[2,1,3,1] => 3
[2,1,4] => 4
[2,2,1,1,1] => 2
[2,2,1,2] => 2
[2,2,2,1] => 2
[2,2,3] => 3
[2,3,1,1] => 3
[2,3,2] => 3
[2,4,1] => 4
[2,5] => 5
[3,1,1,1,1] => 3
[3,1,1,2] => 3
[3,1,2,1] => 3
[3,1,3] => 3
[3,2,1,1] => 3
[3,2,2] => 3
[3,3,1] => 3
[3,4] => 4
[4,1,1,1] => 4
[4,1,2] => 4
[4,2,1] => 4
[4,3] => 4
[5,1,1] => 5
[5,2] => 5
[6,1] => 6
[7] => 7
[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] => 3
[1,1,1,1,2,1,1] => 2
[1,1,1,1,2,2] => 2
[1,1,1,1,3,1] => 3
[1,1,1,1,4] => 4
[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] => 3
[1,1,1,3,2] => 3
[1,1,1,4,1] => 4
[1,1,1,5] => 5
[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] => 4
[1,1,3,1,1,1] => 3
[1,1,3,1,2] => 3
[1,1,3,2,1] => 3
[1,1,3,3] => 3
[1,1,4,1,1] => 4
[1,1,4,2] => 4
[1,1,5,1] => 5
[1,1,6] => 6
[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] => 4
[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] => 4
[1,2,5] => 5
[1,3,1,1,1,1] => 3
[1,3,1,1,2] => 3
[1,3,1,2,1] => 3
[1,3,1,3] => 3
[1,3,2,1,1] => 3
[1,3,2,2] => 3
[1,3,3,1] => 3
[1,3,4] => 4
[1,4,1,1,1] => 4
[1,4,1,2] => 4
[1,4,2,1] => 4
[1,4,3] => 4
[1,5,1,1] => 5
[1,5,2] => 5
[1,6,1] => 6
[1,7] => 7
[2,1,1,1,1,1,1] => 2
[2,1,1,1,1,2] => 2
[2,1,1,1,2,1] => 2
[2,1,1,1,3] => 3
[2,1,1,2,1,1] => 2
[2,1,1,2,2] => 2
[2,1,1,3,1] => 3
[2,1,1,4] => 4
[2,1,2,1,1,1] => 2
[2,1,2,1,2] => 2
[2,1,2,2,1] => 2
[2,1,2,3] => 3
[2,1,3,1,1] => 3
[2,1,3,2] => 3
[2,1,4,1] => 4
[2,1,5] => 5
[2,2,1,1,1,1] => 2
[2,2,1,1,2] => 2
[2,2,1,2,1] => 2
[2,2,1,3] => 3
[2,2,2,1,1] => 2
[2,2,2,2] => 2
[2,2,3,1] => 3
[2,2,4] => 4
[2,3,1,1,1] => 3
[2,3,1,2] => 3
[2,3,2,1] => 3
[2,3,3] => 3
[2,4,1,1] => 4
[2,4,2] => 4
[2,5,1] => 5
[2,6] => 6
[3,1,1,1,1,1] => 3
[3,1,1,1,2] => 3
[3,1,1,2,1] => 3
[3,1,1,3] => 3
[3,1,2,1,1] => 3
[3,1,2,2] => 3
[3,1,3,1] => 3
[3,1,4] => 4
[3,2,1,1,1] => 3
[3,2,1,2] => 3
[3,2,2,1] => 3
[3,2,3] => 3
[3,3,1,1] => 3
[3,3,2] => 3
[3,4,1] => 4
[3,5] => 5
[4,1,1,1,1] => 4
[4,1,1,2] => 4
[4,1,2,1] => 4
[4,1,3] => 4
[4,2,1,1] => 4
[4,2,2] => 4
[4,3,1] => 4
[4,4] => 4
[5,1,1,1] => 5
[5,1,2] => 5
[5,2,1] => 5
[5,3] => 5
[6,1,1] => 6
[6,2] => 6
[7,1] => 7
[8] => 8
[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] => 3
[1,1,1,1,1,2,1,1] => 2
[1,1,1,1,1,2,2] => 2
[1,1,1,1,1,3,1] => 3
[1,1,1,1,1,4] => 4
[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] => 3
[1,1,1,1,3,2] => 3
[1,1,1,1,4,1] => 4
[1,1,1,1,5] => 5
[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] => 4
[1,1,1,3,1,1,1] => 3
[1,1,1,3,1,2] => 3
[1,1,1,3,2,1] => 3
[1,1,1,3,3] => 3
[1,1,1,4,1,1] => 4
[1,1,1,4,2] => 4
[1,1,1,5,1] => 5
[1,1,1,6] => 6
[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] => 4
[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] => 4
[1,1,2,5] => 5
[1,1,3,1,1,1,1] => 3
[1,1,3,1,1,2] => 3
[1,1,3,1,2,1] => 3
[1,1,3,1,3] => 3
[1,1,3,2,1,1] => 3
[1,1,3,2,2] => 3
[1,1,3,3,1] => 3
[1,1,3,4] => 4
[1,1,4,1,1,1] => 4
[1,1,4,1,2] => 4
[1,1,4,2,1] => 4
[1,1,4,3] => 4
[1,1,5,1,1] => 5
[1,1,5,2] => 5
[1,1,6,1] => 6
[1,1,7] => 7
[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] => 4
[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] => 4
[1,2,1,5] => 5
[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] => 4
[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] => 4
[1,2,4,2] => 4
[1,2,5,1] => 5
[1,2,6] => 6
[1,3,1,1,1,1,1] => 3
[1,3,1,1,1,2] => 3
[1,3,1,1,2,1] => 3
[1,3,1,1,3] => 3
[1,3,1,2,1,1] => 3
[1,3,1,2,2] => 3
[1,3,1,3,1] => 3
[1,3,1,4] => 4
[1,3,2,1,1,1] => 3
[1,3,2,1,2] => 3
[1,3,2,2,1] => 3
[1,3,2,3] => 3
[1,3,3,1,1] => 3
[1,3,3,2] => 3
[1,3,4,1] => 4
[1,3,5] => 5
[1,4,1,1,1,1] => 4
[1,4,1,1,2] => 4
[1,4,1,2,1] => 4
[1,4,1,3] => 4
[1,4,2,1,1] => 4
[1,4,2,2] => 4
[1,4,3,1] => 4
[1,4,4] => 4
[1,5,1,1,1] => 5
[1,5,1,2] => 5
[1,5,2,1] => 5
[1,5,3] => 5
[1,6,1,1] => 6
[1,6,2] => 6
[1,7,1] => 7
[1,8] => 8
[2,1,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,2] => 2
[2,1,1,1,1,2,1] => 2
[2,1,1,1,1,3] => 3
[2,1,1,1,2,1,1] => 2
[2,1,1,1,2,2] => 2
[2,1,1,1,3,1] => 3
[2,1,1,1,4] => 4
[2,1,1,2,1,1,1] => 2
[2,1,1,2,1,2] => 2
[2,1,1,2,2,1] => 2
[2,1,1,2,3] => 3
[2,1,1,3,1,1] => 3
[2,1,1,3,2] => 3
[2,1,1,4,1] => 4
[2,1,1,5] => 5
[2,1,2,1,1,1,1] => 2
[2,1,2,1,1,2] => 2
[2,1,2,1,2,1] => 2
[2,1,2,1,3] => 3
[2,1,2,2,1,1] => 2
[2,1,2,2,2] => 2
[2,1,2,3,1] => 3
[2,1,2,4] => 4
[2,1,3,1,1,1] => 3
[2,1,3,1,2] => 3
[2,1,3,2,1] => 3
[2,1,3,3] => 3
[2,1,4,1,1] => 4
[2,1,4,2] => 4
[2,1,5,1] => 5
[2,1,6] => 6
[2,2,1,1,1,1,1] => 2
[2,2,1,1,1,2] => 2
[2,2,1,1,2,1] => 2
[2,2,1,1,3] => 3
[2,2,1,2,1,1] => 2
[2,2,1,2,2] => 2
[2,2,1,3,1] => 3
[2,2,1,4] => 4
[2,2,2,1,1,1] => 2
[2,2,2,1,2] => 2
[2,2,2,2,1] => 2
[2,2,2,3] => 3
[2,2,3,1,1] => 3
[2,2,3,2] => 3
[2,2,4,1] => 4
[2,2,5] => 5
[2,3,1,1,1,1] => 3
[2,3,1,1,2] => 3
[2,3,1,2,1] => 3
[2,3,1,3] => 3
[2,3,2,1,1] => 3
[2,3,2,2] => 3
[2,3,3,1] => 3
[2,3,4] => 4
[2,4,1,1,1] => 4
[2,4,1,2] => 4
[2,4,2,1] => 4
[2,4,3] => 4
[2,5,1,1] => 5
[2,5,2] => 5
[2,6,1] => 6
[2,7] => 7
[3,1,1,1,1,1,1] => 3
[3,1,1,1,1,2] => 3
[3,1,1,1,2,1] => 3
[3,1,1,1,3] => 3
[3,1,1,2,1,1] => 3
[3,1,1,2,2] => 3
[3,1,1,3,1] => 3
[3,1,1,4] => 4
[3,1,2,1,1,1] => 3
[3,1,2,1,2] => 3
[3,1,2,2,1] => 3
[3,1,2,3] => 3
[3,1,3,1,1] => 3
[3,1,3,2] => 3
[3,1,4,1] => 4
[3,1,5] => 5
[3,2,1,1,1,1] => 3
[3,2,1,1,2] => 3
[3,2,1,2,1] => 3
[3,2,1,3] => 3
[3,2,2,1,1] => 3
[3,2,2,2] => 3
[3,2,3,1] => 3
[3,2,4] => 4
[3,3,1,1,1] => 3
[3,3,1,2] => 3
[3,3,2,1] => 3
[3,3,3] => 3
[3,4,1,1] => 4
[3,4,2] => 4
[3,5,1] => 5
[3,6] => 6
[4,1,1,1,1,1] => 4
[4,1,1,1,2] => 4
[4,1,1,2,1] => 4
[4,1,1,3] => 4
[4,1,2,1,1] => 4
[4,1,2,2] => 4
[4,1,3,1] => 4
[4,1,4] => 4
[4,2,1,1,1] => 4
[4,2,1,2] => 4
[4,2,2,1] => 4
[4,2,3] => 4
[4,3,1,1] => 4
[4,3,2] => 4
[4,4,1] => 4
[4,5] => 5
[5,1,1,1,1] => 5
[5,1,1,2] => 5
[5,1,2,1] => 5
[5,1,3] => 5
[5,2,1,1] => 5
[5,2,2] => 5
[5,3,1] => 5
[5,4] => 5
[6,1,1,1] => 6
[6,1,2] => 6
[6,2,1] => 6
[6,3] => 6
[7,1,1] => 7
[7,2] => 7
[8,1] => 8
[9] => 9
[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] => 3
[1,1,1,1,5,1] => 5
[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] => 3
[1,1,3,2,1,2] => 3
[1,1,3,3,1,1] => 3
[1,1,4,4] => 4
[1,1,7,1] => 7
[1,2,1,1,4,1] => 4
[1,2,6,1] => 6
[1,3,1,1,3,1] => 3
[1,3,5,1] => 5
[1,4,1,1,2,1] => 4
[1,4,4,1] => 4
[1,5,1,1,1,1] => 5
[1,5,3,1] => 5
[1,6,1,2] => 6
[1,6,2,1] => 6
[1,7,1,1] => 7
[1,8,1] => 8
[1,9] => 9
[2,1,1,1,1,1,1,2] => 2
[2,1,1,1,1,2,1,1] => 2
[2,1,1,1,2,3] => 3
[2,1,1,2,1,1,1,1] => 2
[2,1,1,2,2,2] => 2
[2,1,2,1,1,3] => 3
[2,1,2,2,1,2] => 2
[2,1,2,3,1,1] => 3
[2,1,3,4] => 4
[2,1,6,1] => 6
[2,2,1,1,1,1,1,1] => 2
[2,2,1,1,2,2] => 2
[2,2,2,1,1,2] => 2
[2,2,2,2,1,1] => 2
[2,2,3,3] => 3
[3,1,1,1,1,3] => 3
[3,1,1,2,1,2] => 3
[3,1,1,3,1,1] => 3
[3,1,2,4] => 4
[3,2,1,1,1,2] => 3
[3,2,1,2,1,1] => 3
[3,2,2,3] => 3
[3,3,1,1,1,1] => 3
[3,3,2,2] => 3
[4,1,1,4] => 4
[4,2,1,3] => 4
[4,3,1,2] => 4
[4,4,1,1] => 4
[5,5] => 5
[8,1,1] => 8
[9,1] => 9
[1,10] => 10
[1,8,1,1] => 8
[1,7,2,1] => 7
[1,6,3,1] => 6
[1,5,4,1] => 5
[1,4,5,1] => 5
[1,3,6,1] => 6
[1,2,7,1] => 7
[1,1,8,1] => 8
[10,1] => 10
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2,2] => 2
[1,1,1,1,1,1,2,2,1,1] => 2
[1,1,1,1,1,1,2,1,1,2] => 2
[1,1,1,1,1,1,3,3] => 3
[1,1,1,1,2,2,1,1,1,1] => 2
[1,1,1,1,2,2,2,2] => 2
[1,1,1,1,2,1,1,2,1,1] => 2
[1,1,1,1,2,1,1,1,1,2] => 2
[1,1,1,1,2,1,2,3] => 3
[1,1,1,1,3,3,1,1] => 3
[1,1,1,1,3,2,1,2] => 3
[1,1,1,1,3,1,1,3] => 3
[1,1,1,1,4,4] => 4
[1,1,2,2,1,1,1,1,1,1] => 2
[1,1,2,2,1,1,2,2] => 2
[1,1,2,2,2,2,1,1] => 2
[1,1,2,2,2,1,1,2] => 2
[1,1,2,2,3,3] => 3
[1,1,2,1,1,2,1,1,1,1] => 2
[1,1,2,1,1,2,2,2] => 2
[1,1,2,1,1,1,1,2,1,1] => 2
[1,1,2,1,1,1,1,1,1,2] => 2
[1,1,2,1,1,1,2,3] => 3
[1,1,2,1,2,3,1,1] => 3
[1,1,2,1,2,2,1,2] => 2
[1,1,2,1,2,1,1,3] => 3
[1,1,2,1,3,4] => 4
[1,1,3,3,1,1,1,1] => 3
[1,1,3,3,2,2] => 3
[1,1,3,2,1,2,1,1] => 3
[1,1,3,2,1,1,1,2] => 3
[1,1,3,2,2,3] => 3
[1,1,3,1,1,3,1,1] => 3
[1,1,3,1,1,2,1,2] => 3
[1,1,3,1,1,1,1,3] => 3
[1,1,3,1,2,4] => 4
[1,1,4,4,1,1] => 4
[1,1,4,3,1,2] => 4
[1,1,4,2,1,3] => 4
[1,1,4,1,1,4] => 4
[1,1,5,5] => 5
[2,2,1,1,1,1,1,1,1,1] => 2
[2,2,1,1,1,1,2,2] => 2
[2,2,1,1,2,2,1,1] => 2
[2,2,1,1,2,1,1,2] => 2
[2,2,1,1,3,3] => 3
[2,2,2,2,1,1,1,1] => 2
[2,2,2,2,2,2] => 2
[2,2,2,1,1,2,1,1] => 2
[2,2,2,1,1,1,1,2] => 2
[2,2,2,1,2,3] => 3
[2,2,3,3,1,1] => 3
[2,2,3,2,1,2] => 3
[2,2,3,1,1,3] => 3
[2,2,4,4] => 4
[2,1,1,2,1,1,1,1,1,1] => 2
[2,1,1,2,1,1,2,2] => 2
[2,1,1,2,2,2,1,1] => 2
[2,1,1,2,2,1,1,2] => 2
[2,1,1,2,3,3] => 3
[2,1,1,1,1,2,1,1,1,1] => 2
[2,1,1,1,1,2,2,2] => 2
[2,1,1,1,1,1,1,2,1,1] => 2
[2,1,1,1,1,1,1,1,1,2] => 2
[2,1,1,1,1,1,2,3] => 3
[2,1,1,1,2,3,1,1] => 3
[2,1,1,1,2,2,1,2] => 2
[2,1,1,1,2,1,1,3] => 3
[2,1,1,1,3,4] => 4
[2,1,2,3,1,1,1,1] => 3
[2,1,2,3,2,2] => 3
[2,1,2,2,1,2,1,1] => 2
[2,1,2,2,1,1,1,2] => 2
[2,1,2,2,2,3] => 3
[2,1,2,1,1,3,1,1] => 3
[2,1,2,1,1,2,1,2] => 2
[2,1,2,1,1,1,1,3] => 3
[2,1,2,1,2,4] => 4
[2,1,3,4,1,1] => 4
[2,1,3,3,1,2] => 3
[2,1,3,2,1,3] => 3
[2,1,3,1,1,4] => 4
[2,1,4,5] => 5
[3,3,1,1,1,1,1,1] => 3
[3,3,1,1,2,2] => 3
[3,3,2,2,1,1] => 3
[3,3,2,1,1,2] => 3
[3,3,3,3] => 3
[3,2,1,2,1,1,1,1] => 3
[3,2,1,2,2,2] => 3
[3,2,1,1,1,2,1,1] => 3
[3,2,1,1,1,1,1,2] => 3
[3,2,1,1,2,3] => 3
[3,2,2,3,1,1] => 3
[3,2,2,2,1,2] => 3
[3,2,2,1,1,3] => 3
[3,2,3,4] => 4
[3,1,1,3,1,1,1,1] => 3
[3,1,1,3,2,2] => 3
[3,1,1,2,1,2,1,1] => 3
[3,1,1,2,1,1,1,2] => 3
[3,1,1,2,2,3] => 3
[3,1,1,1,1,3,1,1] => 3
[3,1,1,1,1,2,1,2] => 3
[3,1,1,1,1,1,1,3] => 3
[3,1,1,1,2,4] => 4
[3,1,2,4,1,1] => 4
[3,1,2,3,1,2] => 3
[3,1,2,2,1,3] => 3
[3,1,2,1,1,4] => 4
[3,1,3,5] => 5
[4,4,1,1,1,1] => 4
[4,4,2,2] => 4
[4,3,1,2,1,1] => 4
[4,3,1,1,1,2] => 4
[4,3,2,3] => 4
[4,2,1,3,1,1] => 4
[4,2,1,2,1,2] => 4
[4,2,1,1,1,3] => 4
[4,2,2,4] => 4
[4,1,1,4,1,1] => 4
[4,1,1,3,1,2] => 4
[4,1,1,2,1,3] => 4
[4,1,1,1,1,4] => 4
[4,1,2,5] => 5
[5,5,1,1] => 5
[5,4,1,2] => 5
[5,3,1,3] => 5
[5,2,1,4] => 5
[5,1,1,5] => 5
[6,6] => 6