Identifier
Values
0 => [1] => 1
1 => [1] => 1
00 => [2] => 1
01 => [1,1] => 1
10 => [1,1] => 1
11 => [2] => 1
000 => [3] => 1
001 => [2,1] => 1
010 => [1,1,1] => 1
011 => [1,2] => 2
100 => [1,2] => 2
101 => [1,1,1] => 1
110 => [2,1] => 1
111 => [3] => 1
0000 => [4] => 1
0001 => [3,1] => 1
0010 => [2,1,1] => 1
0011 => [2,2] => 1
0100 => [1,1,2] => 2
0101 => [1,1,1,1] => 1
0110 => [1,2,1] => 2
0111 => [1,3] => 2
1000 => [1,3] => 2
1001 => [1,2,1] => 2
1010 => [1,1,1,1] => 1
1011 => [1,1,2] => 2
1100 => [2,2] => 1
1101 => [2,1,1] => 1
1110 => [3,1] => 1
1111 => [4] => 1
00000 => [5] => 1
00001 => [4,1] => 1
00010 => [3,1,1] => 1
00011 => [3,2] => 1
00100 => [2,1,2] => 1
00101 => [2,1,1,1] => 1
00110 => [2,2,1] => 1
00111 => [2,3] => 2
01000 => [1,1,3] => 2
01001 => [1,1,2,1] => 2
01010 => [1,1,1,1,1] => 1
01011 => [1,1,1,2] => 2
01100 => [1,2,2] => 2
01101 => [1,2,1,1] => 2
01110 => [1,3,1] => 2
01111 => [1,4] => 2
10000 => [1,4] => 2
10001 => [1,3,1] => 2
10010 => [1,2,1,1] => 2
10011 => [1,2,2] => 2
10100 => [1,1,1,2] => 2
10101 => [1,1,1,1,1] => 1
10110 => [1,1,2,1] => 2
10111 => [1,1,3] => 2
11000 => [2,3] => 2
11001 => [2,2,1] => 1
11010 => [2,1,1,1] => 1
11011 => [2,1,2] => 1
11100 => [3,2] => 1
11101 => [3,1,1] => 1
11110 => [4,1] => 1
11111 => [5] => 1
000000 => [6] => 1
000001 => [5,1] => 1
000010 => [4,1,1] => 1
000011 => [4,2] => 1
000100 => [3,1,2] => 1
000101 => [3,1,1,1] => 1
000110 => [3,2,1] => 1
000111 => [3,3] => 1
001000 => [2,1,3] => 2
001001 => [2,1,2,1] => 1
001010 => [2,1,1,1,1] => 1
001011 => [2,1,1,2] => 1
001100 => [2,2,2] => 1
001101 => [2,2,1,1] => 1
001110 => [2,3,1] => 2
001111 => [2,4] => 2
010000 => [1,1,4] => 2
010001 => [1,1,3,1] => 2
010010 => [1,1,2,1,1] => 2
010011 => [1,1,2,2] => 2
010100 => [1,1,1,1,2] => 2
010101 => [1,1,1,1,1,1] => 1
010110 => [1,1,1,2,1] => 2
010111 => [1,1,1,3] => 2
011000 => [1,2,3] => 3
011001 => [1,2,2,1] => 2
011010 => [1,2,1,1,1] => 2
011011 => [1,2,1,2] => 2
011100 => [1,3,2] => 2
011101 => [1,3,1,1] => 2
011110 => [1,4,1] => 2
011111 => [1,5] => 2
100000 => [1,5] => 2
100001 => [1,4,1] => 2
100010 => [1,3,1,1] => 2
100011 => [1,3,2] => 2
100100 => [1,2,1,2] => 2
100101 => [1,2,1,1,1] => 2
100110 => [1,2,2,1] => 2
>>> Load all 1345 entries. <<<
100111 => [1,2,3] => 3
101000 => [1,1,1,3] => 2
101001 => [1,1,1,2,1] => 2
101010 => [1,1,1,1,1,1] => 1
101011 => [1,1,1,1,2] => 2
101100 => [1,1,2,2] => 2
101101 => [1,1,2,1,1] => 2
101110 => [1,1,3,1] => 2
101111 => [1,1,4] => 2
110000 => [2,4] => 2
110001 => [2,3,1] => 2
110010 => [2,2,1,1] => 1
110011 => [2,2,2] => 1
110100 => [2,1,1,2] => 1
110101 => [2,1,1,1,1] => 1
110110 => [2,1,2,1] => 1
110111 => [2,1,3] => 2
111000 => [3,3] => 1
111001 => [3,2,1] => 1
111010 => [3,1,1,1] => 1
111011 => [3,1,2] => 1
111100 => [4,2] => 1
111101 => [4,1,1] => 1
111110 => [5,1] => 1
111111 => [6] => 1
0000000 => [7] => 1
0000001 => [6,1] => 1
0000010 => [5,1,1] => 1
0000011 => [5,2] => 1
0000100 => [4,1,2] => 1
0000101 => [4,1,1,1] => 1
0000110 => [4,2,1] => 1
0000111 => [4,3] => 1
0001000 => [3,1,3] => 1
0001001 => [3,1,2,1] => 1
0001010 => [3,1,1,1,1] => 1
0001011 => [3,1,1,2] => 1
0001100 => [3,2,2] => 1
0001101 => [3,2,1,1] => 1
0001110 => [3,3,1] => 1
0001111 => [3,4] => 2
0010000 => [2,1,4] => 2
0010001 => [2,1,3,1] => 2
0010010 => [2,1,2,1,1] => 1
0010011 => [2,1,2,2] => 1
0010100 => [2,1,1,1,2] => 1
0010101 => [2,1,1,1,1,1] => 1
0010110 => [2,1,1,2,1] => 1
0010111 => [2,1,1,3] => 2
0011000 => [2,2,3] => 2
0011001 => [2,2,2,1] => 1
0011010 => [2,2,1,1,1] => 1
0011011 => [2,2,1,2] => 1
0011100 => [2,3,2] => 2
0011101 => [2,3,1,1] => 2
0011110 => [2,4,1] => 2
0011111 => [2,5] => 2
0100000 => [1,1,5] => 2
0100001 => [1,1,4,1] => 2
0100010 => [1,1,3,1,1] => 2
0100011 => [1,1,3,2] => 2
0100100 => [1,1,2,1,2] => 2
0100101 => [1,1,2,1,1,1] => 2
0100110 => [1,1,2,2,1] => 2
0100111 => [1,1,2,3] => 3
0101000 => [1,1,1,1,3] => 2
0101001 => [1,1,1,1,2,1] => 2
0101010 => [1,1,1,1,1,1,1] => 1
0101011 => [1,1,1,1,1,2] => 2
0101100 => [1,1,1,2,2] => 2
0101101 => [1,1,1,2,1,1] => 2
0101110 => [1,1,1,3,1] => 2
0101111 => [1,1,1,4] => 2
0110000 => [1,2,4] => 3
0110001 => [1,2,3,1] => 3
0110010 => [1,2,2,1,1] => 2
0110011 => [1,2,2,2] => 2
0110100 => [1,2,1,1,2] => 2
0110101 => [1,2,1,1,1,1] => 2
0110110 => [1,2,1,2,1] => 2
0110111 => [1,2,1,3] => 3
0111000 => [1,3,3] => 2
0111001 => [1,3,2,1] => 2
0111010 => [1,3,1,1,1] => 2
0111011 => [1,3,1,2] => 2
0111100 => [1,4,2] => 2
0111101 => [1,4,1,1] => 2
0111110 => [1,5,1] => 2
0111111 => [1,6] => 2
1000000 => [1,6] => 2
1000001 => [1,5,1] => 2
1000010 => [1,4,1,1] => 2
1000011 => [1,4,2] => 2
1000100 => [1,3,1,2] => 2
1000101 => [1,3,1,1,1] => 2
1000110 => [1,3,2,1] => 2
1000111 => [1,3,3] => 2
1001000 => [1,2,1,3] => 3
1001001 => [1,2,1,2,1] => 2
1001010 => [1,2,1,1,1,1] => 2
1001011 => [1,2,1,1,2] => 2
1001100 => [1,2,2,2] => 2
1001101 => [1,2,2,1,1] => 2
1001110 => [1,2,3,1] => 3
1001111 => [1,2,4] => 3
1010000 => [1,1,1,4] => 2
1010001 => [1,1,1,3,1] => 2
1010010 => [1,1,1,2,1,1] => 2
1010011 => [1,1,1,2,2] => 2
1010100 => [1,1,1,1,1,2] => 2
1010101 => [1,1,1,1,1,1,1] => 1
1010110 => [1,1,1,1,2,1] => 2
1010111 => [1,1,1,1,3] => 2
1011000 => [1,1,2,3] => 3
1011001 => [1,1,2,2,1] => 2
1011010 => [1,1,2,1,1,1] => 2
1011011 => [1,1,2,1,2] => 2
1011100 => [1,1,3,2] => 2
1011101 => [1,1,3,1,1] => 2
1011110 => [1,1,4,1] => 2
1011111 => [1,1,5] => 2
1100000 => [2,5] => 2
1100001 => [2,4,1] => 2
1100010 => [2,3,1,1] => 2
1100011 => [2,3,2] => 2
1100100 => [2,2,1,2] => 1
1100101 => [2,2,1,1,1] => 1
1100110 => [2,2,2,1] => 1
1100111 => [2,2,3] => 2
1101000 => [2,1,1,3] => 2
1101001 => [2,1,1,2,1] => 1
1101010 => [2,1,1,1,1,1] => 1
1101011 => [2,1,1,1,2] => 1
1101100 => [2,1,2,2] => 1
1101101 => [2,1,2,1,1] => 1
1101110 => [2,1,3,1] => 2
1101111 => [2,1,4] => 2
1110000 => [3,4] => 2
1110001 => [3,3,1] => 1
1110010 => [3,2,1,1] => 1
1110011 => [3,2,2] => 1
1110100 => [3,1,1,2] => 1
1110101 => [3,1,1,1,1] => 1
1110110 => [3,1,2,1] => 1
1110111 => [3,1,3] => 1
1111000 => [4,3] => 1
1111001 => [4,2,1] => 1
1111010 => [4,1,1,1] => 1
1111011 => [4,1,2] => 1
1111100 => [5,2] => 1
1111101 => [5,1,1] => 1
1111110 => [6,1] => 1
1111111 => [7] => 1
00000000 => [8] => 1
00000001 => [7,1] => 1
00000010 => [6,1,1] => 1
00000011 => [6,2] => 1
00000100 => [5,1,2] => 1
00000101 => [5,1,1,1] => 1
00000110 => [5,2,1] => 1
00000111 => [5,3] => 1
00001000 => [4,1,3] => 1
00001001 => [4,1,2,1] => 1
00001010 => [4,1,1,1,1] => 1
00001011 => [4,1,1,2] => 1
00001100 => [4,2,2] => 1
00001101 => [4,2,1,1] => 1
00001110 => [4,3,1] => 1
00001111 => [4,4] => 1
00010000 => [3,1,4] => 2
00010001 => [3,1,3,1] => 1
00010010 => [3,1,2,1,1] => 1
00010011 => [3,1,2,2] => 1
00010100 => [3,1,1,1,2] => 1
00010101 => [3,1,1,1,1,1] => 1
00010110 => [3,1,1,2,1] => 1
00010111 => [3,1,1,3] => 1
00011000 => [3,2,3] => 1
00011001 => [3,2,2,1] => 1
00011010 => [3,2,1,1,1] => 1
00011011 => [3,2,1,2] => 1
00011100 => [3,3,2] => 1
00011101 => [3,3,1,1] => 1
00011110 => [3,4,1] => 2
00011111 => [3,5] => 2
00100000 => [2,1,5] => 2
00100001 => [2,1,4,1] => 2
00100010 => [2,1,3,1,1] => 2
00100011 => [2,1,3,2] => 2
00100100 => [2,1,2,1,2] => 1
00100101 => [2,1,2,1,1,1] => 1
00100110 => [2,1,2,2,1] => 1
00100111 => [2,1,2,3] => 2
00101000 => [2,1,1,1,3] => 2
00101001 => [2,1,1,1,2,1] => 1
00101010 => [2,1,1,1,1,1,1] => 1
00101011 => [2,1,1,1,1,2] => 1
00101100 => [2,1,1,2,2] => 1
00101101 => [2,1,1,2,1,1] => 1
00101110 => [2,1,1,3,1] => 2
00101111 => [2,1,1,4] => 2
00110000 => [2,2,4] => 2
00110001 => [2,2,3,1] => 2
00110010 => [2,2,2,1,1] => 1
00110011 => [2,2,2,2] => 1
00110100 => [2,2,1,1,2] => 1
00110101 => [2,2,1,1,1,1] => 1
00110110 => [2,2,1,2,1] => 1
00110111 => [2,2,1,3] => 2
00111000 => [2,3,3] => 2
00111001 => [2,3,2,1] => 2
00111010 => [2,3,1,1,1] => 2
00111011 => [2,3,1,2] => 2
00111100 => [2,4,2] => 2
00111101 => [2,4,1,1] => 2
00111110 => [2,5,1] => 2
00111111 => [2,6] => 2
01000000 => [1,1,6] => 2
01000001 => [1,1,5,1] => 2
01000010 => [1,1,4,1,1] => 2
01000011 => [1,1,4,2] => 2
01000100 => [1,1,3,1,2] => 2
01000101 => [1,1,3,1,1,1] => 2
01000110 => [1,1,3,2,1] => 2
01000111 => [1,1,3,3] => 2
01001000 => [1,1,2,1,3] => 3
01001001 => [1,1,2,1,2,1] => 2
01001010 => [1,1,2,1,1,1,1] => 2
01001011 => [1,1,2,1,1,2] => 2
01001100 => [1,1,2,2,2] => 2
01001101 => [1,1,2,2,1,1] => 2
01001110 => [1,1,2,3,1] => 3
01001111 => [1,1,2,4] => 3
01010000 => [1,1,1,1,4] => 2
01010001 => [1,1,1,1,3,1] => 2
01010010 => [1,1,1,1,2,1,1] => 2
01010011 => [1,1,1,1,2,2] => 2
01010100 => [1,1,1,1,1,1,2] => 2
01010101 => [1,1,1,1,1,1,1,1] => 1
01010110 => [1,1,1,1,1,2,1] => 2
01010111 => [1,1,1,1,1,3] => 2
01011000 => [1,1,1,2,3] => 3
01011001 => [1,1,1,2,2,1] => 2
01011010 => [1,1,1,2,1,1,1] => 2
01011011 => [1,1,1,2,1,2] => 2
01011100 => [1,1,1,3,2] => 2
01011101 => [1,1,1,3,1,1] => 2
01011110 => [1,1,1,4,1] => 2
01011111 => [1,1,1,5] => 2
01100000 => [1,2,5] => 3
01100001 => [1,2,4,1] => 3
01100010 => [1,2,3,1,1] => 3
01100011 => [1,2,3,2] => 3
01100100 => [1,2,2,1,2] => 2
01100101 => [1,2,2,1,1,1] => 2
01100110 => [1,2,2,2,1] => 2
01100111 => [1,2,2,3] => 3
01101000 => [1,2,1,1,3] => 3
01101001 => [1,2,1,1,2,1] => 2
01101010 => [1,2,1,1,1,1,1] => 2
01101011 => [1,2,1,1,1,2] => 2
01101100 => [1,2,1,2,2] => 2
01101101 => [1,2,1,2,1,1] => 2
01101110 => [1,2,1,3,1] => 3
01101111 => [1,2,1,4] => 3
01110000 => [1,3,4] => 3
01110001 => [1,3,3,1] => 2
01110010 => [1,3,2,1,1] => 2
01110011 => [1,3,2,2] => 2
01110100 => [1,3,1,1,2] => 2
01110101 => [1,3,1,1,1,1] => 2
01110110 => [1,3,1,2,1] => 2
01110111 => [1,3,1,3] => 2
01111000 => [1,4,3] => 2
01111001 => [1,4,2,1] => 2
01111010 => [1,4,1,1,1] => 2
01111011 => [1,4,1,2] => 2
01111100 => [1,5,2] => 2
01111101 => [1,5,1,1] => 2
01111110 => [1,6,1] => 2
01111111 => [1,7] => 2
10000000 => [1,7] => 2
10000001 => [1,6,1] => 2
10000010 => [1,5,1,1] => 2
10000011 => [1,5,2] => 2
10000100 => [1,4,1,2] => 2
10000101 => [1,4,1,1,1] => 2
10000110 => [1,4,2,1] => 2
10000111 => [1,4,3] => 2
10001000 => [1,3,1,3] => 2
10001001 => [1,3,1,2,1] => 2
10001010 => [1,3,1,1,1,1] => 2
10001011 => [1,3,1,1,2] => 2
10001100 => [1,3,2,2] => 2
10001101 => [1,3,2,1,1] => 2
10001110 => [1,3,3,1] => 2
10001111 => [1,3,4] => 3
10010000 => [1,2,1,4] => 3
10010001 => [1,2,1,3,1] => 3
10010010 => [1,2,1,2,1,1] => 2
10010011 => [1,2,1,2,2] => 2
10010100 => [1,2,1,1,1,2] => 2
10010101 => [1,2,1,1,1,1,1] => 2
10010110 => [1,2,1,1,2,1] => 2
10010111 => [1,2,1,1,3] => 3
10011000 => [1,2,2,3] => 3
10011001 => [1,2,2,2,1] => 2
10011010 => [1,2,2,1,1,1] => 2
10011011 => [1,2,2,1,2] => 2
10011100 => [1,2,3,2] => 3
10011101 => [1,2,3,1,1] => 3
10011110 => [1,2,4,1] => 3
10011111 => [1,2,5] => 3
10100000 => [1,1,1,5] => 2
10100001 => [1,1,1,4,1] => 2
10100010 => [1,1,1,3,1,1] => 2
10100011 => [1,1,1,3,2] => 2
10100100 => [1,1,1,2,1,2] => 2
10100101 => [1,1,1,2,1,1,1] => 2
10100110 => [1,1,1,2,2,1] => 2
10100111 => [1,1,1,2,3] => 3
10101000 => [1,1,1,1,1,3] => 2
10101001 => [1,1,1,1,1,2,1] => 2
10101010 => [1,1,1,1,1,1,1,1] => 1
10101011 => [1,1,1,1,1,1,2] => 2
10101100 => [1,1,1,1,2,2] => 2
10101101 => [1,1,1,1,2,1,1] => 2
10101110 => [1,1,1,1,3,1] => 2
10101111 => [1,1,1,1,4] => 2
10110000 => [1,1,2,4] => 3
10110001 => [1,1,2,3,1] => 3
10110010 => [1,1,2,2,1,1] => 2
10110011 => [1,1,2,2,2] => 2
10110100 => [1,1,2,1,1,2] => 2
10110101 => [1,1,2,1,1,1,1] => 2
10110110 => [1,1,2,1,2,1] => 2
10110111 => [1,1,2,1,3] => 3
10111000 => [1,1,3,3] => 2
10111001 => [1,1,3,2,1] => 2
10111010 => [1,1,3,1,1,1] => 2
10111011 => [1,1,3,1,2] => 2
10111100 => [1,1,4,2] => 2
10111101 => [1,1,4,1,1] => 2
10111110 => [1,1,5,1] => 2
10111111 => [1,1,6] => 2
11000000 => [2,6] => 2
11000001 => [2,5,1] => 2
11000010 => [2,4,1,1] => 2
11000011 => [2,4,2] => 2
11000100 => [2,3,1,2] => 2
11000101 => [2,3,1,1,1] => 2
11000110 => [2,3,2,1] => 2
11000111 => [2,3,3] => 2
11001000 => [2,2,1,3] => 2
11001001 => [2,2,1,2,1] => 1
11001010 => [2,2,1,1,1,1] => 1
11001011 => [2,2,1,1,2] => 1
11001100 => [2,2,2,2] => 1
11001101 => [2,2,2,1,1] => 1
11001110 => [2,2,3,1] => 2
11001111 => [2,2,4] => 2
11010000 => [2,1,1,4] => 2
11010001 => [2,1,1,3,1] => 2
11010010 => [2,1,1,2,1,1] => 1
11010011 => [2,1,1,2,2] => 1
11010100 => [2,1,1,1,1,2] => 1
11010101 => [2,1,1,1,1,1,1] => 1
11010110 => [2,1,1,1,2,1] => 1
11010111 => [2,1,1,1,3] => 2
11011000 => [2,1,2,3] => 2
11011001 => [2,1,2,2,1] => 1
11011010 => [2,1,2,1,1,1] => 1
11011011 => [2,1,2,1,2] => 1
11011100 => [2,1,3,2] => 2
11011101 => [2,1,3,1,1] => 2
11011110 => [2,1,4,1] => 2
11011111 => [2,1,5] => 2
11100000 => [3,5] => 2
11100001 => [3,4,1] => 2
11100010 => [3,3,1,1] => 1
11100011 => [3,3,2] => 1
11100100 => [3,2,1,2] => 1
11100101 => [3,2,1,1,1] => 1
11100110 => [3,2,2,1] => 1
11100111 => [3,2,3] => 1
11101000 => [3,1,1,3] => 1
11101001 => [3,1,1,2,1] => 1
11101010 => [3,1,1,1,1,1] => 1
11101011 => [3,1,1,1,2] => 1
11101100 => [3,1,2,2] => 1
11101101 => [3,1,2,1,1] => 1
11101110 => [3,1,3,1] => 1
11101111 => [3,1,4] => 2
11110000 => [4,4] => 1
11110001 => [4,3,1] => 1
11110010 => [4,2,1,1] => 1
11110011 => [4,2,2] => 1
11110100 => [4,1,1,2] => 1
11110101 => [4,1,1,1,1] => 1
11110110 => [4,1,2,1] => 1
11110111 => [4,1,3] => 1
11111000 => [5,3] => 1
11111001 => [5,2,1] => 1
11111010 => [5,1,1,1] => 1
11111011 => [5,1,2] => 1
11111100 => [6,2] => 1
11111101 => [6,1,1] => 1
11111110 => [7,1] => 1
11111111 => [8] => 1
000000000 => [9] => 1
000000001 => [8,1] => 1
000000010 => [7,1,1] => 1
000000011 => [7,2] => 1
000000100 => [6,1,2] => 1
000000101 => [6,1,1,1] => 1
000000110 => [6,2,1] => 1
000000111 => [6,3] => 1
000001000 => [5,1,3] => 1
000001001 => [5,1,2,1] => 1
000001010 => [5,1,1,1,1] => 1
000001011 => [5,1,1,2] => 1
000001100 => [5,2,2] => 1
000001101 => [5,2,1,1] => 1
000001110 => [5,3,1] => 1
000001111 => [5,4] => 1
000010000 => [4,1,4] => 1
000010001 => [4,1,3,1] => 1
000010010 => [4,1,2,1,1] => 1
000010011 => [4,1,2,2] => 1
000010100 => [4,1,1,1,2] => 1
000010101 => [4,1,1,1,1,1] => 1
000010110 => [4,1,1,2,1] => 1
000010111 => [4,1,1,3] => 1
000011000 => [4,2,3] => 1
000011001 => [4,2,2,1] => 1
000011010 => [4,2,1,1,1] => 1
000011011 => [4,2,1,2] => 1
000011100 => [4,3,2] => 1
000011101 => [4,3,1,1] => 1
000011110 => [4,4,1] => 1
000011111 => [4,5] => 2
000100000 => [3,1,5] => 2
000100001 => [3,1,4,1] => 2
000100010 => [3,1,3,1,1] => 1
000100011 => [3,1,3,2] => 1
000100100 => [3,1,2,1,2] => 1
000100101 => [3,1,2,1,1,1] => 1
000100110 => [3,1,2,2,1] => 1
000100111 => [3,1,2,3] => 1
000101000 => [3,1,1,1,3] => 1
000101001 => [3,1,1,1,2,1] => 1
000101010 => [3,1,1,1,1,1,1] => 1
000101011 => [3,1,1,1,1,2] => 1
000101100 => [3,1,1,2,2] => 1
000101101 => [3,1,1,2,1,1] => 1
000101110 => [3,1,1,3,1] => 1
000101111 => [3,1,1,4] => 2
000110000 => [3,2,4] => 2
000110001 => [3,2,3,1] => 1
000110010 => [3,2,2,1,1] => 1
000110011 => [3,2,2,2] => 1
000110100 => [3,2,1,1,2] => 1
000110101 => [3,2,1,1,1,1] => 1
000110110 => [3,2,1,2,1] => 1
000110111 => [3,2,1,3] => 1
000111000 => [3,3,3] => 1
000111001 => [3,3,2,1] => 1
000111010 => [3,3,1,1,1] => 1
000111011 => [3,3,1,2] => 1
000111100 => [3,4,2] => 2
000111101 => [3,4,1,1] => 2
000111110 => [3,5,1] => 2
000111111 => [3,6] => 2
001000000 => [2,1,6] => 2
001000001 => [2,1,5,1] => 2
001000010 => [2,1,4,1,1] => 2
001000011 => [2,1,4,2] => 2
001000100 => [2,1,3,1,2] => 2
001000101 => [2,1,3,1,1,1] => 2
001000110 => [2,1,3,2,1] => 2
001000111 => [2,1,3,3] => 2
001001000 => [2,1,2,1,3] => 2
001001001 => [2,1,2,1,2,1] => 1
001001010 => [2,1,2,1,1,1,1] => 1
001001011 => [2,1,2,1,1,2] => 1
001001100 => [2,1,2,2,2] => 1
001001101 => [2,1,2,2,1,1] => 1
001001110 => [2,1,2,3,1] => 2
001001111 => [2,1,2,4] => 2
001010000 => [2,1,1,1,4] => 2
001010001 => [2,1,1,1,3,1] => 2
001010010 => [2,1,1,1,2,1,1] => 1
001010011 => [2,1,1,1,2,2] => 1
001010100 => [2,1,1,1,1,1,2] => 1
001010101 => [2,1,1,1,1,1,1,1] => 1
001010110 => [2,1,1,1,1,2,1] => 1
001010111 => [2,1,1,1,1,3] => 2
001011000 => [2,1,1,2,3] => 2
001011001 => [2,1,1,2,2,1] => 1
001011010 => [2,1,1,2,1,1,1] => 1
001011011 => [2,1,1,2,1,2] => 1
001011100 => [2,1,1,3,2] => 2
001011101 => [2,1,1,3,1,1] => 2
001011110 => [2,1,1,4,1] => 2
001011111 => [2,1,1,5] => 2
001100000 => [2,2,5] => 2
001100001 => [2,2,4,1] => 2
001100010 => [2,2,3,1,1] => 2
001100011 => [2,2,3,2] => 2
001100100 => [2,2,2,1,2] => 1
001100101 => [2,2,2,1,1,1] => 1
001100110 => [2,2,2,2,1] => 1
001100111 => [2,2,2,3] => 2
001101000 => [2,2,1,1,3] => 2
001101001 => [2,2,1,1,2,1] => 1
001101010 => [2,2,1,1,1,1,1] => 1
001101011 => [2,2,1,1,1,2] => 1
001101100 => [2,2,1,2,2] => 1
001101101 => [2,2,1,2,1,1] => 1
001101110 => [2,2,1,3,1] => 2
001101111 => [2,2,1,4] => 2
001110000 => [2,3,4] => 3
001110001 => [2,3,3,1] => 2
001110010 => [2,3,2,1,1] => 2
001110011 => [2,3,2,2] => 2
001110100 => [2,3,1,1,2] => 2
001110101 => [2,3,1,1,1,1] => 2
001110110 => [2,3,1,2,1] => 2
001110111 => [2,3,1,3] => 2
001111000 => [2,4,3] => 2
001111001 => [2,4,2,1] => 2
001111010 => [2,4,1,1,1] => 2
001111011 => [2,4,1,2] => 2
001111100 => [2,5,2] => 2
001111101 => [2,5,1,1] => 2
001111110 => [2,6,1] => 2
001111111 => [2,7] => 2
010000000 => [1,1,7] => 2
010000001 => [1,1,6,1] => 2
010000010 => [1,1,5,1,1] => 2
010000011 => [1,1,5,2] => 2
010000100 => [1,1,4,1,2] => 2
010000101 => [1,1,4,1,1,1] => 2
010000110 => [1,1,4,2,1] => 2
010000111 => [1,1,4,3] => 2
010001000 => [1,1,3,1,3] => 2
010001001 => [1,1,3,1,2,1] => 2
010001010 => [1,1,3,1,1,1,1] => 2
010001011 => [1,1,3,1,1,2] => 2
010001100 => [1,1,3,2,2] => 2
010001101 => [1,1,3,2,1,1] => 2
010001110 => [1,1,3,3,1] => 2
010001111 => [1,1,3,4] => 3
010010000 => [1,1,2,1,4] => 3
010010001 => [1,1,2,1,3,1] => 3
010010010 => [1,1,2,1,2,1,1] => 2
010010011 => [1,1,2,1,2,2] => 2
010010100 => [1,1,2,1,1,1,2] => 2
010010101 => [1,1,2,1,1,1,1,1] => 2
010010110 => [1,1,2,1,1,2,1] => 2
010010111 => [1,1,2,1,1,3] => 3
010011000 => [1,1,2,2,3] => 3
010011001 => [1,1,2,2,2,1] => 2
010011010 => [1,1,2,2,1,1,1] => 2
010011011 => [1,1,2,2,1,2] => 2
010011100 => [1,1,2,3,2] => 3
010011101 => [1,1,2,3,1,1] => 3
010011110 => [1,1,2,4,1] => 3
010011111 => [1,1,2,5] => 3
010100000 => [1,1,1,1,5] => 2
010100001 => [1,1,1,1,4,1] => 2
010100010 => [1,1,1,1,3,1,1] => 2
010100011 => [1,1,1,1,3,2] => 2
010100100 => [1,1,1,1,2,1,2] => 2
010100101 => [1,1,1,1,2,1,1,1] => 2
010100110 => [1,1,1,1,2,2,1] => 2
010100111 => [1,1,1,1,2,3] => 3
010101000 => [1,1,1,1,1,1,3] => 2
010101001 => [1,1,1,1,1,1,2,1] => 2
010101010 => [1,1,1,1,1,1,1,1,1] => 1
010101011 => [1,1,1,1,1,1,1,2] => 2
010101100 => [1,1,1,1,1,2,2] => 2
010101101 => [1,1,1,1,1,2,1,1] => 2
010101110 => [1,1,1,1,1,3,1] => 2
010101111 => [1,1,1,1,1,4] => 2
010110000 => [1,1,1,2,4] => 3
010110001 => [1,1,1,2,3,1] => 3
010110010 => [1,1,1,2,2,1,1] => 2
010110011 => [1,1,1,2,2,2] => 2
010110100 => [1,1,1,2,1,1,2] => 2
010110101 => [1,1,1,2,1,1,1,1] => 2
010110110 => [1,1,1,2,1,2,1] => 2
010110111 => [1,1,1,2,1,3] => 3
010111000 => [1,1,1,3,3] => 2
010111001 => [1,1,1,3,2,1] => 2
010111010 => [1,1,1,3,1,1,1] => 2
010111011 => [1,1,1,3,1,2] => 2
010111100 => [1,1,1,4,2] => 2
010111101 => [1,1,1,4,1,1] => 2
010111110 => [1,1,1,5,1] => 2
010111111 => [1,1,1,6] => 2
011000000 => [1,2,6] => 3
011000001 => [1,2,5,1] => 3
011000010 => [1,2,4,1,1] => 3
011000011 => [1,2,4,2] => 3
011000100 => [1,2,3,1,2] => 3
011000101 => [1,2,3,1,1,1] => 3
011000110 => [1,2,3,2,1] => 3
011000111 => [1,2,3,3] => 3
011001000 => [1,2,2,1,3] => 3
011001001 => [1,2,2,1,2,1] => 2
011001010 => [1,2,2,1,1,1,1] => 2
011001011 => [1,2,2,1,1,2] => 2
011001100 => [1,2,2,2,2] => 2
011001101 => [1,2,2,2,1,1] => 2
011001110 => [1,2,2,3,1] => 3
011001111 => [1,2,2,4] => 3
011010000 => [1,2,1,1,4] => 3
011010001 => [1,2,1,1,3,1] => 3
011010010 => [1,2,1,1,2,1,1] => 2
011010011 => [1,2,1,1,2,2] => 2
011010100 => [1,2,1,1,1,1,2] => 2
011010101 => [1,2,1,1,1,1,1,1] => 2
011010110 => [1,2,1,1,1,2,1] => 2
011010111 => [1,2,1,1,1,3] => 3
011011000 => [1,2,1,2,3] => 3
011011001 => [1,2,1,2,2,1] => 2
011011010 => [1,2,1,2,1,1,1] => 2
011011011 => [1,2,1,2,1,2] => 2
011011100 => [1,2,1,3,2] => 3
011011101 => [1,2,1,3,1,1] => 3
011011110 => [1,2,1,4,1] => 3
011011111 => [1,2,1,5] => 3
011100000 => [1,3,5] => 3
011100001 => [1,3,4,1] => 3
011100010 => [1,3,3,1,1] => 2
011100011 => [1,3,3,2] => 2
011100100 => [1,3,2,1,2] => 2
011100101 => [1,3,2,1,1,1] => 2
011100110 => [1,3,2,2,1] => 2
011100111 => [1,3,2,3] => 2
011101000 => [1,3,1,1,3] => 2
011101001 => [1,3,1,1,2,1] => 2
011101010 => [1,3,1,1,1,1,1] => 2
011101011 => [1,3,1,1,1,2] => 2
011101100 => [1,3,1,2,2] => 2
011101101 => [1,3,1,2,1,1] => 2
011101110 => [1,3,1,3,1] => 2
011101111 => [1,3,1,4] => 3
011110000 => [1,4,4] => 2
011110001 => [1,4,3,1] => 2
011110010 => [1,4,2,1,1] => 2
011110011 => [1,4,2,2] => 2
011110100 => [1,4,1,1,2] => 2
011110101 => [1,4,1,1,1,1] => 2
011110110 => [1,4,1,2,1] => 2
011110111 => [1,4,1,3] => 2
011111000 => [1,5,3] => 2
011111001 => [1,5,2,1] => 2
011111010 => [1,5,1,1,1] => 2
011111011 => [1,5,1,2] => 2
011111100 => [1,6,2] => 2
011111101 => [1,6,1,1] => 2
011111110 => [1,7,1] => 2
011111111 => [1,8] => 2
100000000 => [1,8] => 2
100000001 => [1,7,1] => 2
100000010 => [1,6,1,1] => 2
100000011 => [1,6,2] => 2
100000100 => [1,5,1,2] => 2
100000101 => [1,5,1,1,1] => 2
100000110 => [1,5,2,1] => 2
100000111 => [1,5,3] => 2
100001000 => [1,4,1,3] => 2
100001001 => [1,4,1,2,1] => 2
100001010 => [1,4,1,1,1,1] => 2
100001011 => [1,4,1,1,2] => 2
100001100 => [1,4,2,2] => 2
100001101 => [1,4,2,1,1] => 2
100001110 => [1,4,3,1] => 2
100001111 => [1,4,4] => 2
100010000 => [1,3,1,4] => 3
100010001 => [1,3,1,3,1] => 2
100010010 => [1,3,1,2,1,1] => 2
100010011 => [1,3,1,2,2] => 2
100010100 => [1,3,1,1,1,2] => 2
100010101 => [1,3,1,1,1,1,1] => 2
100010110 => [1,3,1,1,2,1] => 2
100010111 => [1,3,1,1,3] => 2
100011000 => [1,3,2,3] => 2
100011001 => [1,3,2,2,1] => 2
100011010 => [1,3,2,1,1,1] => 2
100011011 => [1,3,2,1,2] => 2
100011100 => [1,3,3,2] => 2
100011101 => [1,3,3,1,1] => 2
100011110 => [1,3,4,1] => 3
100011111 => [1,3,5] => 3
100100000 => [1,2,1,5] => 3
100100001 => [1,2,1,4,1] => 3
100100010 => [1,2,1,3,1,1] => 3
100100011 => [1,2,1,3,2] => 3
100100100 => [1,2,1,2,1,2] => 2
100100101 => [1,2,1,2,1,1,1] => 2
100100110 => [1,2,1,2,2,1] => 2
100100111 => [1,2,1,2,3] => 3
100101000 => [1,2,1,1,1,3] => 3
100101001 => [1,2,1,1,1,2,1] => 2
100101010 => [1,2,1,1,1,1,1,1] => 2
100101011 => [1,2,1,1,1,1,2] => 2
100101100 => [1,2,1,1,2,2] => 2
100101101 => [1,2,1,1,2,1,1] => 2
100101110 => [1,2,1,1,3,1] => 3
100101111 => [1,2,1,1,4] => 3
100110000 => [1,2,2,4] => 3
100110001 => [1,2,2,3,1] => 3
100110010 => [1,2,2,2,1,1] => 2
100110011 => [1,2,2,2,2] => 2
100110100 => [1,2,2,1,1,2] => 2
100110101 => [1,2,2,1,1,1,1] => 2
100110110 => [1,2,2,1,2,1] => 2
100110111 => [1,2,2,1,3] => 3
100111000 => [1,2,3,3] => 3
100111001 => [1,2,3,2,1] => 3
100111010 => [1,2,3,1,1,1] => 3
100111011 => [1,2,3,1,2] => 3
100111100 => [1,2,4,2] => 3
100111101 => [1,2,4,1,1] => 3
100111110 => [1,2,5,1] => 3
100111111 => [1,2,6] => 3
101000000 => [1,1,1,6] => 2
101000001 => [1,1,1,5,1] => 2
101000010 => [1,1,1,4,1,1] => 2
101000011 => [1,1,1,4,2] => 2
101000100 => [1,1,1,3,1,2] => 2
101000101 => [1,1,1,3,1,1,1] => 2
101000110 => [1,1,1,3,2,1] => 2
101000111 => [1,1,1,3,3] => 2
101001000 => [1,1,1,2,1,3] => 3
101001001 => [1,1,1,2,1,2,1] => 2
101001010 => [1,1,1,2,1,1,1,1] => 2
101001011 => [1,1,1,2,1,1,2] => 2
101001100 => [1,1,1,2,2,2] => 2
101001101 => [1,1,1,2,2,1,1] => 2
101001110 => [1,1,1,2,3,1] => 3
101001111 => [1,1,1,2,4] => 3
101010000 => [1,1,1,1,1,4] => 2
101010001 => [1,1,1,1,1,3,1] => 2
101010010 => [1,1,1,1,1,2,1,1] => 2
101010011 => [1,1,1,1,1,2,2] => 2
101010100 => [1,1,1,1,1,1,1,2] => 2
101010101 => [1,1,1,1,1,1,1,1,1] => 1
101010110 => [1,1,1,1,1,1,2,1] => 2
101010111 => [1,1,1,1,1,1,3] => 2
101011000 => [1,1,1,1,2,3] => 3
101011001 => [1,1,1,1,2,2,1] => 2
101011010 => [1,1,1,1,2,1,1,1] => 2
101011011 => [1,1,1,1,2,1,2] => 2
101011100 => [1,1,1,1,3,2] => 2
101011101 => [1,1,1,1,3,1,1] => 2
101011110 => [1,1,1,1,4,1] => 2
101011111 => [1,1,1,1,5] => 2
101100000 => [1,1,2,5] => 3
101100001 => [1,1,2,4,1] => 3
101100010 => [1,1,2,3,1,1] => 3
101100011 => [1,1,2,3,2] => 3
101100100 => [1,1,2,2,1,2] => 2
101100101 => [1,1,2,2,1,1,1] => 2
101100110 => [1,1,2,2,2,1] => 2
101100111 => [1,1,2,2,3] => 3
101101000 => [1,1,2,1,1,3] => 3
101101001 => [1,1,2,1,1,2,1] => 2
101101010 => [1,1,2,1,1,1,1,1] => 2
101101011 => [1,1,2,1,1,1,2] => 2
101101100 => [1,1,2,1,2,2] => 2
101101101 => [1,1,2,1,2,1,1] => 2
101101110 => [1,1,2,1,3,1] => 3
101101111 => [1,1,2,1,4] => 3
101110000 => [1,1,3,4] => 3
101110001 => [1,1,3,3,1] => 2
101110010 => [1,1,3,2,1,1] => 2
101110011 => [1,1,3,2,2] => 2
101110100 => [1,1,3,1,1,2] => 2
101110101 => [1,1,3,1,1,1,1] => 2
101110110 => [1,1,3,1,2,1] => 2
101110111 => [1,1,3,1,3] => 2
101111000 => [1,1,4,3] => 2
101111001 => [1,1,4,2,1] => 2
101111010 => [1,1,4,1,1,1] => 2
101111011 => [1,1,4,1,2] => 2
101111100 => [1,1,5,2] => 2
101111101 => [1,1,5,1,1] => 2
101111110 => [1,1,6,1] => 2
101111111 => [1,1,7] => 2
110000000 => [2,7] => 2
110000001 => [2,6,1] => 2
110000010 => [2,5,1,1] => 2
110000011 => [2,5,2] => 2
110000100 => [2,4,1,2] => 2
110000101 => [2,4,1,1,1] => 2
110000110 => [2,4,2,1] => 2
110000111 => [2,4,3] => 2
110001000 => [2,3,1,3] => 2
110001001 => [2,3,1,2,1] => 2
110001010 => [2,3,1,1,1,1] => 2
110001011 => [2,3,1,1,2] => 2
110001100 => [2,3,2,2] => 2
110001101 => [2,3,2,1,1] => 2
110001110 => [2,3,3,1] => 2
110001111 => [2,3,4] => 3
110010000 => [2,2,1,4] => 2
110010001 => [2,2,1,3,1] => 2
110010010 => [2,2,1,2,1,1] => 1
110010011 => [2,2,1,2,2] => 1
110010100 => [2,2,1,1,1,2] => 1
110010101 => [2,2,1,1,1,1,1] => 1
110010110 => [2,2,1,1,2,1] => 1
110010111 => [2,2,1,1,3] => 2
110011000 => [2,2,2,3] => 2
110011001 => [2,2,2,2,1] => 1
110011010 => [2,2,2,1,1,1] => 1
110011011 => [2,2,2,1,2] => 1
110011100 => [2,2,3,2] => 2
110011101 => [2,2,3,1,1] => 2
110011110 => [2,2,4,1] => 2
110011111 => [2,2,5] => 2
110100000 => [2,1,1,5] => 2
110100001 => [2,1,1,4,1] => 2
110100010 => [2,1,1,3,1,1] => 2
110100011 => [2,1,1,3,2] => 2
110100100 => [2,1,1,2,1,2] => 1
110100101 => [2,1,1,2,1,1,1] => 1
110100110 => [2,1,1,2,2,1] => 1
110100111 => [2,1,1,2,3] => 2
110101000 => [2,1,1,1,1,3] => 2
110101001 => [2,1,1,1,1,2,1] => 1
110101010 => [2,1,1,1,1,1,1,1] => 1
110101011 => [2,1,1,1,1,1,2] => 1
110101100 => [2,1,1,1,2,2] => 1
110101101 => [2,1,1,1,2,1,1] => 1
110101110 => [2,1,1,1,3,1] => 2
110101111 => [2,1,1,1,4] => 2
110110000 => [2,1,2,4] => 2
110110001 => [2,1,2,3,1] => 2
110110010 => [2,1,2,2,1,1] => 1
110110011 => [2,1,2,2,2] => 1
110110100 => [2,1,2,1,1,2] => 1
110110101 => [2,1,2,1,1,1,1] => 1
110110110 => [2,1,2,1,2,1] => 1
110110111 => [2,1,2,1,3] => 2
110111000 => [2,1,3,3] => 2
110111001 => [2,1,3,2,1] => 2
110111010 => [2,1,3,1,1,1] => 2
110111011 => [2,1,3,1,2] => 2
110111100 => [2,1,4,2] => 2
110111101 => [2,1,4,1,1] => 2
110111110 => [2,1,5,1] => 2
110111111 => [2,1,6] => 2
111000000 => [3,6] => 2
111000001 => [3,5,1] => 2
111000010 => [3,4,1,1] => 2
111000011 => [3,4,2] => 2
111000100 => [3,3,1,2] => 1
111000101 => [3,3,1,1,1] => 1
111000110 => [3,3,2,1] => 1
111000111 => [3,3,3] => 1
111001000 => [3,2,1,3] => 1
111001001 => [3,2,1,2,1] => 1
111001010 => [3,2,1,1,1,1] => 1
111001011 => [3,2,1,1,2] => 1
111001100 => [3,2,2,2] => 1
111001101 => [3,2,2,1,1] => 1
111001110 => [3,2,3,1] => 1
111001111 => [3,2,4] => 2
111010000 => [3,1,1,4] => 2
111010001 => [3,1,1,3,1] => 1
111010010 => [3,1,1,2,1,1] => 1
111010011 => [3,1,1,2,2] => 1
111010100 => [3,1,1,1,1,2] => 1
111010101 => [3,1,1,1,1,1,1] => 1
111010110 => [3,1,1,1,2,1] => 1
111010111 => [3,1,1,1,3] => 1
111011000 => [3,1,2,3] => 1
111011001 => [3,1,2,2,1] => 1
111011010 => [3,1,2,1,1,1] => 1
111011011 => [3,1,2,1,2] => 1
111011100 => [3,1,3,2] => 1
111011101 => [3,1,3,1,1] => 1
111011110 => [3,1,4,1] => 2
111011111 => [3,1,5] => 2
111100000 => [4,5] => 2
111100001 => [4,4,1] => 1
111100010 => [4,3,1,1] => 1
111100011 => [4,3,2] => 1
111100100 => [4,2,1,2] => 1
111100101 => [4,2,1,1,1] => 1
111100110 => [4,2,2,1] => 1
111100111 => [4,2,3] => 1
111101000 => [4,1,1,3] => 1
111101001 => [4,1,1,2,1] => 1
111101010 => [4,1,1,1,1,1] => 1
111101011 => [4,1,1,1,2] => 1
111101100 => [4,1,2,2] => 1
111101101 => [4,1,2,1,1] => 1
111101110 => [4,1,3,1] => 1
111101111 => [4,1,4] => 1
111110000 => [5,4] => 1
111110001 => [5,3,1] => 1
111110010 => [5,2,1,1] => 1
111110011 => [5,2,2] => 1
111110100 => [5,1,1,2] => 1
111110101 => [5,1,1,1,1] => 1
111110110 => [5,1,2,1] => 1
111110111 => [5,1,3] => 1
111111000 => [6,3] => 1
111111001 => [6,2,1] => 1
111111010 => [6,1,1,1] => 1
111111011 => [6,1,2] => 1
111111100 => [7,2] => 1
111111101 => [7,1,1] => 1
111111110 => [8,1] => 1
111111111 => [9] => 1
1010101010 => [1,1,1,1,1,1,1,1,1,1] => 1
1010101100 => [1,1,1,1,1,1,2,2] => 2
1010110010 => [1,1,1,1,2,2,1,1] => 2
1010110100 => [1,1,1,1,2,1,1,2] => 2
1010111000 => [1,1,1,1,3,3] => 2
1011001010 => [1,1,2,2,1,1,1,1] => 2
1011001100 => [1,1,2,2,2,2] => 2
1011010010 => [1,1,2,1,1,2,1,1] => 2
1011010100 => [1,1,2,1,1,1,1,2] => 2
1011011000 => [1,1,2,1,2,3] => 3
1011100010 => [1,1,3,3,1,1] => 2
1011100100 => [1,1,3,2,1,2] => 2
1011101000 => [1,1,3,1,1,3] => 2
1011110000 => [1,1,4,4] => 2
1100101010 => [2,2,1,1,1,1,1,1] => 1
1100101100 => [2,2,1,1,2,2] => 1
1100110010 => [2,2,2,2,1,1] => 1
1100110100 => [2,2,2,1,1,2] => 1
1100111000 => [2,2,3,3] => 2
1101001010 => [2,1,1,2,1,1,1,1] => 1
1101001100 => [2,1,1,2,2,2] => 1
1101010010 => [2,1,1,1,1,2,1,1] => 1
1101010100 => [2,1,1,1,1,1,1,2] => 1
1101011000 => [2,1,1,1,2,3] => 2
1101100010 => [2,1,2,3,1,1] => 2
1101100100 => [2,1,2,2,1,2] => 1
1101101000 => [2,1,2,1,1,3] => 2
1101110000 => [2,1,3,4] => 3
1110001010 => [3,3,1,1,1,1] => 1
1110001100 => [3,3,2,2] => 1
1110010010 => [3,2,1,2,1,1] => 1
1110010100 => [3,2,1,1,1,2] => 1
1110011000 => [3,2,2,3] => 1
1110100010 => [3,1,1,3,1,1] => 1
1110100100 => [3,1,1,2,1,2] => 1
1110101000 => [3,1,1,1,1,3] => 1
1110110000 => [3,1,2,4] => 2
1111000010 => [4,4,1,1] => 1
1111000100 => [4,3,1,2] => 1
1111001000 => [4,2,1,3] => 1
1111010000 => [4,1,1,4] => 1
1111100000 => [5,5] => 1
101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
101010101100 => [1,1,1,1,1,1,1,1,2,2] => 2
101010110010 => [1,1,1,1,1,1,2,2,1,1] => 2
101010110100 => [1,1,1,1,1,1,2,1,1,2] => 2
101010111000 => [1,1,1,1,1,1,3,3] => 2
101011001010 => [1,1,1,1,2,2,1,1,1,1] => 2
101011001100 => [1,1,1,1,2,2,2,2] => 2
101011010010 => [1,1,1,1,2,1,1,2,1,1] => 2
101011010100 => [1,1,1,1,2,1,1,1,1,2] => 2
101011011000 => [1,1,1,1,2,1,2,3] => 3
101011100010 => [1,1,1,1,3,3,1,1] => 2
101011100100 => [1,1,1,1,3,2,1,2] => 2
101011101000 => [1,1,1,1,3,1,1,3] => 2
101011110000 => [1,1,1,1,4,4] => 2
101100101010 => [1,1,2,2,1,1,1,1,1,1] => 2
101100101100 => [1,1,2,2,1,1,2,2] => 2
101100110010 => [1,1,2,2,2,2,1,1] => 2
101100110100 => [1,1,2,2,2,1,1,2] => 2
101100111000 => [1,1,2,2,3,3] => 3
101101001010 => [1,1,2,1,1,2,1,1,1,1] => 2
101101001100 => [1,1,2,1,1,2,2,2] => 2
101101010010 => [1,1,2,1,1,1,1,2,1,1] => 2
101101010100 => [1,1,2,1,1,1,1,1,1,2] => 2
101101011000 => [1,1,2,1,1,1,2,3] => 3
101101100010 => [1,1,2,1,2,3,1,1] => 3
101101100100 => [1,1,2,1,2,2,1,2] => 2
101101101000 => [1,1,2,1,2,1,1,3] => 3
101101110000 => [1,1,2,1,3,4] => 4
101110001010 => [1,1,3,3,1,1,1,1] => 2
101110001100 => [1,1,3,3,2,2] => 2
101110010010 => [1,1,3,2,1,2,1,1] => 2
101110010100 => [1,1,3,2,1,1,1,2] => 2
101110011000 => [1,1,3,2,2,3] => 2
101110100010 => [1,1,3,1,1,3,1,1] => 2
101110100100 => [1,1,3,1,1,2,1,2] => 2
101110101000 => [1,1,3,1,1,1,1,3] => 2
101110110000 => [1,1,3,1,2,4] => 3
101111000010 => [1,1,4,4,1,1] => 2
101111000100 => [1,1,4,3,1,2] => 2
101111001000 => [1,1,4,2,1,3] => 2
101111010000 => [1,1,4,1,1,4] => 2
101111100000 => [1,1,5,5] => 2
110010101010 => [2,2,1,1,1,1,1,1,1,1] => 1
110010101100 => [2,2,1,1,1,1,2,2] => 1
110010110010 => [2,2,1,1,2,2,1,1] => 1
110010110100 => [2,2,1,1,2,1,1,2] => 1
110010111000 => [2,2,1,1,3,3] => 2
110011001010 => [2,2,2,2,1,1,1,1] => 1
110011001100 => [2,2,2,2,2,2] => 1
110011010010 => [2,2,2,1,1,2,1,1] => 1
110011010100 => [2,2,2,1,1,1,1,2] => 1
110011011000 => [2,2,2,1,2,3] => 2
110011100010 => [2,2,3,3,1,1] => 2
110011100100 => [2,2,3,2,1,2] => 2
110011101000 => [2,2,3,1,1,3] => 2
110011110000 => [2,2,4,4] => 2
110100101010 => [2,1,1,2,1,1,1,1,1,1] => 1
110100101100 => [2,1,1,2,1,1,2,2] => 1
110100110010 => [2,1,1,2,2,2,1,1] => 1
110100110100 => [2,1,1,2,2,1,1,2] => 1
110100111000 => [2,1,1,2,3,3] => 2
110101001010 => [2,1,1,1,1,2,1,1,1,1] => 1
110101001100 => [2,1,1,1,1,2,2,2] => 1
110101010010 => [2,1,1,1,1,1,1,2,1,1] => 1
110101010100 => [2,1,1,1,1,1,1,1,1,2] => 1
110101011000 => [2,1,1,1,1,1,2,3] => 2
110101100010 => [2,1,1,1,2,3,1,1] => 2
110101100100 => [2,1,1,1,2,2,1,2] => 1
110101101000 => [2,1,1,1,2,1,1,3] => 2
110101110000 => [2,1,1,1,3,4] => 3
110110001010 => [2,1,2,3,1,1,1,1] => 2
110110001100 => [2,1,2,3,2,2] => 2
110110010010 => [2,1,2,2,1,2,1,1] => 1
110110010100 => [2,1,2,2,1,1,1,2] => 1
110110011000 => [2,1,2,2,2,3] => 2
110110100010 => [2,1,2,1,1,3,1,1] => 2
110110100100 => [2,1,2,1,1,2,1,2] => 1
110110101000 => [2,1,2,1,1,1,1,3] => 2
110110110000 => [2,1,2,1,2,4] => 2
110111000010 => [2,1,3,4,1,1] => 3
110111000100 => [2,1,3,3,1,2] => 2
110111001000 => [2,1,3,2,1,3] => 2
110111010000 => [2,1,3,1,1,4] => 3
110111100000 => [2,1,4,5] => 3
111000101010 => [3,3,1,1,1,1,1,1] => 1
111000101100 => [3,3,1,1,2,2] => 1
111000110010 => [3,3,2,2,1,1] => 1
111000110100 => [3,3,2,1,1,2] => 1
111000111000 => [3,3,3,3] => 1
111001001010 => [3,2,1,2,1,1,1,1] => 1
111001001100 => [3,2,1,2,2,2] => 1
111001010010 => [3,2,1,1,1,2,1,1] => 1
111001010100 => [3,2,1,1,1,1,1,2] => 1
111001011000 => [3,2,1,1,2,3] => 1
111001100010 => [3,2,2,3,1,1] => 1
111001100100 => [3,2,2,2,1,2] => 1
111001101000 => [3,2,2,1,1,3] => 1
111001110000 => [3,2,3,4] => 2
111010001010 => [3,1,1,3,1,1,1,1] => 1
111010001100 => [3,1,1,3,2,2] => 1
111010010010 => [3,1,1,2,1,2,1,1] => 1
111010010100 => [3,1,1,2,1,1,1,2] => 1
111010011000 => [3,1,1,2,2,3] => 1
111010100010 => [3,1,1,1,1,3,1,1] => 1
111010100100 => [3,1,1,1,1,2,1,2] => 1
111010101000 => [3,1,1,1,1,1,1,3] => 1
111010110000 => [3,1,1,1,2,4] => 2
111011000010 => [3,1,2,4,1,1] => 2
111011000100 => [3,1,2,3,1,2] => 1
111011001000 => [3,1,2,2,1,3] => 1
111011010000 => [3,1,2,1,1,4] => 2
111011100000 => [3,1,3,5] => 2
111100001010 => [4,4,1,1,1,1] => 1
111100001100 => [4,4,2,2] => 1
111100010010 => [4,3,1,2,1,1] => 1
111100010100 => [4,3,1,1,1,2] => 1
111100011000 => [4,3,2,3] => 1
111100100010 => [4,2,1,3,1,1] => 1
111100100100 => [4,2,1,2,1,2] => 1
111100101000 => [4,2,1,1,1,3] => 1
111100110000 => [4,2,2,4] => 1
111101000010 => [4,1,1,4,1,1] => 1
111101000100 => [4,1,1,3,1,2] => 1
111101001000 => [4,1,1,2,1,3] => 1
111101010000 => [4,1,1,1,1,4] => 1
111101100000 => [4,1,2,5] => 2
111110000010 => [5,5,1,1] => 1
111110000100 => [5,4,1,2] => 1
111110001000 => [5,3,1,3] => 1
111110010000 => [5,2,1,4] => 1
111110100000 => [5,1,1,5] => 1
111111000000 => [6,6] => 1
1111111110 => [9,1] => 1
1111111101 => [8,1,1] => 1
1101111110 => [2,1,6,1] => 2
1011111110 => [1,1,7,1] => 2
1010111110 => [1,1,1,1,5,1] => 2
1001111110 => [1,2,6,1] => 3
1001011110 => [1,2,1,1,4,1] => 3
1000111110 => [1,3,5,1] => 3
1000101110 => [1,3,1,1,3,1] => 2
1000011110 => [1,4,4,1] => 2
1000010110 => [1,4,1,1,2,1] => 2
1000001110 => [1,5,3,1] => 2
1000001010 => [1,5,1,1,1,1] => 2
1000000110 => [1,6,2,1] => 2
1000000100 => [1,6,1,2] => 2
1000000010 => [1,7,1,1] => 2
1000000001 => [1,8,1] => 2
1000000000 => [1,9] => 2
10000000000 => [1,10] => 2
10000000010 => [1,8,1,1] => 2
10000000110 => [1,7,2,1] => 2
10000001110 => [1,6,3,1] => 2
10000011110 => [1,5,4,1] => 2
10000111110 => [1,4,5,1] => 3
10001111110 => [1,3,6,1] => 3
10011111110 => [1,2,7,1] => 3
10111111110 => [1,1,8,1] => 2
11111111110 => [10,1] => 1
0111111111 => [1,9] => 2
0111111101 => [1,7,1,1] => 2
0111111001 => [1,6,2,1] => 2
0111110001 => [1,5,3,1] => 2
0111100001 => [1,4,4,1] => 2
0100000001 => [1,1,7,1] => 2
0000000001 => [9,1] => 1
01111111111 => [1,10] => 2
01111111101 => [1,8,1,1] => 2
0111111011 => [1,6,1,2] => 2
0111110101 => [1,5,1,1,1,1] => 2
0111101001 => [1,4,1,1,2,1] => 2
0111010001 => [1,3,1,1,3,1] => 2
0110100001 => [1,2,1,1,4,1] => 3
0101000001 => [1,1,1,1,5,1] => 2
01000000001 => [1,1,8,1] => 2
00000000001 => [10,1] => 1
0101010101 => [1,1,1,1,1,1,1,1,1,1] => 1
0101001011 => [1,1,1,1,2,1,1,2] => 2
0101000111 => [1,1,1,1,3,3] => 2
0100110011 => [1,1,2,2,2,2] => 2
0100100111 => [1,1,2,1,2,3] => 3
0100011011 => [1,1,3,2,1,2] => 2
0100010111 => [1,1,3,1,1,3] => 2
0100001111 => [1,1,4,4] => 2
0011010011 => [2,2,1,1,2,2] => 1
0011000111 => [2,2,3,3] => 2
0010101011 => [2,1,1,1,1,1,1,2] => 1
0010010111 => [2,1,2,1,1,3] => 2
0010001111 => [2,1,3,4] => 3
0001110011 => [3,3,2,2] => 1
0001101011 => [3,2,1,1,1,2] => 1
0001100111 => [3,2,2,3] => 1
0001011101 => [3,1,1,3,1,1] => 1
0001010111 => [3,1,1,1,1,3] => 1
0001001111 => [3,1,2,4] => 2
0000111101 => [4,4,1,1] => 1
0000110111 => [4,2,1,3] => 1
0000101111 => [4,1,1,4] => 1
0000011111 => [5,5] => 1
010101010101 => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
010101001011 => [1,1,1,1,1,1,2,1,1,2] => 2
010100101011 => [1,1,1,1,2,1,1,1,1,2] => 2
010100100111 => [1,1,1,1,2,1,2,3] => 3
010100011011 => [1,1,1,1,3,2,1,2] => 2
010100010111 => [1,1,1,1,3,1,1,3] => 2
010100001111 => [1,1,1,1,4,4] => 2
010011010101 => [1,1,2,2,1,1,1,1,1,1] => 2
010011010011 => [1,1,2,2,1,1,2,2] => 2
010011001011 => [1,1,2,2,2,1,1,2] => 2
010011000111 => [1,1,2,2,3,3] => 3
010010110101 => [1,1,2,1,1,2,1,1,1,1] => 2
010010110011 => [1,1,2,1,1,2,2,2] => 2
010010101011 => [1,1,2,1,1,1,1,1,1,2] => 2
010010011011 => [1,1,2,1,2,2,1,2] => 2
010010010111 => [1,1,2,1,2,1,1,3] => 3
010010001111 => [1,1,2,1,3,4] => 4
010001110101 => [1,1,3,3,1,1,1,1] => 2
010001101011 => [1,1,3,2,1,1,1,2] => 2
010001011101 => [1,1,3,1,1,3,1,1] => 2
010001011011 => [1,1,3,1,1,2,1,2] => 2
010001010111 => [1,1,3,1,1,1,1,3] => 2
010000111011 => [1,1,4,3,1,2] => 2
010000110111 => [1,1,4,2,1,3] => 2
010000101111 => [1,1,4,1,1,4] => 2
010000011111 => [1,1,5,5] => 2
001101010101 => [2,2,1,1,1,1,1,1,1,1] => 1
001101001011 => [2,2,1,1,2,1,1,2] => 1
001100110011 => [2,2,2,2,2,2] => 1
001100100111 => [2,2,2,1,2,3] => 2
001100011011 => [2,2,3,2,1,2] => 2
001100010111 => [2,2,3,1,1,3] => 2
001100001111 => [2,2,4,4] => 2
001011010101 => [2,1,1,2,1,1,1,1,1,1] => 1
001011001101 => [2,1,1,2,2,2,1,1] => 1
001011000111 => [2,1,1,2,3,3] => 2
001010101011 => [2,1,1,1,1,1,1,1,1,2] => 1
001010010111 => [2,1,1,1,2,1,1,3] => 2
001010001111 => [2,1,1,1,3,4] => 3
001001110101 => [2,1,2,3,1,1,1,1] => 2
001001011101 => [2,1,2,1,1,3,1,1] => 2
001001010111 => [2,1,2,1,1,1,1,3] => 2
001000110111 => [2,1,3,2,1,3] => 2
001000101111 => [2,1,3,1,1,4] => 3
001000011111 => [2,1,4,5] => 3
000111010101 => [3,3,1,1,1,1,1,1] => 1
000111010011 => [3,3,1,1,2,2] => 1
000111001011 => [3,3,2,1,1,2] => 1
000111000111 => [3,3,3,3] => 1
000110110101 => [3,2,1,2,1,1,1,1] => 1
000110110011 => [3,2,1,2,2,2] => 1
000110101011 => [3,2,1,1,1,1,1,2] => 1
000110011011 => [3,2,2,2,1,2] => 1
000110010111 => [3,2,2,1,1,3] => 1
000110001111 => [3,2,3,4] => 2
000101110101 => [3,1,1,3,1,1,1,1] => 1
000101101011 => [3,1,1,2,1,1,1,2] => 1
000101011101 => [3,1,1,1,1,3,1,1] => 1
000101011011 => [3,1,1,1,1,2,1,2] => 1
000101010111 => [3,1,1,1,1,1,1,3] => 1
000100111011 => [3,1,2,3,1,2] => 1
000100110111 => [3,1,2,2,1,3] => 1
000100101111 => [3,1,2,1,1,4] => 2
000100011111 => [3,1,3,5] => 2
000011110101 => [4,4,1,1,1,1] => 1
000011110011 => [4,4,2,2] => 1
000011011101 => [4,2,1,3,1,1] => 1
000011011011 => [4,2,1,2,1,2] => 1
000011010111 => [4,2,1,1,1,3] => 1
000011001111 => [4,2,2,4] => 1
000010110111 => [4,1,1,2,1,3] => 1
000010101111 => [4,1,1,1,1,4] => 1
000010011111 => [4,1,2,5] => 2
000001111101 => [5,5,1,1] => 1
000001111011 => [5,4,1,2] => 1
000001110111 => [5,3,1,3] => 1
000001101111 => [5,2,1,4] => 1
000001011111 => [5,1,1,5] => 1
000000111111 => [6,6] => 1
0111111110 => [1,8,1] => 2
0000000010 => [8,1,1] => 1
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Description
The number of strong records in an integer composition.
A strong record is an element $a_i$ such that $a_i > a_j$ for all $j < i$. In particular, the first part of a composition is a strong record.
Theorem 1.1 of [1] provides the generating function for compositions with parts in a given set according to the sum of the parts, the number of parts and the number of strong records.
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 $w$.