Identifier
Values
01 => [1,1] => [2] => [1,1,0,0] => 1
10 => [1,1] => [2] => [1,1,0,0] => 1
001 => [2,1] => [1,1] => [1,0,1,0] => 0
010 => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
011 => [1,2] => [1,1] => [1,0,1,0] => 0
100 => [1,2] => [1,1] => [1,0,1,0] => 0
101 => [1,1,1] => [3] => [1,1,1,0,0,0] => 1
110 => [2,1] => [1,1] => [1,0,1,0] => 0
0001 => [3,1] => [1,1] => [1,0,1,0] => 0
0010 => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 1
0011 => [2,2] => [2] => [1,1,0,0] => 1
0100 => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 1
0101 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
0110 => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0111 => [1,3] => [1,1] => [1,0,1,0] => 0
1000 => [1,3] => [1,1] => [1,0,1,0] => 0
1001 => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1010 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 1
1011 => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 1
1100 => [2,2] => [2] => [1,1,0,0] => 1
1101 => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 1
1110 => [3,1] => [1,1] => [1,0,1,0] => 0
00001 => [4,1] => [1,1] => [1,0,1,0] => 0
00010 => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 1
00011 => [3,2] => [1,1] => [1,0,1,0] => 0
00100 => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
00101 => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
00110 => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 1
00111 => [2,3] => [1,1] => [1,0,1,0] => 0
01000 => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 1
01001 => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
01010 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
01011 => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
01100 => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 1
01101 => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
01110 => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
01111 => [1,4] => [1,1] => [1,0,1,0] => 0
10000 => [1,4] => [1,1] => [1,0,1,0] => 0
10001 => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
10010 => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
10011 => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 1
10100 => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 1
10101 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
10110 => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
10111 => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 1
11000 => [2,3] => [1,1] => [1,0,1,0] => 0
11001 => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 1
11010 => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
11011 => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
11100 => [3,2] => [1,1] => [1,0,1,0] => 0
11101 => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 1
11110 => [4,1] => [1,1] => [1,0,1,0] => 0
000001 => [5,1] => [1,1] => [1,0,1,0] => 0
000010 => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 1
000011 => [4,2] => [1,1] => [1,0,1,0] => 0
000100 => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
000101 => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
000110 => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
000111 => [3,3] => [2] => [1,1,0,0] => 1
001000 => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
001001 => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001010 => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
001011 => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
001100 => [2,2,2] => [3] => [1,1,1,0,0,0] => 1
001101 => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
001110 => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
001111 => [2,4] => [1,1] => [1,0,1,0] => 0
010000 => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 1
010001 => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010010 => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
010011 => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
010100 => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
010110 => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
010111 => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
011000 => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
011001 => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
011010 => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
011011 => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011100 => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
011101 => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
011110 => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
011111 => [1,5] => [1,1] => [1,0,1,0] => 0
100000 => [1,5] => [1,1] => [1,0,1,0] => 0
100001 => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
100010 => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
100011 => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
100100 => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100101 => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
100110 => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
100111 => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
101000 => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
101001 => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
101011 => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
101100 => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
101101 => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
101110 => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101111 => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 1
110000 => [2,4] => [1,1] => [1,0,1,0] => 0
110001 => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
110010 => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
110011 => [2,2,2] => [3] => [1,1,1,0,0,0] => 1
>>> Load all 1289 entries. <<<
110100 => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
110101 => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
110110 => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110111 => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
111000 => [3,3] => [2] => [1,1,0,0] => 1
111001 => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
111010 => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
111011 => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
111100 => [4,2] => [1,1] => [1,0,1,0] => 0
111101 => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 1
111110 => [5,1] => [1,1] => [1,0,1,0] => 0
0000001 => [6,1] => [1,1] => [1,0,1,0] => 0
0000010 => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 1
0000011 => [5,2] => [1,1] => [1,0,1,0] => 0
0000100 => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
0000101 => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
0000110 => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0000111 => [4,3] => [1,1] => [1,0,1,0] => 0
0001000 => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
0001001 => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0001010 => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
0001011 => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0001100 => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 1
0001101 => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0001110 => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 1
0001111 => [3,4] => [1,1] => [1,0,1,0] => 0
0010000 => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
0010001 => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0010010 => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0010011 => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0010100 => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
0010110 => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0010111 => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0011000 => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 1
0011001 => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 1
0011010 => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
0011011 => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0011100 => [2,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
0011101 => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0011110 => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0011111 => [2,5] => [1,1] => [1,0,1,0] => 0
0100000 => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 1
0100001 => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0100010 => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
0100011 => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0100100 => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0100110 => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
0100111 => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0101000 => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
0101100 => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
0101110 => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
0101111 => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 1
0110000 => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
0110001 => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0110010 => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
0110011 => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
0110100 => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0110110 => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0110111 => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111000 => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 1
0111001 => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111010 => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
0111011 => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111100 => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
0111101 => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0111110 => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0111111 => [1,6] => [1,1] => [1,0,1,0] => 0
1000000 => [1,6] => [1,1] => [1,0,1,0] => 0
1000001 => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1000010 => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1000011 => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1000100 => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000101 => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
1000110 => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000111 => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 1
1001000 => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1001001 => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1001011 => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1001100 => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
1001101 => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
1001110 => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1001111 => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
1010000 => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 1
1010001 => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
1010011 => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
1010111 => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
1011000 => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011001 => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
1011011 => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011100 => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011101 => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
1011110 => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011111 => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 1
1100000 => [2,5] => [1,1] => [1,0,1,0] => 0
1100001 => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1100010 => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1100011 => [2,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1100100 => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1100101 => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
1100110 => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 1
1100111 => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 1
1101000 => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1101001 => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1101011 => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1101100 => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1101101 => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1101110 => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1101111 => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
1110000 => [3,4] => [1,1] => [1,0,1,0] => 0
1110001 => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 1
1110010 => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1110011 => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 1
1110100 => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1110101 => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
1110110 => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1110111 => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
1111000 => [4,3] => [1,1] => [1,0,1,0] => 0
1111001 => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1111010 => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
1111011 => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1111100 => [5,2] => [1,1] => [1,0,1,0] => 0
1111101 => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 1
1111110 => [6,1] => [1,1] => [1,0,1,0] => 0
00000001 => [7,1] => [1,1] => [1,0,1,0] => 0
00000010 => [6,1,1] => [1,2] => [1,0,1,1,0,0] => 1
00000011 => [6,2] => [1,1] => [1,0,1,0] => 0
00000100 => [5,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
00000101 => [5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
00000110 => [5,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
00000111 => [5,3] => [1,1] => [1,0,1,0] => 0
00001000 => [4,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
00001001 => [4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00001010 => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
00001011 => [4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
00001100 => [4,2,2] => [1,2] => [1,0,1,1,0,0] => 1
00001101 => [4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
00001110 => [4,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
00001111 => [4,4] => [2] => [1,1,0,0] => 1
00010000 => [3,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
00010001 => [3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00010010 => [3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
00010011 => [3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
00010100 => [3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
00010110 => [3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
00010111 => [3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
00011000 => [3,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
00011001 => [3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
00011010 => [3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
00011011 => [3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00011100 => [3,3,2] => [2,1] => [1,1,0,0,1,0] => 1
00011101 => [3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
00011110 => [3,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
00011111 => [3,5] => [1,1] => [1,0,1,0] => 0
00100000 => [2,1,5] => [1,1,1] => [1,0,1,0,1,0] => 0
00100001 => [2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00100010 => [2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
00100011 => [2,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00100100 => [2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
00100110 => [2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
00100111 => [2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00101000 => [2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
00101100 => [2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
00101110 => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
00101111 => [2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
00110000 => [2,2,4] => [2,1] => [1,1,0,0,1,0] => 1
00110001 => [2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
00110010 => [2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
00110011 => [2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => 1
00110100 => [2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
00110110 => [2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
00110111 => [2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
00111000 => [2,3,3] => [1,2] => [1,0,1,1,0,0] => 1
00111001 => [2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00111010 => [2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
00111011 => [2,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
00111100 => [2,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
00111101 => [2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
00111110 => [2,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
00111111 => [2,6] => [1,1] => [1,0,1,0] => 0
01000000 => [1,1,6] => [2,1] => [1,1,0,0,1,0] => 1
01000001 => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
01000010 => [1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
01000011 => [1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
01000100 => [1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
01000110 => [1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
01000111 => [1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 1
01001000 => [1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
01001100 => [1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
01001110 => [1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
01001111 => [1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
01010000 => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
01011000 => [1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
01011100 => [1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
01011110 => [1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
01011111 => [1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => 1
01100000 => [1,2,5] => [1,1,1] => [1,0,1,0,1,0] => 0
01100001 => [1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01100010 => [1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
01100011 => [1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01100100 => [1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
01100110 => [1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
01100111 => [1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
01101000 => [1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
01101100 => [1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
01101110 => [1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
01101111 => [1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01110000 => [1,3,4] => [1,1,1] => [1,0,1,0,1,0] => 0
01110001 => [1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
01110010 => [1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
01110011 => [1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
01110100 => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
01110110 => [1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
01110111 => [1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01111000 => [1,4,3] => [1,1,1] => [1,0,1,0,1,0] => 0
01111001 => [1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01111010 => [1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
01111011 => [1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01111100 => [1,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
01111101 => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
01111110 => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
01111111 => [1,7] => [1,1] => [1,0,1,0] => 0
10000000 => [1,7] => [1,1] => [1,0,1,0] => 0
10000001 => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
10000010 => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
10000011 => [1,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
10000100 => [1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000101 => [1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
10000110 => [1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000111 => [1,4,3] => [1,1,1] => [1,0,1,0,1,0] => 0
10001000 => [1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10001001 => [1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
10001011 => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
10001100 => [1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
10001101 => [1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
10001110 => [1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
10001111 => [1,3,4] => [1,1,1] => [1,0,1,0,1,0] => 0
10010000 => [1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10010001 => [1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
10010011 => [1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
10010111 => [1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
10011000 => [1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
10011001 => [1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
10011011 => [1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
10011100 => [1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10011101 => [1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
10011110 => [1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10011111 => [1,2,5] => [1,1,1] => [1,0,1,0,1,0] => 0
10100000 => [1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => 1
10100001 => [1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
10100011 => [1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
10100111 => [1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
10101111 => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
10110000 => [1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
10110001 => [1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
10110011 => [1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
10110111 => [1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
10111000 => [1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 1
10111001 => [1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
10111011 => [1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
10111100 => [1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
10111101 => [1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
10111110 => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
10111111 => [1,1,6] => [2,1] => [1,1,0,0,1,0] => 1
11000000 => [2,6] => [1,1] => [1,0,1,0] => 0
11000001 => [2,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11000010 => [2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
11000011 => [2,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
11000100 => [2,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11000101 => [2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
11000110 => [2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11000111 => [2,3,3] => [1,2] => [1,0,1,1,0,0] => 1
11001000 => [2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
11001001 => [2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
11001011 => [2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
11001100 => [2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => 1
11001101 => [2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
11001110 => [2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
11001111 => [2,2,4] => [2,1] => [1,1,0,0,1,0] => 1
11010000 => [2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
11010001 => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
11010011 => [2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
11010111 => [2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
11011000 => [2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11011001 => [2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
11011011 => [2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
11011100 => [2,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11011101 => [2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
11011110 => [2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11011111 => [2,1,5] => [1,1,1] => [1,0,1,0,1,0] => 0
11100000 => [3,5] => [1,1] => [1,0,1,0] => 0
11100001 => [3,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11100010 => [3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
11100011 => [3,3,2] => [2,1] => [1,1,0,0,1,0] => 1
11100100 => [3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11100101 => [3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
11100110 => [3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
11100111 => [3,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
11101000 => [3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
11101001 => [3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
11101011 => [3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
11101100 => [3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
11101101 => [3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
11101110 => [3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11101111 => [3,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
11110000 => [4,4] => [2] => [1,1,0,0] => 1
11110001 => [4,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11110010 => [4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
11110011 => [4,2,2] => [1,2] => [1,0,1,1,0,0] => 1
11110100 => [4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
11110101 => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
11110110 => [4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11110111 => [4,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
11111000 => [5,3] => [1,1] => [1,0,1,0] => 0
11111001 => [5,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11111010 => [5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
11111011 => [5,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
11111100 => [6,2] => [1,1] => [1,0,1,0] => 0
11111101 => [6,1,1] => [1,2] => [1,0,1,1,0,0] => 1
11111110 => [7,1] => [1,1] => [1,0,1,0] => 0
000000001 => [8,1] => [1,1] => [1,0,1,0] => 0
000000010 => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 1
000000011 => [7,2] => [1,1] => [1,0,1,0] => 0
000000100 => [6,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
000000101 => [6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
000000110 => [6,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
000000111 => [6,3] => [1,1] => [1,0,1,0] => 0
000001000 => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
000001001 => [5,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000001010 => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
000001011 => [5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000001100 => [5,2,2] => [1,2] => [1,0,1,1,0,0] => 1
000001101 => [5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
000001110 => [5,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
000001111 => [5,4] => [1,1] => [1,0,1,0] => 0
000010000 => [4,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
000010001 => [4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000010010 => [4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
000010011 => [4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
000010100 => [4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
000010110 => [4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
000010111 => [4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000011000 => [4,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
000011001 => [4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000011010 => [4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
000011011 => [4,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000011100 => [4,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
000011101 => [4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
000011110 => [4,4,1] => [2,1] => [1,1,0,0,1,0] => 1
000011111 => [4,5] => [1,1] => [1,0,1,0] => 0
000100000 => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 0
000100001 => [3,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000100010 => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
000100011 => [3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000100100 => [3,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
000100110 => [3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
000100111 => [3,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000101000 => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
000101100 => [3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
000101110 => [3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
000101111 => [3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000110000 => [3,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
000110001 => [3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000110010 => [3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
000110011 => [3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
000110100 => [3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
000110110 => [3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
000110111 => [3,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000111000 => [3,3,3] => [3] => [1,1,1,0,0,0] => 1
000111001 => [3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
000111010 => [3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
000111011 => [3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
000111100 => [3,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
000111101 => [3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
000111110 => [3,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
000111111 => [3,6] => [1,1] => [1,0,1,0] => 0
001000000 => [2,1,6] => [1,1,1] => [1,0,1,0,1,0] => 0
001000001 => [2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001000010 => [2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
001000011 => [2,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001000100 => [2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001000110 => [2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001000111 => [2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
001001000 => [2,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001001001 => [2,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
001001100 => [2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
001001110 => [2,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001001111 => [2,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001010000 => [2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
001011000 => [2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
001011100 => [2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
001011110 => [2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
001011111 => [2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
001100000 => [2,2,5] => [2,1] => [1,1,0,0,1,0] => 1
001100001 => [2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
001100010 => [2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
001100011 => [2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
001100100 => [2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
001100110 => [2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
001100111 => [2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
001101000 => [2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
001101100 => [2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
001101110 => [2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
001101111 => [2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
001110000 => [2,3,4] => [1,1,1] => [1,0,1,0,1,0] => 0
001110001 => [2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
001110010 => [2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
001110011 => [2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
001110100 => [2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
001110110 => [2,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001110111 => [2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111000 => [2,4,3] => [1,1,1] => [1,0,1,0,1,0] => 0
001111001 => [2,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111010 => [2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
001111011 => [2,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111100 => [2,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
001111101 => [2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
001111110 => [2,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
001111111 => [2,7] => [1,1] => [1,0,1,0] => 0
010000000 => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 1
010000001 => [1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010000010 => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
010000011 => [1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010000100 => [1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010000110 => [1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010000111 => [1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010001000 => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010001100 => [1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
010001110 => [1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
010001111 => [1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010010000 => [1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010011000 => [1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
010011100 => [1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010011110 => [1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010011111 => [1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
010100000 => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
010110000 => [1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
010111000 => [1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
010111100 => [1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
010111110 => [1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
010111111 => [1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => 1
011000000 => [1,2,6] => [1,1,1] => [1,0,1,0,1,0] => 0
011000001 => [1,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011000010 => [1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011000011 => [1,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011000100 => [1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011000110 => [1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011000111 => [1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
011001000 => [1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011001100 => [1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
011001110 => [1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011001111 => [1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
011010000 => [1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011011000 => [1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011011011 => [1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
011011100 => [1,2,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011011110 => [1,2,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011011111 => [1,2,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011100000 => [1,3,5] => [1,1,1] => [1,0,1,0,1,0] => 0
011100001 => [1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011100010 => [1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
011100011 => [1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
011100100 => [1,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011100110 => [1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011100111 => [1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011101000 => [1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011101100 => [1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011101110 => [1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011101111 => [1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011110000 => [1,4,4] => [1,2] => [1,0,1,1,0,0] => 1
011110001 => [1,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011110010 => [1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011110011 => [1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
011110100 => [1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011110110 => [1,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011110111 => [1,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011111000 => [1,5,3] => [1,1,1] => [1,0,1,0,1,0] => 0
011111001 => [1,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011111010 => [1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
011111011 => [1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011111100 => [1,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
011111101 => [1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
011111110 => [1,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
011111111 => [1,8] => [1,1] => [1,0,1,0] => 0
100000000 => [1,8] => [1,1] => [1,0,1,0] => 0
100000001 => [1,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
100000010 => [1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
100000011 => [1,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
100000100 => [1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100000101 => [1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
100000110 => [1,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100000111 => [1,5,3] => [1,1,1] => [1,0,1,0,1,0] => 0
100001000 => [1,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100001001 => [1,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100001011 => [1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100001100 => [1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
100001101 => [1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100001110 => [1,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100001111 => [1,4,4] => [1,2] => [1,0,1,1,0,0] => 1
100010000 => [1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100010001 => [1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100010011 => [1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100010111 => [1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100011000 => [1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100011001 => [1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100011011 => [1,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100011100 => [1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
100011101 => [1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
100011110 => [1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100011111 => [1,3,5] => [1,1,1] => [1,0,1,0,1,0] => 0
100100000 => [1,2,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100100001 => [1,2,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100100011 => [1,2,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100100100 => [1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
100100111 => [1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100101111 => [1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100110000 => [1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
100110001 => [1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100110011 => [1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
100110111 => [1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100111000 => [1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
100111001 => [1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100111011 => [1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100111100 => [1,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100111101 => [1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100111110 => [1,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100111111 => [1,2,6] => [1,1,1] => [1,0,1,0,1,0] => 0
101000000 => [1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => 1
101000001 => [1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
101000011 => [1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
101000111 => [1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
101001111 => [1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
101011111 => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
101100000 => [1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101100001 => [1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101100011 => [1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101100111 => [1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
101101111 => [1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101110000 => [1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101110001 => [1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
101110011 => [1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
101110111 => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101111000 => [1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101111001 => [1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101111011 => [1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101111100 => [1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101111101 => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
101111110 => [1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
101111111 => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 1
110000000 => [2,7] => [1,1] => [1,0,1,0] => 0
110000001 => [2,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
110000010 => [2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
110000011 => [2,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
110000100 => [2,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000101 => [2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
110000110 => [2,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000111 => [2,4,3] => [1,1,1] => [1,0,1,0,1,0] => 0
110001000 => [2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110001001 => [2,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110001011 => [2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
110001100 => [2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
110001101 => [2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
110001110 => [2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
110001111 => [2,3,4] => [1,1,1] => [1,0,1,0,1,0] => 0
110010000 => [2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
110010001 => [2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
110010011 => [2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
110010111 => [2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
110011000 => [2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
110011001 => [2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
110011011 => [2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
110011100 => [2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
110011101 => [2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
110011110 => [2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
110011111 => [2,2,5] => [2,1] => [1,1,0,0,1,0] => 1
110100000 => [2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
110100001 => [2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
110100011 => [2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
110100111 => [2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
110101111 => [2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
110110000 => [2,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110110001 => [2,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110110011 => [2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
110110110 => [2,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
110110111 => [2,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110111000 => [2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
110111001 => [2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110111011 => [2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110111100 => [2,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110111101 => [2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
110111110 => [2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110111111 => [2,1,6] => [1,1,1] => [1,0,1,0,1,0] => 0
111000000 => [3,6] => [1,1] => [1,0,1,0] => 0
111000001 => [3,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
111000010 => [3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
111000011 => [3,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
111000100 => [3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
111000101 => [3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
111000110 => [3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
111000111 => [3,3,3] => [3] => [1,1,1,0,0,0] => 1
111001000 => [3,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111001001 => [3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
111001011 => [3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
111001100 => [3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
111001101 => [3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
111001110 => [3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111001111 => [3,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
111010000 => [3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111010001 => [3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
111010011 => [3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
111010111 => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
111011000 => [3,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111011001 => [3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
111011011 => [3,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
111011100 => [3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111011101 => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
111011110 => [3,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111011111 => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 0
111100000 => [4,5] => [1,1] => [1,0,1,0] => 0
111100001 => [4,4,1] => [2,1] => [1,1,0,0,1,0] => 1
111100010 => [4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
111100011 => [4,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
111100100 => [4,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100101 => [4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
111100110 => [4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111100111 => [4,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
111101000 => [4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111101001 => [4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
111101011 => [4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
111101100 => [4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
111101101 => [4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
111101110 => [4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111101111 => [4,1,4] => [1,1,1] => [1,0,1,0,1,0] => 0
111110000 => [5,4] => [1,1] => [1,0,1,0] => 0
111110001 => [5,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
111110010 => [5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
111110011 => [5,2,2] => [1,2] => [1,0,1,1,0,0] => 1
111110100 => [5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111110101 => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
111110110 => [5,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110111 => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 0
111111000 => [6,3] => [1,1] => [1,0,1,0] => 0
111111001 => [6,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
111111010 => [6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
111111011 => [6,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
111111100 => [7,2] => [1,1] => [1,0,1,0] => 0
111111101 => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 1
111111110 => [8,1] => [1,1] => [1,0,1,0] => 0
1011110000 => [1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 1
1100111000 => [2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 1
1101110000 => [2,1,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1110001100 => [3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
1110011000 => [3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1110110000 => [3,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111000010 => [4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
1111000100 => [4,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111001000 => [4,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111010000 => [4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1111100000 => [5,5] => [2] => [1,1,0,0] => 1
101111100000 => [1,1,5,5] => [2,2] => [1,1,0,0,1,1,0,0] => 1
110011110000 => [2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 1
110110110000 => [2,1,2,1,2,4] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
110111001000 => [2,1,3,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
110111100000 => [2,1,4,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111000111000 => [3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => 1
111001110000 => [3,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111011000100 => [3,1,2,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
111011100000 => [3,1,3,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100001100 => [4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
111100011000 => [4,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100100100 => [4,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
111100110000 => [4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111101100000 => [4,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110000010 => [5,5,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
111110000100 => [5,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110001000 => [5,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110010000 => [5,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110100000 => [5,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111111000000 => [6,6] => [2] => [1,1,0,0] => 1
1111111110 => [9,1] => [1,1] => [1,0,1,0] => 0
1111111101 => [8,1,1] => [1,2] => [1,0,1,1,0,0] => 1
1111111100 => [8,2] => [1,1] => [1,0,1,0] => 0
1111111011 => [7,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1111111010 => [7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
1111111001 => [7,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1111110110 => [6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111110101 => [6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
1111110011 => [6,2,2] => [1,2] => [1,0,1,1,0,0] => 1
1111110010 => [6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1111110001 => [6,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1111110000 => [6,4] => [1,1] => [1,0,1,0] => 0
1111101001 => [5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1111101000 => [5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1111100100 => [5,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111100011 => [5,3,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1111100010 => [5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1111100001 => [5,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1111011110 => [4,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111011101 => [4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1111011011 => [4,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1111011000 => [4,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111010111 => [4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1111010011 => [4,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
1111010001 => [4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1111001111 => [4,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
1111001100 => [4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
1111001011 => [4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1111001001 => [4,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1111000111 => [4,3,3] => [1,2] => [1,0,1,1,0,0] => 1
1111000110 => [4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1111000101 => [4,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
1111000011 => [4,4,2] => [2,1] => [1,1,0,0,1,0] => 1
1111000001 => [4,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1111000000 => [4,6] => [1,1] => [1,0,1,0] => 0
1110111111 => [3,1,6] => [1,1,1] => [1,0,1,0,1,0] => 0
1110111110 => [3,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1110111101 => [3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1110111011 => [3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1110111000 => [3,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1110110001 => [3,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1110101111 => [3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1110100011 => [3,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1110100001 => [3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1110011111 => [3,2,5] => [1,1,1] => [1,0,1,0,1,0] => 0
1110011110 => [3,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1110011001 => [3,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1110010011 => [3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1110010001 => [3,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1110001101 => [3,3,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
1110001001 => [3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1110000111 => [3,4,3] => [1,1,1] => [1,0,1,0,1,0] => 0
1110000101 => [3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
1110000011 => [3,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1110000010 => [3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1110000001 => [3,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1101111111 => [2,1,7] => [1,1,1] => [1,0,1,0,1,0] => 0
1101111110 => [2,1,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1101111101 => [2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1101111011 => [2,1,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101111001 => [2,1,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101111000 => [2,1,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1101110111 => [2,1,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101110001 => [2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1101101111 => [2,1,2,1,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101100011 => [2,1,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101100001 => [2,1,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1101100000 => [2,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1101011111 => [2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1101001111 => [2,1,1,2,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1101000111 => [2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
1101000011 => [2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1101000001 => [2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1100111111 => [2,2,6] => [2,1] => [1,1,0,0,1,0] => 1
1100111100 => [2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1100111001 => [2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1100110011 => [2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
1100110001 => [2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
1100110000 => [2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => 1
1100100111 => [2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1100100011 => [2,2,1,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1100011110 => [2,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1100011101 => [2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
1100011100 => [2,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1100011011 => [2,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1100011001 => [2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1100011000 => [2,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1100010111 => [2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1100010011 => [2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1100001111 => [2,4,4] => [1,2] => [1,0,1,1,0,0] => 1
1100001101 => [2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1100001100 => [2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1100001011 => [2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1100001000 => [2,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1100000111 => [2,5,3] => [1,1,1] => [1,0,1,0,1,0] => 0
1100000110 => [2,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1100000011 => [2,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1100000010 => [2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1100000001 => [2,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1100000000 => [2,8] => [1,1] => [1,0,1,0] => 0
1011111111 => [1,1,8] => [2,1] => [1,1,0,0,1,0] => 1
1011111110 => [1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011111101 => [1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
1011111100 => [1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011111011 => [1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011111000 => [1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011110111 => [1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011110001 => [1,1,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011100011 => [1,1,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
1011100001 => [1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011100000 => [1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1011000111 => [1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
1011000011 => [1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
1011000000 => [1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1010111111 => [1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
1010001111 => [1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
1010000111 => [1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
1010000001 => [1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
1010000000 => [1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => 1
1001111110 => [1,2,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1001111000 => [1,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1001110011 => [1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1001110001 => [1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1001110000 => [1,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1001100111 => [1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
1001100011 => [1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1001011111 => [1,2,1,1,5] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1001001111 => [1,2,1,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1001001110 => [1,2,1,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
1001000111 => [1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1001000000 => [1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000111110 => [1,3,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000111101 => [1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1000111100 => [1,3,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000111011 => [1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1000111001 => [1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
1000111000 => [1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => 1
1000110111 => [1,3,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1000110110 => [1,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
1000110011 => [1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
1000110001 => [1,3,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1000101111 => [1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1000100111 => [1,3,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1000011111 => [1,4,5] => [1,1,1] => [1,0,1,0,1,0] => 0
1000011110 => [1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1000011101 => [1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1000011011 => [1,4,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1000010111 => [1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1000001111 => [1,5,4] => [1,1,1] => [1,0,1,0,1,0] => 0
1000001110 => [1,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000001101 => [1,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
1000001011 => [1,5,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
1000001001 => [1,5,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
1000000110 => [1,6,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000000101 => [1,6,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
1000000100 => [1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1000000011 => [1,7,2] => [1,1,1] => [1,0,1,0,1,0] => 0
1000000010 => [1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1000000001 => [1,8,1] => [1,1,1] => [1,0,1,0,1,0] => 0
1000000000 => [1,9] => [1,1] => [1,0,1,0] => 0
10000000000 => [1,10] => [1,1] => [1,0,1,0] => 0
10000000010 => [1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
10000000110 => [1,7,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000001110 => [1,6,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000011110 => [1,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000111110 => [1,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10001111110 => [1,3,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10011111110 => [1,2,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10111111110 => [1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
11111111110 => [10,1] => [1,1] => [1,0,1,0] => 0
10000000100 => [1,7,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100000111110 => [1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
11011111110 => [2,1,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11001111110 => [2,2,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
110111111110 => [2,1,8,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000011110 => [2,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100001111100 => [1,4,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10010001000 => [1,2,1,3,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0111111111 => [1,9] => [1,1] => [1,0,1,0] => 0
0111111101 => [1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0111111001 => [1,6,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111110001 => [1,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111100001 => [1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0100000001 => [1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0000000001 => [9,1] => [1,1] => [1,0,1,0] => 0
01111111111 => [1,10] => [1,1] => [1,0,1,0] => 0
01111111101 => [1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0111111011 => [1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01000000001 => [1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
00000000001 => [10,1] => [1,1] => [1,0,1,0] => 0
0100001111 => [1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 1
0011000111 => [2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 1
0010001111 => [2,1,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0001110011 => [3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
0001100111 => [3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0001001111 => [3,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0000111101 => [4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
0000110111 => [4,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0000101111 => [4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0000011111 => [5,5] => [2] => [1,1,0,0] => 1
010000011111 => [1,1,5,5] => [2,2] => [1,1,0,0,1,1,0,0] => 1
001100001111 => [2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 1
001000110111 => [2,1,3,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
001000011111 => [2,1,4,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000111000111 => [3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => 1
000110001111 => [3,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000100111011 => [3,1,2,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
000100011111 => [3,1,3,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000011110011 => [4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 1
000011011011 => [4,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
000011001111 => [4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000010011111 => [4,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000001111101 => [5,5,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 1
000001111011 => [5,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000001110111 => [5,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000001101111 => [5,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000001011111 => [5,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
000000111111 => [6,6] => [2] => [1,1,0,0] => 1
111110000001 => [5,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
111001100001 => [3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
111000011001 => [3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
111000000111 => [3,6,3] => [1,1,1] => [1,0,1,0,1,0] => 0
111000001101 => [3,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
111000110001 => [3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
111011000001 => [3,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100111100001 => [1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100110000111 => [1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100001111001 => [1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100001100111 => [1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100000011111 => [1,6,5] => [1,1,1] => [1,0,1,0,1,0] => 0
100000110111 => [1,5,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100000110001 => [1,5,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
100000111101 => [1,5,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100011000111 => [1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100011110001 => [1,3,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
101100011111 => [1,1,2,3,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101100000111 => [1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101111000111 => [1,1,4,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
101111000001 => [1,1,4,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
101111110001 => [1,1,6,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0000000110 => [7,2,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0000011000 => [5,2,3] => [1,1,1] => [1,0,1,0,1,0] => 0
0000011110 => [5,4,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0001111110 => [3,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0110011000 => [1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
0111100000 => [1,4,5] => [1,1,1] => [1,0,1,0,1,0] => 0
0111111110 => [1,8,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0111001000 => [1,3,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0111000010 => [1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0100111000 => [1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
0100111110 => [1,1,2,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0100000010 => [1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
000001111110 => [5,6,1] => [1,1,1] => [1,0,1,0,1,0] => 0
000110011110 => [3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
000111100110 => [3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
000111111000 => [3,6,3] => [1,1,1] => [1,0,1,0,1,0] => 0
000111110010 => [3,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
000111001110 => [3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
000100111110 => [3,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011000011110 => [1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011001111000 => [1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011110000110 => [1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011110011000 => [1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
011111100000 => [1,6,5] => [1,1,1] => [1,0,1,0,1,0] => 0
011111001000 => [1,5,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
011111000010 => [1,5,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011100111000 => [1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
010011111000 => [1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
010000111110 => [1,1,4,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0010111100 => [2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0011110100 => [2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0000010100 => [5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
0000000010 => [8,1,1] => [1,2] => [1,0,1,1,0,0] => 1
0000001110 => [6,3,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0000111110 => [4,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0011111110 => [2,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0000000100 => [7,1,2] => [1,1,1] => [1,0,1,0,1,0] => 0
0000001010 => [6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
0000010110 => [5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0000101110 => [4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0001011110 => [3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0010111110 => [2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
00011111110 => [3,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0101111110 => [1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
00111111110 => [2,8,1] => [1,1,1] => [1,0,1,0,1,0] => 0
01111111110 => [1,9,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0010111000 => [2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
0011001100 => [2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
0011011000 => [2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0011100010 => [2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
0011100100 => [2,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0011101000 => [2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0011110000 => [2,4,4] => [1,2] => [1,0,1,1,0,0] => 1
0101110000 => [1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
0110001100 => [1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0110110000 => [1,2,1,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0111000100 => [1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0111010000 => [1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
001100111000 => [2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
001110001100 => [2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
001110011000 => [2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
001111100000 => [2,5,5] => [1,2] => [1,0,1,1,0,0] => 1
011000111000 => [1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
011001110000 => [1,2,2,3,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011100001100 => [1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011100011000 => [1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
011100110000 => [1,3,2,2,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
10000100001 => [1,4,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
00010001001 => [3,1,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0100000000 => [1,1,8] => [2,1] => [1,1,0,0,1,0] => 1
0100000011 => [1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0100000111 => [1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0100011111 => [1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0100111111 => [1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0101111111 => [1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => 1
01000000000 => [1,1,9] => [2,1] => [1,1,0,0,1,0] => 1
0110111111 => [1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0101111000 => [1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
0110011100 => [1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0110110001 => [1,2,1,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0110111000 => [1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0111000110 => [1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
0111001001 => [1,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0111001100 => [1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
0111011000 => [1,3,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0111100010 => [1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0111100100 => [1,4,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0111101000 => [1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0111110000 => [1,5,4] => [1,1,1] => [1,0,1,0,1,0] => 0
011100011100 => [1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
011110001100 => [1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011111000001 => [1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0100000100 => [1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0011100110 => [2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0011101100 => [2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0001101110 => [3,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0011110010 => [2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0001110110 => [3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0011111000 => [2,5,3] => [1,1,1] => [1,0,1,0,1,0] => 0
0001111010 => [3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
0100111100 => [1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0001111100 => [3,5,2] => [1,1,1] => [1,0,1,0,1,0] => 0
001111000110 => [2,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001111001100 => [2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
100111110000 => [1,2,5,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111110000 => [2,6,4] => [1,1,1] => [1,0,1,0,1,0] => 0
110001111000 => [2,3,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
100011111000 => [1,3,5,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000011111100 => [4,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
0000000101 => [7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
0000001101 => [6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0000011101 => [5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0001111101 => [3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0011111101 => [2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0000001001 => [6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110001110001 => [2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
110011100001 => [2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0111000011 => [1,3,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0011110001 => [2,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110011000011 => [2,2,2,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
110000111100 => [2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
110000001111 => [2,6,4] => [1,1,1] => [1,0,1,0,1,0] => 0
011100000111 => [1,3,5,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111000011100 => [3,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111000011 => [2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
011110000011 => [1,4,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100000011 => [4,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
000111110001 => [3,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001111100001 => [2,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0001000001 => [3,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0111000111 => [1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => 1
0011110011 => [2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0111100011 => [1,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0011111001 => [2,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0000111111 => [4,6] => [1,1] => [1,0,1,0] => 0
110011000111 => [2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
110001110011 => [2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 1
110011100011 => [2,2,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 1
110001111001 => [2,3,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110011110001 => [2,2,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
110000011111 => [2,5,5] => [1,2] => [1,0,1,1,0,0] => 1
011100111001 => [1,3,2,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
011100001111 => [1,3,4,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
111000110011 => [3,3,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
111001100011 => [3,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
111000111001 => [3,3,3,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
111001110001 => [3,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
111000001111 => [3,5,4] => [1,1,1] => [1,0,1,0,1,0] => 0
001111000111 => [2,4,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
011110000111 => [1,4,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
111100011001 => [4,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
111100110001 => [4,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
111100000111 => [4,5,3] => [1,1,1] => [1,0,1,0,1,0] => 0
000111110011 => [3,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
001111100011 => [2,5,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011111000011 => [1,5,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111110000011 => [5,5,2] => [2,1] => [1,1,0,0,1,0] => 1
111111000001 => [6,5,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0001101100 => [3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0011000110 => [2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0010001110 => [2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0110111001 => [1,2,1,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0000110001 => [4,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0000010001 => [5,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
10000000001 => [1,9,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11000000001 => [2,8,1] => [1,1,1] => [1,0,1,0,1,0] => 0
11100000001 => [3,7,1] => [1,1,1] => [1,0,1,0,1,0] => 0
0110111011 => [1,2,1,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0110110111 => [1,2,1,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
100011100011 => [1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
100001110011 => [1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
0000001100 => [6,2,2] => [1,2] => [1,0,1,1,0,0] => 1
0000011001 => [5,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0000110011 => [4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
0011001111 => [2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => 1
0110011111 => [1,2,2,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0000110100 => [4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0000000011 => [8,2] => [1,1] => [1,0,1,0] => 0
0000011011 => [5,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0001101111 => [3,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0011011111 => [2,2,1,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
00000000011 => [9,2] => [1,1] => [1,0,1,0] => 0
10000000101 => [1,7,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
0111110111 => [1,5,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
11000000000 => [2,9] => [1,1] => [1,0,1,0] => 0
0110000111 => [1,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000111001 => [2,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110000110011 => [2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
001110000111 => [2,3,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011000001111 => [1,2,5,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0110001110 => [1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0011001110 => [2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
0100011110 => [1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0010011110 => [2,1,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
001110001110 => [2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
001100011110 => [2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0101000000 => [1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
0001010000 => [3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
0100010000 => [1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0001000100 => [3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0111011100 => [1,3,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0110001001 => [1,2,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
0001100011 => [3,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0110000011 => [1,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0001110111 => [3,3,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0111101111 => [1,4,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011000110000 => [1,2,3,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
000110001100 => [3,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
011000001100 => [1,2,5,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
000001100011 => [5,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000110000011 => [3,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
011110001111 => [1,4,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01111100000 => [1,5,5] => [1,2] => [1,0,1,1,0,0] => 1
01111110000 => [1,6,4] => [1,1,1] => [1,0,1,0,1,0] => 0
100011110011 => [1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
100111000111 => [1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
110001100111 => [2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
100011100111 => [1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100110001111 => [1,2,2,3,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
100011001111 => [1,3,2,2,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0000000111 => [7,3] => [1,1] => [1,0,1,0] => 0
0000001111 => [6,4] => [1,1] => [1,0,1,0] => 0
0001111111 => [3,7] => [1,1] => [1,0,1,0] => 0
0011111111 => [2,8] => [1,1] => [1,0,1,0] => 0
0000001011 => [6,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0000010111 => [5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0001011111 => [3,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0010111111 => [2,1,1,6] => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
00111111111 => [2,9] => [1,1] => [1,0,1,0] => 0
10111111111 => [1,1,9] => [2,1] => [1,1,0,0,1,0] => 1
10000001011 => [1,6,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
0011011110 => [2,2,1,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
0011101110 => [2,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0011110110 => [2,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0011111010 => [2,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
0011111100 => [2,6,2] => [1,1,1] => [1,0,1,0,1,0] => 0
00101111110 => [2,1,1,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
000111100011 => [3,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
01111100100 => [1,5,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
110001100000 => [2,3,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000011000 => [2,5,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100011110 => [4,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100000110 => [4,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110001100011 => [2,3,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
0110001111 => [1,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0011000011 => [2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0001111011 => [3,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111111001111 => [6,2,4] => [1,1,1] => [1,0,1,0,1,0] => 0
111111000011 => [6,4,2] => [1,1,1] => [1,0,1,0,1,0] => 0
111100110011 => [4,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
111100001111 => [4,4,4] => [3] => [1,1,1,0,0,0] => 1
110011110011 => [2,2,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 1
110011001111 => [2,2,2,2,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 1
001111110011 => [2,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
001111001111 => [2,4,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
001100111111 => [2,2,2,6] => [3,1] => [1,1,1,0,0,0,1,0] => 1
001100000011 => [2,2,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
000011000011 => [4,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
000000110011 => [6,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
000000000011 => [10,2] => [1,1] => [1,0,1,0] => 0
011111111011 => [1,8,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111111111100 => [10,2] => [1,1] => [1,0,1,0] => 0
111111001100 => [6,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 1
111100111100 => [4,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110011111100 => [2,2,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
110011000000 => [2,2,2,6] => [3,1] => [1,1,1,0,0,0,1,0] => 1
110000110000 => [2,4,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
110000001100 => [2,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0111011111 => [1,3,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
111100111001 => [4,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
Description
Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
The modified algebra B is obtained from the stable Auslander algebra kQ/I by deleting all relations which contain walks of length at least three (conjectural this step of deletion is not necessary as the stable higher Auslander algebras might be quadratic) and taking as B then the algebra kQ^(op)/J when J is the quadratic perp of the ideal I.
See www.findstat.org/DyckPaths/NakayamaAlgebras for the definition of Loewy length and Nakayama algebras associated to Dyck paths.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
bounce path
Description
The bounce path determined by an integer composition.
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 $w$.