Identifier
Values
=>
[1]=>0
[1,1]=>1
[1,2]=>0
[2,1]=>1
[1,1,1]=>2
[1,1,2]=>2
[1,2,1]=>1
[2,1,1]=>2
[1,1,3]=>1
[1,3,1]=>1
[3,1,1]=>2
[1,2,2]=>1
[2,1,2]=>2
[2,2,1]=>1
[1,2,3]=>0
[1,3,2]=>1
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>2
[3,2,1]=>1
[1,1,1,1]=>3
[1,1,1,2]=>3
[1,1,2,1]=>3
[1,2,1,1]=>2
[2,1,1,1]=>3
[1,1,1,3]=>3
[1,1,3,1]=>2
[1,3,1,1]=>2
[3,1,1,1]=>3
[1,1,1,4]=>2
[1,1,4,1]=>2
[1,4,1,1]=>2
[4,1,1,1]=>3
[1,1,2,2]=>3
[1,2,1,2]=>2
[1,2,2,1]=>2
[2,1,1,2]=>3
[2,1,2,1]=>3
[2,2,1,1]=>2
[1,1,2,3]=>3
[1,1,3,2]=>2
[1,2,1,3]=>2
[1,2,3,1]=>1
[1,3,1,2]=>2
[1,3,2,1]=>2
[2,1,1,3]=>3
[2,1,3,1]=>2
[2,3,1,1]=>2
[3,1,1,2]=>3
[3,1,2,1]=>3
[3,2,1,1]=>2
[1,1,2,4]=>2
[1,1,4,2]=>2
[1,2,1,4]=>1
[1,2,4,1]=>1
[1,4,1,2]=>2
[1,4,2,1]=>2
[2,1,1,4]=>2
[2,1,4,1]=>2
[2,4,1,1]=>2
[4,1,1,2]=>3
[4,1,2,1]=>3
[4,2,1,1]=>2
[1,1,3,3]=>2
[1,3,1,3]=>2
[1,3,3,1]=>1
[3,1,1,3]=>3
[3,1,3,1]=>2
[3,3,1,1]=>2
[1,1,3,4]=>1
[1,1,4,3]=>2
[1,3,1,4]=>1
[1,3,4,1]=>1
[1,4,1,3]=>2
[1,4,3,1]=>1
[3,1,1,4]=>2
[3,1,4,1]=>2
[3,4,1,1]=>2
[4,1,1,3]=>3
[4,1,3,1]=>2
[4,3,1,1]=>2
[1,2,2,2]=>2
[2,1,2,2]=>3
[2,2,1,2]=>2
[2,2,2,1]=>2
[1,2,2,3]=>2
[1,2,3,2]=>1
[1,3,2,2]=>2
[2,1,2,3]=>3
[2,1,3,2]=>2
[2,2,1,3]=>2
[2,2,3,1]=>1
[2,3,1,2]=>2
[2,3,2,1]=>2
[3,1,2,2]=>3
[3,2,1,2]=>2
[3,2,2,1]=>2
[1,2,2,4]=>1
[1,2,4,2]=>1
[1,4,2,2]=>2
[2,1,2,4]=>2
[2,1,4,2]=>2
[2,2,1,4]=>1
[2,2,4,1]=>1
[2,4,1,2]=>2
[2,4,2,1]=>2
[4,1,2,2]=>3
[4,2,1,2]=>2
[4,2,2,1]=>2
[1,2,3,3]=>1
[1,3,2,3]=>2
[1,3,3,2]=>1
[2,1,3,3]=>2
[2,3,1,3]=>2
[2,3,3,1]=>1
[3,1,2,3]=>3
[3,1,3,2]=>2
[3,2,1,3]=>2
[3,2,3,1]=>1
[3,3,1,2]=>2
[3,3,2,1]=>2
[1,2,3,4]=>0
[1,2,4,3]=>1
[1,3,2,4]=>1
[1,3,4,2]=>1
[1,4,2,3]=>2
[1,4,3,2]=>1
[2,1,3,4]=>1
[2,1,4,3]=>2
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>1
[3,1,2,4]=>2
[3,1,4,2]=>2
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>2
[3,4,2,1]=>2
[4,1,2,3]=>3
[4,1,3,2]=>2
[4,2,1,3]=>2
[4,2,3,1]=>1
[4,3,1,2]=>2
[4,3,2,1]=>2
[1,1,1,1,1]=>4
[1,1,1,1,2]=>4
[1,1,1,2,1]=>4
[1,1,2,1,1]=>4
[1,2,1,1,1]=>3
[2,1,1,1,1]=>4
[1,1,1,1,3]=>4
[1,1,1,3,1]=>4
[1,1,3,1,1]=>3
[1,3,1,1,1]=>3
[3,1,1,1,1]=>4
[1,1,1,1,4]=>4
[1,1,1,4,1]=>3
[1,1,4,1,1]=>3
[1,4,1,1,1]=>3
[4,1,1,1,1]=>4
[1,1,1,1,5]=>3
[1,1,1,5,1]=>3
[1,1,5,1,1]=>3
[1,5,1,1,1]=>3
[5,1,1,1,1]=>4
[1,1,1,2,2]=>4
[1,1,2,1,2]=>4
[1,1,2,2,1]=>4
[1,2,1,1,2]=>3
[1,2,1,2,1]=>3
[1,2,2,1,1]=>3
[2,1,1,1,2]=>4
[2,1,1,2,1]=>4
[2,1,2,1,1]=>4
[2,2,1,1,1]=>3
[1,1,1,2,3]=>4
[1,1,1,3,2]=>4
[1,1,2,1,3]=>4
[1,1,2,3,1]=>4
[1,1,3,1,2]=>3
[1,1,3,2,1]=>3
[1,2,1,1,3]=>3
[1,2,1,3,1]=>3
[1,2,3,1,1]=>2
[1,3,1,1,2]=>3
[1,3,1,2,1]=>3
[1,3,2,1,1]=>3
[2,1,1,1,3]=>4
[2,1,1,3,1]=>4
[2,1,3,1,1]=>3
[2,3,1,1,1]=>3
[3,1,1,1,2]=>4
[3,1,1,2,1]=>4
[3,1,2,1,1]=>4
[3,2,1,1,1]=>3
[1,1,1,2,4]=>4
[1,1,1,4,2]=>3
[1,1,2,1,4]=>4
[1,1,2,4,1]=>3
[1,1,4,1,2]=>3
[1,1,4,2,1]=>3
[1,2,1,1,4]=>3
[1,2,1,4,1]=>2
[1,2,4,1,1]=>2
[1,4,1,1,2]=>3
[1,4,1,2,1]=>3
[1,4,2,1,1]=>3
[2,1,1,1,4]=>4
[2,1,1,4,1]=>3
[2,1,4,1,1]=>3
[2,4,1,1,1]=>3
[4,1,1,1,2]=>4
[4,1,1,2,1]=>4
[4,1,2,1,1]=>4
[4,2,1,1,1]=>3
[1,1,1,2,5]=>3
[1,1,1,5,2]=>3
[1,1,2,1,5]=>3
[1,1,2,5,1]=>3
[1,1,5,1,2]=>3
[1,1,5,2,1]=>3
[1,2,1,1,5]=>2
[1,2,1,5,1]=>2
[1,2,5,1,1]=>2
[1,5,1,1,2]=>3
[1,5,1,2,1]=>3
[1,5,2,1,1]=>3
[2,1,1,1,5]=>3
[2,1,1,5,1]=>3
[2,1,5,1,1]=>3
[2,5,1,1,1]=>3
[5,1,1,1,2]=>4
[5,1,1,2,1]=>4
[5,1,2,1,1]=>4
[5,2,1,1,1]=>3
[1,1,1,3,3]=>4
[1,1,3,1,3]=>3
[1,1,3,3,1]=>3
[1,3,1,1,3]=>3
[1,3,1,3,1]=>3
[1,3,3,1,1]=>2
[3,1,1,1,3]=>4
[3,1,1,3,1]=>4
[3,1,3,1,1]=>3
[3,3,1,1,1]=>3
[1,1,1,3,4]=>4
[1,1,1,4,3]=>3
[1,1,3,1,4]=>3
[1,1,3,4,1]=>2
[1,1,4,1,3]=>3
[1,1,4,3,1]=>3
[1,3,1,1,4]=>3
[1,3,1,4,1]=>2
[1,3,4,1,1]=>2
[1,4,1,1,3]=>3
[1,4,1,3,1]=>3
[1,4,3,1,1]=>2
[3,1,1,1,4]=>4
[3,1,1,4,1]=>3
[3,1,4,1,1]=>3
[3,4,1,1,1]=>3
[4,1,1,1,3]=>4
[4,1,1,3,1]=>4
[4,1,3,1,1]=>3
[4,3,1,1,1]=>3
[1,1,1,3,5]=>3
[1,1,1,5,3]=>3
[1,1,3,1,5]=>2
[1,1,3,5,1]=>2
[1,1,5,1,3]=>3
[1,1,5,3,1]=>3
[1,3,1,1,5]=>2
[1,3,1,5,1]=>2
[1,3,5,1,1]=>2
[1,5,1,1,3]=>3
[1,5,1,3,1]=>3
[1,5,3,1,1]=>2
[3,1,1,1,5]=>3
[3,1,1,5,1]=>3
[3,1,5,1,1]=>3
[3,5,1,1,1]=>3
[5,1,1,1,3]=>4
[5,1,1,3,1]=>4
[5,1,3,1,1]=>3
[5,3,1,1,1]=>3
[1,1,1,4,4]=>3
[1,1,4,1,4]=>3
[1,1,4,4,1]=>2
[1,4,1,1,4]=>3
[1,4,1,4,1]=>2
[1,4,4,1,1]=>2
[4,1,1,1,4]=>4
[4,1,1,4,1]=>3
[4,1,4,1,1]=>3
[4,4,1,1,1]=>3
[1,1,1,4,5]=>2
[1,1,1,5,4]=>3
[1,1,4,1,5]=>2
[1,1,4,5,1]=>2
[1,1,5,1,4]=>3
[1,1,5,4,1]=>2
[1,4,1,1,5]=>2
[1,4,1,5,1]=>2
[1,4,5,1,1]=>2
[1,5,1,1,4]=>3
[1,5,1,4,1]=>2
[1,5,4,1,1]=>2
[4,1,1,1,5]=>3
[4,1,1,5,1]=>3
[4,1,5,1,1]=>3
[4,5,1,1,1]=>3
[5,1,1,1,4]=>4
[5,1,1,4,1]=>3
[5,1,4,1,1]=>3
[5,4,1,1,1]=>3
[1,1,2,2,2]=>4
[1,2,1,2,2]=>3
[1,2,2,1,2]=>3
[1,2,2,2,1]=>3
[2,1,1,2,2]=>4
[2,1,2,1,2]=>4
[2,1,2,2,1]=>4
[2,2,1,1,2]=>3
[2,2,1,2,1]=>3
[2,2,2,1,1]=>3
[1,1,2,2,3]=>4
[1,1,2,3,2]=>4
[1,1,3,2,2]=>3
[1,2,1,2,3]=>3
[1,2,1,3,2]=>3
[1,2,2,1,3]=>3
[1,2,2,3,1]=>3
[1,2,3,1,2]=>2
[1,2,3,2,1]=>2
[1,3,1,2,2]=>3
[1,3,2,1,2]=>3
[1,3,2,2,1]=>3
[2,1,1,2,3]=>4
[2,1,1,3,2]=>4
[2,1,2,1,3]=>4
[2,1,2,3,1]=>4
[2,1,3,1,2]=>3
[2,1,3,2,1]=>3
[2,2,1,1,3]=>3
[2,2,1,3,1]=>3
[2,2,3,1,1]=>2
[2,3,1,1,2]=>3
[2,3,1,2,1]=>3
[2,3,2,1,1]=>3
[3,1,1,2,2]=>4
[3,1,2,1,2]=>4
[3,1,2,2,1]=>4
[3,2,1,1,2]=>3
[3,2,1,2,1]=>3
[3,2,2,1,1]=>3
[1,1,2,2,4]=>4
[1,1,2,4,2]=>3
[1,1,4,2,2]=>3
[1,2,1,2,4]=>3
[1,2,1,4,2]=>2
[1,2,2,1,4]=>3
[1,2,2,4,1]=>2
[1,2,4,1,2]=>2
[1,2,4,2,1]=>2
[1,4,1,2,2]=>3
[1,4,2,1,2]=>3
[1,4,2,2,1]=>3
[2,1,1,2,4]=>4
[2,1,1,4,2]=>3
[2,1,2,1,4]=>4
[2,1,2,4,1]=>3
[2,1,4,1,2]=>3
[2,1,4,2,1]=>3
[2,2,1,1,4]=>3
[2,2,1,4,1]=>2
[2,2,4,1,1]=>2
[2,4,1,1,2]=>3
[2,4,1,2,1]=>3
[2,4,2,1,1]=>3
[4,1,1,2,2]=>4
[4,1,2,1,2]=>4
[4,1,2,2,1]=>4
[4,2,1,1,2]=>3
[4,2,1,2,1]=>3
[4,2,2,1,1]=>3
[1,1,2,2,5]=>3
[1,1,2,5,2]=>3
[1,1,5,2,2]=>3
[1,2,1,2,5]=>2
[1,2,1,5,2]=>2
[1,2,2,1,5]=>2
[1,2,2,5,1]=>2
[1,2,5,1,2]=>2
[1,2,5,2,1]=>2
[1,5,1,2,2]=>3
[1,5,2,1,2]=>3
[1,5,2,2,1]=>3
[2,1,1,2,5]=>3
[2,1,1,5,2]=>3
[2,1,2,1,5]=>3
[2,1,2,5,1]=>3
[2,1,5,1,2]=>3
[2,1,5,2,1]=>3
[2,2,1,1,5]=>2
[2,2,1,5,1]=>2
[2,2,5,1,1]=>2
[2,5,1,1,2]=>3
[2,5,1,2,1]=>3
[2,5,2,1,1]=>3
[5,1,1,2,2]=>4
[5,1,2,1,2]=>4
[5,1,2,2,1]=>4
[5,2,1,1,2]=>3
[5,2,1,2,1]=>3
[5,2,2,1,1]=>3
[1,1,2,3,3]=>4
[1,1,3,2,3]=>3
[1,1,3,3,2]=>3
[1,2,1,3,3]=>3
[1,2,3,1,3]=>2
[1,2,3,3,1]=>2
[1,3,1,2,3]=>3
[1,3,1,3,2]=>3
[1,3,2,1,3]=>3
[1,3,2,3,1]=>3
[1,3,3,1,2]=>2
[1,3,3,2,1]=>2
[2,1,1,3,3]=>4
[2,1,3,1,3]=>3
[2,1,3,3,1]=>3
[2,3,1,1,3]=>3
[2,3,1,3,1]=>3
[2,3,3,1,1]=>2
[3,1,1,2,3]=>4
[3,1,1,3,2]=>4
[3,1,2,1,3]=>4
[3,1,2,3,1]=>4
[3,1,3,1,2]=>3
[3,1,3,2,1]=>3
[3,2,1,1,3]=>3
[3,2,1,3,1]=>3
[3,2,3,1,1]=>2
[3,3,1,1,2]=>3
[3,3,1,2,1]=>3
[3,3,2,1,1]=>3
[1,1,2,3,4]=>4
[1,1,2,4,3]=>3
[1,1,3,2,4]=>3
[1,1,3,4,2]=>2
[1,1,4,2,3]=>3
[1,1,4,3,2]=>3
[1,2,1,3,4]=>3
[1,2,1,4,3]=>2
[1,2,3,1,4]=>2
[1,2,3,4,1]=>1
[1,2,4,1,3]=>2
[1,2,4,3,1]=>2
[1,3,1,2,4]=>3
[1,3,1,4,2]=>2
[1,3,2,1,4]=>3
[1,3,2,4,1]=>2
[1,3,4,1,2]=>2
[1,3,4,2,1]=>2
[1,4,1,2,3]=>3
[1,4,1,3,2]=>3
[1,4,2,1,3]=>3
[1,4,2,3,1]=>3
[1,4,3,1,2]=>2
[1,4,3,2,1]=>2
[2,1,1,3,4]=>4
[2,1,1,4,3]=>3
[2,1,3,1,4]=>3
[2,1,3,4,1]=>2
[2,1,4,1,3]=>3
[2,1,4,3,1]=>3
[2,3,1,1,4]=>3
[2,3,1,4,1]=>2
[2,3,4,1,1]=>2
[2,4,1,1,3]=>3
[2,4,1,3,1]=>3
[2,4,3,1,1]=>2
[3,1,1,2,4]=>4
[3,1,1,4,2]=>3
[3,1,2,1,4]=>4
[3,1,2,4,1]=>3
[3,1,4,1,2]=>3
[3,1,4,2,1]=>3
[3,2,1,1,4]=>3
[3,2,1,4,1]=>2
[3,2,4,1,1]=>2
[3,4,1,1,2]=>3
[3,4,1,2,1]=>3
[3,4,2,1,1]=>3
[4,1,1,2,3]=>4
[4,1,1,3,2]=>4
[4,1,2,1,3]=>4
[4,1,2,3,1]=>4
[4,1,3,1,2]=>3
[4,1,3,2,1]=>3
[4,2,1,1,3]=>3
[4,2,1,3,1]=>3
[4,2,3,1,1]=>2
[4,3,1,1,2]=>3
[4,3,1,2,1]=>3
[4,3,2,1,1]=>3
[1,1,2,3,5]=>3
[1,1,2,5,3]=>3
[1,1,3,2,5]=>2
[1,1,3,5,2]=>2
[1,1,5,2,3]=>3
[1,1,5,3,2]=>3
[1,2,1,3,5]=>2
[1,2,1,5,3]=>2
[1,2,3,1,5]=>1
[1,2,3,5,1]=>1
[1,2,5,1,3]=>2
[1,2,5,3,1]=>2
[1,3,1,2,5]=>2
[1,3,1,5,2]=>2
[1,3,2,1,5]=>2
[1,3,2,5,1]=>2
[1,3,5,1,2]=>2
[1,3,5,2,1]=>2
[1,5,1,2,3]=>3
[1,5,1,3,2]=>3
[1,5,2,1,3]=>3
[1,5,2,3,1]=>3
[1,5,3,1,2]=>2
[1,5,3,2,1]=>2
[2,1,1,3,5]=>3
[2,1,1,5,3]=>3
[2,1,3,1,5]=>2
[2,1,3,5,1]=>2
[2,1,5,1,3]=>3
[2,1,5,3,1]=>3
[2,3,1,1,5]=>2
[2,3,1,5,1]=>2
[2,3,5,1,1]=>2
[2,5,1,1,3]=>3
[2,5,1,3,1]=>3
[2,5,3,1,1]=>2
[3,1,1,2,5]=>3
[3,1,1,5,2]=>3
[3,1,2,1,5]=>3
[3,1,2,5,1]=>3
[3,1,5,1,2]=>3
[3,1,5,2,1]=>3
[3,2,1,1,5]=>2
[3,2,1,5,1]=>2
[3,2,5,1,1]=>2
[3,5,1,1,2]=>3
[3,5,1,2,1]=>3
[3,5,2,1,1]=>3
[5,1,1,2,3]=>4
[5,1,1,3,2]=>4
[5,1,2,1,3]=>4
[5,1,2,3,1]=>4
[5,1,3,1,2]=>3
[5,1,3,2,1]=>3
[5,2,1,1,3]=>3
[5,2,1,3,1]=>3
[5,2,3,1,1]=>2
[5,3,1,1,2]=>3
[5,3,1,2,1]=>3
[5,3,2,1,1]=>3
[1,1,2,4,4]=>3
[1,1,4,2,4]=>3
[1,1,4,4,2]=>2
[1,2,1,4,4]=>2
[1,2,4,1,4]=>2
[1,2,4,4,1]=>1
[1,4,1,2,4]=>3
[1,4,1,4,2]=>2
[1,4,2,1,4]=>3
[1,4,2,4,1]=>2
[1,4,4,1,2]=>2
[1,4,4,2,1]=>2
[2,1,1,4,4]=>3
[2,1,4,1,4]=>3
[2,1,4,4,1]=>2
[2,4,1,1,4]=>3
[2,4,1,4,1]=>2
[2,4,4,1,1]=>2
[4,1,1,2,4]=>4
[4,1,1,4,2]=>3
[4,1,2,1,4]=>4
[4,1,2,4,1]=>3
[4,1,4,1,2]=>3
[4,1,4,2,1]=>3
[4,2,1,1,4]=>3
[4,2,1,4,1]=>2
[4,2,4,1,1]=>2
[4,4,1,1,2]=>3
[4,4,1,2,1]=>3
[4,4,2,1,1]=>3
[1,1,2,4,5]=>2
[1,1,2,5,4]=>3
[1,1,4,2,5]=>2
[1,1,4,5,2]=>2
[1,1,5,2,4]=>3
[1,1,5,4,2]=>2
[1,2,1,4,5]=>1
[1,2,1,5,4]=>2
[1,2,4,1,5]=>1
[1,2,4,5,1]=>1
[1,2,5,1,4]=>2
[1,2,5,4,1]=>1
[1,4,1,2,5]=>2
[1,4,1,5,2]=>2
[1,4,2,1,5]=>2
[1,4,2,5,1]=>2
[1,4,5,1,2]=>2
[1,4,5,2,1]=>2
[1,5,1,2,4]=>3
[1,5,1,4,2]=>2
[1,5,2,1,4]=>3
[1,5,2,4,1]=>2
[1,5,4,1,2]=>2
[1,5,4,2,1]=>2
[2,1,1,4,5]=>2
[2,1,1,5,4]=>3
[2,1,4,1,5]=>2
[2,1,4,5,1]=>2
[2,1,5,1,4]=>3
[2,1,5,4,1]=>2
[2,4,1,1,5]=>2
[2,4,1,5,1]=>2
[2,4,5,1,1]=>2
[2,5,1,1,4]=>3
[2,5,1,4,1]=>2
[2,5,4,1,1]=>2
[4,1,1,2,5]=>3
[4,1,1,5,2]=>3
[4,1,2,1,5]=>3
[4,1,2,5,1]=>3
[4,1,5,1,2]=>3
[4,1,5,2,1]=>3
[4,2,1,1,5]=>2
[4,2,1,5,1]=>2
[4,2,5,1,1]=>2
[4,5,1,1,2]=>3
[4,5,1,2,1]=>3
[4,5,2,1,1]=>3
[5,1,1,2,4]=>4
[5,1,1,4,2]=>3
[5,1,2,1,4]=>4
[5,1,2,4,1]=>3
[5,1,4,1,2]=>3
[5,1,4,2,1]=>3
[5,2,1,1,4]=>3
[5,2,1,4,1]=>2
[5,2,4,1,1]=>2
[5,4,1,1,2]=>3
[5,4,1,2,1]=>3
[5,4,2,1,1]=>3
[1,1,3,3,3]=>3
[1,3,1,3,3]=>3
[1,3,3,1,3]=>2
[1,3,3,3,1]=>2
[3,1,1,3,3]=>4
[3,1,3,1,3]=>3
[3,1,3,3,1]=>3
[3,3,1,1,3]=>3
[3,3,1,3,1]=>3
[3,3,3,1,1]=>2
[1,1,3,3,4]=>3
[1,1,3,4,3]=>2
[1,1,4,3,3]=>3
[1,3,1,3,4]=>3
[1,3,1,4,3]=>2
[1,3,3,1,4]=>2
[1,3,3,4,1]=>1
[1,3,4,1,3]=>2
[1,3,4,3,1]=>2
[1,4,1,3,3]=>3
[1,4,3,1,3]=>2
[1,4,3,3,1]=>2
[3,1,1,3,4]=>4
[3,1,1,4,3]=>3
[3,1,3,1,4]=>3
[3,1,3,4,1]=>2
[3,1,4,1,3]=>3
[3,1,4,3,1]=>3
[3,3,1,1,4]=>3
[3,3,1,4,1]=>2
[3,3,4,1,1]=>2
[3,4,1,1,3]=>3
[3,4,1,3,1]=>3
[3,4,3,1,1]=>2
[4,1,1,3,3]=>4
[4,1,3,1,3]=>3
[4,1,3,3,1]=>3
[4,3,1,1,3]=>3
[4,3,1,3,1]=>3
[4,3,3,1,1]=>2
[1,1,3,3,5]=>2
[1,1,3,5,3]=>2
[1,1,5,3,3]=>3
[1,3,1,3,5]=>2
[1,3,1,5,3]=>2
[1,3,3,1,5]=>1
[1,3,3,5,1]=>1
[1,3,5,1,3]=>2
[1,3,5,3,1]=>2
[1,5,1,3,3]=>3
[1,5,3,1,3]=>2
[1,5,3,3,1]=>2
[3,1,1,3,5]=>3
[3,1,1,5,3]=>3
[3,1,3,1,5]=>2
[3,1,3,5,1]=>2
[3,1,5,1,3]=>3
[3,1,5,3,1]=>3
[3,3,1,1,5]=>2
[3,3,1,5,1]=>2
[3,3,5,1,1]=>2
[3,5,1,1,3]=>3
[3,5,1,3,1]=>3
[3,5,3,1,1]=>2
[5,1,1,3,3]=>4
[5,1,3,1,3]=>3
[5,1,3,3,1]=>3
[5,3,1,1,3]=>3
[5,3,1,3,1]=>3
[5,3,3,1,1]=>2
[1,1,3,4,4]=>2
[1,1,4,3,4]=>3
[1,1,4,4,3]=>2
[1,3,1,4,4]=>2
[1,3,4,1,4]=>2
[1,3,4,4,1]=>1
[1,4,1,3,4]=>3
[1,4,1,4,3]=>2
[1,4,3,1,4]=>2
[1,4,3,4,1]=>1
[1,4,4,1,3]=>2
[1,4,4,3,1]=>2
[3,1,1,4,4]=>3
[3,1,4,1,4]=>3
[3,1,4,4,1]=>2
[3,4,1,1,4]=>3
[3,4,1,4,1]=>2
[3,4,4,1,1]=>2
[4,1,1,3,4]=>4
[4,1,1,4,3]=>3
[4,1,3,1,4]=>3
[4,1,3,4,1]=>2
[4,1,4,1,3]=>3
[4,1,4,3,1]=>3
[4,3,1,1,4]=>3
[4,3,1,4,1]=>2
[4,3,4,1,1]=>2
[4,4,1,1,3]=>3
[4,4,1,3,1]=>3
[4,4,3,1,1]=>2
[1,1,3,4,5]=>1
[1,1,3,5,4]=>2
[1,1,4,3,5]=>2
[1,1,4,5,3]=>2
[1,1,5,3,4]=>3
[1,1,5,4,3]=>2
[1,3,1,4,5]=>1
[1,3,1,5,4]=>2
[1,3,4,1,5]=>1
[1,3,4,5,1]=>1
[1,3,5,1,4]=>2
[1,3,5,4,1]=>1
[1,4,1,3,5]=>2
[1,4,1,5,3]=>2
[1,4,3,1,5]=>1
[1,4,3,5,1]=>1
[1,4,5,1,3]=>2
[1,4,5,3,1]=>2
[1,5,1,3,4]=>3
[1,5,1,4,3]=>2
[1,5,3,1,4]=>2
[1,5,3,4,1]=>1
[1,5,4,1,3]=>2
[1,5,4,3,1]=>2
[3,1,1,4,5]=>2
[3,1,1,5,4]=>3
[3,1,4,1,5]=>2
[3,1,4,5,1]=>2
[3,1,5,1,4]=>3
[3,1,5,4,1]=>2
[3,4,1,1,5]=>2
[3,4,1,5,1]=>2
[3,4,5,1,1]=>2
[3,5,1,1,4]=>3
[3,5,1,4,1]=>2
[3,5,4,1,1]=>2
[4,1,1,3,5]=>3
[4,1,1,5,3]=>3
[4,1,3,1,5]=>2
[4,1,3,5,1]=>2
[4,1,5,1,3]=>3
[4,1,5,3,1]=>3
[4,3,1,1,5]=>2
[4,3,1,5,1]=>2
[4,3,5,1,1]=>2
[4,5,1,1,3]=>3
[4,5,1,3,1]=>3
[4,5,3,1,1]=>2
[5,1,1,3,4]=>4
[5,1,1,4,3]=>3
[5,1,3,1,4]=>3
[5,1,3,4,1]=>2
[5,1,4,1,3]=>3
[5,1,4,3,1]=>3
[5,3,1,1,4]=>3
[5,3,1,4,1]=>2
[5,3,4,1,1]=>2
[5,4,1,1,3]=>3
[5,4,1,3,1]=>3
[5,4,3,1,1]=>2
[1,2,2,2,2]=>3
[2,1,2,2,2]=>4
[2,2,1,2,2]=>3
[2,2,2,1,2]=>3
[2,2,2,2,1]=>3
[1,2,2,2,3]=>3
[1,2,2,3,2]=>3
[1,2,3,2,2]=>2
[1,3,2,2,2]=>3
[2,1,2,2,3]=>4
[2,1,2,3,2]=>4
[2,1,3,2,2]=>3
[2,2,1,2,3]=>3
[2,2,1,3,2]=>3
[2,2,2,1,3]=>3
[2,2,2,3,1]=>3
[2,2,3,1,2]=>2
[2,2,3,2,1]=>2
[2,3,1,2,2]=>3
[2,3,2,1,2]=>3
[2,3,2,2,1]=>3
[3,1,2,2,2]=>4
[3,2,1,2,2]=>3
[3,2,2,1,2]=>3
[3,2,2,2,1]=>3
[1,2,2,2,4]=>3
[1,2,2,4,2]=>2
[1,2,4,2,2]=>2
[1,4,2,2,2]=>3
[2,1,2,2,4]=>4
[2,1,2,4,2]=>3
[2,1,4,2,2]=>3
[2,2,1,2,4]=>3
[2,2,1,4,2]=>2
[2,2,2,1,4]=>3
[2,2,2,4,1]=>2
[2,2,4,1,2]=>2
[2,2,4,2,1]=>2
[2,4,1,2,2]=>3
[2,4,2,1,2]=>3
[2,4,2,2,1]=>3
[4,1,2,2,2]=>4
[4,2,1,2,2]=>3
[4,2,2,1,2]=>3
[4,2,2,2,1]=>3
[1,2,2,2,5]=>2
[1,2,2,5,2]=>2
[1,2,5,2,2]=>2
[1,5,2,2,2]=>3
[2,1,2,2,5]=>3
[2,1,2,5,2]=>3
[2,1,5,2,2]=>3
[2,2,1,2,5]=>2
[2,2,1,5,2]=>2
[2,2,2,1,5]=>2
[2,2,2,5,1]=>2
[2,2,5,1,2]=>2
[2,2,5,2,1]=>2
[2,5,1,2,2]=>3
[2,5,2,1,2]=>3
[2,5,2,2,1]=>3
[5,1,2,2,2]=>4
[5,2,1,2,2]=>3
[5,2,2,1,2]=>3
[5,2,2,2,1]=>3
[1,2,2,3,3]=>3
[1,2,3,2,3]=>2
[1,2,3,3,2]=>2
[1,3,2,2,3]=>3
[1,3,2,3,2]=>3
[1,3,3,2,2]=>2
[2,1,2,3,3]=>4
[2,1,3,2,3]=>3
[2,1,3,3,2]=>3
[2,2,1,3,3]=>3
[2,2,3,1,3]=>2
[2,2,3,3,1]=>2
[2,3,1,2,3]=>3
[2,3,1,3,2]=>3
[2,3,2,1,3]=>3
[2,3,2,3,1]=>3
[2,3,3,1,2]=>2
[2,3,3,2,1]=>2
[3,1,2,2,3]=>4
[3,1,2,3,2]=>4
[3,1,3,2,2]=>3
[3,2,1,2,3]=>3
[3,2,1,3,2]=>3
[3,2,2,1,3]=>3
[3,2,2,3,1]=>3
[3,2,3,1,2]=>2
[3,2,3,2,1]=>2
[3,3,1,2,2]=>3
[3,3,2,1,2]=>3
[3,3,2,2,1]=>3
[1,2,2,3,4]=>3
[1,2,2,4,3]=>2
[1,2,3,2,4]=>2
[1,2,3,4,2]=>1
[1,2,4,2,3]=>2
[1,2,4,3,2]=>2
[1,3,2,2,4]=>3
[1,3,2,4,2]=>2
[1,3,4,2,2]=>2
[1,4,2,2,3]=>3
[1,4,2,3,2]=>3
[1,4,3,2,2]=>2
[2,1,2,3,4]=>4
[2,1,2,4,3]=>3
[2,1,3,2,4]=>3
[2,1,3,4,2]=>2
[2,1,4,2,3]=>3
[2,1,4,3,2]=>3
[2,2,1,3,4]=>3
[2,2,1,4,3]=>2
[2,2,3,1,4]=>2
[2,2,3,4,1]=>1
[2,2,4,1,3]=>2
[2,2,4,3,1]=>2
[2,3,1,2,4]=>3
[2,3,1,4,2]=>2
[2,3,2,1,4]=>3
[2,3,2,4,1]=>2
[2,3,4,1,2]=>2
[2,3,4,2,1]=>2
[2,4,1,2,3]=>3
[2,4,1,3,2]=>3
[2,4,2,1,3]=>3
[2,4,2,3,1]=>3
[2,4,3,1,2]=>2
[2,4,3,2,1]=>2
[3,1,2,2,4]=>4
[3,1,2,4,2]=>3
[3,1,4,2,2]=>3
[3,2,1,2,4]=>3
[3,2,1,4,2]=>2
[3,2,2,1,4]=>3
[3,2,2,4,1]=>2
[3,2,4,1,2]=>2
[3,2,4,2,1]=>2
[3,4,1,2,2]=>3
[3,4,2,1,2]=>3
[3,4,2,2,1]=>3
[4,1,2,2,3]=>4
[4,1,2,3,2]=>4
[4,1,3,2,2]=>3
[4,2,1,2,3]=>3
[4,2,1,3,2]=>3
[4,2,2,1,3]=>3
[4,2,2,3,1]=>3
[4,2,3,1,2]=>2
[4,2,3,2,1]=>2
[4,3,1,2,2]=>3
[4,3,2,1,2]=>3
[4,3,2,2,1]=>3
[1,2,2,3,5]=>2
[1,2,2,5,3]=>2
[1,2,3,2,5]=>1
[1,2,3,5,2]=>1
[1,2,5,2,3]=>2
[1,2,5,3,2]=>2
[1,3,2,2,5]=>2
[1,3,2,5,2]=>2
[1,3,5,2,2]=>2
[1,5,2,2,3]=>3
[1,5,2,3,2]=>3
[1,5,3,2,2]=>2
[2,1,2,3,5]=>3
[2,1,2,5,3]=>3
[2,1,3,2,5]=>2
[2,1,3,5,2]=>2
[2,1,5,2,3]=>3
[2,1,5,3,2]=>3
[2,2,1,3,5]=>2
[2,2,1,5,3]=>2
[2,2,3,1,5]=>1
[2,2,3,5,1]=>1
[2,2,5,1,3]=>2
[2,2,5,3,1]=>2
[2,3,1,2,5]=>2
[2,3,1,5,2]=>2
[2,3,2,1,5]=>2
[2,3,2,5,1]=>2
[2,3,5,1,2]=>2
[2,3,5,2,1]=>2
[2,5,1,2,3]=>3
[2,5,1,3,2]=>3
[2,5,2,1,3]=>3
[2,5,2,3,1]=>3
[2,5,3,1,2]=>2
[2,5,3,2,1]=>2
[3,1,2,2,5]=>3
[3,1,2,5,2]=>3
[3,1,5,2,2]=>3
[3,2,1,2,5]=>2
[3,2,1,5,2]=>2
[3,2,2,1,5]=>2
[3,2,2,5,1]=>2
[3,2,5,1,2]=>2
[3,2,5,2,1]=>2
[3,5,1,2,2]=>3
[3,5,2,1,2]=>3
[3,5,2,2,1]=>3
[5,1,2,2,3]=>4
[5,1,2,3,2]=>4
[5,1,3,2,2]=>3
[5,2,1,2,3]=>3
[5,2,1,3,2]=>3
[5,2,2,1,3]=>3
[5,2,2,3,1]=>3
[5,2,3,1,2]=>2
[5,2,3,2,1]=>2
[5,3,1,2,2]=>3
[5,3,2,1,2]=>3
[5,3,2,2,1]=>3
[1,2,2,4,4]=>2
[1,2,4,2,4]=>2
[1,2,4,4,2]=>1
[1,4,2,2,4]=>3
[1,4,2,4,2]=>2
[1,4,4,2,2]=>2
[2,1,2,4,4]=>3
[2,1,4,2,4]=>3
[2,1,4,4,2]=>2
[2,2,1,4,4]=>2
[2,2,4,1,4]=>2
[2,2,4,4,1]=>1
[2,4,1,2,4]=>3
[2,4,1,4,2]=>2
[2,4,2,1,4]=>3
[2,4,2,4,1]=>2
[2,4,4,1,2]=>2
[2,4,4,2,1]=>2
[4,1,2,2,4]=>4
[4,1,2,4,2]=>3
[4,1,4,2,2]=>3
[4,2,1,2,4]=>3
[4,2,1,4,2]=>2
[4,2,2,1,4]=>3
[4,2,2,4,1]=>2
[4,2,4,1,2]=>2
[4,2,4,2,1]=>2
[4,4,1,2,2]=>3
[4,4,2,1,2]=>3
[4,4,2,2,1]=>3
[1,2,2,4,5]=>1
[1,2,2,5,4]=>2
[1,2,4,2,5]=>1
[1,2,4,5,2]=>1
[1,2,5,2,4]=>2
[1,2,5,4,2]=>1
[1,4,2,2,5]=>2
[1,4,2,5,2]=>2
[1,4,5,2,2]=>2
[1,5,2,2,4]=>3
[1,5,2,4,2]=>2
[1,5,4,2,2]=>2
[2,1,2,4,5]=>2
[2,1,2,5,4]=>3
[2,1,4,2,5]=>2
[2,1,4,5,2]=>2
[2,1,5,2,4]=>3
[2,1,5,4,2]=>2
[2,2,1,4,5]=>1
[2,2,1,5,4]=>2
[2,2,4,1,5]=>1
[2,2,4,5,1]=>1
[2,2,5,1,4]=>2
[2,2,5,4,1]=>1
[2,4,1,2,5]=>2
[2,4,1,5,2]=>2
[2,4,2,1,5]=>2
[2,4,2,5,1]=>2
[2,4,5,1,2]=>2
[2,4,5,2,1]=>2
[2,5,1,2,4]=>3
[2,5,1,4,2]=>2
[2,5,2,1,4]=>3
[2,5,2,4,1]=>2
[2,5,4,1,2]=>2
[2,5,4,2,1]=>2
[4,1,2,2,5]=>3
[4,1,2,5,2]=>3
[4,1,5,2,2]=>3
[4,2,1,2,5]=>2
[4,2,1,5,2]=>2
[4,2,2,1,5]=>2
[4,2,2,5,1]=>2
[4,2,5,1,2]=>2
[4,2,5,2,1]=>2
[4,5,1,2,2]=>3
[4,5,2,1,2]=>3
[4,5,2,2,1]=>3
[5,1,2,2,4]=>4
[5,1,2,4,2]=>3
[5,1,4,2,2]=>3
[5,2,1,2,4]=>3
[5,2,1,4,2]=>2
[5,2,2,1,4]=>3
[5,2,2,4,1]=>2
[5,2,4,1,2]=>2
[5,2,4,2,1]=>2
[5,4,1,2,2]=>3
[5,4,2,1,2]=>3
[5,4,2,2,1]=>3
[1,2,3,3,3]=>2
[1,3,2,3,3]=>3
[1,3,3,2,3]=>2
[1,3,3,3,2]=>2
[2,1,3,3,3]=>3
[2,3,1,3,3]=>3
[2,3,3,1,3]=>2
[2,3,3,3,1]=>2
[3,1,2,3,3]=>4
[3,1,3,2,3]=>3
[3,1,3,3,2]=>3
[3,2,1,3,3]=>3
[3,2,3,1,3]=>2
[3,2,3,3,1]=>2
[3,3,1,2,3]=>3
[3,3,1,3,2]=>3
[3,3,2,1,3]=>3
[3,3,2,3,1]=>3
[3,3,3,1,2]=>2
[3,3,3,2,1]=>2
[1,2,3,3,4]=>2
[1,2,3,4,3]=>1
[1,2,4,3,3]=>2
[1,3,2,3,4]=>3
[1,3,2,4,3]=>2
[1,3,3,2,4]=>2
[1,3,3,4,2]=>1
[1,3,4,2,3]=>2
[1,3,4,3,2]=>2
[1,4,2,3,3]=>3
[1,4,3,2,3]=>2
[1,4,3,3,2]=>2
[2,1,3,3,4]=>3
[2,1,3,4,3]=>2
[2,1,4,3,3]=>3
[2,3,1,3,4]=>3
[2,3,1,4,3]=>2
[2,3,3,1,4]=>2
[2,3,3,4,1]=>1
[2,3,4,1,3]=>2
[2,3,4,3,1]=>2
[2,4,1,3,3]=>3
[2,4,3,1,3]=>2
[2,4,3,3,1]=>2
[3,1,2,3,4]=>4
[3,1,2,4,3]=>3
[3,1,3,2,4]=>3
[3,1,3,4,2]=>2
[3,1,4,2,3]=>3
[3,1,4,3,2]=>3
[3,2,1,3,4]=>3
[3,2,1,4,3]=>2
[3,2,3,1,4]=>2
[3,2,3,4,1]=>1
[3,2,4,1,3]=>2
[3,2,4,3,1]=>2
[3,3,1,2,4]=>3
[3,3,1,4,2]=>2
[3,3,2,1,4]=>3
[3,3,2,4,1]=>2
[3,3,4,1,2]=>2
[3,3,4,2,1]=>2
[3,4,1,2,3]=>3
[3,4,1,3,2]=>3
[3,4,2,1,3]=>3
[3,4,2,3,1]=>3
[3,4,3,1,2]=>2
[3,4,3,2,1]=>2
[4,1,2,3,3]=>4
[4,1,3,2,3]=>3
[4,1,3,3,2]=>3
[4,2,1,3,3]=>3
[4,2,3,1,3]=>2
[4,2,3,3,1]=>2
[4,3,1,2,3]=>3
[4,3,1,3,2]=>3
[4,3,2,1,3]=>3
[4,3,2,3,1]=>3
[4,3,3,1,2]=>2
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Description
The number of preferred parking spots in a parking function less than the index of the car.
Let $(a_1,\dots,a_n)$ be a parking function. Then this statistic returns the number of indices $1\leq i\leq n$ such that $a_i < i$.
Let $(a_1,\dots,a_n)$ be a parking function. Then this statistic returns the number of indices $1\leq i\leq n$ such that $a_i < i$.
Code
def statistic(p):
return sum(1 for i in range(len(p)) if p[i] < i+1)
Created
Jun 11, 2023 at 16:43 by Martin Rubey
Updated
Jun 11, 2023 at 16:43 by Martin Rubey
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