Identifier
Values
0 => [1] => 1
1 => [1] => 1
00 => [2] => 2
01 => [1,1] => 2
10 => [1,1] => 2
11 => [2] => 2
000 => [3] => 2
001 => [2,1] => 3
010 => [1,1,1] => 2
011 => [1,2] => 3
100 => [1,2] => 3
101 => [1,1,1] => 2
110 => [2,1] => 3
111 => [3] => 2
0000 => [4] => 2
0001 => [3,1] => 3
0010 => [2,1,1] => 3
0011 => [2,2] => 4
0100 => [1,1,2] => 3
0101 => [1,1,1,1] => 2
0110 => [1,2,1] => 4
0111 => [1,3] => 3
1000 => [1,3] => 3
1001 => [1,2,1] => 4
1010 => [1,1,1,1] => 2
1011 => [1,1,2] => 3
1100 => [2,2] => 4
1101 => [2,1,1] => 3
1110 => [3,1] => 3
1111 => [4] => 2
00000 => [5] => 2
00001 => [4,1] => 3
00010 => [3,1,1] => 3
00011 => [3,2] => 4
00100 => [2,1,2] => 4
00101 => [2,1,1,1] => 3
00110 => [2,2,1] => 5
00111 => [2,3] => 4
01000 => [1,1,3] => 3
01001 => [1,1,2,1] => 4
01010 => [1,1,1,1,1] => 2
01011 => [1,1,1,2] => 3
01100 => [1,2,2] => 5
01101 => [1,2,1,1] => 4
01110 => [1,3,1] => 4
01111 => [1,4] => 3
10000 => [1,4] => 3
10001 => [1,3,1] => 4
10010 => [1,2,1,1] => 4
10011 => [1,2,2] => 5
10100 => [1,1,1,2] => 3
10101 => [1,1,1,1,1] => 2
10110 => [1,1,2,1] => 4
10111 => [1,1,3] => 3
11000 => [2,3] => 4
11001 => [2,2,1] => 5
11010 => [2,1,1,1] => 3
11011 => [2,1,2] => 4
11100 => [3,2] => 4
11101 => [3,1,1] => 3
11110 => [4,1] => 3
11111 => [5] => 2
000000 => [6] => 2
000001 => [5,1] => 3
000010 => [4,1,1] => 3
000011 => [4,2] => 4
000100 => [3,1,2] => 4
000101 => [3,1,1,1] => 3
000110 => [3,2,1] => 5
000111 => [3,3] => 4
001000 => [2,1,3] => 4
001001 => [2,1,2,1] => 5
001010 => [2,1,1,1,1] => 3
001011 => [2,1,1,2] => 4
001100 => [2,2,2] => 6
001101 => [2,2,1,1] => 5
001110 => [2,3,1] => 5
001111 => [2,4] => 4
010000 => [1,1,4] => 3
010001 => [1,1,3,1] => 4
010010 => [1,1,2,1,1] => 4
010011 => [1,1,2,2] => 5
010100 => [1,1,1,1,2] => 3
010101 => [1,1,1,1,1,1] => 2
010110 => [1,1,1,2,1] => 4
010111 => [1,1,1,3] => 3
011000 => [1,2,3] => 5
011001 => [1,2,2,1] => 6
011010 => [1,2,1,1,1] => 4
011011 => [1,2,1,2] => 5
011100 => [1,3,2] => 5
011101 => [1,3,1,1] => 4
011110 => [1,4,1] => 4
011111 => [1,5] => 3
100000 => [1,5] => 3
100001 => [1,4,1] => 4
100010 => [1,3,1,1] => 4
100011 => [1,3,2] => 5
100100 => [1,2,1,2] => 5
100101 => [1,2,1,1,1] => 4
100110 => [1,2,2,1] => 6
>>> Load all 1655 entries. <<<
100111 => [1,2,3] => 5
101000 => [1,1,1,3] => 3
101001 => [1,1,1,2,1] => 4
101010 => [1,1,1,1,1,1] => 2
101011 => [1,1,1,1,2] => 3
101100 => [1,1,2,2] => 5
101101 => [1,1,2,1,1] => 4
101110 => [1,1,3,1] => 4
101111 => [1,1,4] => 3
110000 => [2,4] => 4
110001 => [2,3,1] => 5
110010 => [2,2,1,1] => 5
110011 => [2,2,2] => 6
110100 => [2,1,1,2] => 4
110101 => [2,1,1,1,1] => 3
110110 => [2,1,2,1] => 5
110111 => [2,1,3] => 4
111000 => [3,3] => 4
111001 => [3,2,1] => 5
111010 => [3,1,1,1] => 3
111011 => [3,1,2] => 4
111100 => [4,2] => 4
111101 => [4,1,1] => 3
111110 => [5,1] => 3
111111 => [6] => 2
0000000 => [7] => 2
0000001 => [6,1] => 3
0000010 => [5,1,1] => 3
0000011 => [5,2] => 4
0000100 => [4,1,2] => 4
0000101 => [4,1,1,1] => 3
0000110 => [4,2,1] => 5
0000111 => [4,3] => 4
0001000 => [3,1,3] => 4
0001001 => [3,1,2,1] => 5
0001010 => [3,1,1,1,1] => 3
0001011 => [3,1,1,2] => 4
0001100 => [3,2,2] => 6
0001101 => [3,2,1,1] => 5
0001110 => [3,3,1] => 5
0001111 => [3,4] => 4
0010000 => [2,1,4] => 4
0010001 => [2,1,3,1] => 5
0010010 => [2,1,2,1,1] => 5
0010011 => [2,1,2,2] => 6
0010100 => [2,1,1,1,2] => 4
0010101 => [2,1,1,1,1,1] => 3
0010110 => [2,1,1,2,1] => 5
0010111 => [2,1,1,3] => 4
0011000 => [2,2,3] => 6
0011001 => [2,2,2,1] => 7
0011010 => [2,2,1,1,1] => 5
0011011 => [2,2,1,2] => 6
0011100 => [2,3,2] => 6
0011101 => [2,3,1,1] => 5
0011110 => [2,4,1] => 5
0011111 => [2,5] => 4
0100000 => [1,1,5] => 3
0100001 => [1,1,4,1] => 4
0100010 => [1,1,3,1,1] => 4
0100011 => [1,1,3,2] => 5
0100100 => [1,1,2,1,2] => 5
0100101 => [1,1,2,1,1,1] => 4
0100110 => [1,1,2,2,1] => 6
0100111 => [1,1,2,3] => 5
0101000 => [1,1,1,1,3] => 3
0101001 => [1,1,1,1,2,1] => 4
0101010 => [1,1,1,1,1,1,1] => 2
0101011 => [1,1,1,1,1,2] => 3
0101100 => [1,1,1,2,2] => 5
0101101 => [1,1,1,2,1,1] => 4
0101110 => [1,1,1,3,1] => 4
0101111 => [1,1,1,4] => 3
0110000 => [1,2,4] => 5
0110001 => [1,2,3,1] => 6
0110010 => [1,2,2,1,1] => 6
0110011 => [1,2,2,2] => 7
0110100 => [1,2,1,1,2] => 5
0110101 => [1,2,1,1,1,1] => 4
0110110 => [1,2,1,2,1] => 6
0110111 => [1,2,1,3] => 5
0111000 => [1,3,3] => 5
0111001 => [1,3,2,1] => 6
0111010 => [1,3,1,1,1] => 4
0111011 => [1,3,1,2] => 5
0111100 => [1,4,2] => 5
0111101 => [1,4,1,1] => 4
0111110 => [1,5,1] => 4
0111111 => [1,6] => 3
1000000 => [1,6] => 3
1000001 => [1,5,1] => 4
1000010 => [1,4,1,1] => 4
1000011 => [1,4,2] => 5
1000100 => [1,3,1,2] => 5
1000101 => [1,3,1,1,1] => 4
1000110 => [1,3,2,1] => 6
1000111 => [1,3,3] => 5
1001000 => [1,2,1,3] => 5
1001001 => [1,2,1,2,1] => 6
1001010 => [1,2,1,1,1,1] => 4
1001011 => [1,2,1,1,2] => 5
1001100 => [1,2,2,2] => 7
1001101 => [1,2,2,1,1] => 6
1001110 => [1,2,3,1] => 6
1001111 => [1,2,4] => 5
1010000 => [1,1,1,4] => 3
1010001 => [1,1,1,3,1] => 4
1010010 => [1,1,1,2,1,1] => 4
1010011 => [1,1,1,2,2] => 5
1010100 => [1,1,1,1,1,2] => 3
1010101 => [1,1,1,1,1,1,1] => 2
1010110 => [1,1,1,1,2,1] => 4
1010111 => [1,1,1,1,3] => 3
1011000 => [1,1,2,3] => 5
1011001 => [1,1,2,2,1] => 6
1011010 => [1,1,2,1,1,1] => 4
1011011 => [1,1,2,1,2] => 5
1011100 => [1,1,3,2] => 5
1011101 => [1,1,3,1,1] => 4
1011110 => [1,1,4,1] => 4
1011111 => [1,1,5] => 3
1100000 => [2,5] => 4
1100001 => [2,4,1] => 5
1100010 => [2,3,1,1] => 5
1100011 => [2,3,2] => 6
1100100 => [2,2,1,2] => 6
1100101 => [2,2,1,1,1] => 5
1100110 => [2,2,2,1] => 7
1100111 => [2,2,3] => 6
1101000 => [2,1,1,3] => 4
1101001 => [2,1,1,2,1] => 5
1101010 => [2,1,1,1,1,1] => 3
1101011 => [2,1,1,1,2] => 4
1101100 => [2,1,2,2] => 6
1101101 => [2,1,2,1,1] => 5
1101110 => [2,1,3,1] => 5
1101111 => [2,1,4] => 4
1110000 => [3,4] => 4
1110001 => [3,3,1] => 5
1110010 => [3,2,1,1] => 5
1110011 => [3,2,2] => 6
1110100 => [3,1,1,2] => 4
1110101 => [3,1,1,1,1] => 3
1110110 => [3,1,2,1] => 5
1110111 => [3,1,3] => 4
1111000 => [4,3] => 4
1111001 => [4,2,1] => 5
1111010 => [4,1,1,1] => 3
1111011 => [4,1,2] => 4
1111100 => [5,2] => 4
1111101 => [5,1,1] => 3
1111110 => [6,1] => 3
1111111 => [7] => 2
00000000 => [8] => 2
00000001 => [7,1] => 3
00000010 => [6,1,1] => 3
00000011 => [6,2] => 4
00000100 => [5,1,2] => 4
00000101 => [5,1,1,1] => 3
00000110 => [5,2,1] => 5
00000111 => [5,3] => 4
00001000 => [4,1,3] => 4
00001001 => [4,1,2,1] => 5
00001010 => [4,1,1,1,1] => 3
00001011 => [4,1,1,2] => 4
00001100 => [4,2,2] => 6
00001101 => [4,2,1,1] => 5
00001110 => [4,3,1] => 5
00001111 => [4,4] => 4
00010000 => [3,1,4] => 4
00010001 => [3,1,3,1] => 5
00010010 => [3,1,2,1,1] => 5
00010011 => [3,1,2,2] => 6
00010100 => [3,1,1,1,2] => 4
00010101 => [3,1,1,1,1,1] => 3
00010110 => [3,1,1,2,1] => 5
00010111 => [3,1,1,3] => 4
00011000 => [3,2,3] => 6
00011001 => [3,2,2,1] => 7
00011010 => [3,2,1,1,1] => 5
00011011 => [3,2,1,2] => 6
00011100 => [3,3,2] => 6
00011101 => [3,3,1,1] => 5
00011110 => [3,4,1] => 5
00011111 => [3,5] => 4
00100000 => [2,1,5] => 4
00100001 => [2,1,4,1] => 5
00100010 => [2,1,3,1,1] => 5
00100011 => [2,1,3,2] => 6
00100100 => [2,1,2,1,2] => 6
00100101 => [2,1,2,1,1,1] => 5
00100110 => [2,1,2,2,1] => 7
00100111 => [2,1,2,3] => 6
00101000 => [2,1,1,1,3] => 4
00101001 => [2,1,1,1,2,1] => 5
00101010 => [2,1,1,1,1,1,1] => 3
00101011 => [2,1,1,1,1,2] => 4
00101100 => [2,1,1,2,2] => 6
00101101 => [2,1,1,2,1,1] => 5
00101110 => [2,1,1,3,1] => 5
00101111 => [2,1,1,4] => 4
00110000 => [2,2,4] => 6
00110001 => [2,2,3,1] => 7
00110010 => [2,2,2,1,1] => 7
00110011 => [2,2,2,2] => 8
00110100 => [2,2,1,1,2] => 6
00110101 => [2,2,1,1,1,1] => 5
00110110 => [2,2,1,2,1] => 7
00110111 => [2,2,1,3] => 6
00111000 => [2,3,3] => 6
00111001 => [2,3,2,1] => 7
00111010 => [2,3,1,1,1] => 5
00111011 => [2,3,1,2] => 6
00111100 => [2,4,2] => 6
00111101 => [2,4,1,1] => 5
00111110 => [2,5,1] => 5
00111111 => [2,6] => 4
01000000 => [1,1,6] => 3
01000001 => [1,1,5,1] => 4
01000010 => [1,1,4,1,1] => 4
01000011 => [1,1,4,2] => 5
01000100 => [1,1,3,1,2] => 5
01000101 => [1,1,3,1,1,1] => 4
01000110 => [1,1,3,2,1] => 6
01000111 => [1,1,3,3] => 5
01001000 => [1,1,2,1,3] => 5
01001001 => [1,1,2,1,2,1] => 6
01001010 => [1,1,2,1,1,1,1] => 4
01001011 => [1,1,2,1,1,2] => 5
01001100 => [1,1,2,2,2] => 7
01001101 => [1,1,2,2,1,1] => 6
01001110 => [1,1,2,3,1] => 6
01001111 => [1,1,2,4] => 5
01010000 => [1,1,1,1,4] => 3
01010001 => [1,1,1,1,3,1] => 4
01010010 => [1,1,1,1,2,1,1] => 4
01010011 => [1,1,1,1,2,2] => 5
01010100 => [1,1,1,1,1,1,2] => 3
01010101 => [1,1,1,1,1,1,1,1] => 2
01010110 => [1,1,1,1,1,2,1] => 4
01010111 => [1,1,1,1,1,3] => 3
01011000 => [1,1,1,2,3] => 5
01011001 => [1,1,1,2,2,1] => 6
01011010 => [1,1,1,2,1,1,1] => 4
01011011 => [1,1,1,2,1,2] => 5
01011100 => [1,1,1,3,2] => 5
01011101 => [1,1,1,3,1,1] => 4
01011110 => [1,1,1,4,1] => 4
01011111 => [1,1,1,5] => 3
01100000 => [1,2,5] => 5
01100001 => [1,2,4,1] => 6
01100010 => [1,2,3,1,1] => 6
01100011 => [1,2,3,2] => 7
01100100 => [1,2,2,1,2] => 7
01100101 => [1,2,2,1,1,1] => 6
01100110 => [1,2,2,2,1] => 8
01100111 => [1,2,2,3] => 7
01101000 => [1,2,1,1,3] => 5
01101001 => [1,2,1,1,2,1] => 6
01101010 => [1,2,1,1,1,1,1] => 4
01101011 => [1,2,1,1,1,2] => 5
01101100 => [1,2,1,2,2] => 7
01101101 => [1,2,1,2,1,1] => 6
01101110 => [1,2,1,3,1] => 6
01101111 => [1,2,1,4] => 5
01110000 => [1,3,4] => 5
01110001 => [1,3,3,1] => 6
01110010 => [1,3,2,1,1] => 6
01110011 => [1,3,2,2] => 7
01110100 => [1,3,1,1,2] => 5
01110101 => [1,3,1,1,1,1] => 4
01110110 => [1,3,1,2,1] => 6
01110111 => [1,3,1,3] => 5
01111000 => [1,4,3] => 5
01111001 => [1,4,2,1] => 6
01111010 => [1,4,1,1,1] => 4
01111011 => [1,4,1,2] => 5
01111100 => [1,5,2] => 5
01111101 => [1,5,1,1] => 4
01111110 => [1,6,1] => 4
01111111 => [1,7] => 3
10000000 => [1,7] => 3
10000001 => [1,6,1] => 4
10000010 => [1,5,1,1] => 4
10000011 => [1,5,2] => 5
10000100 => [1,4,1,2] => 5
10000101 => [1,4,1,1,1] => 4
10000110 => [1,4,2,1] => 6
10000111 => [1,4,3] => 5
10001000 => [1,3,1,3] => 5
10001001 => [1,3,1,2,1] => 6
10001010 => [1,3,1,1,1,1] => 4
10001011 => [1,3,1,1,2] => 5
10001100 => [1,3,2,2] => 7
10001101 => [1,3,2,1,1] => 6
10001110 => [1,3,3,1] => 6
10001111 => [1,3,4] => 5
10010000 => [1,2,1,4] => 5
10010001 => [1,2,1,3,1] => 6
10010010 => [1,2,1,2,1,1] => 6
10010011 => [1,2,1,2,2] => 7
10010100 => [1,2,1,1,1,2] => 5
10010101 => [1,2,1,1,1,1,1] => 4
10010110 => [1,2,1,1,2,1] => 6
10010111 => [1,2,1,1,3] => 5
10011000 => [1,2,2,3] => 7
10011001 => [1,2,2,2,1] => 8
10011010 => [1,2,2,1,1,1] => 6
10011011 => [1,2,2,1,2] => 7
10011100 => [1,2,3,2] => 7
10011101 => [1,2,3,1,1] => 6
10011110 => [1,2,4,1] => 6
10011111 => [1,2,5] => 5
10100000 => [1,1,1,5] => 3
10100001 => [1,1,1,4,1] => 4
10100010 => [1,1,1,3,1,1] => 4
10100011 => [1,1,1,3,2] => 5
10100100 => [1,1,1,2,1,2] => 5
10100101 => [1,1,1,2,1,1,1] => 4
10100110 => [1,1,1,2,2,1] => 6
10100111 => [1,1,1,2,3] => 5
10101000 => [1,1,1,1,1,3] => 3
10101001 => [1,1,1,1,1,2,1] => 4
10101010 => [1,1,1,1,1,1,1,1] => 2
10101011 => [1,1,1,1,1,1,2] => 3
10101100 => [1,1,1,1,2,2] => 5
10101101 => [1,1,1,1,2,1,1] => 4
10101110 => [1,1,1,1,3,1] => 4
10101111 => [1,1,1,1,4] => 3
10110000 => [1,1,2,4] => 5
10110001 => [1,1,2,3,1] => 6
10110010 => [1,1,2,2,1,1] => 6
10110011 => [1,1,2,2,2] => 7
10110100 => [1,1,2,1,1,2] => 5
10110101 => [1,1,2,1,1,1,1] => 4
10110110 => [1,1,2,1,2,1] => 6
10110111 => [1,1,2,1,3] => 5
10111000 => [1,1,3,3] => 5
10111001 => [1,1,3,2,1] => 6
10111010 => [1,1,3,1,1,1] => 4
10111011 => [1,1,3,1,2] => 5
10111100 => [1,1,4,2] => 5
10111101 => [1,1,4,1,1] => 4
10111110 => [1,1,5,1] => 4
10111111 => [1,1,6] => 3
11000000 => [2,6] => 4
11000001 => [2,5,1] => 5
11000010 => [2,4,1,1] => 5
11000011 => [2,4,2] => 6
11000100 => [2,3,1,2] => 6
11000101 => [2,3,1,1,1] => 5
11000110 => [2,3,2,1] => 7
11000111 => [2,3,3] => 6
11001000 => [2,2,1,3] => 6
11001001 => [2,2,1,2,1] => 7
11001010 => [2,2,1,1,1,1] => 5
11001011 => [2,2,1,1,2] => 6
11001100 => [2,2,2,2] => 8
11001101 => [2,2,2,1,1] => 7
11001110 => [2,2,3,1] => 7
11001111 => [2,2,4] => 6
11010000 => [2,1,1,4] => 4
11010001 => [2,1,1,3,1] => 5
11010010 => [2,1,1,2,1,1] => 5
11010011 => [2,1,1,2,2] => 6
11010100 => [2,1,1,1,1,2] => 4
11010101 => [2,1,1,1,1,1,1] => 3
11010110 => [2,1,1,1,2,1] => 5
11010111 => [2,1,1,1,3] => 4
11011000 => [2,1,2,3] => 6
11011001 => [2,1,2,2,1] => 7
11011010 => [2,1,2,1,1,1] => 5
11011011 => [2,1,2,1,2] => 6
11011100 => [2,1,3,2] => 6
11011101 => [2,1,3,1,1] => 5
11011110 => [2,1,4,1] => 5
11011111 => [2,1,5] => 4
11100000 => [3,5] => 4
11100001 => [3,4,1] => 5
11100010 => [3,3,1,1] => 5
11100011 => [3,3,2] => 6
11100100 => [3,2,1,2] => 6
11100101 => [3,2,1,1,1] => 5
11100110 => [3,2,2,1] => 7
11100111 => [3,2,3] => 6
11101000 => [3,1,1,3] => 4
11101001 => [3,1,1,2,1] => 5
11101010 => [3,1,1,1,1,1] => 3
11101011 => [3,1,1,1,2] => 4
11101100 => [3,1,2,2] => 6
11101101 => [3,1,2,1,1] => 5
11101110 => [3,1,3,1] => 5
11101111 => [3,1,4] => 4
11110000 => [4,4] => 4
11110001 => [4,3,1] => 5
11110010 => [4,2,1,1] => 5
11110011 => [4,2,2] => 6
11110100 => [4,1,1,2] => 4
11110101 => [4,1,1,1,1] => 3
11110110 => [4,1,2,1] => 5
11110111 => [4,1,3] => 4
11111000 => [5,3] => 4
11111001 => [5,2,1] => 5
11111010 => [5,1,1,1] => 3
11111011 => [5,1,2] => 4
11111100 => [6,2] => 4
11111101 => [6,1,1] => 3
11111110 => [7,1] => 3
11111111 => [8] => 2
000000000 => [9] => 2
000000001 => [8,1] => 3
000000010 => [7,1,1] => 3
000000011 => [7,2] => 4
000000100 => [6,1,2] => 4
000000101 => [6,1,1,1] => 3
000000110 => [6,2,1] => 5
000000111 => [6,3] => 4
000001000 => [5,1,3] => 4
000001001 => [5,1,2,1] => 5
000001010 => [5,1,1,1,1] => 3
000001011 => [5,1,1,2] => 4
000001100 => [5,2,2] => 6
000001101 => [5,2,1,1] => 5
000001110 => [5,3,1] => 5
000001111 => [5,4] => 4
000010000 => [4,1,4] => 4
000010001 => [4,1,3,1] => 5
000010010 => [4,1,2,1,1] => 5
000010011 => [4,1,2,2] => 6
000010100 => [4,1,1,1,2] => 4
000010101 => [4,1,1,1,1,1] => 3
000010110 => [4,1,1,2,1] => 5
000010111 => [4,1,1,3] => 4
000011000 => [4,2,3] => 6
000011001 => [4,2,2,1] => 7
000011010 => [4,2,1,1,1] => 5
000011011 => [4,2,1,2] => 6
000011100 => [4,3,2] => 6
000011101 => [4,3,1,1] => 5
000011110 => [4,4,1] => 5
000011111 => [4,5] => 4
000100000 => [3,1,5] => 4
000100001 => [3,1,4,1] => 5
000100010 => [3,1,3,1,1] => 5
000100011 => [3,1,3,2] => 6
000100100 => [3,1,2,1,2] => 6
000100101 => [3,1,2,1,1,1] => 5
000100110 => [3,1,2,2,1] => 7
000100111 => [3,1,2,3] => 6
000101000 => [3,1,1,1,3] => 4
000101001 => [3,1,1,1,2,1] => 5
000101010 => [3,1,1,1,1,1,1] => 3
000101011 => [3,1,1,1,1,2] => 4
000101100 => [3,1,1,2,2] => 6
000101101 => [3,1,1,2,1,1] => 5
000101110 => [3,1,1,3,1] => 5
000101111 => [3,1,1,4] => 4
000110000 => [3,2,4] => 6
000110001 => [3,2,3,1] => 7
000110010 => [3,2,2,1,1] => 7
000110011 => [3,2,2,2] => 8
000110100 => [3,2,1,1,2] => 6
000110101 => [3,2,1,1,1,1] => 5
000110110 => [3,2,1,2,1] => 7
000110111 => [3,2,1,3] => 6
000111000 => [3,3,3] => 6
000111001 => [3,3,2,1] => 7
000111010 => [3,3,1,1,1] => 5
000111011 => [3,3,1,2] => 6
000111100 => [3,4,2] => 6
000111101 => [3,4,1,1] => 5
000111110 => [3,5,1] => 5
000111111 => [3,6] => 4
001000000 => [2,1,6] => 4
001000001 => [2,1,5,1] => 5
001000010 => [2,1,4,1,1] => 5
001000011 => [2,1,4,2] => 6
001000100 => [2,1,3,1,2] => 6
001000101 => [2,1,3,1,1,1] => 5
001000110 => [2,1,3,2,1] => 7
001000111 => [2,1,3,3] => 6
001001000 => [2,1,2,1,3] => 6
001001001 => [2,1,2,1,2,1] => 7
001001010 => [2,1,2,1,1,1,1] => 5
001001011 => [2,1,2,1,1,2] => 6
001001100 => [2,1,2,2,2] => 8
001001101 => [2,1,2,2,1,1] => 7
001001110 => [2,1,2,3,1] => 7
001001111 => [2,1,2,4] => 6
001010000 => [2,1,1,1,4] => 4
001010001 => [2,1,1,1,3,1] => 5
001010010 => [2,1,1,1,2,1,1] => 5
001010011 => [2,1,1,1,2,2] => 6
001010100 => [2,1,1,1,1,1,2] => 4
001010101 => [2,1,1,1,1,1,1,1] => 3
001010110 => [2,1,1,1,1,2,1] => 5
001010111 => [2,1,1,1,1,3] => 4
001011000 => [2,1,1,2,3] => 6
001011001 => [2,1,1,2,2,1] => 7
001011010 => [2,1,1,2,1,1,1] => 5
001011011 => [2,1,1,2,1,2] => 6
001011100 => [2,1,1,3,2] => 6
001011101 => [2,1,1,3,1,1] => 5
001011110 => [2,1,1,4,1] => 5
001011111 => [2,1,1,5] => 4
001100000 => [2,2,5] => 6
001100001 => [2,2,4,1] => 7
001100010 => [2,2,3,1,1] => 7
001100011 => [2,2,3,2] => 8
001100100 => [2,2,2,1,2] => 8
001100101 => [2,2,2,1,1,1] => 7
001100110 => [2,2,2,2,1] => 9
001100111 => [2,2,2,3] => 8
001101000 => [2,2,1,1,3] => 6
001101001 => [2,2,1,1,2,1] => 7
001101010 => [2,2,1,1,1,1,1] => 5
001101011 => [2,2,1,1,1,2] => 6
001101100 => [2,2,1,2,2] => 8
001101101 => [2,2,1,2,1,1] => 7
001101110 => [2,2,1,3,1] => 7
001101111 => [2,2,1,4] => 6
001110000 => [2,3,4] => 6
001110001 => [2,3,3,1] => 7
001110010 => [2,3,2,1,1] => 7
001110011 => [2,3,2,2] => 8
001110100 => [2,3,1,1,2] => 6
001110101 => [2,3,1,1,1,1] => 5
001110110 => [2,3,1,2,1] => 7
001110111 => [2,3,1,3] => 6
001111000 => [2,4,3] => 6
001111001 => [2,4,2,1] => 7
001111010 => [2,4,1,1,1] => 5
001111011 => [2,4,1,2] => 6
001111100 => [2,5,2] => 6
001111101 => [2,5,1,1] => 5
001111110 => [2,6,1] => 5
001111111 => [2,7] => 4
010000000 => [1,1,7] => 3
010000001 => [1,1,6,1] => 4
010000010 => [1,1,5,1,1] => 4
010000011 => [1,1,5,2] => 5
010000100 => [1,1,4,1,2] => 5
010000101 => [1,1,4,1,1,1] => 4
010000110 => [1,1,4,2,1] => 6
010000111 => [1,1,4,3] => 5
010001000 => [1,1,3,1,3] => 5
010001001 => [1,1,3,1,2,1] => 6
010001010 => [1,1,3,1,1,1,1] => 4
010001011 => [1,1,3,1,1,2] => 5
010001100 => [1,1,3,2,2] => 7
010001101 => [1,1,3,2,1,1] => 6
010001110 => [1,1,3,3,1] => 6
010001111 => [1,1,3,4] => 5
010010000 => [1,1,2,1,4] => 5
010010001 => [1,1,2,1,3,1] => 6
010010010 => [1,1,2,1,2,1,1] => 6
010010011 => [1,1,2,1,2,2] => 7
010010100 => [1,1,2,1,1,1,2] => 5
010010101 => [1,1,2,1,1,1,1,1] => 4
010010110 => [1,1,2,1,1,2,1] => 6
010010111 => [1,1,2,1,1,3] => 5
010011000 => [1,1,2,2,3] => 7
010011001 => [1,1,2,2,2,1] => 8
010011010 => [1,1,2,2,1,1,1] => 6
010011011 => [1,1,2,2,1,2] => 7
010011100 => [1,1,2,3,2] => 7
010011101 => [1,1,2,3,1,1] => 6
010011110 => [1,1,2,4,1] => 6
010011111 => [1,1,2,5] => 5
010100000 => [1,1,1,1,5] => 3
010100001 => [1,1,1,1,4,1] => 4
010100010 => [1,1,1,1,3,1,1] => 4
010100011 => [1,1,1,1,3,2] => 5
010100100 => [1,1,1,1,2,1,2] => 5
010100101 => [1,1,1,1,2,1,1,1] => 4
010100110 => [1,1,1,1,2,2,1] => 6
010100111 => [1,1,1,1,2,3] => 5
010101000 => [1,1,1,1,1,1,3] => 3
010101001 => [1,1,1,1,1,1,2,1] => 4
010101010 => [1,1,1,1,1,1,1,1,1] => 2
010101011 => [1,1,1,1,1,1,1,2] => 3
010101100 => [1,1,1,1,1,2,2] => 5
010101101 => [1,1,1,1,1,2,1,1] => 4
010101110 => [1,1,1,1,1,3,1] => 4
010101111 => [1,1,1,1,1,4] => 3
010110000 => [1,1,1,2,4] => 5
010110001 => [1,1,1,2,3,1] => 6
010110010 => [1,1,1,2,2,1,1] => 6
010110011 => [1,1,1,2,2,2] => 7
010110100 => [1,1,1,2,1,1,2] => 5
010110101 => [1,1,1,2,1,1,1,1] => 4
010110110 => [1,1,1,2,1,2,1] => 6
010110111 => [1,1,1,2,1,3] => 5
010111000 => [1,1,1,3,3] => 5
010111001 => [1,1,1,3,2,1] => 6
010111010 => [1,1,1,3,1,1,1] => 4
010111011 => [1,1,1,3,1,2] => 5
010111100 => [1,1,1,4,2] => 5
010111101 => [1,1,1,4,1,1] => 4
010111110 => [1,1,1,5,1] => 4
010111111 => [1,1,1,6] => 3
011000000 => [1,2,6] => 5
011000001 => [1,2,5,1] => 6
011000010 => [1,2,4,1,1] => 6
011000011 => [1,2,4,2] => 7
011000100 => [1,2,3,1,2] => 7
011000101 => [1,2,3,1,1,1] => 6
011000110 => [1,2,3,2,1] => 8
011000111 => [1,2,3,3] => 7
011001000 => [1,2,2,1,3] => 7
011001001 => [1,2,2,1,2,1] => 8
011001010 => [1,2,2,1,1,1,1] => 6
011001011 => [1,2,2,1,1,2] => 7
011001100 => [1,2,2,2,2] => 9
011001101 => [1,2,2,2,1,1] => 8
011001110 => [1,2,2,3,1] => 8
011001111 => [1,2,2,4] => 7
011010000 => [1,2,1,1,4] => 5
011010001 => [1,2,1,1,3,1] => 6
011010010 => [1,2,1,1,2,1,1] => 6
011010011 => [1,2,1,1,2,2] => 7
011010100 => [1,2,1,1,1,1,2] => 5
011010101 => [1,2,1,1,1,1,1,1] => 4
011010110 => [1,2,1,1,1,2,1] => 6
011010111 => [1,2,1,1,1,3] => 5
011011000 => [1,2,1,2,3] => 7
011011001 => [1,2,1,2,2,1] => 8
011011010 => [1,2,1,2,1,1,1] => 6
011011011 => [1,2,1,2,1,2] => 7
011011100 => [1,2,1,3,2] => 7
011011101 => [1,2,1,3,1,1] => 6
011011110 => [1,2,1,4,1] => 6
011011111 => [1,2,1,5] => 5
011100000 => [1,3,5] => 5
011100001 => [1,3,4,1] => 6
011100010 => [1,3,3,1,1] => 6
011100011 => [1,3,3,2] => 7
011100100 => [1,3,2,1,2] => 7
011100101 => [1,3,2,1,1,1] => 6
011100110 => [1,3,2,2,1] => 8
011100111 => [1,3,2,3] => 7
011101000 => [1,3,1,1,3] => 5
011101001 => [1,3,1,1,2,1] => 6
011101010 => [1,3,1,1,1,1,1] => 4
011101011 => [1,3,1,1,1,2] => 5
011101100 => [1,3,1,2,2] => 7
011101101 => [1,3,1,2,1,1] => 6
011101110 => [1,3,1,3,1] => 6
011101111 => [1,3,1,4] => 5
011110000 => [1,4,4] => 5
011110001 => [1,4,3,1] => 6
011110010 => [1,4,2,1,1] => 6
011110011 => [1,4,2,2] => 7
011110100 => [1,4,1,1,2] => 5
011110101 => [1,4,1,1,1,1] => 4
011110110 => [1,4,1,2,1] => 6
011110111 => [1,4,1,3] => 5
011111000 => [1,5,3] => 5
011111001 => [1,5,2,1] => 6
011111010 => [1,5,1,1,1] => 4
011111011 => [1,5,1,2] => 5
011111100 => [1,6,2] => 5
011111101 => [1,6,1,1] => 4
011111110 => [1,7,1] => 4
011111111 => [1,8] => 3
100000000 => [1,8] => 3
100000001 => [1,7,1] => 4
100000010 => [1,6,1,1] => 4
100000011 => [1,6,2] => 5
100000100 => [1,5,1,2] => 5
100000101 => [1,5,1,1,1] => 4
100000110 => [1,5,2,1] => 6
100000111 => [1,5,3] => 5
100001000 => [1,4,1,3] => 5
100001001 => [1,4,1,2,1] => 6
100001010 => [1,4,1,1,1,1] => 4
100001011 => [1,4,1,1,2] => 5
100001100 => [1,4,2,2] => 7
100001101 => [1,4,2,1,1] => 6
100001110 => [1,4,3,1] => 6
100001111 => [1,4,4] => 5
100010000 => [1,3,1,4] => 5
100010001 => [1,3,1,3,1] => 6
100010010 => [1,3,1,2,1,1] => 6
100010011 => [1,3,1,2,2] => 7
100010100 => [1,3,1,1,1,2] => 5
100010101 => [1,3,1,1,1,1,1] => 4
100010110 => [1,3,1,1,2,1] => 6
100010111 => [1,3,1,1,3] => 5
100011000 => [1,3,2,3] => 7
100011001 => [1,3,2,2,1] => 8
100011010 => [1,3,2,1,1,1] => 6
100011011 => [1,3,2,1,2] => 7
100011100 => [1,3,3,2] => 7
100011101 => [1,3,3,1,1] => 6
100011110 => [1,3,4,1] => 6
100011111 => [1,3,5] => 5
100100000 => [1,2,1,5] => 5
100100001 => [1,2,1,4,1] => 6
100100010 => [1,2,1,3,1,1] => 6
100100011 => [1,2,1,3,2] => 7
100100100 => [1,2,1,2,1,2] => 7
100100101 => [1,2,1,2,1,1,1] => 6
100100110 => [1,2,1,2,2,1] => 8
100100111 => [1,2,1,2,3] => 7
100101000 => [1,2,1,1,1,3] => 5
100101001 => [1,2,1,1,1,2,1] => 6
100101010 => [1,2,1,1,1,1,1,1] => 4
100101011 => [1,2,1,1,1,1,2] => 5
100101100 => [1,2,1,1,2,2] => 7
100101101 => [1,2,1,1,2,1,1] => 6
100101110 => [1,2,1,1,3,1] => 6
100101111 => [1,2,1,1,4] => 5
100110000 => [1,2,2,4] => 7
100110001 => [1,2,2,3,1] => 8
100110010 => [1,2,2,2,1,1] => 8
100110011 => [1,2,2,2,2] => 9
100110100 => [1,2,2,1,1,2] => 7
100110101 => [1,2,2,1,1,1,1] => 6
100110110 => [1,2,2,1,2,1] => 8
100110111 => [1,2,2,1,3] => 7
100111000 => [1,2,3,3] => 7
100111001 => [1,2,3,2,1] => 8
100111010 => [1,2,3,1,1,1] => 6
100111011 => [1,2,3,1,2] => 7
100111100 => [1,2,4,2] => 7
100111101 => [1,2,4,1,1] => 6
100111110 => [1,2,5,1] => 6
100111111 => [1,2,6] => 5
101000000 => [1,1,1,6] => 3
101000001 => [1,1,1,5,1] => 4
101000010 => [1,1,1,4,1,1] => 4
101000011 => [1,1,1,4,2] => 5
101000100 => [1,1,1,3,1,2] => 5
101000101 => [1,1,1,3,1,1,1] => 4
101000110 => [1,1,1,3,2,1] => 6
101000111 => [1,1,1,3,3] => 5
101001000 => [1,1,1,2,1,3] => 5
101001001 => [1,1,1,2,1,2,1] => 6
101001010 => [1,1,1,2,1,1,1,1] => 4
101001011 => [1,1,1,2,1,1,2] => 5
101001100 => [1,1,1,2,2,2] => 7
101001101 => [1,1,1,2,2,1,1] => 6
101001110 => [1,1,1,2,3,1] => 6
101001111 => [1,1,1,2,4] => 5
101010000 => [1,1,1,1,1,4] => 3
101010001 => [1,1,1,1,1,3,1] => 4
101010010 => [1,1,1,1,1,2,1,1] => 4
101010011 => [1,1,1,1,1,2,2] => 5
101010100 => [1,1,1,1,1,1,1,2] => 3
101010101 => [1,1,1,1,1,1,1,1,1] => 2
101010110 => [1,1,1,1,1,1,2,1] => 4
101010111 => [1,1,1,1,1,1,3] => 3
101011000 => [1,1,1,1,2,3] => 5
101011001 => [1,1,1,1,2,2,1] => 6
101011010 => [1,1,1,1,2,1,1,1] => 4
101011011 => [1,1,1,1,2,1,2] => 5
101011100 => [1,1,1,1,3,2] => 5
101011101 => [1,1,1,1,3,1,1] => 4
101011110 => [1,1,1,1,4,1] => 4
101011111 => [1,1,1,1,5] => 3
101100000 => [1,1,2,5] => 5
101100001 => [1,1,2,4,1] => 6
101100010 => [1,1,2,3,1,1] => 6
101100011 => [1,1,2,3,2] => 7
101100100 => [1,1,2,2,1,2] => 7
101100101 => [1,1,2,2,1,1,1] => 6
101100110 => [1,1,2,2,2,1] => 8
101100111 => [1,1,2,2,3] => 7
101101000 => [1,1,2,1,1,3] => 5
101101001 => [1,1,2,1,1,2,1] => 6
101101010 => [1,1,2,1,1,1,1,1] => 4
101101011 => [1,1,2,1,1,1,2] => 5
101101100 => [1,1,2,1,2,2] => 7
101101101 => [1,1,2,1,2,1,1] => 6
101101110 => [1,1,2,1,3,1] => 6
101101111 => [1,1,2,1,4] => 5
101110000 => [1,1,3,4] => 5
101110001 => [1,1,3,3,1] => 6
101110010 => [1,1,3,2,1,1] => 6
101110011 => [1,1,3,2,2] => 7
101110100 => [1,1,3,1,1,2] => 5
101110101 => [1,1,3,1,1,1,1] => 4
101110110 => [1,1,3,1,2,1] => 6
101110111 => [1,1,3,1,3] => 5
101111000 => [1,1,4,3] => 5
101111001 => [1,1,4,2,1] => 6
101111010 => [1,1,4,1,1,1] => 4
101111011 => [1,1,4,1,2] => 5
101111100 => [1,1,5,2] => 5
101111101 => [1,1,5,1,1] => 4
101111110 => [1,1,6,1] => 4
101111111 => [1,1,7] => 3
110000000 => [2,7] => 4
110000001 => [2,6,1] => 5
110000010 => [2,5,1,1] => 5
110000011 => [2,5,2] => 6
110000100 => [2,4,1,2] => 6
110000101 => [2,4,1,1,1] => 5
110000110 => [2,4,2,1] => 7
110000111 => [2,4,3] => 6
110001000 => [2,3,1,3] => 6
110001001 => [2,3,1,2,1] => 7
110001010 => [2,3,1,1,1,1] => 5
110001011 => [2,3,1,1,2] => 6
110001100 => [2,3,2,2] => 8
110001101 => [2,3,2,1,1] => 7
110001110 => [2,3,3,1] => 7
110001111 => [2,3,4] => 6
110010000 => [2,2,1,4] => 6
110010001 => [2,2,1,3,1] => 7
110010010 => [2,2,1,2,1,1] => 7
110010011 => [2,2,1,2,2] => 8
110010100 => [2,2,1,1,1,2] => 6
110010101 => [2,2,1,1,1,1,1] => 5
110010110 => [2,2,1,1,2,1] => 7
110010111 => [2,2,1,1,3] => 6
110011000 => [2,2,2,3] => 8
110011001 => [2,2,2,2,1] => 9
110011010 => [2,2,2,1,1,1] => 7
110011011 => [2,2,2,1,2] => 8
110011100 => [2,2,3,2] => 8
110011101 => [2,2,3,1,1] => 7
110011110 => [2,2,4,1] => 7
110011111 => [2,2,5] => 6
110100000 => [2,1,1,5] => 4
110100001 => [2,1,1,4,1] => 5
110100010 => [2,1,1,3,1,1] => 5
110100011 => [2,1,1,3,2] => 6
110100100 => [2,1,1,2,1,2] => 6
110100101 => [2,1,1,2,1,1,1] => 5
110100110 => [2,1,1,2,2,1] => 7
110100111 => [2,1,1,2,3] => 6
110101000 => [2,1,1,1,1,3] => 4
110101001 => [2,1,1,1,1,2,1] => 5
110101010 => [2,1,1,1,1,1,1,1] => 3
110101011 => [2,1,1,1,1,1,2] => 4
110101100 => [2,1,1,1,2,2] => 6
110101101 => [2,1,1,1,2,1,1] => 5
110101110 => [2,1,1,1,3,1] => 5
110101111 => [2,1,1,1,4] => 4
110110000 => [2,1,2,4] => 6
110110001 => [2,1,2,3,1] => 7
110110010 => [2,1,2,2,1,1] => 7
110110011 => [2,1,2,2,2] => 8
110110100 => [2,1,2,1,1,2] => 6
110110101 => [2,1,2,1,1,1,1] => 5
110110110 => [2,1,2,1,2,1] => 7
110110111 => [2,1,2,1,3] => 6
110111000 => [2,1,3,3] => 6
110111001 => [2,1,3,2,1] => 7
110111010 => [2,1,3,1,1,1] => 5
110111011 => [2,1,3,1,2] => 6
110111100 => [2,1,4,2] => 6
110111101 => [2,1,4,1,1] => 5
110111110 => [2,1,5,1] => 5
110111111 => [2,1,6] => 4
111000000 => [3,6] => 4
111000001 => [3,5,1] => 5
111000010 => [3,4,1,1] => 5
111000011 => [3,4,2] => 6
111000100 => [3,3,1,2] => 6
111000101 => [3,3,1,1,1] => 5
111000110 => [3,3,2,1] => 7
111000111 => [3,3,3] => 6
111001000 => [3,2,1,3] => 6
111001001 => [3,2,1,2,1] => 7
111001010 => [3,2,1,1,1,1] => 5
111001011 => [3,2,1,1,2] => 6
111001100 => [3,2,2,2] => 8
111001101 => [3,2,2,1,1] => 7
111001110 => [3,2,3,1] => 7
111001111 => [3,2,4] => 6
111010000 => [3,1,1,4] => 4
111010001 => [3,1,1,3,1] => 5
111010010 => [3,1,1,2,1,1] => 5
111010011 => [3,1,1,2,2] => 6
111010100 => [3,1,1,1,1,2] => 4
111010101 => [3,1,1,1,1,1,1] => 3
111010110 => [3,1,1,1,2,1] => 5
111010111 => [3,1,1,1,3] => 4
111011000 => [3,1,2,3] => 6
111011001 => [3,1,2,2,1] => 7
111011010 => [3,1,2,1,1,1] => 5
111011011 => [3,1,2,1,2] => 6
111011100 => [3,1,3,2] => 6
111011101 => [3,1,3,1,1] => 5
111011110 => [3,1,4,1] => 5
111011111 => [3,1,5] => 4
111100000 => [4,5] => 4
111100001 => [4,4,1] => 5
111100010 => [4,3,1,1] => 5
111100011 => [4,3,2] => 6
111100100 => [4,2,1,2] => 6
111100101 => [4,2,1,1,1] => 5
111100110 => [4,2,2,1] => 7
111100111 => [4,2,3] => 6
111101000 => [4,1,1,3] => 4
111101001 => [4,1,1,2,1] => 5
111101010 => [4,1,1,1,1,1] => 3
111101011 => [4,1,1,1,2] => 4
111101100 => [4,1,2,2] => 6
111101101 => [4,1,2,1,1] => 5
111101110 => [4,1,3,1] => 5
111101111 => [4,1,4] => 4
111110000 => [5,4] => 4
111110001 => [5,3,1] => 5
111110010 => [5,2,1,1] => 5
111110011 => [5,2,2] => 6
111110100 => [5,1,1,2] => 4
111110101 => [5,1,1,1,1] => 3
111110110 => [5,1,2,1] => 5
111110111 => [5,1,3] => 4
111111000 => [6,3] => 4
111111001 => [6,2,1] => 5
111111010 => [6,1,1,1] => 3
111111011 => [6,1,2] => 4
111111100 => [7,2] => 4
111111101 => [7,1,1] => 3
111111110 => [8,1] => 3
111111111 => [9] => 2
1010101010 => [1,1,1,1,1,1,1,1,1,1] => 2
1010101100 => [1,1,1,1,1,1,2,2] => 5
1010110010 => [1,1,1,1,2,2,1,1] => 6
1010110100 => [1,1,1,1,2,1,1,2] => 5
1010111000 => [1,1,1,1,3,3] => 5
1011001010 => [1,1,2,2,1,1,1,1] => 6
1011001100 => [1,1,2,2,2,2] => 9
1011010010 => [1,1,2,1,1,2,1,1] => 6
1011010100 => [1,1,2,1,1,1,1,2] => 5
1011011000 => [1,1,2,1,2,3] => 7
1011100010 => [1,1,3,3,1,1] => 6
1011100100 => [1,1,3,2,1,2] => 7
1011101000 => [1,1,3,1,1,3] => 5
1011110000 => [1,1,4,4] => 5
1100101010 => [2,2,1,1,1,1,1,1] => 5
1100101100 => [2,2,1,1,2,2] => 8
1100110010 => [2,2,2,2,1,1] => 9
1100110100 => [2,2,2,1,1,2] => 8
1100111000 => [2,2,3,3] => 8
1101001010 => [2,1,1,2,1,1,1,1] => 5
1101001100 => [2,1,1,2,2,2] => 8
1101010010 => [2,1,1,1,1,2,1,1] => 5
1101010100 => [2,1,1,1,1,1,1,2] => 4
1101011000 => [2,1,1,1,2,3] => 6
1101100010 => [2,1,2,3,1,1] => 7
1101100100 => [2,1,2,2,1,2] => 8
1101101000 => [2,1,2,1,1,3] => 6
1101110000 => [2,1,3,4] => 6
1110001010 => [3,3,1,1,1,1] => 5
1110001100 => [3,3,2,2] => 8
1110010010 => [3,2,1,2,1,1] => 7
1110010100 => [3,2,1,1,1,2] => 6
1110011000 => [3,2,2,3] => 8
1110100010 => [3,1,1,3,1,1] => 5
1110100100 => [3,1,1,2,1,2] => 6
1110101000 => [3,1,1,1,1,3] => 4
1110110000 => [3,1,2,4] => 6
1111000010 => [4,4,1,1] => 5
1111000100 => [4,3,1,2] => 6
1111001000 => [4,2,1,3] => 6
1111010000 => [4,1,1,4] => 4
1111100000 => [5,5] => 4
1111111111 => [10] => 2
1111111110 => [9,1] => 3
1111111101 => [8,1,1] => 3
1111111100 => [8,2] => 4
1111111011 => [7,1,2] => 4
1111111010 => [7,1,1,1] => 3
1111111001 => [7,2,1] => 5
1111110110 => [6,1,2,1] => 5
1111110101 => [6,1,1,1,1] => 3
1111110011 => [6,2,2] => 6
1111110010 => [6,2,1,1] => 5
1111110001 => [6,3,1] => 5
1111110000 => [6,4] => 4
1111101010 => [5,1,1,1,1,1] => 3
1111101001 => [5,1,1,2,1] => 5
1111101000 => [5,1,1,3] => 4
1111100100 => [5,2,1,2] => 6
1111100011 => [5,3,2] => 6
1111100010 => [5,3,1,1] => 5
1111100001 => [5,4,1] => 5
1111011110 => [4,1,4,1] => 5
1111011101 => [4,1,3,1,1] => 5
1111011011 => [4,1,2,1,2] => 6
1111011000 => [4,1,2,3] => 6
1111010111 => [4,1,1,1,3] => 4
1111010101 => [4,1,1,1,1,1,1] => 3
1111010100 => [4,1,1,1,1,2] => 4
1111010011 => [4,1,1,2,2] => 6
1111010010 => [4,1,1,2,1,1] => 5
1111010001 => [4,1,1,3,1] => 5
1111001111 => [4,2,4] => 6
1111001100 => [4,2,2,2] => 8
1111001011 => [4,2,1,1,2] => 6
1111001010 => [4,2,1,1,1,1] => 5
1111001001 => [4,2,1,2,1] => 7
1111000111 => [4,3,3] => 6
1111000110 => [4,3,2,1] => 7
1111000101 => [4,3,1,1,1] => 5
1111000011 => [4,4,2] => 6
1111000001 => [4,5,1] => 5
1111000000 => [4,6] => 4
1110111111 => [3,1,6] => 4
1110111110 => [3,1,5,1] => 5
1110111101 => [3,1,4,1,1] => 5
1110111011 => [3,1,3,1,2] => 6
1110111000 => [3,1,3,3] => 6
1110110101 => [3,1,2,1,1,1,1] => 5
1110110100 => [3,1,2,1,1,2] => 6
1110110010 => [3,1,2,2,1,1] => 7
1110110001 => [3,1,2,3,1] => 7
1110101111 => [3,1,1,1,4] => 4
1110101101 => [3,1,1,1,2,1,1] => 5
1110101100 => [3,1,1,1,2,2] => 6
1110101011 => [3,1,1,1,1,1,2] => 4
1110101010 => [3,1,1,1,1,1,1,1] => 3
1110101001 => [3,1,1,1,1,2,1] => 5
1110100101 => [3,1,1,2,1,1,1] => 5
1110100011 => [3,1,1,3,2] => 6
1110100001 => [3,1,1,4,1] => 5
1110011111 => [3,2,5] => 6
1110011110 => [3,2,4,1] => 7
1110011001 => [3,2,2,2,1] => 9
1110010101 => [3,2,1,1,1,1,1] => 5
1110010011 => [3,2,1,2,2] => 8
1110010001 => [3,2,1,3,1] => 7
1110001101 => [3,3,2,1,1] => 7
1110001001 => [3,3,1,2,1] => 7
1110000111 => [3,4,3] => 6
1110000101 => [3,4,1,1,1] => 5
1110000011 => [3,5,2] => 6
1110000010 => [3,5,1,1] => 5
1110000001 => [3,6,1] => 5
1101111111 => [2,1,7] => 4
1101111110 => [2,1,6,1] => 5
1101111101 => [2,1,5,1,1] => 5
1101111011 => [2,1,4,1,2] => 6
1101111001 => [2,1,4,2,1] => 7
1101111000 => [2,1,4,3] => 6
1101110111 => [2,1,3,1,3] => 6
1101110010 => [2,1,3,2,1,1] => 7
1101110001 => [2,1,3,3,1] => 7
1101101111 => [2,1,2,1,4] => 6
1101101100 => [2,1,2,1,2,2] => 8
1101101001 => [2,1,2,1,1,2,1] => 7
1101100110 => [2,1,2,2,2,1] => 9
1101100101 => [2,1,2,2,1,1,1] => 7
1101100011 => [2,1,2,3,2] => 8
1101100001 => [2,1,2,4,1] => 7
1101100000 => [2,1,2,5] => 6
1101011111 => [2,1,1,1,5] => 4
1101011010 => [2,1,1,1,2,1,1,1] => 5
1101011001 => [2,1,1,1,2,2,1] => 7
1101010111 => [2,1,1,1,1,1,3] => 4
1101010101 => [2,1,1,1,1,1,1,1,1] => 3
1101010011 => [2,1,1,1,1,2,2] => 6
1101010001 => [2,1,1,1,1,3,1] => 5
1101001111 => [2,1,1,2,4] => 6
1101001110 => [2,1,1,2,3,1] => 7
1101001101 => [2,1,1,2,2,1,1] => 7
1101001011 => [2,1,1,2,1,1,2] => 6
1101001001 => [2,1,1,2,1,2,1] => 7
1101001000 => [2,1,1,2,1,3] => 6
1101000111 => [2,1,1,3,3] => 6
1101000101 => [2,1,1,3,1,1,1] => 5
1101000011 => [2,1,1,4,2] => 6
1101000010 => [2,1,1,4,1,1] => 5
1101000001 => [2,1,1,5,1] => 5
1100111111 => [2,2,6] => 6
1100111100 => [2,2,4,2] => 8
1100111001 => [2,2,3,2,1] => 9
1100110110 => [2,2,2,1,2,1] => 9
1100110101 => [2,2,2,1,1,1,1] => 7
1100110011 => [2,2,2,2,2] => 10
1100110001 => [2,2,2,3,1] => 9
1100110000 => [2,2,2,4] => 8
1100101110 => [2,2,1,1,3,1] => 7
1100101101 => [2,2,1,1,2,1,1] => 7
1100101011 => [2,2,1,1,1,1,2] => 6
1100101001 => [2,2,1,1,1,2,1] => 7
1100100111 => [2,2,1,2,3] => 8
1100100110 => [2,2,1,2,2,1] => 9
1100100101 => [2,2,1,2,1,1,1] => 7
1100100011 => [2,2,1,3,2] => 8
1100011110 => [2,3,4,1] => 7
1100011101 => [2,3,3,1,1] => 7
1100011100 => [2,3,3,2] => 8
1100011011 => [2,3,2,1,2] => 8
1100011001 => [2,3,2,2,1] => 9
1100011000 => [2,3,2,3] => 8
1100010111 => [2,3,1,1,3] => 6
1100010101 => [2,3,1,1,1,1,1] => 5
1100010011 => [2,3,1,2,2] => 8
1100010010 => [2,3,1,2,1,1] => 7
1100001111 => [2,4,4] => 6
1100001101 => [2,4,2,1,1] => 7
1100001100 => [2,4,2,2] => 8
1100001011 => [2,4,1,1,2] => 6
1100001010 => [2,4,1,1,1,1] => 5
1100001000 => [2,4,1,3] => 6
1100000111 => [2,5,3] => 6
1100000110 => [2,5,2,1] => 7
1100000011 => [2,6,2] => 6
1100000010 => [2,6,1,1] => 5
1100000001 => [2,7,1] => 5
1100000000 => [2,8] => 4
1011111111 => [1,1,8] => 3
1011111110 => [1,1,7,1] => 4
1011111101 => [1,1,6,1,1] => 4
1011111100 => [1,1,6,2] => 5
1011111011 => [1,1,5,1,2] => 5
1011111010 => [1,1,5,1,1,1] => 4
1011111000 => [1,1,5,3] => 5
1011110111 => [1,1,4,1,3] => 5
1011110100 => [1,1,4,1,1,2] => 5
1011110001 => [1,1,4,3,1] => 6
1011100011 => [1,1,3,3,2] => 7
1011100001 => [1,1,3,4,1] => 6
1011100000 => [1,1,3,5] => 5
1011011001 => [1,1,2,1,2,2,1] => 8
1011010111 => [1,1,2,1,1,1,3] => 5
1011010101 => [1,1,2,1,1,1,1,1,1] => 4
1011010011 => [1,1,2,1,1,2,2] => 7
1011010001 => [1,1,2,1,1,3,1] => 6
1011010000 => [1,1,2,1,1,4] => 5
1011001101 => [1,1,2,2,2,1,1] => 8
1011001011 => [1,1,2,2,1,1,2] => 7
1011001001 => [1,1,2,2,1,2,1] => 8
1011001000 => [1,1,2,2,1,3] => 7
1011000111 => [1,1,2,3,3] => 7
1011000101 => [1,1,2,3,1,1,1] => 6
1011000100 => [1,1,2,3,1,2] => 7
1011000011 => [1,1,2,4,2] => 7
1011000010 => [1,1,2,4,1,1] => 6
1011000000 => [1,1,2,6] => 5
1010111111 => [1,1,1,1,6] => 3
1010111110 => [1,1,1,1,5,1] => 4
1010110111 => [1,1,1,1,2,1,3] => 5
1010110101 => [1,1,1,1,2,1,1,1,1] => 4
1010110011 => [1,1,1,1,2,2,2] => 7
1010110001 => [1,1,1,1,2,3,1] => 6
1010110000 => [1,1,1,1,2,4] => 5
1010101111 => [1,1,1,1,1,1,4] => 3
1010101101 => [1,1,1,1,1,1,2,1,1] => 4
1010101011 => [1,1,1,1,1,1,1,1,2] => 3
1010101001 => [1,1,1,1,1,1,1,2,1] => 4
1010101000 => [1,1,1,1,1,1,1,3] => 3
1010100111 => [1,1,1,1,1,2,3] => 5
1010100110 => [1,1,1,1,1,2,2,1] => 6
1010100101 => [1,1,1,1,1,2,1,1,1] => 4
1010100100 => [1,1,1,1,1,2,1,2] => 5
1010100011 => [1,1,1,1,1,3,2] => 5
1010100010 => [1,1,1,1,1,3,1,1] => 4
1010100000 => [1,1,1,1,1,5] => 3
1010011101 => [1,1,1,2,3,1,1] => 6
1010011011 => [1,1,1,2,2,1,2] => 7
1010011010 => [1,1,1,2,2,1,1,1] => 6
1010011001 => [1,1,1,2,2,2,1] => 8
1010011000 => [1,1,1,2,2,3] => 7
1010010111 => [1,1,1,2,1,1,3] => 5
1010010110 => [1,1,1,2,1,1,2,1] => 6
1010010101 => [1,1,1,2,1,1,1,1,1] => 4
1010010100 => [1,1,1,2,1,1,1,2] => 5
1010010011 => [1,1,1,2,1,2,2] => 7
1010010010 => [1,1,1,2,1,2,1,1] => 6
1010010001 => [1,1,1,2,1,3,1] => 6
1010001111 => [1,1,1,3,4] => 5
1010001110 => [1,1,1,3,3,1] => 6
1010001101 => [1,1,1,3,2,1,1] => 6
1010001100 => [1,1,1,3,2,2] => 7
1010001011 => [1,1,1,3,1,1,2] => 5
1010001010 => [1,1,1,3,1,1,1,1] => 4
1010000111 => [1,1,1,4,3] => 5
1010000010 => [1,1,1,5,1,1] => 4
1010000001 => [1,1,1,6,1] => 4
1010000000 => [1,1,1,7] => 3
1001111110 => [1,2,6,1] => 6
1001111000 => [1,2,4,3] => 7
1001110101 => [1,2,3,1,1,1,1] => 6
1001110100 => [1,2,3,1,1,2] => 7
1001110011 => [1,2,3,2,2] => 9
1001110001 => [1,2,3,3,1] => 8
1001110000 => [1,2,3,4] => 7
1001101101 => [1,2,2,1,2,1,1] => 8
1001101100 => [1,2,2,1,2,2] => 9
1001101011 => [1,2,2,1,1,1,2] => 7
1001101010 => [1,2,2,1,1,1,1,1] => 6
1001101001 => [1,2,2,1,1,2,1] => 8
1001101000 => [1,2,2,1,1,3] => 7
1001100111 => [1,2,2,2,3] => 9
1001100110 => [1,2,2,2,2,1] => 10
1001100101 => [1,2,2,2,1,1,1] => 8
1001100100 => [1,2,2,2,1,2] => 9
1001100011 => [1,2,2,3,2] => 9
1001100010 => [1,2,2,3,1,1] => 8
1001011111 => [1,2,1,1,5] => 5
1001011110 => [1,2,1,1,4,1] => 6
1001011101 => [1,2,1,1,3,1,1] => 6
1001011011 => [1,2,1,1,2,1,2] => 7
1001011010 => [1,2,1,1,2,1,1,1] => 6
1001011001 => [1,2,1,1,2,2,1] => 8
1001011000 => [1,2,1,1,2,3] => 7
1001010111 => [1,2,1,1,1,1,3] => 5
1001010110 => [1,2,1,1,1,1,2,1] => 6
1001010101 => [1,2,1,1,1,1,1,1,1] => 4
1001010100 => [1,2,1,1,1,1,1,2] => 5
1001010011 => [1,2,1,1,1,2,2] => 7
1001010010 => [1,2,1,1,1,2,1,1] => 6
1001001111 => [1,2,1,2,4] => 7
1001001110 => [1,2,1,2,3,1] => 8
1001001101 => [1,2,1,2,2,1,1] => 8
1001001100 => [1,2,1,2,2,2] => 9
1001001011 => [1,2,1,2,1,1,2] => 7
1001001010 => [1,2,1,2,1,1,1,1] => 6
1001000111 => [1,2,1,3,3] => 7
1001000000 => [1,2,1,6] => 5
1000111110 => [1,3,5,1] => 6
1000111101 => [1,3,4,1,1] => 6
1000111100 => [1,3,4,2] => 7
1000111011 => [1,3,3,1,2] => 7
1000111010 => [1,3,3,1,1,1] => 6
1000111001 => [1,3,3,2,1] => 8
1000111000 => [1,3,3,3] => 7
1000110111 => [1,3,2,1,3] => 7
1000110110 => [1,3,2,1,2,1] => 8
1000110101 => [1,3,2,1,1,1,1] => 6
1000110100 => [1,3,2,1,1,2] => 7
1000110011 => [1,3,2,2,2] => 9
1000110010 => [1,3,2,2,1,1] => 8
1000110001 => [1,3,2,3,1] => 8
1000101111 => [1,3,1,1,4] => 5
1000101110 => [1,3,1,1,3,1] => 6
1000101101 => [1,3,1,1,2,1,1] => 6
1000101100 => [1,3,1,1,2,2] => 7
1000101011 => [1,3,1,1,1,1,2] => 5
1000101010 => [1,3,1,1,1,1,1,1] => 4
1000100111 => [1,3,1,2,3] => 7
1000011111 => [1,4,5] => 5
1000011110 => [1,4,4,1] => 6
1000011101 => [1,4,3,1,1] => 6
1000011011 => [1,4,2,1,2] => 7
1000010111 => [1,4,1,1,3] => 5
1000010110 => [1,4,1,1,2,1] => 6
1000010101 => [1,4,1,1,1,1,1] => 4
1000001111 => [1,5,4] => 5
1000001110 => [1,5,3,1] => 6
1000001101 => [1,5,2,1,1] => 6
1000001011 => [1,5,1,1,2] => 5
1000001010 => [1,5,1,1,1,1] => 4
1000001001 => [1,5,1,2,1] => 6
1000000110 => [1,6,2,1] => 6
1000000101 => [1,6,1,1,1] => 4
1000000100 => [1,6,1,2] => 5
1000000011 => [1,7,2] => 5
1000000010 => [1,7,1,1] => 4
1000000001 => [1,8,1] => 4
1000000000 => [1,9] => 3
0111111111 => [1,9] => 3
0111111101 => [1,7,1,1] => 4
0111111001 => [1,6,2,1] => 6
0111110001 => [1,5,3,1] => 6
0111100001 => [1,4,4,1] => 6
0100000001 => [1,1,7,1] => 4
0000000001 => [9,1] => 3
0111111011 => [1,6,1,2] => 5
0111110101 => [1,5,1,1,1,1] => 4
0111101001 => [1,4,1,1,2,1] => 6
0111010001 => [1,3,1,1,3,1] => 6
0110100001 => [1,2,1,1,4,1] => 6
0101000001 => [1,1,1,1,5,1] => 4
0101010101 => [1,1,1,1,1,1,1,1,1,1] => 2
0101001011 => [1,1,1,1,2,1,1,2] => 5
0101000111 => [1,1,1,1,3,3] => 5
0100110011 => [1,1,2,2,2,2] => 9
0100100111 => [1,1,2,1,2,3] => 7
0100011011 => [1,1,3,2,1,2] => 7
0100010111 => [1,1,3,1,1,3] => 5
0100001111 => [1,1,4,4] => 5
0011010011 => [2,2,1,1,2,2] => 8
0011000111 => [2,2,3,3] => 8
0010101011 => [2,1,1,1,1,1,1,2] => 4
0010010111 => [2,1,2,1,1,3] => 6
0010001111 => [2,1,3,4] => 6
0001110011 => [3,3,2,2] => 8
0001101011 => [3,2,1,1,1,2] => 6
0001100111 => [3,2,2,3] => 8
0001011101 => [3,1,1,3,1,1] => 5
0001010111 => [3,1,1,1,1,3] => 4
0001001111 => [3,1,2,4] => 6
0000111101 => [4,4,1,1] => 5
0000110111 => [4,2,1,3] => 6
0000101111 => [4,1,1,4] => 4
0000011111 => [5,5] => 4
0000000000 => [10] => 2
0000000110 => [7,2,1] => 5
0000011000 => [5,2,3] => 6
0000011110 => [5,4,1] => 5
0001111110 => [3,6,1] => 5
0110011000 => [1,2,2,2,3] => 9
0110010010 => [1,2,2,1,2,1,1] => 8
0111100000 => [1,4,5] => 5
0111111110 => [1,8,1] => 4
0111001000 => [1,3,2,1,3] => 7
0111000010 => [1,3,4,1,1] => 6
0100111000 => [1,1,2,3,3] => 7
0100111110 => [1,1,2,5,1] => 6
0100110010 => [1,1,2,2,2,1,1] => 8
0100000010 => [1,1,6,1,1] => 4
0101101000 => [1,1,1,2,1,1,3] => 5
0101100010 => [1,1,1,2,3,1,1] => 6
0101001010 => [1,1,1,1,2,1,1,1,1] => 4
0010101010 => [2,1,1,1,1,1,1,1,1] => 3
0010101100 => [2,1,1,1,1,2,2] => 6
0010110100 => [2,1,1,2,1,1,2] => 6
0011010100 => [2,2,1,1,1,1,2] => 6
0101010100 => [1,1,1,1,1,1,1,1,2] => 3
0010101110 => [2,1,1,1,1,3,1] => 5
0010111100 => [2,1,1,4,2] => 6
0011110100 => [2,4,1,1,2] => 6
0000010100 => [5,1,1,1,2] => 4
0111010100 => [1,3,1,1,1,1,2] => 5
0000000010 => [8,1,1] => 3
0000001110 => [6,3,1] => 5
0000111110 => [4,5,1] => 5
0011111110 => [2,7,1] => 5
0000000100 => [7,1,2] => 4
0000001010 => [6,1,1,1,1] => 3
0000010110 => [5,1,1,2,1] => 5
0000101110 => [4,1,1,3,1] => 5
0001011110 => [3,1,1,4,1] => 5
0010111110 => [2,1,1,5,1] => 5
0101111110 => [1,1,1,6,1] => 4
0010110010 => [2,1,1,2,2,1,1] => 7
0010111000 => [2,1,1,3,3] => 6
0011001010 => [2,2,2,1,1,1,1] => 7
0011001100 => [2,2,2,2,2] => 10
0011010010 => [2,2,1,1,2,1,1] => 7
0011011000 => [2,2,1,2,3] => 8
0011100010 => [2,3,3,1,1] => 7
0011100100 => [2,3,2,1,2] => 8
0011101000 => [2,3,1,1,3] => 6
0011110000 => [2,4,4] => 6
0100101010 => [1,1,2,1,1,1,1,1,1] => 4
0100101100 => [1,1,2,1,1,2,2] => 7
0100110100 => [1,1,2,2,1,1,2] => 7
0101001100 => [1,1,1,1,2,2,2] => 7
0101010010 => [1,1,1,1,1,1,2,1,1] => 4
0101011000 => [1,1,1,1,1,2,3] => 5
0101100100 => [1,1,1,2,2,1,2] => 7
0101110000 => [1,1,1,3,4] => 5
0110001010 => [1,2,3,1,1,1,1] => 6
0110001100 => [1,2,3,2,2] => 9
0110010100 => [1,2,2,1,1,1,2] => 7
0110100010 => [1,2,1,1,3,1,1] => 6
0110100100 => [1,2,1,1,2,1,2] => 7
0110101000 => [1,2,1,1,1,1,3] => 5
0110110000 => [1,2,1,2,4] => 7
0111000100 => [1,3,3,1,2] => 7
0111010000 => [1,3,1,1,4] => 5
0100000000 => [1,1,8] => 3
0100000011 => [1,1,6,2] => 5
0100000111 => [1,1,5,3] => 5
0100011111 => [1,1,3,5] => 5
0100111111 => [1,1,2,6] => 5
0101111111 => [1,1,1,7] => 3
0100000101 => [1,1,5,1,1,1] => 4
0100001011 => [1,1,4,1,1,2] => 5
0100101111 => [1,1,2,1,1,4] => 5
0101011111 => [1,1,1,1,1,5] => 3
0110111111 => [1,2,1,6] => 5
0101010110 => [1,1,1,1,1,1,1,2,1] => 4
0101011001 => [1,1,1,1,1,2,2,1] => 6
0101011010 => [1,1,1,1,1,2,1,1,1] => 4
0101011100 => [1,1,1,1,1,3,2] => 5
0101100101 => [1,1,1,2,2,1,1,1] => 6
0101100110 => [1,1,1,2,2,2,1] => 8
0101101001 => [1,1,1,2,1,1,2,1] => 6
0101101010 => [1,1,1,2,1,1,1,1,1] => 4
0101101100 => [1,1,1,2,1,2,2] => 7
0101110001 => [1,1,1,3,3,1] => 6
0101110010 => [1,1,1,3,2,1,1] => 6
0101110100 => [1,1,1,3,1,1,2] => 5
0101111000 => [1,1,1,4,3] => 5
0110010101 => [1,2,2,1,1,1,1,1] => 6
0110010110 => [1,2,2,1,1,2,1] => 8
0110011001 => [1,2,2,2,2,1] => 10
0110011010 => [1,2,2,2,1,1,1] => 8
0110011100 => [1,2,2,3,2] => 9
0110100101 => [1,2,1,1,2,1,1,1] => 6
0110100110 => [1,2,1,1,2,2,1] => 8
0110101001 => [1,2,1,1,1,1,2,1] => 6
0110101010 => [1,2,1,1,1,1,1,1,1] => 4
0110101100 => [1,2,1,1,1,2,2] => 7
0110110001 => [1,2,1,2,3,1] => 8
0110110010 => [1,2,1,2,2,1,1] => 8
0110110100 => [1,2,1,2,1,1,2] => 7
0110111000 => [1,2,1,3,3] => 7
0111000101 => [1,3,3,1,1,1] => 6
0111000110 => [1,3,3,2,1] => 8
0111001001 => [1,3,2,1,2,1] => 8
0111001010 => [1,3,2,1,1,1,1] => 6
0111001100 => [1,3,2,2,2] => 9
0111010010 => [1,3,1,1,2,1,1] => 6
0111011000 => [1,3,1,2,3] => 7
0111100010 => [1,4,3,1,1] => 6
0111100100 => [1,4,2,1,2] => 7
0111101000 => [1,4,1,1,3] => 5
0111110000 => [1,5,4] => 5
0100000100 => [1,1,5,1,2] => 5
0011100110 => [2,3,2,2,1] => 9
0011101010 => [2,3,1,1,1,1,1] => 5
0011101100 => [2,3,1,2,2] => 8
0001101110 => [3,2,1,3,1] => 7
0010110110 => [2,1,1,2,1,2,1] => 7
0011110010 => [2,4,2,1,1] => 7
0001110110 => [3,3,1,2,1] => 7
0100111010 => [1,1,2,3,1,1,1] => 6
0010111010 => [2,1,1,3,1,1,1] => 5
0011111000 => [2,5,3] => 6
0001111010 => [3,4,1,1,1] => 5
0100111100 => [1,1,2,4,2] => 7
0001111100 => [3,5,2] => 6
0000000101 => [7,1,1,1] => 3
0000001101 => [6,2,1,1] => 5
0000011101 => [5,3,1,1] => 5
0001111101 => [3,5,1,1] => 5
0011111101 => [2,6,1,1] => 5
0000001001 => [6,1,2,1] => 5
0000010101 => [5,1,1,1,1,1] => 3
0000101101 => [4,1,1,2,1,1] => 5
0010111101 => [2,1,1,4,1,1] => 5
0101111101 => [1,1,1,5,1,1] => 4
0111000011 => [1,3,4,2] => 7
0011110001 => [2,4,3,1] => 7
0011011001 => [2,2,1,2,2,1] => 9
0010110001 => [2,1,1,2,3,1] => 7
0001000001 => [3,1,5,1] => 5
0111010101 => [1,3,1,1,1,1,1,1] => 4
0111010011 => [1,3,1,1,2,2] => 7
0111001101 => [1,3,2,2,1,1] => 8
0111011001 => [1,3,1,2,2,1] => 8
0111000111 => [1,3,3,3] => 7
0011110101 => [2,4,1,1,1,1] => 5
0011110011 => [2,4,2,2] => 8
0111100101 => [1,4,2,1,1,1] => 6
0111100011 => [1,4,3,2] => 7
0011111001 => [2,5,2,1] => 7
0000111111 => [4,6] => 4
0001101100 => [3,2,1,2,2] => 8
0011000110 => [2,2,3,2,1] => 9
0010001110 => [2,1,3,3,1] => 7
0110111001 => [1,2,1,3,2,1] => 8
0001101001 => [3,2,1,1,2,1] => 7
0000110001 => [4,2,3,1] => 7
0000010001 => [5,1,3,1] => 5
0100011001 => [1,1,3,2,2,1] => 8
0100111001 => [1,1,2,3,2,1] => 8
0101111001 => [1,1,1,4,2,1] => 6
0110010001 => [1,2,2,1,3,1] => 8
0100010001 => [1,1,3,1,3,1] => 6
0100110001 => [1,1,2,2,3,1] => 8
0100100001 => [1,1,2,1,4,1] => 6
0101100001 => [1,1,1,2,4,1] => 6
0110011011 => [1,2,2,2,1,2] => 9
0110111011 => [1,2,1,3,1,2] => 7
0100111011 => [1,1,2,3,1,2] => 7
0101111011 => [1,1,1,4,1,2] => 5
0110010011 => [1,2,2,1,2,2] => 9
0100010011 => [1,1,3,1,2,2] => 7
0110110011 => [1,2,1,2,2,2] => 9
0101110011 => [1,1,1,3,2,2] => 7
0110100011 => [1,2,1,1,3,2] => 7
0100100011 => [1,1,2,1,3,2] => 7
0101100011 => [1,1,1,2,3,2] => 7
0101000011 => [1,1,1,1,4,2] => 5
0110010111 => [1,2,2,1,1,3] => 7
0110110111 => [1,2,1,2,1,3] => 7
0100110111 => [1,1,2,2,1,3] => 7
0101110111 => [1,1,1,3,1,3] => 5
0110100111 => [1,2,1,1,2,3] => 7
0101100111 => [1,1,1,2,2,3] => 7
0110101111 => [1,2,1,1,1,4] => 5
0101101111 => [1,1,1,2,1,4] => 5
0101001111 => [1,1,1,1,2,4] => 5
0000001100 => [6,2,2] => 6
0000011001 => [5,2,2,1] => 7
0000110011 => [4,2,2,2] => 8
0011001111 => [2,2,2,4] => 8
0110011111 => [1,2,2,5] => 7
0000110100 => [4,2,1,1,2] => 6
0000000011 => [8,2] => 4
0000011011 => [5,2,1,2] => 6
0001101111 => [3,2,1,4] => 6
0011011111 => [2,2,1,5] => 6
0000110101 => [4,2,1,1,1,1] => 5
0011010111 => [2,2,1,1,1,3] => 6
0111001011 => [1,3,2,1,1,2] => 7
0111110111 => [1,5,1,3] => 5
0110001011 => [1,2,3,1,1,2] => 7
0110000111 => [1,2,4,3] => 7
0011011010 => [2,2,1,2,1,1,1] => 7
0011010110 => [2,2,1,1,1,2,1] => 7
0100110110 => [1,1,2,2,1,2,1] => 8
0110001110 => [1,2,3,3,1] => 8
0101001110 => [1,1,1,1,2,3,1] => 6
0011001110 => [2,2,2,3,1] => 9
0100101110 => [1,1,2,1,1,3,1] => 6
0100011110 => [1,1,3,4,1] => 6
0010011110 => [2,1,2,4,1] => 7
0101000000 => [1,1,1,1,6] => 3
0001010000 => [3,1,1,1,4] => 4
0100010000 => [1,1,3,1,4] => 5
0001000100 => [3,1,3,1,2] => 6
0111011100 => [1,3,1,3,2] => 7
0101000101 => [1,1,1,1,3,1,1,1] => 4
0001010101 => [3,1,1,1,1,1,1,1] => 3
0100010101 => [1,1,3,1,1,1,1,1] => 4
0110110101 => [1,2,1,2,1,1,1,1] => 6
0101010001 => [1,1,1,1,1,1,3,1] => 4
0100101001 => [1,1,2,1,1,1,2,1] => 6
0110001001 => [1,2,3,1,2,1] => 8
0101011011 => [1,1,1,1,1,2,1,2] => 5
0001001011 => [3,1,2,1,1,2] => 6
0110101011 => [1,2,1,1,1,1,1,2] => 5
0001100011 => [3,2,3,2] => 8
0110000011 => [1,2,5,2] => 7
0001110111 => [3,3,1,3] => 6
0111101111 => [1,4,1,4] => 5
0000000111 => [7,3] => 4
0000001111 => [6,4] => 4
0001111111 => [3,7] => 4
0011111111 => [2,8] => 4
0000001011 => [6,1,1,2] => 4
0000010111 => [5,1,1,3] => 4
0001011111 => [3,1,1,5] => 4
0010111111 => [2,1,1,6] => 4
0011011110 => [2,2,1,4,1] => 7
0011101110 => [2,3,1,3,1] => 7
0011110110 => [2,4,1,2,1] => 7
0011111010 => [2,5,1,1,1] => 5
0011111100 => [2,6,2] => 6
0010010101 => [2,1,2,1,1,1,1,1] => 5
0101010111 => [1,1,1,1,1,1,1,3] => 3
0101110101 => [1,1,1,3,1,1,1,1] => 4
0110001111 => [1,2,3,4] => 7
0101101011 => [1,1,1,2,1,1,1,2] => 5
0101011101 => [1,1,1,1,1,3,1,1] => 4
0011000011 => [2,2,4,2] => 8
0011011011 => [2,2,1,2,1,2] => 8
0001111011 => [3,4,1,2] => 6
0011011101 => [2,2,1,3,1,1] => 7
0111011111 => [1,3,1,5] => 5
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Description
The number of corners of the ribbon associated with an integer composition.
We associate a ribbon shape to a composition $c=(c_1,\dots,c_n)$ with $c_i$ cells in the $i$-th row from bottom to top, such that the cells in two rows overlap in precisely one cell.
This statistic records the total number of corners of the ribbon shape.
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 $w$.