Identifier
-
Mp00178:
Binary words
—to composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000380: Integer partitions ⟶ ℤ
Values
0 => [2] => [2] => 3
1 => [1,1] => [1,1] => 3
00 => [3] => [3] => 4
01 => [2,1] => [2,1] => 3
10 => [1,2] => [2,1] => 3
11 => [1,1,1] => [1,1,1] => 4
000 => [4] => [4] => 5
001 => [3,1] => [3,1] => 4
010 => [2,2] => [2,2] => 4
011 => [2,1,1] => [2,1,1] => 4
100 => [1,3] => [3,1] => 4
101 => [1,2,1] => [2,1,1] => 4
110 => [1,1,2] => [2,1,1] => 4
111 => [1,1,1,1] => [1,1,1,1] => 5
0000 => [5] => [5] => 6
0001 => [4,1] => [4,1] => 5
0010 => [3,2] => [3,2] => 4
0011 => [3,1,1] => [3,1,1] => 4
0100 => [2,3] => [3,2] => 4
0101 => [2,2,1] => [2,2,1] => 4
0110 => [2,1,2] => [2,2,1] => 4
0111 => [2,1,1,1] => [2,1,1,1] => 5
1000 => [1,4] => [4,1] => 5
1001 => [1,3,1] => [3,1,1] => 4
1010 => [1,2,2] => [2,2,1] => 4
1011 => [1,2,1,1] => [2,1,1,1] => 5
1100 => [1,1,3] => [3,1,1] => 4
1101 => [1,1,2,1] => [2,1,1,1] => 5
1110 => [1,1,1,2] => [2,1,1,1] => 5
1111 => [1,1,1,1,1] => [1,1,1,1,1] => 6
00000 => [6] => [6] => 7
00001 => [5,1] => [5,1] => 6
00010 => [4,2] => [4,2] => 5
00011 => [4,1,1] => [4,1,1] => 5
00100 => [3,3] => [3,3] => 5
00101 => [3,2,1] => [3,2,1] => 4
00110 => [3,1,2] => [3,2,1] => 4
00111 => [3,1,1,1] => [3,1,1,1] => 5
01000 => [2,4] => [4,2] => 5
01001 => [2,3,1] => [3,2,1] => 4
01010 => [2,2,2] => [2,2,2] => 5
01011 => [2,2,1,1] => [2,2,1,1] => 5
01100 => [2,1,3] => [3,2,1] => 4
01101 => [2,1,2,1] => [2,2,1,1] => 5
01110 => [2,1,1,2] => [2,2,1,1] => 5
01111 => [2,1,1,1,1] => [2,1,1,1,1] => 6
10000 => [1,5] => [5,1] => 6
10001 => [1,4,1] => [4,1,1] => 5
10010 => [1,3,2] => [3,2,1] => 4
10011 => [1,3,1,1] => [3,1,1,1] => 5
10100 => [1,2,3] => [3,2,1] => 4
10101 => [1,2,2,1] => [2,2,1,1] => 5
10110 => [1,2,1,2] => [2,2,1,1] => 5
10111 => [1,2,1,1,1] => [2,1,1,1,1] => 6
11000 => [1,1,4] => [4,1,1] => 5
11001 => [1,1,3,1] => [3,1,1,1] => 5
11010 => [1,1,2,2] => [2,2,1,1] => 5
11011 => [1,1,2,1,1] => [2,1,1,1,1] => 6
11100 => [1,1,1,3] => [3,1,1,1] => 5
11101 => [1,1,1,2,1] => [2,1,1,1,1] => 6
11110 => [1,1,1,1,2] => [2,1,1,1,1] => 6
11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 7
000000 => [7] => [7] => 8
000001 => [6,1] => [6,1] => 7
000010 => [5,2] => [5,2] => 6
000011 => [5,1,1] => [5,1,1] => 6
000100 => [4,3] => [4,3] => 5
000101 => [4,2,1] => [4,2,1] => 5
000110 => [4,1,2] => [4,2,1] => 5
000111 => [4,1,1,1] => [4,1,1,1] => 5
001000 => [3,4] => [4,3] => 5
001001 => [3,3,1] => [3,3,1] => 5
001010 => [3,2,2] => [3,2,2] => 5
001011 => [3,2,1,1] => [3,2,1,1] => 5
001100 => [3,1,3] => [3,3,1] => 5
001101 => [3,1,2,1] => [3,2,1,1] => 5
001110 => [3,1,1,2] => [3,2,1,1] => 5
001111 => [3,1,1,1,1] => [3,1,1,1,1] => 6
010000 => [2,5] => [5,2] => 6
010001 => [2,4,1] => [4,2,1] => 5
010010 => [2,3,2] => [3,2,2] => 5
010011 => [2,3,1,1] => [3,2,1,1] => 5
010100 => [2,2,3] => [3,2,2] => 5
010101 => [2,2,2,1] => [2,2,2,1] => 5
010110 => [2,2,1,2] => [2,2,2,1] => 5
010111 => [2,2,1,1,1] => [2,2,1,1,1] => 6
011000 => [2,1,4] => [4,2,1] => 5
011001 => [2,1,3,1] => [3,2,1,1] => 5
011010 => [2,1,2,2] => [2,2,2,1] => 5
011011 => [2,1,2,1,1] => [2,2,1,1,1] => 6
011100 => [2,1,1,3] => [3,2,1,1] => 5
011101 => [2,1,1,2,1] => [2,2,1,1,1] => 6
011110 => [2,1,1,1,2] => [2,2,1,1,1] => 6
011111 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => 7
100000 => [1,6] => [6,1] => 7
100001 => [1,5,1] => [5,1,1] => 6
100010 => [1,4,2] => [4,2,1] => 5
100011 => [1,4,1,1] => [4,1,1,1] => 5
100100 => [1,3,3] => [3,3,1] => 5
100101 => [1,3,2,1] => [3,2,1,1] => 5
100110 => [1,3,1,2] => [3,2,1,1] => 5
>>> Load all 1567 entries. <<<100111 => [1,3,1,1,1] => [3,1,1,1,1] => 6
101000 => [1,2,4] => [4,2,1] => 5
101001 => [1,2,3,1] => [3,2,1,1] => 5
101010 => [1,2,2,2] => [2,2,2,1] => 5
101011 => [1,2,2,1,1] => [2,2,1,1,1] => 6
101100 => [1,2,1,3] => [3,2,1,1] => 5
101101 => [1,2,1,2,1] => [2,2,1,1,1] => 6
101110 => [1,2,1,1,2] => [2,2,1,1,1] => 6
101111 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => 7
110000 => [1,1,5] => [5,1,1] => 6
110001 => [1,1,4,1] => [4,1,1,1] => 5
110010 => [1,1,3,2] => [3,2,1,1] => 5
110011 => [1,1,3,1,1] => [3,1,1,1,1] => 6
110100 => [1,1,2,3] => [3,2,1,1] => 5
110101 => [1,1,2,2,1] => [2,2,1,1,1] => 6
110110 => [1,1,2,1,2] => [2,2,1,1,1] => 6
110111 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => 7
111000 => [1,1,1,4] => [4,1,1,1] => 5
111001 => [1,1,1,3,1] => [3,1,1,1,1] => 6
111010 => [1,1,1,2,2] => [2,2,1,1,1] => 6
111011 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => 7
111100 => [1,1,1,1,3] => [3,1,1,1,1] => 6
111101 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => 7
111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => 7
111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 8
0000000 => [8] => [8] => 9
0000001 => [7,1] => [7,1] => 8
0000010 => [6,2] => [6,2] => 7
0000011 => [6,1,1] => [6,1,1] => 7
0000100 => [5,3] => [5,3] => 6
0000101 => [5,2,1] => [5,2,1] => 6
0000110 => [5,1,2] => [5,2,1] => 6
0000111 => [5,1,1,1] => [5,1,1,1] => 6
0001000 => [4,4] => [4,4] => 6
0001001 => [4,3,1] => [4,3,1] => 5
0001010 => [4,2,2] => [4,2,2] => 5
0001011 => [4,2,1,1] => [4,2,1,1] => 5
0001100 => [4,1,3] => [4,3,1] => 5
0001101 => [4,1,2,1] => [4,2,1,1] => 5
0001110 => [4,1,1,2] => [4,2,1,1] => 5
0001111 => [4,1,1,1,1] => [4,1,1,1,1] => 6
0010000 => [3,5] => [5,3] => 6
0010001 => [3,4,1] => [4,3,1] => 5
0010010 => [3,3,2] => [3,3,2] => 5
0010011 => [3,3,1,1] => [3,3,1,1] => 5
0010100 => [3,2,3] => [3,3,2] => 5
0010101 => [3,2,2,1] => [3,2,2,1] => 5
0010110 => [3,2,1,2] => [3,2,2,1] => 5
0010111 => [3,2,1,1,1] => [3,2,1,1,1] => 6
0011000 => [3,1,4] => [4,3,1] => 5
0011001 => [3,1,3,1] => [3,3,1,1] => 5
0011010 => [3,1,2,2] => [3,2,2,1] => 5
0011011 => [3,1,2,1,1] => [3,2,1,1,1] => 6
0011100 => [3,1,1,3] => [3,3,1,1] => 5
0011101 => [3,1,1,2,1] => [3,2,1,1,1] => 6
0011110 => [3,1,1,1,2] => [3,2,1,1,1] => 6
0011111 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => 7
0100000 => [2,6] => [6,2] => 7
0100001 => [2,5,1] => [5,2,1] => 6
0100010 => [2,4,2] => [4,2,2] => 5
0100011 => [2,4,1,1] => [4,2,1,1] => 5
0100100 => [2,3,3] => [3,3,2] => 5
0100101 => [2,3,2,1] => [3,2,2,1] => 5
0100110 => [2,3,1,2] => [3,2,2,1] => 5
0100111 => [2,3,1,1,1] => [3,2,1,1,1] => 6
0101000 => [2,2,4] => [4,2,2] => 5
0101001 => [2,2,3,1] => [3,2,2,1] => 5
0101010 => [2,2,2,2] => [2,2,2,2] => 6
0101011 => [2,2,2,1,1] => [2,2,2,1,1] => 6
0101100 => [2,2,1,3] => [3,2,2,1] => 5
0101101 => [2,2,1,2,1] => [2,2,2,1,1] => 6
0101110 => [2,2,1,1,2] => [2,2,2,1,1] => 6
0101111 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => 7
0110000 => [2,1,5] => [5,2,1] => 6
0110001 => [2,1,4,1] => [4,2,1,1] => 5
0110010 => [2,1,3,2] => [3,2,2,1] => 5
0110011 => [2,1,3,1,1] => [3,2,1,1,1] => 6
0110100 => [2,1,2,3] => [3,2,2,1] => 5
0110101 => [2,1,2,2,1] => [2,2,2,1,1] => 6
0110110 => [2,1,2,1,2] => [2,2,2,1,1] => 6
0110111 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => 7
0111000 => [2,1,1,4] => [4,2,1,1] => 5
0111001 => [2,1,1,3,1] => [3,2,1,1,1] => 6
0111010 => [2,1,1,2,2] => [2,2,2,1,1] => 6
0111011 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => 7
0111100 => [2,1,1,1,3] => [3,2,1,1,1] => 6
0111101 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => 7
0111110 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => 7
0111111 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
1000000 => [1,7] => [7,1] => 8
1000001 => [1,6,1] => [6,1,1] => 7
1000010 => [1,5,2] => [5,2,1] => 6
1000011 => [1,5,1,1] => [5,1,1,1] => 6
1000100 => [1,4,3] => [4,3,1] => 5
1000101 => [1,4,2,1] => [4,2,1,1] => 5
1000110 => [1,4,1,2] => [4,2,1,1] => 5
1000111 => [1,4,1,1,1] => [4,1,1,1,1] => 6
1001000 => [1,3,4] => [4,3,1] => 5
1001001 => [1,3,3,1] => [3,3,1,1] => 5
1001010 => [1,3,2,2] => [3,2,2,1] => 5
1001011 => [1,3,2,1,1] => [3,2,1,1,1] => 6
1001100 => [1,3,1,3] => [3,3,1,1] => 5
1001101 => [1,3,1,2,1] => [3,2,1,1,1] => 6
1001110 => [1,3,1,1,2] => [3,2,1,1,1] => 6
1001111 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => 7
1010000 => [1,2,5] => [5,2,1] => 6
1010001 => [1,2,4,1] => [4,2,1,1] => 5
1010010 => [1,2,3,2] => [3,2,2,1] => 5
1010011 => [1,2,3,1,1] => [3,2,1,1,1] => 6
1010100 => [1,2,2,3] => [3,2,2,1] => 5
1010101 => [1,2,2,2,1] => [2,2,2,1,1] => 6
1010110 => [1,2,2,1,2] => [2,2,2,1,1] => 6
1010111 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => 7
1011000 => [1,2,1,4] => [4,2,1,1] => 5
1011001 => [1,2,1,3,1] => [3,2,1,1,1] => 6
1011010 => [1,2,1,2,2] => [2,2,2,1,1] => 6
1011011 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => 7
1011100 => [1,2,1,1,3] => [3,2,1,1,1] => 6
1011101 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => 7
1011110 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => 7
1011111 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 8
1100000 => [1,1,6] => [6,1,1] => 7
1100001 => [1,1,5,1] => [5,1,1,1] => 6
1100010 => [1,1,4,2] => [4,2,1,1] => 5
1100011 => [1,1,4,1,1] => [4,1,1,1,1] => 6
1100100 => [1,1,3,3] => [3,3,1,1] => 5
1100101 => [1,1,3,2,1] => [3,2,1,1,1] => 6
1100110 => [1,1,3,1,2] => [3,2,1,1,1] => 6
1100111 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => 7
1101000 => [1,1,2,4] => [4,2,1,1] => 5
1101001 => [1,1,2,3,1] => [3,2,1,1,1] => 6
1101010 => [1,1,2,2,2] => [2,2,2,1,1] => 6
1101011 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => 7
1101100 => [1,1,2,1,3] => [3,2,1,1,1] => 6
1101101 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => 7
1101110 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => 7
1101111 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 8
1110000 => [1,1,1,5] => [5,1,1,1] => 6
1110001 => [1,1,1,4,1] => [4,1,1,1,1] => 6
1110010 => [1,1,1,3,2] => [3,2,1,1,1] => 6
1110011 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => 7
1110100 => [1,1,1,2,3] => [3,2,1,1,1] => 6
1110101 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => 7
1110110 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => 7
1110111 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 8
1111000 => [1,1,1,1,4] => [4,1,1,1,1] => 6
1111001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => 7
1111010 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => 7
1111011 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 8
1111100 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => 7
1111101 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 8
1111110 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 8
1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 9
00000000 => [9] => [9] => 10
00000001 => [8,1] => [8,1] => 9
00000010 => [7,2] => [7,2] => 8
00000011 => [7,1,1] => [7,1,1] => 8
00000100 => [6,3] => [6,3] => 7
00000101 => [6,2,1] => [6,2,1] => 7
00000110 => [6,1,2] => [6,2,1] => 7
00000111 => [6,1,1,1] => [6,1,1,1] => 7
00001000 => [5,4] => [5,4] => 6
00001001 => [5,3,1] => [5,3,1] => 6
00001010 => [5,2,2] => [5,2,2] => 6
00001011 => [5,2,1,1] => [5,2,1,1] => 6
00001100 => [5,1,3] => [5,3,1] => 6
00001101 => [5,1,2,1] => [5,2,1,1] => 6
00001110 => [5,1,1,2] => [5,2,1,1] => 6
00001111 => [5,1,1,1,1] => [5,1,1,1,1] => 6
00010000 => [4,5] => [5,4] => 6
00010001 => [4,4,1] => [4,4,1] => 6
00010010 => [4,3,2] => [4,3,2] => 5
00010011 => [4,3,1,1] => [4,3,1,1] => 5
00010100 => [4,2,3] => [4,3,2] => 5
00010101 => [4,2,2,1] => [4,2,2,1] => 5
00010110 => [4,2,1,2] => [4,2,2,1] => 5
00010111 => [4,2,1,1,1] => [4,2,1,1,1] => 6
00011000 => [4,1,4] => [4,4,1] => 6
00011001 => [4,1,3,1] => [4,3,1,1] => 5
00011010 => [4,1,2,2] => [4,2,2,1] => 5
00011011 => [4,1,2,1,1] => [4,2,1,1,1] => 6
00011100 => [4,1,1,3] => [4,3,1,1] => 5
00011101 => [4,1,1,2,1] => [4,2,1,1,1] => 6
00011110 => [4,1,1,1,2] => [4,2,1,1,1] => 6
00011111 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => 7
00100000 => [3,6] => [6,3] => 7
00100001 => [3,5,1] => [5,3,1] => 6
00100010 => [3,4,2] => [4,3,2] => 5
00100011 => [3,4,1,1] => [4,3,1,1] => 5
00100100 => [3,3,3] => [3,3,3] => 6
00100101 => [3,3,2,1] => [3,3,2,1] => 5
00100110 => [3,3,1,2] => [3,3,2,1] => 5
00100111 => [3,3,1,1,1] => [3,3,1,1,1] => 6
00101000 => [3,2,4] => [4,3,2] => 5
00101001 => [3,2,3,1] => [3,3,2,1] => 5
00101010 => [3,2,2,2] => [3,2,2,2] => 6
00101011 => [3,2,2,1,1] => [3,2,2,1,1] => 6
00101100 => [3,2,1,3] => [3,3,2,1] => 5
00101101 => [3,2,1,2,1] => [3,2,2,1,1] => 6
00101110 => [3,2,1,1,2] => [3,2,2,1,1] => 6
00101111 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => 7
00110000 => [3,1,5] => [5,3,1] => 6
00110001 => [3,1,4,1] => [4,3,1,1] => 5
00110010 => [3,1,3,2] => [3,3,2,1] => 5
00110011 => [3,1,3,1,1] => [3,3,1,1,1] => 6
00110100 => [3,1,2,3] => [3,3,2,1] => 5
00110101 => [3,1,2,2,1] => [3,2,2,1,1] => 6
00110110 => [3,1,2,1,2] => [3,2,2,1,1] => 6
00110111 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => 7
00111000 => [3,1,1,4] => [4,3,1,1] => 5
00111001 => [3,1,1,3,1] => [3,3,1,1,1] => 6
00111010 => [3,1,1,2,2] => [3,2,2,1,1] => 6
00111011 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => 7
00111100 => [3,1,1,1,3] => [3,3,1,1,1] => 6
00111101 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => 7
00111110 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => 7
00111111 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 8
01000000 => [2,7] => [7,2] => 8
01000001 => [2,6,1] => [6,2,1] => 7
01000010 => [2,5,2] => [5,2,2] => 6
01000011 => [2,5,1,1] => [5,2,1,1] => 6
01000100 => [2,4,3] => [4,3,2] => 5
01000101 => [2,4,2,1] => [4,2,2,1] => 5
01000110 => [2,4,1,2] => [4,2,2,1] => 5
01000111 => [2,4,1,1,1] => [4,2,1,1,1] => 6
01001000 => [2,3,4] => [4,3,2] => 5
01001001 => [2,3,3,1] => [3,3,2,1] => 5
01001010 => [2,3,2,2] => [3,2,2,2] => 6
01001011 => [2,3,2,1,1] => [3,2,2,1,1] => 6
01001100 => [2,3,1,3] => [3,3,2,1] => 5
01001101 => [2,3,1,2,1] => [3,2,2,1,1] => 6
01001110 => [2,3,1,1,2] => [3,2,2,1,1] => 6
01001111 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => 7
01010000 => [2,2,5] => [5,2,2] => 6
01010001 => [2,2,4,1] => [4,2,2,1] => 5
01010010 => [2,2,3,2] => [3,2,2,2] => 6
01010011 => [2,2,3,1,1] => [3,2,2,1,1] => 6
01010100 => [2,2,2,3] => [3,2,2,2] => 6
01010101 => [2,2,2,2,1] => [2,2,2,2,1] => 6
01010110 => [2,2,2,1,2] => [2,2,2,2,1] => 6
01010111 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => 7
01011000 => [2,2,1,4] => [4,2,2,1] => 5
01011001 => [2,2,1,3,1] => [3,2,2,1,1] => 6
01011010 => [2,2,1,2,2] => [2,2,2,2,1] => 6
01011011 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => 7
01011100 => [2,2,1,1,3] => [3,2,2,1,1] => 6
01011101 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => 7
01011110 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => 7
01011111 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 8
01100000 => [2,1,6] => [6,2,1] => 7
01100001 => [2,1,5,1] => [5,2,1,1] => 6
01100010 => [2,1,4,2] => [4,2,2,1] => 5
01100011 => [2,1,4,1,1] => [4,2,1,1,1] => 6
01100100 => [2,1,3,3] => [3,3,2,1] => 5
01100101 => [2,1,3,2,1] => [3,2,2,1,1] => 6
01100110 => [2,1,3,1,2] => [3,2,2,1,1] => 6
01100111 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => 7
01101000 => [2,1,2,4] => [4,2,2,1] => 5
01101001 => [2,1,2,3,1] => [3,2,2,1,1] => 6
01101010 => [2,1,2,2,2] => [2,2,2,2,1] => 6
01101011 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => 7
01101100 => [2,1,2,1,3] => [3,2,2,1,1] => 6
01101101 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => 7
01101110 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => 7
01101111 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 8
01110000 => [2,1,1,5] => [5,2,1,1] => 6
01110001 => [2,1,1,4,1] => [4,2,1,1,1] => 6
01110010 => [2,1,1,3,2] => [3,2,2,1,1] => 6
01110011 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => 7
01110100 => [2,1,1,2,3] => [3,2,2,1,1] => 6
01110101 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => 7
01110110 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => 7
01110111 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 8
01111000 => [2,1,1,1,4] => [4,2,1,1,1] => 6
01111001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => 7
01111010 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => 7
01111011 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 8
01111100 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => 7
01111101 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 8
01111110 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 8
01111111 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
10000000 => [1,8] => [8,1] => 9
10000001 => [1,7,1] => [7,1,1] => 8
10000010 => [1,6,2] => [6,2,1] => 7
10000011 => [1,6,1,1] => [6,1,1,1] => 7
10000100 => [1,5,3] => [5,3,1] => 6
10000101 => [1,5,2,1] => [5,2,1,1] => 6
10000110 => [1,5,1,2] => [5,2,1,1] => 6
10000111 => [1,5,1,1,1] => [5,1,1,1,1] => 6
10001000 => [1,4,4] => [4,4,1] => 6
10001001 => [1,4,3,1] => [4,3,1,1] => 5
10001010 => [1,4,2,2] => [4,2,2,1] => 5
10001011 => [1,4,2,1,1] => [4,2,1,1,1] => 6
10001100 => [1,4,1,3] => [4,3,1,1] => 5
10001101 => [1,4,1,2,1] => [4,2,1,1,1] => 6
10001110 => [1,4,1,1,2] => [4,2,1,1,1] => 6
10001111 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => 7
10010000 => [1,3,5] => [5,3,1] => 6
10010001 => [1,3,4,1] => [4,3,1,1] => 5
10010010 => [1,3,3,2] => [3,3,2,1] => 5
10010011 => [1,3,3,1,1] => [3,3,1,1,1] => 6
10010100 => [1,3,2,3] => [3,3,2,1] => 5
10010101 => [1,3,2,2,1] => [3,2,2,1,1] => 6
10010110 => [1,3,2,1,2] => [3,2,2,1,1] => 6
10010111 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => 7
10011000 => [1,3,1,4] => [4,3,1,1] => 5
10011001 => [1,3,1,3,1] => [3,3,1,1,1] => 6
10011010 => [1,3,1,2,2] => [3,2,2,1,1] => 6
10011011 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => 7
10011100 => [1,3,1,1,3] => [3,3,1,1,1] => 6
10011101 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => 7
10011110 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => 7
10011111 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 8
10100000 => [1,2,6] => [6,2,1] => 7
10100001 => [1,2,5,1] => [5,2,1,1] => 6
10100010 => [1,2,4,2] => [4,2,2,1] => 5
10100011 => [1,2,4,1,1] => [4,2,1,1,1] => 6
10100100 => [1,2,3,3] => [3,3,2,1] => 5
10100101 => [1,2,3,2,1] => [3,2,2,1,1] => 6
10100110 => [1,2,3,1,2] => [3,2,2,1,1] => 6
10100111 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => 7
10101000 => [1,2,2,4] => [4,2,2,1] => 5
10101001 => [1,2,2,3,1] => [3,2,2,1,1] => 6
10101010 => [1,2,2,2,2] => [2,2,2,2,1] => 6
10101011 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => 7
10101100 => [1,2,2,1,3] => [3,2,2,1,1] => 6
10101101 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => 7
10101110 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => 7
10101111 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 8
10110000 => [1,2,1,5] => [5,2,1,1] => 6
10110001 => [1,2,1,4,1] => [4,2,1,1,1] => 6
10110010 => [1,2,1,3,2] => [3,2,2,1,1] => 6
10110011 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => 7
10110100 => [1,2,1,2,3] => [3,2,2,1,1] => 6
10110101 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => 7
10110110 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => 7
10110111 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 8
10111000 => [1,2,1,1,4] => [4,2,1,1,1] => 6
10111001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => 7
10111010 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => 7
10111011 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 8
10111100 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => 7
10111101 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 8
10111110 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 8
10111111 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
11000000 => [1,1,7] => [7,1,1] => 8
11000001 => [1,1,6,1] => [6,1,1,1] => 7
11000010 => [1,1,5,2] => [5,2,1,1] => 6
11000011 => [1,1,5,1,1] => [5,1,1,1,1] => 6
11000100 => [1,1,4,3] => [4,3,1,1] => 5
11000101 => [1,1,4,2,1] => [4,2,1,1,1] => 6
11000110 => [1,1,4,1,2] => [4,2,1,1,1] => 6
11000111 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => 7
11001000 => [1,1,3,4] => [4,3,1,1] => 5
11001001 => [1,1,3,3,1] => [3,3,1,1,1] => 6
11001010 => [1,1,3,2,2] => [3,2,2,1,1] => 6
11001011 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => 7
11001100 => [1,1,3,1,3] => [3,3,1,1,1] => 6
11001101 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => 7
11001110 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => 7
11001111 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 8
11010000 => [1,1,2,5] => [5,2,1,1] => 6
11010001 => [1,1,2,4,1] => [4,2,1,1,1] => 6
11010010 => [1,1,2,3,2] => [3,2,2,1,1] => 6
11010011 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => 7
11010100 => [1,1,2,2,3] => [3,2,2,1,1] => 6
11010101 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => 7
11010110 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => 7
11010111 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 8
11011000 => [1,1,2,1,4] => [4,2,1,1,1] => 6
11011001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => 7
11011010 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => 7
11011011 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 8
11011100 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => 7
11011101 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 8
11011110 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 8
11011111 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
11100000 => [1,1,1,6] => [6,1,1,1] => 7
11100001 => [1,1,1,5,1] => [5,1,1,1,1] => 6
11100010 => [1,1,1,4,2] => [4,2,1,1,1] => 6
11100011 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => 7
11100100 => [1,1,1,3,3] => [3,3,1,1,1] => 6
11100101 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => 7
11100110 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => 7
11100111 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 8
11101000 => [1,1,1,2,4] => [4,2,1,1,1] => 6
11101001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => 7
11101010 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => 7
11101011 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 8
11101100 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => 7
11101101 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 8
11101110 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 8
11101111 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 9
11110000 => [1,1,1,1,5] => [5,1,1,1,1] => 6
11110001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => 7
11110010 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => 7
11110011 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 8
11110100 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => 7
11110101 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 8
11110110 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 8
11110111 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 9
11111000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => 7
11111001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 8
11111010 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 8
11111011 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 9
11111100 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 8
11111101 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 9
11111110 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 9
11111111 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 10
000000000 => [10] => [10] => 11
000000001 => [9,1] => [9,1] => 10
000000010 => [8,2] => [8,2] => 9
000000011 => [8,1,1] => [8,1,1] => 9
000000100 => [7,3] => [7,3] => 8
000000101 => [7,2,1] => [7,2,1] => 8
000000110 => [7,1,2] => [7,2,1] => 8
000000111 => [7,1,1,1] => [7,1,1,1] => 8
000001000 => [6,4] => [6,4] => 7
000001001 => [6,3,1] => [6,3,1] => 7
000001010 => [6,2,2] => [6,2,2] => 7
000001011 => [6,2,1,1] => [6,2,1,1] => 7
000001100 => [6,1,3] => [6,3,1] => 7
000001101 => [6,1,2,1] => [6,2,1,1] => 7
000001110 => [6,1,1,2] => [6,2,1,1] => 7
000001111 => [6,1,1,1,1] => [6,1,1,1,1] => 7
000010000 => [5,5] => [5,5] => 7
000010001 => [5,4,1] => [5,4,1] => 6
000010010 => [5,3,2] => [5,3,2] => 6
000010011 => [5,3,1,1] => [5,3,1,1] => 6
000010100 => [5,2,3] => [5,3,2] => 6
000010101 => [5,2,2,1] => [5,2,2,1] => 6
000010110 => [5,2,1,2] => [5,2,2,1] => 6
000010111 => [5,2,1,1,1] => [5,2,1,1,1] => 6
000011000 => [5,1,4] => [5,4,1] => 6
000011001 => [5,1,3,1] => [5,3,1,1] => 6
000011010 => [5,1,2,2] => [5,2,2,1] => 6
000011011 => [5,1,2,1,1] => [5,2,1,1,1] => 6
000011100 => [5,1,1,3] => [5,3,1,1] => 6
000011101 => [5,1,1,2,1] => [5,2,1,1,1] => 6
000011110 => [5,1,1,1,2] => [5,2,1,1,1] => 6
000011111 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => 7
000100000 => [4,6] => [6,4] => 7
000100001 => [4,5,1] => [5,4,1] => 6
000100010 => [4,4,2] => [4,4,2] => 6
000100011 => [4,4,1,1] => [4,4,1,1] => 6
000100100 => [4,3,3] => [4,3,3] => 6
000100101 => [4,3,2,1] => [4,3,2,1] => 5
000100110 => [4,3,1,2] => [4,3,2,1] => 5
000100111 => [4,3,1,1,1] => [4,3,1,1,1] => 6
000101000 => [4,2,4] => [4,4,2] => 6
000101001 => [4,2,3,1] => [4,3,2,1] => 5
000101010 => [4,2,2,2] => [4,2,2,2] => 6
000101011 => [4,2,2,1,1] => [4,2,2,1,1] => 6
000101100 => [4,2,1,3] => [4,3,2,1] => 5
000101101 => [4,2,1,2,1] => [4,2,2,1,1] => 6
000101110 => [4,2,1,1,2] => [4,2,2,1,1] => 6
000101111 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => 7
000110000 => [4,1,5] => [5,4,1] => 6
000110001 => [4,1,4,1] => [4,4,1,1] => 6
000110010 => [4,1,3,2] => [4,3,2,1] => 5
000110011 => [4,1,3,1,1] => [4,3,1,1,1] => 6
000110100 => [4,1,2,3] => [4,3,2,1] => 5
000110101 => [4,1,2,2,1] => [4,2,2,1,1] => 6
000110110 => [4,1,2,1,2] => [4,2,2,1,1] => 6
000110111 => [4,1,2,1,1,1] => [4,2,1,1,1,1] => 7
000111000 => [4,1,1,4] => [4,4,1,1] => 6
000111001 => [4,1,1,3,1] => [4,3,1,1,1] => 6
000111010 => [4,1,1,2,2] => [4,2,2,1,1] => 6
000111011 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => 7
000111100 => [4,1,1,1,3] => [4,3,1,1,1] => 6
000111101 => [4,1,1,1,2,1] => [4,2,1,1,1,1] => 7
000111110 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => 7
000111111 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 8
001000000 => [3,7] => [7,3] => 8
001000001 => [3,6,1] => [6,3,1] => 7
001000010 => [3,5,2] => [5,3,2] => 6
001000011 => [3,5,1,1] => [5,3,1,1] => 6
001000100 => [3,4,3] => [4,3,3] => 6
001000101 => [3,4,2,1] => [4,3,2,1] => 5
001000110 => [3,4,1,2] => [4,3,2,1] => 5
001000111 => [3,4,1,1,1] => [4,3,1,1,1] => 6
001001000 => [3,3,4] => [4,3,3] => 6
001001001 => [3,3,3,1] => [3,3,3,1] => 6
001001010 => [3,3,2,2] => [3,3,2,2] => 6
001001011 => [3,3,2,1,1] => [3,3,2,1,1] => 6
001001100 => [3,3,1,3] => [3,3,3,1] => 6
001001101 => [3,3,1,2,1] => [3,3,2,1,1] => 6
001001110 => [3,3,1,1,2] => [3,3,2,1,1] => 6
001001111 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => 7
001010000 => [3,2,5] => [5,3,2] => 6
001010001 => [3,2,4,1] => [4,3,2,1] => 5
001010010 => [3,2,3,2] => [3,3,2,2] => 6
001010011 => [3,2,3,1,1] => [3,3,2,1,1] => 6
001010100 => [3,2,2,3] => [3,3,2,2] => 6
001010101 => [3,2,2,2,1] => [3,2,2,2,1] => 6
001010110 => [3,2,2,1,2] => [3,2,2,2,1] => 6
001010111 => [3,2,2,1,1,1] => [3,2,2,1,1,1] => 7
001011000 => [3,2,1,4] => [4,3,2,1] => 5
001011001 => [3,2,1,3,1] => [3,3,2,1,1] => 6
001011010 => [3,2,1,2,2] => [3,2,2,2,1] => 6
001011011 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => 7
001011100 => [3,2,1,1,3] => [3,3,2,1,1] => 6
001011101 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => 7
001011110 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => 7
001011111 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 8
001100000 => [3,1,6] => [6,3,1] => 7
001100001 => [3,1,5,1] => [5,3,1,1] => 6
001100010 => [3,1,4,2] => [4,3,2,1] => 5
001100011 => [3,1,4,1,1] => [4,3,1,1,1] => 6
001100100 => [3,1,3,3] => [3,3,3,1] => 6
001100101 => [3,1,3,2,1] => [3,3,2,1,1] => 6
001100110 => [3,1,3,1,2] => [3,3,2,1,1] => 6
001100111 => [3,1,3,1,1,1] => [3,3,1,1,1,1] => 7
001101000 => [3,1,2,4] => [4,3,2,1] => 5
001101001 => [3,1,2,3,1] => [3,3,2,1,1] => 6
001101010 => [3,1,2,2,2] => [3,2,2,2,1] => 6
001101011 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => 7
001101100 => [3,1,2,1,3] => [3,3,2,1,1] => 6
001101101 => [3,1,2,1,2,1] => [3,2,2,1,1,1] => 7
001101110 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => 7
001101111 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 8
001110000 => [3,1,1,5] => [5,3,1,1] => 6
001110001 => [3,1,1,4,1] => [4,3,1,1,1] => 6
001110010 => [3,1,1,3,2] => [3,3,2,1,1] => 6
001110011 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => 7
001110100 => [3,1,1,2,3] => [3,3,2,1,1] => 6
001110101 => [3,1,1,2,2,1] => [3,2,2,1,1,1] => 7
001110110 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => 7
001110111 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 8
001111000 => [3,1,1,1,4] => [4,3,1,1,1] => 6
001111001 => [3,1,1,1,3,1] => [3,3,1,1,1,1] => 7
001111010 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => 7
001111011 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 8
001111100 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => 7
001111101 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 8
001111110 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 8
001111111 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 9
010000000 => [2,8] => [8,2] => 9
010000001 => [2,7,1] => [7,2,1] => 8
010000010 => [2,6,2] => [6,2,2] => 7
010000011 => [2,6,1,1] => [6,2,1,1] => 7
010000100 => [2,5,3] => [5,3,2] => 6
010000101 => [2,5,2,1] => [5,2,2,1] => 6
010000110 => [2,5,1,2] => [5,2,2,1] => 6
010000111 => [2,5,1,1,1] => [5,2,1,1,1] => 6
010001000 => [2,4,4] => [4,4,2] => 6
010001001 => [2,4,3,1] => [4,3,2,1] => 5
010001010 => [2,4,2,2] => [4,2,2,2] => 6
010001011 => [2,4,2,1,1] => [4,2,2,1,1] => 6
010001100 => [2,4,1,3] => [4,3,2,1] => 5
010001101 => [2,4,1,2,1] => [4,2,2,1,1] => 6
010001110 => [2,4,1,1,2] => [4,2,2,1,1] => 6
010001111 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => 7
010010000 => [2,3,5] => [5,3,2] => 6
010010001 => [2,3,4,1] => [4,3,2,1] => 5
010010010 => [2,3,3,2] => [3,3,2,2] => 6
010010011 => [2,3,3,1,1] => [3,3,2,1,1] => 6
010010100 => [2,3,2,3] => [3,3,2,2] => 6
010010101 => [2,3,2,2,1] => [3,2,2,2,1] => 6
010010110 => [2,3,2,1,2] => [3,2,2,2,1] => 6
010010111 => [2,3,2,1,1,1] => [3,2,2,1,1,1] => 7
010011000 => [2,3,1,4] => [4,3,2,1] => 5
010011001 => [2,3,1,3,1] => [3,3,2,1,1] => 6
010011010 => [2,3,1,2,2] => [3,2,2,2,1] => 6
010011011 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => 7
010011100 => [2,3,1,1,3] => [3,3,2,1,1] => 6
010011101 => [2,3,1,1,2,1] => [3,2,2,1,1,1] => 7
010011110 => [2,3,1,1,1,2] => [3,2,2,1,1,1] => 7
010011111 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 8
010100000 => [2,2,6] => [6,2,2] => 7
010100001 => [2,2,5,1] => [5,2,2,1] => 6
010100010 => [2,2,4,2] => [4,2,2,2] => 6
010100011 => [2,2,4,1,1] => [4,2,2,1,1] => 6
010100100 => [2,2,3,3] => [3,3,2,2] => 6
010100101 => [2,2,3,2,1] => [3,2,2,2,1] => 6
010100110 => [2,2,3,1,2] => [3,2,2,2,1] => 6
010100111 => [2,2,3,1,1,1] => [3,2,2,1,1,1] => 7
010101000 => [2,2,2,4] => [4,2,2,2] => 6
010101001 => [2,2,2,3,1] => [3,2,2,2,1] => 6
010101010 => [2,2,2,2,2] => [2,2,2,2,2] => 7
010101011 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => 7
010101100 => [2,2,2,1,3] => [3,2,2,2,1] => 6
010101101 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => 7
010101110 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => 7
010101111 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 8
010110000 => [2,2,1,5] => [5,2,2,1] => 6
010110001 => [2,2,1,4,1] => [4,2,2,1,1] => 6
010110010 => [2,2,1,3,2] => [3,2,2,2,1] => 6
010110011 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => 7
010110100 => [2,2,1,2,3] => [3,2,2,2,1] => 6
010110101 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => 7
010110110 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => 7
010110111 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 8
010111000 => [2,2,1,1,4] => [4,2,2,1,1] => 6
010111001 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => 7
010111010 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => 7
010111011 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 8
010111100 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => 7
010111101 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 8
010111110 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 8
010111111 => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
011000000 => [2,1,7] => [7,2,1] => 8
011000001 => [2,1,6,1] => [6,2,1,1] => 7
011000010 => [2,1,5,2] => [5,2,2,1] => 6
011000011 => [2,1,5,1,1] => [5,2,1,1,1] => 6
011000100 => [2,1,4,3] => [4,3,2,1] => 5
011000101 => [2,1,4,2,1] => [4,2,2,1,1] => 6
011000110 => [2,1,4,1,2] => [4,2,2,1,1] => 6
011000111 => [2,1,4,1,1,1] => [4,2,1,1,1,1] => 7
011001000 => [2,1,3,4] => [4,3,2,1] => 5
011001001 => [2,1,3,3,1] => [3,3,2,1,1] => 6
011001010 => [2,1,3,2,2] => [3,2,2,2,1] => 6
011001011 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => 7
011001100 => [2,1,3,1,3] => [3,3,2,1,1] => 6
011001101 => [2,1,3,1,2,1] => [3,2,2,1,1,1] => 7
011001110 => [2,1,3,1,1,2] => [3,2,2,1,1,1] => 7
011001111 => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => 8
011010000 => [2,1,2,5] => [5,2,2,1] => 6
011010001 => [2,1,2,4,1] => [4,2,2,1,1] => 6
011010010 => [2,1,2,3,2] => [3,2,2,2,1] => 6
011010011 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => 7
011010100 => [2,1,2,2,3] => [3,2,2,2,1] => 6
011010101 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => 7
011010110 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => 7
011010111 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 8
011011000 => [2,1,2,1,4] => [4,2,2,1,1] => 6
011011001 => [2,1,2,1,3,1] => [3,2,2,1,1,1] => 7
011011010 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => 7
011011011 => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => 8
011011100 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => 7
011011101 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 8
011011110 => [2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => 8
011011111 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
011100000 => [2,1,1,6] => [6,2,1,1] => 7
011100001 => [2,1,1,5,1] => [5,2,1,1,1] => 6
011100010 => [2,1,1,4,2] => [4,2,2,1,1] => 6
011100011 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => 7
011100100 => [2,1,1,3,3] => [3,3,2,1,1] => 6
011100101 => [2,1,1,3,2,1] => [3,2,2,1,1,1] => 7
011100110 => [2,1,1,3,1,2] => [3,2,2,1,1,1] => 7
011100111 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 8
011101000 => [2,1,1,2,4] => [4,2,2,1,1] => 6
011101001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => 7
011101010 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => 7
011101011 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 8
011101100 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => 7
011101101 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 8
011101110 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 8
011101111 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
011110000 => [2,1,1,1,5] => [5,2,1,1,1] => 6
011110001 => [2,1,1,1,4,1] => [4,2,1,1,1,1] => 7
011110010 => [2,1,1,1,3,2] => [3,2,2,1,1,1] => 7
011110011 => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => 8
011110100 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => 7
011110101 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 8
011110110 => [2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => 8
011110111 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 9
011111000 => [2,1,1,1,1,4] => [4,2,1,1,1,1] => 7
011111001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 8
011111010 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 8
011111011 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 9
011111100 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 8
011111101 => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 9
011111110 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 9
011111111 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
100000000 => [1,9] => [9,1] => 10
100000001 => [1,8,1] => [8,1,1] => 9
100000010 => [1,7,2] => [7,2,1] => 8
100000011 => [1,7,1,1] => [7,1,1,1] => 8
100000100 => [1,6,3] => [6,3,1] => 7
100000101 => [1,6,2,1] => [6,2,1,1] => 7
100000110 => [1,6,1,2] => [6,2,1,1] => 7
100000111 => [1,6,1,1,1] => [6,1,1,1,1] => 7
100001000 => [1,5,4] => [5,4,1] => 6
100001001 => [1,5,3,1] => [5,3,1,1] => 6
100001010 => [1,5,2,2] => [5,2,2,1] => 6
100001011 => [1,5,2,1,1] => [5,2,1,1,1] => 6
100001100 => [1,5,1,3] => [5,3,1,1] => 6
100001101 => [1,5,1,2,1] => [5,2,1,1,1] => 6
100001110 => [1,5,1,1,2] => [5,2,1,1,1] => 6
100001111 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => 7
100010000 => [1,4,5] => [5,4,1] => 6
100010001 => [1,4,4,1] => [4,4,1,1] => 6
100010010 => [1,4,3,2] => [4,3,2,1] => 5
100010011 => [1,4,3,1,1] => [4,3,1,1,1] => 6
100010100 => [1,4,2,3] => [4,3,2,1] => 5
100010101 => [1,4,2,2,1] => [4,2,2,1,1] => 6
100010110 => [1,4,2,1,2] => [4,2,2,1,1] => 6
100010111 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => 7
100011000 => [1,4,1,4] => [4,4,1,1] => 6
100011001 => [1,4,1,3,1] => [4,3,1,1,1] => 6
100011010 => [1,4,1,2,2] => [4,2,2,1,1] => 6
100011011 => [1,4,1,2,1,1] => [4,2,1,1,1,1] => 7
100011100 => [1,4,1,1,3] => [4,3,1,1,1] => 6
100011101 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => 7
100011110 => [1,4,1,1,1,2] => [4,2,1,1,1,1] => 7
100011111 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 8
100100000 => [1,3,6] => [6,3,1] => 7
100100001 => [1,3,5,1] => [5,3,1,1] => 6
100100010 => [1,3,4,2] => [4,3,2,1] => 5
100100011 => [1,3,4,1,1] => [4,3,1,1,1] => 6
100100100 => [1,3,3,3] => [3,3,3,1] => 6
100100101 => [1,3,3,2,1] => [3,3,2,1,1] => 6
100100110 => [1,3,3,1,2] => [3,3,2,1,1] => 6
100100111 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => 7
100101000 => [1,3,2,4] => [4,3,2,1] => 5
100101001 => [1,3,2,3,1] => [3,3,2,1,1] => 6
100101010 => [1,3,2,2,2] => [3,2,2,2,1] => 6
100101011 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => 7
100101100 => [1,3,2,1,3] => [3,3,2,1,1] => 6
100101101 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => 7
100101110 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => 7
100101111 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 8
100110000 => [1,3,1,5] => [5,3,1,1] => 6
100110001 => [1,3,1,4,1] => [4,3,1,1,1] => 6
100110010 => [1,3,1,3,2] => [3,3,2,1,1] => 6
100110011 => [1,3,1,3,1,1] => [3,3,1,1,1,1] => 7
100110100 => [1,3,1,2,3] => [3,3,2,1,1] => 6
100110101 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => 7
100110110 => [1,3,1,2,1,2] => [3,2,2,1,1,1] => 7
100110111 => [1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => 8
100111000 => [1,3,1,1,4] => [4,3,1,1,1] => 6
100111001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => 7
100111010 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => 7
100111011 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 8
100111100 => [1,3,1,1,1,3] => [3,3,1,1,1,1] => 7
100111101 => [1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => 8
100111110 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 8
100111111 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 9
101000000 => [1,2,7] => [7,2,1] => 8
101000001 => [1,2,6,1] => [6,2,1,1] => 7
101000010 => [1,2,5,2] => [5,2,2,1] => 6
101000011 => [1,2,5,1,1] => [5,2,1,1,1] => 6
101000100 => [1,2,4,3] => [4,3,2,1] => 5
101000101 => [1,2,4,2,1] => [4,2,2,1,1] => 6
101000110 => [1,2,4,1,2] => [4,2,2,1,1] => 6
101000111 => [1,2,4,1,1,1] => [4,2,1,1,1,1] => 7
101001000 => [1,2,3,4] => [4,3,2,1] => 5
101001001 => [1,2,3,3,1] => [3,3,2,1,1] => 6
101001010 => [1,2,3,2,2] => [3,2,2,2,1] => 6
101001011 => [1,2,3,2,1,1] => [3,2,2,1,1,1] => 7
101001100 => [1,2,3,1,3] => [3,3,2,1,1] => 6
101001101 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => 7
101001110 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => 7
101001111 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 8
101010000 => [1,2,2,5] => [5,2,2,1] => 6
101010001 => [1,2,2,4,1] => [4,2,2,1,1] => 6
101010010 => [1,2,2,3,2] => [3,2,2,2,1] => 6
101010011 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => 7
101010100 => [1,2,2,2,3] => [3,2,2,2,1] => 6
101010101 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => 7
101010110 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => 7
101010111 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 8
101011000 => [1,2,2,1,4] => [4,2,2,1,1] => 6
101011001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => 7
101011010 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => 7
101011011 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 8
101011100 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => 7
101011101 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 8
101011110 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 8
101011111 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
101100000 => [1,2,1,6] => [6,2,1,1] => 7
101100001 => [1,2,1,5,1] => [5,2,1,1,1] => 6
101100010 => [1,2,1,4,2] => [4,2,2,1,1] => 6
101100011 => [1,2,1,4,1,1] => [4,2,1,1,1,1] => 7
101100100 => [1,2,1,3,3] => [3,3,2,1,1] => 6
101100101 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => 7
101100110 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => 7
101100111 => [1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => 8
101101000 => [1,2,1,2,4] => [4,2,2,1,1] => 6
101101001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => 7
101101010 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => 7
101101011 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 8
101101100 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => 7
101101101 => [1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => 8
101101110 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 8
101101111 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
101110000 => [1,2,1,1,5] => [5,2,1,1,1] => 6
101110001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => 7
101110010 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => 7
101110011 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 8
101110100 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => 7
101110101 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 8
101110110 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 8
101110111 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 9
101111000 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => 7
101111001 => [1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 8
101111010 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 8
101111011 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 9
101111100 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 8
101111101 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 9
101111110 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 9
101111111 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
110000000 => [1,1,8] => [8,1,1] => 9
110000001 => [1,1,7,1] => [7,1,1,1] => 8
110000010 => [1,1,6,2] => [6,2,1,1] => 7
110000011 => [1,1,6,1,1] => [6,1,1,1,1] => 7
110000100 => [1,1,5,3] => [5,3,1,1] => 6
110000101 => [1,1,5,2,1] => [5,2,1,1,1] => 6
110000110 => [1,1,5,1,2] => [5,2,1,1,1] => 6
110000111 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => 7
110001000 => [1,1,4,4] => [4,4,1,1] => 6
110001001 => [1,1,4,3,1] => [4,3,1,1,1] => 6
110001010 => [1,1,4,2,2] => [4,2,2,1,1] => 6
110001011 => [1,1,4,2,1,1] => [4,2,1,1,1,1] => 7
110001100 => [1,1,4,1,3] => [4,3,1,1,1] => 6
110001101 => [1,1,4,1,2,1] => [4,2,1,1,1,1] => 7
110001110 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => 7
110001111 => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 8
110010000 => [1,1,3,5] => [5,3,1,1] => 6
110010001 => [1,1,3,4,1] => [4,3,1,1,1] => 6
110010010 => [1,1,3,3,2] => [3,3,2,1,1] => 6
110010011 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => 7
110010100 => [1,1,3,2,3] => [3,3,2,1,1] => 6
110010101 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => 7
110010110 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => 7
110010111 => [1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => 8
110011000 => [1,1,3,1,4] => [4,3,1,1,1] => 6
110011001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => 7
110011010 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => 7
110011011 => [1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => 8
110011100 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => 7
110011101 => [1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => 8
110011110 => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 8
110011111 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 9
110100000 => [1,1,2,6] => [6,2,1,1] => 7
110100001 => [1,1,2,5,1] => [5,2,1,1,1] => 6
110100010 => [1,1,2,4,2] => [4,2,2,1,1] => 6
110100011 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => 7
110100100 => [1,1,2,3,3] => [3,3,2,1,1] => 6
110100101 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => 7
110100110 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => 7
110100111 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 8
110101000 => [1,1,2,2,4] => [4,2,2,1,1] => 6
110101001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => 7
110101010 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => 7
110101011 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 8
110101100 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => 7
110101101 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 8
110101110 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 8
110101111 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 9
110110000 => [1,1,2,1,5] => [5,2,1,1,1] => 6
110110001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => 7
110110010 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => 7
110110011 => [1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => 8
110110100 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => 7
110110101 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 8
110110110 => [1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => 8
110110111 => [1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 9
110111000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => 7
110111001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 8
110111010 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 8
110111011 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 9
110111100 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 8
110111101 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 9
110111110 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 9
110111111 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
111000000 => [1,1,1,7] => [7,1,1,1] => 8
111000001 => [1,1,1,6,1] => [6,1,1,1,1] => 7
111000010 => [1,1,1,5,2] => [5,2,1,1,1] => 6
111000011 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => 7
111000100 => [1,1,1,4,3] => [4,3,1,1,1] => 6
111000101 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => 7
111000110 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => 7
111000111 => [1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => 8
111001000 => [1,1,1,3,4] => [4,3,1,1,1] => 6
111001001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => 7
111001010 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => 7
111001011 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 8
111001100 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => 7
111001101 => [1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => 8
111001110 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 8
111001111 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 9
111010000 => [1,1,1,2,5] => [5,2,1,1,1] => 6
111010001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => 7
111010010 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => 7
111010011 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 8
111010100 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => 7
111010101 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 8
111010110 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 8
111010111 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 9
111011000 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => 7
111011001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 8
111011010 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 8
111011011 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 9
111011100 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 8
111011101 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 9
111011110 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 9
111011111 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
111100000 => [1,1,1,1,6] => [6,1,1,1,1] => 7
111100001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => 7
111100010 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => 7
111100011 => [1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => 8
111100100 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => 7
111100101 => [1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => 8
111100110 => [1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => 8
111100111 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 9
111101000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => 7
111101001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 8
111101010 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 8
111101011 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 9
111101100 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 8
111101101 => [1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => 9
111101110 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 9
111101111 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
111110000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => 7
111110001 => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 8
111110010 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 8
111110011 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 9
111110100 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 8
111110101 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 9
111110110 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 9
111110111 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 10
111111000 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 8
111111001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 9
111111010 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 9
111111011 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 10
111111100 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 9
111111101 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 10
111111110 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 10
111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 11
1010101010 => [1,2,2,2,2,2] => [2,2,2,2,2,1] => 7
1010101100 => [1,2,2,2,1,3] => [3,2,2,2,1,1] => 7
1010110010 => [1,2,2,1,3,2] => [3,2,2,2,1,1] => 7
1010110100 => [1,2,2,1,2,3] => [3,2,2,2,1,1] => 7
1010111000 => [1,2,2,1,1,4] => [4,2,2,1,1,1] => 7
1011001010 => [1,2,1,3,2,2] => [3,2,2,2,1,1] => 7
1011001100 => [1,2,1,3,1,3] => [3,3,2,1,1,1] => 7
1011010010 => [1,2,1,2,3,2] => [3,2,2,2,1,1] => 7
1011010100 => [1,2,1,2,2,3] => [3,2,2,2,1,1] => 7
1011011000 => [1,2,1,2,1,4] => [4,2,2,1,1,1] => 7
1011100010 => [1,2,1,1,4,2] => [4,2,2,1,1,1] => 7
1011100100 => [1,2,1,1,3,3] => [3,3,2,1,1,1] => 7
1011101000 => [1,2,1,1,2,4] => [4,2,2,1,1,1] => 7
1011110000 => [1,2,1,1,1,5] => [5,2,1,1,1,1] => 7
1100101010 => [1,1,3,2,2,2] => [3,2,2,2,1,1] => 7
1100101100 => [1,1,3,2,1,3] => [3,3,2,1,1,1] => 7
1100110010 => [1,1,3,1,3,2] => [3,3,2,1,1,1] => 7
1100110100 => [1,1,3,1,2,3] => [3,3,2,1,1,1] => 7
1100111000 => [1,1,3,1,1,4] => [4,3,1,1,1,1] => 7
1101001010 => [1,1,2,3,2,2] => [3,2,2,2,1,1] => 7
1101001100 => [1,1,2,3,1,3] => [3,3,2,1,1,1] => 7
1101010010 => [1,1,2,2,3,2] => [3,2,2,2,1,1] => 7
1101010100 => [1,1,2,2,2,3] => [3,2,2,2,1,1] => 7
1101011000 => [1,1,2,2,1,4] => [4,2,2,1,1,1] => 7
1101100010 => [1,1,2,1,4,2] => [4,2,2,1,1,1] => 7
1101100100 => [1,1,2,1,3,3] => [3,3,2,1,1,1] => 7
1101101000 => [1,1,2,1,2,4] => [4,2,2,1,1,1] => 7
1101110000 => [1,1,2,1,1,5] => [5,2,1,1,1,1] => 7
1110001010 => [1,1,1,4,2,2] => [4,2,2,1,1,1] => 7
1110001100 => [1,1,1,4,1,3] => [4,3,1,1,1,1] => 7
1110010010 => [1,1,1,3,3,2] => [3,3,2,1,1,1] => 7
1110010100 => [1,1,1,3,2,3] => [3,3,2,1,1,1] => 7
1110011000 => [1,1,1,3,1,4] => [4,3,1,1,1,1] => 7
1110100010 => [1,1,1,2,4,2] => [4,2,2,1,1,1] => 7
1110100100 => [1,1,1,2,3,3] => [3,3,2,1,1,1] => 7
1110101000 => [1,1,1,2,2,4] => [4,2,2,1,1,1] => 7
1110110000 => [1,1,1,2,1,5] => [5,2,1,1,1,1] => 7
1111000010 => [1,1,1,1,5,2] => [5,2,1,1,1,1] => 7
1111000100 => [1,1,1,1,4,3] => [4,3,1,1,1,1] => 7
1111001000 => [1,1,1,1,3,4] => [4,3,1,1,1,1] => 7
1111010000 => [1,1,1,1,2,5] => [5,2,1,1,1,1] => 7
1111100000 => [1,1,1,1,1,6] => [6,1,1,1,1,1] => 7
1111111111 => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 12
1111111110 => [1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 11
1111111101 => [1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 11
1111111100 => [1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 10
1111111001 => [1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => 10
1111101101 => [1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1] => 10
1111101011 => [1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1111100111 => [1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1] => 10
1111100001 => [1,1,1,1,1,5,1] => [5,1,1,1,1,1,1] => 8
1110111101 => [1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 10
1110110111 => [1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1110110001 => [1,1,1,2,1,4,1] => [4,2,1,1,1,1,1] => 8
1110101011 => [1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => 9
1110100101 => [1,1,1,2,3,2,1] => [3,2,2,1,1,1,1] => 8
1110011111 => [1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 10
1110011001 => [1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => 8
1110001101 => [1,1,1,4,1,2,1] => [4,2,1,1,1,1,1] => 8
1110000111 => [1,1,1,5,1,1,1] => [5,1,1,1,1,1,1] => 8
1110000001 => [1,1,1,7,1] => [7,1,1,1,1] => 8
1101111110 => [1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 10
1101111011 => [1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1101101011 => [1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1] => 9
1101011111 => [1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1101011011 => [1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1] => 9
1101010111 => [1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => 9
1101010101 => [1,1,2,2,2,2,1] => [2,2,2,2,1,1,1] => 8
1101010011 => [1,1,2,2,3,1,1] => [3,2,2,1,1,1,1] => 8
1101010001 => [1,1,2,2,4,1] => [4,2,2,1,1,1] => 7
1101001011 => [1,1,2,3,2,1,1] => [3,2,2,1,1,1,1] => 8
1101000011 => [1,1,2,5,1,1] => [5,2,1,1,1,1] => 7
1100101011 => [1,1,3,2,2,1,1] => [3,2,2,1,1,1,1] => 8
1100001011 => [1,1,5,2,1,1] => [5,2,1,1,1,1] => 7
1100000001 => [1,1,8,1] => [8,1,1,1] => 9
1100000000 => [1,1,9] => [9,1,1] => 10
1011111110 => [1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 10
1011111101 => [1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 10
1011110111 => [1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1011110001 => [1,2,1,1,1,4,1] => [4,2,1,1,1,1,1] => 8
1011100101 => [1,2,1,1,3,2,1] => [3,2,2,1,1,1,1] => 8
1011011111 => [1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 10
1011011001 => [1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => 8
1011001101 => [1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => 8
1011000111 => [1,2,1,4,1,1,1] => [4,2,1,1,1,1,1] => 8
1011000001 => [1,2,1,6,1] => [6,2,1,1,1] => 7
1010111110 => [1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 9
1010110101 => [1,2,2,1,2,2,1] => [2,2,2,2,1,1,1] => 8
1010101011 => [1,2,2,2,2,1,1] => [2,2,2,2,1,1,1] => 8
1010011101 => [1,2,3,1,1,2,1] => [3,2,2,1,1,1,1] => 8
1010010111 => [1,2,3,2,1,1,1] => [3,2,2,1,1,1,1] => 8
1010010001 => [1,2,3,4,1] => [4,3,2,1,1] => 6
1010000101 => [1,2,5,2,1] => [5,2,2,1,1] => 6
1010000001 => [1,2,7,1] => [7,2,1,1] => 8
1010000000 => [1,2,8] => [8,2,1] => 9
1001111111 => [1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 10
1001111110 => [1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 9
1001111001 => [1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => 8
1001101101 => [1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => 8
1001100111 => [1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => 8
1001100001 => [1,3,1,5,1] => [5,3,1,1,1] => 6
1001011110 => [1,3,2,1,1,1,2] => [3,2,2,1,1,1,1] => 8
1001000000 => [1,3,7] => [7,3,1] => 8
1000111110 => [1,4,1,1,1,1,2] => [4,2,1,1,1,1,1] => 8
1000111101 => [1,4,1,1,1,2,1] => [4,2,1,1,1,1,1] => 8
1000110111 => [1,4,1,2,1,1,1] => [4,2,1,1,1,1,1] => 8
1000110001 => [1,4,1,4,1] => [4,4,1,1,1] => 6
1000101110 => [1,4,2,1,1,2] => [4,2,2,1,1,1] => 7
1000101011 => [1,4,2,2,1,1] => [4,2,2,1,1,1] => 7
1000100101 => [1,4,3,2,1] => [4,3,2,1,1] => 6
1000100000 => [1,4,6] => [6,4,1] => 7
1000011111 => [1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => 8
1000011110 => [1,5,1,1,1,2] => [5,2,1,1,1,1] => 7
1000011001 => [1,5,1,3,1] => [5,3,1,1,1] => 6
1000010110 => [1,5,2,1,2] => [5,2,2,1,1] => 6
1000010000 => [1,5,5] => [5,5,1] => 7
1000001110 => [1,6,1,1,2] => [6,2,1,1,1] => 7
1000001101 => [1,6,1,2,1] => [6,2,1,1,1] => 7
1000001010 => [1,6,2,2] => [6,2,2,1] => 7
1000001001 => [1,6,3,1] => [6,3,1,1] => 7
1000000111 => [1,7,1,1,1] => [7,1,1,1,1] => 8
1000000110 => [1,7,1,2] => [7,2,1,1] => 8
1000000101 => [1,7,2,1] => [7,2,1,1] => 8
1000000100 => [1,7,3] => [7,3,1] => 8
1000000011 => [1,8,1,1] => [8,1,1,1] => 9
1000000010 => [1,8,2] => [8,2,1] => 9
1000000001 => [1,9,1] => [9,1,1] => 10
1000000000 => [1,10] => [10,1] => 11
10000000000 => [1,11] => [11,1] => 12
10000000010 => [1,9,2] => [9,2,1] => 10
10000000110 => [1,8,1,2] => [8,2,1,1] => 9
10000001110 => [1,7,1,1,2] => [7,2,1,1,1] => 8
10000011110 => [1,6,1,1,1,2] => [6,2,1,1,1,1] => 7
10000111110 => [1,5,1,1,1,1,2] => [5,2,1,1,1,1,1] => 8
10001111110 => [1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1] => 9
10011111110 => [1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1] => 10
10111111110 => [1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 11
11111111110 => [1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => 12
10000000100 => [1,8,3] => [8,3,1] => 9
11011111110 => [1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 11
10000010000 => [1,6,5] => [6,5,1] => 7
10000100010 => [1,5,4,2] => [5,4,2,1] => 6
10111011110 => [1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
11110111110 => [1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 11
10001000010 => [1,4,5,2] => [5,4,2,1] => 6
10000100100 => [1,5,3,3] => [5,3,3,1] => 6
10001001010 => [1,4,3,2,2] => [4,3,2,2,1] => 6
10101101110 => [1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
11011011110 => [1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
10111101110 => [1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
10001000100 => [1,4,4,3] => [4,4,3,1] => 6
10000101000 => [1,5,2,4] => [5,4,2,1] => 6
10010001010 => [1,3,4,2,2] => [4,3,2,2,1] => 6
10001010010 => [1,4,2,3,2] => [4,3,2,2,1] => 6
10110101110 => [1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
10101110110 => [1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9
11101011110 => [1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
11011101110 => [1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
11111101110 => [1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 11
10010000100 => [1,3,5,3] => [5,3,3,1] => 6
10001001000 => [1,4,3,4] => [4,4,3,1] => 6
10010010010 => [1,3,3,3,2] => [3,3,3,2,1] => 6
10001010100 => [1,4,2,2,3] => [4,3,2,2,1] => 6
10010101010 => [1,3,2,2,2,2] => [3,2,2,2,2,1] => 7
10101010110 => [1,2,2,2,2,1,2] => [2,2,2,2,2,1,1] => 8
11010101110 => [1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
10110110110 => [1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9
11101101110 => [1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
11011110110 => [1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 10
10100000000 => [1,2,9] => [9,2,1] => 10
10010001000 => [1,3,4,4] => [4,4,3,1] => 6
10100010010 => [1,2,4,3,2] => [4,3,2,2,1] => 6
10010100010 => [1,3,2,4,2] => [4,3,2,2,1] => 6
10010010100 => [1,3,3,2,3] => [3,3,3,2,1] => 6
10100101010 => [1,2,3,2,2,2] => [3,2,2,2,2,1] => 7
10101011010 => [1,2,2,2,1,2,2] => [2,2,2,2,2,1,1] => 8
11010110110 => [1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9
10111010110 => [1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9
10110111010 => [1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9
11101110110 => [1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 10
11111111010 => [1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => 11
=> [1] => [1] => 2
0111111111 => [2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 11
0111111101 => [2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 10
0111111001 => [2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => 9
0111110001 => [2,1,1,1,1,4,1] => [4,2,1,1,1,1,1] => 8
0111100001 => [2,1,1,1,5,1] => [5,2,1,1,1,1] => 7
0111000001 => [2,1,1,6,1] => [6,2,1,1,1] => 7
0110000001 => [2,1,7,1] => [7,2,1,1] => 8
0100000001 => [2,8,1] => [8,2,1] => 9
0000000001 => [10,1] => [10,1] => 11
01111111111 => [2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 12
01111111101 => [2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 11
0111111011 => [2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 10
01111111001 => [2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 10
0111110101 => [2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => 9
01111110001 => [2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1] => 9
0111101001 => [2,1,1,1,2,3,1] => [3,2,2,1,1,1,1] => 8
01111100001 => [2,1,1,1,1,5,1] => [5,2,1,1,1,1,1] => 8
0111010001 => [2,1,1,2,4,1] => [4,2,2,1,1,1] => 7
01111000001 => [2,1,1,1,6,1] => [6,2,1,1,1,1] => 7
0110100001 => [2,1,2,5,1] => [5,2,2,1,1] => 6
01110000001 => [2,1,1,7,1] => [7,2,1,1,1] => 8
0101000001 => [2,2,6,1] => [6,2,2,1] => 7
01100000001 => [2,1,8,1] => [8,2,1,1] => 9
0010000001 => [3,7,1] => [7,3,1] => 8
01000000001 => [2,9,1] => [9,2,1] => 10
00000000001 => [11,1] => [11,1] => 12
0101010101 => [2,2,2,2,2,1] => [2,2,2,2,2,1] => 7
0101010011 => [2,2,2,3,1,1] => [3,2,2,2,1,1] => 7
0101001101 => [2,2,3,1,2,1] => [3,2,2,2,1,1] => 7
0101001011 => [2,2,3,2,1,1] => [3,2,2,2,1,1] => 7
0101000111 => [2,2,4,1,1,1] => [4,2,2,1,1,1] => 7
0100110101 => [2,3,1,2,2,1] => [3,2,2,2,1,1] => 7
0100110011 => [2,3,1,3,1,1] => [3,3,2,1,1,1] => 7
0100101101 => [2,3,2,1,2,1] => [3,2,2,2,1,1] => 7
0100101011 => [2,3,2,2,1,1] => [3,2,2,2,1,1] => 7
0100100111 => [2,3,3,1,1,1] => [3,3,2,1,1,1] => 7
0100011101 => [2,4,1,1,2,1] => [4,2,2,1,1,1] => 7
0100011011 => [2,4,1,2,1,1] => [4,2,2,1,1,1] => 7
0100010111 => [2,4,2,1,1,1] => [4,2,2,1,1,1] => 7
0100001111 => [2,5,1,1,1,1] => [5,2,1,1,1,1] => 7
0011010101 => [3,1,2,2,2,1] => [3,2,2,2,1,1] => 7
0011010011 => [3,1,2,3,1,1] => [3,3,2,1,1,1] => 7
0011001101 => [3,1,3,1,2,1] => [3,3,2,1,1,1] => 7
0011001011 => [3,1,3,2,1,1] => [3,3,2,1,1,1] => 7
0011000111 => [3,1,4,1,1,1] => [4,3,1,1,1,1] => 7
0010110101 => [3,2,1,2,2,1] => [3,2,2,2,1,1] => 7
0010110011 => [3,2,1,3,1,1] => [3,3,2,1,1,1] => 7
0010101101 => [3,2,2,1,2,1] => [3,2,2,2,1,1] => 7
0010101011 => [3,2,2,2,1,1] => [3,2,2,2,1,1] => 7
0010100111 => [3,2,3,1,1,1] => [3,3,2,1,1,1] => 7
0010011101 => [3,3,1,1,2,1] => [3,3,2,1,1,1] => 7
0010011011 => [3,3,1,2,1,1] => [3,3,2,1,1,1] => 7
0010010111 => [3,3,2,1,1,1] => [3,3,2,1,1,1] => 7
0010001111 => [3,4,1,1,1,1] => [4,3,1,1,1,1] => 7
0001110101 => [4,1,1,2,2,1] => [4,2,2,1,1,1] => 7
0001110011 => [4,1,1,3,1,1] => [4,3,1,1,1,1] => 7
0001101101 => [4,1,2,1,2,1] => [4,2,2,1,1,1] => 7
0001101011 => [4,1,2,2,1,1] => [4,2,2,1,1,1] => 7
0001100111 => [4,1,3,1,1,1] => [4,3,1,1,1,1] => 7
0001011101 => [4,2,1,1,2,1] => [4,2,2,1,1,1] => 7
0001011011 => [4,2,1,2,1,1] => [4,2,2,1,1,1] => 7
0001010111 => [4,2,2,1,1,1] => [4,2,2,1,1,1] => 7
0001001111 => [4,3,1,1,1,1] => [4,3,1,1,1,1] => 7
0000111101 => [5,1,1,1,2,1] => [5,2,1,1,1,1] => 7
0000111011 => [5,1,1,2,1,1] => [5,2,1,1,1,1] => 7
0000110111 => [5,1,2,1,1,1] => [5,2,1,1,1,1] => 7
0000101111 => [5,2,1,1,1,1] => [5,2,1,1,1,1] => 7
0000011111 => [6,1,1,1,1,1] => [6,1,1,1,1,1] => 7
11010101010 => [1,1,2,2,2,2,2] => [2,2,2,2,2,1,1] => 8
11010101000 => [1,1,2,2,2,4] => [4,2,2,2,1,1] => 7
11010101100 => [1,1,2,2,2,1,3] => [3,2,2,2,1,1,1] => 8
11010100100 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => 7
11010110100 => [1,1,2,2,1,2,3] => [3,2,2,2,1,1,1] => 8
11010010100 => [1,1,2,3,2,3] => [3,3,2,2,1,1] => 7
11011010100 => [1,1,2,1,2,2,3] => [3,2,2,2,1,1,1] => 8
11001010100 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => 7
11101010100 => [1,1,1,2,2,2,3] => [3,2,2,2,1,1,1] => 8
10101010100 => [1,2,2,2,2,3] => [3,2,2,2,2,1] => 7
100010010001 => [1,4,3,4,1] => [4,4,3,1,1] => 6
100010000101 => [1,4,5,2,1] => [5,4,2,1,1] => 6
101000010001 => [1,2,5,4,1] => [5,4,2,1,1] => 6
0000000000 => [11] => [11] => 12
00101010101 => [3,2,2,2,2,1] => [3,2,2,2,2,1] => 7
00101010111 => [3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 8
00101010011 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => 7
00101011011 => [3,2,2,1,2,1,1] => [3,2,2,2,1,1,1] => 8
00101101011 => [3,2,1,2,2,1,1] => [3,2,2,2,1,1,1] => 8
00100101011 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => 7
00110101011 => [3,1,2,2,2,1,1] => [3,2,2,2,1,1,1] => 8
01010101011 => [2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 8
0000000010 => [9,2] => [9,2] => 10
0000111110 => [5,1,1,1,1,2] => [5,2,1,1,1,1] => 7
0011111110 => [3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 9
00000000000 => [12] => [12] => 13
00000000010 => [10,2] => [10,2] => 11
0101111110 => [2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 9
01111111110 => [2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 11
10101010101 => [1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => 8
10101010010 => [1,2,2,2,3,2] => [3,2,2,2,2,1] => 7
10101001001 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => 7
10101001010 => [1,2,2,3,2,2] => [3,2,2,2,2,1] => 7
10101000100 => [1,2,2,4,3] => [4,3,2,2,1] => 6
10100100101 => [1,2,3,3,2,1] => [3,3,2,2,1,1] => 7
10100100010 => [1,2,3,4,2] => [4,3,2,2,1] => 6
10100101001 => [1,2,3,2,3,1] => [3,3,2,2,1,1] => 7
10100100100 => [1,2,3,3,3] => [3,3,3,2,1] => 6
10100010001 => [1,2,4,4,1] => [4,4,2,1,1] => 6
10100010100 => [1,2,4,2,3] => [4,3,2,2,1] => 6
10100001000 => [1,2,5,4] => [5,4,2,1] => 6
10010010101 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => 7
10010001001 => [1,3,4,3,1] => [4,3,3,1,1] => 6
10010100101 => [1,3,2,3,2,1] => [3,3,2,2,1,1] => 7
10010101001 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => 7
10010100100 => [1,3,2,3,3] => [3,3,3,2,1] => 6
10010010001 => [1,3,3,4,1] => [4,3,3,1,1] => 6
10001000101 => [1,4,4,2,1] => [4,4,2,1,1] => 6
10001001001 => [1,4,3,3,1] => [4,3,3,1,1] => 6
10001010001 => [1,4,2,4,1] => [4,4,2,1,1] => 6
10000100001 => [1,5,5,1] => [5,5,1,1] => 7
01001010101 => [2,3,2,2,2,1] => [3,2,2,2,2,1] => 7
01001010010 => [2,3,2,3,2] => [3,3,2,2,2] => 7
01001001001 => [2,3,3,3,1] => [3,3,3,2,1] => 6
01001001010 => [2,3,3,2,2] => [3,3,2,2,2] => 7
01001000100 => [2,3,4,3] => [4,3,3,2] => 6
01000100101 => [2,4,3,2,1] => [4,3,2,2,1] => 6
01000100010 => [2,4,4,2] => [4,4,2,2] => 6
01000101001 => [2,4,2,3,1] => [4,3,2,2,1] => 6
01000101010 => [2,4,2,2,2] => [4,2,2,2,2] => 7
01000100100 => [2,4,3,3] => [4,3,3,2] => 6
01000010001 => [2,5,4,1] => [5,4,2,1] => 6
01000010010 => [2,5,3,2] => [5,3,2,2] => 6
01000010100 => [2,5,2,3] => [5,3,2,2] => 6
01000001000 => [2,6,4] => [6,4,2] => 7
01010010101 => [2,2,3,2,2,1] => [3,2,2,2,2,1] => 7
01010010010 => [2,2,3,3,2] => [3,3,2,2,2] => 7
01010001001 => [2,2,4,3,1] => [4,3,2,2,1] => 6
01010001010 => [2,2,4,2,2] => [4,2,2,2,2] => 7
01010000100 => [2,2,5,3] => [5,3,2,2] => 6
01010100101 => [2,2,2,3,2,1] => [3,2,2,2,2,1] => 7
01010100010 => [2,2,2,4,2] => [4,2,2,2,2] => 7
01010101001 => [2,2,2,2,3,1] => [3,2,2,2,2,1] => 7
01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => 8
01010100100 => [2,2,2,3,3] => [3,3,2,2,2] => 7
01010010001 => [2,2,3,4,1] => [4,3,2,2,1] => 6
01010010100 => [2,2,3,2,3] => [3,3,2,2,2] => 7
01010001000 => [2,2,4,4] => [4,4,2,2] => 6
01001000101 => [2,3,4,2,1] => [4,3,2,2,1] => 6
01001000010 => [2,3,5,2] => [5,3,2,2] => 6
01001010001 => [2,3,2,4,1] => [4,3,2,2,1] => 6
01001010100 => [2,3,2,2,3] => [3,3,2,2,2] => 7
01001001000 => [2,3,3,4] => [4,3,3,2] => 6
01000100001 => [2,4,5,1] => [5,4,2,1] => 6
01000101000 => [2,4,2,4] => [4,4,2,2] => 6
01000010000 => [2,5,5] => [5,5,2] => 7
00100010101 => [3,4,2,2,1] => [4,3,2,2,1] => 6
00100010010 => [3,4,3,2] => [4,3,3,2] => 6
00100001001 => [3,5,3,1] => [5,3,3,1] => 6
00100001010 => [3,5,2,2] => [5,3,2,2] => 6
00100000100 => [3,6,3] => [6,3,3] => 7
00100100101 => [3,3,3,2,1] => [3,3,3,2,1] => 6
00100100010 => [3,3,4,2] => [4,3,3,2] => 6
00100101001 => [3,3,2,3,1] => [3,3,3,2,1] => 6
00100101010 => [3,3,2,2,2] => [3,3,2,2,2] => 7
00100100100 => [3,3,3,3] => [3,3,3,3] => 7
00100010001 => [3,4,4,1] => [4,4,3,1] => 6
00100010100 => [3,4,2,3] => [4,3,3,2] => 6
00100001000 => [3,5,4] => [5,4,3] => 6
00101000101 => [3,2,4,2,1] => [4,3,2,2,1] => 6
00101000010 => [3,2,5,2] => [5,3,2,2] => 6
00101001001 => [3,2,3,3,1] => [3,3,3,2,1] => 6
00101001010 => [3,2,3,2,2] => [3,3,2,2,2] => 7
00101000100 => [3,2,4,3] => [4,3,3,2] => 6
00101010001 => [3,2,2,4,1] => [4,3,2,2,1] => 6
00101010010 => [3,2,2,3,2] => [3,3,2,2,2] => 7
00101010100 => [3,2,2,2,3] => [3,3,2,2,2] => 7
00101001000 => [3,2,3,4] => [4,3,3,2] => 6
00100100001 => [3,3,5,1] => [5,3,3,1] => 6
00100101000 => [3,3,2,4] => [4,3,3,2] => 6
00100010000 => [3,4,5] => [5,4,3] => 6
00010000101 => [4,5,2,1] => [5,4,2,1] => 6
00010000010 => [4,6,2] => [6,4,2] => 7
00010001001 => [4,4,3,1] => [4,4,3,1] => 6
00010001010 => [4,4,2,2] => [4,4,2,2] => 6
00010000100 => [4,5,3] => [5,4,3] => 6
00010010001 => [4,3,4,1] => [4,4,3,1] => 6
00010010010 => [4,3,3,2] => [4,3,3,2] => 6
00010010100 => [4,3,2,3] => [4,3,3,2] => 6
00010001000 => [4,4,4] => [4,4,4] => 7
00010100001 => [4,2,5,1] => [5,4,2,1] => 6
00010100010 => [4,2,4,2] => [4,4,2,2] => 6
00010100100 => [4,2,3,3] => [4,3,3,2] => 6
00010101000 => [4,2,2,4] => [4,4,2,2] => 6
00010010000 => [4,3,5] => [5,4,3] => 6
00001000001 => [5,6,1] => [6,5,1] => 7
00001000010 => [5,5,2] => [5,5,2] => 7
00001000100 => [5,4,3] => [5,4,3] => 6
00001001000 => [5,3,4] => [5,4,3] => 6
00001010000 => [5,2,5] => [5,5,2] => 7
00000100000 => [6,6] => [6,6] => 8
0100000000 => [2,9] => [9,2] => 10
01000011111 => [2,5,1,1,1,1,1] => [5,2,1,1,1,1,1] => 8
01011111111 => [2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
00000000101 => [9,2,1] => [9,2,1] => 10
00001111101 => [5,1,1,1,1,2,1] => [5,2,1,1,1,1,1] => 8
11111111101 => [1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => 12
01111111011 => [2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
00100000001 => [3,8,1] => [8,3,1] => 9
10111111101 => [1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 11
00010111101 => [4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => 8
10000000001 => [1,10,1] => [10,1,1] => 11
11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 13
01010101101 => [2,2,2,2,1,2,1] => [2,2,2,2,2,1,1] => 8
01010110110 => [2,2,2,1,2,1,2] => [2,2,2,2,2,1,1] => 8
01010110101 => [2,2,2,1,2,2,1] => [2,2,2,2,2,1,1] => 8
01010111011 => [2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01011011010 => [2,2,1,2,1,2,2] => [2,2,2,2,2,1,1] => 8
01011011101 => [2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9
01011010110 => [2,2,1,2,2,1,2] => [2,2,2,2,2,1,1] => 8
01011010101 => [2,2,1,2,2,2,1] => [2,2,2,2,2,1,1] => 8
01011011011 => [2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01011101110 => [2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
01011101101 => [2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
01011101011 => [2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01011110111 => [2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01101101010 => [2,1,2,1,2,2,2] => [2,2,2,2,2,1,1] => 8
01101101101 => [2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
01101110110 => [2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9
01101110101 => [2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9
01101111011 => [2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01101011010 => [2,1,2,2,1,2,2] => [2,2,2,2,2,1,1] => 8
01101011101 => [2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9
01101010110 => [2,1,2,2,2,1,2] => [2,2,2,2,2,1,1] => 8
01101010101 => [2,1,2,2,2,2,1] => [2,2,2,2,2,1,1] => 8
01101011011 => [2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01101101110 => [2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
01101101011 => [2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01101110111 => [2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01110111010 => [2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9
01110111101 => [2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
01110110110 => [2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9
01110110101 => [2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9
01110111011 => [2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01110101110 => [2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9
01110101101 => [2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
01110101011 => [2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
01110110111 => [2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01111011110 => [2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 10
01111011101 => [2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
01111011011 => [2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01111010111 => [2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
01111101111 => [2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
10110101010 => [1,2,1,2,2,2,2] => [2,2,2,2,2,1,1] => 8
10110101101 => [1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
10110110101 => [1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9
10110111011 => [1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10111011010 => [1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9
10111011101 => [1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
10111010101 => [1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9
10111011011 => [1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10111101101 => [1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
10111101011 => [1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10111110111 => [1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
10101101010 => [1,2,2,1,2,2,2] => [2,2,2,2,2,1,1] => 8
10101101101 => [1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
10101110101 => [1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9
10101111011 => [1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10101011101 => [1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9
10101011011 => [1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9
10101101011 => [1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
10101110111 => [1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10110111101 => [1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
10110101011 => [1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
10110110111 => [1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10111010111 => [1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
10111101111 => [1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11011101010 => [1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 9
11011101101 => [1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11011110101 => [1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11011111011 => [1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11011011010 => [1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9
11011011101 => [1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11011010110 => [1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9
11011010101 => [1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9
11011011011 => [1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11011101011 => [1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11011110111 => [1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11010111010 => [1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9
11010111101 => [1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11010110101 => [1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9
11010111011 => [1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11010101101 => [1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9
11010101011 => [1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9
11010110111 => [1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11011010111 => [1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11011101111 => [1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11101111010 => [1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1] => 10
11101111101 => [1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11101110101 => [1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11101111011 => [1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11101101101 => [1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11101101011 => [1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11101110111 => [1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11101011101 => [1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 10
11101011011 => [1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11101010111 => [1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 10
11101101111 => [1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11110111101 => [1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11110111011 => [1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11110110111 => [1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11110101111 => [1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11111011111 => [1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 12
00011001111 => [4,1,3,1,1,1,1] => [4,3,1,1,1,1,1] => 8
00000011011 => [7,1,2,1,1] => [7,2,1,1,1] => 8
00001101111 => [5,1,2,1,1,1,1] => [5,2,1,1,1,1,1] => 8
11011111111 => [1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 12
10001010101 => [1,4,2,2,2,1] => [4,2,2,2,1,1] => 7
01111010101 => [2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9
10000010101 => [1,6,2,2,1] => [6,2,2,1,1] => 7
0111111100 => [2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1] => 9
0111111010 => [2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => 9
00000111111 => [6,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => 8
10111111111 => [1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 12
10000001011 => [1,7,2,1,1] => [7,2,1,1,1] => 8
10000101111 => [1,5,2,1,1,1,1] => [5,2,1,1,1,1,1] => 8
10101111111 => [1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
00101111110 => [3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1] => 9
00111011110 => [3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 9
00111110110 => [3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 9
00111111100 => [3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 9
11000000011 => [1,1,8,1,1] => [8,1,1,1,1] => 9
00010010101 => [4,3,2,2,1] => [4,3,2,2,1] => 6
00010100101 => [4,2,3,2,1] => [4,3,2,2,1] => 6
00010101001 => [4,2,2,3,1] => [4,3,2,2,1] => 6
00010101010 => [4,2,2,2,2] => [4,2,2,2,2] => 7
00000100010 => [6,4,2] => [6,4,2] => 7
00001010101 => [5,2,2,2,1] => [5,2,2,2,1] => 6
10101101001 => [1,2,2,1,2,3,1] => [3,2,2,2,1,1,1] => 8
11010101001 => [1,1,2,2,2,3,1] => [3,2,2,2,1,1,1] => 8
01101010100 => [2,1,2,2,2,3] => [3,2,2,2,2,1] => 7
01101001010 => [2,1,2,3,2,2] => [3,2,2,2,2,1] => 7
01110101010 => [2,1,1,2,2,2,2] => [2,2,2,2,2,1,1] => 8
01000101111 => [2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => 8
10000011111 => [1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => 8
01010100111 => [2,2,2,3,1,1,1] => [3,2,2,2,1,1,1] => 8
01010010111 => [2,2,3,2,1,1,1] => [3,2,2,2,1,1,1] => 8
01001010111 => [2,3,2,2,1,1,1] => [3,2,2,2,1,1,1] => 8
01000111011 => [2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => 8
00010111011 => [4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => 8
01010101111 => [2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 9
10101010111 => [1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 9
11010000100 => [1,1,2,5,3] => [5,3,2,1,1] => 6
11011110100 => [1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 9
01010110100 => [2,2,2,1,2,3] => [3,2,2,2,2,1] => 7
01110111111 => [2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 11
11110001111 => [1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 10
11110001000 => [1,1,1,1,4,4] => [4,4,1,1,1,1] => 7
11000111000 => [1,1,4,1,1,4] => [4,4,1,1,1,1] => 7
11000100011 => [1,1,4,4,1,1] => [4,4,1,1,1,1] => 7
11010001011 => [1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => 8
00011111000 => [4,1,1,1,1,4] => [4,4,1,1,1,1] => 7
00011100011 => [4,1,1,4,1,1] => [4,4,1,1,1,1] => 7
00010001111 => [4,4,1,1,1,1] => [4,4,1,1,1,1] => 7
01011111010 => [2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9
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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:
2,2 6,2 8,6,2 6,17,7,2 34,20,8,2 42,49,26,9,2 42,101,68,33,10,2 24,182,156,96,41,11,2
$F_{1} = 2\ q^{3}$
$F_{2} = 2\ q^{3} + 2\ q^{4}$
$F_{3} = 6\ q^{4} + 2\ q^{5}$
$F_{4} = 8\ q^{4} + 6\ q^{5} + 2\ q^{6}$
$F_{5} = 6\ q^{4} + 17\ q^{5} + 7\ q^{6} + 2\ q^{7}$
$F_{6} = 34\ q^{5} + 20\ q^{6} + 8\ q^{7} + 2\ q^{8}$
$F_{7} = 42\ q^{5} + 49\ q^{6} + 26\ q^{7} + 9\ q^{8} + 2\ q^{9}$
$F_{8} = 42\ q^{5} + 101\ q^{6} + 68\ q^{7} + 33\ q^{8} + 10\ q^{9} + 2\ q^{10}$
$F_{9} = 24\ q^{5} + 182\ q^{6} + 156\ q^{7} + 96\ q^{8} + 41\ q^{9} + 11\ q^{10} + 2\ q^{11}$
Description
Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition.
Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.
Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
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