Identifier
Values
=>
[1]=>1
[1,1]=>2
[1,2]=>2
[2,1]=>1
[1,1,1]=>3
[1,1,2]=>3
[1,2,1]=>3
[2,1,1]=>2
[1,1,3]=>3
[1,3,1]=>2
[3,1,1]=>2
[1,2,2]=>3
[2,1,2]=>2
[2,2,1]=>1
[1,2,3]=>3
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>2
[3,2,1]=>1
[1,1,1,1]=>4
[1,1,1,2]=>4
[1,1,2,1]=>4
[1,2,1,1]=>4
[2,1,1,1]=>3
[1,1,1,3]=>4
[1,1,3,1]=>4
[1,3,1,1]=>3
[3,1,1,1]=>3
[1,1,1,4]=>4
[1,1,4,1]=>3
[1,4,1,1]=>3
[4,1,1,1]=>3
[1,1,2,2]=>4
[1,2,1,2]=>4
[1,2,2,1]=>4
[2,1,1,2]=>3
[2,1,2,1]=>3
[2,2,1,1]=>2
[1,1,2,3]=>4
[1,1,3,2]=>4
[1,2,1,3]=>4
[1,2,3,1]=>4
[1,3,1,2]=>3
[1,3,2,1]=>3
[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]=>4
[1,1,4,2]=>3
[1,2,1,4]=>4
[1,2,4,1]=>3
[1,4,1,2]=>3
[1,4,2,1]=>3
[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]=>4
[1,3,1,3]=>3
[1,3,3,1]=>2
[3,1,1,3]=>3
[3,1,3,1]=>2
[3,3,1,1]=>2
[1,1,3,4]=>4
[1,1,4,3]=>3
[1,3,1,4]=>2
[1,3,4,1]=>2
[1,4,1,3]=>3
[1,4,3,1]=>2
[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]=>4
[2,1,2,2]=>3
[2,2,1,2]=>2
[2,2,2,1]=>1
[1,2,2,3]=>4
[1,2,3,2]=>4
[1,3,2,2]=>3
[2,1,2,3]=>3
[2,1,3,2]=>2
[2,2,1,3]=>1
[2,2,3,1]=>1
[2,3,1,2]=>2
[2,3,2,1]=>1
[3,1,2,2]=>3
[3,2,1,2]=>2
[3,2,2,1]=>1
[1,2,2,4]=>4
[1,2,4,2]=>3
[1,4,2,2]=>3
[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]=>1
[4,1,2,2]=>3
[4,2,1,2]=>2
[4,2,2,1]=>1
[1,2,3,3]=>4
[1,3,2,3]=>3
[1,3,3,2]=>2
[2,1,3,3]=>1
[2,3,1,3]=>1
[2,3,3,1]=>1
[3,1,2,3]=>3
[3,1,3,2]=>2
[3,2,1,3]=>1
[3,2,3,1]=>1
[3,3,1,2]=>2
[3,3,2,1]=>1
[1,2,3,4]=>4
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>2
[1,4,2,3]=>3
[1,4,3,2]=>2
[2,1,3,4]=>1
[2,1,4,3]=>1
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>1
[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]=>1
[4,1,2,3]=>3
[4,1,3,2]=>2
[4,2,1,3]=>1
[4,2,3,1]=>1
[4,3,1,2]=>2
[4,3,2,1]=>1
[1,1,1,1,1]=>5
[1,1,1,1,2]=>5
[1,1,1,2,1]=>5
[1,1,2,1,1]=>5
[1,2,1,1,1]=>5
[2,1,1,1,1]=>4
[1,1,1,1,3]=>5
[1,1,1,3,1]=>5
[1,1,3,1,1]=>5
[1,3,1,1,1]=>4
[3,1,1,1,1]=>4
[1,1,1,1,4]=>5
[1,1,1,4,1]=>5
[1,1,4,1,1]=>4
[1,4,1,1,1]=>4
[4,1,1,1,1]=>4
[1,1,1,1,5]=>5
[1,1,1,5,1]=>4
[1,1,5,1,1]=>4
[1,5,1,1,1]=>4
[5,1,1,1,1]=>4
[1,1,1,2,2]=>5
[1,1,2,1,2]=>5
[1,1,2,2,1]=>5
[1,2,1,1,2]=>5
[1,2,1,2,1]=>5
[1,2,2,1,1]=>5
[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]=>5
[1,1,1,3,2]=>5
[1,1,2,1,3]=>5
[1,1,2,3,1]=>5
[1,1,3,1,2]=>5
[1,1,3,2,1]=>5
[1,2,1,1,3]=>5
[1,2,1,3,1]=>5
[1,2,3,1,1]=>5
[1,3,1,1,2]=>4
[1,3,1,2,1]=>4
[1,3,2,1,1]=>4
[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]=>5
[1,1,1,4,2]=>5
[1,1,2,1,4]=>5
[1,1,2,4,1]=>5
[1,1,4,1,2]=>4
[1,1,4,2,1]=>4
[1,2,1,1,4]=>5
[1,2,1,4,1]=>5
[1,2,4,1,1]=>4
[1,4,1,1,2]=>4
[1,4,1,2,1]=>4
[1,4,2,1,1]=>4
[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]=>5
[1,1,1,5,2]=>4
[1,1,2,1,5]=>5
[1,1,2,5,1]=>4
[1,1,5,1,2]=>4
[1,1,5,2,1]=>4
[1,2,1,1,5]=>5
[1,2,1,5,1]=>4
[1,2,5,1,1]=>4
[1,5,1,1,2]=>4
[1,5,1,2,1]=>4
[1,5,2,1,1]=>4
[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]=>5
[1,1,3,1,3]=>5
[1,1,3,3,1]=>5
[1,3,1,1,3]=>4
[1,3,1,3,1]=>4
[1,3,3,1,1]=>3
[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]=>5
[1,1,1,4,3]=>5
[1,1,3,1,4]=>5
[1,1,3,4,1]=>5
[1,1,4,1,3]=>4
[1,1,4,3,1]=>4
[1,3,1,1,4]=>4
[1,3,1,4,1]=>3
[1,3,4,1,1]=>3
[1,4,1,1,3]=>4
[1,4,1,3,1]=>4
[1,4,3,1,1]=>3
[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]=>5
[1,1,1,5,3]=>4
[1,1,3,1,5]=>5
[1,1,3,5,1]=>4
[1,1,5,1,3]=>4
[1,1,5,3,1]=>4
[1,3,1,1,5]=>3
[1,3,1,5,1]=>3
[1,3,5,1,1]=>3
[1,5,1,1,3]=>4
[1,5,1,3,1]=>4
[1,5,3,1,1]=>3
[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]=>5
[1,1,4,1,4]=>4
[1,1,4,4,1]=>3
[1,4,1,1,4]=>4
[1,4,1,4,1]=>3
[1,4,4,1,1]=>3
[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]=>5
[1,1,1,5,4]=>4
[1,1,4,1,5]=>3
[1,1,4,5,1]=>3
[1,1,5,1,4]=>4
[1,1,5,4,1]=>3
[1,4,1,1,5]=>3
[1,4,1,5,1]=>3
[1,4,5,1,1]=>3
[1,5,1,1,4]=>4
[1,5,1,4,1]=>3
[1,5,4,1,1]=>3
[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]=>5
[1,2,1,2,2]=>5
[1,2,2,1,2]=>5
[1,2,2,2,1]=>5
[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]=>2
[1,1,2,2,3]=>5
[1,1,2,3,2]=>5
[1,1,3,2,2]=>5
[1,2,1,2,3]=>5
[1,2,1,3,2]=>5
[1,2,2,1,3]=>5
[1,2,2,3,1]=>5
[1,2,3,1,2]=>5
[1,2,3,2,1]=>5
[1,3,1,2,2]=>4
[1,3,2,1,2]=>4
[1,3,2,2,1]=>4
[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]=>2
[2,2,3,1,1]=>2
[2,3,1,1,2]=>3
[2,3,1,2,1]=>3
[2,3,2,1,1]=>2
[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]=>2
[1,1,2,2,4]=>5
[1,1,2,4,2]=>5
[1,1,4,2,2]=>4
[1,2,1,2,4]=>5
[1,2,1,4,2]=>5
[1,2,2,1,4]=>5
[1,2,2,4,1]=>5
[1,2,4,1,2]=>4
[1,2,4,2,1]=>4
[1,4,1,2,2]=>4
[1,4,2,1,2]=>4
[1,4,2,2,1]=>4
[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]=>2
[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]=>2
[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]=>2
[1,1,2,2,5]=>5
[1,1,2,5,2]=>4
[1,1,5,2,2]=>4
[1,2,1,2,5]=>5
[1,2,1,5,2]=>4
[1,2,2,1,5]=>5
[1,2,2,5,1]=>4
[1,2,5,1,2]=>4
[1,2,5,2,1]=>4
[1,5,1,2,2]=>4
[1,5,2,1,2]=>4
[1,5,2,2,1]=>4
[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]=>2
[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]=>2
[1,1,2,3,3]=>5
[1,1,3,2,3]=>5
[1,1,3,3,2]=>5
[1,2,1,3,3]=>5
[1,2,3,1,3]=>5
[1,2,3,3,1]=>5
[1,3,1,2,3]=>4
[1,3,1,3,2]=>4
[1,3,2,1,3]=>4
[1,3,2,3,1]=>4
[1,3,3,1,2]=>3
[1,3,3,2,1]=>3
[2,1,1,3,3]=>4
[2,1,3,1,3]=>3
[2,1,3,3,1]=>2
[2,3,1,1,3]=>3
[2,3,1,3,1]=>2
[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]=>2
[3,2,3,1,1]=>2
[3,3,1,1,2]=>3
[3,3,1,2,1]=>3
[3,3,2,1,1]=>2
[1,1,2,3,4]=>5
[1,1,2,4,3]=>5
[1,1,3,2,4]=>5
[1,1,3,4,2]=>5
[1,1,4,2,3]=>4
[1,1,4,3,2]=>4
[1,2,1,3,4]=>5
[1,2,1,4,3]=>5
[1,2,3,1,4]=>5
[1,2,3,4,1]=>5
[1,2,4,1,3]=>4
[1,2,4,3,1]=>4
[1,3,1,2,4]=>4
[1,3,1,4,2]=>3
[1,3,2,1,4]=>4
[1,3,2,4,1]=>3
[1,3,4,1,2]=>3
[1,3,4,2,1]=>3
[1,4,1,2,3]=>4
[1,4,1,3,2]=>4
[1,4,2,1,3]=>4
[1,4,2,3,1]=>4
[1,4,3,1,2]=>3
[1,4,3,2,1]=>3
[2,1,1,3,4]=>4
[2,1,1,4,3]=>3
[2,1,3,1,4]=>2
[2,1,3,4,1]=>2
[2,1,4,1,3]=>3
[2,1,4,3,1]=>2
[2,3,1,1,4]=>2
[2,3,1,4,1]=>2
[2,3,4,1,1]=>2
[2,4,1,1,3]=>3
[2,4,1,3,1]=>2
[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]=>2
[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]=>2
[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]=>2
[4,2,3,1,1]=>2
[4,3,1,1,2]=>3
[4,3,1,2,1]=>3
[4,3,2,1,1]=>2
[1,1,2,3,5]=>5
[1,1,2,5,3]=>4
[1,1,3,2,5]=>5
[1,1,3,5,2]=>4
[1,1,5,2,3]=>4
[1,1,5,3,2]=>4
[1,2,1,3,5]=>5
[1,2,1,5,3]=>4
[1,2,3,1,5]=>5
[1,2,3,5,1]=>4
[1,2,5,1,3]=>4
[1,2,5,3,1]=>4
[1,3,1,2,5]=>3
[1,3,1,5,2]=>3
[1,3,2,1,5]=>3
[1,3,2,5,1]=>3
[1,3,5,1,2]=>3
[1,3,5,2,1]=>3
[1,5,1,2,3]=>4
[1,5,1,3,2]=>4
[1,5,2,1,3]=>4
[1,5,2,3,1]=>4
[1,5,3,1,2]=>3
[1,5,3,2,1]=>3
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[5,2,3,1,1]=>2
[5,3,1,1,2]=>3
[5,3,1,2,1]=>3
[5,3,2,1,1]=>2
[1,1,2,4,4]=>5
[1,1,4,2,4]=>4
[1,1,4,4,2]=>3
[1,2,1,4,4]=>5
[1,2,4,1,4]=>4
[1,2,4,4,1]=>3
[1,4,1,2,4]=>4
[1,4,1,4,2]=>3
[1,4,2,1,4]=>4
[1,4,2,4,1]=>3
[1,4,4,1,2]=>3
[1,4,4,2,1]=>3
[2,1,1,4,4]=>2
[2,1,4,1,4]=>2
[2,1,4,4,1]=>2
[2,4,1,1,4]=>2
[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]=>2
[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]=>2
[1,1,2,4,5]=>5
[1,1,2,5,4]=>4
[1,1,4,2,5]=>3
[1,1,4,5,2]=>3
[1,1,5,2,4]=>4
[1,1,5,4,2]=>3
[1,2,1,4,5]=>5
[1,2,1,5,4]=>4
[1,2,4,1,5]=>3
[1,2,4,5,1]=>3
[1,2,5,1,4]=>4
[1,2,5,4,1]=>3
[1,4,1,2,5]=>3
[1,4,1,5,2]=>3
[1,4,2,1,5]=>3
[1,4,2,5,1]=>3
[1,4,5,1,2]=>3
[1,4,5,2,1]=>3
[1,5,1,2,4]=>4
[1,5,1,4,2]=>3
[1,5,2,1,4]=>4
[1,5,2,4,1]=>3
[1,5,4,1,2]=>3
[1,5,4,2,1]=>3
[2,1,1,4,5]=>2
[2,1,1,5,4]=>2
[2,1,4,1,5]=>2
[2,1,4,5,1]=>2
[2,1,5,1,4]=>2
[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]=>2
[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]=>2
[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]=>2
[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]=>2
[1,1,3,3,3]=>5
[1,3,1,3,3]=>4
[1,3,3,1,3]=>3
[1,3,3,3,1]=>2
[3,1,1,3,3]=>4
[3,1,3,1,3]=>3
[3,1,3,3,1]=>2
[3,3,1,1,3]=>3
[3,3,1,3,1]=>2
[3,3,3,1,1]=>2
[1,1,3,3,4]=>5
[1,1,3,4,3]=>5
[1,1,4,3,3]=>4
[1,3,1,3,4]=>4
[1,3,1,4,3]=>3
[1,3,3,1,4]=>2
[1,3,3,4,1]=>2
[1,3,4,1,3]=>3
[1,3,4,3,1]=>2
[1,4,1,3,3]=>4
[1,4,3,1,3]=>3
[1,4,3,3,1]=>2
[3,1,1,3,4]=>4
[3,1,1,4,3]=>3
[3,1,3,1,4]=>2
[3,1,3,4,1]=>2
[3,1,4,1,3]=>3
[3,1,4,3,1]=>2
[3,3,1,1,4]=>2
[3,3,1,4,1]=>2
[3,3,4,1,1]=>2
[3,4,1,1,3]=>3
[3,4,1,3,1]=>2
[3,4,3,1,1]=>2
[4,1,1,3,3]=>4
[4,1,3,1,3]=>3
[4,1,3,3,1]=>2
[4,3,1,1,3]=>3
[4,3,1,3,1]=>2
[4,3,3,1,1]=>2
[1,1,3,3,5]=>5
[1,1,3,5,3]=>4
[1,1,5,3,3]=>4
[1,3,1,3,5]=>3
[1,3,1,5,3]=>3
[1,3,3,1,5]=>2
[1,3,3,5,1]=>2
[1,3,5,1,3]=>3
[1,3,5,3,1]=>2
[1,5,1,3,3]=>4
[1,5,3,1,3]=>3
[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]=>2
[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]=>2
[3,5,3,1,1]=>2
[5,1,1,3,3]=>4
[5,1,3,1,3]=>3
[5,1,3,3,1]=>2
[5,3,1,1,3]=>3
[5,3,1,3,1]=>2
[5,3,3,1,1]=>2
[1,1,3,4,4]=>5
[1,1,4,3,4]=>4
[1,1,4,4,3]=>3
[1,3,1,4,4]=>2
[1,3,4,1,4]=>2
[1,3,4,4,1]=>2
[1,4,1,3,4]=>4
[1,4,1,4,3]=>3
[1,4,3,1,4]=>2
[1,4,3,4,1]=>2
[1,4,4,1,3]=>3
[1,4,4,3,1]=>2
[3,1,1,4,4]=>2
[3,1,4,1,4]=>2
[3,1,4,4,1]=>2
[3,4,1,1,4]=>2
[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]=>2
[4,1,3,4,1]=>2
[4,1,4,1,3]=>3
[4,1,4,3,1]=>2
[4,3,1,1,4]=>2
[4,3,1,4,1]=>2
[4,3,4,1,1]=>2
[4,4,1,1,3]=>3
[4,4,1,3,1]=>2
[4,4,3,1,1]=>2
[1,1,3,4,5]=>5
[1,1,3,5,4]=>4
[1,1,4,3,5]=>3
[1,1,4,5,3]=>3
[1,1,5,3,4]=>4
[1,1,5,4,3]=>3
[1,3,1,4,5]=>2
[1,3,1,5,4]=>2
[1,3,4,1,5]=>2
[1,3,4,5,1]=>2
[1,3,5,1,4]=>2
[1,3,5,4,1]=>2
[1,4,1,3,5]=>3
[1,4,1,5,3]=>3
[1,4,3,1,5]=>2
[1,4,3,5,1]=>2
[1,4,5,1,3]=>3
[1,4,5,3,1]=>2
[1,5,1,3,4]=>4
[1,5,1,4,3]=>3
[1,5,3,1,4]=>2
[1,5,3,4,1]=>2
[1,5,4,1,3]=>3
[1,5,4,3,1]=>2
[3,1,1,4,5]=>2
[3,1,1,5,4]=>2
[3,1,4,1,5]=>2
[3,1,4,5,1]=>2
[3,1,5,1,4]=>2
[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]=>2
[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]=>2
[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]=>2
[4,5,3,1,1]=>2
[5,1,1,3,4]=>4
[5,1,1,4,3]=>3
[5,1,3,1,4]=>2
[5,1,3,4,1]=>2
[5,1,4,1,3]=>3
[5,1,4,3,1]=>2
[5,3,1,1,4]=>2
[5,3,1,4,1]=>2
[5,3,4,1,1]=>2
[5,4,1,1,3]=>3
[5,4,1,3,1]=>2
[5,4,3,1,1]=>2
[1,2,2,2,2]=>5
[2,1,2,2,2]=>4
[2,2,1,2,2]=>3
[2,2,2,1,2]=>2
[2,2,2,2,1]=>1
[1,2,2,2,3]=>5
[1,2,2,3,2]=>5
[1,2,3,2,2]=>5
[1,3,2,2,2]=>4
[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]=>2
[2,2,2,1,3]=>1
[2,2,2,3,1]=>1
[2,2,3,1,2]=>2
[2,2,3,2,1]=>1
[2,3,1,2,2]=>3
[2,3,2,1,2]=>2
[2,3,2,2,1]=>1
[3,1,2,2,2]=>4
[3,2,1,2,2]=>3
[3,2,2,1,2]=>2
[3,2,2,2,1]=>1
[1,2,2,2,4]=>5
[1,2,2,4,2]=>5
[1,2,4,2,2]=>4
[1,4,2,2,2]=>4
[2,1,2,2,4]=>4
[2,1,2,4,2]=>3
[2,1,4,2,2]=>3
[2,2,1,2,4]=>2
[2,2,1,4,2]=>2
[2,2,2,1,4]=>1
[2,2,2,4,1]=>1
[2,2,4,1,2]=>2
[2,2,4,2,1]=>1
[2,4,1,2,2]=>3
[2,4,2,1,2]=>2
[2,4,2,2,1]=>1
[4,1,2,2,2]=>4
[4,2,1,2,2]=>3
[4,2,2,1,2]=>2
[4,2,2,2,1]=>1
[1,2,2,2,5]=>5
[1,2,2,5,2]=>4
[1,2,5,2,2]=>4
[1,5,2,2,2]=>4
[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]=>1
[2,2,2,5,1]=>1
[2,2,5,1,2]=>2
[2,2,5,2,1]=>1
[2,5,1,2,2]=>3
[2,5,2,1,2]=>2
[2,5,2,2,1]=>1
[5,1,2,2,2]=>4
[5,2,1,2,2]=>3
[5,2,2,1,2]=>2
[5,2,2,2,1]=>1
[1,2,2,3,3]=>5
[1,2,3,2,3]=>5
[1,2,3,3,2]=>5
[1,3,2,2,3]=>4
[1,3,2,3,2]=>4
[1,3,3,2,2]=>3
[2,1,2,3,3]=>4
[2,1,3,2,3]=>3
[2,1,3,3,2]=>2
[2,2,1,3,3]=>1
[2,2,3,1,3]=>1
[2,2,3,3,1]=>1
[2,3,1,2,3]=>3
[2,3,1,3,2]=>2
[2,3,2,1,3]=>1
[2,3,2,3,1]=>1
[2,3,3,1,2]=>2
[2,3,3,2,1]=>1
[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]=>2
[3,2,2,1,3]=>1
[3,2,2,3,1]=>1
[3,2,3,1,2]=>2
[3,2,3,2,1]=>1
[3,3,1,2,2]=>3
[3,3,2,1,2]=>2
[3,3,2,2,1]=>1
[1,2,2,3,4]=>5
[1,2,2,4,3]=>5
[1,2,3,2,4]=>5
[1,2,3,4,2]=>5
[1,2,4,2,3]=>4
[1,2,4,3,2]=>4
[1,3,2,2,4]=>4
[1,3,2,4,2]=>3
[1,3,4,2,2]=>3
[1,4,2,2,3]=>4
[1,4,2,3,2]=>4
[1,4,3,2,2]=>3
[2,1,2,3,4]=>4
[2,1,2,4,3]=>3
[2,1,3,2,4]=>2
[2,1,3,4,2]=>2
[2,1,4,2,3]=>3
[2,1,4,3,2]=>2
[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]=>2
[2,3,1,4,2]=>2
[2,3,2,1,4]=>1
[2,3,2,4,1]=>1
[2,3,4,1,2]=>2
[2,3,4,2,1]=>1
[2,4,1,2,3]=>3
[2,4,1,3,2]=>2
[2,4,2,1,3]=>1
[2,4,2,3,1]=>1
[2,4,3,1,2]=>2
[2,4,3,2,1]=>1
[3,1,2,2,4]=>4
[3,1,2,4,2]=>3
[3,1,4,2,2]=>3
[3,2,1,2,4]=>2
[3,2,1,4,2]=>2
[3,2,2,1,4]=>1
[3,2,2,4,1]=>1
[3,2,4,1,2]=>2
[3,2,4,2,1]=>1
[3,4,1,2,2]=>3
[3,4,2,1,2]=>2
[3,4,2,2,1]=>1
[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]=>2
[4,2,2,1,3]=>1
[4,2,2,3,1]=>1
[4,2,3,1,2]=>2
[4,2,3,2,1]=>1
[4,3,1,2,2]=>3
[4,3,2,1,2]=>2
[4,3,2,2,1]=>1
[1,2,2,3,5]=>5
[1,2,2,5,3]=>4
[1,2,3,2,5]=>5
[1,2,3,5,2]=>4
[1,2,5,2,3]=>4
[1,2,5,3,2]=>4
[1,3,2,2,5]=>3
[1,3,2,5,2]=>3
[1,3,5,2,2]=>3
[1,5,2,2,3]=>4
[1,5,2,3,2]=>4
[1,5,3,2,2]=>3
[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]=>2
[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]=>2
[2,3,1,5,2]=>2
[2,3,2,1,5]=>1
[2,3,2,5,1]=>1
[2,3,5,1,2]=>2
[2,3,5,2,1]=>1
[2,5,1,2,3]=>3
[2,5,1,3,2]=>2
[2,5,2,1,3]=>1
[2,5,2,3,1]=>1
[2,5,3,1,2]=>2
[2,5,3,2,1]=>1
[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]=>1
[3,2,2,5,1]=>1
[3,2,5,1,2]=>2
[3,2,5,2,1]=>1
[3,5,1,2,2]=>3
[3,5,2,1,2]=>2
[3,5,2,2,1]=>1
[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]=>2
[5,2,2,1,3]=>1
[5,2,2,3,1]=>1
[5,2,3,1,2]=>2
[5,2,3,2,1]=>1
[5,3,1,2,2]=>3
[5,3,2,1,2]=>2
[5,3,2,2,1]=>1
[1,2,2,4,4]=>5
[1,2,4,2,4]=>4
[1,2,4,4,2]=>3
[1,4,2,2,4]=>4
[1,4,2,4,2]=>3
[1,4,4,2,2]=>3
[2,1,2,4,4]=>2
[2,1,4,2,4]=>2
[2,1,4,4,2]=>2
[2,2,1,4,4]=>1
[2,2,4,1,4]=>1
[2,2,4,4,1]=>1
[2,4,1,2,4]=>2
[2,4,1,4,2]=>2
[2,4,2,1,4]=>1
[2,4,2,4,1]=>1
[2,4,4,1,2]=>2
[2,4,4,2,1]=>1
[4,1,2,2,4]=>4
[4,1,2,4,2]=>3
[4,1,4,2,2]=>3
[4,2,1,2,4]=>2
[4,2,1,4,2]=>2
[4,2,2,1,4]=>1
[4,2,2,4,1]=>1
[4,2,4,1,2]=>2
[4,2,4,2,1]=>1
[4,4,1,2,2]=>3
[4,4,2,1,2]=>2
[4,4,2,2,1]=>1
[1,2,2,4,5]=>5
[1,2,2,5,4]=>4
[1,2,4,2,5]=>3
[1,2,4,5,2]=>3
[1,2,5,2,4]=>4
[1,2,5,4,2]=>3
[1,4,2,2,5]=>3
[1,4,2,5,2]=>3
[1,4,5,2,2]=>3
[1,5,2,2,4]=>4
[1,5,2,4,2]=>3
[1,5,4,2,2]=>3
[2,1,2,4,5]=>2
[2,1,2,5,4]=>2
[2,1,4,2,5]=>2
[2,1,4,5,2]=>2
[2,1,5,2,4]=>2
[2,1,5,4,2]=>2
[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]=>2
[2,4,1,5,2]=>2
[2,4,2,1,5]=>1
[2,4,2,5,1]=>1
[2,4,5,1,2]=>2
[2,4,5,2,1]=>1
[2,5,1,2,4]=>2
[2,5,1,4,2]=>2
[2,5,2,1,4]=>1
[2,5,2,4,1]=>1
[2,5,4,1,2]=>2
[2,5,4,2,1]=>1
[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]=>1
[4,2,2,5,1]=>1
[4,2,5,1,2]=>2
[4,2,5,2,1]=>1
[4,5,1,2,2]=>3
[4,5,2,1,2]=>2
[4,5,2,2,1]=>1
[5,1,2,2,4]=>4
[5,1,2,4,2]=>3
[5,1,4,2,2]=>3
[5,2,1,2,4]=>2
[5,2,1,4,2]=>2
[5,2,2,1,4]=>1
[5,2,2,4,1]=>1
[5,2,4,1,2]=>2
[5,2,4,2,1]=>1
[5,4,1,2,2]=>3
[5,4,2,1,2]=>2
[5,4,2,2,1]=>1
[1,2,3,3,3]=>5
[1,3,2,3,3]=>4
[1,3,3,2,3]=>3
[1,3,3,3,2]=>2
[2,1,3,3,3]=>1
[2,3,1,3,3]=>1
[2,3,3,1,3]=>1
[2,3,3,3,1]=>1
[3,1,2,3,3]=>4
[3,1,3,2,3]=>3
[3,1,3,3,2]=>2
[3,2,1,3,3]=>1
[3,2,3,1,3]=>1
[3,2,3,3,1]=>1
[3,3,1,2,3]=>3
[3,3,1,3,2]=>2
[3,3,2,1,3]=>1
[3,3,2,3,1]=>1
[3,3,3,1,2]=>2
[3,3,3,2,1]=>1
[1,2,3,3,4]=>5
[1,2,3,4,3]=>5
[1,2,4,3,3]=>4
[1,3,2,3,4]=>4
[1,3,2,4,3]=>3
[1,3,3,2,4]=>2
[1,3,3,4,2]=>2
[1,3,4,2,3]=>3
[1,3,4,3,2]=>2
[1,4,2,3,3]=>4
[1,4,3,2,3]=>3
[1,4,3,3,2]=>2
[2,1,3,3,4]=>1
[2,1,3,4,3]=>1
[2,1,4,3,3]=>1
[2,3,1,3,4]=>1
[2,3,1,4,3]=>1
[2,3,3,1,4]=>1
[2,3,3,4,1]=>1
[2,3,4,1,3]=>1
[2,3,4,3,1]=>1
[2,4,1,3,3]=>1
[2,4,3,1,3]=>1
[2,4,3,3,1]=>1
[3,1,2,3,4]=>4
[3,1,2,4,3]=>3
[3,1,3,2,4]=>2
[3,1,3,4,2]=>2
[3,1,4,2,3]=>3
[3,1,4,3,2]=>2
[3,2,1,3,4]=>1
[3,2,1,4,3]=>1
[3,2,3,1,4]=>1
[3,2,3,4,1]=>1
[3,2,4,1,3]=>1
[3,2,4,3,1]=>1
[3,3,1,2,4]=>2
[3,3,1,4,2]=>2
[3,3,2,1,4]=>1
[3,3,2,4,1]=>1
[3,3,4,1,2]=>2
[3,3,4,2,1]=>1
[3,4,1,2,3]=>3
[3,4,1,3,2]=>2
[3,4,2,1,3]=>1
[3,4,2,3,1]=>1
[3,4,3,1,2]=>2
[3,4,3,2,1]=>1
[4,1,2,3,3]=>4
[4,1,3,2,3]=>3
[4,1,3,3,2]=>2
[4,2,1,3,3]=>1
[4,2,3,1,3]=>1
[4,2,3,3,1]=>1
[4,3,1,2,3]=>3
[4,3,1,3,2]=>2
[4,3,2,1,3]=>1
[4,3,2,3,1]=>1
[4,3,3,1,2]=>2
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Description
The size of the center of a parking function.
The center of a parking function $p_1,\dots,p_n$ is the longest subsequence $a_1,\dots,a_k$ such that $a_i\leq i$.
The center of a parking function $p_1,\dots,p_n$ is the longest subsequence $a_1,\dots,a_k$ such that $a_i\leq i$.
References
[1] Duarte, R., Guedes de Oliveira, António The number of parking functions with center of a given length arXiv:1611.03707
Code
def statistic(p):
c = []
j = 1
for e in p:
if e <= j:
c.append(e)
j += 1
return len(c)
Created
Dec 30, 2023 at 10:45 by Martin Rubey
Updated
Dec 30, 2023 at 10:45 by Martin Rubey
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