Identifier
Values
=>
[1]=>0
[-1]=>0
[1,2]=>0
[1,-2]=>1
[-1,2]=>0
[-1,-2]=>0
[2,1]=>0
[2,-1]=>0
[-2,1]=>0
[-2,-1]=>0
[1,2,3]=>0
[1,2,-3]=>2
[1,-2,3]=>1
[1,-2,-3]=>2
[-1,2,3]=>0
[-1,2,-3]=>1
[-1,-2,3]=>0
[-1,-2,-3]=>0
[1,3,2]=>0
[1,3,-2]=>1
[1,-3,2]=>1
[1,-3,-2]=>2
[-1,3,2]=>0
[-1,3,-2]=>0
[-1,-3,2]=>0
[-1,-3,-2]=>0
[2,1,3]=>0
[2,1,-3]=>2
[2,-1,3]=>0
[2,-1,-3]=>1
[-2,1,3]=>0
[-2,1,-3]=>1
[-2,-1,3]=>0
[-2,-1,-3]=>0
[2,3,1]=>0
[2,3,-1]=>0
[2,-3,1]=>1
[2,-3,-1]=>1
[-2,3,1]=>0
[-2,3,-1]=>0
[-2,-3,1]=>0
[-2,-3,-1]=>0
[3,1,2]=>0
[3,1,-2]=>1
[3,-1,2]=>0
[3,-1,-2]=>0
[-3,1,2]=>0
[-3,1,-2]=>1
[-3,-1,2]=>0
[-3,-1,-2]=>0
[3,2,1]=>0
[3,2,-1]=>0
[3,-2,1]=>0
[3,-2,-1]=>0
[-3,2,1]=>0
[-3,2,-1]=>0
[-3,-2,1]=>0
[-3,-2,-1]=>0
[1,2,3,4]=>0
[1,2,3,-4]=>3
[1,2,-3,4]=>2
[1,2,-3,-4]=>4
[1,-2,3,4]=>1
[1,-2,3,-4]=>3
[1,-2,-3,4]=>2
[1,-2,-3,-4]=>3
[-1,2,3,4]=>0
[-1,2,3,-4]=>2
[-1,2,-3,4]=>1
[-1,2,-3,-4]=>2
[-1,-2,3,4]=>0
[-1,-2,3,-4]=>1
[-1,-2,-3,4]=>0
[-1,-2,-3,-4]=>0
[1,2,4,3]=>0
[1,2,4,-3]=>2
[1,2,-4,3]=>2
[1,2,-4,-3]=>4
[1,-2,4,3]=>1
[1,-2,4,-3]=>2
[1,-2,-4,3]=>2
[1,-2,-4,-3]=>3
[-1,2,4,3]=>0
[-1,2,4,-3]=>1
[-1,2,-4,3]=>1
[-1,2,-4,-3]=>2
[-1,-2,4,3]=>0
[-1,-2,4,-3]=>0
[-1,-2,-4,3]=>0
[-1,-2,-4,-3]=>0
[1,3,2,4]=>0
[1,3,2,-4]=>3
[1,3,-2,4]=>1
[1,3,-2,-4]=>3
[1,-3,2,4]=>1
[1,-3,2,-4]=>3
[1,-3,-2,4]=>2
[1,-3,-2,-4]=>3
[-1,3,2,4]=>0
[-1,3,2,-4]=>2
[-1,3,-2,4]=>0
[-1,3,-2,-4]=>1
[-1,-3,2,4]=>0
[-1,-3,2,-4]=>1
[-1,-3,-2,4]=>0
[-1,-3,-2,-4]=>0
[1,3,4,2]=>0
[1,3,4,-2]=>1
[1,3,-4,2]=>2
[1,3,-4,-2]=>3
[1,-3,4,2]=>1
[1,-3,4,-2]=>2
[1,-3,-4,2]=>2
[1,-3,-4,-2]=>3
[-1,3,4,2]=>0
[-1,3,4,-2]=>0
[-1,3,-4,2]=>1
[-1,3,-4,-2]=>1
[-1,-3,4,2]=>0
[-1,-3,4,-2]=>0
[-1,-3,-4,2]=>0
[-1,-3,-4,-2]=>0
[1,4,2,3]=>0
[1,4,2,-3]=>2
[1,4,-2,3]=>1
[1,4,-2,-3]=>2
[1,-4,2,3]=>1
[1,-4,2,-3]=>3
[1,-4,-2,3]=>2
[1,-4,-2,-3]=>3
[-1,4,2,3]=>0
[-1,4,2,-3]=>1
[-1,4,-2,3]=>0
[-1,4,-2,-3]=>0
[-1,-4,2,3]=>0
[-1,-4,2,-3]=>1
[-1,-4,-2,3]=>0
[-1,-4,-2,-3]=>0
[1,4,3,2]=>0
[1,4,3,-2]=>1
[1,4,-3,2]=>1
[1,4,-3,-2]=>2
[1,-4,3,2]=>1
[1,-4,3,-2]=>2
[1,-4,-3,2]=>2
[1,-4,-3,-2]=>3
[-1,4,3,2]=>0
[-1,4,3,-2]=>0
[-1,4,-3,2]=>0
[-1,4,-3,-2]=>0
[-1,-4,3,2]=>0
[-1,-4,3,-2]=>0
[-1,-4,-3,2]=>0
[-1,-4,-3,-2]=>0
[2,1,3,4]=>0
[2,1,3,-4]=>3
[2,1,-3,4]=>2
[2,1,-3,-4]=>4
[2,-1,3,4]=>0
[2,-1,3,-4]=>2
[2,-1,-3,4]=>1
[2,-1,-3,-4]=>2
[-2,1,3,4]=>0
[-2,1,3,-4]=>2
[-2,1,-3,4]=>1
[-2,1,-3,-4]=>2
[-2,-1,3,4]=>0
[-2,-1,3,-4]=>1
[-2,-1,-3,4]=>0
[-2,-1,-3,-4]=>0
[2,1,4,3]=>0
[2,1,4,-3]=>2
[2,1,-4,3]=>2
[2,1,-4,-3]=>4
[2,-1,4,3]=>0
[2,-1,4,-3]=>1
[2,-1,-4,3]=>1
[2,-1,-4,-3]=>2
[-2,1,4,3]=>0
[-2,1,4,-3]=>1
[-2,1,-4,3]=>1
[-2,1,-4,-3]=>2
[-2,-1,4,3]=>0
[-2,-1,4,-3]=>0
[-2,-1,-4,3]=>0
[-2,-1,-4,-3]=>0
[2,3,1,4]=>0
[2,3,1,-4]=>3
[2,3,-1,4]=>0
[2,3,-1,-4]=>2
[2,-3,1,4]=>1
[2,-3,1,-4]=>3
[2,-3,-1,4]=>1
[2,-3,-1,-4]=>2
[-2,3,1,4]=>0
[-2,3,1,-4]=>2
[-2,3,-1,4]=>0
[-2,3,-1,-4]=>1
[-2,-3,1,4]=>0
[-2,-3,1,-4]=>1
[-2,-3,-1,4]=>0
[-2,-3,-1,-4]=>0
[2,3,4,1]=>0
[2,3,4,-1]=>0
[2,3,-4,1]=>2
[2,3,-4,-1]=>2
[2,-3,4,1]=>1
[2,-3,4,-1]=>1
[2,-3,-4,1]=>2
[2,-3,-4,-1]=>2
[-2,3,4,1]=>0
[-2,3,4,-1]=>0
[-2,3,-4,1]=>1
[-2,3,-4,-1]=>1
[-2,-3,4,1]=>0
[-2,-3,4,-1]=>0
[-2,-3,-4,1]=>0
[-2,-3,-4,-1]=>0
[2,4,1,3]=>0
[2,4,1,-3]=>2
[2,4,-1,3]=>0
[2,4,-1,-3]=>1
[2,-4,1,3]=>1
[2,-4,1,-3]=>3
[2,-4,-1,3]=>1
[2,-4,-1,-3]=>2
[-2,4,1,3]=>0
[-2,4,1,-3]=>1
[-2,4,-1,3]=>0
[-2,4,-1,-3]=>0
[-2,-4,1,3]=>0
[-2,-4,1,-3]=>1
[-2,-4,-1,3]=>0
[-2,-4,-1,-3]=>0
[2,4,3,1]=>0
[2,4,3,-1]=>0
[2,4,-3,1]=>1
[2,4,-3,-1]=>1
[2,-4,3,1]=>1
[2,-4,3,-1]=>1
[2,-4,-3,1]=>2
[2,-4,-3,-1]=>2
[-2,4,3,1]=>0
[-2,4,3,-1]=>0
[-2,4,-3,1]=>0
[-2,4,-3,-1]=>0
[-2,-4,3,1]=>0
[-2,-4,3,-1]=>0
[-2,-4,-3,1]=>0
[-2,-4,-3,-1]=>0
[3,1,2,4]=>0
[3,1,2,-4]=>3
[3,1,-2,4]=>1
[3,1,-2,-4]=>3
[3,-1,2,4]=>0
[3,-1,2,-4]=>2
[3,-1,-2,4]=>0
[3,-1,-2,-4]=>1
[-3,1,2,4]=>0
[-3,1,2,-4]=>2
[-3,1,-2,4]=>1
[-3,1,-2,-4]=>2
[-3,-1,2,4]=>0
[-3,-1,2,-4]=>1
[-3,-1,-2,4]=>0
[-3,-1,-2,-4]=>0
[3,1,4,2]=>0
[3,1,4,-2]=>1
[3,1,-4,2]=>2
[3,1,-4,-2]=>3
[3,-1,4,2]=>0
[3,-1,4,-2]=>0
[3,-1,-4,2]=>1
[3,-1,-4,-2]=>1
[-3,1,4,2]=>0
[-3,1,4,-2]=>1
[-3,1,-4,2]=>1
[-3,1,-4,-2]=>2
[-3,-1,4,2]=>0
[-3,-1,4,-2]=>0
[-3,-1,-4,2]=>0
[-3,-1,-4,-2]=>0
[3,2,1,4]=>0
[3,2,1,-4]=>3
[3,2,-1,4]=>0
[3,2,-1,-4]=>2
[3,-2,1,4]=>0
[3,-2,1,-4]=>2
[3,-2,-1,4]=>0
[3,-2,-1,-4]=>1
[-3,2,1,4]=>0
[-3,2,1,-4]=>2
[-3,2,-1,4]=>0
[-3,2,-1,-4]=>1
[-3,-2,1,4]=>0
[-3,-2,1,-4]=>1
[-3,-2,-1,4]=>0
[-3,-2,-1,-4]=>0
[3,2,4,1]=>0
[3,2,4,-1]=>0
[3,2,-4,1]=>2
[3,2,-4,-1]=>2
[3,-2,4,1]=>0
[3,-2,4,-1]=>0
[3,-2,-4,1]=>1
[3,-2,-4,-1]=>1
[-3,2,4,1]=>0
[-3,2,4,-1]=>0
[-3,2,-4,1]=>1
[-3,2,-4,-1]=>1
[-3,-2,4,1]=>0
[-3,-2,4,-1]=>0
[-3,-2,-4,1]=>0
[-3,-2,-4,-1]=>0
[3,4,1,2]=>0
[3,4,1,-2]=>1
[3,4,-1,2]=>0
[3,4,-1,-2]=>0
[3,-4,1,2]=>1
[3,-4,1,-2]=>2
[3,-4,-1,2]=>1
[3,-4,-1,-2]=>1
[-3,4,1,2]=>0
[-3,4,1,-2]=>1
[-3,4,-1,2]=>0
[-3,4,-1,-2]=>0
[-3,-4,1,2]=>0
[-3,-4,1,-2]=>1
[-3,-4,-1,2]=>0
[-3,-4,-1,-2]=>0
[3,4,2,1]=>0
[3,4,2,-1]=>0
[3,4,-2,1]=>0
[3,4,-2,-1]=>0
[3,-4,2,1]=>1
[3,-4,2,-1]=>1
[3,-4,-2,1]=>1
[3,-4,-2,-1]=>1
[-3,4,2,1]=>0
[-3,4,2,-1]=>0
[-3,4,-2,1]=>0
[-3,4,-2,-1]=>0
[-3,-4,2,1]=>0
[-3,-4,2,-1]=>0
[-3,-4,-2,1]=>0
[-3,-4,-2,-1]=>0
[4,1,2,3]=>0
[4,1,2,-3]=>2
[4,1,-2,3]=>1
[4,1,-2,-3]=>2
[4,-1,2,3]=>0
[4,-1,2,-3]=>1
[4,-1,-2,3]=>0
[4,-1,-2,-3]=>0
[-4,1,2,3]=>0
[-4,1,2,-3]=>2
[-4,1,-2,3]=>1
[-4,1,-2,-3]=>2
[-4,-1,2,3]=>0
[-4,-1,2,-3]=>1
[-4,-1,-2,3]=>0
[-4,-1,-2,-3]=>0
[4,1,3,2]=>0
[4,1,3,-2]=>1
[4,1,-3,2]=>1
[4,1,-3,-2]=>2
[4,-1,3,2]=>0
[4,-1,3,-2]=>0
[4,-1,-3,2]=>0
[4,-1,-3,-2]=>0
[-4,1,3,2]=>0
[-4,1,3,-2]=>1
[-4,1,-3,2]=>1
[-4,1,-3,-2]=>2
[-4,-1,3,2]=>0
[-4,-1,3,-2]=>0
[-4,-1,-3,2]=>0
[-4,-1,-3,-2]=>0
[4,2,1,3]=>0
[4,2,1,-3]=>2
[4,2,-1,3]=>0
[4,2,-1,-3]=>1
[4,-2,1,3]=>0
[4,-2,1,-3]=>1
[4,-2,-1,3]=>0
[4,-2,-1,-3]=>0
[-4,2,1,3]=>0
[-4,2,1,-3]=>2
[-4,2,-1,3]=>0
[-4,2,-1,-3]=>1
[-4,-2,1,3]=>0
[-4,-2,1,-3]=>1
[-4,-2,-1,3]=>0
[-4,-2,-1,-3]=>0
[4,2,3,1]=>0
[4,2,3,-1]=>0
[4,2,-3,1]=>1
[4,2,-3,-1]=>1
[4,-2,3,1]=>0
[4,-2,3,-1]=>0
[4,-2,-3,1]=>0
[4,-2,-3,-1]=>0
[-4,2,3,1]=>0
[-4,2,3,-1]=>0
[-4,2,-3,1]=>1
[-4,2,-3,-1]=>1
[-4,-2,3,1]=>0
[-4,-2,3,-1]=>0
[-4,-2,-3,1]=>0
[-4,-2,-3,-1]=>0
[4,3,1,2]=>0
[4,3,1,-2]=>1
[4,3,-1,2]=>0
[4,3,-1,-2]=>0
[4,-3,1,2]=>0
[4,-3,1,-2]=>1
[4,-3,-1,2]=>0
[4,-3,-1,-2]=>0
[-4,3,1,2]=>0
[-4,3,1,-2]=>1
[-4,3,-1,2]=>0
[-4,3,-1,-2]=>0
[-4,-3,1,2]=>0
[-4,-3,1,-2]=>1
[-4,-3,-1,2]=>0
[-4,-3,-1,-2]=>0
[4,3,2,1]=>0
[4,3,2,-1]=>0
[4,3,-2,1]=>0
[4,3,-2,-1]=>0
[4,-3,2,1]=>0
[4,-3,2,-1]=>0
[4,-3,-2,1]=>0
[4,-3,-2,-1]=>0
[-4,3,2,1]=>0
[-4,3,2,-1]=>0
[-4,3,-2,1]=>0
[-4,3,-2,-1]=>0
[-4,-3,2,1]=>0
[-4,-3,2,-1]=>0
[-4,-3,-2,1]=>0
[-4,-3,-2,-1]=>0
[1,2,3,4,5]=>0
[1,2,3,4,-5]=>4
[1,2,3,-4,5]=>3
[1,2,3,-4,-5]=>6
[1,2,-3,4,5]=>2
[1,2,-3,4,-5]=>5
[1,2,-3,-4,5]=>4
[1,2,-3,-4,-5]=>6
[1,-2,3,4,5]=>1
[1,-2,3,4,-5]=>4
[1,-2,3,-4,5]=>3
[1,-2,3,-4,-5]=>5
[1,-2,-3,4,5]=>2
[1,-2,-3,4,-5]=>4
[1,-2,-3,-4,5]=>3
[1,-2,-3,-4,-5]=>4
[-1,2,3,4,5]=>0
[-1,2,3,4,-5]=>3
[-1,2,3,-4,5]=>2
[-1,2,3,-4,-5]=>4
[-1,2,-3,4,5]=>1
[-1,2,-3,4,-5]=>3
[-1,2,-3,-4,5]=>2
[-1,2,-3,-4,-5]=>3
[-1,-2,3,4,5]=>0
[-1,-2,3,4,-5]=>2
[-1,-2,3,-4,5]=>1
[-1,-2,3,-4,-5]=>2
[-1,-2,-3,4,5]=>0
[-1,-2,-3,4,-5]=>1
[-1,-2,-3,-4,5]=>0
[-1,-2,-3,-4,-5]=>0
[1,2,3,5,4]=>0
[1,2,3,5,-4]=>3
[1,2,3,-5,4]=>3
[1,2,3,-5,-4]=>6
[1,2,-3,5,4]=>2
[1,2,-3,5,-4]=>4
[1,2,-3,-5,4]=>4
[1,2,-3,-5,-4]=>6
[1,-2,3,5,4]=>1
[1,-2,3,5,-4]=>3
[1,-2,3,-5,4]=>3
[1,-2,3,-5,-4]=>5
[1,-2,-3,5,4]=>2
[1,-2,-3,5,-4]=>3
[1,-2,-3,-5,4]=>3
[1,-2,-3,-5,-4]=>4
[-1,2,3,5,4]=>0
[-1,2,3,5,-4]=>2
[-1,2,3,-5,4]=>2
[-1,2,3,-5,-4]=>4
[-1,2,-3,5,4]=>1
[-1,2,-3,5,-4]=>2
[-1,2,-3,-5,4]=>2
[-1,2,-3,-5,-4]=>3
[-1,-2,3,5,4]=>0
[-1,-2,3,5,-4]=>1
[-1,-2,3,-5,4]=>1
[-1,-2,3,-5,-4]=>2
[-1,-2,-3,5,4]=>0
[-1,-2,-3,5,-4]=>0
[-1,-2,-3,-5,4]=>0
[-1,-2,-3,-5,-4]=>0
[1,2,4,3,5]=>0
[1,2,4,3,-5]=>4
[1,2,4,-3,5]=>2
[1,2,4,-3,-5]=>5
[1,2,-4,3,5]=>2
[1,2,-4,3,-5]=>5
[1,2,-4,-3,5]=>4
[1,2,-4,-3,-5]=>6
[1,-2,4,3,5]=>1
[1,-2,4,3,-5]=>4
[1,-2,4,-3,5]=>2
[1,-2,4,-3,-5]=>4
[1,-2,-4,3,5]=>2
[1,-2,-4,3,-5]=>4
[1,-2,-4,-3,5]=>3
[1,-2,-4,-3,-5]=>4
[-1,2,4,3,5]=>0
[-1,2,4,3,-5]=>3
[-1,2,4,-3,5]=>1
[-1,2,4,-3,-5]=>3
[-1,2,-4,3,5]=>1
[-1,2,-4,3,-5]=>3
[-1,2,-4,-3,5]=>2
[-1,2,-4,-3,-5]=>3
[-1,-2,4,3,5]=>0
[-1,-2,4,3,-5]=>2
[-1,-2,4,-3,5]=>0
[-1,-2,4,-3,-5]=>1
[-1,-2,-4,3,5]=>0
[-1,-2,-4,3,-5]=>1
[-1,-2,-4,-3,5]=>0
[-1,-2,-4,-3,-5]=>0
[1,2,4,5,3]=>0
[1,2,4,5,-3]=>2
[1,2,4,-5,3]=>3
[1,2,4,-5,-3]=>5
[1,2,-4,5,3]=>2
[1,2,-4,5,-3]=>4
[1,2,-4,-5,3]=>4
[1,2,-4,-5,-3]=>6
[1,-2,4,5,3]=>1
[1,-2,4,5,-3]=>2
[1,-2,4,-5,3]=>3
[1,-2,4,-5,-3]=>4
[1,-2,-4,5,3]=>2
[1,-2,-4,5,-3]=>3
[1,-2,-4,-5,3]=>3
[1,-2,-4,-5,-3]=>4
[-1,2,4,5,3]=>0
[-1,2,4,5,-3]=>1
[-1,2,4,-5,3]=>2
[-1,2,4,-5,-3]=>3
[-1,2,-4,5,3]=>1
[-1,2,-4,5,-3]=>2
[-1,2,-4,-5,3]=>2
[-1,2,-4,-5,-3]=>3
[-1,-2,4,5,3]=>0
[-1,-2,4,5,-3]=>0
[-1,-2,4,-5,3]=>1
[-1,-2,4,-5,-3]=>1
[-1,-2,-4,5,3]=>0
[-1,-2,-4,5,-3]=>0
[-1,-2,-4,-5,3]=>0
[-1,-2,-4,-5,-3]=>0
[1,2,5,3,4]=>0
[1,2,5,3,-4]=>3
[1,2,5,-3,4]=>2
[1,2,5,-3,-4]=>4
[1,2,-5,3,4]=>2
[1,2,-5,3,-4]=>5
[1,2,-5,-3,4]=>4
[1,2,-5,-3,-4]=>6
[1,-2,5,3,4]=>1
[1,-2,5,3,-4]=>3
[1,-2,5,-3,4]=>2
[1,-2,5,-3,-4]=>3
[1,-2,-5,3,4]=>2
[1,-2,-5,3,-4]=>4
[1,-2,-5,-3,4]=>3
[1,-2,-5,-3,-4]=>4
[-1,2,5,3,4]=>0
[-1,2,5,3,-4]=>2
[-1,2,5,-3,4]=>1
[-1,2,5,-3,-4]=>2
[-1,2,-5,3,4]=>1
[-1,2,-5,3,-4]=>3
[-1,2,-5,-3,4]=>2
[-1,2,-5,-3,-4]=>3
[-1,-2,5,3,4]=>0
[-1,-2,5,3,-4]=>1
[-1,-2,5,-3,4]=>0
[-1,-2,5,-3,-4]=>0
[-1,-2,-5,3,4]=>0
[-1,-2,-5,3,-4]=>1
[-1,-2,-5,-3,4]=>0
[-1,-2,-5,-3,-4]=>0
[1,2,5,4,3]=>0
[1,2,5,4,-3]=>2
[1,2,5,-4,3]=>2
[1,2,5,-4,-3]=>4
[1,2,-5,4,3]=>2
[1,2,-5,4,-3]=>4
[1,2,-5,-4,3]=>4
[1,2,-5,-4,-3]=>6
[1,-2,5,4,3]=>1
[1,-2,5,4,-3]=>2
[1,-2,5,-4,3]=>2
[1,-2,5,-4,-3]=>3
[1,-2,-5,4,3]=>2
[1,-2,-5,4,-3]=>3
[1,-2,-5,-4,3]=>3
[1,-2,-5,-4,-3]=>4
[-1,2,5,4,3]=>0
[-1,2,5,4,-3]=>1
[-1,2,5,-4,3]=>1
[-1,2,5,-4,-3]=>2
[-1,2,-5,4,3]=>1
[-1,2,-5,4,-3]=>2
[-1,2,-5,-4,3]=>2
[-1,2,-5,-4,-3]=>3
[-1,-2,5,4,3]=>0
[-1,-2,5,4,-3]=>0
[-1,-2,5,-4,3]=>0
[-1,-2,5,-4,-3]=>0
[-1,-2,-5,4,3]=>0
[-1,-2,-5,4,-3]=>0
[-1,-2,-5,-4,3]=>0
[-1,-2,-5,-4,-3]=>0
[1,3,2,4,5]=>0
[1,3,2,4,-5]=>4
[1,3,2,-4,5]=>3
[1,3,2,-4,-5]=>6
[1,3,-2,4,5]=>1
[1,3,-2,4,-5]=>4
[1,3,-2,-4,5]=>3
[1,3,-2,-4,-5]=>5
[1,-3,2,4,5]=>1
[1,-3,2,4,-5]=>4
[1,-3,2,-4,5]=>3
[1,-3,2,-4,-5]=>5
[1,-3,-2,4,5]=>2
[1,-3,-2,4,-5]=>4
[1,-3,-2,-4,5]=>3
[1,-3,-2,-4,-5]=>4
[-1,3,2,4,5]=>0
[-1,3,2,4,-5]=>3
[-1,3,2,-4,5]=>2
[-1,3,2,-4,-5]=>4
[-1,3,-2,4,5]=>0
[-1,3,-2,4,-5]=>2
[-1,3,-2,-4,5]=>1
[-1,3,-2,-4,-5]=>2
[-1,-3,2,4,5]=>0
[-1,-3,2,4,-5]=>2
[-1,-3,2,-4,5]=>1
[-1,-3,2,-4,-5]=>2
[-1,-3,-2,4,5]=>0
[-1,-3,-2,4,-5]=>1
[-1,-3,-2,-4,5]=>0
[-1,-3,-2,-4,-5]=>0
[1,3,2,5,4]=>0
[1,3,2,5,-4]=>3
[1,3,2,-5,4]=>3
[1,3,2,-5,-4]=>6
[1,3,-2,5,4]=>1
[1,3,-2,5,-4]=>3
[1,3,-2,-5,4]=>3
[1,3,-2,-5,-4]=>5
[1,-3,2,5,4]=>1
[1,-3,2,5,-4]=>3
[1,-3,2,-5,4]=>3
[1,-3,2,-5,-4]=>5
[1,-3,-2,5,4]=>2
[1,-3,-2,5,-4]=>3
[1,-3,-2,-5,4]=>3
[1,-3,-2,-5,-4]=>4
[-1,3,2,5,4]=>0
[-1,3,2,5,-4]=>2
[-1,3,2,-5,4]=>2
[-1,3,2,-5,-4]=>4
[-1,3,-2,5,4]=>0
[-1,3,-2,5,-4]=>1
[-1,3,-2,-5,4]=>1
[-1,3,-2,-5,-4]=>2
[-1,-3,2,5,4]=>0
[-1,-3,2,5,-4]=>1
[-1,-3,2,-5,4]=>1
[-1,-3,2,-5,-4]=>2
[-1,-3,-2,5,4]=>0
[-1,-3,-2,5,-4]=>0
[-1,-3,-2,-5,4]=>0
[-1,-3,-2,-5,-4]=>0
[1,3,4,2,5]=>0
[1,3,4,2,-5]=>4
[1,3,4,-2,5]=>1
[1,3,4,-2,-5]=>4
[1,3,-4,2,5]=>2
[1,3,-4,2,-5]=>5
[1,3,-4,-2,5]=>3
[1,3,-4,-2,-5]=>5
[1,-3,4,2,5]=>1
[1,-3,4,2,-5]=>4
[1,-3,4,-2,5]=>2
[1,-3,4,-2,-5]=>4
[1,-3,-4,2,5]=>2
[1,-3,-4,2,-5]=>4
[1,-3,-4,-2,5]=>3
[1,-3,-4,-2,-5]=>4
[-1,3,4,2,5]=>0
[-1,3,4,2,-5]=>3
[-1,3,4,-2,5]=>0
[-1,3,4,-2,-5]=>2
[-1,3,-4,2,5]=>1
[-1,3,-4,2,-5]=>3
[-1,3,-4,-2,5]=>1
[-1,3,-4,-2,-5]=>2
[-1,-3,4,2,5]=>0
[-1,-3,4,2,-5]=>2
[-1,-3,4,-2,5]=>0
[-1,-3,4,-2,-5]=>1
[-1,-3,-4,2,5]=>0
[-1,-3,-4,2,-5]=>1
[-1,-3,-4,-2,5]=>0
[-1,-3,-4,-2,-5]=>0
[1,3,4,5,2]=>0
[1,3,4,5,-2]=>1
[1,3,4,-5,2]=>3
[1,3,4,-5,-2]=>4
[1,3,-4,5,2]=>2
[1,3,-4,5,-2]=>3
[1,3,-4,-5,2]=>4
[1,3,-4,-5,-2]=>5
[1,-3,4,5,2]=>1
[1,-3,4,5,-2]=>2
[1,-3,4,-5,2]=>3
[1,-3,4,-5,-2]=>4
[1,-3,-4,5,2]=>2
[1,-3,-4,5,-2]=>3
[1,-3,-4,-5,2]=>3
[1,-3,-4,-5,-2]=>4
[-1,3,4,5,2]=>0
[-1,3,4,5,-2]=>0
[-1,3,4,-5,2]=>2
[-1,3,4,-5,-2]=>2
[-1,3,-4,5,2]=>1
[-1,3,-4,5,-2]=>1
[-1,3,-4,-5,2]=>2
[-1,3,-4,-5,-2]=>2
[-1,-3,4,5,2]=>0
[-1,-3,4,5,-2]=>0
[-1,-3,4,-5,2]=>1
[-1,-3,4,-5,-2]=>1
[-1,-3,-4,5,2]=>0
[-1,-3,-4,5,-2]=>0
[-1,-3,-4,-5,2]=>0
[-1,-3,-4,-5,-2]=>0
[1,3,5,2,4]=>0
[1,3,5,2,-4]=>3
[1,3,5,-2,4]=>1
[1,3,5,-2,-4]=>3
[1,3,-5,2,4]=>2
[1,3,-5,2,-4]=>5
[1,3,-5,-2,4]=>3
[1,3,-5,-2,-4]=>5
[1,-3,5,2,4]=>1
[1,-3,5,2,-4]=>3
[1,-3,5,-2,4]=>2
[1,-3,5,-2,-4]=>3
[1,-3,-5,2,4]=>2
[1,-3,-5,2,-4]=>4
[1,-3,-5,-2,4]=>3
[1,-3,-5,-2,-4]=>4
[-1,3,5,2,4]=>0
[-1,3,5,2,-4]=>2
[-1,3,5,-2,4]=>0
[-1,3,5,-2,-4]=>1
[-1,3,-5,2,4]=>1
[-1,3,-5,2,-4]=>3
[-1,3,-5,-2,4]=>1
[-1,3,-5,-2,-4]=>2
[-1,-3,5,2,4]=>0
[-1,-3,5,2,-4]=>1
[-1,-3,5,-2,4]=>0
[-1,-3,5,-2,-4]=>0
[-1,-3,-5,2,4]=>0
[-1,-3,-5,2,-4]=>1
[-1,-3,-5,-2,4]=>0
[-1,-3,-5,-2,-4]=>0
[1,3,5,4,2]=>0
[1,3,5,4,-2]=>1
[1,3,5,-4,2]=>2
[1,3,5,-4,-2]=>3
[1,3,-5,4,2]=>2
[1,3,-5,4,-2]=>3
[1,3,-5,-4,2]=>4
[1,3,-5,-4,-2]=>5
[1,-3,5,4,2]=>1
[1,-3,5,4,-2]=>2
[1,-3,5,-4,2]=>2
[1,-3,5,-4,-2]=>3
[1,-3,-5,4,2]=>2
[1,-3,-5,4,-2]=>3
[1,-3,-5,-4,2]=>3
[1,-3,-5,-4,-2]=>4
[-1,3,5,4,2]=>0
[-1,3,5,4,-2]=>0
[-1,3,5,-4,2]=>1
[-1,3,5,-4,-2]=>1
[-1,3,-5,4,2]=>1
[-1,3,-5,4,-2]=>1
[-1,3,-5,-4,2]=>2
[-1,3,-5,-4,-2]=>2
[-1,-3,5,4,2]=>0
[-1,-3,5,4,-2]=>0
[-1,-3,5,-4,2]=>0
[-1,-3,5,-4,-2]=>0
[-1,-3,-5,4,2]=>0
[-1,-3,-5,4,-2]=>0
[-1,-3,-5,-4,2]=>0
[-1,-3,-5,-4,-2]=>0
[1,4,2,3,5]=>0
[1,4,2,3,-5]=>4
[1,4,2,-3,5]=>2
[1,4,2,-3,-5]=>5
[1,4,-2,3,5]=>1
[1,4,-2,3,-5]=>4
[1,4,-2,-3,5]=>2
[1,4,-2,-3,-5]=>4
[1,-4,2,3,5]=>1
[1,-4,2,3,-5]=>4
[1,-4,2,-3,5]=>3
[1,-4,2,-3,-5]=>5
[1,-4,-2,3,5]=>2
[1,-4,-2,3,-5]=>4
[1,-4,-2,-3,5]=>3
[1,-4,-2,-3,-5]=>4
[-1,4,2,3,5]=>0
[-1,4,2,3,-5]=>3
[-1,4,2,-3,5]=>1
[-1,4,2,-3,-5]=>3
[-1,4,-2,3,5]=>0
[-1,4,-2,3,-5]=>2
[-1,4,-2,-3,5]=>0
[-1,4,-2,-3,-5]=>1
[-1,-4,2,3,5]=>0
[-1,-4,2,3,-5]=>2
[-1,-4,2,-3,5]=>1
[-1,-4,2,-3,-5]=>2
[-1,-4,-2,3,5]=>0
[-1,-4,-2,3,-5]=>1
[-1,-4,-2,-3,5]=>0
[-1,-4,-2,-3,-5]=>0
[1,4,2,5,3]=>0
[1,4,2,5,-3]=>2
[1,4,2,-5,3]=>3
[1,4,2,-5,-3]=>5
[1,4,-2,5,3]=>1
[1,4,-2,5,-3]=>2
[1,4,-2,-5,3]=>3
[1,4,-2,-5,-3]=>4
[1,-4,2,5,3]=>1
[1,-4,2,5,-3]=>3
[1,-4,2,-5,3]=>3
[1,-4,2,-5,-3]=>5
[1,-4,-2,5,3]=>2
[1,-4,-2,5,-3]=>3
[1,-4,-2,-5,3]=>3
[1,-4,-2,-5,-3]=>4
[-1,4,2,5,3]=>0
[-1,4,2,5,-3]=>1
[-1,4,2,-5,3]=>2
[-1,4,2,-5,-3]=>3
[-1,4,-2,5,3]=>0
[-1,4,-2,5,-3]=>0
[-1,4,-2,-5,3]=>1
[-1,4,-2,-5,-3]=>1
[-1,-4,2,5,3]=>0
[-1,-4,2,5,-3]=>1
[-1,-4,2,-5,3]=>1
[-1,-4,2,-5,-3]=>2
[-1,-4,-2,5,3]=>0
[-1,-4,-2,5,-3]=>0
[-1,-4,-2,-5,3]=>0
[-1,-4,-2,-5,-3]=>0
[1,4,3,2,5]=>0
[1,4,3,2,-5]=>4
[1,4,3,-2,5]=>1
[1,4,3,-2,-5]=>4
[1,4,-3,2,5]=>1
[1,4,-3,2,-5]=>4
[1,4,-3,-2,5]=>2
[1,4,-3,-2,-5]=>4
[1,-4,3,2,5]=>1
[1,-4,3,2,-5]=>4
[1,-4,3,-2,5]=>2
[1,-4,3,-2,-5]=>4
[1,-4,-3,2,5]=>2
[1,-4,-3,2,-5]=>4
[1,-4,-3,-2,5]=>3
[1,-4,-3,-2,-5]=>4
[-1,4,3,2,5]=>0
[-1,4,3,2,-5]=>3
[-1,4,3,-2,5]=>0
[-1,4,3,-2,-5]=>2
[-1,4,-3,2,5]=>0
[-1,4,-3,2,-5]=>2
[-1,4,-3,-2,5]=>0
[-1,4,-3,-2,-5]=>1
[-1,-4,3,2,5]=>0
[-1,-4,3,2,-5]=>2
[-1,-4,3,-2,5]=>0
[-1,-4,3,-2,-5]=>1
[-1,-4,-3,2,5]=>0
[-1,-4,-3,2,-5]=>1
[-1,-4,-3,-2,5]=>0
[-1,-4,-3,-2,-5]=>0
[1,4,3,5,2]=>0
[1,4,3,5,-2]=>1
[1,4,3,-5,2]=>3
[1,4,3,-5,-2]=>4
[1,4,-3,5,2]=>1
[1,4,-3,5,-2]=>2
[1,4,-3,-5,2]=>3
[1,4,-3,-5,-2]=>4
[1,-4,3,5,2]=>1
[1,-4,3,5,-2]=>2
[1,-4,3,-5,2]=>3
[1,-4,3,-5,-2]=>4
[1,-4,-3,5,2]=>2
[1,-4,-3,5,-2]=>3
[1,-4,-3,-5,2]=>3
[1,-4,-3,-5,-2]=>4
[-1,4,3,5,2]=>0
[-1,4,3,5,-2]=>0
[-1,4,3,-5,2]=>2
[-1,4,3,-5,-2]=>2
[-1,4,-3,5,2]=>0
[-1,4,-3,5,-2]=>0
[-1,4,-3,-5,2]=>1
[-1,4,-3,-5,-2]=>1
[-1,-4,3,5,2]=>0
[-1,-4,3,5,-2]=>0
[-1,-4,3,-5,2]=>1
[-1,-4,3,-5,-2]=>1
[-1,-4,-3,5,2]=>0
[-1,-4,-3,5,-2]=>0
[-1,-4,-3,-5,2]=>0
[-1,-4,-3,-5,-2]=>0
[1,4,5,2,3]=>0
[1,4,5,2,-3]=>2
[1,4,5,-2,3]=>1
[1,4,5,-2,-3]=>2
[1,4,-5,2,3]=>2
[1,4,-5,2,-3]=>4
[1,4,-5,-2,3]=>3
[1,4,-5,-2,-3]=>4
[1,-4,5,2,3]=>1
[1,-4,5,2,-3]=>3
[1,-4,5,-2,3]=>2
[1,-4,5,-2,-3]=>3
[1,-4,-5,2,3]=>2
[1,-4,-5,2,-3]=>4
[1,-4,-5,-2,3]=>3
[1,-4,-5,-2,-3]=>4
[-1,4,5,2,3]=>0
[-1,4,5,2,-3]=>1
[-1,4,5,-2,3]=>0
[-1,4,5,-2,-3]=>0
[-1,4,-5,2,3]=>1
[-1,4,-5,2,-3]=>2
[-1,4,-5,-2,3]=>1
[-1,4,-5,-2,-3]=>1
[-1,-4,5,2,3]=>0
[-1,-4,5,2,-3]=>1
[-1,-4,5,-2,3]=>0
[-1,-4,5,-2,-3]=>0
[-1,-4,-5,2,3]=>0
[-1,-4,-5,2,-3]=>1
[-1,-4,-5,-2,3]=>0
[-1,-4,-5,-2,-3]=>0
[1,4,5,3,2]=>0
[1,4,5,3,-2]=>1
[1,4,5,-3,2]=>1
[1,4,5,-3,-2]=>2
[1,4,-5,3,2]=>2
[1,4,-5,3,-2]=>3
[1,4,-5,-3,2]=>3
[1,4,-5,-3,-2]=>4
[1,-4,5,3,2]=>1
[1,-4,5,3,-2]=>2
[1,-4,5,-3,2]=>2
[1,-4,5,-3,-2]=>3
[1,-4,-5,3,2]=>2
[1,-4,-5,3,-2]=>3
[1,-4,-5,-3,2]=>3
[1,-4,-5,-3,-2]=>4
[-1,4,5,3,2]=>0
[-1,4,5,3,-2]=>0
[-1,4,5,-3,2]=>0
[-1,4,5,-3,-2]=>0
[-1,4,-5,3,2]=>1
[-1,4,-5,3,-2]=>1
[-1,4,-5,-3,2]=>1
[-1,4,-5,-3,-2]=>1
[-1,-4,5,3,2]=>0
[-1,-4,5,3,-2]=>0
[-1,-4,5,-3,2]=>0
[-1,-4,5,-3,-2]=>0
[-1,-4,-5,3,2]=>0
[-1,-4,-5,3,-2]=>0
[-1,-4,-5,-3,2]=>0
[-1,-4,-5,-3,-2]=>0
[1,5,2,3,4]=>0
[1,5,2,3,-4]=>3
[1,5,2,-3,4]=>2
[1,5,2,-3,-4]=>4
[1,5,-2,3,4]=>1
[1,5,-2,3,-4]=>3
[1,5,-2,-3,4]=>2
[1,5,-2,-3,-4]=>3
[1,-5,2,3,4]=>1
[1,-5,2,3,-4]=>4
[1,-5,2,-3,4]=>3
[1,-5,2,-3,-4]=>5
[1,-5,-2,3,4]=>2
[1,-5,-2,3,-4]=>4
[1,-5,-2,-3,4]=>3
[1,-5,-2,-3,-4]=>4
[-1,5,2,3,4]=>0
[-1,5,2,3,-4]=>2
[-1,5,2,-3,4]=>1
[-1,5,2,-3,-4]=>2
[-1,5,-2,3,4]=>0
[-1,5,-2,3,-4]=>1
[-1,5,-2,-3,4]=>0
[-1,5,-2,-3,-4]=>0
[-1,-5,2,3,4]=>0
[-1,-5,2,3,-4]=>2
[-1,-5,2,-3,4]=>1
[-1,-5,2,-3,-4]=>2
[-1,-5,-2,3,4]=>0
[-1,-5,-2,3,-4]=>1
[-1,-5,-2,-3,4]=>0
[-1,-5,-2,-3,-4]=>0
[1,5,2,4,3]=>0
[1,5,2,4,-3]=>2
[1,5,2,-4,3]=>2
[1,5,2,-4,-3]=>4
[1,5,-2,4,3]=>1
[1,5,-2,4,-3]=>2
[1,5,-2,-4,3]=>2
[1,5,-2,-4,-3]=>3
[1,-5,2,4,3]=>1
[1,-5,2,4,-3]=>3
[1,-5,2,-4,3]=>3
[1,-5,2,-4,-3]=>5
[1,-5,-2,4,3]=>2
[1,-5,-2,4,-3]=>3
[1,-5,-2,-4,3]=>3
[1,-5,-2,-4,-3]=>4
[-1,5,2,4,3]=>0
[-1,5,2,4,-3]=>1
[-1,5,2,-4,3]=>1
[-1,5,2,-4,-3]=>2
[-1,5,-2,4,3]=>0
[-1,5,-2,4,-3]=>0
[-1,5,-2,-4,3]=>0
[-1,5,-2,-4,-3]=>0
[-1,-5,2,4,3]=>0
[-1,-5,2,4,-3]=>1
[-1,-5,2,-4,3]=>1
[-1,-5,2,-4,-3]=>2
[-1,-5,-2,4,3]=>0
[-1,-5,-2,4,-3]=>0
[-1,-5,-2,-4,3]=>0
[-1,-5,-2,-4,-3]=>0
[1,5,3,2,4]=>0
[1,5,3,2,-4]=>3
[1,5,3,-2,4]=>1
[1,5,3,-2,-4]=>3
[1,5,-3,2,4]=>1
[1,5,-3,2,-4]=>3
[1,5,-3,-2,4]=>2
[1,5,-3,-2,-4]=>3
[1,-5,3,2,4]=>1
[1,-5,3,2,-4]=>4
[1,-5,3,-2,4]=>2
[1,-5,3,-2,-4]=>4
[1,-5,-3,2,4]=>2
[1,-5,-3,2,-4]=>4
[1,-5,-3,-2,4]=>3
[1,-5,-3,-2,-4]=>4
[-1,5,3,2,4]=>0
[-1,5,3,2,-4]=>2
[-1,5,3,-2,4]=>0
[-1,5,3,-2,-4]=>1
[-1,5,-3,2,4]=>0
[-1,5,-3,2,-4]=>1
[-1,5,-3,-2,4]=>0
[-1,5,-3,-2,-4]=>0
[-1,-5,3,2,4]=>0
[-1,-5,3,2,-4]=>2
[-1,-5,3,-2,4]=>0
[-1,-5,3,-2,-4]=>1
[-1,-5,-3,2,4]=>0
[-1,-5,-3,2,-4]=>1
[-1,-5,-3,-2,4]=>0
[-1,-5,-3,-2,-4]=>0
[1,5,3,4,2]=>0
[1,5,3,4,-2]=>1
[1,5,3,-4,2]=>2
[1,5,3,-4,-2]=>3
[1,5,-3,4,2]=>1
[1,5,-3,4,-2]=>2
[1,5,-3,-4,2]=>2
[1,5,-3,-4,-2]=>3
[1,-5,3,4,2]=>1
[1,-5,3,4,-2]=>2
[1,-5,3,-4,2]=>3
[1,-5,3,-4,-2]=>4
[1,-5,-3,4,2]=>2
[1,-5,-3,4,-2]=>3
[1,-5,-3,-4,2]=>3
[1,-5,-3,-4,-2]=>4
[-1,5,3,4,2]=>0
[-1,5,3,4,-2]=>0
[-1,5,3,-4,2]=>1
[-1,5,3,-4,-2]=>1
[-1,5,-3,4,2]=>0
[-1,5,-3,4,-2]=>0
[-1,5,-3,-4,2]=>0
[-1,5,-3,-4,-2]=>0
[-1,-5,3,4,2]=>0
[-1,-5,3,4,-2]=>0
[-1,-5,3,-4,2]=>1
[-1,-5,3,-4,-2]=>1
[-1,-5,-3,4,2]=>0
[-1,-5,-3,4,-2]=>0
[-1,-5,-3,-4,2]=>0
[-1,-5,-3,-4,-2]=>0
[1,5,4,2,3]=>0
[1,5,4,2,-3]=>2
[1,5,4,-2,3]=>1
[1,5,4,-2,-3]=>2
[1,5,-4,2,3]=>1
[1,5,-4,2,-3]=>3
[1,5,-4,-2,3]=>2
[1,5,-4,-2,-3]=>3
[1,-5,4,2,3]=>1
[1,-5,4,2,-3]=>3
[1,-5,4,-2,3]=>2
[1,-5,4,-2,-3]=>3
[1,-5,-4,2,3]=>2
[1,-5,-4,2,-3]=>4
[1,-5,-4,-2,3]=>3
[1,-5,-4,-2,-3]=>4
[-1,5,4,2,3]=>0
[-1,5,4,2,-3]=>1
[-1,5,4,-2,3]=>0
[-1,5,4,-2,-3]=>0
[-1,5,-4,2,3]=>0
[-1,5,-4,2,-3]=>1
[-1,5,-4,-2,3]=>0
[-1,5,-4,-2,-3]=>0
[-1,-5,4,2,3]=>0
[-1,-5,4,2,-3]=>1
[-1,-5,4,-2,3]=>0
[-1,-5,4,-2,-3]=>0
[-1,-5,-4,2,3]=>0
[-1,-5,-4,2,-3]=>1
[-1,-5,-4,-2,3]=>0
[-1,-5,-4,-2,-3]=>0
[1,5,4,3,2]=>0
[1,5,4,3,-2]=>1
[1,5,4,-3,2]=>1
[1,5,4,-3,-2]=>2
[1,5,-4,3,2]=>1
[1,5,-4,3,-2]=>2
[1,5,-4,-3,2]=>2
[1,5,-4,-3,-2]=>3
[1,-5,4,3,2]=>1
[1,-5,4,3,-2]=>2
[1,-5,4,-3,2]=>2
[1,-5,4,-3,-2]=>3
[1,-5,-4,3,2]=>2
[1,-5,-4,3,-2]=>3
[1,-5,-4,-3,2]=>3
[1,-5,-4,-3,-2]=>4
[-1,5,4,3,2]=>0
[-1,5,4,3,-2]=>0
[-1,5,4,-3,2]=>0
[-1,5,4,-3,-2]=>0
[-1,5,-4,3,2]=>0
[-1,5,-4,3,-2]=>0
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Description
The number of occurrences of the signed pattern 1-2 in a signed permutation.
This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < -\pi(j)$.
This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < -\pi(j)$.
References
[1] Simion, R. Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations MathSciNet:1741331
Code
def signed_pattern_positions(pi, pat):
signs = [1 if e > 0 else -1 for e in pat]
perm = [e if e > 0 else -e for e in pat]
lpi = list(pi)
result = []
for occ in pi.permutation().pattern_positions(perm):
if all((e > 0) == (lpi[i] > 0) for i, e in zip(occ, signs)):
result.append(occ)
return result
def statistic(pi):
return len(signed_pattern_positions(pi, [1,-2]))
Created
Feb 09, 2022 at 10:26 by Martin Rubey
Updated
Feb 09, 2022 at 10:26 by Martin Rubey
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