Identifier
Identifier
Values
[1] => 1
[1,1] => 1
[2] => 1
[1,1,1] => 1
[1,2] => 2
[2,1] => 1
[3] => 1
[1,1,1,1] => 1
[1,1,2] => 2
[1,2,1] => 2
[1,3] => 2
[2,1,1] => 1
[2,2] => 1
[3,1] => 1
[4] => 1
[1,1,1,1,1] => 1
[1,1,1,2] => 2
[1,1,2,1] => 2
[1,1,3] => 2
[1,2,1,1] => 2
[1,2,2] => 2
[1,3,1] => 2
[1,4] => 2
[2,1,1,1] => 1
[2,1,2] => 1
[2,2,1] => 1
[2,3] => 2
[3,1,1] => 1
[3,2] => 1
[4,1] => 1
[5] => 1
[1,1,1,1,1,1] => 1
[1,1,1,1,2] => 2
[1,1,1,2,1] => 2
[1,1,1,3] => 2
[1,1,2,1,1] => 2
[1,1,2,2] => 2
[1,1,3,1] => 2
[1,1,4] => 2
[1,2,1,1,1] => 2
[1,2,1,2] => 2
[1,2,2,1] => 2
[1,2,3] => 3
[1,3,1,1] => 2
[1,3,2] => 2
[1,4,1] => 2
[1,5] => 2
[2,1,1,1,1] => 1
[2,1,1,2] => 1
[2,1,2,1] => 1
[2,1,3] => 2
[2,2,1,1] => 1
[2,2,2] => 1
[2,3,1] => 2
[2,4] => 2
[3,1,1,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[3,3] => 1
[4,1,1] => 1
[4,2] => 1
[5,1] => 1
[6] => 1
[1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2] => 2
[1,1,1,1,2,1] => 2
[1,1,1,1,3] => 2
[1,1,1,2,1,1] => 2
[1,1,1,2,2] => 2
[1,1,1,3,1] => 2
[1,1,1,4] => 2
[1,1,2,1,1,1] => 2
[1,1,2,1,2] => 2
[1,1,2,2,1] => 2
[1,1,2,3] => 3
[1,1,3,1,1] => 2
[1,1,3,2] => 2
[1,1,4,1] => 2
[1,1,5] => 2
[1,2,1,1,1,1] => 2
[1,2,1,1,2] => 2
[1,2,1,2,1] => 2
[1,2,1,3] => 3
[1,2,2,1,1] => 2
[1,2,2,2] => 2
[1,2,3,1] => 3
[1,2,4] => 3
[1,3,1,1,1] => 2
[1,3,1,2] => 2
[1,3,2,1] => 2
[1,3,3] => 2
[1,4,1,1] => 2
[1,4,2] => 2
[1,5,1] => 2
[1,6] => 2
[2,1,1,1,1,1] => 1
[2,1,1,1,2] => 1
[2,1,1,2,1] => 1
[2,1,1,3] => 2
[2,1,2,1,1] => 1
[2,1,2,2] => 1
[2,1,3,1] => 2
[2,1,4] => 2
[2,2,1,1,1] => 1
[2,2,1,2] => 1
[2,2,2,1] => 1
[2,2,3] => 2
[2,3,1,1] => 2
[2,3,2] => 2
[2,4,1] => 2
[2,5] => 2
[3,1,1,1,1] => 1
[3,1,1,2] => 1
[3,1,2,1] => 1
[3,1,3] => 1
[3,2,1,1] => 1
[3,2,2] => 1
[3,3,1] => 1
[3,4] => 2
[4,1,1,1] => 1
[4,1,2] => 1
[4,2,1] => 1
[4,3] => 1
[5,1,1] => 1
[5,2] => 1
[6,1] => 1
[7] => 1
[1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2] => 2
[1,1,1,1,1,2,1] => 2
[1,1,1,1,1,3] => 2
[1,1,1,1,2,1,1] => 2
[1,1,1,1,2,2] => 2
[1,1,1,1,3,1] => 2
[1,1,1,1,4] => 2
[1,1,1,2,1,1,1] => 2
[1,1,1,2,1,2] => 2
[1,1,1,2,2,1] => 2
[1,1,1,2,3] => 3
[1,1,1,3,1,1] => 2
[1,1,1,3,2] => 2
[1,1,1,4,1] => 2
[1,1,1,5] => 2
[1,1,2,1,1,1,1] => 2
[1,1,2,1,1,2] => 2
[1,1,2,1,2,1] => 2
[1,1,2,1,3] => 3
[1,1,2,2,1,1] => 2
[1,1,2,2,2] => 2
[1,1,2,3,1] => 3
[1,1,2,4] => 3
[1,1,3,1,1,1] => 2
[1,1,3,1,2] => 2
[1,1,3,2,1] => 2
[1,1,3,3] => 2
[1,1,4,1,1] => 2
[1,1,4,2] => 2
[1,1,5,1] => 2
[1,1,6] => 2
[1,2,1,1,1,1,1] => 2
[1,2,1,1,1,2] => 2
[1,2,1,1,2,1] => 2
[1,2,1,1,3] => 3
[1,2,1,2,1,1] => 2
[1,2,1,2,2] => 2
[1,2,1,3,1] => 3
[1,2,1,4] => 3
[1,2,2,1,1,1] => 2
[1,2,2,1,2] => 2
[1,2,2,2,1] => 2
[1,2,2,3] => 3
[1,2,3,1,1] => 3
[1,2,3,2] => 3
[1,2,4,1] => 3
[1,2,5] => 3
[1,3,1,1,1,1] => 2
[1,3,1,1,2] => 2
[1,3,1,2,1] => 2
[1,3,1,3] => 2
[1,3,2,1,1] => 2
[1,3,2,2] => 2
[1,3,3,1] => 2
[1,3,4] => 3
[1,4,1,1,1] => 2
[1,4,1,2] => 2
[1,4,2,1] => 2
[1,4,3] => 2
[1,5,1,1] => 2
[1,5,2] => 2
[1,6,1] => 2
[1,7] => 2
[2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2] => 1
[2,1,1,1,2,1] => 1
[2,1,1,1,3] => 2
[2,1,1,2,1,1] => 1
[2,1,1,2,2] => 1
[2,1,1,3,1] => 2
[2,1,1,4] => 2
[2,1,2,1,1,1] => 1
[2,1,2,1,2] => 1
[2,1,2,2,1] => 1
[2,1,2,3] => 2
[2,1,3,1,1] => 2
[2,1,3,2] => 2
[2,1,4,1] => 2
[2,1,5] => 2
[2,2,1,1,1,1] => 1
[2,2,1,1,2] => 1
[2,2,1,2,1] => 1
[2,2,1,3] => 2
[2,2,2,1,1] => 1
[2,2,2,2] => 1
[2,2,3,1] => 2
[2,2,4] => 2
[2,3,1,1,1] => 2
[2,3,1,2] => 2
[2,3,2,1] => 2
[2,3,3] => 2
[2,4,1,1] => 2
[2,4,2] => 2
[2,5,1] => 2
[2,6] => 2
[3,1,1,1,1,1] => 1
[3,1,1,1,2] => 1
[3,1,1,2,1] => 1
[3,1,1,3] => 1
[3,1,2,1,1] => 1
[3,1,2,2] => 1
[3,1,3,1] => 1
[3,1,4] => 2
[3,2,1,1,1] => 1
[3,2,1,2] => 1
[3,2,2,1] => 1
[3,2,3] => 1
[3,3,1,1] => 1
[3,3,2] => 1
[3,4,1] => 2
[3,5] => 2
[4,1,1,1,1] => 1
[4,1,1,2] => 1
[4,1,2,1] => 1
[4,1,3] => 1
[4,2,1,1] => 1
[4,2,2] => 1
[4,3,1] => 1
[4,4] => 1
[5,1,1,1] => 1
[5,1,2] => 1
[5,2,1] => 1
[5,3] => 1
[6,1,1] => 1
[6,2] => 1
[7,1] => 1
[8] => 1
[1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2] => 2
[1,1,1,1,1,1,2,1] => 2
[1,1,1,1,1,1,3] => 2
[1,1,1,1,1,2,1,1] => 2
[1,1,1,1,1,2,2] => 2
[1,1,1,1,1,3,1] => 2
[1,1,1,1,1,4] => 2
[1,1,1,1,2,1,1,1] => 2
[1,1,1,1,2,1,2] => 2
[1,1,1,1,2,2,1] => 2
[1,1,1,1,2,3] => 3
[1,1,1,1,3,1,1] => 2
[1,1,1,1,3,2] => 2
[1,1,1,1,4,1] => 2
[1,1,1,1,5] => 2
[1,1,1,2,1,1,1,1] => 2
[1,1,1,2,1,1,2] => 2
[1,1,1,2,1,2,1] => 2
[1,1,1,2,1,3] => 3
[1,1,1,2,2,1,1] => 2
[1,1,1,2,2,2] => 2
[1,1,1,2,3,1] => 3
[1,1,1,2,4] => 3
[1,1,1,3,1,1,1] => 2
[1,1,1,3,1,2] => 2
[1,1,1,3,2,1] => 2
[1,1,1,3,3] => 2
[1,1,1,4,1,1] => 2
[1,1,1,4,2] => 2
[1,1,1,5,1] => 2
[1,1,1,6] => 2
[1,1,2,1,1,1,1,1] => 2
[1,1,2,1,1,1,2] => 2
[1,1,2,1,1,2,1] => 2
[1,1,2,1,1,3] => 3
[1,1,2,1,2,1,1] => 2
[1,1,2,1,2,2] => 2
[1,1,2,1,3,1] => 3
[1,1,2,1,4] => 3
[1,1,2,2,1,1,1] => 2
[1,1,2,2,1,2] => 2
[1,1,2,2,2,1] => 2
[1,1,2,2,3] => 3
[1,1,2,3,1,1] => 3
[1,1,2,3,2] => 3
[1,1,2,4,1] => 3
[1,1,2,5] => 3
[1,1,3,1,1,1,1] => 2
[1,1,3,1,1,2] => 2
[1,1,3,1,2,1] => 2
[1,1,3,1,3] => 2
[1,1,3,2,1,1] => 2
[1,1,3,2,2] => 2
[1,1,3,3,1] => 2
[1,1,3,4] => 3
[1,1,4,1,1,1] => 2
[1,1,4,1,2] => 2
[1,1,4,2,1] => 2
[1,1,4,3] => 2
[1,1,5,1,1] => 2
[1,1,5,2] => 2
[1,1,6,1] => 2
[1,1,7] => 2
[1,2,1,1,1,1,1,1] => 2
[1,2,1,1,1,1,2] => 2
[1,2,1,1,1,2,1] => 2
[1,2,1,1,1,3] => 3
[1,2,1,1,2,1,1] => 2
[1,2,1,1,2,2] => 2
[1,2,1,1,3,1] => 3
[1,2,1,1,4] => 3
[1,2,1,2,1,1,1] => 2
[1,2,1,2,1,2] => 2
[1,2,1,2,2,1] => 2
[1,2,1,2,3] => 3
[1,2,1,3,1,1] => 3
[1,2,1,3,2] => 3
[1,2,1,4,1] => 3
[1,2,1,5] => 3
[1,2,2,1,1,1,1] => 2
[1,2,2,1,1,2] => 2
[1,2,2,1,2,1] => 2
[1,2,2,1,3] => 3
[1,2,2,2,1,1] => 2
[1,2,2,2,2] => 2
[1,2,2,3,1] => 3
[1,2,2,4] => 3
[1,2,3,1,1,1] => 3
[1,2,3,1,2] => 3
[1,2,3,2,1] => 3
[1,2,3,3] => 3
[1,2,4,1,1] => 3
[1,2,4,2] => 3
[1,2,5,1] => 3
[1,2,6] => 3
[1,3,1,1,1,1,1] => 2
[1,3,1,1,1,2] => 2
[1,3,1,1,2,1] => 2
[1,3,1,1,3] => 2
[1,3,1,2,1,1] => 2
[1,3,1,2,2] => 2
[1,3,1,3,1] => 2
[1,3,1,4] => 3
[1,3,2,1,1,1] => 2
[1,3,2,1,2] => 2
[1,3,2,2,1] => 2
[1,3,2,3] => 2
[1,3,3,1,1] => 2
[1,3,3,2] => 2
[1,3,4,1] => 3
[1,3,5] => 3
[1,4,1,1,1,1] => 2
[1,4,1,1,2] => 2
[1,4,1,2,1] => 2
[1,4,1,3] => 2
[1,4,2,1,1] => 2
[1,4,2,2] => 2
[1,4,3,1] => 2
[1,4,4] => 2
[1,5,1,1,1] => 2
[1,5,1,2] => 2
[1,5,2,1] => 2
[1,5,3] => 2
[1,6,1,1] => 2
[1,6,2] => 2
[1,7,1] => 2
[1,8] => 2
[2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1] => 1
[2,1,1,1,1,3] => 2
[2,1,1,1,2,1,1] => 1
[2,1,1,1,2,2] => 1
[2,1,1,1,3,1] => 2
[2,1,1,1,4] => 2
[2,1,1,2,1,1,1] => 1
[2,1,1,2,1,2] => 1
[2,1,1,2,2,1] => 1
[2,1,1,2,3] => 2
[2,1,1,3,1,1] => 2
[2,1,1,3,2] => 2
[2,1,1,4,1] => 2
[2,1,1,5] => 2
[2,1,2,1,1,1,1] => 1
[2,1,2,1,1,2] => 1
[2,1,2,1,2,1] => 1
[2,1,2,1,3] => 2
[2,1,2,2,1,1] => 1
[2,1,2,2,2] => 1
[2,1,2,3,1] => 2
[2,1,2,4] => 2
[2,1,3,1,1,1] => 2
[2,1,3,1,2] => 2
[2,1,3,2,1] => 2
[2,1,3,3] => 2
[2,1,4,1,1] => 2
[2,1,4,2] => 2
[2,1,5,1] => 2
[2,1,6] => 2
[2,2,1,1,1,1,1] => 1
[2,2,1,1,1,2] => 1
[2,2,1,1,2,1] => 1
[2,2,1,1,3] => 2
[2,2,1,2,1,1] => 1
[2,2,1,2,2] => 1
[2,2,1,3,1] => 2
[2,2,1,4] => 2
[2,2,2,1,1,1] => 1
[2,2,2,1,2] => 1
[2,2,2,2,1] => 1
[2,2,2,3] => 2
[2,2,3,1,1] => 2
[2,2,3,2] => 2
[2,2,4,1] => 2
[2,2,5] => 2
[2,3,1,1,1,1] => 2
[2,3,1,1,2] => 2
[2,3,1,2,1] => 2
[2,3,1,3] => 2
[2,3,2,1,1] => 2
[2,3,2,2] => 2
[2,3,3,1] => 2
[2,3,4] => 3
[2,4,1,1,1] => 2
[2,4,1,2] => 2
[2,4,2,1] => 2
[2,4,3] => 2
[2,5,1,1] => 2
[2,5,2] => 2
[2,6,1] => 2
[2,7] => 2
[3,1,1,1,1,1,1] => 1
[3,1,1,1,1,2] => 1
[3,1,1,1,2,1] => 1
[3,1,1,1,3] => 1
[3,1,1,2,1,1] => 1
[3,1,1,2,2] => 1
[3,1,1,3,1] => 1
[3,1,1,4] => 2
[3,1,2,1,1,1] => 1
[3,1,2,1,2] => 1
[3,1,2,2,1] => 1
[3,1,2,3] => 1
[3,1,3,1,1] => 1
[3,1,3,2] => 1
[3,1,4,1] => 2
[3,1,5] => 2
[3,2,1,1,1,1] => 1
[3,2,1,1,2] => 1
[3,2,1,2,1] => 1
[3,2,1,3] => 1
[3,2,2,1,1] => 1
[3,2,2,2] => 1
[3,2,3,1] => 1
[3,2,4] => 2
[3,3,1,1,1] => 1
[3,3,1,2] => 1
[3,3,2,1] => 1
[3,3,3] => 1
[3,4,1,1] => 2
[3,4,2] => 2
[3,5,1] => 2
[3,6] => 2
[4,1,1,1,1,1] => 1
[4,1,1,1,2] => 1
[4,1,1,2,1] => 1
[4,1,1,3] => 1
[4,1,2,1,1] => 1
[4,1,2,2] => 1
[4,1,3,1] => 1
[4,1,4] => 1
[4,2,1,1,1] => 1
[4,2,1,2] => 1
[4,2,2,1] => 1
[4,2,3] => 1
[4,3,1,1] => 1
[4,3,2] => 1
[4,4,1] => 1
[4,5] => 2
[5,1,1,1,1] => 1
[5,1,1,2] => 1
[5,1,2,1] => 1
[5,1,3] => 1
[5,2,1,1] => 1
[5,2,2] => 1
[5,3,1] => 1
[5,4] => 1
[6,1,1,1] => 1
[6,1,2] => 1
[6,2,1] => 1
[6,3] => 1
[7,1,1] => 1
[7,2] => 1
[8,1] => 1
[9] => 1
[1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2] => 2
[1,1,1,1,2,1,1,2] => 2
[1,1,1,1,2,2,1,1] => 2
[1,1,1,1,3,3] => 2
[1,1,1,1,5,1] => 2
[1,1,2,1,1,1,1,2] => 2
[1,1,2,1,1,2,1,1] => 2
[1,1,2,1,2,3] => 3
[1,1,2,2,1,1,1,1] => 2
[1,1,2,2,2,2] => 2
[1,1,3,1,1,3] => 2
[1,1,3,2,1,2] => 2
[1,1,3,3,1,1] => 2
[1,1,4,4] => 2
[1,1,7,1] => 2
[1,2,1,1,4,1] => 3
[1,2,6,1] => 3
[1,3,1,1,3,1] => 2
[1,3,5,1] => 3
[1,4,1,1,2,1] => 2
[1,4,4,1] => 2
[1,5,1,1,1,1] => 2
[1,5,3,1] => 2
[1,6,1,2] => 2
[1,6,2,1] => 2
[1,7,1,1] => 2
[1,8,1] => 2
[1,9] => 2
[2,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,1,1] => 1
[2,1,1,1,2,3] => 2
[2,1,1,2,1,1,1,1] => 1
[2,1,1,2,2,2] => 1
[2,1,2,1,1,3] => 2
[2,1,2,2,1,2] => 1
[2,1,2,3,1,1] => 2
[2,1,3,4] => 3
[2,1,6,1] => 2
[2,2,1,1,1,1,1,1] => 1
[2,2,1,1,2,2] => 1
[2,2,2,1,1,2] => 1
[2,2,2,2,1,1] => 1
[2,2,3,3] => 2
[3,1,1,1,1,3] => 1
[3,1,1,2,1,2] => 1
[3,1,1,3,1,1] => 1
[3,1,2,4] => 2
[3,2,1,1,1,2] => 1
[3,2,1,2,1,1] => 1
[3,2,2,3] => 1
[3,3,1,1,1,1] => 1
[3,3,2,2] => 1
[4,1,1,4] => 1
[4,2,1,3] => 1
[4,3,1,2] => 1
[4,4,1,1] => 1
[5,5] => 1
[8,1,1] => 1
[9,1] => 1
[10,1] => 1
[1,10] => 2
[1,8,1,1] => 2
[1,7,2,1] => 2
[1,6,3,1] => 2
[1,5,4,1] => 2
[1,4,5,1] => 3
[1,3,6,1] => 3
[1,2,7,1] => 3
[1,1,8,1] => 2
[5,5,1,1] => 1
[1,1,5,5] => 2
[1,1,4,1,1,4] => 2
[4,1,1,4,1,1] => 1
[1,1,3,1,2,4] => 3
[1,1,4,2,1,3] => 2
[3,1,2,4,1,1] => 2
[4,2,1,3,1,1] => 1
[1,1,2,1,3,4] => 4
[1,1,3,1,1,1,1,3] => 2
[1,1,4,3,1,2] => 2
[2,2,4,4] => 2
[2,1,3,4,1,1] => 3
[3,1,1,1,1,3,1,1] => 1
[4,4,2,2] => 1
[4,3,1,2,1,1] => 1
[1,1,1,1,4,4] => 2
[1,1,2,1,2,1,1,3] => 3
[1,1,3,2,2,3] => 2
[1,1,3,1,1,2,1,2] => 2
[1,1,4,4,1,1] => 2
[2,2,3,1,1,3] => 2
[2,1,2,1,1,3,1,1] => 2
[3,3,3,3] => 1
[3,2,2,3,1,1] => 1
[3,1,1,3,2,2] => 1
[3,1,1,2,1,2,1,1] => 1
[4,4,1,1,1,1] => 1
[1,1,1,1,3,1,1,3] => 2
[1,1,2,1,1,1,2,3] => 3
[1,1,2,1,2,2,1,2] => 2
[1,1,3,2,1,1,1,2] => 2
[1,1,3,1,1,3,1,1] => 2
[2,2,2,1,2,3] => 2
[2,2,3,2,1,2] => 2
[2,1,1,2,3,3] => 2
[2,1,1,1,2,3,1,1] => 2
[2,1,2,3,2,2] => 2
[2,1,2,2,1,2,1,1] => 1
[3,3,2,1,1,2] => 1
[3,2,1,2,2,2] => 1
[3,2,1,1,1,2,1,1] => 1
[3,1,1,3,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1,2] => 2
[1,1,1,1,1,1,1,1,2,2] => 2
[2,2,1,1,2,1,1,2] => 1
[2,2,1,1,1,1,2,2] => 1
[2,1,1,2,2,1,1,2] => 1
[1,1,2,2,2,1,1,2] => 2
[2,1,1,2,1,1,2,2] => 1
[1,1,2,2,1,1,2,2] => 2
[1,1,1,1,3,2,1,2] => 2
[1,1,2,1,1,1,1,1,1,2] => 2
[1,1,2,1,1,2,2,2] => 2
[3,3,1,1,2,2] => 1
[1,1,1,1,2,1,1,1,1,2] => 2
[1,1,1,1,2,2,2,2] => 2
[3,2,2,2,1,2] => 1
[2,1,1,1,2,2,1,2] => 1
[1,1,1,1,2,1,2,3] => 3
[3,2,1,1,1,1,1,2] => 1
[2,1,1,1,1,1,1,1,1,2] => 1
[2,1,1,1,1,2,2,2] => 1
[2,2,2,1,1,1,1,2] => 1
[2,2,2,2,2,2] => 1
[1,1,1,1,1,1,3,3] => 2
[3,1,2,3,1,2] => 1
[2,1,3,3,1,2] => 2
[3,1,1,1,1,2,1,2] => 1
[2,1,2,1,1,2,1,2] => 1
[3,1,1,2,1,1,1,2] => 1
[2,1,2,2,1,1,1,2] => 1
[1,1,3,3,2,2] => 2
[2,2,1,1,3,3] => 2
[3,3,1,1,1,1,1,1] => 1
[2,1,2,3,1,1,1,1] => 2
[1,1,3,3,1,1,1,1] => 2
[2,2,3,3,1,1] => 2
[1,1,1,1,3,3,1,1] => 2
[3,1,1,1,1,1,1,3] => 1
[3,1,1,2,2,3] => 1
[3,2,1,1,2,3] => 1
[2,1,1,1,1,1,2,3] => 2
[1,1,2,1,2,3,1,1] => 3
[4,2,1,1,1,3] => 1
[3,2,2,1,1,3] => 1
[4,2,1,2,1,2] => 1
[2,1,2,2,2,3] => 2
[4,3,1,1,1,2] => 1
[1,1,2,2,3,3] => 3
[3,3,2,2,1,1] => 1
[1,1,2,2,2,2,1,1] => 2
[2,2,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,2,2,1,1] => 1
[2,1,1,1,2,1,1,3] => 2
[2,2,2,2,1,1,1,1] => 1
[2,1,1,2,1,1,1,1,1,1] => 1
[2,1,1,1,3,4] => 3
[2,1,1,1,1,1,1,2,1,1] => 1
[2,1,2,1,1,1,1,3] => 2
[2,2,2,1,1,2,1,1] => 1
[2,1,1,1,1,2,1,1,1,1] => 1
[2,1,2,1,2,4] => 2
[2,1,1,2,2,2,1,1] => 1
[2,1,3,2,1,3] => 2
[2,1,3,1,1,4] => 3
[3,1,1,1,2,4] => 2
[1,1,2,1,1,2,1,1,1,1] => 2
[1,1,1,1,2,1,1,2,1,1] => 2
[1,1,2,2,1,1,1,1,1,1] => 2
[1,1,1,1,2,2,1,1,1,1] => 2
[1,1,1,1,1,1,2,2,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[5,4,1,2] => 1
[4,1,1,3,1,2] => 1
[4,3,2,3] => 1
[5,3,1,3] => 1
[4,1,1,2,1,3] => 1
[3,2,1,2,1,1,1,1] => 1
[1,1,3,2,1,2,1,1] => 2
[5,2,1,4] => 1
[5,1,1,5] => 1
[3,1,2,2,1,3] => 1
[4,2,2,4] => 1
[3,1,2,1,1,4] => 2
[4,1,1,1,1,4] => 1
[3,1,3,5] => 2
[6,6] => 1
[4,1,2,5] => 2
[2,1,4,5] => 3
[3,2,3,4] => 2
[1,1,2,1,1,1,1,2,1,1] => 2
click to show generating function       
Description
The number of strong records in an integer composition.
A strong record is an element $a_i$ such that $a_i > a_j$ for all $j < i$. In particular, the first part of a composition is a strong record.
Theorem 1.1 of [1] provides the generating function for compositions with parts in a given set according to the sum of the parts, the number of parts and the number of strong records.
References
[1] Knopfmacher, A., Mansour, T. Record statistics in integer compositions MathSciNet:2721540
Code
def statistic(pi):
    pi = list(pi)
    i = 0
    res = 0
    for j in range(len(pi)):
        if pi[j] > i:
            i = pi[j] 
            res += 1
    return res

Created
Apr 08, 2017 at 21:56 by Martin Rubey
Updated
Jul 02, 2019 at 22:33 by Martin Rubey