Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000225: Integer partitions ⟶ ℤ
Values
0 => [1] => [1] => 0
1 => [1] => [1] => 0
00 => [2] => [2] => 0
01 => [1,1] => [1,1] => 0
10 => [1,1] => [1,1] => 0
11 => [2] => [2] => 0
000 => [3] => [3] => 0
001 => [2,1] => [2,1] => 1
010 => [1,1,1] => [1,1,1] => 0
011 => [1,2] => [2,1] => 1
100 => [1,2] => [2,1] => 1
101 => [1,1,1] => [1,1,1] => 0
110 => [2,1] => [2,1] => 1
111 => [3] => [3] => 0
0000 => [4] => [4] => 0
0001 => [3,1] => [3,1] => 2
0010 => [2,1,1] => [2,1,1] => 1
0011 => [2,2] => [2,2] => 0
0100 => [1,1,2] => [2,1,1] => 1
0101 => [1,1,1,1] => [1,1,1,1] => 0
0110 => [1,2,1] => [2,1,1] => 1
0111 => [1,3] => [3,1] => 2
1000 => [1,3] => [3,1] => 2
1001 => [1,2,1] => [2,1,1] => 1
1010 => [1,1,1,1] => [1,1,1,1] => 0
1011 => [1,1,2] => [2,1,1] => 1
1100 => [2,2] => [2,2] => 0
1101 => [2,1,1] => [2,1,1] => 1
1110 => [3,1] => [3,1] => 2
1111 => [4] => [4] => 0
00000 => [5] => [5] => 0
00001 => [4,1] => [4,1] => 3
00010 => [3,1,1] => [3,1,1] => 2
00011 => [3,2] => [3,2] => 1
00100 => [2,1,2] => [2,2,1] => 1
00101 => [2,1,1,1] => [2,1,1,1] => 1
00110 => [2,2,1] => [2,2,1] => 1
00111 => [2,3] => [3,2] => 1
01000 => [1,1,3] => [3,1,1] => 2
01001 => [1,1,2,1] => [2,1,1,1] => 1
01010 => [1,1,1,1,1] => [1,1,1,1,1] => 0
01011 => [1,1,1,2] => [2,1,1,1] => 1
01100 => [1,2,2] => [2,2,1] => 1
01101 => [1,2,1,1] => [2,1,1,1] => 1
01110 => [1,3,1] => [3,1,1] => 2
01111 => [1,4] => [4,1] => 3
10000 => [1,4] => [4,1] => 3
10001 => [1,3,1] => [3,1,1] => 2
10010 => [1,2,1,1] => [2,1,1,1] => 1
10011 => [1,2,2] => [2,2,1] => 1
10100 => [1,1,1,2] => [2,1,1,1] => 1
10101 => [1,1,1,1,1] => [1,1,1,1,1] => 0
10110 => [1,1,2,1] => [2,1,1,1] => 1
10111 => [1,1,3] => [3,1,1] => 2
11000 => [2,3] => [3,2] => 1
11001 => [2,2,1] => [2,2,1] => 1
11010 => [2,1,1,1] => [2,1,1,1] => 1
11011 => [2,1,2] => [2,2,1] => 1
11100 => [3,2] => [3,2] => 1
11101 => [3,1,1] => [3,1,1] => 2
11110 => [4,1] => [4,1] => 3
11111 => [5] => [5] => 0
000000 => [6] => [6] => 0
000001 => [5,1] => [5,1] => 4
000010 => [4,1,1] => [4,1,1] => 3
000011 => [4,2] => [4,2] => 2
000100 => [3,1,2] => [3,2,1] => 2
000101 => [3,1,1,1] => [3,1,1,1] => 2
000110 => [3,2,1] => [3,2,1] => 2
000111 => [3,3] => [3,3] => 0
001000 => [2,1,3] => [3,2,1] => 2
001001 => [2,1,2,1] => [2,2,1,1] => 1
001010 => [2,1,1,1,1] => [2,1,1,1,1] => 1
001011 => [2,1,1,2] => [2,2,1,1] => 1
001100 => [2,2,2] => [2,2,2] => 0
001101 => [2,2,1,1] => [2,2,1,1] => 1
001110 => [2,3,1] => [3,2,1] => 2
001111 => [2,4] => [4,2] => 2
010000 => [1,1,4] => [4,1,1] => 3
010001 => [1,1,3,1] => [3,1,1,1] => 2
010010 => [1,1,2,1,1] => [2,1,1,1,1] => 1
010011 => [1,1,2,2] => [2,2,1,1] => 1
010100 => [1,1,1,1,2] => [2,1,1,1,1] => 1
010101 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010110 => [1,1,1,2,1] => [2,1,1,1,1] => 1
010111 => [1,1,1,3] => [3,1,1,1] => 2
011000 => [1,2,3] => [3,2,1] => 2
011001 => [1,2,2,1] => [2,2,1,1] => 1
011010 => [1,2,1,1,1] => [2,1,1,1,1] => 1
011011 => [1,2,1,2] => [2,2,1,1] => 1
011100 => [1,3,2] => [3,2,1] => 2
011101 => [1,3,1,1] => [3,1,1,1] => 2
011110 => [1,4,1] => [4,1,1] => 3
011111 => [1,5] => [5,1] => 4
100000 => [1,5] => [5,1] => 4
100001 => [1,4,1] => [4,1,1] => 3
100010 => [1,3,1,1] => [3,1,1,1] => 2
100011 => [1,3,2] => [3,2,1] => 2
100100 => [1,2,1,2] => [2,2,1,1] => 1
100101 => [1,2,1,1,1] => [2,1,1,1,1] => 1
100110 => [1,2,2,1] => [2,2,1,1] => 1
>>> Load all 1810 entries. <<<100111 => [1,2,3] => [3,2,1] => 2
101000 => [1,1,1,3] => [3,1,1,1] => 2
101001 => [1,1,1,2,1] => [2,1,1,1,1] => 1
101010 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101011 => [1,1,1,1,2] => [2,1,1,1,1] => 1
101100 => [1,1,2,2] => [2,2,1,1] => 1
101101 => [1,1,2,1,1] => [2,1,1,1,1] => 1
101110 => [1,1,3,1] => [3,1,1,1] => 2
101111 => [1,1,4] => [4,1,1] => 3
110000 => [2,4] => [4,2] => 2
110001 => [2,3,1] => [3,2,1] => 2
110010 => [2,2,1,1] => [2,2,1,1] => 1
110011 => [2,2,2] => [2,2,2] => 0
110100 => [2,1,1,2] => [2,2,1,1] => 1
110101 => [2,1,1,1,1] => [2,1,1,1,1] => 1
110110 => [2,1,2,1] => [2,2,1,1] => 1
110111 => [2,1,3] => [3,2,1] => 2
111000 => [3,3] => [3,3] => 0
111001 => [3,2,1] => [3,2,1] => 2
111010 => [3,1,1,1] => [3,1,1,1] => 2
111011 => [3,1,2] => [3,2,1] => 2
111100 => [4,2] => [4,2] => 2
111101 => [4,1,1] => [4,1,1] => 3
111110 => [5,1] => [5,1] => 4
111111 => [6] => [6] => 0
0000000 => [7] => [7] => 0
0000001 => [6,1] => [6,1] => 5
0000010 => [5,1,1] => [5,1,1] => 4
0000011 => [5,2] => [5,2] => 3
0000100 => [4,1,2] => [4,2,1] => 3
0000101 => [4,1,1,1] => [4,1,1,1] => 3
0000110 => [4,2,1] => [4,2,1] => 3
0000111 => [4,3] => [4,3] => 1
0001000 => [3,1,3] => [3,3,1] => 2
0001001 => [3,1,2,1] => [3,2,1,1] => 2
0001010 => [3,1,1,1,1] => [3,1,1,1,1] => 2
0001011 => [3,1,1,2] => [3,2,1,1] => 2
0001100 => [3,2,2] => [3,2,2] => 1
0001101 => [3,2,1,1] => [3,2,1,1] => 2
0001110 => [3,3,1] => [3,3,1] => 2
0001111 => [3,4] => [4,3] => 1
0010000 => [2,1,4] => [4,2,1] => 3
0010001 => [2,1,3,1] => [3,2,1,1] => 2
0010010 => [2,1,2,1,1] => [2,2,1,1,1] => 1
0010011 => [2,1,2,2] => [2,2,2,1] => 1
0010100 => [2,1,1,1,2] => [2,2,1,1,1] => 1
0010101 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
0010110 => [2,1,1,2,1] => [2,2,1,1,1] => 1
0010111 => [2,1,1,3] => [3,2,1,1] => 2
0011000 => [2,2,3] => [3,2,2] => 1
0011001 => [2,2,2,1] => [2,2,2,1] => 1
0011010 => [2,2,1,1,1] => [2,2,1,1,1] => 1
0011011 => [2,2,1,2] => [2,2,2,1] => 1
0011100 => [2,3,2] => [3,2,2] => 1
0011101 => [2,3,1,1] => [3,2,1,1] => 2
0011110 => [2,4,1] => [4,2,1] => 3
0011111 => [2,5] => [5,2] => 3
0100000 => [1,1,5] => [5,1,1] => 4
0100001 => [1,1,4,1] => [4,1,1,1] => 3
0100010 => [1,1,3,1,1] => [3,1,1,1,1] => 2
0100011 => [1,1,3,2] => [3,2,1,1] => 2
0100100 => [1,1,2,1,2] => [2,2,1,1,1] => 1
0100101 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 1
0100110 => [1,1,2,2,1] => [2,2,1,1,1] => 1
0100111 => [1,1,2,3] => [3,2,1,1] => 2
0101000 => [1,1,1,1,3] => [3,1,1,1,1] => 2
0101001 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 1
0101010 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
0101011 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 1
0101100 => [1,1,1,2,2] => [2,2,1,1,1] => 1
0101101 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 1
0101110 => [1,1,1,3,1] => [3,1,1,1,1] => 2
0101111 => [1,1,1,4] => [4,1,1,1] => 3
0110000 => [1,2,4] => [4,2,1] => 3
0110001 => [1,2,3,1] => [3,2,1,1] => 2
0110010 => [1,2,2,1,1] => [2,2,1,1,1] => 1
0110011 => [1,2,2,2] => [2,2,2,1] => 1
0110100 => [1,2,1,1,2] => [2,2,1,1,1] => 1
0110101 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 1
0110110 => [1,2,1,2,1] => [2,2,1,1,1] => 1
0110111 => [1,2,1,3] => [3,2,1,1] => 2
0111000 => [1,3,3] => [3,3,1] => 2
0111001 => [1,3,2,1] => [3,2,1,1] => 2
0111010 => [1,3,1,1,1] => [3,1,1,1,1] => 2
0111011 => [1,3,1,2] => [3,2,1,1] => 2
0111100 => [1,4,2] => [4,2,1] => 3
0111101 => [1,4,1,1] => [4,1,1,1] => 3
0111110 => [1,5,1] => [5,1,1] => 4
0111111 => [1,6] => [6,1] => 5
1000000 => [1,6] => [6,1] => 5
1000001 => [1,5,1] => [5,1,1] => 4
1000010 => [1,4,1,1] => [4,1,1,1] => 3
1000011 => [1,4,2] => [4,2,1] => 3
1000100 => [1,3,1,2] => [3,2,1,1] => 2
1000101 => [1,3,1,1,1] => [3,1,1,1,1] => 2
1000110 => [1,3,2,1] => [3,2,1,1] => 2
1000111 => [1,3,3] => [3,3,1] => 2
1001000 => [1,2,1,3] => [3,2,1,1] => 2
1001001 => [1,2,1,2,1] => [2,2,1,1,1] => 1
1001010 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 1
1001011 => [1,2,1,1,2] => [2,2,1,1,1] => 1
1001100 => [1,2,2,2] => [2,2,2,1] => 1
1001101 => [1,2,2,1,1] => [2,2,1,1,1] => 1
1001110 => [1,2,3,1] => [3,2,1,1] => 2
1001111 => [1,2,4] => [4,2,1] => 3
1010000 => [1,1,1,4] => [4,1,1,1] => 3
1010001 => [1,1,1,3,1] => [3,1,1,1,1] => 2
1010010 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 1
1010011 => [1,1,1,2,2] => [2,2,1,1,1] => 1
1010100 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 1
1010101 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
1010110 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 1
1010111 => [1,1,1,1,3] => [3,1,1,1,1] => 2
1011000 => [1,1,2,3] => [3,2,1,1] => 2
1011001 => [1,1,2,2,1] => [2,2,1,1,1] => 1
1011010 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 1
1011011 => [1,1,2,1,2] => [2,2,1,1,1] => 1
1011100 => [1,1,3,2] => [3,2,1,1] => 2
1011101 => [1,1,3,1,1] => [3,1,1,1,1] => 2
1011110 => [1,1,4,1] => [4,1,1,1] => 3
1011111 => [1,1,5] => [5,1,1] => 4
1100000 => [2,5] => [5,2] => 3
1100001 => [2,4,1] => [4,2,1] => 3
1100010 => [2,3,1,1] => [3,2,1,1] => 2
1100011 => [2,3,2] => [3,2,2] => 1
1100100 => [2,2,1,2] => [2,2,2,1] => 1
1100101 => [2,2,1,1,1] => [2,2,1,1,1] => 1
1100110 => [2,2,2,1] => [2,2,2,1] => 1
1100111 => [2,2,3] => [3,2,2] => 1
1101000 => [2,1,1,3] => [3,2,1,1] => 2
1101001 => [2,1,1,2,1] => [2,2,1,1,1] => 1
1101010 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
1101011 => [2,1,1,1,2] => [2,2,1,1,1] => 1
1101100 => [2,1,2,2] => [2,2,2,1] => 1
1101101 => [2,1,2,1,1] => [2,2,1,1,1] => 1
1101110 => [2,1,3,1] => [3,2,1,1] => 2
1101111 => [2,1,4] => [4,2,1] => 3
1110000 => [3,4] => [4,3] => 1
1110001 => [3,3,1] => [3,3,1] => 2
1110010 => [3,2,1,1] => [3,2,1,1] => 2
1110011 => [3,2,2] => [3,2,2] => 1
1110100 => [3,1,1,2] => [3,2,1,1] => 2
1110101 => [3,1,1,1,1] => [3,1,1,1,1] => 2
1110110 => [3,1,2,1] => [3,2,1,1] => 2
1110111 => [3,1,3] => [3,3,1] => 2
1111000 => [4,3] => [4,3] => 1
1111001 => [4,2,1] => [4,2,1] => 3
1111010 => [4,1,1,1] => [4,1,1,1] => 3
1111011 => [4,1,2] => [4,2,1] => 3
1111100 => [5,2] => [5,2] => 3
1111101 => [5,1,1] => [5,1,1] => 4
1111110 => [6,1] => [6,1] => 5
1111111 => [7] => [7] => 0
00000000 => [8] => [8] => 0
00000001 => [7,1] => [7,1] => 6
00000010 => [6,1,1] => [6,1,1] => 5
00000011 => [6,2] => [6,2] => 4
00000100 => [5,1,2] => [5,2,1] => 4
00000101 => [5,1,1,1] => [5,1,1,1] => 4
00000110 => [5,2,1] => [5,2,1] => 4
00000111 => [5,3] => [5,3] => 2
00001000 => [4,1,3] => [4,3,1] => 3
00001001 => [4,1,2,1] => [4,2,1,1] => 3
00001010 => [4,1,1,1,1] => [4,1,1,1,1] => 3
00001011 => [4,1,1,2] => [4,2,1,1] => 3
00001100 => [4,2,2] => [4,2,2] => 2
00001101 => [4,2,1,1] => [4,2,1,1] => 3
00001110 => [4,3,1] => [4,3,1] => 3
00001111 => [4,4] => [4,4] => 0
00010000 => [3,1,4] => [4,3,1] => 3
00010001 => [3,1,3,1] => [3,3,1,1] => 2
00010010 => [3,1,2,1,1] => [3,2,1,1,1] => 2
00010011 => [3,1,2,2] => [3,2,2,1] => 2
00010100 => [3,1,1,1,2] => [3,2,1,1,1] => 2
00010101 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 2
00010110 => [3,1,1,2,1] => [3,2,1,1,1] => 2
00010111 => [3,1,1,3] => [3,3,1,1] => 2
00011000 => [3,2,3] => [3,3,2] => 1
00011001 => [3,2,2,1] => [3,2,2,1] => 2
00011010 => [3,2,1,1,1] => [3,2,1,1,1] => 2
00011011 => [3,2,1,2] => [3,2,2,1] => 2
00011100 => [3,3,2] => [3,3,2] => 1
00011101 => [3,3,1,1] => [3,3,1,1] => 2
00011110 => [3,4,1] => [4,3,1] => 3
00011111 => [3,5] => [5,3] => 2
00100000 => [2,1,5] => [5,2,1] => 4
00100001 => [2,1,4,1] => [4,2,1,1] => 3
00100010 => [2,1,3,1,1] => [3,2,1,1,1] => 2
00100011 => [2,1,3,2] => [3,2,2,1] => 2
00100100 => [2,1,2,1,2] => [2,2,2,1,1] => 1
00100101 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 1
00100110 => [2,1,2,2,1] => [2,2,2,1,1] => 1
00100111 => [2,1,2,3] => [3,2,2,1] => 2
00101000 => [2,1,1,1,3] => [3,2,1,1,1] => 2
00101001 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 1
00101010 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
00101011 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 1
00101100 => [2,1,1,2,2] => [2,2,2,1,1] => 1
00101101 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 1
00101110 => [2,1,1,3,1] => [3,2,1,1,1] => 2
00101111 => [2,1,1,4] => [4,2,1,1] => 3
00110000 => [2,2,4] => [4,2,2] => 2
00110001 => [2,2,3,1] => [3,2,2,1] => 2
00110010 => [2,2,2,1,1] => [2,2,2,1,1] => 1
00110011 => [2,2,2,2] => [2,2,2,2] => 0
00110100 => [2,2,1,1,2] => [2,2,2,1,1] => 1
00110101 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
00110110 => [2,2,1,2,1] => [2,2,2,1,1] => 1
00110111 => [2,2,1,3] => [3,2,2,1] => 2
00111000 => [2,3,3] => [3,3,2] => 1
00111001 => [2,3,2,1] => [3,2,2,1] => 2
00111010 => [2,3,1,1,1] => [3,2,1,1,1] => 2
00111011 => [2,3,1,2] => [3,2,2,1] => 2
00111100 => [2,4,2] => [4,2,2] => 2
00111101 => [2,4,1,1] => [4,2,1,1] => 3
00111110 => [2,5,1] => [5,2,1] => 4
00111111 => [2,6] => [6,2] => 4
01000000 => [1,1,6] => [6,1,1] => 5
01000001 => [1,1,5,1] => [5,1,1,1] => 4
01000010 => [1,1,4,1,1] => [4,1,1,1,1] => 3
01000011 => [1,1,4,2] => [4,2,1,1] => 3
01000100 => [1,1,3,1,2] => [3,2,1,1,1] => 2
01000101 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 2
01000110 => [1,1,3,2,1] => [3,2,1,1,1] => 2
01000111 => [1,1,3,3] => [3,3,1,1] => 2
01001000 => [1,1,2,1,3] => [3,2,1,1,1] => 2
01001001 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 1
01001010 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 1
01001011 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 1
01001100 => [1,1,2,2,2] => [2,2,2,1,1] => 1
01001101 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 1
01001110 => [1,1,2,3,1] => [3,2,1,1,1] => 2
01001111 => [1,1,2,4] => [4,2,1,1] => 3
01010000 => [1,1,1,1,4] => [4,1,1,1,1] => 3
01010001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 2
01010010 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 1
01010011 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 1
01010100 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 1
01010101 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
01010110 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 1
01010111 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 2
01011000 => [1,1,1,2,3] => [3,2,1,1,1] => 2
01011001 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 1
01011010 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 1
01011011 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 1
01011100 => [1,1,1,3,2] => [3,2,1,1,1] => 2
01011101 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 2
01011110 => [1,1,1,4,1] => [4,1,1,1,1] => 3
01011111 => [1,1,1,5] => [5,1,1,1] => 4
01100000 => [1,2,5] => [5,2,1] => 4
01100001 => [1,2,4,1] => [4,2,1,1] => 3
01100010 => [1,2,3,1,1] => [3,2,1,1,1] => 2
01100011 => [1,2,3,2] => [3,2,2,1] => 2
01100100 => [1,2,2,1,2] => [2,2,2,1,1] => 1
01100101 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 1
01100110 => [1,2,2,2,1] => [2,2,2,1,1] => 1
01100111 => [1,2,2,3] => [3,2,2,1] => 2
01101000 => [1,2,1,1,3] => [3,2,1,1,1] => 2
01101001 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 1
01101010 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
01101011 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 1
01101100 => [1,2,1,2,2] => [2,2,2,1,1] => 1
01101101 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 1
01101110 => [1,2,1,3,1] => [3,2,1,1,1] => 2
01101111 => [1,2,1,4] => [4,2,1,1] => 3
01110000 => [1,3,4] => [4,3,1] => 3
01110001 => [1,3,3,1] => [3,3,1,1] => 2
01110010 => [1,3,2,1,1] => [3,2,1,1,1] => 2
01110011 => [1,3,2,2] => [3,2,2,1] => 2
01110100 => [1,3,1,1,2] => [3,2,1,1,1] => 2
01110101 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 2
01110110 => [1,3,1,2,1] => [3,2,1,1,1] => 2
01110111 => [1,3,1,3] => [3,3,1,1] => 2
01111000 => [1,4,3] => [4,3,1] => 3
01111001 => [1,4,2,1] => [4,2,1,1] => 3
01111010 => [1,4,1,1,1] => [4,1,1,1,1] => 3
01111011 => [1,4,1,2] => [4,2,1,1] => 3
01111100 => [1,5,2] => [5,2,1] => 4
01111101 => [1,5,1,1] => [5,1,1,1] => 4
01111110 => [1,6,1] => [6,1,1] => 5
01111111 => [1,7] => [7,1] => 6
10000000 => [1,7] => [7,1] => 6
10000001 => [1,6,1] => [6,1,1] => 5
10000010 => [1,5,1,1] => [5,1,1,1] => 4
10000011 => [1,5,2] => [5,2,1] => 4
10000100 => [1,4,1,2] => [4,2,1,1] => 3
10000101 => [1,4,1,1,1] => [4,1,1,1,1] => 3
10000110 => [1,4,2,1] => [4,2,1,1] => 3
10000111 => [1,4,3] => [4,3,1] => 3
10001000 => [1,3,1,3] => [3,3,1,1] => 2
10001001 => [1,3,1,2,1] => [3,2,1,1,1] => 2
10001010 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 2
10001011 => [1,3,1,1,2] => [3,2,1,1,1] => 2
10001100 => [1,3,2,2] => [3,2,2,1] => 2
10001101 => [1,3,2,1,1] => [3,2,1,1,1] => 2
10001110 => [1,3,3,1] => [3,3,1,1] => 2
10001111 => [1,3,4] => [4,3,1] => 3
10010000 => [1,2,1,4] => [4,2,1,1] => 3
10010001 => [1,2,1,3,1] => [3,2,1,1,1] => 2
10010010 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 1
10010011 => [1,2,1,2,2] => [2,2,2,1,1] => 1
10010100 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 1
10010101 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
10010110 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 1
10010111 => [1,2,1,1,3] => [3,2,1,1,1] => 2
10011000 => [1,2,2,3] => [3,2,2,1] => 2
10011001 => [1,2,2,2,1] => [2,2,2,1,1] => 1
10011010 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 1
10011011 => [1,2,2,1,2] => [2,2,2,1,1] => 1
10011100 => [1,2,3,2] => [3,2,2,1] => 2
10011101 => [1,2,3,1,1] => [3,2,1,1,1] => 2
10011110 => [1,2,4,1] => [4,2,1,1] => 3
10011111 => [1,2,5] => [5,2,1] => 4
10100000 => [1,1,1,5] => [5,1,1,1] => 4
10100001 => [1,1,1,4,1] => [4,1,1,1,1] => 3
10100010 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 2
10100011 => [1,1,1,3,2] => [3,2,1,1,1] => 2
10100100 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 1
10100101 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 1
10100110 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 1
10100111 => [1,1,1,2,3] => [3,2,1,1,1] => 2
10101000 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 2
10101001 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 1
10101010 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
10101011 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 1
10101100 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 1
10101101 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 1
10101110 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 2
10101111 => [1,1,1,1,4] => [4,1,1,1,1] => 3
10110000 => [1,1,2,4] => [4,2,1,1] => 3
10110001 => [1,1,2,3,1] => [3,2,1,1,1] => 2
10110010 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 1
10110011 => [1,1,2,2,2] => [2,2,2,1,1] => 1
10110100 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 1
10110101 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 1
10110110 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 1
10110111 => [1,1,2,1,3] => [3,2,1,1,1] => 2
10111000 => [1,1,3,3] => [3,3,1,1] => 2
10111001 => [1,1,3,2,1] => [3,2,1,1,1] => 2
10111010 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 2
10111011 => [1,1,3,1,2] => [3,2,1,1,1] => 2
10111100 => [1,1,4,2] => [4,2,1,1] => 3
10111101 => [1,1,4,1,1] => [4,1,1,1,1] => 3
10111110 => [1,1,5,1] => [5,1,1,1] => 4
10111111 => [1,1,6] => [6,1,1] => 5
11000000 => [2,6] => [6,2] => 4
11000001 => [2,5,1] => [5,2,1] => 4
11000010 => [2,4,1,1] => [4,2,1,1] => 3
11000011 => [2,4,2] => [4,2,2] => 2
11000100 => [2,3,1,2] => [3,2,2,1] => 2
11000101 => [2,3,1,1,1] => [3,2,1,1,1] => 2
11000110 => [2,3,2,1] => [3,2,2,1] => 2
11000111 => [2,3,3] => [3,3,2] => 1
11001000 => [2,2,1,3] => [3,2,2,1] => 2
11001001 => [2,2,1,2,1] => [2,2,2,1,1] => 1
11001010 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
11001011 => [2,2,1,1,2] => [2,2,2,1,1] => 1
11001100 => [2,2,2,2] => [2,2,2,2] => 0
11001101 => [2,2,2,1,1] => [2,2,2,1,1] => 1
11001110 => [2,2,3,1] => [3,2,2,1] => 2
11001111 => [2,2,4] => [4,2,2] => 2
11010000 => [2,1,1,4] => [4,2,1,1] => 3
11010001 => [2,1,1,3,1] => [3,2,1,1,1] => 2
11010010 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 1
11010011 => [2,1,1,2,2] => [2,2,2,1,1] => 1
11010100 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 1
11010101 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
11010110 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 1
11010111 => [2,1,1,1,3] => [3,2,1,1,1] => 2
11011000 => [2,1,2,3] => [3,2,2,1] => 2
11011001 => [2,1,2,2,1] => [2,2,2,1,1] => 1
11011010 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 1
11011011 => [2,1,2,1,2] => [2,2,2,1,1] => 1
11011100 => [2,1,3,2] => [3,2,2,1] => 2
11011101 => [2,1,3,1,1] => [3,2,1,1,1] => 2
11011110 => [2,1,4,1] => [4,2,1,1] => 3
11011111 => [2,1,5] => [5,2,1] => 4
11100000 => [3,5] => [5,3] => 2
11100001 => [3,4,1] => [4,3,1] => 3
11100010 => [3,3,1,1] => [3,3,1,1] => 2
11100011 => [3,3,2] => [3,3,2] => 1
11100100 => [3,2,1,2] => [3,2,2,1] => 2
11100101 => [3,2,1,1,1] => [3,2,1,1,1] => 2
11100110 => [3,2,2,1] => [3,2,2,1] => 2
11100111 => [3,2,3] => [3,3,2] => 1
11101000 => [3,1,1,3] => [3,3,1,1] => 2
11101001 => [3,1,1,2,1] => [3,2,1,1,1] => 2
11101010 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 2
11101011 => [3,1,1,1,2] => [3,2,1,1,1] => 2
11101100 => [3,1,2,2] => [3,2,2,1] => 2
11101101 => [3,1,2,1,1] => [3,2,1,1,1] => 2
11101110 => [3,1,3,1] => [3,3,1,1] => 2
11101111 => [3,1,4] => [4,3,1] => 3
11110000 => [4,4] => [4,4] => 0
11110001 => [4,3,1] => [4,3,1] => 3
11110010 => [4,2,1,1] => [4,2,1,1] => 3
11110011 => [4,2,2] => [4,2,2] => 2
11110100 => [4,1,1,2] => [4,2,1,1] => 3
11110101 => [4,1,1,1,1] => [4,1,1,1,1] => 3
11110110 => [4,1,2,1] => [4,2,1,1] => 3
11110111 => [4,1,3] => [4,3,1] => 3
11111000 => [5,3] => [5,3] => 2
11111001 => [5,2,1] => [5,2,1] => 4
11111010 => [5,1,1,1] => [5,1,1,1] => 4
11111011 => [5,1,2] => [5,2,1] => 4
11111100 => [6,2] => [6,2] => 4
11111101 => [6,1,1] => [6,1,1] => 5
11111110 => [7,1] => [7,1] => 6
11111111 => [8] => [8] => 0
000000000 => [9] => [9] => 0
000000001 => [8,1] => [8,1] => 7
000000010 => [7,1,1] => [7,1,1] => 6
000000011 => [7,2] => [7,2] => 5
000000100 => [6,1,2] => [6,2,1] => 5
000000101 => [6,1,1,1] => [6,1,1,1] => 5
000000110 => [6,2,1] => [6,2,1] => 5
000000111 => [6,3] => [6,3] => 3
000001000 => [5,1,3] => [5,3,1] => 4
000001001 => [5,1,2,1] => [5,2,1,1] => 4
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => 4
000001011 => [5,1,1,2] => [5,2,1,1] => 4
000001100 => [5,2,2] => [5,2,2] => 3
000001101 => [5,2,1,1] => [5,2,1,1] => 4
000001110 => [5,3,1] => [5,3,1] => 4
000001111 => [5,4] => [5,4] => 1
000010000 => [4,1,4] => [4,4,1] => 3
000010001 => [4,1,3,1] => [4,3,1,1] => 3
000010010 => [4,1,2,1,1] => [4,2,1,1,1] => 3
000010011 => [4,1,2,2] => [4,2,2,1] => 3
000010100 => [4,1,1,1,2] => [4,2,1,1,1] => 3
000010101 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 3
000010110 => [4,1,1,2,1] => [4,2,1,1,1] => 3
000010111 => [4,1,1,3] => [4,3,1,1] => 3
000011000 => [4,2,3] => [4,3,2] => 2
000011001 => [4,2,2,1] => [4,2,2,1] => 3
000011010 => [4,2,1,1,1] => [4,2,1,1,1] => 3
000011011 => [4,2,1,2] => [4,2,2,1] => 3
000011100 => [4,3,2] => [4,3,2] => 2
000011101 => [4,3,1,1] => [4,3,1,1] => 3
000011110 => [4,4,1] => [4,4,1] => 3
000011111 => [4,5] => [5,4] => 1
000100000 => [3,1,5] => [5,3,1] => 4
000100001 => [3,1,4,1] => [4,3,1,1] => 3
000100010 => [3,1,3,1,1] => [3,3,1,1,1] => 2
000100011 => [3,1,3,2] => [3,3,2,1] => 2
000100100 => [3,1,2,1,2] => [3,2,2,1,1] => 2
000100101 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 2
000100110 => [3,1,2,2,1] => [3,2,2,1,1] => 2
000100111 => [3,1,2,3] => [3,3,2,1] => 2
000101000 => [3,1,1,1,3] => [3,3,1,1,1] => 2
000101001 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 2
000101010 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 2
000101011 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 2
000101100 => [3,1,1,2,2] => [3,2,2,1,1] => 2
000101101 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => 2
000101110 => [3,1,1,3,1] => [3,3,1,1,1] => 2
000101111 => [3,1,1,4] => [4,3,1,1] => 3
000110000 => [3,2,4] => [4,3,2] => 2
000110001 => [3,2,3,1] => [3,3,2,1] => 2
000110010 => [3,2,2,1,1] => [3,2,2,1,1] => 2
000110011 => [3,2,2,2] => [3,2,2,2] => 1
000110100 => [3,2,1,1,2] => [3,2,2,1,1] => 2
000110101 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 2
000110110 => [3,2,1,2,1] => [3,2,2,1,1] => 2
000110111 => [3,2,1,3] => [3,3,2,1] => 2
000111000 => [3,3,3] => [3,3,3] => 0
000111001 => [3,3,2,1] => [3,3,2,1] => 2
000111010 => [3,3,1,1,1] => [3,3,1,1,1] => 2
000111011 => [3,3,1,2] => [3,3,2,1] => 2
000111100 => [3,4,2] => [4,3,2] => 2
000111101 => [3,4,1,1] => [4,3,1,1] => 3
000111110 => [3,5,1] => [5,3,1] => 4
000111111 => [3,6] => [6,3] => 3
001000000 => [2,1,6] => [6,2,1] => 5
001000001 => [2,1,5,1] => [5,2,1,1] => 4
001000010 => [2,1,4,1,1] => [4,2,1,1,1] => 3
001000011 => [2,1,4,2] => [4,2,2,1] => 3
001000100 => [2,1,3,1,2] => [3,2,2,1,1] => 2
001000101 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 2
001000110 => [2,1,3,2,1] => [3,2,2,1,1] => 2
001000111 => [2,1,3,3] => [3,3,2,1] => 2
001001000 => [2,1,2,1,3] => [3,2,2,1,1] => 2
001001001 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => 1
001001010 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
001001011 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => 1
001001100 => [2,1,2,2,2] => [2,2,2,2,1] => 1
001001101 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => 1
001001110 => [2,1,2,3,1] => [3,2,2,1,1] => 2
001001111 => [2,1,2,4] => [4,2,2,1] => 3
001010000 => [2,1,1,1,4] => [4,2,1,1,1] => 3
001010001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 2
001010010 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
001010011 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 1
001010100 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
001010101 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
001010110 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
001010111 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 2
001011000 => [2,1,1,2,3] => [3,2,2,1,1] => 2
001011001 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => 1
001011010 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
001011011 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => 1
001011100 => [2,1,1,3,2] => [3,2,2,1,1] => 2
001011101 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => 2
001011110 => [2,1,1,4,1] => [4,2,1,1,1] => 3
001011111 => [2,1,1,5] => [5,2,1,1] => 4
001100000 => [2,2,5] => [5,2,2] => 3
001100001 => [2,2,4,1] => [4,2,2,1] => 3
001100010 => [2,2,3,1,1] => [3,2,2,1,1] => 2
001100011 => [2,2,3,2] => [3,2,2,2] => 1
001100100 => [2,2,2,1,2] => [2,2,2,2,1] => 1
001100101 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => 1
001100111 => [2,2,2,3] => [3,2,2,2] => 1
001101000 => [2,2,1,1,3] => [3,2,2,1,1] => 2
001101001 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => 1
001101010 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
001101011 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 1
001101100 => [2,2,1,2,2] => [2,2,2,2,1] => 1
001101101 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => 1
001101110 => [2,2,1,3,1] => [3,2,2,1,1] => 2
001101111 => [2,2,1,4] => [4,2,2,1] => 3
001110000 => [2,3,4] => [4,3,2] => 2
001110001 => [2,3,3,1] => [3,3,2,1] => 2
001110010 => [2,3,2,1,1] => [3,2,2,1,1] => 2
001110011 => [2,3,2,2] => [3,2,2,2] => 1
001110100 => [2,3,1,1,2] => [3,2,2,1,1] => 2
001110101 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 2
001110110 => [2,3,1,2,1] => [3,2,2,1,1] => 2
001110111 => [2,3,1,3] => [3,3,2,1] => 2
001111000 => [2,4,3] => [4,3,2] => 2
001111001 => [2,4,2,1] => [4,2,2,1] => 3
001111010 => [2,4,1,1,1] => [4,2,1,1,1] => 3
001111011 => [2,4,1,2] => [4,2,2,1] => 3
001111100 => [2,5,2] => [5,2,2] => 3
001111101 => [2,5,1,1] => [5,2,1,1] => 4
001111110 => [2,6,1] => [6,2,1] => 5
001111111 => [2,7] => [7,2] => 5
010000000 => [1,1,7] => [7,1,1] => 6
010000001 => [1,1,6,1] => [6,1,1,1] => 5
010000010 => [1,1,5,1,1] => [5,1,1,1,1] => 4
010000011 => [1,1,5,2] => [5,2,1,1] => 4
010000100 => [1,1,4,1,2] => [4,2,1,1,1] => 3
010000101 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 3
010000110 => [1,1,4,2,1] => [4,2,1,1,1] => 3
010000111 => [1,1,4,3] => [4,3,1,1] => 3
010001000 => [1,1,3,1,3] => [3,3,1,1,1] => 2
010001001 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => 2
010001010 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 2
010001011 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 2
010001100 => [1,1,3,2,2] => [3,2,2,1,1] => 2
010001101 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => 2
010001110 => [1,1,3,3,1] => [3,3,1,1,1] => 2
010001111 => [1,1,3,4] => [4,3,1,1] => 3
010010000 => [1,1,2,1,4] => [4,2,1,1,1] => 3
010010001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 2
010010010 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 1
010010011 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 1
010010100 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 1
010010101 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
010010110 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 1
010010111 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 2
010011000 => [1,1,2,2,3] => [3,2,2,1,1] => 2
010011001 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 1
010011010 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 1
010011011 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => 1
010011100 => [1,1,2,3,2] => [3,2,2,1,1] => 2
010011101 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => 2
010011110 => [1,1,2,4,1] => [4,2,1,1,1] => 3
010011111 => [1,1,2,5] => [5,2,1,1] => 4
010100000 => [1,1,1,1,5] => [5,1,1,1,1] => 4
010100001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 3
010100010 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 2
010100011 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 2
010100100 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 1
010100101 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 1
010100110 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 1
010100111 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 2
010101000 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 2
010101001 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 1
010101010 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
010101011 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 1
010101100 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 1
010101101 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 1
010101110 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 2
010101111 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 3
010110000 => [1,1,1,2,4] => [4,2,1,1,1] => 3
010110001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => 2
010110010 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 1
010110011 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 1
010110100 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 1
010110101 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
010110110 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 1
010110111 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 2
010111000 => [1,1,1,3,3] => [3,3,1,1,1] => 2
010111001 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 2
010111010 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 2
010111011 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => 2
010111100 => [1,1,1,4,2] => [4,2,1,1,1] => 3
010111101 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 3
010111110 => [1,1,1,5,1] => [5,1,1,1,1] => 4
010111111 => [1,1,1,6] => [6,1,1,1] => 5
011000000 => [1,2,6] => [6,2,1] => 5
011000001 => [1,2,5,1] => [5,2,1,1] => 4
011000010 => [1,2,4,1,1] => [4,2,1,1,1] => 3
011000011 => [1,2,4,2] => [4,2,2,1] => 3
011000100 => [1,2,3,1,2] => [3,2,2,1,1] => 2
011000101 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 2
011000110 => [1,2,3,2,1] => [3,2,2,1,1] => 2
011000111 => [1,2,3,3] => [3,3,2,1] => 2
011001000 => [1,2,2,1,3] => [3,2,2,1,1] => 2
011001001 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => 1
011001010 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
011001011 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 1
011001100 => [1,2,2,2,2] => [2,2,2,2,1] => 1
011001101 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 1
011001110 => [1,2,2,3,1] => [3,2,2,1,1] => 2
011001111 => [1,2,2,4] => [4,2,2,1] => 3
011010000 => [1,2,1,1,4] => [4,2,1,1,1] => 3
011010001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 2
011010010 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
011010011 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => 1
011010100 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
011010101 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
011010110 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
011010111 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 2
011011000 => [1,2,1,2,3] => [3,2,2,1,1] => 2
011011001 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => 1
011011010 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
011011011 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => 1
011011100 => [1,2,1,3,2] => [3,2,2,1,1] => 2
011011101 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => 2
011011110 => [1,2,1,4,1] => [4,2,1,1,1] => 3
011011111 => [1,2,1,5] => [5,2,1,1] => 4
011100000 => [1,3,5] => [5,3,1] => 4
011100001 => [1,3,4,1] => [4,3,1,1] => 3
011100010 => [1,3,3,1,1] => [3,3,1,1,1] => 2
011100011 => [1,3,3,2] => [3,3,2,1] => 2
011100100 => [1,3,2,1,2] => [3,2,2,1,1] => 2
011100101 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 2
011100110 => [1,3,2,2,1] => [3,2,2,1,1] => 2
011100111 => [1,3,2,3] => [3,3,2,1] => 2
011101000 => [1,3,1,1,3] => [3,3,1,1,1] => 2
011101001 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 2
011101010 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 2
011101011 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => 2
011101100 => [1,3,1,2,2] => [3,2,2,1,1] => 2
011101101 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => 2
011101110 => [1,3,1,3,1] => [3,3,1,1,1] => 2
011101111 => [1,3,1,4] => [4,3,1,1] => 3
011110000 => [1,4,4] => [4,4,1] => 3
011110001 => [1,4,3,1] => [4,3,1,1] => 3
011110010 => [1,4,2,1,1] => [4,2,1,1,1] => 3
011110011 => [1,4,2,2] => [4,2,2,1] => 3
011110100 => [1,4,1,1,2] => [4,2,1,1,1] => 3
011110101 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 3
011110110 => [1,4,1,2,1] => [4,2,1,1,1] => 3
011110111 => [1,4,1,3] => [4,3,1,1] => 3
011111000 => [1,5,3] => [5,3,1] => 4
011111001 => [1,5,2,1] => [5,2,1,1] => 4
011111010 => [1,5,1,1,1] => [5,1,1,1,1] => 4
011111011 => [1,5,1,2] => [5,2,1,1] => 4
011111100 => [1,6,2] => [6,2,1] => 5
011111101 => [1,6,1,1] => [6,1,1,1] => 5
011111110 => [1,7,1] => [7,1,1] => 6
011111111 => [1,8] => [8,1] => 7
100000000 => [1,8] => [8,1] => 7
100000001 => [1,7,1] => [7,1,1] => 6
100000010 => [1,6,1,1] => [6,1,1,1] => 5
100000011 => [1,6,2] => [6,2,1] => 5
100000100 => [1,5,1,2] => [5,2,1,1] => 4
100000101 => [1,5,1,1,1] => [5,1,1,1,1] => 4
100000110 => [1,5,2,1] => [5,2,1,1] => 4
100000111 => [1,5,3] => [5,3,1] => 4
100001000 => [1,4,1,3] => [4,3,1,1] => 3
100001001 => [1,4,1,2,1] => [4,2,1,1,1] => 3
100001010 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 3
100001011 => [1,4,1,1,2] => [4,2,1,1,1] => 3
100001100 => [1,4,2,2] => [4,2,2,1] => 3
100001101 => [1,4,2,1,1] => [4,2,1,1,1] => 3
100001110 => [1,4,3,1] => [4,3,1,1] => 3
100001111 => [1,4,4] => [4,4,1] => 3
100010000 => [1,3,1,4] => [4,3,1,1] => 3
100010001 => [1,3,1,3,1] => [3,3,1,1,1] => 2
100010010 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => 2
100010011 => [1,3,1,2,2] => [3,2,2,1,1] => 2
100010100 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => 2
100010101 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 2
100010110 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 2
100010111 => [1,3,1,1,3] => [3,3,1,1,1] => 2
100011000 => [1,3,2,3] => [3,3,2,1] => 2
100011001 => [1,3,2,2,1] => [3,2,2,1,1] => 2
100011010 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 2
100011011 => [1,3,2,1,2] => [3,2,2,1,1] => 2
100011100 => [1,3,3,2] => [3,3,2,1] => 2
100011101 => [1,3,3,1,1] => [3,3,1,1,1] => 2
100011110 => [1,3,4,1] => [4,3,1,1] => 3
100011111 => [1,3,5] => [5,3,1] => 4
100100000 => [1,2,1,5] => [5,2,1,1] => 4
100100001 => [1,2,1,4,1] => [4,2,1,1,1] => 3
100100010 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => 2
100100011 => [1,2,1,3,2] => [3,2,2,1,1] => 2
100100100 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => 1
100100101 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
100100110 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => 1
100100111 => [1,2,1,2,3] => [3,2,2,1,1] => 2
100101000 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 2
100101001 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
100101010 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
100101011 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
100101100 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => 1
100101101 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
100101110 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 2
100101111 => [1,2,1,1,4] => [4,2,1,1,1] => 3
100110000 => [1,2,2,4] => [4,2,2,1] => 3
100110001 => [1,2,2,3,1] => [3,2,2,1,1] => 2
100110010 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 1
100110011 => [1,2,2,2,2] => [2,2,2,2,1] => 1
100110100 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 1
100110101 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
100110110 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => 1
100110111 => [1,2,2,1,3] => [3,2,2,1,1] => 2
100111000 => [1,2,3,3] => [3,3,2,1] => 2
100111001 => [1,2,3,2,1] => [3,2,2,1,1] => 2
100111010 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 2
100111011 => [1,2,3,1,2] => [3,2,2,1,1] => 2
100111100 => [1,2,4,2] => [4,2,2,1] => 3
100111101 => [1,2,4,1,1] => [4,2,1,1,1] => 3
100111110 => [1,2,5,1] => [5,2,1,1] => 4
100111111 => [1,2,6] => [6,2,1] => 5
101000000 => [1,1,1,6] => [6,1,1,1] => 5
101000001 => [1,1,1,5,1] => [5,1,1,1,1] => 4
101000010 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 3
101000011 => [1,1,1,4,2] => [4,2,1,1,1] => 3
101000100 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => 2
101000101 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 2
101000110 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 2
101000111 => [1,1,1,3,3] => [3,3,1,1,1] => 2
101001000 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 2
101001001 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 1
101001010 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
101001011 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 1
101001100 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 1
101001101 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 1
101001110 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => 2
101001111 => [1,1,1,2,4] => [4,2,1,1,1] => 3
101010000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 3
101010001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 2
101010010 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 1
101010011 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 1
101010100 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 1
101010101 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
101010110 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 1
101010111 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 2
101011000 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 2
101011001 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 1
101011010 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 1
101011011 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 1
101011100 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 2
101011101 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 2
101011110 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 3
101011111 => [1,1,1,1,5] => [5,1,1,1,1] => 4
101100000 => [1,1,2,5] => [5,2,1,1] => 4
101100001 => [1,1,2,4,1] => [4,2,1,1,1] => 3
101100010 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => 2
101100011 => [1,1,2,3,2] => [3,2,2,1,1] => 2
101100100 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => 1
101100101 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 1
101100110 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 1
101100111 => [1,1,2,2,3] => [3,2,2,1,1] => 2
101101000 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 2
101101001 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 1
101101010 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
101101011 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 1
101101100 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 1
101101101 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 1
101101110 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 2
101101111 => [1,1,2,1,4] => [4,2,1,1,1] => 3
101110000 => [1,1,3,4] => [4,3,1,1] => 3
101110001 => [1,1,3,3,1] => [3,3,1,1,1] => 2
101110010 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => 2
101110011 => [1,1,3,2,2] => [3,2,2,1,1] => 2
101110100 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 2
101110101 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 2
101110110 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => 2
101110111 => [1,1,3,1,3] => [3,3,1,1,1] => 2
101111000 => [1,1,4,3] => [4,3,1,1] => 3
101111001 => [1,1,4,2,1] => [4,2,1,1,1] => 3
101111010 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 3
101111011 => [1,1,4,1,2] => [4,2,1,1,1] => 3
101111100 => [1,1,5,2] => [5,2,1,1] => 4
101111101 => [1,1,5,1,1] => [5,1,1,1,1] => 4
101111110 => [1,1,6,1] => [6,1,1,1] => 5
101111111 => [1,1,7] => [7,1,1] => 6
110000000 => [2,7] => [7,2] => 5
110000001 => [2,6,1] => [6,2,1] => 5
110000010 => [2,5,1,1] => [5,2,1,1] => 4
110000011 => [2,5,2] => [5,2,2] => 3
110000100 => [2,4,1,2] => [4,2,2,1] => 3
110000101 => [2,4,1,1,1] => [4,2,1,1,1] => 3
110000110 => [2,4,2,1] => [4,2,2,1] => 3
110000111 => [2,4,3] => [4,3,2] => 2
110001000 => [2,3,1,3] => [3,3,2,1] => 2
110001001 => [2,3,1,2,1] => [3,2,2,1,1] => 2
110001010 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 2
110001011 => [2,3,1,1,2] => [3,2,2,1,1] => 2
110001100 => [2,3,2,2] => [3,2,2,2] => 1
110001101 => [2,3,2,1,1] => [3,2,2,1,1] => 2
110001110 => [2,3,3,1] => [3,3,2,1] => 2
110001111 => [2,3,4] => [4,3,2] => 2
110010000 => [2,2,1,4] => [4,2,2,1] => 3
110010001 => [2,2,1,3,1] => [3,2,2,1,1] => 2
110010010 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => 1
110010011 => [2,2,1,2,2] => [2,2,2,2,1] => 1
110010100 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 1
110010101 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
110010110 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => 1
110010111 => [2,2,1,1,3] => [3,2,2,1,1] => 2
110011000 => [2,2,2,3] => [3,2,2,2] => 1
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => 1
110011010 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
110011011 => [2,2,2,1,2] => [2,2,2,2,1] => 1
110011100 => [2,2,3,2] => [3,2,2,2] => 1
110011101 => [2,2,3,1,1] => [3,2,2,1,1] => 2
110011110 => [2,2,4,1] => [4,2,2,1] => 3
110011111 => [2,2,5] => [5,2,2] => 3
110100000 => [2,1,1,5] => [5,2,1,1] => 4
110100001 => [2,1,1,4,1] => [4,2,1,1,1] => 3
110100010 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => 2
110100011 => [2,1,1,3,2] => [3,2,2,1,1] => 2
110100100 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => 1
110100101 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
110100110 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => 1
110100111 => [2,1,1,2,3] => [3,2,2,1,1] => 2
110101000 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 2
110101001 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
110101010 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
110101011 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
110101100 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 1
110101101 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
110101110 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 2
110101111 => [2,1,1,1,4] => [4,2,1,1,1] => 3
110110000 => [2,1,2,4] => [4,2,2,1] => 3
110110001 => [2,1,2,3,1] => [3,2,2,1,1] => 2
110110010 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => 1
110110011 => [2,1,2,2,2] => [2,2,2,2,1] => 1
110110100 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => 1
110110101 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
110110110 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => 1
110110111 => [2,1,2,1,3] => [3,2,2,1,1] => 2
110111000 => [2,1,3,3] => [3,3,2,1] => 2
110111001 => [2,1,3,2,1] => [3,2,2,1,1] => 2
110111010 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 2
110111011 => [2,1,3,1,2] => [3,2,2,1,1] => 2
110111100 => [2,1,4,2] => [4,2,2,1] => 3
110111101 => [2,1,4,1,1] => [4,2,1,1,1] => 3
110111110 => [2,1,5,1] => [5,2,1,1] => 4
110111111 => [2,1,6] => [6,2,1] => 5
111000000 => [3,6] => [6,3] => 3
111000001 => [3,5,1] => [5,3,1] => 4
111000010 => [3,4,1,1] => [4,3,1,1] => 3
111000011 => [3,4,2] => [4,3,2] => 2
111000100 => [3,3,1,2] => [3,3,2,1] => 2
111000101 => [3,3,1,1,1] => [3,3,1,1,1] => 2
111000110 => [3,3,2,1] => [3,3,2,1] => 2
111000111 => [3,3,3] => [3,3,3] => 0
111001000 => [3,2,1,3] => [3,3,2,1] => 2
111001001 => [3,2,1,2,1] => [3,2,2,1,1] => 2
111001010 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 2
111001011 => [3,2,1,1,2] => [3,2,2,1,1] => 2
111001100 => [3,2,2,2] => [3,2,2,2] => 1
111001101 => [3,2,2,1,1] => [3,2,2,1,1] => 2
111001110 => [3,2,3,1] => [3,3,2,1] => 2
111001111 => [3,2,4] => [4,3,2] => 2
111010000 => [3,1,1,4] => [4,3,1,1] => 3
111010001 => [3,1,1,3,1] => [3,3,1,1,1] => 2
111010010 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => 2
111010011 => [3,1,1,2,2] => [3,2,2,1,1] => 2
111010100 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 2
111010101 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 2
111010110 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 2
111010111 => [3,1,1,1,3] => [3,3,1,1,1] => 2
111011000 => [3,1,2,3] => [3,3,2,1] => 2
111011001 => [3,1,2,2,1] => [3,2,2,1,1] => 2
111011010 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 2
111011011 => [3,1,2,1,2] => [3,2,2,1,1] => 2
111011100 => [3,1,3,2] => [3,3,2,1] => 2
111011101 => [3,1,3,1,1] => [3,3,1,1,1] => 2
111011110 => [3,1,4,1] => [4,3,1,1] => 3
111011111 => [3,1,5] => [5,3,1] => 4
111100000 => [4,5] => [5,4] => 1
111100001 => [4,4,1] => [4,4,1] => 3
111100010 => [4,3,1,1] => [4,3,1,1] => 3
111100011 => [4,3,2] => [4,3,2] => 2
111100100 => [4,2,1,2] => [4,2,2,1] => 3
111100101 => [4,2,1,1,1] => [4,2,1,1,1] => 3
111100110 => [4,2,2,1] => [4,2,2,1] => 3
111100111 => [4,2,3] => [4,3,2] => 2
111101000 => [4,1,1,3] => [4,3,1,1] => 3
111101001 => [4,1,1,2,1] => [4,2,1,1,1] => 3
111101010 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 3
111101011 => [4,1,1,1,2] => [4,2,1,1,1] => 3
111101100 => [4,1,2,2] => [4,2,2,1] => 3
111101101 => [4,1,2,1,1] => [4,2,1,1,1] => 3
111101110 => [4,1,3,1] => [4,3,1,1] => 3
111101111 => [4,1,4] => [4,4,1] => 3
111110000 => [5,4] => [5,4] => 1
111110001 => [5,3,1] => [5,3,1] => 4
111110010 => [5,2,1,1] => [5,2,1,1] => 4
111110011 => [5,2,2] => [5,2,2] => 3
111110100 => [5,1,1,2] => [5,2,1,1] => 4
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => 4
111110110 => [5,1,2,1] => [5,2,1,1] => 4
111110111 => [5,1,3] => [5,3,1] => 4
111111000 => [6,3] => [6,3] => 3
111111001 => [6,2,1] => [6,2,1] => 5
111111010 => [6,1,1,1] => [6,1,1,1] => 5
111111011 => [6,1,2] => [6,2,1] => 5
111111100 => [7,2] => [7,2] => 5
111111101 => [7,1,1] => [7,1,1] => 6
111111110 => [8,1] => [8,1] => 7
111111111 => [9] => [9] => 0
1010101010 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
1010101100 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 1
1010110010 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 1
1010110100 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 1
1010111000 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => 2
1011001010 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1011001100 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 1
1011010010 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
1011010100 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
1011011000 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => 2
1011100010 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => 2
1011100100 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => 2
1011101000 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => 2
1011110000 => [1,1,4,4] => [4,4,1,1] => 3
1100101010 => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1100101100 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 1
1100110010 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
1100110100 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => 1
1100111000 => [2,2,3,3] => [3,3,2,2] => 1
1101001010 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1101001100 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => 1
1101010010 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
1101010100 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
1101011000 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => 2
1101100010 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => 2
1101100100 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => 1
1101101000 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => 2
1101110000 => [2,1,3,4] => [4,3,2,1] => 3
1110001010 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => 2
1110001100 => [3,3,2,2] => [3,3,2,2] => 1
1110010010 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => 2
1110010100 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => 2
1110011000 => [3,2,2,3] => [3,3,2,2] => 1
1110100010 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => 2
1110100100 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => 2
1110101000 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => 2
1110110000 => [3,1,2,4] => [4,3,2,1] => 3
1111000010 => [4,4,1,1] => [4,4,1,1] => 3
1111000100 => [4,3,1,2] => [4,3,2,1] => 3
1111001000 => [4,2,1,3] => [4,3,2,1] => 3
1111010000 => [4,1,1,4] => [4,4,1,1] => 3
1111100000 => [5,5] => [5,5] => 0
101100111000 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => 2
101110001100 => [1,1,3,3,2,2] => [3,3,2,2,1,1] => 2
101110011000 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => 2
110010111000 => [2,2,1,1,3,3] => [3,3,2,2,1,1] => 2
110011100010 => [2,2,3,3,1,1] => [3,3,2,2,1,1] => 2
110011101000 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => 2
110011110000 => [2,2,4,4] => [4,4,2,2] => 2
110100111000 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => 2
110111000100 => [2,1,3,3,1,2] => [3,3,2,2,1,1] => 2
110111001000 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => 2
110111100000 => [2,1,4,5] => [5,4,2,1] => 4
111000101100 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => 2
111000110010 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => 2
111000110100 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => 2
111001011000 => [3,2,1,1,2,3] => [3,3,2,2,1,1] => 2
111001100010 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => 2
111001101000 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => 2
111001110000 => [3,2,3,4] => [4,3,3,2] => 2
111010001100 => [3,1,1,3,2,2] => [3,3,2,2,1,1] => 2
111010011000 => [3,1,1,2,2,3] => [3,3,2,2,1,1] => 2
111011000100 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => 2
111011001000 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => 2
111011100000 => [3,1,3,5] => [5,3,3,1] => 4
111100001100 => [4,4,2,2] => [4,4,2,2] => 2
111100011000 => [4,3,2,3] => [4,3,3,2] => 2
111100110000 => [4,2,2,4] => [4,4,2,2] => 2
111101100000 => [4,1,2,5] => [5,4,2,1] => 4
111110000100 => [5,4,1,2] => [5,4,2,1] => 4
111110001000 => [5,3,1,3] => [5,3,3,1] => 4
111110010000 => [5,2,1,4] => [5,4,2,1] => 4
1111111111 => [10] => [10] => 0
1111111110 => [9,1] => [9,1] => 8
1111111101 => [8,1,1] => [8,1,1] => 7
1111111100 => [8,2] => [8,2] => 6
1111111011 => [7,1,2] => [7,2,1] => 6
1111111010 => [7,1,1,1] => [7,1,1,1] => 6
1111111001 => [7,2,1] => [7,2,1] => 6
1111110110 => [6,1,2,1] => [6,2,1,1] => 5
1111110101 => [6,1,1,1,1] => [6,1,1,1,1] => 5
1111110011 => [6,2,2] => [6,2,2] => 4
1111110010 => [6,2,1,1] => [6,2,1,1] => 5
1111110001 => [6,3,1] => [6,3,1] => 5
1111110000 => [6,4] => [6,4] => 2
1111101010 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 4
1111101001 => [5,1,1,2,1] => [5,2,1,1,1] => 4
1111101000 => [5,1,1,3] => [5,3,1,1] => 4
1111100100 => [5,2,1,2] => [5,2,2,1] => 4
1111100011 => [5,3,2] => [5,3,2] => 3
1111100010 => [5,3,1,1] => [5,3,1,1] => 4
1111100001 => [5,4,1] => [5,4,1] => 4
1111011110 => [4,1,4,1] => [4,4,1,1] => 3
1111011101 => [4,1,3,1,1] => [4,3,1,1,1] => 3
1111011011 => [4,1,2,1,2] => [4,2,2,1,1] => 3
1111011000 => [4,1,2,3] => [4,3,2,1] => 3
1111010111 => [4,1,1,1,3] => [4,3,1,1,1] => 3
1111010101 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 3
1111010100 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => 3
1111010011 => [4,1,1,2,2] => [4,2,2,1,1] => 3
1111010010 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => 3
1111010001 => [4,1,1,3,1] => [4,3,1,1,1] => 3
1111001111 => [4,2,4] => [4,4,2] => 2
1111001100 => [4,2,2,2] => [4,2,2,2] => 2
1111001011 => [4,2,1,1,2] => [4,2,2,1,1] => 3
1111001010 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => 3
1111001001 => [4,2,1,2,1] => [4,2,2,1,1] => 3
1111000111 => [4,3,3] => [4,3,3] => 1
1111000110 => [4,3,2,1] => [4,3,2,1] => 3
1111000101 => [4,3,1,1,1] => [4,3,1,1,1] => 3
1111000011 => [4,4,2] => [4,4,2] => 2
1111000001 => [4,5,1] => [5,4,1] => 4
1111000000 => [4,6] => [6,4] => 2
1110111111 => [3,1,6] => [6,3,1] => 5
1110111110 => [3,1,5,1] => [5,3,1,1] => 4
1110111101 => [3,1,4,1,1] => [4,3,1,1,1] => 3
1110111011 => [3,1,3,1,2] => [3,3,2,1,1] => 2
1110111000 => [3,1,3,3] => [3,3,3,1] => 2
1110110101 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 2
1110110100 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => 2
1110110010 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => 2
1110110001 => [3,1,2,3,1] => [3,3,2,1,1] => 2
1110101111 => [3,1,1,1,4] => [4,3,1,1,1] => 3
1110101101 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 2
1110101100 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => 2
1110101011 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 2
1110101010 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
1110101001 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 2
1110100101 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 2
1110100011 => [3,1,1,3,2] => [3,3,2,1,1] => 2
1110100001 => [3,1,1,4,1] => [4,3,1,1,1] => 3
1110011111 => [3,2,5] => [5,3,2] => 3
1110011110 => [3,2,4,1] => [4,3,2,1] => 3
1110011001 => [3,2,2,2,1] => [3,2,2,2,1] => 2
1110010101 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 2
1110010011 => [3,2,1,2,2] => [3,2,2,2,1] => 2
1110010001 => [3,2,1,3,1] => [3,3,2,1,1] => 2
1110001101 => [3,3,2,1,1] => [3,3,2,1,1] => 2
1110001001 => [3,3,1,2,1] => [3,3,2,1,1] => 2
1110000111 => [3,4,3] => [4,3,3] => 1
1110000101 => [3,4,1,1,1] => [4,3,1,1,1] => 3
1110000011 => [3,5,2] => [5,3,2] => 3
1110000010 => [3,5,1,1] => [5,3,1,1] => 4
1110000001 => [3,6,1] => [6,3,1] => 5
1101111111 => [2,1,7] => [7,2,1] => 6
1101111110 => [2,1,6,1] => [6,2,1,1] => 5
1101111101 => [2,1,5,1,1] => [5,2,1,1,1] => 4
1101111011 => [2,1,4,1,2] => [4,2,2,1,1] => 3
1101111001 => [2,1,4,2,1] => [4,2,2,1,1] => 3
1101111000 => [2,1,4,3] => [4,3,2,1] => 3
1101110111 => [2,1,3,1,3] => [3,3,2,1,1] => 2
1101110010 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => 2
1101110001 => [2,1,3,3,1] => [3,3,2,1,1] => 2
1101101111 => [2,1,2,1,4] => [4,2,2,1,1] => 3
1101101100 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => 1
1101101001 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1
1101100110 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => 1
1101100101 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1
1101100011 => [2,1,2,3,2] => [3,2,2,2,1] => 2
1101100001 => [2,1,2,4,1] => [4,2,2,1,1] => 3
1101100000 => [2,1,2,5] => [5,2,2,1] => 4
1101011111 => [2,1,1,1,5] => [5,2,1,1,1] => 4
1101011010 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1101011001 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1
1101010111 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 2
1101010101 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1101010011 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
1101010001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 2
1101001111 => [2,1,1,2,4] => [4,2,2,1,1] => 3
1101001110 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => 2
1101001101 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
1101001011 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
1101001001 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1
1101001000 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => 2
1101000111 => [2,1,1,3,3] => [3,3,2,1,1] => 2
1101000101 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 2
1101000011 => [2,1,1,4,2] => [4,2,2,1,1] => 3
1101000010 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => 3
1101000001 => [2,1,1,5,1] => [5,2,1,1,1] => 4
1100111111 => [2,2,6] => [6,2,2] => 4
1100111100 => [2,2,4,2] => [4,2,2,2] => 2
1100111001 => [2,2,3,2,1] => [3,2,2,2,1] => 2
1100110110 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => 1
1100110101 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
1100110011 => [2,2,2,2,2] => [2,2,2,2,2] => 0
1100110001 => [2,2,2,3,1] => [3,2,2,2,1] => 2
1100110000 => [2,2,2,4] => [4,2,2,2] => 2
1100101110 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => 2
1100101101 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 1
1100101011 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 1
1100101001 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 1
1100100111 => [2,2,1,2,3] => [3,2,2,2,1] => 2
1100100110 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => 1
1100100101 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 1
1100100011 => [2,2,1,3,2] => [3,2,2,2,1] => 2
1100011110 => [2,3,4,1] => [4,3,2,1] => 3
1100011101 => [2,3,3,1,1] => [3,3,2,1,1] => 2
1100011100 => [2,3,3,2] => [3,3,2,2] => 1
1100011011 => [2,3,2,1,2] => [3,2,2,2,1] => 2
1100011001 => [2,3,2,2,1] => [3,2,2,2,1] => 2
1100011000 => [2,3,2,3] => [3,3,2,2] => 1
1100010111 => [2,3,1,1,3] => [3,3,2,1,1] => 2
1100010101 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 2
1100010011 => [2,3,1,2,2] => [3,2,2,2,1] => 2
1100010010 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => 2
1100001111 => [2,4,4] => [4,4,2] => 2
1100001101 => [2,4,2,1,1] => [4,2,2,1,1] => 3
1100001100 => [2,4,2,2] => [4,2,2,2] => 2
1100001011 => [2,4,1,1,2] => [4,2,2,1,1] => 3
1100001010 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 3
1100001000 => [2,4,1,3] => [4,3,2,1] => 3
1100000111 => [2,5,3] => [5,3,2] => 3
1100000110 => [2,5,2,1] => [5,2,2,1] => 4
1100000011 => [2,6,2] => [6,2,2] => 4
1100000010 => [2,6,1,1] => [6,2,1,1] => 5
1100000001 => [2,7,1] => [7,2,1] => 6
1100000000 => [2,8] => [8,2] => 6
1011111111 => [1,1,8] => [8,1,1] => 7
1011111110 => [1,1,7,1] => [7,1,1,1] => 6
1011111101 => [1,1,6,1,1] => [6,1,1,1,1] => 5
1011111100 => [1,1,6,2] => [6,2,1,1] => 5
1011111011 => [1,1,5,1,2] => [5,2,1,1,1] => 4
1011111010 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 4
1011111000 => [1,1,5,3] => [5,3,1,1] => 4
1011110111 => [1,1,4,1,3] => [4,3,1,1,1] => 3
1011110100 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => 3
1011110001 => [1,1,4,3,1] => [4,3,1,1,1] => 3
1011100011 => [1,1,3,3,2] => [3,3,2,1,1] => 2
1011100001 => [1,1,3,4,1] => [4,3,1,1,1] => 3
1011100000 => [1,1,3,5] => [5,3,1,1] => 4
1011011001 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 1
1011010111 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 2
1011010101 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1011010011 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 1
1011010001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 2
1011010000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => 3
1011001101 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 1
1011001011 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 1
1011001001 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 1
1011001000 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => 2
1011000111 => [1,1,2,3,3] => [3,3,2,1,1] => 2
1011000101 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 2
1011000100 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => 2
1011000011 => [1,1,2,4,2] => [4,2,2,1,1] => 3
1011000010 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => 3
1011000000 => [1,1,2,6] => [6,2,1,1] => 5
1010111111 => [1,1,1,1,6] => [6,1,1,1,1] => 5
1010111110 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 4
1010110111 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 2
1010110101 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1010110011 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 1
1010110001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 2
1010110000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => 3
1010101111 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 3
1010101101 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1010101011 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 1
1010101001 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 1
1010101000 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 2
1010100111 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 2
1010100110 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 1
1010100101 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1010100100 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 1
1010100011 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 2
1010100010 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 2
1010100000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 4
1010011101 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 2
1010011011 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 1
1010011010 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1010011001 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 1
1010011000 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => 2
1010010111 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 2
1010010110 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
1010010101 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1010010100 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
1010010011 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 1
1010010010 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
1010010001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 2
1010001111 => [1,1,1,3,4] => [4,3,1,1,1] => 3
1010001110 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => 2
1010001101 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 2
1010001100 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => 2
1010001011 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 2
1010001010 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
1010000111 => [1,1,1,4,3] => [4,3,1,1,1] => 3
1010000010 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 4
1010000001 => [1,1,1,6,1] => [6,1,1,1,1] => 5
1010000000 => [1,1,1,7] => [7,1,1,1] => 6
1001111110 => [1,2,6,1] => [6,2,1,1] => 5
1001111000 => [1,2,4,3] => [4,3,2,1] => 3
1001110101 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 2
1001110100 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => 2
1001110011 => [1,2,3,2,2] => [3,2,2,2,1] => 2
1001110001 => [1,2,3,3,1] => [3,3,2,1,1] => 2
1001110000 => [1,2,3,4] => [4,3,2,1] => 3
1001101101 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1
1001101100 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => 1
1001101011 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1
1001101010 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1001101001 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1
1001101000 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => 2
1001100111 => [1,2,2,2,3] => [3,2,2,2,1] => 2
1001100110 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 1
1001100101 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1
1001100100 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => 1
1001100011 => [1,2,2,3,2] => [3,2,2,2,1] => 2
1001100010 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => 2
1001011111 => [1,2,1,1,5] => [5,2,1,1,1] => 4
1001011110 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => 3
1001011101 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 2
1001011011 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1
1001011010 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1001011001 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1
1001011000 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => 2
1001010111 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 2
1001010110 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
1001010101 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
1001010100 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
1001010011 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
1001010010 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
1001001111 => [1,2,1,2,4] => [4,2,2,1,1] => 3
1001001110 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => 2
1001001101 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
1001001100 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => 1
1001001011 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
1001001010 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
1001000111 => [1,2,1,3,3] => [3,3,2,1,1] => 2
1001000000 => [1,2,1,6] => [6,2,1,1] => 5
1000111110 => [1,3,5,1] => [5,3,1,1] => 4
1000111101 => [1,3,4,1,1] => [4,3,1,1,1] => 3
1000111100 => [1,3,4,2] => [4,3,2,1] => 3
1000111011 => [1,3,3,1,2] => [3,3,2,1,1] => 2
1000111010 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 2
1000111001 => [1,3,3,2,1] => [3,3,2,1,1] => 2
1000111000 => [1,3,3,3] => [3,3,3,1] => 2
1000110111 => [1,3,2,1,3] => [3,3,2,1,1] => 2
1000110110 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => 2
1000110101 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 2
1000110100 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => 2
1000110011 => [1,3,2,2,2] => [3,2,2,2,1] => 2
1000110010 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => 2
1000110001 => [1,3,2,3,1] => [3,3,2,1,1] => 2
1000101111 => [1,3,1,1,4] => [4,3,1,1,1] => 3
1000101110 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => 2
1000101101 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 2
1000101100 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => 2
1000101011 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 2
1000101010 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
1000100111 => [1,3,1,2,3] => [3,3,2,1,1] => 2
1000011111 => [1,4,5] => [5,4,1] => 4
1000011110 => [1,4,4,1] => [4,4,1,1] => 3
1000011101 => [1,4,3,1,1] => [4,3,1,1,1] => 3
1000011011 => [1,4,2,1,2] => [4,2,2,1,1] => 3
1000010111 => [1,4,1,1,3] => [4,3,1,1,1] => 3
1000010110 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => 3
1000010101 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 3
1000001111 => [1,5,4] => [5,4,1] => 4
1000001110 => [1,5,3,1] => [5,3,1,1] => 4
1000001101 => [1,5,2,1,1] => [5,2,1,1,1] => 4
1000001011 => [1,5,1,1,2] => [5,2,1,1,1] => 4
1000001010 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 4
1000001001 => [1,5,1,2,1] => [5,2,1,1,1] => 4
1000000110 => [1,6,2,1] => [6,2,1,1] => 5
1000000101 => [1,6,1,1,1] => [6,1,1,1,1] => 5
1000000100 => [1,6,1,2] => [6,2,1,1] => 5
1000000011 => [1,7,2] => [7,2,1] => 6
1000000010 => [1,7,1,1] => [7,1,1,1] => 6
1000000001 => [1,8,1] => [8,1,1] => 7
1000000000 => [1,9] => [9,1] => 8
10000011110 => [1,5,4,1] => [5,4,1,1] => 4
10000111110 => [1,4,5,1] => [5,4,1,1] => 4
100011001110 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => 2
110000011110 => [2,5,4,1] => [5,4,2,1] => 4
100001111100 => [1,4,5,2] => [5,4,2,1] => 4
100110001110 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => 2
100011100110 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => 2
0111111111 => [1,9] => [9,1] => 8
0111111101 => [1,7,1,1] => [7,1,1,1] => 6
0111111001 => [1,6,2,1] => [6,2,1,1] => 5
0111110001 => [1,5,3,1] => [5,3,1,1] => 4
0111100001 => [1,4,4,1] => [4,4,1,1] => 3
0100000001 => [1,1,7,1] => [7,1,1,1] => 6
0000000001 => [9,1] => [9,1] => 8
0111111011 => [1,6,1,2] => [6,2,1,1] => 5
0111110101 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 4
0111101001 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => 3
0111010001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => 2
0110100001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => 3
0101000001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 4
0101010101 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
0101001011 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 1
0101000111 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => 2
0100110011 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 1
0100100111 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => 2
0100011011 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => 2
0100010111 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => 2
0100001111 => [1,1,4,4] => [4,4,1,1] => 3
0011010011 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 1
0011000111 => [2,2,3,3] => [3,3,2,2] => 1
0010101011 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
0010010111 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => 2
0010001111 => [2,1,3,4] => [4,3,2,1] => 3
0001110011 => [3,3,2,2] => [3,3,2,2] => 1
0001101011 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => 2
0001100111 => [3,2,2,3] => [3,3,2,2] => 1
0001011101 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => 2
0001010111 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => 2
0001001111 => [3,1,2,4] => [4,3,2,1] => 3
0000111101 => [4,4,1,1] => [4,4,1,1] => 3
0000110111 => [4,2,1,3] => [4,3,2,1] => 3
0000101111 => [4,1,1,4] => [4,4,1,1] => 3
0000011111 => [5,5] => [5,5] => 0
010011000111 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => 2
001100010111 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => 2
001100001111 => [2,2,4,4] => [4,4,2,2] => 2
001011000111 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => 2
001000110111 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => 2
001000011111 => [2,1,4,5] => [5,4,2,1] => 4
000111010011 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => 2
000111001011 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => 2
000110010111 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => 2
000110001111 => [3,2,3,4] => [4,3,3,2] => 2
000100111011 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => 2
000100110111 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => 2
000100011111 => [3,1,3,5] => [5,3,3,1] => 4
000011110011 => [4,4,2,2] => [4,4,2,2] => 2
000011001111 => [4,2,2,4] => [4,4,2,2] => 2
000010011111 => [4,1,2,5] => [5,4,2,1] => 4
000001111011 => [5,4,1,2] => [5,4,2,1] => 4
000001110111 => [5,3,1,3] => [5,3,3,1] => 4
000001101111 => [5,2,1,4] => [5,4,2,1] => 4
111001100001 => [3,2,2,4,1] => [4,3,2,2,1] => 3
111000011001 => [3,4,2,2,1] => [4,3,2,2,1] => 3
111000001101 => [3,5,2,1,1] => [5,3,2,1,1] => 4
111000110001 => [3,3,2,3,1] => [3,3,3,2,1] => 2
111011000001 => [3,1,2,5,1] => [5,3,2,1,1] => 4
100111100001 => [1,2,4,4,1] => [4,4,2,1,1] => 3
100110000111 => [1,2,2,4,3] => [4,3,2,2,1] => 3
100001111001 => [1,4,4,2,1] => [4,4,2,1,1] => 3
100001100111 => [1,4,2,2,3] => [4,3,2,2,1] => 3
100000110111 => [1,5,2,1,3] => [5,3,2,1,1] => 4
100000110001 => [1,5,2,3,1] => [5,3,2,1,1] => 4
100000111101 => [1,5,4,1,1] => [5,4,1,1,1] => 4
100011000111 => [1,3,2,3,3] => [3,3,3,2,1] => 2
100011110001 => [1,3,4,3,1] => [4,3,3,1,1] => 3
101100011111 => [1,1,2,3,5] => [5,3,2,1,1] => 4
101100000111 => [1,1,2,5,3] => [5,3,2,1,1] => 4
101111000111 => [1,1,4,3,3] => [4,3,3,1,1] => 3
101111000001 => [1,1,4,5,1] => [5,4,1,1,1] => 4
0000000000 => [10] => [10] => 0
0000000110 => [7,2,1] => [7,2,1] => 6
0000011000 => [5,2,3] => [5,3,2] => 3
0000011110 => [5,4,1] => [5,4,1] => 4
0001111110 => [3,6,1] => [6,3,1] => 5
0110011000 => [1,2,2,2,3] => [3,2,2,2,1] => 2
0110010010 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1
0111100000 => [1,4,5] => [5,4,1] => 4
0111111110 => [1,8,1] => [8,1,1] => 7
0111001000 => [1,3,2,1,3] => [3,3,2,1,1] => 2
0111000010 => [1,3,4,1,1] => [4,3,1,1,1] => 3
0100111000 => [1,1,2,3,3] => [3,3,2,1,1] => 2
0100111110 => [1,1,2,5,1] => [5,2,1,1,1] => 4
0100110010 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 1
0100000010 => [1,1,6,1,1] => [6,1,1,1,1] => 5
0101101000 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 2
0101100010 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 2
0101001010 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
000110011110 => [3,2,2,4,1] => [4,3,2,2,1] => 3
000111100110 => [3,4,2,2,1] => [4,3,2,2,1] => 3
000111110010 => [3,5,2,1,1] => [5,3,2,1,1] => 4
000111001110 => [3,3,2,3,1] => [3,3,3,2,1] => 2
000100111110 => [3,1,2,5,1] => [5,3,2,1,1] => 4
011000011110 => [1,2,4,4,1] => [4,4,2,1,1] => 3
011001111000 => [1,2,2,4,3] => [4,3,2,2,1] => 3
011110000110 => [1,4,4,2,1] => [4,4,2,1,1] => 3
011110011000 => [1,4,2,2,3] => [4,3,2,2,1] => 3
011111001000 => [1,5,2,1,3] => [5,3,2,1,1] => 4
011111000010 => [1,5,4,1,1] => [5,4,1,1,1] => 4
011100111000 => [1,3,2,3,3] => [3,3,3,2,1] => 2
010011111000 => [1,1,2,5,3] => [5,3,2,1,1] => 4
010000111110 => [1,1,4,5,1] => [5,4,1,1,1] => 4
0010101010 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0010101100 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
0010110100 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
0011010100 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 1
0101010100 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 1
0010101110 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 2
0010111100 => [2,1,1,4,2] => [4,2,2,1,1] => 3
0011110100 => [2,4,1,1,2] => [4,2,2,1,1] => 3
0000010100 => [5,1,1,1,2] => [5,2,1,1,1] => 4
0111010100 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 2
0000000010 => [8,1,1] => [8,1,1] => 7
0000001110 => [6,3,1] => [6,3,1] => 5
0000111110 => [4,5,1] => [5,4,1] => 4
0011111110 => [2,7,1] => [7,2,1] => 6
0000000100 => [7,1,2] => [7,2,1] => 6
0000001010 => [6,1,1,1,1] => [6,1,1,1,1] => 5
0000010110 => [5,1,1,2,1] => [5,2,1,1,1] => 4
0000101110 => [4,1,1,3,1] => [4,3,1,1,1] => 3
0001011110 => [3,1,1,4,1] => [4,3,1,1,1] => 3
0010111110 => [2,1,1,5,1] => [5,2,1,1,1] => 4
0101111110 => [1,1,1,6,1] => [6,1,1,1,1] => 5
0010110010 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
0010111000 => [2,1,1,3,3] => [3,3,2,1,1] => 2
0011001010 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
0011001100 => [2,2,2,2,2] => [2,2,2,2,2] => 0
0011010010 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 1
0011011000 => [2,2,1,2,3] => [3,2,2,2,1] => 2
0011100010 => [2,3,3,1,1] => [3,3,2,1,1] => 2
0011100100 => [2,3,2,1,2] => [3,2,2,2,1] => 2
0011101000 => [2,3,1,1,3] => [3,3,2,1,1] => 2
0011110000 => [2,4,4] => [4,4,2] => 2
0100101010 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0100101100 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 1
0100110100 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 1
0101001100 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 1
0101010010 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0101011000 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 2
0101100100 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 1
0101110000 => [1,1,1,3,4] => [4,3,1,1,1] => 3
0110001010 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 2
0110001100 => [1,2,3,2,2] => [3,2,2,2,1] => 2
0110010100 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1
0110100010 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 2
0110100100 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1
0110101000 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 2
0110110000 => [1,2,1,2,4] => [4,2,2,1,1] => 3
0111000100 => [1,3,3,1,2] => [3,3,2,1,1] => 2
0111010000 => [1,3,1,1,4] => [4,3,1,1,1] => 3
011000111000 => [1,2,3,3,3] => [3,3,3,2,1] => 2
011100001100 => [1,3,4,2,2] => [4,3,2,2,1] => 3
011100011000 => [1,3,3,2,3] => [3,3,3,2,1] => 2
10000100001 => [1,4,1,4,1] => [4,4,1,1,1] => 3
0100000000 => [1,1,8] => [8,1,1] => 7
0100000011 => [1,1,6,2] => [6,2,1,1] => 5
0100000111 => [1,1,5,3] => [5,3,1,1] => 4
0100011111 => [1,1,3,5] => [5,3,1,1] => 4
0100111111 => [1,1,2,6] => [6,2,1,1] => 5
0101111111 => [1,1,1,7] => [7,1,1,1] => 6
0100000101 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 4
0100001011 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => 3
0100101111 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => 3
0101011111 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 4
0110111111 => [1,2,1,6] => [6,2,1,1] => 5
0101010110 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 1
0101011001 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 1
0101011010 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0101011100 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 2
0101100101 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
0101100110 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 1
0101101001 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
0101101010 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0101101100 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 1
0101110001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => 2
0101110010 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 2
0101110100 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 2
0101111000 => [1,1,1,4,3] => [4,3,1,1,1] => 3
0110010101 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
0110010110 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1
0110011001 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 1
0110011010 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1
0110011100 => [1,2,2,3,2] => [3,2,2,2,1] => 2
0110100101 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
0110100110 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1
0110101001 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
0110101010 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
0110101100 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
0110110001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => 2
0110110010 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
0110110100 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
0110111000 => [1,2,1,3,3] => [3,3,2,1,1] => 2
0111000101 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 2
0111000110 => [1,3,3,2,1] => [3,3,2,1,1] => 2
0111001001 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => 2
0111001010 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 2
0111001100 => [1,3,2,2,2] => [3,2,2,2,1] => 2
0111010010 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 2
0111011000 => [1,3,1,2,3] => [3,3,2,1,1] => 2
0111100010 => [1,4,3,1,1] => [4,3,1,1,1] => 3
0111100100 => [1,4,2,1,2] => [4,2,2,1,1] => 3
0111101000 => [1,4,1,1,3] => [4,3,1,1,1] => 3
0111110000 => [1,5,4] => [5,4,1] => 4
011001110001 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => 2
011100011001 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => 2
011100011100 => [1,3,3,3,2] => [3,3,3,2,1] => 2
011100110001 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => 2
011110001100 => [1,4,3,2,2] => [4,3,2,2,1] => 3
0100000100 => [1,1,5,1,2] => [5,2,1,1,1] => 4
0011100110 => [2,3,2,2,1] => [3,2,2,2,1] => 2
0011101010 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 2
0011101100 => [2,3,1,2,2] => [3,2,2,2,1] => 2
0001101110 => [3,2,1,3,1] => [3,3,2,1,1] => 2
0010110110 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1
0011110010 => [2,4,2,1,1] => [4,2,2,1,1] => 3
0001110110 => [3,3,1,2,1] => [3,3,2,1,1] => 2
0100111010 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 2
0010111010 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 2
0011111000 => [2,5,3] => [5,3,2] => 3
0001111010 => [3,4,1,1,1] => [4,3,1,1,1] => 3
0100111100 => [1,1,2,4,2] => [4,2,2,1,1] => 3
0001111100 => [3,5,2] => [5,3,2] => 3
001111000110 => [2,4,3,2,1] => [4,3,2,2,1] => 3
100111110000 => [1,2,5,4] => [5,4,2,1] => 4
001111110000 => [2,6,4] => [6,4,2] => 4
110001111000 => [2,3,4,3] => [4,3,3,2] => 2
100011111000 => [1,3,5,3] => [5,3,3,1] => 4
000011111100 => [4,6,2] => [6,4,2] => 4
0000000101 => [7,1,1,1] => [7,1,1,1] => 6
0000001101 => [6,2,1,1] => [6,2,1,1] => 5
0000011101 => [5,3,1,1] => [5,3,1,1] => 4
0001111101 => [3,5,1,1] => [5,3,1,1] => 4
0011111101 => [2,6,1,1] => [6,2,1,1] => 5
0000001001 => [6,1,2,1] => [6,2,1,1] => 5
0000010101 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 4
0000101101 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => 3
0010111101 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => 3
0101111101 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 4
110001110001 => [2,3,3,3,1] => [3,3,3,2,1] => 2
110011100001 => [2,2,3,4,1] => [4,3,2,2,1] => 3
0111000011 => [1,3,4,2] => [4,3,2,1] => 3
0011110001 => [2,4,3,1] => [4,3,2,1] => 3
110000111100 => [2,4,4,2] => [4,4,2,2] => 2
110000001111 => [2,6,4] => [6,4,2] => 4
011100000111 => [1,3,5,3] => [5,3,3,1] => 4
111000011100 => [3,4,3,2] => [4,3,3,2] => 2
001111000011 => [2,4,4,2] => [4,4,2,2] => 2
011110000011 => [1,4,5,2] => [5,4,2,1] => 4
111100000011 => [4,6,2] => [6,4,2] => 4
000111110001 => [3,5,3,1] => [5,3,3,1] => 4
001111100001 => [2,5,4,1] => [5,4,2,1] => 4
0011011001 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => 1
0010110001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => 2
0001000001 => [3,1,5,1] => [5,3,1,1] => 4
0111010101 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
0111010011 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => 2
0111001101 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => 2
0111011001 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => 2
0111000111 => [1,3,3,3] => [3,3,3,1] => 2
0011110101 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 3
0011110011 => [2,4,2,2] => [4,2,2,2] => 2
0111100101 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => 3
0111100011 => [1,4,3,2] => [4,3,2,1] => 3
0011111001 => [2,5,2,1] => [5,2,2,1] => 4
0000111111 => [4,6] => [6,4] => 2
110001111001 => [2,3,4,2,1] => [4,3,2,2,1] => 3
110011110001 => [2,2,4,3,1] => [4,3,2,2,1] => 3
011100111001 => [1,3,2,3,2,1] => [3,3,2,2,1,1] => 2
011100001111 => [1,3,4,4] => [4,4,3,1] => 3
111000111001 => [3,3,3,2,1] => [3,3,3,2,1] => 2
111001110001 => [3,2,3,3,1] => [3,3,3,2,1] => 2
111000001111 => [3,5,4] => [5,4,3] => 2
001111000111 => [2,4,3,3] => [4,3,3,2] => 2
011110000111 => [1,4,4,3] => [4,4,3,1] => 3
111100011001 => [4,3,2,2,1] => [4,3,2,2,1] => 3
111100110001 => [4,2,2,3,1] => [4,3,2,2,1] => 3
111100000111 => [4,5,3] => [5,4,3] => 2
000111110011 => [3,5,2,2] => [5,3,2,2] => 3
001111100011 => [2,5,3,2] => [5,3,2,2] => 3
011111000011 => [1,5,4,2] => [5,4,2,1] => 4
0001101100 => [3,2,1,2,2] => [3,2,2,2,1] => 2
0011000110 => [2,2,3,2,1] => [3,2,2,2,1] => 2
0010001110 => [2,1,3,3,1] => [3,3,2,1,1] => 2
0110111001 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => 2
0001101001 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => 2
0000110001 => [4,2,3,1] => [4,3,2,1] => 3
0000010001 => [5,1,3,1] => [5,3,1,1] => 4
0100011001 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => 2
0100111001 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => 2
0101111001 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 3
0110010001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => 2
0100010001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => 2
0100110001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => 2
0100100001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => 3
0101100001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => 3
0110011011 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => 1
0110111011 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => 2
0100111011 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => 2
0101111011 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => 3
0110010011 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => 1
0100010011 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => 2
0110110011 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => 1
0101110011 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => 2
0110100011 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => 2
0100100011 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => 2
0101100011 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => 2
0101000011 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 3
0110010111 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => 2
0110110111 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => 2
0100110111 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => 2
0101110111 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => 2
0110100111 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => 2
0101100111 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => 2
0110101111 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => 3
0101101111 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => 3
0101001111 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => 3
100011100011 => [1,3,3,3,2] => [3,3,3,2,1] => 2
100001110011 => [1,4,3,2,2] => [4,3,2,2,1] => 3
0000001100 => [6,2,2] => [6,2,2] => 4
0000011001 => [5,2,2,1] => [5,2,2,1] => 4
0000110011 => [4,2,2,2] => [4,2,2,2] => 2
0011001111 => [2,2,2,4] => [4,2,2,2] => 2
0110011111 => [1,2,2,5] => [5,2,2,1] => 4
0000110100 => [4,2,1,1,2] => [4,2,2,1,1] => 3
0000000011 => [8,2] => [8,2] => 6
0000011011 => [5,2,1,2] => [5,2,2,1] => 4
0001101111 => [3,2,1,4] => [4,3,2,1] => 3
0011011111 => [2,2,1,5] => [5,2,2,1] => 4
0000110101 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => 3
0011010111 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => 2
0111001011 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => 2
0111110111 => [1,5,1,3] => [5,3,1,1] => 4
0110001011 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => 2
0110000111 => [1,2,4,3] => [4,3,2,1] => 3
110000111001 => [2,4,3,2,1] => [4,3,2,2,1] => 3
001110000111 => [2,3,4,3] => [4,3,3,2] => 2
011000001111 => [1,2,5,4] => [5,4,2,1] => 4
0011011010 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 1
0011010110 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 1
0100110110 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 1
0110001110 => [1,2,3,3,1] => [3,3,2,1,1] => 2
0101001110 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 2
0011001110 => [2,2,2,3,1] => [3,2,2,2,1] => 2
0100101110 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 2
0100011110 => [1,1,3,4,1] => [4,3,1,1,1] => 3
0010011110 => [2,1,2,4,1] => [4,2,2,1,1] => 3
001110001110 => [2,3,3,3,1] => [3,3,3,2,1] => 2
001100011110 => [2,2,3,4,1] => [4,3,2,2,1] => 3
0101000000 => [1,1,1,1,6] => [6,1,1,1,1] => 5
0001010000 => [3,1,1,1,4] => [4,3,1,1,1] => 3
0100010000 => [1,1,3,1,4] => [4,3,1,1,1] => 3
0001000100 => [3,1,3,1,2] => [3,3,2,1,1] => 2
0111011100 => [1,3,1,3,2] => [3,3,2,1,1] => 2
0101000101 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 2
0001010101 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
0100010101 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
0110110101 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
0101010001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 2
0100101001 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
0110001001 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => 2
0101011011 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 1
0001001011 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => 2
0110101011 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
0001100011 => [3,2,3,2] => [3,3,2,2] => 1
0110000011 => [1,2,5,2] => [5,2,2,1] => 4
0001110111 => [3,3,1,3] => [3,3,3,1] => 2
0111101111 => [1,4,1,4] => [4,4,1,1] => 3
011000001100 => [1,2,5,2,2] => [5,2,2,2,1] => 4
000001100011 => [5,2,3,2] => [5,3,2,2] => 3
000110000011 => [3,2,5,2] => [5,3,2,2] => 3
011110001111 => [1,4,3,4] => [4,4,3,1] => 3
100011110011 => [1,3,4,2,2] => [4,3,2,2,1] => 3
100111000111 => [1,2,3,3,3] => [3,3,3,2,1] => 2
100011100111 => [1,3,3,2,3] => [3,3,3,2,1] => 2
0000000111 => [7,3] => [7,3] => 4
0000001111 => [6,4] => [6,4] => 2
0001111111 => [3,7] => [7,3] => 4
0011111111 => [2,8] => [8,2] => 6
0000001011 => [6,1,1,2] => [6,2,1,1] => 5
0000010111 => [5,1,1,3] => [5,3,1,1] => 4
0001011111 => [3,1,1,5] => [5,3,1,1] => 4
0010111111 => [2,1,1,6] => [6,2,1,1] => 5
0011011110 => [2,2,1,4,1] => [4,2,2,1,1] => 3
0011101110 => [2,3,1,3,1] => [3,3,2,1,1] => 2
0011110110 => [2,4,1,2,1] => [4,2,2,1,1] => 3
0011111010 => [2,5,1,1,1] => [5,2,1,1,1] => 4
0011111100 => [2,6,2] => [6,2,2] => 4
000111100011 => [3,4,3,2] => [4,3,3,2] => 2
0010010101 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
0101010111 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 2
0101110101 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 2
01111100100 => [1,5,2,1,2] => [5,2,2,1,1] => 4
110000011000 => [2,5,2,3] => [5,3,2,2] => 3
111100011110 => [4,3,4,1] => [4,4,3,1] => 3
111100000110 => [4,5,2,1] => [5,4,2,1] => 4
0110001111 => [1,2,3,4] => [4,3,2,1] => 3
0101101011 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
0101011101 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 2
0011000011 => [2,2,4,2] => [4,2,2,2] => 2
0011011011 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => 1
0001111011 => [3,4,1,2] => [4,3,2,1] => 3
111111001111 => [6,2,4] => [6,4,2] => 4
111111000011 => [6,4,2] => [6,4,2] => 4
001111001111 => [2,4,2,4] => [4,4,2,2] => 2
000011000011 => [4,2,4,2] => [4,4,2,2] => 2
111100111100 => [4,2,4,2] => [4,4,2,2] => 2
110000110000 => [2,4,2,4] => [4,4,2,2] => 2
0011011101 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => 2
0111011111 => [1,3,1,5] => [5,3,1,1] => 4
111100111001 => [4,2,3,2,1] => [4,3,2,2,1] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,4 6,6,4 4,18,6,4 8,22,24,6,4 4,50,40,24,6,4 8,70,98,46,24,6,4 6,120,190,116,46,24,6,4
$F_{1} = 2$
$F_{2} = 4$
$F_{3} = 4 + 4\ q$
$F_{4} = 6 + 6\ q + 4\ q^{2}$
$F_{5} = 4 + 18\ q + 6\ q^{2} + 4\ q^{3}$
$F_{6} = 8 + 22\ q + 24\ q^{2} + 6\ q^{3} + 4\ q^{4}$
$F_{7} = 4 + 50\ q + 40\ q^{2} + 24\ q^{3} + 6\ q^{4} + 4\ q^{5}$
$F_{8} = 8 + 70\ q + 98\ q^{2} + 46\ q^{3} + 24\ q^{4} + 6\ q^{5} + 4\ q^{6}$
$F_{9} = 6 + 120\ q + 190\ q^{2} + 116\ q^{3} + 46\ q^{4} + 24\ q^{5} + 6\ q^{6} + 4\ q^{7}$
Description
Difference between largest and smallest parts in a partition.
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 $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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