Identifier
Values
0 => 0 => [2] => 2
1 => 1 => [1,1] => 1
00 => 01 => [2,1] => 2
01 => 10 => [1,2] => 2
10 => 00 => [3] => 3
11 => 11 => [1,1,1] => 1
000 => 011 => [2,1,1] => 2
001 => 101 => [1,2,1] => 2
010 => 000 => [4] => 4
011 => 110 => [1,1,2] => 2
100 => 010 => [2,2] => 2
101 => 100 => [1,3] => 3
110 => 001 => [3,1] => 3
111 => 111 => [1,1,1,1] => 1
0000 => 0111 => [2,1,1,1] => 2
0001 => 1011 => [1,2,1,1] => 2
0010 => 0001 => [4,1] => 4
0011 => 1101 => [1,1,2,1] => 2
0100 => 0100 => [2,3] => 3
0101 => 1000 => [1,4] => 4
0110 => 0010 => [3,2] => 3
0111 => 1110 => [1,1,1,2] => 2
1000 => 0110 => [2,1,2] => 3
1001 => 1010 => [1,2,2] => 2
1010 => 0000 => [5] => 5
1011 => 1100 => [1,1,3] => 3
1100 => 0101 => [2,2,1] => 2
1101 => 1001 => [1,3,1] => 3
1110 => 0011 => [3,1,1] => 3
1111 => 1111 => [1,1,1,1,1] => 1
00000 => 01111 => [2,1,1,1,1] => 2
00001 => 10111 => [1,2,1,1,1] => 2
00010 => 00011 => [4,1,1] => 4
00011 => 11011 => [1,1,2,1,1] => 2
00100 => 01001 => [2,3,1] => 3
00101 => 10001 => [1,4,1] => 4
00110 => 00101 => [3,2,1] => 3
00111 => 11101 => [1,1,1,2,1] => 2
01000 => 01100 => [2,1,3] => 4
01001 => 10100 => [1,2,3] => 3
01010 => 00000 => [6] => 6
01011 => 11000 => [1,1,4] => 4
01100 => 01010 => [2,2,2] => 2
01101 => 10010 => [1,3,2] => 3
01110 => 00110 => [3,1,2] => 4
01111 => 11110 => [1,1,1,1,2] => 2
10000 => 01110 => [2,1,1,2] => 3
10001 => 10110 => [1,2,1,2] => 3
10010 => 00010 => [4,2] => 4
10011 => 11010 => [1,1,2,2] => 2
10100 => 01000 => [2,4] => 4
10101 => 10000 => [1,5] => 5
10110 => 00100 => [3,3] => 3
10111 => 11100 => [1,1,1,3] => 3
11000 => 01101 => [2,1,2,1] => 3
11001 => 10101 => [1,2,2,1] => 2
11010 => 00001 => [5,1] => 5
11011 => 11001 => [1,1,3,1] => 3
11100 => 01011 => [2,2,1,1] => 2
11101 => 10011 => [1,3,1,1] => 3
11110 => 00111 => [3,1,1,1] => 3
11111 => 11111 => [1,1,1,1,1,1] => 1
000000 => 011111 => [2,1,1,1,1,1] => 2
000001 => 101111 => [1,2,1,1,1,1] => 2
000010 => 000111 => [4,1,1,1] => 4
000011 => 110111 => [1,1,2,1,1,1] => 2
000100 => 010011 => [2,3,1,1] => 3
000101 => 100011 => [1,4,1,1] => 4
000110 => 001011 => [3,2,1,1] => 3
000111 => 111011 => [1,1,1,2,1,1] => 2
001000 => 011001 => [2,1,3,1] => 4
001001 => 101001 => [1,2,3,1] => 3
001010 => 000001 => [6,1] => 6
001011 => 110001 => [1,1,4,1] => 4
001100 => 010101 => [2,2,2,1] => 2
001101 => 100101 => [1,3,2,1] => 3
001110 => 001101 => [3,1,2,1] => 4
001111 => 111101 => [1,1,1,1,2,1] => 2
010000 => 011100 => [2,1,1,3] => 4
010001 => 101100 => [1,2,1,3] => 4
010010 => 000100 => [4,3] => 4
010011 => 110100 => [1,1,2,3] => 3
010100 => 010000 => [2,5] => 5
010101 => 100000 => [1,6] => 6
010110 => 001000 => [3,4] => 4
010111 => 111000 => [1,1,1,4] => 4
011000 => 011010 => [2,1,2,2] => 3
011001 => 101010 => [1,2,2,2] => 2
011010 => 000010 => [5,2] => 5
011011 => 110010 => [1,1,3,2] => 3
011100 => 010110 => [2,2,1,2] => 3
011101 => 100110 => [1,3,1,2] => 4
011110 => 001110 => [3,1,1,2] => 4
011111 => 111110 => [1,1,1,1,1,2] => 2
100000 => 011110 => [2,1,1,1,2] => 3
100001 => 101110 => [1,2,1,1,2] => 3
100010 => 000110 => [4,1,2] => 5
100011 => 110110 => [1,1,2,1,2] => 3
100100 => 010010 => [2,3,2] => 3
100101 => 100010 => [1,4,2] => 4
100110 => 001010 => [3,2,2] => 3
>>> Load all 511 entries. <<<
100111 => 111010 => [1,1,1,2,2] => 2
101000 => 011000 => [2,1,4] => 5
101001 => 101000 => [1,2,4] => 4
101010 => 000000 => [7] => 7
101011 => 110000 => [1,1,5] => 5
101100 => 010100 => [2,2,3] => 3
101101 => 100100 => [1,3,3] => 3
101110 => 001100 => [3,1,3] => 5
101111 => 111100 => [1,1,1,1,3] => 3
110000 => 011101 => [2,1,1,2,1] => 3
110001 => 101101 => [1,2,1,2,1] => 3
110010 => 000101 => [4,2,1] => 4
110011 => 110101 => [1,1,2,2,1] => 2
110100 => 010001 => [2,4,1] => 4
110101 => 100001 => [1,5,1] => 5
110110 => 001001 => [3,3,1] => 3
110111 => 111001 => [1,1,1,3,1] => 3
111000 => 011011 => [2,1,2,1,1] => 3
111001 => 101011 => [1,2,2,1,1] => 2
111010 => 000011 => [5,1,1] => 5
111011 => 110011 => [1,1,3,1,1] => 3
111100 => 010111 => [2,2,1,1,1] => 2
111101 => 100111 => [1,3,1,1,1] => 3
111110 => 001111 => [3,1,1,1,1] => 3
111111 => 111111 => [1,1,1,1,1,1,1] => 1
0000000 => 0111111 => [2,1,1,1,1,1,1] => 2
0000001 => 1011111 => [1,2,1,1,1,1,1] => 2
0000010 => 0001111 => [4,1,1,1,1] => 4
0000011 => 1101111 => [1,1,2,1,1,1,1] => 2
0000100 => 0100111 => [2,3,1,1,1] => 3
0000101 => 1000111 => [1,4,1,1,1] => 4
0000110 => 0010111 => [3,2,1,1,1] => 3
0000111 => 1110111 => [1,1,1,2,1,1,1] => 2
0001000 => 0110011 => [2,1,3,1,1] => 4
0001001 => 1010011 => [1,2,3,1,1] => 3
0001010 => 0000011 => [6,1,1] => 6
0001011 => 1100011 => [1,1,4,1,1] => 4
0001100 => 0101011 => [2,2,2,1,1] => 2
0001101 => 1001011 => [1,3,2,1,1] => 3
0001110 => 0011011 => [3,1,2,1,1] => 4
0001111 => 1111011 => [1,1,1,1,2,1,1] => 2
0010000 => 0111001 => [2,1,1,3,1] => 4
0010001 => 1011001 => [1,2,1,3,1] => 4
0010010 => 0001001 => [4,3,1] => 4
0010011 => 1101001 => [1,1,2,3,1] => 3
0010100 => 0100001 => [2,5,1] => 5
0010101 => 1000001 => [1,6,1] => 6
0010110 => 0010001 => [3,4,1] => 4
0010111 => 1110001 => [1,1,1,4,1] => 4
0011000 => 0110101 => [2,1,2,2,1] => 3
0011001 => 1010101 => [1,2,2,2,1] => 2
0011010 => 0000101 => [5,2,1] => 5
0011011 => 1100101 => [1,1,3,2,1] => 3
0011100 => 0101101 => [2,2,1,2,1] => 3
0011101 => 1001101 => [1,3,1,2,1] => 4
0011110 => 0011101 => [3,1,1,2,1] => 4
0011111 => 1111101 => [1,1,1,1,1,2,1] => 2
0100000 => 0111100 => [2,1,1,1,3] => 4
0100001 => 1011100 => [1,2,1,1,3] => 4
0100010 => 0001100 => [4,1,3] => 6
0100011 => 1101100 => [1,1,2,1,3] => 4
0100100 => 0100100 => [2,3,3] => 3
0100101 => 1000100 => [1,4,3] => 4
0100110 => 0010100 => [3,2,3] => 4
0100111 => 1110100 => [1,1,1,2,3] => 3
0101000 => 0110000 => [2,1,5] => 6
0101001 => 1010000 => [1,2,5] => 5
0101010 => 0000000 => [8] => 8
0101011 => 1100000 => [1,1,6] => 6
0101100 => 0101000 => [2,2,4] => 4
0101101 => 1001000 => [1,3,4] => 4
0101110 => 0011000 => [3,1,4] => 6
0101111 => 1111000 => [1,1,1,1,4] => 4
0110000 => 0111010 => [2,1,1,2,2] => 3
0110001 => 1011010 => [1,2,1,2,2] => 3
0110010 => 0001010 => [4,2,2] => 4
0110011 => 1101010 => [1,1,2,2,2] => 2
0110100 => 0100010 => [2,4,2] => 4
0110101 => 1000010 => [1,5,2] => 5
0110110 => 0010010 => [3,3,2] => 3
0110111 => 1110010 => [1,1,1,3,2] => 3
0111000 => 0110110 => [2,1,2,1,2] => 4
0111001 => 1010110 => [1,2,2,1,2] => 3
0111010 => 0000110 => [5,1,2] => 6
0111011 => 1100110 => [1,1,3,1,2] => 4
0111100 => 0101110 => [2,2,1,1,2] => 3
0111101 => 1001110 => [1,3,1,1,2] => 4
0111110 => 0011110 => [3,1,1,1,2] => 4
0111111 => 1111110 => [1,1,1,1,1,1,2] => 2
1000000 => 0111110 => [2,1,1,1,1,2] => 3
1000001 => 1011110 => [1,2,1,1,1,2] => 3
1000010 => 0001110 => [4,1,1,2] => 5
1000011 => 1101110 => [1,1,2,1,1,2] => 3
1000100 => 0100110 => [2,3,1,2] => 4
1000101 => 1000110 => [1,4,1,2] => 5
1000110 => 0010110 => [3,2,1,2] => 4
1000111 => 1110110 => [1,1,1,2,1,2] => 3
1001000 => 0110010 => [2,1,3,2] => 4
1001001 => 1010010 => [1,2,3,2] => 3
1001010 => 0000010 => [6,2] => 6
1001011 => 1100010 => [1,1,4,2] => 4
1001100 => 0101010 => [2,2,2,2] => 2
1001101 => 1001010 => [1,3,2,2] => 3
1001110 => 0011010 => [3,1,2,2] => 4
1001111 => 1111010 => [1,1,1,1,2,2] => 2
1010000 => 0111000 => [2,1,1,4] => 5
1010001 => 1011000 => [1,2,1,4] => 5
1010010 => 0001000 => [4,4] => 4
1010011 => 1101000 => [1,1,2,4] => 4
1010100 => 0100000 => [2,6] => 6
1010101 => 1000000 => [1,7] => 7
1010110 => 0010000 => [3,5] => 5
1010111 => 1110000 => [1,1,1,5] => 5
1011000 => 0110100 => [2,1,2,3] => 4
1011001 => 1010100 => [1,2,2,3] => 3
1011010 => 0000100 => [5,3] => 5
1011011 => 1100100 => [1,1,3,3] => 3
1011100 => 0101100 => [2,2,1,3] => 4
1011101 => 1001100 => [1,3,1,3] => 5
1011110 => 0011100 => [3,1,1,3] => 5
1011111 => 1111100 => [1,1,1,1,1,3] => 3
1100000 => 0111101 => [2,1,1,1,2,1] => 3
1100001 => 1011101 => [1,2,1,1,2,1] => 3
1100010 => 0001101 => [4,1,2,1] => 5
1100011 => 1101101 => [1,1,2,1,2,1] => 3
1100100 => 0100101 => [2,3,2,1] => 3
1100101 => 1000101 => [1,4,2,1] => 4
1100110 => 0010101 => [3,2,2,1] => 3
1100111 => 1110101 => [1,1,1,2,2,1] => 2
1101000 => 0110001 => [2,1,4,1] => 5
1101001 => 1010001 => [1,2,4,1] => 4
1101010 => 0000001 => [7,1] => 7
1101011 => 1100001 => [1,1,5,1] => 5
1101100 => 0101001 => [2,2,3,1] => 3
1101101 => 1001001 => [1,3,3,1] => 3
1101110 => 0011001 => [3,1,3,1] => 5
1101111 => 1111001 => [1,1,1,1,3,1] => 3
1110000 => 0111011 => [2,1,1,2,1,1] => 3
1110001 => 1011011 => [1,2,1,2,1,1] => 3
1110010 => 0001011 => [4,2,1,1] => 4
1110011 => 1101011 => [1,1,2,2,1,1] => 2
1110100 => 0100011 => [2,4,1,1] => 4
1110101 => 1000011 => [1,5,1,1] => 5
1110110 => 0010011 => [3,3,1,1] => 3
1110111 => 1110011 => [1,1,1,3,1,1] => 3
1111000 => 0110111 => [2,1,2,1,1,1] => 3
1111001 => 1010111 => [1,2,2,1,1,1] => 2
1111010 => 0000111 => [5,1,1,1] => 5
1111011 => 1100111 => [1,1,3,1,1,1] => 3
1111100 => 0101111 => [2,2,1,1,1,1] => 2
1111101 => 1001111 => [1,3,1,1,1,1] => 3
1111110 => 0011111 => [3,1,1,1,1,1] => 3
1111111 => 1111111 => [1,1,1,1,1,1,1,1] => 1
00000000 => 01111111 => [2,1,1,1,1,1,1,1] => 2
00000001 => 10111111 => [1,2,1,1,1,1,1,1] => 2
00000010 => 00011111 => [4,1,1,1,1,1] => 4
00000011 => 11011111 => [1,1,2,1,1,1,1,1] => 2
00000100 => 01001111 => [2,3,1,1,1,1] => 3
00000101 => 10001111 => [1,4,1,1,1,1] => 4
00000110 => 00101111 => [3,2,1,1,1,1] => 3
00000111 => 11101111 => [1,1,1,2,1,1,1,1] => 2
00001000 => 01100111 => [2,1,3,1,1,1] => 4
00001001 => 10100111 => [1,2,3,1,1,1] => 3
00001010 => 00000111 => [6,1,1,1] => 6
00001011 => 11000111 => [1,1,4,1,1,1] => 4
00001100 => 01010111 => [2,2,2,1,1,1] => 2
00001101 => 10010111 => [1,3,2,1,1,1] => 3
00001110 => 00110111 => [3,1,2,1,1,1] => 4
00001111 => 11110111 => [1,1,1,1,2,1,1,1] => 2
00010000 => 01110011 => [2,1,1,3,1,1] => 4
00010001 => 10110011 => [1,2,1,3,1,1] => 4
00010010 => 00010011 => [4,3,1,1] => 4
00010011 => 11010011 => [1,1,2,3,1,1] => 3
00010100 => 01000011 => [2,5,1,1] => 5
00010101 => 10000011 => [1,6,1,1] => 6
00010110 => 00100011 => [3,4,1,1] => 4
00010111 => 11100011 => [1,1,1,4,1,1] => 4
00011000 => 01101011 => [2,1,2,2,1,1] => 3
00011001 => 10101011 => [1,2,2,2,1,1] => 2
00011010 => 00001011 => [5,2,1,1] => 5
00011011 => 11001011 => [1,1,3,2,1,1] => 3
00011100 => 01011011 => [2,2,1,2,1,1] => 3
00011101 => 10011011 => [1,3,1,2,1,1] => 4
00011110 => 00111011 => [3,1,1,2,1,1] => 4
00011111 => 11111011 => [1,1,1,1,1,2,1,1] => 2
00100000 => 01111001 => [2,1,1,1,3,1] => 4
00100001 => 10111001 => [1,2,1,1,3,1] => 4
00100010 => 00011001 => [4,1,3,1] => 6
00100011 => 11011001 => [1,1,2,1,3,1] => 4
00100100 => 01001001 => [2,3,3,1] => 3
00100101 => 10001001 => [1,4,3,1] => 4
00100110 => 00101001 => [3,2,3,1] => 4
00100111 => 11101001 => [1,1,1,2,3,1] => 3
00101000 => 01100001 => [2,1,5,1] => 6
00101001 => 10100001 => [1,2,5,1] => 5
00101010 => 00000001 => [8,1] => 8
00101011 => 11000001 => [1,1,6,1] => 6
00101100 => 01010001 => [2,2,4,1] => 4
00101101 => 10010001 => [1,3,4,1] => 4
00101110 => 00110001 => [3,1,4,1] => 6
00101111 => 11110001 => [1,1,1,1,4,1] => 4
00110000 => 01110101 => [2,1,1,2,2,1] => 3
00110001 => 10110101 => [1,2,1,2,2,1] => 3
00110010 => 00010101 => [4,2,2,1] => 4
00110011 => 11010101 => [1,1,2,2,2,1] => 2
00110100 => 01000101 => [2,4,2,1] => 4
00110101 => 10000101 => [1,5,2,1] => 5
00110110 => 00100101 => [3,3,2,1] => 3
00110111 => 11100101 => [1,1,1,3,2,1] => 3
00111000 => 01101101 => [2,1,2,1,2,1] => 4
00111001 => 10101101 => [1,2,2,1,2,1] => 3
00111010 => 00001101 => [5,1,2,1] => 6
00111011 => 11001101 => [1,1,3,1,2,1] => 4
00111100 => 01011101 => [2,2,1,1,2,1] => 3
00111101 => 10011101 => [1,3,1,1,2,1] => 4
00111110 => 00111101 => [3,1,1,1,2,1] => 4
00111111 => 11111101 => [1,1,1,1,1,1,2,1] => 2
01000000 => 01111100 => [2,1,1,1,1,3] => 4
01000001 => 10111100 => [1,2,1,1,1,3] => 4
01000010 => 00011100 => [4,1,1,3] => 6
01000011 => 11011100 => [1,1,2,1,1,3] => 4
01000100 => 01001100 => [2,3,1,3] => 5
01000101 => 10001100 => [1,4,1,3] => 6
01000110 => 00101100 => [3,2,1,3] => 5
01000111 => 11101100 => [1,1,1,2,1,3] => 4
01001000 => 01100100 => [2,1,3,3] => 4
01001001 => 10100100 => [1,2,3,3] => 3
01001010 => 00000100 => [6,3] => 6
01001011 => 11000100 => [1,1,4,3] => 4
01001100 => 01010100 => [2,2,2,3] => 3
01001101 => 10010100 => [1,3,2,3] => 4
01001110 => 00110100 => [3,1,2,3] => 5
01001111 => 11110100 => [1,1,1,1,2,3] => 3
01010000 => 01110000 => [2,1,1,5] => 6
01010001 => 10110000 => [1,2,1,5] => 6
01010010 => 00010000 => [4,5] => 5
01010011 => 11010000 => [1,1,2,5] => 5
01010100 => 01000000 => [2,7] => 7
01010101 => 10000000 => [1,8] => 8
01010110 => 00100000 => [3,6] => 6
01010111 => 11100000 => [1,1,1,6] => 6
01011000 => 01101000 => [2,1,2,4] => 5
01011001 => 10101000 => [1,2,2,4] => 4
01011010 => 00001000 => [5,4] => 5
01011011 => 11001000 => [1,1,3,4] => 4
01011100 => 01011000 => [2,2,1,4] => 5
01011101 => 10011000 => [1,3,1,4] => 6
01011110 => 00111000 => [3,1,1,4] => 6
01011111 => 11111000 => [1,1,1,1,1,4] => 4
01100000 => 01111010 => [2,1,1,1,2,2] => 3
01100001 => 10111010 => [1,2,1,1,2,2] => 3
01100010 => 00011010 => [4,1,2,2] => 5
01100011 => 11011010 => [1,1,2,1,2,2] => 3
01100100 => 01001010 => [2,3,2,2] => 3
01100101 => 10001010 => [1,4,2,2] => 4
01100110 => 00101010 => [3,2,2,2] => 3
01100111 => 11101010 => [1,1,1,2,2,2] => 2
01101000 => 01100010 => [2,1,4,2] => 5
01101001 => 10100010 => [1,2,4,2] => 4
01101010 => 00000010 => [7,2] => 7
01101011 => 11000010 => [1,1,5,2] => 5
01101100 => 01010010 => [2,2,3,2] => 3
01101101 => 10010010 => [1,3,3,2] => 3
01101110 => 00110010 => [3,1,3,2] => 5
01101111 => 11110010 => [1,1,1,1,3,2] => 3
01110000 => 01110110 => [2,1,1,2,1,2] => 4
01110001 => 10110110 => [1,2,1,2,1,2] => 4
01110010 => 00010110 => [4,2,1,2] => 5
01110011 => 11010110 => [1,1,2,2,1,2] => 3
01110100 => 01000110 => [2,4,1,2] => 5
01110101 => 10000110 => [1,5,1,2] => 6
01110110 => 00100110 => [3,3,1,2] => 4
01110111 => 11100110 => [1,1,1,3,1,2] => 4
01111000 => 01101110 => [2,1,2,1,1,2] => 4
01111001 => 10101110 => [1,2,2,1,1,2] => 3
01111010 => 00001110 => [5,1,1,2] => 6
01111011 => 11001110 => [1,1,3,1,1,2] => 4
01111100 => 01011110 => [2,2,1,1,1,2] => 3
01111101 => 10011110 => [1,3,1,1,1,2] => 4
01111110 => 00111110 => [3,1,1,1,1,2] => 4
01111111 => 11111110 => [1,1,1,1,1,1,1,2] => 2
10000000 => 01111110 => [2,1,1,1,1,1,2] => 3
10000001 => 10111110 => [1,2,1,1,1,1,2] => 3
10000010 => 00011110 => [4,1,1,1,2] => 5
10000011 => 11011110 => [1,1,2,1,1,1,2] => 3
10000100 => 01001110 => [2,3,1,1,2] => 4
10000101 => 10001110 => [1,4,1,1,2] => 5
10000110 => 00101110 => [3,2,1,1,2] => 4
10000111 => 11101110 => [1,1,1,2,1,1,2] => 3
10001000 => 01100110 => [2,1,3,1,2] => 5
10001001 => 10100110 => [1,2,3,1,2] => 4
10001010 => 00000110 => [6,1,2] => 7
10001011 => 11000110 => [1,1,4,1,2] => 5
10001100 => 01010110 => [2,2,2,1,2] => 3
10001101 => 10010110 => [1,3,2,1,2] => 4
10001110 => 00110110 => [3,1,2,1,2] => 5
10001111 => 11110110 => [1,1,1,1,2,1,2] => 3
10010000 => 01110010 => [2,1,1,3,2] => 4
10010001 => 10110010 => [1,2,1,3,2] => 4
10010010 => 00010010 => [4,3,2] => 4
10010011 => 11010010 => [1,1,2,3,2] => 3
10010100 => 01000010 => [2,5,2] => 5
10010101 => 10000010 => [1,6,2] => 6
10010110 => 00100010 => [3,4,2] => 4
10010111 => 11100010 => [1,1,1,4,2] => 4
10011000 => 01101010 => [2,1,2,2,2] => 3
10011001 => 10101010 => [1,2,2,2,2] => 2
10011010 => 00001010 => [5,2,2] => 5
10011011 => 11001010 => [1,1,3,2,2] => 3
10011100 => 01011010 => [2,2,1,2,2] => 3
10011101 => 10011010 => [1,3,1,2,2] => 4
10011110 => 00111010 => [3,1,1,2,2] => 4
10011111 => 11111010 => [1,1,1,1,1,2,2] => 2
10100000 => 01111000 => [2,1,1,1,4] => 5
10100001 => 10111000 => [1,2,1,1,4] => 5
10100010 => 00011000 => [4,1,4] => 7
10100011 => 11011000 => [1,1,2,1,4] => 5
10100100 => 01001000 => [2,3,4] => 4
10100101 => 10001000 => [1,4,4] => 4
10100110 => 00101000 => [3,2,4] => 5
10100111 => 11101000 => [1,1,1,2,4] => 4
10101000 => 01100000 => [2,1,6] => 7
10101001 => 10100000 => [1,2,6] => 6
10101010 => 00000000 => [9] => 9
10101011 => 11000000 => [1,1,7] => 7
10101100 => 01010000 => [2,2,5] => 5
10101101 => 10010000 => [1,3,5] => 5
10101110 => 00110000 => [3,1,5] => 7
10101111 => 11110000 => [1,1,1,1,5] => 5
10110000 => 01110100 => [2,1,1,2,3] => 4
10110001 => 10110100 => [1,2,1,2,3] => 4
10110010 => 00010100 => [4,2,3] => 5
10110011 => 11010100 => [1,1,2,2,3] => 3
10110100 => 01000100 => [2,4,3] => 4
10110101 => 10000100 => [1,5,3] => 5
10110110 => 00100100 => [3,3,3] => 3
10110111 => 11100100 => [1,1,1,3,3] => 3
10111000 => 01101100 => [2,1,2,1,3] => 5
10111001 => 10101100 => [1,2,2,1,3] => 4
10111010 => 00001100 => [5,1,3] => 7
10111011 => 11001100 => [1,1,3,1,3] => 5
10111100 => 01011100 => [2,2,1,1,3] => 4
10111101 => 10011100 => [1,3,1,1,3] => 5
10111110 => 00111100 => [3,1,1,1,3] => 5
10111111 => 11111100 => [1,1,1,1,1,1,3] => 3
11000000 => 01111101 => [2,1,1,1,1,2,1] => 3
11000001 => 10111101 => [1,2,1,1,1,2,1] => 3
11000010 => 00011101 => [4,1,1,2,1] => 5
11000011 => 11011101 => [1,1,2,1,1,2,1] => 3
11000100 => 01001101 => [2,3,1,2,1] => 4
11000101 => 10001101 => [1,4,1,2,1] => 5
11000110 => 00101101 => [3,2,1,2,1] => 4
11000111 => 11101101 => [1,1,1,2,1,2,1] => 3
11001000 => 01100101 => [2,1,3,2,1] => 4
11001001 => 10100101 => [1,2,3,2,1] => 3
11001010 => 00000101 => [6,2,1] => 6
11001011 => 11000101 => [1,1,4,2,1] => 4
11001100 => 01010101 => [2,2,2,2,1] => 2
11001101 => 10010101 => [1,3,2,2,1] => 3
11001110 => 00110101 => [3,1,2,2,1] => 4
11001111 => 11110101 => [1,1,1,1,2,2,1] => 2
11010000 => 01110001 => [2,1,1,4,1] => 5
11010001 => 10110001 => [1,2,1,4,1] => 5
11010010 => 00010001 => [4,4,1] => 4
11010011 => 11010001 => [1,1,2,4,1] => 4
11010100 => 01000001 => [2,6,1] => 6
11010101 => 10000001 => [1,7,1] => 7
11010110 => 00100001 => [3,5,1] => 5
11010111 => 11100001 => [1,1,1,5,1] => 5
11011000 => 01101001 => [2,1,2,3,1] => 4
11011001 => 10101001 => [1,2,2,3,1] => 3
11011010 => 00001001 => [5,3,1] => 5
11011011 => 11001001 => [1,1,3,3,1] => 3
11011100 => 01011001 => [2,2,1,3,1] => 4
11011101 => 10011001 => [1,3,1,3,1] => 5
11011110 => 00111001 => [3,1,1,3,1] => 5
11011111 => 11111001 => [1,1,1,1,1,3,1] => 3
11100000 => 01111011 => [2,1,1,1,2,1,1] => 3
11100001 => 10111011 => [1,2,1,1,2,1,1] => 3
11100010 => 00011011 => [4,1,2,1,1] => 5
11100011 => 11011011 => [1,1,2,1,2,1,1] => 3
11100100 => 01001011 => [2,3,2,1,1] => 3
11100101 => 10001011 => [1,4,2,1,1] => 4
11100110 => 00101011 => [3,2,2,1,1] => 3
11100111 => 11101011 => [1,1,1,2,2,1,1] => 2
11101000 => 01100011 => [2,1,4,1,1] => 5
11101001 => 10100011 => [1,2,4,1,1] => 4
11101010 => 00000011 => [7,1,1] => 7
11101011 => 11000011 => [1,1,5,1,1] => 5
11101100 => 01010011 => [2,2,3,1,1] => 3
11101101 => 10010011 => [1,3,3,1,1] => 3
11101110 => 00110011 => [3,1,3,1,1] => 5
11101111 => 11110011 => [1,1,1,1,3,1,1] => 3
11110000 => 01110111 => [2,1,1,2,1,1,1] => 3
11110001 => 10110111 => [1,2,1,2,1,1,1] => 3
11110010 => 00010111 => [4,2,1,1,1] => 4
11110011 => 11010111 => [1,1,2,2,1,1,1] => 2
11110100 => 01000111 => [2,4,1,1,1] => 4
11110101 => 10000111 => [1,5,1,1,1] => 5
11110110 => 00100111 => [3,3,1,1,1] => 3
11110111 => 11100111 => [1,1,1,3,1,1,1] => 3
11111000 => 01101111 => [2,1,2,1,1,1,1] => 3
11111001 => 10101111 => [1,2,2,1,1,1,1] => 2
11111010 => 00001111 => [5,1,1,1,1] => 5
11111011 => 11001111 => [1,1,3,1,1,1,1] => 3
11111100 => 01011111 => [2,2,1,1,1,1,1] => 2
11111101 => 10011111 => [1,3,1,1,1,1,1] => 3
11111110 => 00111111 => [3,1,1,1,1,1,1] => 3
11111111 => 11111111 => [1,1,1,1,1,1,1,1,1] => 1
=> => [1] => 1
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Description
The number of up steps of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of up steps.
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.
Map
flag zeros to zeros
Description
Return a binary word of the same length, such that the number of zeros equals the number of occurrences of $10$ in the word obtained from the original word by prepending the reverse of the complement.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.