Identifier
Values
00 => [2] => [1,1] => [1,0,1,0] => 1
01 => [1,1] => [2] => [1,1,0,0] => 2
10 => [1,1] => [2] => [1,1,0,0] => 2
11 => [2] => [1,1] => [1,0,1,0] => 1
000 => [3] => [1,1,1] => [1,0,1,0,1,0] => 1
001 => [2,1] => [1,2] => [1,0,1,1,0,0] => 2
010 => [1,1,1] => [3] => [1,1,1,0,0,0] => 3
011 => [1,2] => [2,1] => [1,1,0,0,1,0] => 2
100 => [1,2] => [2,1] => [1,1,0,0,1,0] => 2
101 => [1,1,1] => [3] => [1,1,1,0,0,0] => 3
110 => [2,1] => [1,2] => [1,0,1,1,0,0] => 2
111 => [3] => [1,1,1] => [1,0,1,0,1,0] => 1
0000 => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
0001 => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
0010 => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 3
0011 => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
0100 => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 3
0101 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
0110 => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
0111 => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
1000 => [1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
1001 => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
1010 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
1011 => [1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 3
1100 => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
1101 => [2,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 3
1110 => [3,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1111 => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
00000 => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
00001 => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
00010 => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
00011 => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
00100 => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
00101 => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
00110 => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
00111 => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
01000 => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
01001 => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
01010 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
01011 => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
01100 => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
01101 => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
01110 => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
01111 => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
10000 => [1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
10001 => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
10010 => [1,2,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
10011 => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
10100 => [1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
10101 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
10110 => [1,1,2,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
10111 => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
11000 => [2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
11001 => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
11010 => [2,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
11011 => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
11100 => [3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
11101 => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
11110 => [4,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
11111 => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
000000 => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
000001 => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
000010 => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
000011 => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
000100 => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
000101 => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
000110 => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
000111 => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
001000 => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
001001 => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
001010 => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
001011 => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
001100 => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
001101 => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
001110 => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
001111 => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
010000 => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
010001 => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
010010 => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
010011 => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
010100 => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
010101 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
010110 => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
010111 => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
011000 => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
011001 => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
011010 => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
011011 => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
011100 => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
011101 => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
011110 => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
011111 => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
100000 => [1,5] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
100001 => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
100010 => [1,3,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
100011 => [1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
100100 => [1,2,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
100101 => [1,2,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
100110 => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
100111 => [1,2,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
101000 => [1,1,1,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
>>> Load all 444 entries. <<<
101001 => [1,1,1,2,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
101010 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
101011 => [1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
101100 => [1,1,2,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
101101 => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
101110 => [1,1,3,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
101111 => [1,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
110000 => [2,4] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
110001 => [2,3,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
110010 => [2,2,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
110011 => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
110100 => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
110101 => [2,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
110110 => [2,1,2,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
110111 => [2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
111000 => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
111001 => [3,2,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
111010 => [3,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
111011 => [3,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
111100 => [4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
111101 => [4,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
111110 => [5,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
111111 => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000000 => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000001 => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0000010 => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
0000011 => [5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
0000100 => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
0000101 => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
0000110 => [4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
0000111 => [4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
0001000 => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
0001001 => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0001010 => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
0001011 => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
0001100 => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
0001101 => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
0001110 => [3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
0001111 => [3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
0010000 => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
0010001 => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
0010010 => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
0010011 => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
0010100 => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
0010101 => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
0010110 => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0010111 => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
0011000 => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
0011001 => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0011010 => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0011011 => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
0011100 => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
0011101 => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
0011110 => [2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
0011111 => [2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
0100000 => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
0100001 => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
0100010 => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
0100011 => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
0100100 => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
0100101 => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0100110 => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
0100111 => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
0101000 => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
0101001 => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
0101010 => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
0101011 => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
0101100 => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
0101101 => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
0101110 => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
0101111 => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
0110000 => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
0110001 => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
0110010 => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
0110011 => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
0110100 => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0110101 => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0110110 => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
0110111 => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
0111000 => [1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
0111001 => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
0111010 => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
0111011 => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
0111100 => [1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
0111101 => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
0111110 => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
0111111 => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
1000000 => [1,6] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
1000001 => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
1000010 => [1,4,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
1000011 => [1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
1000100 => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
1000101 => [1,3,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
1000110 => [1,3,2,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
1000111 => [1,3,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
1001000 => [1,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
1001001 => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
1001010 => [1,2,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1001011 => [1,2,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1001100 => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
1001101 => [1,2,2,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
1001110 => [1,2,3,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
1001111 => [1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
1010000 => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
1010001 => [1,1,1,3,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
1010010 => [1,1,1,2,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
1010011 => [1,1,1,2,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
1010100 => [1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
1010101 => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
1010110 => [1,1,1,1,2,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
1010111 => [1,1,1,1,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
1011000 => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
1011001 => [1,1,2,2,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
1011010 => [1,1,2,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1011011 => [1,1,2,1,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
1011100 => [1,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
1011101 => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
1011110 => [1,1,4,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
1011111 => [1,1,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
1100000 => [2,5] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
1100001 => [2,4,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
1100010 => [2,3,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
1100011 => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
1100100 => [2,2,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
1100101 => [2,2,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1100110 => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1100111 => [2,2,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
1101000 => [2,1,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
1101001 => [2,1,1,2,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1101010 => [2,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1101011 => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
1101100 => [2,1,2,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
1101101 => [2,1,2,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
1101110 => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
1101111 => [2,1,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
1110000 => [3,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
1110001 => [3,3,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
1110010 => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
1110011 => [3,2,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
1110100 => [3,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
1110101 => [3,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
1110110 => [3,1,2,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
1110111 => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
1111000 => [4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
1111001 => [4,2,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1111010 => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
1111011 => [4,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
1111100 => [5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
1111101 => [5,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
1111110 => [6,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1111111 => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
00000000 => [8] => [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
00000001 => [7,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
00000010 => [6,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
00000011 => [6,2] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
00000100 => [5,1,2] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
00000101 => [5,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
00000110 => [5,2,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
00000111 => [5,3] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
00001000 => [4,1,3] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
00001001 => [4,1,2,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
00001010 => [4,1,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
00001011 => [4,1,1,2] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
00001100 => [4,2,2] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
00001101 => [4,2,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
00001110 => [4,3,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
00001111 => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
00010000 => [3,1,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
00010001 => [3,1,3,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
00010010 => [3,1,2,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
00010011 => [3,1,2,2] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
00010100 => [3,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
00010101 => [3,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
00010110 => [3,1,1,2,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
00010111 => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
00011000 => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
00011001 => [3,2,2,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
00011010 => [3,2,1,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
00011011 => [3,2,1,2] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
00011100 => [3,3,2] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
00011101 => [3,3,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
00011110 => [3,4,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
00011111 => [3,5] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
00100000 => [2,1,5] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
00100001 => [2,1,4,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
00100010 => [2,1,3,1,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
00100011 => [2,1,3,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
00100100 => [2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
00100101 => [2,1,2,1,1,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
00100110 => [2,1,2,2,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
00100111 => [2,1,2,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
00101000 => [2,1,1,1,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
00101001 => [2,1,1,1,2,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
00101010 => [2,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
00101011 => [2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
00101100 => [2,1,1,2,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
00101101 => [2,1,1,2,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
00101110 => [2,1,1,3,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
00101111 => [2,1,1,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
00110000 => [2,2,4] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
00110001 => [2,2,3,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
00110010 => [2,2,2,1,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
00110011 => [2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
00110100 => [2,2,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
00110101 => [2,2,1,1,1,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
00110110 => [2,2,1,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
00110111 => [2,2,1,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
00111000 => [2,3,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
00111001 => [2,3,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
00111010 => [2,3,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
00111011 => [2,3,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
00111100 => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
00111101 => [2,4,1,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
00111110 => [2,5,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
00111111 => [2,6] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
01100000 => [1,2,5] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
01100001 => [1,2,4,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
01100010 => [1,2,3,1,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
01100011 => [1,2,3,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
01100100 => [1,2,2,1,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
01100101 => [1,2,2,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
01100110 => [1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
01100111 => [1,2,2,3] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
01101000 => [1,2,1,1,3] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
01101001 => [1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01101010 => [1,2,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
01101011 => [1,2,1,1,1,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
01101100 => [1,2,1,2,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
01101101 => [1,2,1,2,1,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
01101110 => [1,2,1,3,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
01101111 => [1,2,1,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
01110000 => [1,3,4] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
01110001 => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
01110010 => [1,3,2,1,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
01110011 => [1,3,2,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
01110100 => [1,3,1,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
01110101 => [1,3,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
01110110 => [1,3,1,2,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
01110111 => [1,3,1,3] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
01111000 => [1,4,3] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
01111001 => [1,4,2,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
01111010 => [1,4,1,1,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
01111011 => [1,4,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
01111100 => [1,5,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
01111101 => [1,5,1,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
01111110 => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
01111111 => [1,7] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
10000000 => [1,7] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
10000001 => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000010 => [1,5,1,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
10000011 => [1,5,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
10000100 => [1,4,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
10000101 => [1,4,1,1,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
10000110 => [1,4,2,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
10000111 => [1,4,3] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
10001000 => [1,3,1,3] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
10001001 => [1,3,1,2,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
10001010 => [1,3,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
10001011 => [1,3,1,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
10001100 => [1,3,2,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
10001101 => [1,3,2,1,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
10001110 => [1,3,3,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
10001111 => [1,3,4] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
10010000 => [1,2,1,4] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
10010001 => [1,2,1,3,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
10010010 => [1,2,1,2,1,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
10010011 => [1,2,1,2,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
10010100 => [1,2,1,1,1,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
10010101 => [1,2,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
10010110 => [1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10010111 => [1,2,1,1,3] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
10011000 => [1,2,2,3] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
10011001 => [1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
10011010 => [1,2,2,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10011011 => [1,2,2,1,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
10011100 => [1,2,3,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
10011101 => [1,2,3,1,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
10011110 => [1,2,4,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
10011111 => [1,2,5] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11000000 => [2,6] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
11000001 => [2,5,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
11000010 => [2,4,1,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
11000011 => [2,4,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
11000100 => [2,3,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
11000101 => [2,3,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
11000110 => [2,3,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
11000111 => [2,3,3] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
11001000 => [2,2,1,3] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
11001001 => [2,2,1,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
11001010 => [2,2,1,1,1,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
11001011 => [2,2,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
11001100 => [2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
11001101 => [2,2,2,1,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
11001110 => [2,2,3,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
11001111 => [2,2,4] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
11010000 => [2,1,1,4] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
11010001 => [2,1,1,3,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
11010010 => [2,1,1,2,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
11010011 => [2,1,1,2,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
11010100 => [2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
11010101 => [2,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
11010110 => [2,1,1,1,2,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
11010111 => [2,1,1,1,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
11011000 => [2,1,2,3] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
11011001 => [2,1,2,2,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
11011010 => [2,1,2,1,1,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
11011011 => [2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
11011100 => [2,1,3,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
11011101 => [2,1,3,1,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
11011110 => [2,1,4,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
11011111 => [2,1,5] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
11100000 => [3,5] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11100001 => [3,4,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
11100010 => [3,3,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
11100011 => [3,3,2] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
11100100 => [3,2,1,2] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
11100101 => [3,2,1,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
11100110 => [3,2,2,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
11100111 => [3,2,3] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
11101000 => [3,1,1,3] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
11101001 => [3,1,1,2,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
11101010 => [3,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
11101011 => [3,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
11101100 => [3,1,2,2] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
11101101 => [3,1,2,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
11101110 => [3,1,3,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
11101111 => [3,1,4] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
11110000 => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
11110001 => [4,3,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
11110010 => [4,2,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
11110011 => [4,2,2] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
11110100 => [4,1,1,2] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
11110101 => [4,1,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
11110110 => [4,1,2,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
11110111 => [4,1,3] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
11111000 => [5,3] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
11111001 => [5,2,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
11111010 => [5,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
11111011 => [5,1,2] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
11111100 => [6,2] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
11111101 => [6,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
11111110 => [7,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
11111111 => [8] => [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
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Description
The length of the maximal rise of a Dyck path.
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 $w$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.