Identifier
Values
0 => 1 => [1,1] => [1,0,1,0] => 1
1 => 0 => [2] => [1,1,0,0] => 2
00 => 11 => [1,1,1] => [1,0,1,0,1,0] => 1
01 => 10 => [1,2] => [1,0,1,1,0,0] => 2
10 => 01 => [2,1] => [1,1,0,0,1,0] => 2
11 => 00 => [3] => [1,1,1,0,0,0] => 3
000 => 111 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
001 => 110 => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
010 => 101 => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
011 => 100 => [1,3] => [1,0,1,1,1,0,0,0] => 3
100 => 011 => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
101 => 010 => [2,2] => [1,1,0,0,1,1,0,0] => 2
110 => 001 => [3,1] => [1,1,1,0,0,0,1,0] => 3
111 => 000 => [4] => [1,1,1,1,0,0,0,0] => 4
0000 => 1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
0001 => 1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
0010 => 1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
0011 => 1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
0100 => 1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
0101 => 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
0110 => 1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
0111 => 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
1000 => 0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
1001 => 0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
1010 => 0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
1011 => 0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
1100 => 0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
1101 => 0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
1110 => 0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
1111 => 0000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
00000 => 11111 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
00001 => 11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
00010 => 11101 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
00011 => 11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
00100 => 11011 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
00101 => 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
00110 => 11001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
00111 => 11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
01000 => 10111 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
01001 => 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
01010 => 10101 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
01011 => 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
01100 => 10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
01101 => 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
01110 => 10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
01111 => 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
10000 => 01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
10001 => 01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
10010 => 01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
10011 => 01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
10100 => 01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
10101 => 01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
10110 => 01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
10111 => 01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
11000 => 00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
11001 => 00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
11010 => 00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
11011 => 00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
11100 => 00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
11101 => 00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
11110 => 00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
11111 => 00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
000000 => 111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
000001 => 111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
000010 => 111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
000011 => 111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
000100 => 111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
000101 => 111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
000110 => 111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
000111 => 111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
001000 => 110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
001001 => 110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
001010 => 110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
001011 => 110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
001100 => 110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
001101 => 110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
001110 => 110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
001111 => 110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
010000 => 101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
010001 => 101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
010010 => 101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
010011 => 101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
010100 => 101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
010101 => 101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
010110 => 101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
010111 => 101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
011000 => 100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
011001 => 100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
011010 => 100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
011011 => 100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
011100 => 100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
011101 => 100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
011110 => 100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
011111 => 100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
100000 => 011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
100001 => 011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
100010 => 011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
100011 => 011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
100100 => 011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
100101 => 011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
100110 => 011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
>>> Load all 350 entries. <<<
100111 => 011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
101000 => 010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
101001 => 010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
101010 => 010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
101011 => 010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
101100 => 010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
101101 => 010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
101110 => 010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
101111 => 010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
110000 => 001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
110001 => 001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
110010 => 001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
110011 => 001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
110100 => 001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
110101 => 001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
110110 => 001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
110111 => 001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
111000 => 000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
111001 => 000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
111010 => 000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
111011 => 000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
111100 => 000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
111101 => 000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
111110 => 000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
111111 => 000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
0000000 => 1111111 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000001 => 1111110 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0000010 => 1111101 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
0000011 => 1111100 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
0000100 => 1111011 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
0000101 => 1111010 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
0000110 => 1111001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
0000111 => 1111000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
0001000 => 1110111 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
0001001 => 1110110 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
0001101 => 1110010 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0001111 => 1110000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
0010000 => 1101111 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
0010001 => 1101110 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
0010101 => 1101010 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0010111 => 1101000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0011000 => 1100111 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
0011011 => 1100100 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
0011101 => 1100010 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0011110 => 1100001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
0011111 => 1100000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
0100000 => 1011111 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
0100001 => 1011110 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
0100111 => 1011000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
0101010 => 1010101 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
0101011 => 1010100 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
0101101 => 1010010 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
0101110 => 1010001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0101111 => 1010000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0110000 => 1001111 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
0110011 => 1001100 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
0110101 => 1001010 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
0110110 => 1001001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
0110111 => 1001000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0111001 => 1000110 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
0111010 => 1000101 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
0111100 => 1000011 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
0111101 => 1000010 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
0111110 => 1000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
0111111 => 1000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
1000000 => 0111111 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
1000001 => 0111110 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1000010 => 0111101 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
1000011 => 0111100 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
1000100 => 0111011 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
1000111 => 0111000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
1001011 => 0110100 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
1001101 => 0110010 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
1001110 => 0110001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
1001111 => 0110000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
1010000 => 0101111 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
1010011 => 0101100 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
1010101 => 0101010 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1010110 => 0101001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
1010111 => 0101000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1011000 => 0100111 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
1011001 => 0100110 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
1011010 => 0100101 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
1011100 => 0100011 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
1011101 => 0100010 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1011110 => 0100001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
1011111 => 0100000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1100000 => 0011111 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
1100001 => 0011110 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
1100011 => 0011100 => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 3
1100101 => 0011010 => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 3
1100110 => 0011001 => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 3
1101001 => 0010110 => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 3
1101010 => 0010101 => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
1101100 => 0010011 => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 3
1101110 => 0010001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1101111 => 0010000 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1110000 => 0001111 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
1110001 => 0001110 => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 4
1110010 => 0001101 => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 4
1110100 => 0001011 => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 4
1110101 => 0001010 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
1110111 => 0001000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
1111000 => 0000111 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 5
1111011 => 0000100 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
1111100 => 0000011 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
1111101 => 0000010 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
1111110 => 0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
1111111 => 0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
00000000 => 11111111 => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
00000001 => 11111110 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
00000011 => 11111100 => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
00000101 => 11111010 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
00000111 => 11111000 => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
00001101 => 11110010 => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
00010000 => 11101111 => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
00010101 => 11101010 => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
00011111 => 11100000 => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
00100000 => 11011111 => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
00110101 => 11001010 => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
00110111 => 11001000 => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
00111011 => 11000100 => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
00111110 => 11000001 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
00111111 => 11000000 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
01000000 => 10111111 => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
01000001 => 10111110 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
01010000 => 10101111 => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
01010101 => 10101010 => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
01010111 => 10101000 => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
01011011 => 10100100 => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
01011101 => 10100010 => [1,2,4,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01011111 => 10100000 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
01100000 => 10011111 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
01100111 => 10011000 => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
01101011 => 10010100 => [1,3,2,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 3
01101101 => 10010010 => [1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 3
01101110 => 10010001 => [1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
01110011 => 10001100 => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
01110101 => 10001010 => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
01110110 => 10001001 => [1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
01111100 => 10000011 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
01111101 => 10000010 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
01111110 => 10000001 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
01111111 => 10000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
10000000 => 01111111 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
10000001 => 01111110 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000010 => 01111101 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
10010111 => 01101000 => [2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10011011 => 01100100 => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
10011101 => 01100010 => [2,1,4,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10100000 => 01011111 => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
10100111 => 01011000 => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
10101010 => 01010101 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
10101110 => 01010001 => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
10110011 => 01001100 => [2,3,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
10110110 => 01001001 => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
10111001 => 01000110 => [2,4,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
10111010 => 01000101 => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
10111110 => 01000001 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
10111111 => 01000000 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
11000000 => 00111111 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
11000111 => 00111000 => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
11001011 => 00110100 => [3,1,2,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
11001101 => 00110010 => [3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
11001110 => 00110001 => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
11010011 => 00101100 => [3,2,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
11010101 => 00101010 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
11010110 => 00101001 => [3,2,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
11011001 => 00100110 => [3,3,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
11011010 => 00100101 => [3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
11011100 => 00100011 => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
11011111 => 00100000 => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
11100000 => 00011111 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
11100011 => 00011100 => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 4
11100101 => 00011010 => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 4
11100110 => 00011001 => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 4
11101001 => 00010110 => [4,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] => 4
11101010 => 00010101 => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
11101100 => 00010011 => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 4
11101111 => 00010000 => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
11110000 => 00001111 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
11110111 => 00001000 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 5
11111000 => 00000111 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 6
11111011 => 00000100 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 6
11111100 => 00000011 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
11111101 => 00000010 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
11111110 => 00000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
11111111 => 00000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
000000000 => 111111111 => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
000000001 => 111111110 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
000000101 => 111111010 => [1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
000001000 => 111110111 => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
000010101 => 111101010 => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
001010101 => 110101010 => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
001111110 => 110000001 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
001111111 => 110000000 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
010101010 => 101010101 => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
010110111 => 101001000 => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
010111011 => 101000100 => [1,2,4,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
011010111 => 100101000 => [1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
011011101 => 100100010 => [1,3,4,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
011101011 => 100010100 => [1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 4
011101101 => 100010010 => [1,4,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => 4
011111100 => 100000011 => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
011111110 => 100000001 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
011111111 => 100000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
100000000 => 011111111 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
100000001 => 011111110 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100110111 => 011001000 => [2,1,3,4] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
100111011 => 011000100 => [2,1,4,3] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
101010101 => 010101010 => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
101100111 => 010011000 => [2,3,1,4] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
101101110 => 010010001 => [2,3,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
101110011 => 010001100 => [2,4,1,3] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
101110110 => 010001001 => [2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
101111111 => 010000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
110000000 => 001111111 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
110010111 => 001101000 => [3,1,2,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
110011101 => 001100010 => [3,1,4,2] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
110100111 => 001011000 => [3,2,1,4] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
110101110 => 001010001 => [3,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
110111001 => 001000110 => [3,4,1,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
110111010 => 001000101 => [3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
110111111 => 001000000 => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
111000000 => 000111111 => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
111001011 => 000110100 => [4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
111001101 => 000110010 => [4,1,3,2] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
111010011 => 000101100 => [4,2,1,3] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
111010110 => 000101001 => [4,2,3,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
111011001 => 000100110 => [4,3,1,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
111011010 => 000100101 => [4,3,2,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
111011111 => 000100000 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
111100000 => 000011111 => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
111101111 => 000010000 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
111110000 => 000001111 => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 6
111110111 => 000001000 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 6
111111000 => 000000111 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 7
111111011 => 000000100 => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 7
111111100 => 000000011 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
111111101 => 000000010 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
111111110 => 000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
111111111 => 000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
1111111110 => 0000000001 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 10
=> => [1] => [1,0] => 1
0111111111 => 1000000000 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
0000000001 => 1111111110 => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0011111110 => 1100000001 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
00000000000 => 11111111111 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0111111100 => 1000000011 => [1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
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Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
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
bounce path
Description
The bounce path determined by an integer composition.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.