]=>1
[6,2,4,5,3,1]=>1
[6,2,5,1,3,4]=>0
[6,2,5,1,4,3]=>0
[6,2,5,3,1,4]=>0
[6,2,5,3,4,1]=>0
[6,2,5,4,1,3]=>0
[6,2,5,4,3,1]=>0
[6,3,1,2,4,5]=>0
[6,3,1,2,5,4]=>0
[6,3,1,4,2,5]=>0
[6,3,1,4,5,2]=>0
[6,3,1,5,2,4]=>0
[6,3,1,5,4,2]=>0
[6,3,2,1,4,5]=>0
[6,3,2,1,5,4]=>0
[6,3,2,4,1,5]=>0
[6,3,2,4,5,1]=>0
[6,3,2,5,1,4]=>0
[6,3,2,5,4,1]=>0
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>1
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>2
[6,3,4,5,2,1]=>2
[6,3,5,1,2,4]=>1
[6,3,5,1,4,2]=>1
[6,3,5,2,1,4]=>1
[6,3,5,2,4,1]=>1
[6,3,5,4,1,2]=>1
[6,3,5,4,2,1]=>1
[6,4,1,2,3,5]=>0
[6,4,1,2,5,3]=>0
[6,4,1,3,2,5]=>0
[6,4,1,3,5,2]=>0
[6,4,1,5,2,3]=>1
[6,4,1,5,3,2]=>1
[6,4,2,1,3,5]=>0
[6,4,2,1,5,3]=>0
[6,4,2,3,1,5]=>0
[6,4,2,3,5,1]=>0
[6,4,2,5,1,3]=>1
[6,4,2,5,3,1]=>1
[6,4,3,1,2,5]=>0
[6,4,3,1,5,2]=>0
[6,4,3,2,1,5]=>0
[6,4,3,2,5,1]=>0
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>0
[6,4,5,1,3,2]=>0
[6,4,5,2,1,3]=>0
[6,4,5,2,3,1]=>0
[6,4,5,3,1,2]=>0
[6,4,5,3,2,1]=>0
[6,5,1,2,3,4]=>0
[6,5,1,2,4,3]=>0
[6,5,1,3,2,4]=>0
[6,5,1,3,4,2]=>0
[6,5,1,4,2,3]=>0
[6,5,1,4,3,2]=>0
[6,5,2,1,3,4]=>0
[6,5,2,1,4,3]=>0
[6,5,2,3,1,4]=>0
[6,5,2,3,4,1]=>0
[6,5,2,4,1,3]=>0
[6,5,2,4,3,1]=>0
[6,5,3,1,2,4]=>0
[6,5,3,1,4,2]=>0
[6,5,3,2,1,4]=>0
[6,5,3,2,4,1]=>0
[6,5,3,4,1,2]=>0
[6,5,3,4,2,1]=>0
[6,5,4,1,2,3]=>0
[6,5,4,1,3,2]=>0
[6,5,4,2,1,3]=>0
[6,5,4,2,3,1]=>0
[6,5,4,3,1,2]=>0
[6,5,4,3,2,1]=>0
[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>0
[1,2,3,4,6,5,7]=>0
[1,2,3,4,6,7,5]=>0
[1,2,3,4,7,5,6]=>0
[1,2,3,4,7,6,5]=>0
[1,2,3,5,4,6,7]=>0
[1,2,3,5,4,7,6]=>0
[1,2,3,5,6,4,7]=>0
[1,2,3,5,6,7,4]=>0
[1,2,3,5,7,4,6]=>0
[1,2,3,5,7,6,4]=>0
[1,2,3,6,4,5,7]=>0
[1,2,3,6,4,7,5]=>0
[1,2,3,6,5,4,7]=>0
[1,2,3,6,5,7,4]=>0
[1,2,3,6,7,4,5]=>0
[1,2,3,6,7,5,4]=>0
[1,2,3,7,4,5,6]=>0
[1,2,3,7,4,6,5]=>0
[1,2,3,7,5,4,6]=>0
[1,2,3,7,5,6,4]=>0
[1,2,3,7,6,4,5]=>0
[1,2,3,7,6,5,4]=>0
[1,2,4,3,5,6,7]=>0
[1,2,4,3,5,7,6]=>0
[1,2,4,3,6,5,7]=>0
[1,2,4,3,6,7,5]=>0
[1,2,4,3,7,5,6]=>0
[1,2,4,3,7,6,5]=>0
[1,2,4,5,3,6,7]=>0
[1,2,4,5,3,7,6]=>0
[1,2,4,5,6,3,7]=>0
[1,2,4,5,6,7,3]=>0
[1,2,4,5,7,3,6]=>0
[1,2,4,5,7,6,3]=>0
[1,2,4,6,3,5,7]=>0
[1,2,4,6,3,7,5]=>0
[1,2,4,6,5,3,7]=>0
[1,2,4,6,5,7,3]=>0
[1,2,4,6,7,3,5]=>0
[1,2,4,6,7,5,3]=>0
[1,2,4,7,3,5,6]=>0
[1,2,4,7,3,6,5]=>0
[1,2,4,7,5,3,6]=>0
[1,2,4,7,5,6,3]=>0
[1,2,4,7,6,3,5]=>0
[1,2,4,7,6,5,3]=>0
[1,2,5,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>0
[1,2,5,3,6,4,7]=>0
[1,2,5,3,6,7,4]=>0
[1,2,5,3,7,4,6]=>0
[1,2,5,3,7,6,4]=>0
[1,2,5,4,3,6,7]=>0
[1,2,5,4,3,7,6]=>0
[1,2,5,4,6,3,7]=>0
[1,2,5,4,6,7,3]=>0
[1,2,5,4,7,3,6]=>0
[1,2,5,4,7,6,3]=>0
[1,2,5,6,3,4,7]=>0
[1,2,5,6,3,7,4]=>0
[1,2,5,6,4,3,7]=>0
[1,2,5,6,4,7,3]=>0
[1,2,5,6,7,3,4]=>0
[1,2,5,6,7,4,3]=>0
[1,2,5,7,3,4,6]=>0
[1,2,5,7,3,6,4]=>0
[1,2,5,7,4,3,6]=>0
[1,2,5,7,4,6,3]=>0
[1,2,5,7,6,3,4]=>1
[1,2,5,7,6,4,3]=>1
[1,2,6,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>0
[1,2,6,3,5,4,7]=>0
[1,2,6,3,5,7,4]=>0
[1,2,6,3,7,4,5]=>0
[1,2,6,3,7,5,4]=>0
[1,2,6,4,3,5,7]=>0
[1,2,6,4,3,7,5]=>0
[1,2,6,4,5,3,7]=>0
[1,2,6,4,5,7,3]=>0
[1,2,6,4,7,3,5]=>0
[1,2,6,4,7,5,3]=>0
[1,2,6,5,3,4,7]=>0
[1,2,6,5,3,7,4]=>0
[1,2,6,5,4,3,7]=>0
[1,2,6,5,4,7,3]=>0
[1,2,6,5,7,3,4]=>0
[1,2,6,5,7,4,3]=>0
[1,2,6,7,3,4,5]=>0
[1,2,6,7,3,5,4]=>0
[1,2,6,7,4,3,5]=>0
[1,2,6,7,4,5,3]=>0
[1,2,6,7,5,3,4]=>0
[1,2,6,7,5,4,3]=>0
[1,2,7,3,4,5,6]=>0
[1,2,7,3,4,6,5]=>0
[1,2,7,3,5,4,6]=>0
[1,2,7,3,5,6,4]=>0
[1,2,7,3,6,4,5]=>0
[1,2,7,3,6,5,4]=>0
[1,2,7,4,3,5,6]=>0
[1,2,7,4,3,6,5]=>0
[1,2,7,4,5,3,6]=>0
[1,2,7,4,5,6,3]=>0
[1,2,7,4,6,3,5]=>0
[1,2,7,4,6,5,3]=>0
[1,2,7,5,3,4,6]=>0
[1,2,7,5,3,6,4]=>0
[1,2,7,5,4,3,6]=>0
[1,2,7,5,4,6,3]=>0
[1,2,7,5,6,3,4]=>1
[1,2,7,5,6,4,3]=>1
[1,2,7,6,3,4,5]=>0
[1,2,7,6,3,5,4]=>0
[1,2,7,6,4,3,5]=>0
[1,2,7,6,4,5,3]=>0
[1,2,7,6,5,3,4]=>0
[1,2,7,6,5,4,3]=>0
[1,3,2,4,5,6,7]=>0
[1,3,2,4,5,7,6]=>0
[1,3,2,4,6,5,7]=>0
[1,3,2,4,6,7,5]=>0
[1,3,2,4,7,5,6]=>0
[1,3,2,4,7,6,5]=>0
[1,3,2,5,4,6,7]=>0
[1,3,2,5,4,7,6]=>0
[1,3,2,5,6,4,7]=>0
[1,3,2,5,6,7,4]=>0
[1,3,2,5,7,4,6]=>0
[1,3,2,5,7,6,4]=>0
[1,3,2,6,4,5,7]=>0
[1,3,2,6,4,7,5]=>0
[1,3,2,6,5,4,7]=>0
[1,3,2,6,5,7,4]=>0
[1,3,2,6,7,4,5]=>0
[1,3,2,6,7,5,4]=>0
[1,3,2,7,4,5,6]=>0
[1,3,2,7,4,6,5]=>0
[1,3,2,7,5,4,6]=>0
[1,3,2,7,5,6,4]=>0
[1,3,2,7,6,4,5]=>0
[1,3,2,7,6,5,4]=>0
[1,3,4,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>0
[1,3,4,2,6,5,7]=>0
[1,3,4,2,6,7,5]=>0
[1,3,4,2,7,5,6]=>0
[1,3,4,2,7,6,5]=>0
[1,3,4,5,2,6,7]=>0
[1,3,4,5,2,7,6]=>0
[1,3,4,5,6,2,7]=>0
[1,3,4,5,6,7,2]=>0
[1,3,4,5,7,2,6]=>0
[1,3,4,5,7,6,2]=>0
[1,3,4,6,2,5,7]=>0
[1,3,4,6,2,7,5]=>0
[1,3,4,6,5,2,7]=>0
[1,3,4,6,5,7,2]=>0
[1,3,4,6,7,2,5]=>0
[1,3,4,6,7,5,2]=>0
[1,3,4,7,2,5,6]=>0
[1,3,4,7,2,6,5]=>0
[1,3,4,7,5,2,6]=>0
[1,3,4,7,5,6,2]=>0
[1,3,4,7,6,2,5]=>0
[1,3,4,7,6,5,2]=>0
[1,3,5,2,4,6,7]=>0
[1,3,5,2,4,7,6]=>0
[1,3,5,2,6,4,7]=>0
[1,3,5,2,6,7,4]=>0
[1,3,5,2,7,4,6]=>0
[1,3,5,2,7,6,4]=>0
[1,3,5,4,2,6,7]=>0
[1,3,5,4,2,7,6]=>0
[1,3,5,4,6,2,7]=>0
[1,3,5,4,6,7,2]=>0
[1,3,5,4,7,2,6]=>0
[1,3,5,4,7,6,2]=>0
[1,3,5,6,2,4,7]=>0
[1,3,5,6,2,7,4]=>0
[1,3,5,6,4,2,7]=>0
[1,3,5,6,4,7,2]=>0
[1,3,5,6,7,2,4]=>0
[1,3,5,6,7,4,2]=>0
[1,3,5,7,2,4,6]=>0
[1,3,5,7,2,6,4]=>0
[1,3,5,7,4,2,6]=>0
[1,3,5,7,4,6,2]=>0
[1,3,5,7,6,2,4]=>1
[1,3,5,7,6,4,2]=>1
[1,3,6,2,4,5,7]=>0
[1,3,6,2,4,7,5]=>0
[1,3,6,2,5,4,7]=>0
[1,3,6,2,5,7,4]=>0
[1,3,6,2,7,4,5]=>0
[1,3,6,2,7,5,4]=>0
[1,3,6,4,2,5,7]=>0
[1,3,6,4,2,7,5]=>0
[1,3,6,4,5,2,7]=>0
[1,3,6,4,5,7,2]=>0
[1,3,6,4,7,2,5]=>0
[1,3,6,4,7,5,2]=>0
[1,3,6,5,2,4,7]=>0
[1,3,6,5,2,7,4]=>0
[1,3,6,5,4,2,7]=>0
[1,3,6,5,4,7,2]=>0
[1,3,6,5,7,2,4]=>0
[1,3,6,5,7,4,2]=>0
[1,3,6,7,2,4,5]=>0
[1,3,6,7,2,5,4]=>0
[1,3,6,7,4,2,5]=>0
[1,3,6,7,4,5,2]=>0
[1,3,6,7,5,2,4]=>0
[1,3,6,7,5,4,2]=>0
[1,3,7,2,4,5,6]=>0
[1,3,7,2,4,6,5]=>0
[1,3,7,2,5,4,6]=>0
[1,3,7,2,5,6,4]=>0
[1,3,7,2,6,4,5]=>0
[1,3,7,2,6,5,4]=>0
[1,3,7,4,2,5,6]=>0
[1,3,7,4,2,6,5]=>0
[1,3,7,4,5,2,6]=>0
[1,3,7,4,5,6,2]=>0
[1,3,7,4,6,2,5]=>0
[1,3,7,4,6,5,2]=>0
[1,3,7,5,2,4,6]=>0
[1,3,7,5,2,6,4]=>0
[1,3,7,5,4,2,6]=>0
[1,3,7,5,4,6,2]=>0
[1,3,7,5,6,2,4]=>1
[1,3,7,5,6,4,2]=>1
[1,3,7,6,2,4,5]=>0
[1,3,7,6,2,5,4]=>0
[1,3,7,6,4,2,5]=>0
[1,3,7,6,4,5,2]=>0
[1,3,7,6,5,2,4]=>0
[1,3,7,6,5,4,2]=>0
[1,4,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>0
[1,4,2,3,6,5,7]=>0
[1,4,2,3,6,7,5]=>0
[1,4,2,3,7,5,6]=>0
[1,4,2,3,7,6,5]=>0
[1,4,2,5,3,6,7]=>0
[1,4,2,5,3,7,6]=>0
[1,4,2,5,6,3,7]=>0
[1,4,2,5,6,7,3]=>0
[1,4,2,5,7,3,6]=>0
[1,4,2,5,7,6,3]=>0
[1,4,2,6,3,5,7]=>0
[1,4,2,6,3,7,5]=>0
[1,4,2,6,5,3,7]=>0
[1,4,2,6,5,7,3]=>0
[1,4,2,6,7,3,5]=>0
[1,4,2,6,7,5,3]=>0
[1,4,2,7,3,5,6]=>0
[1,4,2,7,3,6,5]=>0
[1,4,2,7,5,3,6]=>0
[1,4,2,7,5,6,3]=>0
[1,4,2,7,6,3,5]=>0
[1,4,2,7,6,5,3]=>0
[1,4,3,2,5,6,7]=>0
[1,4,3,2,5,7,6]=>0
[1,4,3,2,6,5,7]=>0
[1,4,3,2,6,7,5]=>0
[1,4,3,2,7,5,6]=>0
[1,4,3,2,7,6,5]=>0
[1,4,3,5,2,6,7]=>0
[1,4,3,5,2,7,6]=>0
[1,4,3,5,6,2,7]=>0
[1,4,3,5,6,7,2]=>0
[1,4,3,5,7,2,6]=>0
[1,4,3,5,7,6,2]=>0
[1,4,3,6,2,5,7]=>0
[1,4,3,6,2,7,5]=>0
[1,4,3,6,5,2,7]=>0
[1,4,3,6,5,7,2]=>0
[1,4,3,6,7,2,5]=>0
[1,4,3,6,7,5,2]=>0
[1,4,3,7,2,5,6]=>0
[1,4,3,7,2,6,5]=>0
[1,4,3,7,5,2,6]=>0
[1,4,3,7,5,6,2]=>0
[1,4,3,7,6,2,5]=>0
[1,4,3,7,6,5,2]=>0
[1,4,5,2,3,6,7]=>0
[1,4,5,2,3,7,6]=>0
[1,4,5,2,6,3,7]=>0
[1,4,5,2,6,7,3]=>0
[1,4,5,2,7,3,6]=>0
[1,4,5,2,7,6,3]=>0
[1,4,5,3,2,6,7]=>0
[1,4,5,3,2,7,6]=>0
[1,4,5,3,6,2,7]=>0
[1,4,5,3,6,7,2]=>0
[1,4,5,3,7,2,6]=>0
[1,4,5,3,7,6,2]=>0
[1,4,5,6,2,3,7]=>0
[1,4,5,6,2,7,3]=>0
[1,4,5,6,3,2,7]=>0
[1,4,5,6,3,7,2]=>0
[1,4,5,6,7,2,3]=>0
[1,4,5,6,7,3,2]=>0
[1,4,5,7,2,3,6]=>0
[1,4,5,7,2,6,3]=>0
[1,4,5,7,3,2,6]=>0
[1,4,5,7,3,6,2]=>0
[1,4,5,7,6,2,3]=>1
[1,4,5,7,6,3,2]=>1
[1,4,6,2,3,5,7]=>0
[1,4,6,2,3,7,5]=>0
[1,4,6,2,5,3,7]=>0
[1,4,6,2,5,7,3]=>0
[1,4,6,2,7,3,5]=>0
[1,4,6,2,7,5,3]=>0
[1,4,6,3,2,5,7]=>0
[1,4,6,3,2,7,5]=>0
[1,4,6,3,5,2,7]=>0
[1,4,6,3,5,7,2]=>0
[1,4,6,3,7,2,5]=>0
[1,4,6,3,7,5,2]=>0
[1,4,6,5,2,3,7]=>1
[1,4,6,5,2,7,3]=>1
[1,4,6,5,3,2,7]=>1
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Description
The number of inversions between exceedances where the greater exceedance is linked.
This is for a permutation $\sigma$ of length $n$ given by
$$\operatorname{ile}(\sigma) = \#\{1 \leq i, j \leq n \mid i < j < \sigma(j) < \sigma(i) \wedge \sigma^{-1}(j) < j \}.$$
This is for a permutation $\sigma$ of length $n$ given by
$$\operatorname{ile}(\sigma) = \#\{1 \leq i, j \leq n \mid i < j < \sigma(j) < \sigma(i) \wedge \sigma^{-1}(j) < j \}.$$
References
[1] Blitvić, N., Steingrímsson, E. Permutations, moments, measures arXiv:2001.00280
Code
def statistic(pi):
n = len(pi)
return sum(1 for j in [1 .. n] for i in [1 .. n] if i < j < pi(j) < pi(i) and pi.inverse()(j) < j )
Created
May 19, 2020 at 10:24 by Christian Stump
Updated
May 19, 2020 at 10:24 by Christian Stump
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