Identifier
Values
=>
[1]=>0
[1,1]=>1
[1,2]=>0
[2,1]=>0
[1,1,1]=>2
[1,1,2]=>1
[1,2,1]=>0
[2,1,1]=>1
[1,1,3]=>1
[1,3,1]=>0
[3,1,1]=>1
[1,2,2]=>1
[2,1,2]=>0
[2,2,1]=>1
[1,2,3]=>0
[1,3,2]=>0
[2,1,3]=>0
[2,3,1]=>0
[3,1,2]=>0
[3,2,1]=>0
[1,1,1,1]=>3
[1,1,1,2]=>2
[1,1,2,1]=>1
[1,2,1,1]=>1
[2,1,1,1]=>2
[1,1,1,3]=>2
[1,1,3,1]=>1
[1,3,1,1]=>1
[3,1,1,1]=>2
[1,1,1,4]=>2
[1,1,4,1]=>1
[1,4,1,1]=>1
[4,1,1,1]=>2
[1,1,2,2]=>2
[1,2,1,2]=>0
[1,2,2,1]=>1
[2,1,1,2]=>1
[2,1,2,1]=>0
[2,2,1,1]=>2
[1,1,2,3]=>1
[1,1,3,2]=>1
[1,2,1,3]=>0
[1,2,3,1]=>0
[1,3,1,2]=>0
[1,3,2,1]=>0
[2,1,1,3]=>1
[2,1,3,1]=>0
[2,3,1,1]=>1
[3,1,1,2]=>1
[3,1,2,1]=>0
[3,2,1,1]=>1
[1,1,2,4]=>1
[1,1,4,2]=>1
[1,2,1,4]=>0
[1,2,4,1]=>0
[1,4,1,2]=>0
[1,4,2,1]=>0
[2,1,1,4]=>1
[2,1,4,1]=>0
[2,4,1,1]=>1
[4,1,1,2]=>1
[4,1,2,1]=>0
[4,2,1,1]=>1
[1,1,3,3]=>2
[1,3,1,3]=>0
[1,3,3,1]=>1
[3,1,1,3]=>1
[3,1,3,1]=>0
[3,3,1,1]=>2
[1,1,3,4]=>1
[1,1,4,3]=>1
[1,3,1,4]=>0
[1,3,4,1]=>0
[1,4,1,3]=>0
[1,4,3,1]=>0
[3,1,1,4]=>1
[3,1,4,1]=>0
[3,4,1,1]=>1
[4,1,1,3]=>1
[4,1,3,1]=>0
[4,3,1,1]=>1
[1,2,2,2]=>2
[2,1,2,2]=>1
[2,2,1,2]=>1
[2,2,2,1]=>2
[1,2,2,3]=>1
[1,2,3,2]=>0
[1,3,2,2]=>1
[2,1,2,3]=>0
[2,1,3,2]=>0
[2,2,1,3]=>1
[2,2,3,1]=>1
[2,3,1,2]=>0
[2,3,2,1]=>0
[3,1,2,2]=>1
[3,2,1,2]=>0
[3,2,2,1]=>1
[1,2,2,4]=>1
[1,2,4,2]=>0
[1,4,2,2]=>1
[2,1,2,4]=>0
[2,1,4,2]=>0
[2,2,1,4]=>1
[2,2,4,1]=>1
[2,4,1,2]=>0
[2,4,2,1]=>0
[4,1,2,2]=>1
[4,2,1,2]=>0
[4,2,2,1]=>1
[1,2,3,3]=>1
[1,3,2,3]=>0
[1,3,3,2]=>1
[2,1,3,3]=>1
[2,3,1,3]=>0
[2,3,3,1]=>1
[3,1,2,3]=>0
[3,1,3,2]=>0
[3,2,1,3]=>0
[3,2,3,1]=>0
[3,3,1,2]=>1
[3,3,2,1]=>1
[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
[1,1,1,1,1]=>4
[1,1,1,1,2]=>3
[1,1,1,2,1]=>2
[1,1,2,1,1]=>2
[1,2,1,1,1]=>2
[2,1,1,1,1]=>3
[1,1,1,1,3]=>3
[1,1,1,3,1]=>2
[1,1,3,1,1]=>2
[1,3,1,1,1]=>2
[3,1,1,1,1]=>3
[1,1,1,1,4]=>3
[1,1,1,4,1]=>2
[1,1,4,1,1]=>2
[1,4,1,1,1]=>2
[4,1,1,1,1]=>3
[1,1,1,1,5]=>3
[1,1,1,5,1]=>2
[1,1,5,1,1]=>2
[1,5,1,1,1]=>2
[5,1,1,1,1]=>3
[1,1,1,2,2]=>3
[1,1,2,1,2]=>1
[1,1,2,2,1]=>2
[1,2,1,1,2]=>1
[1,2,1,2,1]=>0
[1,2,2,1,1]=>2
[2,1,1,1,2]=>2
[2,1,1,2,1]=>1
[2,1,2,1,1]=>1
[2,2,1,1,1]=>3
[1,1,1,2,3]=>2
[1,1,1,3,2]=>2
[1,1,2,1,3]=>1
[1,1,2,3,1]=>1
[1,1,3,1,2]=>1
[1,1,3,2,1]=>1
[1,2,1,1,3]=>1
[1,2,1,3,1]=>0
[1,2,3,1,1]=>1
[1,3,1,1,2]=>1
[1,3,1,2,1]=>0
[1,3,2,1,1]=>1
[2,1,1,1,3]=>2
[2,1,1,3,1]=>1
[2,1,3,1,1]=>1
[2,3,1,1,1]=>2
[3,1,1,1,2]=>2
[3,1,1,2,1]=>1
[3,1,2,1,1]=>1
[3,2,1,1,1]=>2
[1,1,1,2,4]=>2
[1,1,1,4,2]=>2
[1,1,2,1,4]=>1
[1,1,2,4,1]=>1
[1,1,4,1,2]=>1
[1,1,4,2,1]=>1
[1,2,1,1,4]=>1
[1,2,1,4,1]=>0
[1,2,4,1,1]=>1
[1,4,1,1,2]=>1
[1,4,1,2,1]=>0
[1,4,2,1,1]=>1
[2,1,1,1,4]=>2
[2,1,1,4,1]=>1
[2,1,4,1,1]=>1
[2,4,1,1,1]=>2
[4,1,1,1,2]=>2
[4,1,1,2,1]=>1
[4,1,2,1,1]=>1
[4,2,1,1,1]=>2
[1,1,1,2,5]=>2
[1,1,1,5,2]=>2
[1,1,2,1,5]=>1
[1,1,2,5,1]=>1
[1,1,5,1,2]=>1
[1,1,5,2,1]=>1
[1,2,1,1,5]=>1
[1,2,1,5,1]=>0
[1,2,5,1,1]=>1
[1,5,1,1,2]=>1
[1,5,1,2,1]=>0
[1,5,2,1,1]=>1
[2,1,1,1,5]=>2
[2,1,1,5,1]=>1
[2,1,5,1,1]=>1
[2,5,1,1,1]=>2
[5,1,1,1,2]=>2
[5,1,1,2,1]=>1
[5,1,2,1,1]=>1
[5,2,1,1,1]=>2
[1,1,1,3,3]=>3
[1,1,3,1,3]=>1
[1,1,3,3,1]=>2
[1,3,1,1,3]=>1
[1,3,1,3,1]=>0
[1,3,3,1,1]=>2
[3,1,1,1,3]=>2
[3,1,1,3,1]=>1
[3,1,3,1,1]=>1
[3,3,1,1,1]=>3
[1,1,1,3,4]=>2
[1,1,1,4,3]=>2
[1,1,3,1,4]=>1
[1,1,3,4,1]=>1
[1,1,4,1,3]=>1
[1,1,4,3,1]=>1
[1,3,1,1,4]=>1
[1,3,1,4,1]=>0
[1,3,4,1,1]=>1
[1,4,1,1,3]=>1
[1,4,1,3,1]=>0
[1,4,3,1,1]=>1
[3,1,1,1,4]=>2
[3,1,1,4,1]=>1
[3,1,4,1,1]=>1
[3,4,1,1,1]=>2
[4,1,1,1,3]=>2
[4,1,1,3,1]=>1
[4,1,3,1,1]=>1
[4,3,1,1,1]=>2
[1,1,1,3,5]=>2
[1,1,1,5,3]=>2
[1,1,3,1,5]=>1
[1,1,3,5,1]=>1
[1,1,5,1,3]=>1
[1,1,5,3,1]=>1
[1,3,1,1,5]=>1
[1,3,1,5,1]=>0
[1,3,5,1,1]=>1
[1,5,1,1,3]=>1
[1,5,1,3,1]=>0
[1,5,3,1,1]=>1
[3,1,1,1,5]=>2
[3,1,1,5,1]=>1
[3,1,5,1,1]=>1
[3,5,1,1,1]=>2
[5,1,1,1,3]=>2
[5,1,1,3,1]=>1
[5,1,3,1,1]=>1
[5,3,1,1,1]=>2
[1,1,1,4,4]=>3
[1,1,4,1,4]=>1
[1,1,4,4,1]=>2
[1,4,1,1,4]=>1
[1,4,1,4,1]=>0
[1,4,4,1,1]=>2
[4,1,1,1,4]=>2
[4,1,1,4,1]=>1
[4,1,4,1,1]=>1
[4,4,1,1,1]=>3
[1,1,1,4,5]=>2
[1,1,1,5,4]=>2
[1,1,4,1,5]=>1
[1,1,4,5,1]=>1
[1,1,5,1,4]=>1
[1,1,5,4,1]=>1
[1,4,1,1,5]=>1
[1,4,1,5,1]=>0
[1,4,5,1,1]=>1
[1,5,1,1,4]=>1
[1,5,1,4,1]=>0
[1,5,4,1,1]=>1
[4,1,1,1,5]=>2
[4,1,1,5,1]=>1
[4,1,5,1,1]=>1
[4,5,1,1,1]=>2
[5,1,1,1,4]=>2
[5,1,1,4,1]=>1
[5,1,4,1,1]=>1
[5,4,1,1,1]=>2
[1,1,2,2,2]=>3
[1,2,1,2,2]=>1
[1,2,2,1,2]=>1
[1,2,2,2,1]=>2
[2,1,1,2,2]=>2
[2,1,2,1,2]=>0
[2,1,2,2,1]=>1
[2,2,1,1,2]=>2
[2,2,1,2,1]=>1
[2,2,2,1,1]=>3
[1,1,2,2,3]=>2
[1,1,2,3,2]=>1
[1,1,3,2,2]=>2
[1,2,1,2,3]=>0
[1,2,1,3,2]=>0
[1,2,2,1,3]=>1
[1,2,2,3,1]=>1
[1,2,3,1,2]=>0
[1,2,3,2,1]=>0
[1,3,1,2,2]=>1
[1,3,2,1,2]=>0
[1,3,2,2,1]=>1
[2,1,1,2,3]=>1
[2,1,1,3,2]=>1
[2,1,2,1,3]=>0
[2,1,2,3,1]=>0
[2,1,3,1,2]=>0
[2,1,3,2,1]=>0
[2,2,1,1,3]=>2
[2,2,1,3,1]=>1
[2,2,3,1,1]=>2
[2,3,1,1,2]=>1
[2,3,1,2,1]=>0
[2,3,2,1,1]=>1
[3,1,1,2,2]=>2
[3,1,2,1,2]=>0
[3,1,2,2,1]=>1
[3,2,1,1,2]=>1
[3,2,1,2,1]=>0
[3,2,2,1,1]=>2
[1,1,2,2,4]=>2
[1,1,2,4,2]=>1
[1,1,4,2,2]=>2
[1,2,1,2,4]=>0
[1,2,1,4,2]=>0
[1,2,2,1,4]=>1
[1,2,2,4,1]=>1
[1,2,4,1,2]=>0
[1,2,4,2,1]=>0
[1,4,1,2,2]=>1
[1,4,2,1,2]=>0
[1,4,2,2,1]=>1
[2,1,1,2,4]=>1
[2,1,1,4,2]=>1
[2,1,2,1,4]=>0
[2,1,2,4,1]=>0
[2,1,4,1,2]=>0
[2,1,4,2,1]=>0
[2,2,1,1,4]=>2
[2,2,1,4,1]=>1
[2,2,4,1,1]=>2
[2,4,1,1,2]=>1
[2,4,1,2,1]=>0
[2,4,2,1,1]=>1
[4,1,1,2,2]=>2
[4,1,2,1,2]=>0
[4,1,2,2,1]=>1
[4,2,1,1,2]=>1
[4,2,1,2,1]=>0
[4,2,2,1,1]=>2
[1,1,2,2,5]=>2
[1,1,2,5,2]=>1
[1,1,5,2,2]=>2
[1,2,1,2,5]=>0
[1,2,1,5,2]=>0
[1,2,2,1,5]=>1
[1,2,2,5,1]=>1
[1,2,5,1,2]=>0
[1,2,5,2,1]=>0
[1,5,1,2,2]=>1
[1,5,2,1,2]=>0
[1,5,2,2,1]=>1
[2,1,1,2,5]=>1
[2,1,1,5,2]=>1
[2,1,2,1,5]=>0
[2,1,2,5,1]=>0
[2,1,5,1,2]=>0
[2,1,5,2,1]=>0
[2,2,1,1,5]=>2
[2,2,1,5,1]=>1
[2,2,5,1,1]=>2
[2,5,1,1,2]=>1
[2,5,1,2,1]=>0
[2,5,2,1,1]=>1
[5,1,1,2,2]=>2
[5,1,2,1,2]=>0
[5,1,2,2,1]=>1
[5,2,1,1,2]=>1
[5,2,1,2,1]=>0
[5,2,2,1,1]=>2
[1,1,2,3,3]=>2
[1,1,3,2,3]=>1
[1,1,3,3,2]=>2
[1,2,1,3,3]=>1
[1,2,3,1,3]=>0
[1,2,3,3,1]=>1
[1,3,1,2,3]=>0
[1,3,1,3,2]=>0
[1,3,2,1,3]=>0
[1,3,2,3,1]=>0
[1,3,3,1,2]=>1
[1,3,3,2,1]=>1
[2,1,1,3,3]=>2
[2,1,3,1,3]=>0
[2,1,3,3,1]=>1
[2,3,1,1,3]=>1
[2,3,1,3,1]=>0
[2,3,3,1,1]=>2
[3,1,1,2,3]=>1
[3,1,1,3,2]=>1
[3,1,2,1,3]=>0
[3,1,2,3,1]=>0
[3,1,3,1,2]=>0
[3,1,3,2,1]=>0
[3,2,1,1,3]=>1
[3,2,1,3,1]=>0
[3,2,3,1,1]=>1
[3,3,1,1,2]=>2
[3,3,1,2,1]=>1
[3,3,2,1,1]=>2
[1,1,2,3,4]=>1
[1,1,2,4,3]=>1
[1,1,3,2,4]=>1
[1,1,3,4,2]=>1
[1,1,4,2,3]=>1
[1,1,4,3,2]=>1
[1,2,1,3,4]=>0
[1,2,1,4,3]=>0
[1,2,3,1,4]=>0
[1,2,3,4,1]=>0
[1,2,4,1,3]=>0
[1,2,4,3,1]=>0
[1,3,1,2,4]=>0
[1,3,1,4,2]=>0
[1,3,2,1,4]=>0
[1,3,2,4,1]=>0
[1,3,4,1,2]=>0
[1,3,4,2,1]=>0
[1,4,1,2,3]=>0
[1,4,1,3,2]=>0
[1,4,2,1,3]=>0
[1,4,2,3,1]=>0
[1,4,3,1,2]=>0
[1,4,3,2,1]=>0
[2,1,1,3,4]=>1
[2,1,1,4,3]=>1
[2,1,3,1,4]=>0
[2,1,3,4,1]=>0
[2,1,4,1,3]=>0
[2,1,4,3,1]=>0
[2,3,1,1,4]=>1
[2,3,1,4,1]=>0
[2,3,4,1,1]=>1
[2,4,1,1,3]=>1
[2,4,1,3,1]=>0
[2,4,3,1,1]=>1
[3,1,1,2,4]=>1
[3,1,1,4,2]=>1
[3,1,2,1,4]=>0
[3,1,2,4,1]=>0
[3,1,4,1,2]=>0
[3,1,4,2,1]=>0
[3,2,1,1,4]=>1
[3,2,1,4,1]=>0
[3,2,4,1,1]=>1
[3,4,1,1,2]=>1
[3,4,1,2,1]=>0
[3,4,2,1,1]=>1
[4,1,1,2,3]=>1
[4,1,1,3,2]=>1
[4,1,2,1,3]=>0
[4,1,2,3,1]=>0
[4,1,3,1,2]=>0
[4,1,3,2,1]=>0
[4,2,1,1,3]=>1
[4,2,1,3,1]=>0
[4,2,3,1,1]=>1
[4,3,1,1,2]=>1
[4,3,1,2,1]=>0
[4,3,2,1,1]=>1
[1,1,2,3,5]=>1
[1,1,2,5,3]=>1
[1,1,3,2,5]=>1
[1,1,3,5,2]=>1
[1,1,5,2,3]=>1
[1,1,5,3,2]=>1
[1,2,1,3,5]=>0
[1,2,1,5,3]=>0
[1,2,3,1,5]=>0
[1,2,3,5,1]=>0
[1,2,5,1,3]=>0
[1,2,5,3,1]=>0
[1,3,1,2,5]=>0
[1,3,1,5,2]=>0
[1,3,2,1,5]=>0
[1,3,2,5,1]=>0
[1,3,5,1,2]=>0
[1,3,5,2,1]=>0
[1,5,1,2,3]=>0
[1,5,1,3,2]=>0
[1,5,2,1,3]=>0
[1,5,2,3,1]=>0
[1,5,3,1,2]=>0
[1,5,3,2,1]=>0
[2,1,1,3,5]=>1
[2,1,1,5,3]=>1
[2,1,3,1,5]=>0
[2,1,3,5,1]=>0
[2,1,5,1,3]=>0
[2,1,5,3,1]=>0
[2,3,1,1,5]=>1
[2,3,1,5,1]=>0
[2,3,5,1,1]=>1
[2,5,1,1,3]=>1
[2,5,1,3,1]=>0
[2,5,3,1,1]=>1
[3,1,1,2,5]=>1
[3,1,1,5,2]=>1
[3,1,2,1,5]=>0
[3,1,2,5,1]=>0
[3,1,5,1,2]=>0
[3,1,5,2,1]=>0
[3,2,1,1,5]=>1
[3,2,1,5,1]=>0
[3,2,5,1,1]=>1
[3,5,1,1,2]=>1
[3,5,1,2,1]=>0
[3,5,2,1,1]=>1
[5,1,1,2,3]=>1
[5,1,1,3,2]=>1
[5,1,2,1,3]=>0
[5,1,2,3,1]=>0
[5,1,3,1,2]=>0
[5,1,3,2,1]=>0
[5,2,1,1,3]=>1
[5,2,1,3,1]=>0
[5,2,3,1,1]=>1
[5,3,1,1,2]=>1
[5,3,1,2,1]=>0
[5,3,2,1,1]=>1
[1,1,2,4,4]=>2
[1,1,4,2,4]=>1
[1,1,4,4,2]=>2
[1,2,1,4,4]=>1
[1,2,4,1,4]=>0
[1,2,4,4,1]=>1
[1,4,1,2,4]=>0
[1,4,1,4,2]=>0
[1,4,2,1,4]=>0
[1,4,2,4,1]=>0
[1,4,4,1,2]=>1
[1,4,4,2,1]=>1
[2,1,1,4,4]=>2
[2,1,4,1,4]=>0
[2,1,4,4,1]=>1
[2,4,1,1,4]=>1
[2,4,1,4,1]=>0
[2,4,4,1,1]=>2
[4,1,1,2,4]=>1
[4,1,1,4,2]=>1
[4,1,2,1,4]=>0
[4,1,2,4,1]=>0
[4,1,4,1,2]=>0
[4,1,4,2,1]=>0
[4,2,1,1,4]=>1
[4,2,1,4,1]=>0
[4,2,4,1,1]=>1
[4,4,1,1,2]=>2
[4,4,1,2,1]=>1
[4,4,2,1,1]=>2
[1,1,2,4,5]=>1
[1,1,2,5,4]=>1
[1,1,4,2,5]=>1
[1,1,4,5,2]=>1
[1,1,5,2,4]=>1
[1,1,5,4,2]=>1
[1,2,1,4,5]=>0
[1,2,1,5,4]=>0
[1,2,4,1,5]=>0
[1,2,4,5,1]=>0
[1,2,5,1,4]=>0
[1,2,5,4,1]=>0
[1,4,1,2,5]=>0
[1,4,1,5,2]=>0
[1,4,2,1,5]=>0
[1,4,2,5,1]=>0
[1,4,5,1,2]=>0
[1,4,5,2,1]=>0
[1,5,1,2,4]=>0
[1,5,1,4,2]=>0
[1,5,2,1,4]=>0
[1,5,2,4,1]=>0
[1,5,4,1,2]=>0
[1,5,4,2,1]=>0
[2,1,1,4,5]=>1
[2,1,1,5,4]=>1
[2,1,4,1,5]=>0
[2,1,4,5,1]=>0
[2,1,5,1,4]=>0
[2,1,5,4,1]=>0
[2,4,1,1,5]=>1
[2,4,1,5,1]=>0
[2,4,5,1,1]=>1
[2,5,1,1,4]=>1
[2,5,1,4,1]=>0
[2,5,4,1,1]=>1
[4,1,1,2,5]=>1
[4,1,1,5,2]=>1
[4,1,2,1,5]=>0
[4,1,2,5,1]=>0
[4,1,5,1,2]=>0
[4,1,5,2,1]=>0
[4,2,1,1,5]=>1
[4,2,1,5,1]=>0
[4,2,5,1,1]=>1
[4,5,1,1,2]=>1
[4,5,1,2,1]=>0
[4,5,2,1,1]=>1
[5,1,1,2,4]=>1
[5,1,1,4,2]=>1
[5,1,2,1,4]=>0
[5,1,2,4,1]=>0
[5,1,4,1,2]=>0
[5,1,4,2,1]=>0
[5,2,1,1,4]=>1
[5,2,1,4,1]=>0
[5,2,4,1,1]=>1
[5,4,1,1,2]=>1
[5,4,1,2,1]=>0
[5,4,2,1,1]=>1
[1,1,3,3,3]=>3
[1,3,1,3,3]=>1
[1,3,3,1,3]=>1
[1,3,3,3,1]=>2
[3,1,1,3,3]=>2
[3,1,3,1,3]=>0
[3,1,3,3,1]=>1
[3,3,1,1,3]=>2
[3,3,1,3,1]=>1
[3,3,3,1,1]=>3
[1,1,3,3,4]=>2
[1,1,3,4,3]=>1
[1,1,4,3,3]=>2
[1,3,1,3,4]=>0
[1,3,1,4,3]=>0
[1,3,3,1,4]=>1
[1,3,3,4,1]=>1
[1,3,4,1,3]=>0
[1,3,4,3,1]=>0
[1,4,1,3,3]=>1
[1,4,3,1,3]=>0
[1,4,3,3,1]=>1
[3,1,1,3,4]=>1
[3,1,1,4,3]=>1
[3,1,3,1,4]=>0
[3,1,3,4,1]=>0
[3,1,4,1,3]=>0
[3,1,4,3,1]=>0
[3,3,1,1,4]=>2
[3,3,1,4,1]=>1
[3,3,4,1,1]=>2
[3,4,1,1,3]=>1
[3,4,1,3,1]=>0
[3,4,3,1,1]=>1
[4,1,1,3,3]=>2
[4,1,3,1,3]=>0
[4,1,3,3,1]=>1
[4,3,1,1,3]=>1
[4,3,1,3,1]=>0
[4,3,3,1,1]=>2
[1,1,3,3,5]=>2
[1,1,3,5,3]=>1
[1,1,5,3,3]=>2
[1,3,1,3,5]=>0
[1,3,1,5,3]=>0
[1,3,3,1,5]=>1
[1,3,3,5,1]=>1
[1,3,5,1,3]=>0
[1,3,5,3,1]=>0
[1,5,1,3,3]=>1
[1,5,3,1,3]=>0
[1,5,3,3,1]=>1
[3,1,1,3,5]=>1
[3,1,1,5,3]=>1
[3,1,3,1,5]=>0
[3,1,3,5,1]=>0
[3,1,5,1,3]=>0
[3,1,5,3,1]=>0
[3,3,1,1,5]=>2
[3,3,1,5,1]=>1
[3,3,5,1,1]=>2
[3,5,1,1,3]=>1
[3,5,1,3,1]=>0
[3,5,3,1,1]=>1
[5,1,1,3,3]=>2
[5,1,3,1,3]=>0
[5,1,3,3,1]=>1
[5,3,1,1,3]=>1
[5,3,1,3,1]=>0
[5,3,3,1,1]=>2
[1,1,3,4,4]=>2
[1,1,4,3,4]=>1
[1,1,4,4,3]=>2
[1,3,1,4,4]=>1
[1,3,4,1,4]=>0
[1,3,4,4,1]=>1
[1,4,1,3,4]=>0
[1,4,1,4,3]=>0
[1,4,3,1,4]=>0
[1,4,3,4,1]=>0
[1,4,4,1,3]=>1
[1,4,4,3,1]=>1
[3,1,1,4,4]=>2
[3,1,4,1,4]=>0
[3,1,4,4,1]=>1
[3,4,1,1,4]=>1
[3,4,1,4,1]=>0
[3,4,4,1,1]=>2
[4,1,1,3,4]=>1
[4,1,1,4,3]=>1
[4,1,3,1,4]=>0
[4,1,3,4,1]=>0
[4,1,4,1,3]=>0
[4,1,4,3,1]=>0
[4,3,1,1,4]=>1
[4,3,1,4,1]=>0
[4,3,4,1,1]=>1
[4,4,1,1,3]=>2
[4,4,1,3,1]=>1
[4,4,3,1,1]=>2
[1,1,3,4,5]=>1
[1,1,3,5,4]=>1
[1,1,4,3,5]=>1
[1,1,4,5,3]=>1
[1,1,5,3,4]=>1
[1,1,5,4,3]=>1
[1,3,1,4,5]=>0
[1,3,1,5,4]=>0
[1,3,4,1,5]=>0
[1,3,4,5,1]=>0
[1,3,5,1,4]=>0
[1,3,5,4,1]=>0
[1,4,1,3,5]=>0
[1,4,1,5,3]=>0
[1,4,3,1,5]=>0
[1,4,3,5,1]=>0
[1,4,5,1,3]=>0
[1,4,5,3,1]=>0
[1,5,1,3,4]=>0
[1,5,1,4,3]=>0
[1,5,3,1,4]=>0
[1,5,3,4,1]=>0
[1,5,4,1,3]=>0
[1,5,4,3,1]=>0
[3,1,1,4,5]=>1
[3,1,1,5,4]=>1
[3,1,4,1,5]=>0
[3,1,4,5,1]=>0
[3,1,5,1,4]=>0
[3,1,5,4,1]=>0
[3,4,1,1,5]=>1
[3,4,1,5,1]=>0
[3,4,5,1,1]=>1
[3,5,1,1,4]=>1
[3,5,1,4,1]=>0
[3,5,4,1,1]=>1
[4,1,1,3,5]=>1
[4,1,1,5,3]=>1
[4,1,3,1,5]=>0
[4,1,3,5,1]=>0
[4,1,5,1,3]=>0
[4,1,5,3,1]=>0
[4,3,1,1,5]=>1
[4,3,1,5,1]=>0
[4,3,5,1,1]=>1
[4,5,1,1,3]=>1
[4,5,1,3,1]=>0
[4,5,3,1,1]=>1
[5,1,1,3,4]=>1
[5,1,1,4,3]=>1
[5,1,3,1,4]=>0
[5,1,3,4,1]=>0
[5,1,4,1,3]=>0
[5,1,4,3,1]=>0
[5,3,1,1,4]=>1
[5,3,1,4,1]=>0
[5,3,4,1,1]=>1
[5,4,1,1,3]=>1
[5,4,1,3,1]=>0
[5,4,3,1,1]=>1
[1,2,2,2,2]=>3
[2,1,2,2,2]=>2
[2,2,1,2,2]=>2
[2,2,2,1,2]=>2
[2,2,2,2,1]=>3
[1,2,2,2,3]=>2
[1,2,2,3,2]=>1
[1,2,3,2,2]=>1
[1,3,2,2,2]=>2
[2,1,2,2,3]=>1
[2,1,2,3,2]=>0
[2,1,3,2,2]=>1
[2,2,1,2,3]=>1
[2,2,1,3,2]=>1
[2,2,2,1,3]=>2
[2,2,2,3,1]=>2
[2,2,3,1,2]=>1
[2,2,3,2,1]=>1
[2,3,1,2,2]=>1
[2,3,2,1,2]=>0
[2,3,2,2,1]=>1
[3,1,2,2,2]=>2
[3,2,1,2,2]=>1
[3,2,2,1,2]=>1
[3,2,2,2,1]=>2
[1,2,2,2,4]=>2
[1,2,2,4,2]=>1
[1,2,4,2,2]=>1
[1,4,2,2,2]=>2
[2,1,2,2,4]=>1
[2,1,2,4,2]=>0
[2,1,4,2,2]=>1
[2,2,1,2,4]=>1
[2,2,1,4,2]=>1
[2,2,2,1,4]=>2
[2,2,2,4,1]=>2
[2,2,4,1,2]=>1
[2,2,4,2,1]=>1
[2,4,1,2,2]=>1
[2,4,2,1,2]=>0
[2,4,2,2,1]=>1
[4,1,2,2,2]=>2
[4,2,1,2,2]=>1
[4,2,2,1,2]=>1
[4,2,2,2,1]=>2
[1,2,2,2,5]=>2
[1,2,2,5,2]=>1
[1,2,5,2,2]=>1
[1,5,2,2,2]=>2
[2,1,2,2,5]=>1
[2,1,2,5,2]=>0
[2,1,5,2,2]=>1
[2,2,1,2,5]=>1
[2,2,1,5,2]=>1
[2,2,2,1,5]=>2
[2,2,2,5,1]=>2
[2,2,5,1,2]=>1
[2,2,5,2,1]=>1
[2,5,1,2,2]=>1
[2,5,2,1,2]=>0
[2,5,2,2,1]=>1
[5,1,2,2,2]=>2
[5,2,1,2,2]=>1
[5,2,2,1,2]=>1
[5,2,2,2,1]=>2
[1,2,2,3,3]=>2
[1,2,3,2,3]=>0
[1,2,3,3,2]=>1
[1,3,2,2,3]=>1
[1,3,2,3,2]=>0
[1,3,3,2,2]=>2
[2,1,2,3,3]=>1
[2,1,3,2,3]=>0
[2,1,3,3,2]=>1
[2,2,1,3,3]=>2
[2,2,3,1,3]=>1
[2,2,3,3,1]=>2
[2,3,1,2,3]=>0
[2,3,1,3,2]=>0
[2,3,2,1,3]=>0
[2,3,2,3,1]=>0
[2,3,3,1,2]=>1
[2,3,3,2,1]=>1
[3,1,2,2,3]=>1
[3,1,2,3,2]=>0
[3,1,3,2,2]=>1
[3,2,1,2,3]=>0
[3,2,1,3,2]=>0
[3,2,2,1,3]=>1
[3,2,2,3,1]=>1
[3,2,3,1,2]=>0
[3,2,3,2,1]=>0
[3,3,1,2,2]=>2
[3,3,2,1,2]=>1
[3,3,2,2,1]=>2
[1,2,2,3,4]=>1
[1,2,2,4,3]=>1
[1,2,3,2,4]=>0
[1,2,3,4,2]=>0
[1,2,4,2,3]=>0
[1,2,4,3,2]=>0
[1,3,2,2,4]=>1
[1,3,2,4,2]=>0
[1,3,4,2,2]=>1
[1,4,2,2,3]=>1
[1,4,2,3,2]=>0
[1,4,3,2,2]=>1
[2,1,2,3,4]=>0
[2,1,2,4,3]=>0
[2,1,3,2,4]=>0
[2,1,3,4,2]=>0
[2,1,4,2,3]=>0
[2,1,4,3,2]=>0
[2,2,1,3,4]=>1
[2,2,1,4,3]=>1
[2,2,3,1,4]=>1
[2,2,3,4,1]=>1
[2,2,4,1,3]=>1
[2,2,4,3,1]=>1
[2,3,1,2,4]=>0
[2,3,1,4,2]=>0
[2,3,2,1,4]=>0
[2,3,2,4,1]=>0
[2,3,4,1,2]=>0
[2,3,4,2,1]=>0
[2,4,1,2,3]=>0
[2,4,1,3,2]=>0
[2,4,2,1,3]=>0
[2,4,2,3,1]=>0
[2,4,3,1,2]=>0
[2,4,3,2,1]=>0
[3,1,2,2,4]=>1
[3,1,2,4,2]=>0
[3,1,4,2,2]=>1
[3,2,1,2,4]=>0
[3,2,1,4,2]=>0
[3,2,2,1,4]=>1
[3,2,2,4,1]=>1
[3,2,4,1,2]=>0
[3,2,4,2,1]=>0
[3,4,1,2,2]=>1
[3,4,2,1,2]=>0
[3,4,2,2,1]=>1
[4,1,2,2,3]=>1
[4,1,2,3,2]=>0
[4,1,3,2,2]=>1
[4,2,1,2,3]=>0
[4,2,1,3,2]=>0
[4,2,2,1,3]=>1
[4,2,2,3,1]=>1
[4,2,3,1,2]=>0
[4,2,3,2,1]=>0
[4,3,1,2,2]=>1
[4,3,2,1,2]=>0
[4,3,2,2,1]=>1
[1,2,2,3,5]=>1
[1,2,2,5,3]=>1
[1,2,3,2,5]=>0
[1,2,3,5,2]=>0
[1,2,5,2,3]=>0
[1,2,5,3,2]=>0
[1,3,2,2,5]=>1
[1,3,2,5,2]=>0
[1,3,5,2,2]=>1
[1,5,2,2,3]=>1
[1,5,2,3,2]=>0
[1,5,3,2,2]=>1
[2,1,2,3,5]=>0
[2,1,2,5,3]=>0
[2,1,3,2,5]=>0
[2,1,3,5,2]=>0
[2,1,5,2,3]=>0
[2,1,5,3,2]=>0
[2,2,1,3,5]=>1
[2,2,1,5,3]=>1
[2,2,3,1,5]=>1
[2,2,3,5,1]=>1
[2,2,5,1,3]=>1
[2,2,5,3,1]=>1
[2,3,1,2,5]=>0
[2,3,1,5,2]=>0
[2,3,2,1,5]=>0
[2,3,2,5,1]=>0
[2,3,5,1,2]=>0
[2,3,5,2,1]=>0
[2,5,1,2,3]=>0
[2,5,1,3,2]=>0
[2,5,2,1,3]=>0
[2,5,2,3,1]=>0
[2,5,3,1,2]=>0
[2,5,3,2,1]=>0
[3,1,2,2,5]=>1
[3,1,2,5,2]=>0
[3,1,5,2,2]=>1
[3,2,1,2,5]=>0
[3,2,1,5,2]=>0
[3,2,2,1,5]=>1
[3,2,2,5,1]=>1
[3,2,5,1,2]=>0
[3,2,5,2,1]=>0
[3,5,1,2,2]=>1
[3,5,2,1,2]=>0
[3,5,2,2,1]=>1
[5,1,2,2,3]=>1
[5,1,2,3,2]=>0
[5,1,3,2,2]=>1
[5,2,1,2,3]=>0
[5,2,1,3,2]=>0
[5,2,2,1,3]=>1
[5,2,2,3,1]=>1
[5,2,3,1,2]=>0
[5,2,3,2,1]=>0
[5,3,1,2,2]=>1
[5,3,2,1,2]=>0
[5,3,2,2,1]=>1
[1,2,2,4,4]=>2
[1,2,4,2,4]=>0
[1,2,4,4,2]=>1
[1,4,2,2,4]=>1
[1,4,2,4,2]=>0
[1,4,4,2,2]=>2
[2,1,2,4,4]=>1
[2,1,4,2,4]=>0
[2,1,4,4,2]=>1
[2,2,1,4,4]=>2
[2,2,4,1,4]=>1
[2,2,4,4,1]=>2
[2,4,1,2,4]=>0
[2,4,1,4,2]=>0
[2,4,2,1,4]=>0
[2,4,2,4,1]=>0
[2,4,4,1,2]=>1
[2,4,4,2,1]=>1
[4,1,2,2,4]=>1
[4,1,2,4,2]=>0
[4,1,4,2,2]=>1
[4,2,1,2,4]=>0
[4,2,1,4,2]=>0
[4,2,2,1,4]=>1
[4,2,2,4,1]=>1
[4,2,4,1,2]=>0
[4,2,4,2,1]=>0
[4,4,1,2,2]=>2
[4,4,2,1,2]=>1
[4,4,2,2,1]=>2
[1,2,2,4,5]=>1
[1,2,2,5,4]=>1
[1,2,4,2,5]=>0
[1,2,4,5,2]=>0
[1,2,5,2,4]=>0
[1,2,5,4,2]=>0
[1,4,2,2,5]=>1
[1,4,2,5,2]=>0
[1,4,5,2,2]=>1
[1,5,2,2,4]=>1
[1,5,2,4,2]=>0
[1,5,4,2,2]=>1
[2,1,2,4,5]=>0
[2,1,2,5,4]=>0
[2,1,4,2,5]=>0
[2,1,4,5,2]=>0
[2,1,5,2,4]=>0
[2,1,5,4,2]=>0
[2,2,1,4,5]=>1
[2,2,1,5,4]=>1
[2,2,4,1,5]=>1
[2,2,4,5,1]=>1
[2,2,5,1,4]=>1
[2,2,5,4,1]=>1
[2,4,1,2,5]=>0
[2,4,1,5,2]=>0
[2,4,2,1,5]=>0
[2,4,2,5,1]=>0
[2,4,5,1,2]=>0
[2,4,5,2,1]=>0
[2,5,1,2,4]=>0
[2,5,1,4,2]=>0
[2,5,2,1,4]=>0
[2,5,2,4,1]=>0
[2,5,4,1,2]=>0
[2,5,4,2,1]=>0
[4,1,2,2,5]=>1
[4,1,2,5,2]=>0
[4,1,5,2,2]=>1
[4,2,1,2,5]=>0
[4,2,1,5,2]=>0
[4,2,2,1,5]=>1
[4,2,2,5,1]=>1
[4,2,5,1,2]=>0
[4,2,5,2,1]=>0
[4,5,1,2,2]=>1
[4,5,2,1,2]=>0
[4,5,2,2,1]=>1
[5,1,2,2,4]=>1
[5,1,2,4,2]=>0
[5,1,4,2,2]=>1
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[5,2,1,4,2]=>0
[5,2,2,1,4]=>1
[5,2,2,4,1]=>1
[5,2,4,1,2]=>0
[5,2,4,2,1]=>0
[5,4,1,2,2]=>1
[5,4,2,1,2]=>0
[5,4,2,2,1]=>1
[1,2,3,3,3]=>2
[1,3,2,3,3]=>1
[1,3,3,2,3]=>1
[1,3,3,3,2]=>2
[2,1,3,3,3]=>2
[2,3,1,3,3]=>1
[2,3,3,1,3]=>1
[2,3,3,3,1]=>2
[3,1,2,3,3]=>1
[3,1,3,2,3]=>0
[3,1,3,3,2]=>1
[3,2,1,3,3]=>1
[3,2,3,1,3]=>0
[3,2,3,3,1]=>1
[3,3,1,2,3]=>1
[3,3,1,3,2]=>1
[3,3,2,1,3]=>1
[3,3,2,3,1]=>1
[3,3,3,1,2]=>2
[3,3,3,2,1]=>2
[1,2,3,3,4]=>1
[1,2,3,4,3]=>0
[1,2,4,3,3]=>1
[1,3,2,3,4]=>0
[1,3,2,4,3]=>0
[1,3,3,2,4]=>1
[1,3,3,4,2]=>1
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[1,3,4,3,2]=>0
[1,4,2,3,3]=>1
[1,4,3,2,3]=>0
[1,4,3,3,2]=>1
[2,1,3,3,4]=>1
[2,1,3,4,3]=>0
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[2,3,1,4,3]=>0
[2,3,3,1,4]=>1
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[2,3,4,1,3]=>0
[2,3,4,3,1]=>0
[2,4,1,3,3]=>1
[2,4,3,1,3]=>0
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[3,1,2,3,4]=>0
[3,1,2,4,3]=>0
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[3,1,4,2,3]=>0
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[3,3,1,2,4]=>1
[3,3,1,4,2]=>1
[3,3,2,1,4]=>1
[3,3,2,4,1]=>1
[3,3,4,1,2]=>1
[3,3,4,2,1]=>1
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[3,4,1,3,2]=>0
[3,4,2,1,3]=>0
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[3,4,3,2,1]=>0
[4,1,2,3,3]=>1
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[4,1,3,3,2]=>1
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[4,3,1,3,2]=>0
[4,3,2,1,3]=>0
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[1,3,2,5,3]=>0
[1,3,3,2,5]=>1
[1,5,2,3,3]=>1
[2,1,5,3,3]=>1
[2,3,3,5,1]=>1
[3,1,3,2,5]=>0
[3,5,2,3,1]=>0
[5,1,2,3,3]=>1
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[5,3,3,2,1]=>1
[1,4,2,4,3]=>0
[1,4,3,4,2]=>0
[2,1,4,3,4]=>0
[2,1,4,4,3]=>1
[2,3,4,1,4]=>0
[2,3,4,4,1]=>1
[2,4,1,4,3]=>0
[2,4,3,1,4]=>0
[2,4,3,4,1]=>0
[3,4,2,1,4]=>0
[3,4,2,4,1]=>0
[4,1,2,4,3]=>0
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[4,2,1,3,4]=>0
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[1,2,3,4,5]=>0
[1,2,3,5,4]=>0
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[3,1,2,4,5]=>0
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[4,1,2,3,5]=>0
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[4,1,3,2,5]=>0
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[5,1,2,3,4]=>0
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[5,2,1,3,4]=>0
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[5,3,1,2,4]=>0
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[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>0
[1,2,3,5,4,6]=>0
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[1,2,3,6,4,5]=>0
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[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
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[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
[1,2,6,4,5,3]=>0
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[1,3,2,4,5,6]=>0
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[1,3,2,5,4,6]=>0
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[1,3,4,2,5,6]=>0
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[1,3,4,5,6,2]=>0
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[1,3,5,2,4,6]=>0
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[1,3,5,4,6,2]=>0
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[1,4,2,3,5,6]=>0
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[1,4,3,2,5,6]=>0
[1,4,3,2,6,5]=>0
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[1,4,3,6,5,2]=>0
[1,4,5,2,3,6]=>0
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[1,4,5,3,2,6]=>0
[1,4,5,3,6,2]=>0
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[1,4,5,6,3,2]=>0
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[1,5,2,3,4,6]=>0
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[1,5,2,6,3,4]=>0
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[1,5,4,3,2,6]=>0
[1,5,4,3,6,2]=>0
[1,5,4,6,3,2]=>0
[1,5,6,2,3,4]=>0
[1,5,6,4,3,2]=>0
[1,6,2,3,4,5]=>0
[1,6,3,4,5,2]=>0
[1,6,3,5,4,2]=>0
[1,6,4,3,5,2]=>0
[1,6,4,5,3,2]=>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
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[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
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[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
[2,1,6,4,5,3]=>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
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[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
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[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
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[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
[2,4,3,1,5,6]=>0
[2,4,3,1,6,5]=>0
[2,4,3,5,1,6]=>0
[2,4,3,5,6,1]=>0
[2,4,3,6,5,1]=>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
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[2,5,1,3,4,6]=>0
[2,5,1,3,6,4]=>0
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[2,5,3,4,1,6]=>0
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[2,5,4,1,6,3]=>0
[2,5,4,3,1,6]=>0
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[2,5,6,1,3,4]=>0
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[2,6,1,3,4,5]=>0
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[2,6,4,1,3,5]=>0
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[2,6,4,5,1,3]=>0
[2,6,4,5,3,1]=>0
[2,6,5,1,3,4]=>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
[3,1,4,2,5,6]=>0
[3,1,4,2,6,5]=>0
[3,1,4,5,2,6]=>0
[3,1,4,5,6,2]=>0
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[3,1,5,2,4,6]=>0
[3,1,5,2,6,4]=>0
[3,1,5,6,2,4]=>0
[3,1,6,2,4,5]=>0
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[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
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[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
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[3,2,5,1,4,6]=>0
[3,2,5,4,1,6]=>0
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[3,2,6,1,4,5]=>0
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[3,2,6,5,4,1]=>0
[3,4,1,2,5,6]=>0
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[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>0
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[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
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[3,4,6,1,2,5]=>0
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[3,5,1,2,4,6]=>0
[3,5,1,2,6,4]=>0
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[3,5,1,6,4,2]=>0
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[3,5,6,1,2,4]=>0
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[3,6,1,2,4,5]=>0
[3,6,1,5,4,2]=>0
[3,6,2,5,1,4]=>0
[3,6,5,4,2,1]=>0
[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
[4,1,5,2,3,6]=>0
[4,1,5,2,6,3]=>0
[4,1,5,6,2,3]=>0
[4,1,6,2,3,5]=>0
[4,2,1,3,5,6]=>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
[4,2,3,6,5,1]=>0
[4,2,5,1,3,6]=>0
[4,2,6,1,3,5]=>0
[4,3,1,2,5,6]=>0
[4,3,1,5,6,2]=>0
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[4,3,2,5,6,1]=>0
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[4,3,5,1,2,6]=>0
[4,3,5,2,1,6]=>0
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[4,3,6,1,2,5]=>0
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[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>0
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[4,5,2,1,3,6]=>0
[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>0
[4,5,3,1,2,6]=>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
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[2,1,7,6,8,4,3,5]=>0
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[6,5,7,8,2,1,3,4]=>0
[5,4,7,2,1,8,3,6]=>0
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[5,3,2,7,1,8,4,6]=>0
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[3,4,1,2,8,7,6,5]=>0
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[6,3,2,8,7,1,5,4]=>0
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[8,3,2,7,6,5,4,1]=>0
[8,4,7,2,6,5,3,1]=>0
[7,4,8,2,6,5,1,3]=>0
[6,4,8,2,7,1,5,3]=>0
[5,4,8,2,1,7,6,3]=>0
[4,5,8,1,2,7,6,3]=>0
[3,5,1,8,2,7,6,4]=>0
[2,1,5,8,3,7,6,4]=>0
[2,1,6,8,7,3,5,4]=>0
[3,6,1,8,7,2,5,4]=>0
[4,6,8,1,7,2,5,3]=>0
[5,6,8,7,1,2,4,3]=>0
[6,5,8,7,2,1,4,3]=>0
[7,5,8,6,2,4,1,3]=>0
[8,5,7,6,2,4,3,1]=>0
[8,6,7,5,4,2,3,1]=>0
[7,6,8,5,4,2,1,3]=>0
[6,7,8,5,4,1,2,3]=>0
[5,7,8,6,1,4,2,3]=>0
[4,7,8,1,6,5,2,3]=>0
[3,7,1,8,6,5,2,4]=>0
[2,1,7,8,6,5,3,4]=>0
[2,1,8,7,6,5,4,3]=>0
[3,8,1,7,6,5,4,2]=>0
[4,8,7,1,6,5,3,2]=>0
[5,8,7,6,1,4,3,2]=>0
[6,8,7,5,4,1,3,2]=>0
[7,8,6,5,4,3,1,2]=>0
[8,7,6,5,4,3,2,1]=>0
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Description
The number of ties in a parking function.
This is the number of indices $i$ such that $p_i=p_{i+1}$.
This is the number of indices $i$ such that $p_i=p_{i+1}$.
References
[1] Schumacher, P.R.F. Descents in Parking Functions, Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.3. https://www.emis.de/journals/JIS/VOL21/Schumacher/schu5.pdf
Code
def statistic(p):
return sum(1 for i in range(len(p)-1) if p[i] == p[i+1])
Created
May 26, 2024 at 16:24 by Jennifer Elder
Updated
Jul 30, 2024 at 11:30 by Martin Rubey
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