Values
[1] => 1 => [1] => [1] => 1
[2] => 0 => [1] => [1] => 1
[1,1] => 11 => [2] => [2] => 2
[3] => 1 => [1] => [1] => 1
[2,1] => 01 => [1,1] => [1,1] => 2
[1,1,1] => 111 => [3] => [3] => 3
[4] => 0 => [1] => [1] => 1
[3,1] => 11 => [2] => [2] => 2
[2,2] => 00 => [2] => [2] => 2
[2,1,1] => 011 => [1,2] => [2,1] => 3
[1,1,1,1] => 1111 => [4] => [4] => 4
[5] => 1 => [1] => [1] => 1
[4,1] => 01 => [1,1] => [1,1] => 2
[3,2] => 10 => [1,1] => [1,1] => 2
[3,1,1] => 111 => [3] => [3] => 3
[2,2,1] => 001 => [2,1] => [2,1] => 3
[2,1,1,1] => 0111 => [1,3] => [3,1] => 4
[1,1,1,1,1] => 11111 => [5] => [5] => 5
[6] => 0 => [1] => [1] => 1
[5,1] => 11 => [2] => [2] => 2
[4,2] => 00 => [2] => [2] => 2
[4,1,1] => 011 => [1,2] => [2,1] => 3
[3,3] => 11 => [2] => [2] => 2
[3,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[3,1,1,1] => 1111 => [4] => [4] => 4
[2,2,2] => 000 => [3] => [3] => 3
[2,2,1,1] => 0011 => [2,2] => [2,2] => 4
[2,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[1,1,1,1,1,1] => 111111 => [6] => [6] => 6
[7] => 1 => [1] => [1] => 1
[6,1] => 01 => [1,1] => [1,1] => 2
[5,2] => 10 => [1,1] => [1,1] => 2
[5,1,1] => 111 => [3] => [3] => 3
[4,3] => 01 => [1,1] => [1,1] => 2
[4,2,1] => 001 => [2,1] => [2,1] => 3
[4,1,1,1] => 0111 => [1,3] => [3,1] => 4
[3,3,1] => 111 => [3] => [3] => 3
[3,2,2] => 100 => [1,2] => [2,1] => 3
[3,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[3,1,1,1,1] => 11111 => [5] => [5] => 5
[2,2,2,1] => 0001 => [3,1] => [3,1] => 4
[2,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[2,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[1,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[8] => 0 => [1] => [1] => 1
[7,1] => 11 => [2] => [2] => 2
[6,2] => 00 => [2] => [2] => 2
[6,1,1] => 011 => [1,2] => [2,1] => 3
[5,3] => 11 => [2] => [2] => 2
[5,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[5,1,1,1] => 1111 => [4] => [4] => 4
[4,4] => 00 => [2] => [2] => 2
[4,3,1] => 011 => [1,2] => [2,1] => 3
[4,2,2] => 000 => [3] => [3] => 3
[4,2,1,1] => 0011 => [2,2] => [2,2] => 4
[4,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[3,3,2] => 110 => [2,1] => [2,1] => 3
[3,3,1,1] => 1111 => [4] => [4] => 4
[3,2,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[3,2,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[3,1,1,1,1,1] => 111111 => [6] => [6] => 6
[2,2,2,2] => 0000 => [4] => [4] => 4
[2,2,2,1,1] => 00011 => [3,2] => [3,2] => 5
[2,2,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[2,1,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[1,1,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[9] => 1 => [1] => [1] => 1
[8,1] => 01 => [1,1] => [1,1] => 2
[7,2] => 10 => [1,1] => [1,1] => 2
[7,1,1] => 111 => [3] => [3] => 3
[6,3] => 01 => [1,1] => [1,1] => 2
[6,2,1] => 001 => [2,1] => [2,1] => 3
[6,1,1,1] => 0111 => [1,3] => [3,1] => 4
[5,4] => 10 => [1,1] => [1,1] => 2
[5,3,1] => 111 => [3] => [3] => 3
[5,2,2] => 100 => [1,2] => [2,1] => 3
[5,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[5,1,1,1,1] => 11111 => [5] => [5] => 5
[4,4,1] => 001 => [2,1] => [2,1] => 3
[4,3,2] => 010 => [1,1,1] => [1,1,1] => 3
[4,3,1,1] => 0111 => [1,3] => [3,1] => 4
[4,2,2,1] => 0001 => [3,1] => [3,1] => 4
[4,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[4,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[3,3,3] => 111 => [3] => [3] => 3
[3,3,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[3,3,1,1,1] => 11111 => [5] => [5] => 5
[3,2,2,2] => 1000 => [1,3] => [3,1] => 4
[3,2,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[3,2,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[3,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[2,2,2,2,1] => 00001 => [4,1] => [4,1] => 5
[2,2,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[2,2,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[2,1,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[1,1,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[10] => 0 => [1] => [1] => 1
[9,1] => 11 => [2] => [2] => 2
[8,2] => 00 => [2] => [2] => 2
[8,1,1] => 011 => [1,2] => [2,1] => 3
[7,3] => 11 => [2] => [2] => 2
>>> Load all 1131 entries. <<<
[7,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[7,1,1,1] => 1111 => [4] => [4] => 4
[6,4] => 00 => [2] => [2] => 2
[6,3,1] => 011 => [1,2] => [2,1] => 3
[6,2,2] => 000 => [3] => [3] => 3
[6,2,1,1] => 0011 => [2,2] => [2,2] => 4
[6,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[5,5] => 11 => [2] => [2] => 2
[5,4,1] => 101 => [1,1,1] => [1,1,1] => 3
[5,3,2] => 110 => [2,1] => [2,1] => 3
[5,3,1,1] => 1111 => [4] => [4] => 4
[5,2,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[5,2,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[5,1,1,1,1,1] => 111111 => [6] => [6] => 6
[4,4,2] => 000 => [3] => [3] => 3
[4,4,1,1] => 0011 => [2,2] => [2,2] => 4
[4,3,3] => 011 => [1,2] => [2,1] => 3
[4,3,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[4,3,1,1,1] => 01111 => [1,4] => [4,1] => 5
[4,2,2,2] => 0000 => [4] => [4] => 4
[4,2,2,1,1] => 00011 => [3,2] => [3,2] => 5
[4,2,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[4,1,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[3,3,3,1] => 1111 => [4] => [4] => 4
[3,3,2,2] => 1100 => [2,2] => [2,2] => 4
[3,3,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[3,3,1,1,1,1] => 111111 => [6] => [6] => 6
[3,2,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[3,2,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[3,2,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[3,1,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[2,2,2,2,2] => 00000 => [5] => [5] => 5
[2,2,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[2,2,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[2,2,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[2,1,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[1,1,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[11] => 1 => [1] => [1] => 1
[10,1] => 01 => [1,1] => [1,1] => 2
[9,2] => 10 => [1,1] => [1,1] => 2
[9,1,1] => 111 => [3] => [3] => 3
[8,3] => 01 => [1,1] => [1,1] => 2
[8,2,1] => 001 => [2,1] => [2,1] => 3
[8,1,1,1] => 0111 => [1,3] => [3,1] => 4
[7,4] => 10 => [1,1] => [1,1] => 2
[7,3,1] => 111 => [3] => [3] => 3
[7,2,2] => 100 => [1,2] => [2,1] => 3
[7,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[7,1,1,1,1] => 11111 => [5] => [5] => 5
[6,5] => 01 => [1,1] => [1,1] => 2
[6,4,1] => 001 => [2,1] => [2,1] => 3
[6,3,2] => 010 => [1,1,1] => [1,1,1] => 3
[6,3,1,1] => 0111 => [1,3] => [3,1] => 4
[6,2,2,1] => 0001 => [3,1] => [3,1] => 4
[6,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[6,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[5,5,1] => 111 => [3] => [3] => 3
[5,4,2] => 100 => [1,2] => [2,1] => 3
[5,4,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[5,3,3] => 111 => [3] => [3] => 3
[5,3,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[5,3,1,1,1] => 11111 => [5] => [5] => 5
[5,2,2,2] => 1000 => [1,3] => [3,1] => 4
[5,2,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[5,2,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[5,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[4,4,3] => 001 => [2,1] => [2,1] => 3
[4,4,2,1] => 0001 => [3,1] => [3,1] => 4
[4,4,1,1,1] => 00111 => [2,3] => [3,2] => 5
[4,3,3,1] => 0111 => [1,3] => [3,1] => 4
[4,3,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[4,3,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[4,3,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[4,2,2,2,1] => 00001 => [4,1] => [4,1] => 5
[4,2,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[4,2,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[4,1,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[3,3,3,2] => 1110 => [3,1] => [3,1] => 4
[3,3,3,1,1] => 11111 => [5] => [5] => 5
[3,3,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[3,3,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[3,3,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[3,2,2,2,2] => 10000 => [1,4] => [4,1] => 5
[3,2,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[3,2,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[3,2,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[3,1,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[2,2,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[2,2,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[2,2,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[2,2,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[2,1,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[12] => 0 => [1] => [1] => 1
[11,1] => 11 => [2] => [2] => 2
[10,2] => 00 => [2] => [2] => 2
[10,1,1] => 011 => [1,2] => [2,1] => 3
[9,3] => 11 => [2] => [2] => 2
[9,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[9,1,1,1] => 1111 => [4] => [4] => 4
[8,4] => 00 => [2] => [2] => 2
[8,3,1] => 011 => [1,2] => [2,1] => 3
[8,2,2] => 000 => [3] => [3] => 3
[8,2,1,1] => 0011 => [2,2] => [2,2] => 4
[8,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[7,5] => 11 => [2] => [2] => 2
[7,4,1] => 101 => [1,1,1] => [1,1,1] => 3
[7,3,2] => 110 => [2,1] => [2,1] => 3
[7,3,1,1] => 1111 => [4] => [4] => 4
[7,2,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[7,2,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[7,1,1,1,1,1] => 111111 => [6] => [6] => 6
[6,6] => 00 => [2] => [2] => 2
[6,5,1] => 011 => [1,2] => [2,1] => 3
[6,4,2] => 000 => [3] => [3] => 3
[6,4,1,1] => 0011 => [2,2] => [2,2] => 4
[6,3,3] => 011 => [1,2] => [2,1] => 3
[6,3,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[6,3,1,1,1] => 01111 => [1,4] => [4,1] => 5
[6,2,2,2] => 0000 => [4] => [4] => 4
[6,2,2,1,1] => 00011 => [3,2] => [3,2] => 5
[6,2,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[6,1,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[5,5,2] => 110 => [2,1] => [2,1] => 3
[5,5,1,1] => 1111 => [4] => [4] => 4
[5,4,3] => 101 => [1,1,1] => [1,1,1] => 3
[5,4,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[5,4,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[5,3,3,1] => 1111 => [4] => [4] => 4
[5,3,2,2] => 1100 => [2,2] => [2,2] => 4
[5,3,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[5,3,1,1,1,1] => 111111 => [6] => [6] => 6
[5,2,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[5,2,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[5,2,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[5,1,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[4,4,4] => 000 => [3] => [3] => 3
[4,4,3,1] => 0011 => [2,2] => [2,2] => 4
[4,4,2,2] => 0000 => [4] => [4] => 4
[4,4,2,1,1] => 00011 => [3,2] => [3,2] => 5
[4,4,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[4,3,3,2] => 0110 => [1,2,1] => [2,1,1] => 4
[4,3,3,1,1] => 01111 => [1,4] => [4,1] => 5
[4,3,2,2,1] => 01001 => [1,1,2,1] => [2,1,1,1] => 5
[4,3,2,1,1,1] => 010111 => [1,1,1,3] => [3,1,1,1] => 6
[4,3,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[4,2,2,2,2] => 00000 => [5] => [5] => 5
[4,2,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[4,2,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[4,2,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[4,1,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[3,3,3,3] => 1111 => [4] => [4] => 4
[3,3,3,2,1] => 11101 => [3,1,1] => [3,1,1] => 5
[3,3,3,1,1,1] => 111111 => [6] => [6] => 6
[3,3,2,2,2] => 11000 => [2,3] => [3,2] => 5
[3,3,2,2,1,1] => 110011 => [2,2,2] => [2,2,2] => 6
[3,3,2,1,1,1,1] => 1101111 => [2,1,4] => [4,2,1] => 7
[3,3,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[3,2,2,2,2,1] => 100001 => [1,4,1] => [4,1,1] => 6
[3,2,2,2,1,1,1] => 1000111 => [1,3,3] => [3,3,1] => 7
[3,2,2,1,1,1,1,1] => 10011111 => [1,2,5] => [5,2,1] => 8
[3,2,1,1,1,1,1,1,1] => 101111111 => [1,1,7] => [7,1,1] => 9
[3,1,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[2,2,2,2,2,2] => 000000 => [6] => [6] => 6
[2,2,2,2,2,1,1] => 0000011 => [5,2] => [5,2] => 7
[2,2,2,2,1,1,1,1] => 00001111 => [4,4] => [4,4] => 8
[2,2,2,1,1,1,1,1,1] => 000111111 => [3,6] => [6,3] => 9
[2,2,1,1,1,1,1,1,1,1] => 0011111111 => [2,8] => [8,2] => 10
[13] => 1 => [1] => [1] => 1
[12,1] => 01 => [1,1] => [1,1] => 2
[11,2] => 10 => [1,1] => [1,1] => 2
[11,1,1] => 111 => [3] => [3] => 3
[10,3] => 01 => [1,1] => [1,1] => 2
[10,2,1] => 001 => [2,1] => [2,1] => 3
[10,1,1,1] => 0111 => [1,3] => [3,1] => 4
[9,4] => 10 => [1,1] => [1,1] => 2
[9,3,1] => 111 => [3] => [3] => 3
[9,2,2] => 100 => [1,2] => [2,1] => 3
[9,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[9,1,1,1,1] => 11111 => [5] => [5] => 5
[8,5] => 01 => [1,1] => [1,1] => 2
[8,4,1] => 001 => [2,1] => [2,1] => 3
[8,3,2] => 010 => [1,1,1] => [1,1,1] => 3
[8,3,1,1] => 0111 => [1,3] => [3,1] => 4
[8,2,2,1] => 0001 => [3,1] => [3,1] => 4
[8,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[8,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[7,6] => 10 => [1,1] => [1,1] => 2
[7,5,1] => 111 => [3] => [3] => 3
[7,4,2] => 100 => [1,2] => [2,1] => 3
[7,4,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[7,3,3] => 111 => [3] => [3] => 3
[7,3,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[7,3,1,1,1] => 11111 => [5] => [5] => 5
[7,2,2,2] => 1000 => [1,3] => [3,1] => 4
[7,2,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[7,2,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[7,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[6,6,1] => 001 => [2,1] => [2,1] => 3
[6,5,2] => 010 => [1,1,1] => [1,1,1] => 3
[6,5,1,1] => 0111 => [1,3] => [3,1] => 4
[6,4,3] => 001 => [2,1] => [2,1] => 3
[6,4,2,1] => 0001 => [3,1] => [3,1] => 4
[6,4,1,1,1] => 00111 => [2,3] => [3,2] => 5
[6,3,3,1] => 0111 => [1,3] => [3,1] => 4
[6,3,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[6,3,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[6,3,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[6,2,2,2,1] => 00001 => [4,1] => [4,1] => 5
[6,2,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[6,2,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[6,1,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[5,5,3] => 111 => [3] => [3] => 3
[5,5,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[5,5,1,1,1] => 11111 => [5] => [5] => 5
[5,4,4] => 100 => [1,2] => [2,1] => 3
[5,4,3,1] => 1011 => [1,1,2] => [2,1,1] => 4
[5,4,2,2] => 1000 => [1,3] => [3,1] => 4
[5,4,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[5,4,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[5,3,3,2] => 1110 => [3,1] => [3,1] => 4
[5,3,3,1,1] => 11111 => [5] => [5] => 5
[5,3,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[5,3,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[5,3,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[5,2,2,2,2] => 10000 => [1,4] => [4,1] => 5
[5,2,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[5,2,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[5,2,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[5,1,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[4,4,4,1] => 0001 => [3,1] => [3,1] => 4
[4,4,3,2] => 0010 => [2,1,1] => [2,1,1] => 4
[4,4,3,1,1] => 00111 => [2,3] => [3,2] => 5
[4,4,2,2,1] => 00001 => [4,1] => [4,1] => 5
[4,4,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[4,4,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[4,3,3,3] => 0111 => [1,3] => [3,1] => 4
[4,3,3,2,1] => 01101 => [1,2,1,1] => [2,1,1,1] => 5
[4,3,3,1,1,1] => 011111 => [1,5] => [5,1] => 6
[4,3,2,2,2] => 01000 => [1,1,3] => [3,1,1] => 5
[4,3,2,2,1,1] => 010011 => [1,1,2,2] => [2,2,1,1] => 6
[4,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => [4,1,1,1] => 7
[4,3,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[4,2,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[4,2,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[4,2,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[4,2,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[4,1,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[3,3,3,3,1] => 11111 => [5] => [5] => 5
[3,3,3,2,2] => 11100 => [3,2] => [3,2] => 5
[3,3,3,2,1,1] => 111011 => [3,1,2] => [3,2,1] => 6
[3,3,3,1,1,1,1] => 1111111 => [7] => [7] => 7
[3,3,2,2,2,1] => 110001 => [2,3,1] => [3,2,1] => 6
[3,3,2,2,1,1,1] => 1100111 => [2,2,3] => [3,2,2] => 7
[3,3,2,1,1,1,1,1] => 11011111 => [2,1,5] => [5,2,1] => 8
[3,3,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[3,2,2,2,2,2] => 100000 => [1,5] => [5,1] => 6
[3,2,2,2,2,1,1] => 1000011 => [1,4,2] => [4,2,1] => 7
[3,2,2,2,1,1,1,1] => 10001111 => [1,3,4] => [4,3,1] => 8
[3,2,2,1,1,1,1,1,1] => 100111111 => [1,2,6] => [6,2,1] => 9
[3,2,1,1,1,1,1,1,1,1] => 1011111111 => [1,1,8] => [8,1,1] => 10
[2,2,2,2,2,2,1] => 0000001 => [6,1] => [6,1] => 7
[2,2,2,2,2,1,1,1] => 00000111 => [5,3] => [5,3] => 8
[2,2,2,2,1,1,1,1,1] => 000011111 => [4,5] => [5,4] => 9
[2,2,2,1,1,1,1,1,1,1] => 0001111111 => [3,7] => [7,3] => 10
[14] => 0 => [1] => [1] => 1
[13,1] => 11 => [2] => [2] => 2
[12,2] => 00 => [2] => [2] => 2
[12,1,1] => 011 => [1,2] => [2,1] => 3
[11,3] => 11 => [2] => [2] => 2
[11,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[11,1,1,1] => 1111 => [4] => [4] => 4
[10,4] => 00 => [2] => [2] => 2
[10,3,1] => 011 => [1,2] => [2,1] => 3
[10,2,2] => 000 => [3] => [3] => 3
[10,2,1,1] => 0011 => [2,2] => [2,2] => 4
[10,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[9,5] => 11 => [2] => [2] => 2
[9,4,1] => 101 => [1,1,1] => [1,1,1] => 3
[9,3,2] => 110 => [2,1] => [2,1] => 3
[9,3,1,1] => 1111 => [4] => [4] => 4
[9,2,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[9,2,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[9,1,1,1,1,1] => 111111 => [6] => [6] => 6
[8,6] => 00 => [2] => [2] => 2
[8,5,1] => 011 => [1,2] => [2,1] => 3
[8,4,2] => 000 => [3] => [3] => 3
[8,4,1,1] => 0011 => [2,2] => [2,2] => 4
[8,3,3] => 011 => [1,2] => [2,1] => 3
[8,3,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[8,3,1,1,1] => 01111 => [1,4] => [4,1] => 5
[8,2,2,2] => 0000 => [4] => [4] => 4
[8,2,2,1,1] => 00011 => [3,2] => [3,2] => 5
[8,2,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[8,1,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[7,7] => 11 => [2] => [2] => 2
[7,6,1] => 101 => [1,1,1] => [1,1,1] => 3
[7,5,2] => 110 => [2,1] => [2,1] => 3
[7,5,1,1] => 1111 => [4] => [4] => 4
[7,4,3] => 101 => [1,1,1] => [1,1,1] => 3
[7,4,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[7,4,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[7,3,3,1] => 1111 => [4] => [4] => 4
[7,3,2,2] => 1100 => [2,2] => [2,2] => 4
[7,3,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[7,3,1,1,1,1] => 111111 => [6] => [6] => 6
[7,2,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[7,2,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[7,2,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[7,1,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[6,6,2] => 000 => [3] => [3] => 3
[6,6,1,1] => 0011 => [2,2] => [2,2] => 4
[6,5,3] => 011 => [1,2] => [2,1] => 3
[6,5,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[6,5,1,1,1] => 01111 => [1,4] => [4,1] => 5
[6,4,4] => 000 => [3] => [3] => 3
[6,4,3,1] => 0011 => [2,2] => [2,2] => 4
[6,4,2,2] => 0000 => [4] => [4] => 4
[6,4,2,1,1] => 00011 => [3,2] => [3,2] => 5
[6,4,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[6,3,3,2] => 0110 => [1,2,1] => [2,1,1] => 4
[6,3,3,1,1] => 01111 => [1,4] => [4,1] => 5
[6,3,2,2,1] => 01001 => [1,1,2,1] => [2,1,1,1] => 5
[6,3,2,1,1,1] => 010111 => [1,1,1,3] => [3,1,1,1] => 6
[6,3,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[6,2,2,2,2] => 00000 => [5] => [5] => 5
[6,2,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[6,2,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[6,2,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[6,1,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[5,5,4] => 110 => [2,1] => [2,1] => 3
[5,5,3,1] => 1111 => [4] => [4] => 4
[5,5,2,2] => 1100 => [2,2] => [2,2] => 4
[5,5,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[5,5,1,1,1,1] => 111111 => [6] => [6] => 6
[5,4,4,1] => 1001 => [1,2,1] => [2,1,1] => 4
[5,4,3,2] => 1010 => [1,1,1,1] => [1,1,1,1] => 4
[5,4,3,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[5,4,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[5,4,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[5,4,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[5,3,3,3] => 1111 => [4] => [4] => 4
[5,3,3,2,1] => 11101 => [3,1,1] => [3,1,1] => 5
[5,3,3,1,1,1] => 111111 => [6] => [6] => 6
[5,3,2,2,2] => 11000 => [2,3] => [3,2] => 5
[5,3,2,2,1,1] => 110011 => [2,2,2] => [2,2,2] => 6
[5,3,2,1,1,1,1] => 1101111 => [2,1,4] => [4,2,1] => 7
[5,3,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[5,2,2,2,2,1] => 100001 => [1,4,1] => [4,1,1] => 6
[5,2,2,2,1,1,1] => 1000111 => [1,3,3] => [3,3,1] => 7
[5,2,2,1,1,1,1,1] => 10011111 => [1,2,5] => [5,2,1] => 8
[5,2,1,1,1,1,1,1,1] => 101111111 => [1,1,7] => [7,1,1] => 9
[5,1,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[4,4,4,2] => 0000 => [4] => [4] => 4
[4,4,4,1,1] => 00011 => [3,2] => [3,2] => 5
[4,4,3,3] => 0011 => [2,2] => [2,2] => 4
[4,4,3,2,1] => 00101 => [2,1,1,1] => [2,1,1,1] => 5
[4,4,3,1,1,1] => 001111 => [2,4] => [4,2] => 6
[4,4,2,2,2] => 00000 => [5] => [5] => 5
[4,4,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[4,4,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[4,4,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[4,3,3,3,1] => 01111 => [1,4] => [4,1] => 5
[4,3,3,2,2] => 01100 => [1,2,2] => [2,2,1] => 5
[4,3,3,2,1,1] => 011011 => [1,2,1,2] => [2,2,1,1] => 6
[4,3,3,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[4,3,2,2,2,1] => 010001 => [1,1,3,1] => [3,1,1,1] => 6
[4,3,2,2,1,1,1] => 0100111 => [1,1,2,3] => [3,2,1,1] => 7
[4,3,2,1,1,1,1,1] => 01011111 => [1,1,1,5] => [5,1,1,1] => 8
[4,3,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[4,2,2,2,2,2] => 000000 => [6] => [6] => 6
[4,2,2,2,2,1,1] => 0000011 => [5,2] => [5,2] => 7
[4,2,2,2,1,1,1,1] => 00001111 => [4,4] => [4,4] => 8
[4,2,2,1,1,1,1,1,1] => 000111111 => [3,6] => [6,3] => 9
[4,2,1,1,1,1,1,1,1,1] => 0011111111 => [2,8] => [8,2] => 10
[3,3,3,3,2] => 11110 => [4,1] => [4,1] => 5
[3,3,3,3,1,1] => 111111 => [6] => [6] => 6
[3,3,3,2,2,1] => 111001 => [3,2,1] => [3,2,1] => 6
[3,3,3,2,1,1,1] => 1110111 => [3,1,3] => [3,3,1] => 7
[3,3,3,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[3,3,2,2,2,2] => 110000 => [2,4] => [4,2] => 6
[3,3,2,2,2,1,1] => 1100011 => [2,3,2] => [3,2,2] => 7
[3,3,2,2,1,1,1,1] => 11001111 => [2,2,4] => [4,2,2] => 8
[3,3,2,1,1,1,1,1,1] => 110111111 => [2,1,6] => [6,2,1] => 9
[3,3,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[3,2,2,2,2,2,1] => 1000001 => [1,5,1] => [5,1,1] => 7
[3,2,2,2,2,1,1,1] => 10000111 => [1,4,3] => [4,3,1] => 8
[3,2,2,2,1,1,1,1,1] => 100011111 => [1,3,5] => [5,3,1] => 9
[2,2,2,2,2,2,2] => 0000000 => [7] => [7] => 7
[2,2,2,2,2,2,1,1] => 00000011 => [6,2] => [6,2] => 8
[2,2,2,2,2,1,1,1,1] => 000001111 => [5,4] => [5,4] => 9
[2,2,2,2,1,1,1,1,1,1] => 0000111111 => [4,6] => [6,4] => 10
[15] => 1 => [1] => [1] => 1
[14,1] => 01 => [1,1] => [1,1] => 2
[13,2] => 10 => [1,1] => [1,1] => 2
[13,1,1] => 111 => [3] => [3] => 3
[12,3] => 01 => [1,1] => [1,1] => 2
[12,2,1] => 001 => [2,1] => [2,1] => 3
[12,1,1,1] => 0111 => [1,3] => [3,1] => 4
[11,4] => 10 => [1,1] => [1,1] => 2
[11,3,1] => 111 => [3] => [3] => 3
[11,2,2] => 100 => [1,2] => [2,1] => 3
[11,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[11,1,1,1,1] => 11111 => [5] => [5] => 5
[10,5] => 01 => [1,1] => [1,1] => 2
[10,4,1] => 001 => [2,1] => [2,1] => 3
[10,3,2] => 010 => [1,1,1] => [1,1,1] => 3
[10,3,1,1] => 0111 => [1,3] => [3,1] => 4
[10,2,2,1] => 0001 => [3,1] => [3,1] => 4
[10,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[10,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[9,6] => 10 => [1,1] => [1,1] => 2
[9,5,1] => 111 => [3] => [3] => 3
[9,4,2] => 100 => [1,2] => [2,1] => 3
[9,4,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[9,3,3] => 111 => [3] => [3] => 3
[9,3,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[9,3,1,1,1] => 11111 => [5] => [5] => 5
[9,2,2,2] => 1000 => [1,3] => [3,1] => 4
[9,2,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[9,2,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[9,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[8,7] => 01 => [1,1] => [1,1] => 2
[8,6,1] => 001 => [2,1] => [2,1] => 3
[8,5,2] => 010 => [1,1,1] => [1,1,1] => 3
[8,5,1,1] => 0111 => [1,3] => [3,1] => 4
[8,4,3] => 001 => [2,1] => [2,1] => 3
[8,4,2,1] => 0001 => [3,1] => [3,1] => 4
[8,4,1,1,1] => 00111 => [2,3] => [3,2] => 5
[8,3,3,1] => 0111 => [1,3] => [3,1] => 4
[8,3,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[8,3,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[8,3,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[8,2,2,2,1] => 00001 => [4,1] => [4,1] => 5
[8,2,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[8,2,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[8,1,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[7,7,1] => 111 => [3] => [3] => 3
[7,6,2] => 100 => [1,2] => [2,1] => 3
[7,6,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[7,5,3] => 111 => [3] => [3] => 3
[7,5,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[7,5,1,1,1] => 11111 => [5] => [5] => 5
[7,4,4] => 100 => [1,2] => [2,1] => 3
[7,4,3,1] => 1011 => [1,1,2] => [2,1,1] => 4
[7,4,2,2] => 1000 => [1,3] => [3,1] => 4
[7,4,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[7,4,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[7,3,3,2] => 1110 => [3,1] => [3,1] => 4
[7,3,3,1,1] => 11111 => [5] => [5] => 5
[7,3,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[7,3,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[7,3,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[7,2,2,2,2] => 10000 => [1,4] => [4,1] => 5
[7,2,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[7,2,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[7,2,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[7,1,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[6,6,3] => 001 => [2,1] => [2,1] => 3
[6,6,2,1] => 0001 => [3,1] => [3,1] => 4
[6,6,1,1,1] => 00111 => [2,3] => [3,2] => 5
[6,5,4] => 010 => [1,1,1] => [1,1,1] => 3
[6,5,3,1] => 0111 => [1,3] => [3,1] => 4
[6,5,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[6,5,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[6,5,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[6,4,4,1] => 0001 => [3,1] => [3,1] => 4
[6,4,3,2] => 0010 => [2,1,1] => [2,1,1] => 4
[6,4,3,1,1] => 00111 => [2,3] => [3,2] => 5
[6,4,2,2,1] => 00001 => [4,1] => [4,1] => 5
[6,4,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[6,4,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[6,3,3,3] => 0111 => [1,3] => [3,1] => 4
[6,3,3,2,1] => 01101 => [1,2,1,1] => [2,1,1,1] => 5
[6,3,3,1,1,1] => 011111 => [1,5] => [5,1] => 6
[6,3,2,2,2] => 01000 => [1,1,3] => [3,1,1] => 5
[6,3,2,2,1,1] => 010011 => [1,1,2,2] => [2,2,1,1] => 6
[6,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => [4,1,1,1] => 7
[6,3,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[6,2,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[6,2,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[6,2,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[6,2,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[6,1,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[5,5,5] => 111 => [3] => [3] => 3
[5,5,4,1] => 1101 => [2,1,1] => [2,1,1] => 4
[5,5,3,2] => 1110 => [3,1] => [3,1] => 4
[5,5,3,1,1] => 11111 => [5] => [5] => 5
[5,5,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[5,5,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[5,5,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[5,4,4,2] => 1000 => [1,3] => [3,1] => 4
[5,4,4,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[5,4,3,3] => 1011 => [1,1,2] => [2,1,1] => 4
[5,4,3,2,1] => 10101 => [1,1,1,1,1] => [1,1,1,1,1] => 5
[5,4,3,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[5,4,2,2,2] => 10000 => [1,4] => [4,1] => 5
[5,4,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[5,4,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[5,4,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[5,3,3,3,1] => 11111 => [5] => [5] => 5
[5,3,3,2,2] => 11100 => [3,2] => [3,2] => 5
[5,3,3,2,1,1] => 111011 => [3,1,2] => [3,2,1] => 6
[5,3,3,1,1,1,1] => 1111111 => [7] => [7] => 7
[5,3,2,2,2,1] => 110001 => [2,3,1] => [3,2,1] => 6
[5,3,2,2,1,1,1] => 1100111 => [2,2,3] => [3,2,2] => 7
[5,3,2,1,1,1,1,1] => 11011111 => [2,1,5] => [5,2,1] => 8
[5,3,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[5,2,2,2,2,2] => 100000 => [1,5] => [5,1] => 6
[5,2,2,2,2,1,1] => 1000011 => [1,4,2] => [4,2,1] => 7
[5,2,2,2,1,1,1,1] => 10001111 => [1,3,4] => [4,3,1] => 8
[5,2,2,1,1,1,1,1,1] => 100111111 => [1,2,6] => [6,2,1] => 9
[5,2,1,1,1,1,1,1,1,1] => 1011111111 => [1,1,8] => [8,1,1] => 10
[4,4,4,3] => 0001 => [3,1] => [3,1] => 4
[4,4,4,2,1] => 00001 => [4,1] => [4,1] => 5
[4,4,4,1,1,1] => 000111 => [3,3] => [3,3] => 6
[4,4,3,3,1] => 00111 => [2,3] => [3,2] => 5
[4,4,3,2,2] => 00100 => [2,1,2] => [2,2,1] => 5
[4,4,3,2,1,1] => 001011 => [2,1,1,2] => [2,2,1,1] => 6
[4,4,3,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[4,4,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[4,4,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[4,4,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[4,4,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[4,3,3,3,2] => 01110 => [1,3,1] => [3,1,1] => 5
[4,3,3,3,1,1] => 011111 => [1,5] => [5,1] => 6
[4,3,3,2,2,1] => 011001 => [1,2,2,1] => [2,2,1,1] => 6
[4,3,3,2,1,1,1] => 0110111 => [1,2,1,3] => [3,2,1,1] => 7
[4,3,3,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[4,3,2,2,2,2] => 010000 => [1,1,4] => [4,1,1] => 6
[4,3,2,2,2,1,1] => 0100011 => [1,1,3,2] => [3,2,1,1] => 7
[4,3,2,2,1,1,1,1] => 01001111 => [1,1,2,4] => [4,2,1,1] => 8
[4,3,2,1,1,1,1,1,1] => 010111111 => [1,1,1,6] => [6,1,1,1] => 9
[4,3,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[4,2,2,2,2,2,1] => 0000001 => [6,1] => [6,1] => 7
[4,2,2,2,2,1,1,1] => 00000111 => [5,3] => [5,3] => 8
[4,2,2,2,1,1,1,1,1] => 000011111 => [4,5] => [5,4] => 9
[4,2,2,1,1,1,1,1,1,1] => 0001111111 => [3,7] => [7,3] => 10
[3,3,3,3,3] => 11111 => [5] => [5] => 5
[3,3,3,3,2,1] => 111101 => [4,1,1] => [4,1,1] => 6
[3,3,3,3,1,1,1] => 1111111 => [7] => [7] => 7
[3,3,3,2,2,2] => 111000 => [3,3] => [3,3] => 6
[3,3,3,2,2,1,1] => 1110011 => [3,2,2] => [3,2,2] => 7
[3,3,3,2,1,1,1,1] => 11101111 => [3,1,4] => [4,3,1] => 8
[3,3,3,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[3,3,2,2,2,2,1] => 1100001 => [2,4,1] => [4,2,1] => 7
[3,3,2,2,2,1,1,1] => 11000111 => [2,3,3] => [3,3,2] => 8
[3,3,2,2,1,1,1,1,1] => 110011111 => [2,2,5] => [5,2,2] => 9
[3,3,2,1,1,1,1,1,1,1] => 1101111111 => [2,1,7] => [7,2,1] => 10
[3,2,2,2,2,2,2] => 1000000 => [1,6] => [6,1] => 7
[3,2,2,2,2,2,1,1] => 10000011 => [1,5,2] => [5,2,1] => 8
[3,2,2,2,2,1,1,1,1] => 100001111 => [1,4,4] => [4,4,1] => 9
[2,2,2,2,2,2,2,1] => 00000001 => [7,1] => [7,1] => 8
[2,2,2,2,2,2,1,1,1] => 000000111 => [6,3] => [6,3] => 9
[2,2,2,2,2,1,1,1,1,1] => 0000011111 => [5,5] => [5,5] => 10
[16] => 0 => [1] => [1] => 1
[15,1] => 11 => [2] => [2] => 2
[14,2] => 00 => [2] => [2] => 2
[14,1,1] => 011 => [1,2] => [2,1] => 3
[13,3] => 11 => [2] => [2] => 2
[13,2,1] => 101 => [1,1,1] => [1,1,1] => 3
[13,1,1,1] => 1111 => [4] => [4] => 4
[12,4] => 00 => [2] => [2] => 2
[12,3,1] => 011 => [1,2] => [2,1] => 3
[12,2,2] => 000 => [3] => [3] => 3
[12,2,1,1] => 0011 => [2,2] => [2,2] => 4
[12,1,1,1,1] => 01111 => [1,4] => [4,1] => 5
[11,5] => 11 => [2] => [2] => 2
[11,4,1] => 101 => [1,1,1] => [1,1,1] => 3
[11,3,2] => 110 => [2,1] => [2,1] => 3
[11,3,1,1] => 1111 => [4] => [4] => 4
[11,2,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[11,2,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[11,1,1,1,1,1] => 111111 => [6] => [6] => 6
[10,6] => 00 => [2] => [2] => 2
[10,5,1] => 011 => [1,2] => [2,1] => 3
[10,4,2] => 000 => [3] => [3] => 3
[10,4,1,1] => 0011 => [2,2] => [2,2] => 4
[10,3,3] => 011 => [1,2] => [2,1] => 3
[10,3,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[10,3,1,1,1] => 01111 => [1,4] => [4,1] => 5
[10,2,2,2] => 0000 => [4] => [4] => 4
[10,2,2,1,1] => 00011 => [3,2] => [3,2] => 5
[10,2,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[10,1,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[9,7] => 11 => [2] => [2] => 2
[9,6,1] => 101 => [1,1,1] => [1,1,1] => 3
[9,5,2] => 110 => [2,1] => [2,1] => 3
[9,5,1,1] => 1111 => [4] => [4] => 4
[9,4,3] => 101 => [1,1,1] => [1,1,1] => 3
[9,4,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[9,4,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[9,3,3,1] => 1111 => [4] => [4] => 4
[9,3,2,2] => 1100 => [2,2] => [2,2] => 4
[9,3,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[9,3,1,1,1,1] => 111111 => [6] => [6] => 6
[9,2,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[9,2,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[9,2,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[9,1,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[8,8] => 00 => [2] => [2] => 2
[8,7,1] => 011 => [1,2] => [2,1] => 3
[8,6,2] => 000 => [3] => [3] => 3
[8,6,1,1] => 0011 => [2,2] => [2,2] => 4
[8,5,3] => 011 => [1,2] => [2,1] => 3
[8,5,2,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[8,5,1,1,1] => 01111 => [1,4] => [4,1] => 5
[8,4,4] => 000 => [3] => [3] => 3
[8,4,3,1] => 0011 => [2,2] => [2,2] => 4
[8,4,2,2] => 0000 => [4] => [4] => 4
[8,4,2,1,1] => 00011 => [3,2] => [3,2] => 5
[8,4,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[8,3,3,2] => 0110 => [1,2,1] => [2,1,1] => 4
[8,3,3,1,1] => 01111 => [1,4] => [4,1] => 5
[8,3,2,2,1] => 01001 => [1,1,2,1] => [2,1,1,1] => 5
[8,3,2,1,1,1] => 010111 => [1,1,1,3] => [3,1,1,1] => 6
[8,3,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[8,2,2,2,2] => 00000 => [5] => [5] => 5
[8,2,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[8,2,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[8,2,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[8,1,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[7,7,2] => 110 => [2,1] => [2,1] => 3
[7,7,1,1] => 1111 => [4] => [4] => 4
[7,6,3] => 101 => [1,1,1] => [1,1,1] => 3
[7,6,2,1] => 1001 => [1,2,1] => [2,1,1] => 4
[7,6,1,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[7,5,4] => 110 => [2,1] => [2,1] => 3
[7,5,3,1] => 1111 => [4] => [4] => 4
[7,5,2,2] => 1100 => [2,2] => [2,2] => 4
[7,5,2,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[7,5,1,1,1,1] => 111111 => [6] => [6] => 6
[7,4,4,1] => 1001 => [1,2,1] => [2,1,1] => 4
[7,4,3,2] => 1010 => [1,1,1,1] => [1,1,1,1] => 4
[7,4,3,1,1] => 10111 => [1,1,3] => [3,1,1] => 5
[7,4,2,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[7,4,2,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[7,4,1,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[7,3,3,3] => 1111 => [4] => [4] => 4
[7,3,3,2,1] => 11101 => [3,1,1] => [3,1,1] => 5
[7,3,3,1,1,1] => 111111 => [6] => [6] => 6
[7,3,2,2,2] => 11000 => [2,3] => [3,2] => 5
[7,3,2,2,1,1] => 110011 => [2,2,2] => [2,2,2] => 6
[7,3,2,1,1,1,1] => 1101111 => [2,1,4] => [4,2,1] => 7
[7,3,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[7,2,2,2,2,1] => 100001 => [1,4,1] => [4,1,1] => 6
[7,2,2,2,1,1,1] => 1000111 => [1,3,3] => [3,3,1] => 7
[7,2,2,1,1,1,1,1] => 10011111 => [1,2,5] => [5,2,1] => 8
[7,2,1,1,1,1,1,1,1] => 101111111 => [1,1,7] => [7,1,1] => 9
[7,1,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[6,6,4] => 000 => [3] => [3] => 3
[6,6,3,1] => 0011 => [2,2] => [2,2] => 4
[6,6,2,2] => 0000 => [4] => [4] => 4
[6,6,2,1,1] => 00011 => [3,2] => [3,2] => 5
[6,6,1,1,1,1] => 001111 => [2,4] => [4,2] => 6
[6,5,5] => 011 => [1,2] => [2,1] => 3
[6,5,4,1] => 0101 => [1,1,1,1] => [1,1,1,1] => 4
[6,5,3,2] => 0110 => [1,2,1] => [2,1,1] => 4
[6,5,3,1,1] => 01111 => [1,4] => [4,1] => 5
[6,5,2,2,1] => 01001 => [1,1,2,1] => [2,1,1,1] => 5
[6,5,2,1,1,1] => 010111 => [1,1,1,3] => [3,1,1,1] => 6
[6,5,1,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[6,4,4,2] => 0000 => [4] => [4] => 4
[6,4,4,1,1] => 00011 => [3,2] => [3,2] => 5
[6,4,3,3] => 0011 => [2,2] => [2,2] => 4
[6,4,3,2,1] => 00101 => [2,1,1,1] => [2,1,1,1] => 5
[6,4,3,1,1,1] => 001111 => [2,4] => [4,2] => 6
[6,4,2,2,2] => 00000 => [5] => [5] => 5
[6,4,2,2,1,1] => 000011 => [4,2] => [4,2] => 6
[6,4,2,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[6,4,1,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[6,3,3,3,1] => 01111 => [1,4] => [4,1] => 5
[6,3,3,2,2] => 01100 => [1,2,2] => [2,2,1] => 5
[6,3,3,2,1,1] => 011011 => [1,2,1,2] => [2,2,1,1] => 6
[6,3,3,1,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[6,3,2,2,2,1] => 010001 => [1,1,3,1] => [3,1,1,1] => 6
[6,3,2,2,1,1,1] => 0100111 => [1,1,2,3] => [3,2,1,1] => 7
[6,3,2,1,1,1,1,1] => 01011111 => [1,1,1,5] => [5,1,1,1] => 8
[6,3,1,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[6,2,2,2,2,2] => 000000 => [6] => [6] => 6
[6,2,2,2,2,1,1] => 0000011 => [5,2] => [5,2] => 7
[6,2,2,2,1,1,1,1] => 00001111 => [4,4] => [4,4] => 8
[6,2,2,1,1,1,1,1,1] => 000111111 => [3,6] => [6,3] => 9
[6,2,1,1,1,1,1,1,1,1] => 0011111111 => [2,8] => [8,2] => 10
[5,5,5,1] => 1111 => [4] => [4] => 4
[5,5,4,2] => 1100 => [2,2] => [2,2] => 4
[5,5,4,1,1] => 11011 => [2,1,2] => [2,2,1] => 5
[5,5,3,3] => 1111 => [4] => [4] => 4
[5,5,3,2,1] => 11101 => [3,1,1] => [3,1,1] => 5
[5,5,3,1,1,1] => 111111 => [6] => [6] => 6
[5,5,2,2,2] => 11000 => [2,3] => [3,2] => 5
[5,5,2,2,1,1] => 110011 => [2,2,2] => [2,2,2] => 6
[5,5,2,1,1,1,1] => 1101111 => [2,1,4] => [4,2,1] => 7
[5,5,1,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[5,4,4,3] => 1001 => [1,2,1] => [2,1,1] => 4
[5,4,4,2,1] => 10001 => [1,3,1] => [3,1,1] => 5
[5,4,4,1,1,1] => 100111 => [1,2,3] => [3,2,1] => 6
[5,4,3,3,1] => 10111 => [1,1,3] => [3,1,1] => 5
[5,4,3,2,2] => 10100 => [1,1,1,2] => [2,1,1,1] => 5
[5,4,3,2,1,1] => 101011 => [1,1,1,1,2] => [2,1,1,1,1] => 6
[5,4,3,1,1,1,1] => 1011111 => [1,1,5] => [5,1,1] => 7
[5,4,2,2,2,1] => 100001 => [1,4,1] => [4,1,1] => 6
[5,4,2,2,1,1,1] => 1000111 => [1,3,3] => [3,3,1] => 7
[5,4,2,1,1,1,1,1] => 10011111 => [1,2,5] => [5,2,1] => 8
[5,4,1,1,1,1,1,1,1] => 101111111 => [1,1,7] => [7,1,1] => 9
[5,3,3,3,2] => 11110 => [4,1] => [4,1] => 5
[5,3,3,3,1,1] => 111111 => [6] => [6] => 6
[5,3,3,2,2,1] => 111001 => [3,2,1] => [3,2,1] => 6
[5,3,3,2,1,1,1] => 1110111 => [3,1,3] => [3,3,1] => 7
[5,3,3,1,1,1,1,1] => 11111111 => [8] => [8] => 8
[5,3,2,2,2,2] => 110000 => [2,4] => [4,2] => 6
[5,3,2,2,2,1,1] => 1100011 => [2,3,2] => [3,2,2] => 7
[5,3,2,2,1,1,1,1] => 11001111 => [2,2,4] => [4,2,2] => 8
[5,3,2,1,1,1,1,1,1] => 110111111 => [2,1,6] => [6,2,1] => 9
[5,3,1,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[5,2,2,2,2,2,1] => 1000001 => [1,5,1] => [5,1,1] => 7
[5,2,2,2,2,1,1,1] => 10000111 => [1,4,3] => [4,3,1] => 8
[5,2,2,2,1,1,1,1,1] => 100011111 => [1,3,5] => [5,3,1] => 9
[4,4,4,4] => 0000 => [4] => [4] => 4
[4,4,4,3,1] => 00011 => [3,2] => [3,2] => 5
[4,4,4,2,2] => 00000 => [5] => [5] => 5
[4,4,4,2,1,1] => 000011 => [4,2] => [4,2] => 6
[4,4,4,1,1,1,1] => 0001111 => [3,4] => [4,3] => 7
[4,4,3,3,2] => 00110 => [2,2,1] => [2,2,1] => 5
[4,4,3,3,1,1] => 001111 => [2,4] => [4,2] => 6
[4,4,3,2,2,1] => 001001 => [2,1,2,1] => [2,2,1,1] => 6
[4,4,3,2,1,1,1] => 0010111 => [2,1,1,3] => [3,2,1,1] => 7
[4,4,3,1,1,1,1,1] => 00111111 => [2,6] => [6,2] => 8
[4,4,2,2,2,2] => 000000 => [6] => [6] => 6
[4,4,2,2,2,1,1] => 0000011 => [5,2] => [5,2] => 7
[4,4,2,2,1,1,1,1] => 00001111 => [4,4] => [4,4] => 8
[4,4,2,1,1,1,1,1,1] => 000111111 => [3,6] => [6,3] => 9
[4,4,1,1,1,1,1,1,1,1] => 0011111111 => [2,8] => [8,2] => 10
[4,3,3,3,3] => 01111 => [1,4] => [4,1] => 5
[4,3,3,3,2,1] => 011101 => [1,3,1,1] => [3,1,1,1] => 6
[4,3,3,3,1,1,1] => 0111111 => [1,6] => [6,1] => 7
[4,3,3,2,2,2] => 011000 => [1,2,3] => [3,2,1] => 6
[4,3,3,2,2,1,1] => 0110011 => [1,2,2,2] => [2,2,2,1] => 7
[4,3,3,2,1,1,1,1] => 01101111 => [1,2,1,4] => [4,2,1,1] => 8
[4,3,3,1,1,1,1,1,1] => 011111111 => [1,8] => [8,1] => 9
[4,3,2,2,2,2,1] => 0100001 => [1,1,4,1] => [4,1,1,1] => 7
[4,3,2,2,2,1,1,1] => 01000111 => [1,1,3,3] => [3,3,1,1] => 8
[4,3,2,2,1,1,1,1,1] => 010011111 => [1,1,2,5] => [5,2,1,1] => 9
[4,3,2,1,1,1,1,1,1,1] => 0101111111 => [1,1,1,7] => [7,1,1,1] => 10
[4,2,2,2,2,2,2] => 0000000 => [7] => [7] => 7
[4,2,2,2,2,2,1,1] => 00000011 => [6,2] => [6,2] => 8
[4,2,2,2,2,1,1,1,1] => 000001111 => [5,4] => [5,4] => 9
[4,2,2,2,1,1,1,1,1,1] => 0000111111 => [4,6] => [6,4] => 10
[3,3,3,3,3,1] => 111111 => [6] => [6] => 6
[3,3,3,3,2,2] => 111100 => [4,2] => [4,2] => 6
[3,3,3,3,2,1,1] => 1111011 => [4,1,2] => [4,2,1] => 7
[3,3,3,3,1,1,1,1] => 11111111 => [8] => [8] => 8
[3,3,3,2,2,2,1] => 1110001 => [3,3,1] => [3,3,1] => 7
[3,3,3,2,2,1,1,1] => 11100111 => [3,2,3] => [3,3,2] => 8
[3,3,3,2,1,1,1,1,1] => 111011111 => [3,1,5] => [5,3,1] => 9
[3,3,3,1,1,1,1,1,1,1] => 1111111111 => [10] => [10] => 10
[3,3,2,2,2,2,2] => 1100000 => [2,5] => [5,2] => 7
[3,3,2,2,2,2,1,1] => 11000011 => [2,4,2] => [4,2,2] => 8
[3,3,2,2,2,1,1,1,1] => 110001111 => [2,3,4] => [4,3,2] => 9
[3,3,2,2,1,1,1,1,1,1] => 1100111111 => [2,2,6] => [6,2,2] => 10
[3,2,2,2,2,2,2,1] => 10000001 => [1,6,1] => [6,1,1] => 8
[3,2,2,2,2,2,1,1,1] => 100000111 => [1,5,3] => [5,3,1] => 9
[3,2,2,2,2,1,1,1,1,1] => 1000011111 => [1,4,5] => [5,4,1] => 10
[2,2,2,2,2,2,2,2] => 00000000 => [8] => [8] => 8
[2,2,2,2,2,2,2,1,1] => 000000011 => [7,2] => [7,2] => 9
[2,2,2,2,2,2,1,1,1,1] => 0000001111 => [6,4] => [6,4] => 10
[17] => 1 => [1] => [1] => 1
[16,1] => 01 => [1,1] => [1,1] => 2
[15,2] => 10 => [1,1] => [1,1] => 2
[15,1,1] => 111 => [3] => [3] => 3
[14,3] => 01 => [1,1] => [1,1] => 2
[14,2,1] => 001 => [2,1] => [2,1] => 3
[14,1,1,1] => 0111 => [1,3] => [3,1] => 4
[13,4] => 10 => [1,1] => [1,1] => 2
[13,3,1] => 111 => [3] => [3] => 3
[13,2,2] => 100 => [1,2] => [2,1] => 3
[13,2,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[13,1,1,1,1] => 11111 => [5] => [5] => 5
[12,5] => 01 => [1,1] => [1,1] => 2
[12,4,1] => 001 => [2,1] => [2,1] => 3
[12,3,2] => 010 => [1,1,1] => [1,1,1] => 3
[12,3,1,1] => 0111 => [1,3] => [3,1] => 4
[12,2,2,1] => 0001 => [3,1] => [3,1] => 4
[12,2,1,1,1] => 00111 => [2,3] => [3,2] => 5
[12,1,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[11,6] => 10 => [1,1] => [1,1] => 2
[11,5,1] => 111 => [3] => [3] => 3
[11,4,2] => 100 => [1,2] => [2,1] => 3
[11,4,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[11,3,3] => 111 => [3] => [3] => 3
[11,3,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[11,3,1,1,1] => 11111 => [5] => [5] => 5
[11,2,2,2] => 1000 => [1,3] => [3,1] => 4
[11,2,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[11,2,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[11,1,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[10,7] => 01 => [1,1] => [1,1] => 2
[10,6,1] => 001 => [2,1] => [2,1] => 3
[10,5,2] => 010 => [1,1,1] => [1,1,1] => 3
[10,5,1,1] => 0111 => [1,3] => [3,1] => 4
[10,4,3] => 001 => [2,1] => [2,1] => 3
[10,4,2,1] => 0001 => [3,1] => [3,1] => 4
[10,4,1,1,1] => 00111 => [2,3] => [3,2] => 5
[10,3,3,1] => 0111 => [1,3] => [3,1] => 4
[10,3,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[10,3,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[10,3,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[10,2,2,2,1] => 00001 => [4,1] => [4,1] => 5
[10,2,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[10,2,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[10,1,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[9,8] => 10 => [1,1] => [1,1] => 2
[9,7,1] => 111 => [3] => [3] => 3
[9,6,2] => 100 => [1,2] => [2,1] => 3
[9,6,1,1] => 1011 => [1,1,2] => [2,1,1] => 4
[9,5,3] => 111 => [3] => [3] => 3
[9,5,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[9,5,1,1,1] => 11111 => [5] => [5] => 5
[9,4,4] => 100 => [1,2] => [2,1] => 3
[9,4,3,1] => 1011 => [1,1,2] => [2,1,1] => 4
[9,4,2,2] => 1000 => [1,3] => [3,1] => 4
[9,4,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[9,4,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[9,3,3,2] => 1110 => [3,1] => [3,1] => 4
[9,3,3,1,1] => 11111 => [5] => [5] => 5
[9,3,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[9,3,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[9,3,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[9,2,2,2,2] => 10000 => [1,4] => [4,1] => 5
[9,2,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[9,2,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[9,2,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[9,1,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[8,8,1] => 001 => [2,1] => [2,1] => 3
[8,7,2] => 010 => [1,1,1] => [1,1,1] => 3
[8,7,1,1] => 0111 => [1,3] => [3,1] => 4
[8,6,3] => 001 => [2,1] => [2,1] => 3
[8,6,2,1] => 0001 => [3,1] => [3,1] => 4
[8,6,1,1,1] => 00111 => [2,3] => [3,2] => 5
[8,5,4] => 010 => [1,1,1] => [1,1,1] => 3
[8,5,3,1] => 0111 => [1,3] => [3,1] => 4
[8,5,2,2] => 0100 => [1,1,2] => [2,1,1] => 4
[8,5,2,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[8,5,1,1,1,1] => 011111 => [1,5] => [5,1] => 6
[8,4,4,1] => 0001 => [3,1] => [3,1] => 4
[8,4,3,2] => 0010 => [2,1,1] => [2,1,1] => 4
[8,4,3,1,1] => 00111 => [2,3] => [3,2] => 5
[8,4,2,2,1] => 00001 => [4,1] => [4,1] => 5
[8,4,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[8,4,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[8,3,3,3] => 0111 => [1,3] => [3,1] => 4
[8,3,3,2,1] => 01101 => [1,2,1,1] => [2,1,1,1] => 5
[8,3,3,1,1,1] => 011111 => [1,5] => [5,1] => 6
[8,3,2,2,2] => 01000 => [1,1,3] => [3,1,1] => 5
[8,3,2,2,1,1] => 010011 => [1,1,2,2] => [2,2,1,1] => 6
[8,3,2,1,1,1,1] => 0101111 => [1,1,1,4] => [4,1,1,1] => 7
[8,3,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[8,2,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[8,2,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[8,2,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[8,2,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[8,1,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[7,7,3] => 111 => [3] => [3] => 3
[7,7,2,1] => 1101 => [2,1,1] => [2,1,1] => 4
[7,7,1,1,1] => 11111 => [5] => [5] => 5
[7,6,4] => 100 => [1,2] => [2,1] => 3
[7,6,3,1] => 1011 => [1,1,2] => [2,1,1] => 4
[7,6,2,2] => 1000 => [1,3] => [3,1] => 4
[7,6,2,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[7,6,1,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[7,5,5] => 111 => [3] => [3] => 3
[7,5,4,1] => 1101 => [2,1,1] => [2,1,1] => 4
[7,5,3,2] => 1110 => [3,1] => [3,1] => 4
[7,5,3,1,1] => 11111 => [5] => [5] => 5
[7,5,2,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[7,5,2,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[7,5,1,1,1,1,1] => 1111111 => [7] => [7] => 7
[7,4,4,2] => 1000 => [1,3] => [3,1] => 4
[7,4,4,1,1] => 10011 => [1,2,2] => [2,2,1] => 5
[7,4,3,3] => 1011 => [1,1,2] => [2,1,1] => 4
[7,4,3,2,1] => 10101 => [1,1,1,1,1] => [1,1,1,1,1] => 5
[7,4,3,1,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[7,4,2,2,2] => 10000 => [1,4] => [4,1] => 5
[7,4,2,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[7,4,2,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[7,4,1,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[7,3,3,3,1] => 11111 => [5] => [5] => 5
[7,3,3,2,2] => 11100 => [3,2] => [3,2] => 5
[7,3,3,2,1,1] => 111011 => [3,1,2] => [3,2,1] => 6
[7,3,3,1,1,1,1] => 1111111 => [7] => [7] => 7
[7,3,2,2,2,1] => 110001 => [2,3,1] => [3,2,1] => 6
[7,3,2,2,1,1,1] => 1100111 => [2,2,3] => [3,2,2] => 7
[7,3,2,1,1,1,1,1] => 11011111 => [2,1,5] => [5,2,1] => 8
[7,3,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[7,2,2,2,2,2] => 100000 => [1,5] => [5,1] => 6
[7,2,2,2,2,1,1] => 1000011 => [1,4,2] => [4,2,1] => 7
[7,2,2,2,1,1,1,1] => 10001111 => [1,3,4] => [4,3,1] => 8
[7,2,2,1,1,1,1,1,1] => 100111111 => [1,2,6] => [6,2,1] => 9
[7,2,1,1,1,1,1,1,1,1] => 1011111111 => [1,1,8] => [8,1,1] => 10
[6,6,5] => 001 => [2,1] => [2,1] => 3
[6,6,4,1] => 0001 => [3,1] => [3,1] => 4
[6,6,3,2] => 0010 => [2,1,1] => [2,1,1] => 4
[6,6,3,1,1] => 00111 => [2,3] => [3,2] => 5
[6,6,2,2,1] => 00001 => [4,1] => [4,1] => 5
[6,6,2,1,1,1] => 000111 => [3,3] => [3,3] => 6
[6,6,1,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[6,5,5,1] => 0111 => [1,3] => [3,1] => 4
[6,5,4,2] => 0100 => [1,1,2] => [2,1,1] => 4
[6,5,4,1,1] => 01011 => [1,1,1,2] => [2,1,1,1] => 5
[6,5,3,3] => 0111 => [1,3] => [3,1] => 4
[6,5,3,2,1] => 01101 => [1,2,1,1] => [2,1,1,1] => 5
[6,5,3,1,1,1] => 011111 => [1,5] => [5,1] => 6
[6,5,2,2,2] => 01000 => [1,1,3] => [3,1,1] => 5
[6,5,2,2,1,1] => 010011 => [1,1,2,2] => [2,2,1,1] => 6
[6,5,2,1,1,1,1] => 0101111 => [1,1,1,4] => [4,1,1,1] => 7
[6,5,1,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[6,4,4,3] => 0001 => [3,1] => [3,1] => 4
[6,4,4,2,1] => 00001 => [4,1] => [4,1] => 5
[6,4,4,1,1,1] => 000111 => [3,3] => [3,3] => 6
[6,4,3,3,1] => 00111 => [2,3] => [3,2] => 5
[6,4,3,2,2] => 00100 => [2,1,2] => [2,2,1] => 5
[6,4,3,2,1,1] => 001011 => [2,1,1,2] => [2,2,1,1] => 6
[6,4,3,1,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[6,4,2,2,2,1] => 000001 => [5,1] => [5,1] => 6
[6,4,2,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[6,4,2,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[6,4,1,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[6,3,3,3,2] => 01110 => [1,3,1] => [3,1,1] => 5
[6,3,3,3,1,1] => 011111 => [1,5] => [5,1] => 6
[6,3,3,2,2,1] => 011001 => [1,2,2,1] => [2,2,1,1] => 6
[6,3,3,2,1,1,1] => 0110111 => [1,2,1,3] => [3,2,1,1] => 7
[6,3,3,1,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[6,3,2,2,2,2] => 010000 => [1,1,4] => [4,1,1] => 6
[6,3,2,2,2,1,1] => 0100011 => [1,1,3,2] => [3,2,1,1] => 7
[6,3,2,2,1,1,1,1] => 01001111 => [1,1,2,4] => [4,2,1,1] => 8
[6,3,2,1,1,1,1,1,1] => 010111111 => [1,1,1,6] => [6,1,1,1] => 9
[6,3,1,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[6,2,2,2,2,2,1] => 0000001 => [6,1] => [6,1] => 7
[6,2,2,2,2,1,1,1] => 00000111 => [5,3] => [5,3] => 8
[6,2,2,2,1,1,1,1,1] => 000011111 => [4,5] => [5,4] => 9
[6,2,2,1,1,1,1,1,1,1] => 0001111111 => [3,7] => [7,3] => 10
[5,5,5,2] => 1110 => [3,1] => [3,1] => 4
[5,5,5,1,1] => 11111 => [5] => [5] => 5
[5,5,4,3] => 1101 => [2,1,1] => [2,1,1] => 4
[5,5,4,2,1] => 11001 => [2,2,1] => [2,2,1] => 5
[5,5,4,1,1,1] => 110111 => [2,1,3] => [3,2,1] => 6
[5,5,3,3,1] => 11111 => [5] => [5] => 5
[5,5,3,2,2] => 11100 => [3,2] => [3,2] => 5
[5,5,3,2,1,1] => 111011 => [3,1,2] => [3,2,1] => 6
[5,5,3,1,1,1,1] => 1111111 => [7] => [7] => 7
[5,5,2,2,2,1] => 110001 => [2,3,1] => [3,2,1] => 6
[5,5,2,2,1,1,1] => 1100111 => [2,2,3] => [3,2,2] => 7
[5,5,2,1,1,1,1,1] => 11011111 => [2,1,5] => [5,2,1] => 8
[5,5,1,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[5,4,4,4] => 1000 => [1,3] => [3,1] => 4
[5,4,4,3,1] => 10011 => [1,2,2] => [2,2,1] => 5
[5,4,4,2,2] => 10000 => [1,4] => [4,1] => 5
[5,4,4,2,1,1] => 100011 => [1,3,2] => [3,2,1] => 6
[5,4,4,1,1,1,1] => 1001111 => [1,2,4] => [4,2,1] => 7
[5,4,3,3,2] => 10110 => [1,1,2,1] => [2,1,1,1] => 5
[5,4,3,3,1,1] => 101111 => [1,1,4] => [4,1,1] => 6
[5,4,3,2,2,1] => 101001 => [1,1,1,2,1] => [2,1,1,1,1] => 6
[5,4,3,2,1,1,1] => 1010111 => [1,1,1,1,3] => [3,1,1,1,1] => 7
[5,4,3,1,1,1,1,1] => 10111111 => [1,1,6] => [6,1,1] => 8
[5,4,2,2,2,2] => 100000 => [1,5] => [5,1] => 6
[5,4,2,2,2,1,1] => 1000011 => [1,4,2] => [4,2,1] => 7
[5,4,2,2,1,1,1,1] => 10001111 => [1,3,4] => [4,3,1] => 8
[5,4,2,1,1,1,1,1,1] => 100111111 => [1,2,6] => [6,2,1] => 9
[5,4,1,1,1,1,1,1,1,1] => 1011111111 => [1,1,8] => [8,1,1] => 10
[5,3,3,3,3] => 11111 => [5] => [5] => 5
[5,3,3,3,2,1] => 111101 => [4,1,1] => [4,1,1] => 6
[5,3,3,3,1,1,1] => 1111111 => [7] => [7] => 7
[5,3,3,2,2,2] => 111000 => [3,3] => [3,3] => 6
[5,3,3,2,2,1,1] => 1110011 => [3,2,2] => [3,2,2] => 7
[5,3,3,2,1,1,1,1] => 11101111 => [3,1,4] => [4,3,1] => 8
[5,3,3,1,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[5,3,2,2,2,2,1] => 1100001 => [2,4,1] => [4,2,1] => 7
[5,3,2,2,2,1,1,1] => 11000111 => [2,3,3] => [3,3,2] => 8
[5,3,2,2,1,1,1,1,1] => 110011111 => [2,2,5] => [5,2,2] => 9
[5,3,2,1,1,1,1,1,1,1] => 1101111111 => [2,1,7] => [7,2,1] => 10
[5,2,2,2,2,2,2] => 1000000 => [1,6] => [6,1] => 7
[5,2,2,2,2,2,1,1] => 10000011 => [1,5,2] => [5,2,1] => 8
[5,2,2,2,2,1,1,1,1] => 100001111 => [1,4,4] => [4,4,1] => 9
[4,4,4,4,1] => 00001 => [4,1] => [4,1] => 5
[4,4,4,3,2] => 00010 => [3,1,1] => [3,1,1] => 5
[4,4,4,3,1,1] => 000111 => [3,3] => [3,3] => 6
[4,4,4,2,2,1] => 000001 => [5,1] => [5,1] => 6
[4,4,4,2,1,1,1] => 0000111 => [4,3] => [4,3] => 7
[4,4,4,1,1,1,1,1] => 00011111 => [3,5] => [5,3] => 8
[4,4,3,3,3] => 00111 => [2,3] => [3,2] => 5
[4,4,3,3,2,1] => 001101 => [2,2,1,1] => [2,2,1,1] => 6
[4,4,3,3,1,1,1] => 0011111 => [2,5] => [5,2] => 7
[4,4,3,2,2,2] => 001000 => [2,1,3] => [3,2,1] => 6
[4,4,3,2,2,1,1] => 0010011 => [2,1,2,2] => [2,2,2,1] => 7
[4,4,3,2,1,1,1,1] => 00101111 => [2,1,1,4] => [4,2,1,1] => 8
[4,4,3,1,1,1,1,1,1] => 001111111 => [2,7] => [7,2] => 9
[4,4,2,2,2,2,1] => 0000001 => [6,1] => [6,1] => 7
[4,4,2,2,2,1,1,1] => 00000111 => [5,3] => [5,3] => 8
[4,4,2,2,1,1,1,1,1] => 000011111 => [4,5] => [5,4] => 9
[4,4,2,1,1,1,1,1,1,1] => 0001111111 => [3,7] => [7,3] => 10
[4,3,3,3,3,1] => 011111 => [1,5] => [5,1] => 6
[4,3,3,3,2,2] => 011100 => [1,3,2] => [3,2,1] => 6
[4,3,3,3,2,1,1] => 0111011 => [1,3,1,2] => [3,2,1,1] => 7
[4,3,3,3,1,1,1,1] => 01111111 => [1,7] => [7,1] => 8
[4,3,3,2,2,2,1] => 0110001 => [1,2,3,1] => [3,2,1,1] => 7
[4,3,3,2,2,1,1,1] => 01100111 => [1,2,2,3] => [3,2,2,1] => 8
[4,3,3,2,1,1,1,1,1] => 011011111 => [1,2,1,5] => [5,2,1,1] => 9
[4,3,3,1,1,1,1,1,1,1] => 0111111111 => [1,9] => [9,1] => 10
[4,3,2,2,2,2,2] => 0100000 => [1,1,5] => [5,1,1] => 7
[4,3,2,2,2,2,1,1] => 01000011 => [1,1,4,2] => [4,2,1,1] => 8
[4,3,2,2,2,1,1,1,1] => 010001111 => [1,1,3,4] => [4,3,1,1] => 9
[4,3,2,2,1,1,1,1,1,1] => 0100111111 => [1,1,2,6] => [6,2,1,1] => 10
[4,2,2,2,2,2,2,1] => 00000001 => [7,1] => [7,1] => 8
[4,2,2,2,2,2,1,1,1] => 000000111 => [6,3] => [6,3] => 9
[4,2,2,2,2,1,1,1,1,1] => 0000011111 => [5,5] => [5,5] => 10
[3,3,3,3,3,2] => 111110 => [5,1] => [5,1] => 6
[3,3,3,3,3,1,1] => 1111111 => [7] => [7] => 7
[3,3,3,3,2,2,1] => 1111001 => [4,2,1] => [4,2,1] => 7
[3,3,3,3,2,1,1,1] => 11110111 => [4,1,3] => [4,3,1] => 8
[3,3,3,3,1,1,1,1,1] => 111111111 => [9] => [9] => 9
[3,3,3,2,2,2,2] => 1110000 => [3,4] => [4,3] => 7
[3,3,3,2,2,2,1,1] => 11100011 => [3,3,2] => [3,3,2] => 8
[3,3,3,2,2,1,1,1,1] => 111001111 => [3,2,4] => [4,3,2] => 9
[3,3,3,2,1,1,1,1,1,1] => 1110111111 => [3,1,6] => [6,3,1] => 10
[3,3,2,2,2,2,2,1] => 11000001 => [2,5,1] => [5,2,1] => 8
[3,3,2,2,2,2,1,1,1] => 110000111 => [2,4,3] => [4,3,2] => 9
[3,2,2,2,2,2,2,2] => 10000000 => [1,7] => [7,1] => 8
[3,2,2,2,2,2,2,1,1] => 100000011 => [1,6,2] => [6,2,1] => 9
[3,2,2,2,2,2,1,1,1,1] => 1000001111 => [1,5,4] => [5,4,1] => 10
[2,2,2,2,2,2,2,2,1] => 000000001 => [8,1] => [8,1] => 9
[2,2,2,2,2,2,2,1,1,1] => 0000000111 => [7,3] => [7,3] => 10
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Description
The size of a partition.
This statistic is the constant statistic of the level sets.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.