Identifier
Values
0 => [1] => [1,0] => [1] => 0
1 => [1] => [1,0] => [1] => 0
00 => [2] => [1,1,0,0] => [1,2] => 0
01 => [1,1] => [1,0,1,0] => [2,1] => 0
10 => [1,1] => [1,0,1,0] => [2,1] => 0
11 => [2] => [1,1,0,0] => [1,2] => 0
000 => [3] => [1,1,1,0,0,0] => [1,2,3] => 0
001 => [2,1] => [1,1,0,0,1,0] => [3,1,2] => 0
010 => [1,1,1] => [1,0,1,0,1,0] => [3,2,1] => 0
011 => [1,2] => [1,0,1,1,0,0] => [2,3,1] => 0
100 => [1,2] => [1,0,1,1,0,0] => [2,3,1] => 0
101 => [1,1,1] => [1,0,1,0,1,0] => [3,2,1] => 0
110 => [2,1] => [1,1,0,0,1,0] => [3,1,2] => 0
111 => [3] => [1,1,1,0,0,0] => [1,2,3] => 0
0000 => [4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
0001 => [3,1] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 0
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 0
0011 => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 0
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 0
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 0
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 0
0111 => [1,3] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 0
1000 => [1,3] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => 0
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => [4,2,3,1] => 0
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => 0
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => 0
1100 => [2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => 0
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => [4,3,1,2] => 0
1110 => [3,1] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => 0
1111 => [4] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 0
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 0
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 0
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 0
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 0
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 0
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 0
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 0
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 0
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 0
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 0
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => 0
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => 0
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => 0
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => 0
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 0
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => 0
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => 0
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => 0
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => 0
11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => 0
11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => 0
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => 0
11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => 0
11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => 0
11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => 0
000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 0
000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 0
000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 0
000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 0
000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 0
000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 0
000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 0
000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 0
001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 0
001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 0
001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 0
001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 0
001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 0
001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 0
001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 0
001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 0
010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 0
010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 0
010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 0
010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 0
010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 0
010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 0
010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 0
010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 0
011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 0
011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 0
011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 0
011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 0
011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 0
011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 0
011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 0
011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => 0
100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => 0
100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => 0
100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => 0
100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => 0
100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => 0
>>> Load all 361 entries. <<<
100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => 0
101000 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => 0
101001 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => 0
101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 0
101011 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => 0
101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => 0
101101 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => 0
101110 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => 0
101111 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => 0
110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => 0
110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => 0
110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => 0
110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => 0
110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => 0
110101 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => 0
110110 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => 0
110111 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => 0
111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => 0
111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => 0
111010 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => 0
111011 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => 0
111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => 0
111101 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => 0
111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => 0
111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => 0
0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 0
0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 0
0000010 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 0
0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 0
0000101 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 0
0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 0
0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 0
0001010 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 0
0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 0
0001101 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 0
0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 0
0010101 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 0
0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 0
0011010 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 0
0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 0
0101010 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 0
0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => 0
1010101 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 0
1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => 0
1100101 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => 0
1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => 0
1101010 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => 0
1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => 0
1110010 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => 0
1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => 0
1110101 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => 0
1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => 0
1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => 0
1111010 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => 0
1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => 0
1111101 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => 0
1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => 0
1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => 0
00000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 0
00000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 0
00000010 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 0
00000011 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0
00000101 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 0
00000110 => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 0
00000111 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0
00001010 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 0
00001100 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 0
00001101 => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => 0
00001110 => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => 0
00001111 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0
00010001 => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 0
00010101 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 0
00010111 => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 0
00011001 => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 0
00011010 => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => 0
00011100 => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 0
00011101 => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => 0
00100101 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 0
00101001 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 0
00101010 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => 0
00101011 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 0
00101101 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 0
00110000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 0
00110010 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 0
00110011 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 0
00110101 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => 0
00111100 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 0
00111111 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0
01000111 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => 0
01001001 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 0
01001011 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 0
01001101 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 0
01010011 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 0
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] => [8,7,6,5,4,3,2,1] => 0
01011001 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => 0
01011011 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 0
01100101 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => 0
01101001 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 0
01101011 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 0
01101101 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 0
01110001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => 0
01110111 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 0
01111111 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
10000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => 0
10001000 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => 0
10001110 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => 0
10010010 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => 0
10010100 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => 0
10010110 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => 0
10011010 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => 0
10100100 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => 0
10100110 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => 0
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] => [8,7,6,5,4,3,2,1] => 0
10101100 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => 0
10110010 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => 0
10110100 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => 0
10110110 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => 0
10111000 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => 0
11000000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => 0
11000011 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => 0
11001010 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => 0
11001100 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => 0
11001101 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => 0
11001111 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => 0
11010010 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => 0
11010100 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => 0
11010101 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => 0
11010110 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => 0
11011010 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => 0
11100010 => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => 0
11100011 => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => 0
11100101 => [3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => 0
11100110 => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => 0
11101000 => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => 0
11101010 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => 0
11101110 => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => 0
11110000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => 0
11110001 => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => 0
11110010 => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => 0
11110011 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => 0
11110101 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => 0
11111000 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => 0
11111001 => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => 0
11111010 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => 0
11111100 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => 0
11111101 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => 0
11111110 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => 0
11111111 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => 0
000000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 0
000000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => 0
000000010 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => 0
000000011 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => 0
000000101 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => 0
000000110 => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => 0
000000111 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => 0
000001010 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => 0
000001101 => [5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => 0
000001110 => [5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => 0
000001111 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 0
000010101 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => 0
000011001 => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => 0
000011010 => [4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => 0
000011100 => [4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => 0
000011101 => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => 0
000011110 => [4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => 0
000101010 => [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] => [9,8,7,6,5,4,1,2,3] => 0
000110011 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => 0
000110101 => [3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => 0
000111000 => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => 0
000111010 => [3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => 0
001010101 => [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] => [9,8,7,6,5,4,3,1,2] => 0
001100101 => [2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => 0
001100110 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => 0
001101010 => [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] => [9,8,7,6,5,3,4,1,2] => 0
010101010 => [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] => [9,8,7,6,5,4,3,2,1] => 0
011111111 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
100000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => 0
101010101 => [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] => [9,8,7,6,5,4,3,2,1] => 0
110010101 => [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] => [9,8,7,6,5,3,4,1,2] => 0
110011001 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,3,4,1,2] => 0
110011010 => [2,2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,3,4,1,2] => 0
110101010 => [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] => [9,8,7,6,5,4,3,1,2] => 0
111000101 => [3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => 0
111000111 => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => 0
111001010 => [3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => 0
111001100 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => 0
111010101 => [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] => [9,8,7,6,5,4,1,2,3] => 0
111100001 => [4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => 0
111100010 => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => 0
111100011 => [4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => 0
111100101 => [4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => 0
111100110 => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => 0
111101010 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => 0
111110000 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => 0
111110001 => [5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => 0
111110010 => [5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => 0
111110101 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => 0
111111000 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => 0
111111001 => [6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => 0
111111010 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => 0
111111100 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => 0
111111101 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => 0
111111110 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => 0
111111111 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => 0
1010101010 => [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] => [10,9,8,7,6,5,4,3,2,1] => 0
1100101010 => [2,2,1,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => 0
1100110010 => [2,2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => 0
1110001100 => [3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => 0
1111000010 => [4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => 0
1111100000 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 0
1111111111 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 0
1111111110 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => 0
1111111101 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => 0
1111111100 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => 0
1111111010 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => 0
1111111001 => [7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => 0
1111110101 => [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] => [10,9,8,7,1,2,3,4,5,6] => 0
1111110001 => [6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => 0
1111110000 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 0
1111101010 => [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] => [10,9,8,7,6,1,2,3,4,5] => 0
1111100001 => [5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => 0
1111010101 => [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] => [10,9,8,7,6,5,1,2,3,4] => 0
1111001100 => [4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => 0
1111000111 => [4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => 0
1111000011 => [4,4,2] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => 0
1110101010 => [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] => [10,9,8,7,6,5,4,1,2,3] => 0
1110011001 => [3,2,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => 0
1110010101 => [3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => 0
1101010101 => [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] => [10,9,8,7,6,5,4,3,1,2] => 0
1100110101 => [2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => 0
1100110011 => [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] => [9,10,7,8,5,6,3,4,1,2] => 0
1000000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
10000000000 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
11111111110 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0
0111111111 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => 0
0000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => 0
01111111111 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => 0
00000000001 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => 0
0101010101 => [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] => [10,9,8,7,6,5,4,3,2,1] => 0
0001110011 => [3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => 0
0000111101 => [4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => 0
0000011111 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => 0
0000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => 0
0000000110 => [7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => 0
0000011110 => [5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => 0
0010101010 => [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] => [10,9,8,7,6,5,4,3,1,2] => 0
0000000010 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => 0
0000001110 => [6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => 0
0000001010 => [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] => [10,9,8,7,1,2,3,4,5,6] => 0
0011001010 => [2,2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => 0
0011001100 => [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] => [9,10,7,8,5,6,3,4,1,2] => 0
0000000101 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => 0
0000010101 => [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] => [10,9,8,7,6,1,2,3,4,5] => 0
0000011001 => [5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => 0
0000110011 => [4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => 0
0000000011 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => 0
0001010101 => [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] => [10,9,8,7,6,5,4,1,2,3] => 0
0000000111 => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => 0
0000001111 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => 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 occurrences of the pattern 213 in a permutation.
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
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].