Identifier
Values
00 => 00 => [2] => [1,1,0,0] => 0
01 => 10 => [1,1] => [1,0,1,0] => 0
10 => 01 => [1,1] => [1,0,1,0] => 0
11 => 11 => [2] => [1,1,0,0] => 0
000 => 000 => [3] => [1,1,1,0,0,0] => 0
001 => 100 => [1,2] => [1,0,1,1,0,0] => 0
010 => 001 => [2,1] => [1,1,0,0,1,0] => 0
011 => 101 => [1,1,1] => [1,0,1,0,1,0] => 0
100 => 010 => [1,1,1] => [1,0,1,0,1,0] => 0
101 => 110 => [2,1] => [1,1,0,0,1,0] => 0
110 => 011 => [1,2] => [1,0,1,1,0,0] => 0
111 => 111 => [3] => [1,1,1,0,0,0] => 0
0000 => 0000 => [4] => [1,1,1,1,0,0,0,0] => 0
0001 => 1000 => [1,3] => [1,0,1,1,1,0,0,0] => 0
0010 => 0001 => [3,1] => [1,1,1,0,0,0,1,0] => 0
0011 => 1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
0100 => 0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
0101 => 1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0110 => 0011 => [2,2] => [1,1,0,0,1,1,0,0] => 0
0111 => 1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
1000 => 0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
1001 => 1100 => [2,2] => [1,1,0,0,1,1,0,0] => 0
1010 => 0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1011 => 1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
1100 => 0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
1101 => 1110 => [3,1] => [1,1,1,0,0,0,1,0] => 0
1110 => 0111 => [1,3] => [1,0,1,1,1,0,0,0] => 0
1111 => 1111 => [4] => [1,1,1,1,0,0,0,0] => 0
00000 => 00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
00001 => 10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
00010 => 00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
00011 => 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
00100 => 00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
00101 => 10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
00110 => 00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
00111 => 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
01000 => 00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
01001 => 10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
01010 => 00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
01011 => 10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
01100 => 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
01101 => 10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
01110 => 00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
01111 => 10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
10000 => 01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 0
10001 => 11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 0
10010 => 01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
10011 => 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
10100 => 01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
10101 => 11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
10110 => 01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
10111 => 11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
11000 => 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
11001 => 11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 0
11010 => 01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
11011 => 11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 0
11100 => 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 0
11101 => 11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 0
11110 => 01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 0
11111 => 11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 0
000000 => 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
000001 => 100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
000010 => 000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
000011 => 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
000100 => 000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
000101 => 100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
000110 => 000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
000111 => 100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
001000 => 000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
001001 => 100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
001010 => 000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
001011 => 100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
001100 => 000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
001101 => 100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
001110 => 000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
001111 => 100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
010000 => 001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
010001 => 101000 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
010010 => 001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
010011 => 101001 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
010100 => 001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
010101 => 101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
010110 => 001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
010111 => 101011 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
011000 => 001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
011001 => 101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
011010 => 001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
011011 => 101101 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
011100 => 001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
011101 => 101110 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
011110 => 001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
011111 => 101111 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
100000 => 010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
100001 => 110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
100010 => 010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
100011 => 110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
100100 => 010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
100101 => 110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
100110 => 010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
100111 => 110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
101000 => 010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
>>> Load all 444 entries. <<<
101001 => 110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
101010 => 010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
101011 => 110101 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
101100 => 010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
101101 => 110110 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
101110 => 010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
101111 => 110111 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
110000 => 011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
110001 => 111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
110010 => 011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
110011 => 111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
110100 => 011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
110101 => 111010 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 0
110110 => 011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
110111 => 111011 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
111000 => 011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
111001 => 111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
111010 => 011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
111011 => 111101 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
111100 => 011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
111101 => 111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
111110 => 011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
111111 => 111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
0000000 => 0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
0000001 => 1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
0000010 => 0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
0000011 => 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
0000100 => 0000010 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
0000101 => 1000010 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
0000110 => 0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
0000111 => 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
0001000 => 0000100 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
0001001 => 1000100 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
0001010 => 0000101 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
0001011 => 1000101 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
0001100 => 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
0001101 => 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
0001110 => 0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
0001111 => 1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
0010000 => 0001000 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
0010001 => 1001000 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
0010010 => 0001001 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
0010011 => 1001001 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
0010100 => 0001010 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
0010101 => 1001010 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
0010110 => 0001011 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
0010111 => 1001011 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
0011000 => 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
0011001 => 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
0011010 => 0001101 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
0011011 => 1001101 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
0011100 => 0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
0011101 => 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
0011110 => 0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
0011111 => 1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
0100000 => 0010000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
0100001 => 1010000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
0100010 => 0010001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
0100011 => 1010001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
0100100 => 0010010 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
0100101 => 1010010 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
0100110 => 0010011 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
0100111 => 1010011 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
0101000 => 0010100 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
0101001 => 1010100 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
0101010 => 0010101 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
0101011 => 1010101 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
0101100 => 0010110 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
0101101 => 1010110 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
0101110 => 0010111 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
0101111 => 1010111 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
0110000 => 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
0110001 => 1011000 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
0110010 => 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
0110011 => 1011001 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
0110100 => 0011010 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
0110101 => 1011010 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
0110110 => 0011011 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
0110111 => 1011011 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
0111000 => 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
0111001 => 1011100 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
0111010 => 0011101 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
0111011 => 1011101 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
0111100 => 0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
0111101 => 1011110 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
0111110 => 0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
0111111 => 1011111 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
1000000 => 0100000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
1000001 => 1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
1000010 => 0100001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
1000011 => 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
1000100 => 0100010 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
1000101 => 1100010 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
1000110 => 0100011 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
1000111 => 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
1001000 => 0100100 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
1001001 => 1100100 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
1001010 => 0100101 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
1001011 => 1100101 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
1001100 => 0100110 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
1001101 => 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
1001110 => 0100111 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
1001111 => 1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
1010000 => 0101000 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
1010001 => 1101000 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
1010010 => 0101001 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
1010011 => 1101001 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
1010100 => 0101010 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
1010101 => 1101010 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
1010110 => 0101011 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
1010111 => 1101011 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
1011000 => 0101100 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
1011001 => 1101100 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
1011010 => 0101101 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
1011011 => 1101101 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
1011100 => 0101110 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
1011101 => 1101110 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
1011110 => 0101111 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
1011111 => 1101111 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
1100000 => 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
1100001 => 1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
1100010 => 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
1100011 => 1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
1100100 => 0110010 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
1100101 => 1110010 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
1100110 => 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
1100111 => 1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
1101000 => 0110100 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
1101001 => 1110100 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
1101010 => 0110101 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
1101011 => 1110101 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
1101100 => 0110110 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
1101101 => 1110110 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
1101110 => 0110111 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
1101111 => 1110111 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
1110000 => 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
1110001 => 1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
1110010 => 0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
1110011 => 1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
1110100 => 0111010 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
1110101 => 1111010 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
1110110 => 0111011 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
1110111 => 1111011 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
1111000 => 0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
1111001 => 1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
1111010 => 0111101 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
1111011 => 1111101 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
1111100 => 0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
1111101 => 1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
1111110 => 0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
1111111 => 1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
00000001 => 10000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
00000011 => 10000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
00000101 => 10000010 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
00000111 => 10000011 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
00001001 => 10000100 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
00001011 => 10000101 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
00001101 => 10000110 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
00001111 => 10000111 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
00010001 => 10001000 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
00010011 => 10001001 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
00010101 => 10001010 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
00010111 => 10001011 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
00011001 => 10001100 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
00011011 => 10001101 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
00011101 => 10001110 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
00011111 => 10001111 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
00100001 => 10010000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
00100011 => 10010001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
00100101 => 10010010 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
00100111 => 10010011 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
00101001 => 10010100 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
00101011 => 10010101 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
00101101 => 10010110 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
00101111 => 10010111 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
00110001 => 10011000 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
00110011 => 10011001 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
00110101 => 10011010 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
00110111 => 10011011 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
00111001 => 10011100 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
00111011 => 10011101 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
00111101 => 10011110 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
00111111 => 10011111 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
01000000 => 00100000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
01000001 => 10100000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
01000010 => 00100001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
01000011 => 10100001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
01000100 => 00100010 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
01000101 => 10100010 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
01000110 => 00100011 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
01000111 => 10100011 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
01001000 => 00100100 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
01001001 => 10100100 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
01001010 => 00100101 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
01001011 => 10100101 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
01001100 => 00100110 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
01001101 => 10100110 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
01001110 => 00100111 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
01001111 => 10100111 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
01010000 => 00101000 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
01010001 => 10101000 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
01010010 => 00101001 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
01010011 => 10101001 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
01010100 => 00101010 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
01010101 => 10101010 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
01010110 => 00101011 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
01010111 => 10101011 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
01011000 => 00101100 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
01011001 => 10101100 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
01011010 => 00101101 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
01011011 => 10101101 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
01011100 => 00101110 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
01011101 => 10101110 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
01011110 => 00101111 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
01011111 => 10101111 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
01100000 => 00110000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
01100001 => 10110000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
01100010 => 00110001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
01100011 => 10110001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
01100100 => 00110010 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
01100101 => 10110010 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
01100110 => 00110011 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
01100111 => 10110011 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
01101000 => 00110100 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
01101001 => 10110100 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
01101010 => 00110101 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
01101011 => 10110101 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
01101100 => 00110110 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
01101101 => 10110110 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
01101110 => 00110111 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
01101111 => 10110111 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
01110000 => 00111000 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
01110001 => 10111000 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
01110010 => 00111001 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
01110011 => 10111001 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
01110100 => 00111010 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
01110101 => 10111010 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
01110110 => 00111011 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
01110111 => 10111011 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
01111000 => 00111100 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
01111001 => 10111100 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
01111010 => 00111101 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
01111011 => 10111101 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
01111100 => 00111110 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
01111101 => 10111110 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
01111110 => 00111111 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
01111111 => 10111111 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
10000000 => 01000000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
10000001 => 11000000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
10000010 => 01000001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
10000011 => 11000001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
10000100 => 01000010 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
10000101 => 11000010 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 0
10000110 => 01000011 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
10000111 => 11000011 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
10001000 => 01000100 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
10001001 => 11000100 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
10001010 => 01000101 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
10001011 => 11000101 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 0
10001100 => 01000110 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
10001101 => 11000110 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
10001110 => 01000111 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
10001111 => 11000111 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
10010000 => 01001000 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
10010001 => 11001000 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
10010010 => 01001001 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
10010011 => 11001001 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
10010100 => 01001010 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
10010101 => 11001010 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
10010110 => 01001011 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
10010111 => 11001011 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
10011000 => 01001100 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
10011001 => 11001100 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
10011010 => 01001101 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
10011011 => 11001101 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
10011100 => 01001110 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
10011101 => 11001110 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
10011110 => 01001111 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
10011111 => 11001111 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
10100000 => 01010000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
10100001 => 11010000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 0
10100010 => 01010001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
10100011 => 11010001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 0
10100100 => 01010010 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
10100101 => 11010010 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
10100110 => 01010011 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
10100111 => 11010011 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
10101000 => 01010100 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
10101001 => 11010100 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
10101010 => 01010101 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
10101011 => 11010101 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
10101100 => 01010110 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
10101101 => 11010110 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
10101110 => 01010111 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
10101111 => 11010111 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 0
10110000 => 01011000 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
10110001 => 11011000 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
10110010 => 01011001 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
10110011 => 11011001 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
10110100 => 01011010 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
10110101 => 11011010 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
10110110 => 01011011 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
10110111 => 11011011 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
10111000 => 01011100 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
10111001 => 11011100 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
10111010 => 01011101 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
10111011 => 11011101 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 0
10111100 => 01011110 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
10111101 => 11011110 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 0
10111110 => 01011111 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
10111111 => 11011111 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
11000000 => 01100000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
11000010 => 01100001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
11000100 => 01100010 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 0
11000110 => 01100011 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
11001000 => 01100100 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
11001010 => 01100101 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
11001100 => 01100110 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
11001110 => 01100111 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
11010000 => 01101000 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 0
11010010 => 01101001 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
11010100 => 01101010 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
11010110 => 01101011 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
11011000 => 01101100 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
11011010 => 01101101 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
11011100 => 01101110 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 0
11011110 => 01101111 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
11100000 => 01110000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
11100010 => 01110001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
11100100 => 01110010 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 0
11100110 => 01110011 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
11101000 => 01110100 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 0
11101010 => 01110101 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 0
11101100 => 01110110 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 0
11101110 => 01110111 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
11110000 => 01111000 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
11110010 => 01111001 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
11110100 => 01111010 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 0
11110110 => 01111011 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
11111000 => 01111100 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
11111010 => 01111101 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 0
11111100 => 01111110 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
11111110 => 01111111 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of boxes weakly below the path and above the diagonal that lie below at least two peaks.
For example, the path $111011010000$ has three peaks in positions $03, 15, 26$. The boxes below $03$ are $01,02,\textbf{12}$, the boxes below $15$ are $\textbf{12},13,14,\textbf{23},\textbf{24},\textbf{34}$, and the boxes below $26$ are $\textbf{23},\textbf{24},25,\textbf{34},35,45$.
We thus obtain the four boxes in positions $12,23,24,34$ that are below at least two peaks.
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
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.