Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000046: Integer partitions ⟶ ℤ
Values
01 => [1,1] => [1,1] => [1] => 1
10 => [1,1] => [1,1] => [1] => 1
001 => [2,1] => [2,1] => [1] => 1
010 => [1,1,1] => [1,1,1] => [1,1] => 0
011 => [1,2] => [2,1] => [1] => 1
100 => [1,2] => [2,1] => [1] => 1
101 => [1,1,1] => [1,1,1] => [1,1] => 0
110 => [2,1] => [2,1] => [1] => 1
0001 => [3,1] => [3,1] => [1] => 1
0010 => [2,1,1] => [2,1,1] => [1,1] => 0
0011 => [2,2] => [2,2] => [2] => 4
0100 => [1,1,2] => [2,1,1] => [1,1] => 0
0101 => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
0110 => [1,2,1] => [2,1,1] => [1,1] => 0
0111 => [1,3] => [3,1] => [1] => 1
1000 => [1,3] => [3,1] => [1] => 1
1001 => [1,2,1] => [2,1,1] => [1,1] => 0
1010 => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
1011 => [1,1,2] => [2,1,1] => [1,1] => 0
1100 => [2,2] => [2,2] => [2] => 4
1101 => [2,1,1] => [2,1,1] => [1,1] => 0
1110 => [3,1] => [3,1] => [1] => 1
00001 => [4,1] => [4,1] => [1] => 1
00010 => [3,1,1] => [3,1,1] => [1,1] => 0
00011 => [3,2] => [3,2] => [2] => 4
00100 => [2,1,2] => [2,2,1] => [2,1] => 4
00101 => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
00110 => [2,2,1] => [2,2,1] => [2,1] => 4
00111 => [2,3] => [3,2] => [2] => 4
01000 => [1,1,3] => [3,1,1] => [1,1] => 0
01001 => [1,1,2,1] => [2,1,1,1] => [1,1,1] => 1
01010 => [1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
01011 => [1,1,1,2] => [2,1,1,1] => [1,1,1] => 1
01100 => [1,2,2] => [2,2,1] => [2,1] => 4
01101 => [1,2,1,1] => [2,1,1,1] => [1,1,1] => 1
01110 => [1,3,1] => [3,1,1] => [1,1] => 0
01111 => [1,4] => [4,1] => [1] => 1
10000 => [1,4] => [4,1] => [1] => 1
10001 => [1,3,1] => [3,1,1] => [1,1] => 0
10010 => [1,2,1,1] => [2,1,1,1] => [1,1,1] => 1
10011 => [1,2,2] => [2,2,1] => [2,1] => 4
10100 => [1,1,1,2] => [2,1,1,1] => [1,1,1] => 1
10101 => [1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 0
10110 => [1,1,2,1] => [2,1,1,1] => [1,1,1] => 1
10111 => [1,1,3] => [3,1,1] => [1,1] => 0
11000 => [2,3] => [3,2] => [2] => 4
11001 => [2,2,1] => [2,2,1] => [2,1] => 4
11010 => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
11011 => [2,1,2] => [2,2,1] => [2,1] => 4
11100 => [3,2] => [3,2] => [2] => 4
11101 => [3,1,1] => [3,1,1] => [1,1] => 0
11110 => [4,1] => [4,1] => [1] => 1
000001 => [5,1] => [5,1] => [1] => 1
000010 => [4,1,1] => [4,1,1] => [1,1] => 0
000011 => [4,2] => [4,2] => [2] => 4
000100 => [3,1,2] => [3,2,1] => [2,1] => 4
000101 => [3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
000110 => [3,2,1] => [3,2,1] => [2,1] => 4
000111 => [3,3] => [3,3] => [3] => 9
001000 => [2,1,3] => [3,2,1] => [2,1] => 4
001001 => [2,1,2,1] => [2,2,1,1] => [2,1,1] => 6
001010 => [2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
001011 => [2,1,1,2] => [2,2,1,1] => [2,1,1] => 6
001100 => [2,2,2] => [2,2,2] => [2,2] => 4
001101 => [2,2,1,1] => [2,2,1,1] => [2,1,1] => 6
001110 => [2,3,1] => [3,2,1] => [2,1] => 4
001111 => [2,4] => [4,2] => [2] => 4
010000 => [1,1,4] => [4,1,1] => [1,1] => 0
010001 => [1,1,3,1] => [3,1,1,1] => [1,1,1] => 1
010010 => [1,1,2,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
010011 => [1,1,2,2] => [2,2,1,1] => [2,1,1] => 6
010100 => [1,1,1,1,2] => [2,1,1,1,1] => [1,1,1,1] => 0
010101 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
010110 => [1,1,1,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
010111 => [1,1,1,3] => [3,1,1,1] => [1,1,1] => 1
011000 => [1,2,3] => [3,2,1] => [2,1] => 4
011001 => [1,2,2,1] => [2,2,1,1] => [2,1,1] => 6
011010 => [1,2,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
011011 => [1,2,1,2] => [2,2,1,1] => [2,1,1] => 6
011100 => [1,3,2] => [3,2,1] => [2,1] => 4
011101 => [1,3,1,1] => [3,1,1,1] => [1,1,1] => 1
011110 => [1,4,1] => [4,1,1] => [1,1] => 0
011111 => [1,5] => [5,1] => [1] => 1
100000 => [1,5] => [5,1] => [1] => 1
100001 => [1,4,1] => [4,1,1] => [1,1] => 0
100010 => [1,3,1,1] => [3,1,1,1] => [1,1,1] => 1
100011 => [1,3,2] => [3,2,1] => [2,1] => 4
100100 => [1,2,1,2] => [2,2,1,1] => [2,1,1] => 6
100101 => [1,2,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
100110 => [1,2,2,1] => [2,2,1,1] => [2,1,1] => 6
100111 => [1,2,3] => [3,2,1] => [2,1] => 4
101000 => [1,1,1,3] => [3,1,1,1] => [1,1,1] => 1
101001 => [1,1,1,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
101010 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
101011 => [1,1,1,1,2] => [2,1,1,1,1] => [1,1,1,1] => 0
101100 => [1,1,2,2] => [2,2,1,1] => [2,1,1] => 6
101101 => [1,1,2,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
101110 => [1,1,3,1] => [3,1,1,1] => [1,1,1] => 1
101111 => [1,1,4] => [4,1,1] => [1,1] => 0
110000 => [2,4] => [4,2] => [2] => 4
110001 => [2,3,1] => [3,2,1] => [2,1] => 4
>>> Load all 1907 entries. <<<110010 => [2,2,1,1] => [2,2,1,1] => [2,1,1] => 6
110011 => [2,2,2] => [2,2,2] => [2,2] => 4
110100 => [2,1,1,2] => [2,2,1,1] => [2,1,1] => 6
110101 => [2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 0
110110 => [2,1,2,1] => [2,2,1,1] => [2,1,1] => 6
110111 => [2,1,3] => [3,2,1] => [2,1] => 4
111000 => [3,3] => [3,3] => [3] => 9
111001 => [3,2,1] => [3,2,1] => [2,1] => 4
111010 => [3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
111011 => [3,1,2] => [3,2,1] => [2,1] => 4
111100 => [4,2] => [4,2] => [2] => 4
111101 => [4,1,1] => [4,1,1] => [1,1] => 0
111110 => [5,1] => [5,1] => [1] => 1
0000001 => [6,1] => [6,1] => [1] => 1
0000010 => [5,1,1] => [5,1,1] => [1,1] => 0
0000011 => [5,2] => [5,2] => [2] => 4
0000100 => [4,1,2] => [4,2,1] => [2,1] => 4
0000101 => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
0000110 => [4,2,1] => [4,2,1] => [2,1] => 4
0000111 => [4,3] => [4,3] => [3] => 9
0001000 => [3,1,3] => [3,3,1] => [3,1] => 10
0001001 => [3,1,2,1] => [3,2,1,1] => [2,1,1] => 6
0001010 => [3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
0001011 => [3,1,1,2] => [3,2,1,1] => [2,1,1] => 6
0001100 => [3,2,2] => [3,2,2] => [2,2] => 4
0001101 => [3,2,1,1] => [3,2,1,1] => [2,1,1] => 6
0001110 => [3,3,1] => [3,3,1] => [3,1] => 10
0001111 => [3,4] => [4,3] => [3] => 9
0010000 => [2,1,4] => [4,2,1] => [2,1] => 4
0010001 => [2,1,3,1] => [3,2,1,1] => [2,1,1] => 6
0010010 => [2,1,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0010011 => [2,1,2,2] => [2,2,2,1] => [2,2,1] => 7
0010100 => [2,1,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
0010101 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0010110 => [2,1,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0010111 => [2,1,1,3] => [3,2,1,1] => [2,1,1] => 6
0011000 => [2,2,3] => [3,2,2] => [2,2] => 4
0011001 => [2,2,2,1] => [2,2,2,1] => [2,2,1] => 7
0011010 => [2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0011011 => [2,2,1,2] => [2,2,2,1] => [2,2,1] => 7
0011100 => [2,3,2] => [3,2,2] => [2,2] => 4
0011101 => [2,3,1,1] => [3,2,1,1] => [2,1,1] => 6
0011110 => [2,4,1] => [4,2,1] => [2,1] => 4
0011111 => [2,5] => [5,2] => [2] => 4
0100000 => [1,1,5] => [5,1,1] => [1,1] => 0
0100001 => [1,1,4,1] => [4,1,1,1] => [1,1,1] => 1
0100010 => [1,1,3,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
0100011 => [1,1,3,2] => [3,2,1,1] => [2,1,1] => 6
0100100 => [1,1,2,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
0100101 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0100110 => [1,1,2,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0100111 => [1,1,2,3] => [3,2,1,1] => [2,1,1] => 6
0101000 => [1,1,1,1,3] => [3,1,1,1,1] => [1,1,1,1] => 0
0101001 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0101010 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
0101011 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0101100 => [1,1,1,2,2] => [2,2,1,1,1] => [2,1,1,1] => 6
0101101 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0101110 => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,1] => 0
0101111 => [1,1,1,4] => [4,1,1,1] => [1,1,1] => 1
0110000 => [1,2,4] => [4,2,1] => [2,1] => 4
0110001 => [1,2,3,1] => [3,2,1,1] => [2,1,1] => 6
0110010 => [1,2,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0110011 => [1,2,2,2] => [2,2,2,1] => [2,2,1] => 7
0110100 => [1,2,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
0110101 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
0110110 => [1,2,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
0110111 => [1,2,1,3] => [3,2,1,1] => [2,1,1] => 6
0111000 => [1,3,3] => [3,3,1] => [3,1] => 10
0111001 => [1,3,2,1] => [3,2,1,1] => [2,1,1] => 6
0111010 => [1,3,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
0111011 => [1,3,1,2] => [3,2,1,1] => [2,1,1] => 6
0111100 => [1,4,2] => [4,2,1] => [2,1] => 4
0111101 => [1,4,1,1] => [4,1,1,1] => [1,1,1] => 1
0111110 => [1,5,1] => [5,1,1] => [1,1] => 0
0111111 => [1,6] => [6,1] => [1] => 1
1000000 => [1,6] => [6,1] => [1] => 1
1000001 => [1,5,1] => [5,1,1] => [1,1] => 0
1000010 => [1,4,1,1] => [4,1,1,1] => [1,1,1] => 1
1000011 => [1,4,2] => [4,2,1] => [2,1] => 4
1000100 => [1,3,1,2] => [3,2,1,1] => [2,1,1] => 6
1000101 => [1,3,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
1000110 => [1,3,2,1] => [3,2,1,1] => [2,1,1] => 6
1000111 => [1,3,3] => [3,3,1] => [3,1] => 10
1001000 => [1,2,1,3] => [3,2,1,1] => [2,1,1] => 6
1001001 => [1,2,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1001010 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1001011 => [1,2,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
1001100 => [1,2,2,2] => [2,2,2,1] => [2,2,1] => 7
1001101 => [1,2,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1001110 => [1,2,3,1] => [3,2,1,1] => [2,1,1] => 6
1001111 => [1,2,4] => [4,2,1] => [2,1] => 4
1010000 => [1,1,1,4] => [4,1,1,1] => [1,1,1] => 1
1010001 => [1,1,1,3,1] => [3,1,1,1,1] => [1,1,1,1] => 0
1010010 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1010011 => [1,1,1,2,2] => [2,2,1,1,1] => [2,1,1,1] => 6
1010100 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1010101 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
1010110 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1010111 => [1,1,1,1,3] => [3,1,1,1,1] => [1,1,1,1] => 0
1011000 => [1,1,2,3] => [3,2,1,1] => [2,1,1] => 6
1011001 => [1,1,2,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1011010 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1011011 => [1,1,2,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
1011100 => [1,1,3,2] => [3,2,1,1] => [2,1,1] => 6
1011101 => [1,1,3,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
1011110 => [1,1,4,1] => [4,1,1,1] => [1,1,1] => 1
1011111 => [1,1,5] => [5,1,1] => [1,1] => 0
1100000 => [2,5] => [5,2] => [2] => 4
1100001 => [2,4,1] => [4,2,1] => [2,1] => 4
1100010 => [2,3,1,1] => [3,2,1,1] => [2,1,1] => 6
1100011 => [2,3,2] => [3,2,2] => [2,2] => 4
1100100 => [2,2,1,2] => [2,2,2,1] => [2,2,1] => 7
1100101 => [2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1100110 => [2,2,2,1] => [2,2,2,1] => [2,2,1] => 7
1100111 => [2,2,3] => [3,2,2] => [2,2] => 4
1101000 => [2,1,1,3] => [3,2,1,1] => [2,1,1] => 6
1101001 => [2,1,1,2,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1101010 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
1101011 => [2,1,1,1,2] => [2,2,1,1,1] => [2,1,1,1] => 6
1101100 => [2,1,2,2] => [2,2,2,1] => [2,2,1] => 7
1101101 => [2,1,2,1,1] => [2,2,1,1,1] => [2,1,1,1] => 6
1101110 => [2,1,3,1] => [3,2,1,1] => [2,1,1] => 6
1101111 => [2,1,4] => [4,2,1] => [2,1] => 4
1110000 => [3,4] => [4,3] => [3] => 9
1110001 => [3,3,1] => [3,3,1] => [3,1] => 10
1110010 => [3,2,1,1] => [3,2,1,1] => [2,1,1] => 6
1110011 => [3,2,2] => [3,2,2] => [2,2] => 4
1110100 => [3,1,1,2] => [3,2,1,1] => [2,1,1] => 6
1110101 => [3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 0
1110110 => [3,1,2,1] => [3,2,1,1] => [2,1,1] => 6
1110111 => [3,1,3] => [3,3,1] => [3,1] => 10
1111000 => [4,3] => [4,3] => [3] => 9
1111001 => [4,2,1] => [4,2,1] => [2,1] => 4
1111010 => [4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
1111011 => [4,1,2] => [4,2,1] => [2,1] => 4
1111100 => [5,2] => [5,2] => [2] => 4
1111101 => [5,1,1] => [5,1,1] => [1,1] => 0
1111110 => [6,1] => [6,1] => [1] => 1
00000001 => [7,1] => [7,1] => [1] => 1
00000010 => [6,1,1] => [6,1,1] => [1,1] => 0
00000011 => [6,2] => [6,2] => [2] => 4
00000100 => [5,1,2] => [5,2,1] => [2,1] => 4
00000101 => [5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
00000110 => [5,2,1] => [5,2,1] => [2,1] => 4
00000111 => [5,3] => [5,3] => [3] => 9
00001000 => [4,1,3] => [4,3,1] => [3,1] => 10
00001001 => [4,1,2,1] => [4,2,1,1] => [2,1,1] => 6
00001010 => [4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
00001011 => [4,1,1,2] => [4,2,1,1] => [2,1,1] => 6
00001100 => [4,2,2] => [4,2,2] => [2,2] => 4
00001101 => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 6
00001110 => [4,3,1] => [4,3,1] => [3,1] => 10
00001111 => [4,4] => [4,4] => [4] => 16
00010000 => [3,1,4] => [4,3,1] => [3,1] => 10
00010001 => [3,1,3,1] => [3,3,1,1] => [3,1,1] => 13
00010010 => [3,1,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00010011 => [3,1,2,2] => [3,2,2,1] => [2,2,1] => 7
00010100 => [3,1,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
00010101 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
00010110 => [3,1,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00010111 => [3,1,1,3] => [3,3,1,1] => [3,1,1] => 13
00011000 => [3,2,3] => [3,3,2] => [3,2] => 11
00011001 => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 7
00011010 => [3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00011011 => [3,2,1,2] => [3,2,2,1] => [2,2,1] => 7
00011100 => [3,3,2] => [3,3,2] => [3,2] => 11
00011101 => [3,3,1,1] => [3,3,1,1] => [3,1,1] => 13
00011110 => [3,4,1] => [4,3,1] => [3,1] => 10
00011111 => [3,5] => [5,3] => [3] => 9
00100000 => [2,1,5] => [5,2,1] => [2,1] => 4
00100001 => [2,1,4,1] => [4,2,1,1] => [2,1,1] => 6
00100010 => [2,1,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00100011 => [2,1,3,2] => [3,2,2,1] => [2,2,1] => 7
00100100 => [2,1,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
00100101 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
00100110 => [2,1,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
00100111 => [2,1,2,3] => [3,2,2,1] => [2,2,1] => 7
00101000 => [2,1,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
00101001 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
00101010 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
00101011 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
00101100 => [2,1,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
00101101 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
00101110 => [2,1,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00101111 => [2,1,1,4] => [4,2,1,1] => [2,1,1] => 6
00110000 => [2,2,4] => [4,2,2] => [2,2] => 4
00110001 => [2,2,3,1] => [3,2,2,1] => [2,2,1] => 7
00110010 => [2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 8
00110011 => [2,2,2,2] => [2,2,2,2] => [2,2,2] => 8
00110100 => [2,2,1,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
00110101 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
00110110 => [2,2,1,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
00110111 => [2,2,1,3] => [3,2,2,1] => [2,2,1] => 7
00111000 => [2,3,3] => [3,3,2] => [3,2] => 11
00111001 => [2,3,2,1] => [3,2,2,1] => [2,2,1] => 7
00111010 => [2,3,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
00111011 => [2,3,1,2] => [3,2,2,1] => [2,2,1] => 7
00111100 => [2,4,2] => [4,2,2] => [2,2] => 4
00111101 => [2,4,1,1] => [4,2,1,1] => [2,1,1] => 6
00111110 => [2,5,1] => [5,2,1] => [2,1] => 4
00111111 => [2,6] => [6,2] => [2] => 4
01000000 => [1,1,6] => [6,1,1] => [1,1] => 0
01000001 => [1,1,5,1] => [5,1,1,1] => [1,1,1] => 1
01000010 => [1,1,4,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
01000011 => [1,1,4,2] => [4,2,1,1] => [2,1,1] => 6
01000100 => [1,1,3,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
01000101 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
01000110 => [1,1,3,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01000111 => [1,1,3,3] => [3,3,1,1] => [3,1,1] => 13
01001000 => [1,1,2,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
01001001 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01001010 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01001011 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01001100 => [1,1,2,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
01001101 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01001110 => [1,1,2,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01001111 => [1,1,2,4] => [4,2,1,1] => [2,1,1] => 6
01010000 => [1,1,1,1,4] => [4,1,1,1,1] => [1,1,1,1] => 0
01010001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
01010010 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01010011 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01010100 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01010101 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
01010110 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01010111 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
01011000 => [1,1,1,2,3] => [3,2,1,1,1] => [2,1,1,1] => 6
01011001 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01011010 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01011011 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01011100 => [1,1,1,3,2] => [3,2,1,1,1] => [2,1,1,1] => 6
01011101 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
01011110 => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1] => 0
01011111 => [1,1,1,5] => [5,1,1,1] => [1,1,1] => 1
01100000 => [1,2,5] => [5,2,1] => [2,1] => 4
01100001 => [1,2,4,1] => [4,2,1,1] => [2,1,1] => 6
01100010 => [1,2,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01100011 => [1,2,3,2] => [3,2,2,1] => [2,2,1] => 7
01100100 => [1,2,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
01100101 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01100110 => [1,2,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
01100111 => [1,2,2,3] => [3,2,2,1] => [2,2,1] => 7
01101000 => [1,2,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
01101001 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01101010 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
01101011 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01101100 => [1,2,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
01101101 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
01101110 => [1,2,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01101111 => [1,2,1,4] => [4,2,1,1] => [2,1,1] => 6
01110000 => [1,3,4] => [4,3,1] => [3,1] => 10
01110001 => [1,3,3,1] => [3,3,1,1] => [3,1,1] => 13
01110010 => [1,3,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01110011 => [1,3,2,2] => [3,2,2,1] => [2,2,1] => 7
01110100 => [1,3,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
01110101 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
01110110 => [1,3,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
01110111 => [1,3,1,3] => [3,3,1,1] => [3,1,1] => 13
01111000 => [1,4,3] => [4,3,1] => [3,1] => 10
01111001 => [1,4,2,1] => [4,2,1,1] => [2,1,1] => 6
01111010 => [1,4,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
01111011 => [1,4,1,2] => [4,2,1,1] => [2,1,1] => 6
01111100 => [1,5,2] => [5,2,1] => [2,1] => 4
01111101 => [1,5,1,1] => [5,1,1,1] => [1,1,1] => 1
01111110 => [1,6,1] => [6,1,1] => [1,1] => 0
01111111 => [1,7] => [7,1] => [1] => 1
10000000 => [1,7] => [7,1] => [1] => 1
10000001 => [1,6,1] => [6,1,1] => [1,1] => 0
10000010 => [1,5,1,1] => [5,1,1,1] => [1,1,1] => 1
10000011 => [1,5,2] => [5,2,1] => [2,1] => 4
10000100 => [1,4,1,2] => [4,2,1,1] => [2,1,1] => 6
10000101 => [1,4,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
10000110 => [1,4,2,1] => [4,2,1,1] => [2,1,1] => 6
10000111 => [1,4,3] => [4,3,1] => [3,1] => 10
10001000 => [1,3,1,3] => [3,3,1,1] => [3,1,1] => 13
10001001 => [1,3,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10001010 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
10001011 => [1,3,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
10001100 => [1,3,2,2] => [3,2,2,1] => [2,2,1] => 7
10001101 => [1,3,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10001110 => [1,3,3,1] => [3,3,1,1] => [3,1,1] => 13
10001111 => [1,3,4] => [4,3,1] => [3,1] => 10
10010000 => [1,2,1,4] => [4,2,1,1] => [2,1,1] => 6
10010001 => [1,2,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10010010 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10010011 => [1,2,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
10010100 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10010101 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10010110 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10010111 => [1,2,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
10011000 => [1,2,2,3] => [3,2,2,1] => [2,2,1] => 7
10011001 => [1,2,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
10011010 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10011011 => [1,2,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
10011100 => [1,2,3,2] => [3,2,2,1] => [2,2,1] => 7
10011101 => [1,2,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10011110 => [1,2,4,1] => [4,2,1,1] => [2,1,1] => 6
10011111 => [1,2,5] => [5,2,1] => [2,1] => 4
10100000 => [1,1,1,5] => [5,1,1,1] => [1,1,1] => 1
10100001 => [1,1,1,4,1] => [4,1,1,1,1] => [1,1,1,1] => 0
10100010 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
10100011 => [1,1,1,3,2] => [3,2,1,1,1] => [2,1,1,1] => 6
10100100 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10100101 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10100110 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10100111 => [1,1,1,2,3] => [3,2,1,1,1] => [2,1,1,1] => 6
10101000 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
10101001 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10101010 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
10101011 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10101100 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10101101 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10101110 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
10101111 => [1,1,1,1,4] => [4,1,1,1,1] => [1,1,1,1] => 0
10110000 => [1,1,2,4] => [4,2,1,1] => [2,1,1] => 6
10110001 => [1,1,2,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10110010 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10110011 => [1,1,2,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
10110100 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10110101 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10110110 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
10110111 => [1,1,2,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
10111000 => [1,1,3,3] => [3,3,1,1] => [3,1,1] => 13
10111001 => [1,1,3,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
10111010 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
10111011 => [1,1,3,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
10111100 => [1,1,4,2] => [4,2,1,1] => [2,1,1] => 6
10111101 => [1,1,4,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
10111110 => [1,1,5,1] => [5,1,1,1] => [1,1,1] => 1
10111111 => [1,1,6] => [6,1,1] => [1,1] => 0
11000000 => [2,6] => [6,2] => [2] => 4
11000001 => [2,5,1] => [5,2,1] => [2,1] => 4
11000010 => [2,4,1,1] => [4,2,1,1] => [2,1,1] => 6
11000011 => [2,4,2] => [4,2,2] => [2,2] => 4
11000100 => [2,3,1,2] => [3,2,2,1] => [2,2,1] => 7
11000101 => [2,3,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11000110 => [2,3,2,1] => [3,2,2,1] => [2,2,1] => 7
11000111 => [2,3,3] => [3,3,2] => [3,2] => 11
11001000 => [2,2,1,3] => [3,2,2,1] => [2,2,1] => 7
11001001 => [2,2,1,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
11001010 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
11001011 => [2,2,1,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
11001100 => [2,2,2,2] => [2,2,2,2] => [2,2,2] => 8
11001101 => [2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 8
11001110 => [2,2,3,1] => [3,2,2,1] => [2,2,1] => 7
11001111 => [2,2,4] => [4,2,2] => [2,2] => 4
11010000 => [2,1,1,4] => [4,2,1,1] => [2,1,1] => 6
11010001 => [2,1,1,3,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11010010 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
11010011 => [2,1,1,2,2] => [2,2,2,1,1] => [2,2,1,1] => 8
11010100 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
11010101 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
11010110 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
11010111 => [2,1,1,1,3] => [3,2,1,1,1] => [2,1,1,1] => 6
11011000 => [2,1,2,3] => [3,2,2,1] => [2,2,1] => 7
11011001 => [2,1,2,2,1] => [2,2,2,1,1] => [2,2,1,1] => 8
11011010 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 8
11011011 => [2,1,2,1,2] => [2,2,2,1,1] => [2,2,1,1] => 8
11011100 => [2,1,3,2] => [3,2,2,1] => [2,2,1] => 7
11011101 => [2,1,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11011110 => [2,1,4,1] => [4,2,1,1] => [2,1,1] => 6
11011111 => [2,1,5] => [5,2,1] => [2,1] => 4
11100000 => [3,5] => [5,3] => [3] => 9
11100001 => [3,4,1] => [4,3,1] => [3,1] => 10
11100010 => [3,3,1,1] => [3,3,1,1] => [3,1,1] => 13
11100011 => [3,3,2] => [3,3,2] => [3,2] => 11
11100100 => [3,2,1,2] => [3,2,2,1] => [2,2,1] => 7
11100101 => [3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11100110 => [3,2,2,1] => [3,2,2,1] => [2,2,1] => 7
11100111 => [3,2,3] => [3,3,2] => [3,2] => 11
11101000 => [3,1,1,3] => [3,3,1,1] => [3,1,1] => 13
11101001 => [3,1,1,2,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11101010 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
11101011 => [3,1,1,1,2] => [3,2,1,1,1] => [2,1,1,1] => 6
11101100 => [3,1,2,2] => [3,2,2,1] => [2,2,1] => 7
11101101 => [3,1,2,1,1] => [3,2,1,1,1] => [2,1,1,1] => 6
11101110 => [3,1,3,1] => [3,3,1,1] => [3,1,1] => 13
11101111 => [3,1,4] => [4,3,1] => [3,1] => 10
11110000 => [4,4] => [4,4] => [4] => 16
11110001 => [4,3,1] => [4,3,1] => [3,1] => 10
11110010 => [4,2,1,1] => [4,2,1,1] => [2,1,1] => 6
11110011 => [4,2,2] => [4,2,2] => [2,2] => 4
11110100 => [4,1,1,2] => [4,2,1,1] => [2,1,1] => 6
11110101 => [4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 0
11110110 => [4,1,2,1] => [4,2,1,1] => [2,1,1] => 6
11110111 => [4,1,3] => [4,3,1] => [3,1] => 10
11111000 => [5,3] => [5,3] => [3] => 9
11111001 => [5,2,1] => [5,2,1] => [2,1] => 4
11111010 => [5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
11111011 => [5,1,2] => [5,2,1] => [2,1] => 4
11111100 => [6,2] => [6,2] => [2] => 4
11111101 => [6,1,1] => [6,1,1] => [1,1] => 0
11111110 => [7,1] => [7,1] => [1] => 1
000000001 => [8,1] => [8,1] => [1] => 1
000000010 => [7,1,1] => [7,1,1] => [1,1] => 0
000000011 => [7,2] => [7,2] => [2] => 4
000000100 => [6,1,2] => [6,2,1] => [2,1] => 4
000000101 => [6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
000000110 => [6,2,1] => [6,2,1] => [2,1] => 4
000000111 => [6,3] => [6,3] => [3] => 9
000001000 => [5,1,3] => [5,3,1] => [3,1] => 10
000001001 => [5,1,2,1] => [5,2,1,1] => [2,1,1] => 6
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
000001011 => [5,1,1,2] => [5,2,1,1] => [2,1,1] => 6
000001100 => [5,2,2] => [5,2,2] => [2,2] => 4
000001101 => [5,2,1,1] => [5,2,1,1] => [2,1,1] => 6
000001110 => [5,3,1] => [5,3,1] => [3,1] => 10
000001111 => [5,4] => [5,4] => [4] => 16
000010000 => [4,1,4] => [4,4,1] => [4,1] => 18
000010001 => [4,1,3,1] => [4,3,1,1] => [3,1,1] => 13
000010010 => [4,1,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
000010011 => [4,1,2,2] => [4,2,2,1] => [2,2,1] => 7
000010100 => [4,1,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
000010101 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
000010110 => [4,1,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
000010111 => [4,1,1,3] => [4,3,1,1] => [3,1,1] => 13
000011000 => [4,2,3] => [4,3,2] => [3,2] => 11
000011001 => [4,2,2,1] => [4,2,2,1] => [2,2,1] => 7
000011010 => [4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
000011011 => [4,2,1,2] => [4,2,2,1] => [2,2,1] => 7
000011100 => [4,3,2] => [4,3,2] => [3,2] => 11
000011101 => [4,3,1,1] => [4,3,1,1] => [3,1,1] => 13
000011110 => [4,4,1] => [4,4,1] => [4,1] => 18
000011111 => [4,5] => [5,4] => [4] => 16
000100000 => [3,1,5] => [5,3,1] => [3,1] => 10
000100001 => [3,1,4,1] => [4,3,1,1] => [3,1,1] => 13
000100010 => [3,1,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
000100011 => [3,1,3,2] => [3,3,2,1] => [3,2,1] => 15
000100100 => [3,1,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
000100101 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
000100110 => [3,1,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
000100111 => [3,1,2,3] => [3,3,2,1] => [3,2,1] => 15
000101000 => [3,1,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
000101001 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
000101010 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
000101011 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
000101100 => [3,1,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
000101101 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
000101110 => [3,1,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
000101111 => [3,1,1,4] => [4,3,1,1] => [3,1,1] => 13
000110000 => [3,2,4] => [4,3,2] => [3,2] => 11
000110001 => [3,2,3,1] => [3,3,2,1] => [3,2,1] => 15
000110010 => [3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
000110011 => [3,2,2,2] => [3,2,2,2] => [2,2,2] => 8
000110100 => [3,2,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
000110101 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
000110110 => [3,2,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
000110111 => [3,2,1,3] => [3,3,2,1] => [3,2,1] => 15
000111000 => [3,3,3] => [3,3,3] => [3,3] => 12
000111001 => [3,3,2,1] => [3,3,2,1] => [3,2,1] => 15
000111010 => [3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
000111011 => [3,3,1,2] => [3,3,2,1] => [3,2,1] => 15
000111100 => [3,4,2] => [4,3,2] => [3,2] => 11
000111101 => [3,4,1,1] => [4,3,1,1] => [3,1,1] => 13
000111110 => [3,5,1] => [5,3,1] => [3,1] => 10
000111111 => [3,6] => [6,3] => [3] => 9
001000000 => [2,1,6] => [6,2,1] => [2,1] => 4
001000001 => [2,1,5,1] => [5,2,1,1] => [2,1,1] => 6
001000010 => [2,1,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
001000011 => [2,1,4,2] => [4,2,2,1] => [2,2,1] => 7
001000100 => [2,1,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
001000101 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
001000110 => [2,1,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001000111 => [2,1,3,3] => [3,3,2,1] => [3,2,1] => 15
001001000 => [2,1,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
001001001 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001001010 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001001011 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001001100 => [2,1,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
001001101 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001001110 => [2,1,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001001111 => [2,1,2,4] => [4,2,2,1] => [2,2,1] => 7
001010000 => [2,1,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
001010001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
001010010 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001010011 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001010100 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001010101 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
001010110 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001010111 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
001011000 => [2,1,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
001011001 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001011010 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001011011 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001011100 => [2,1,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
001011101 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
001011110 => [2,1,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
001011111 => [2,1,1,5] => [5,2,1,1] => [2,1,1] => 6
001100000 => [2,2,5] => [5,2,2] => [2,2] => 4
001100001 => [2,2,4,1] => [4,2,2,1] => [2,2,1] => 7
001100010 => [2,2,3,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001100011 => [2,2,3,2] => [3,2,2,2] => [2,2,2] => 8
001100100 => [2,2,2,1,2] => [2,2,2,2,1] => [2,2,2,1] => 9
001100101 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
001100111 => [2,2,2,3] => [3,2,2,2] => [2,2,2] => 8
001101000 => [2,2,1,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
001101001 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001101010 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
001101011 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001101100 => [2,2,1,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
001101101 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
001101110 => [2,2,1,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001101111 => [2,2,1,4] => [4,2,2,1] => [2,2,1] => 7
001110000 => [2,3,4] => [4,3,2] => [3,2] => 11
001110001 => [2,3,3,1] => [3,3,2,1] => [3,2,1] => 15
001110010 => [2,3,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001110011 => [2,3,2,2] => [3,2,2,2] => [2,2,2] => 8
001110100 => [2,3,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
001110101 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
001110110 => [2,3,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
001110111 => [2,3,1,3] => [3,3,2,1] => [3,2,1] => 15
001111000 => [2,4,3] => [4,3,2] => [3,2] => 11
001111001 => [2,4,2,1] => [4,2,2,1] => [2,2,1] => 7
001111010 => [2,4,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
001111011 => [2,4,1,2] => [4,2,2,1] => [2,2,1] => 7
001111100 => [2,5,2] => [5,2,2] => [2,2] => 4
001111101 => [2,5,1,1] => [5,2,1,1] => [2,1,1] => 6
001111110 => [2,6,1] => [6,2,1] => [2,1] => 4
001111111 => [2,7] => [7,2] => [2] => 4
010000000 => [1,1,7] => [7,1,1] => [1,1] => 0
010000001 => [1,1,6,1] => [6,1,1,1] => [1,1,1] => 1
010000010 => [1,1,5,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
010000011 => [1,1,5,2] => [5,2,1,1] => [2,1,1] => 6
010000100 => [1,1,4,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
010000101 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
010000110 => [1,1,4,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
010000111 => [1,1,4,3] => [4,3,1,1] => [3,1,1] => 13
010001000 => [1,1,3,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
010001001 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010001010 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010001011 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010001100 => [1,1,3,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
010001101 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010001110 => [1,1,3,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
010001111 => [1,1,3,4] => [4,3,1,1] => [3,1,1] => 13
010010000 => [1,1,2,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
010010001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010010010 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010010011 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
010010100 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010010101 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010010110 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010010111 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010011000 => [1,1,2,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
010011001 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
010011010 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010011011 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
010011100 => [1,1,2,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
010011101 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010011110 => [1,1,2,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
010011111 => [1,1,2,5] => [5,2,1,1] => [2,1,1] => 6
010100000 => [1,1,1,1,5] => [5,1,1,1,1] => [1,1,1,1] => 0
010100001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
010100010 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010100011 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010100100 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010100101 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010100110 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010100111 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010101000 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010101001 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010101010 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
010101011 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010101100 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010101101 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010101110 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010101111 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
010110000 => [1,1,1,2,4] => [4,2,1,1,1] => [2,1,1,1] => 6
010110001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010110010 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010110011 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
010110100 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010110101 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
010110110 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
010110111 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010111000 => [1,1,1,3,3] => [3,3,1,1,1] => [3,1,1,1] => 14
010111001 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010111010 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
010111011 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
010111100 => [1,1,1,4,2] => [4,2,1,1,1] => [2,1,1,1] => 6
010111101 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
010111110 => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1] => 0
010111111 => [1,1,1,6] => [6,1,1,1] => [1,1,1] => 1
011000000 => [1,2,6] => [6,2,1] => [2,1] => 4
011000001 => [1,2,5,1] => [5,2,1,1] => [2,1,1] => 6
011000010 => [1,2,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
011000011 => [1,2,4,2] => [4,2,2,1] => [2,2,1] => 7
011000100 => [1,2,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
011000101 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011000110 => [1,2,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
011000111 => [1,2,3,3] => [3,3,2,1] => [3,2,1] => 15
011001000 => [1,2,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
011001001 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011001010 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
011001011 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011001100 => [1,2,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
011001101 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011001110 => [1,2,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
011001111 => [1,2,2,4] => [4,2,2,1] => [2,2,1] => 7
011010000 => [1,2,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
011010001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011010010 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
011010011 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011010100 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
011010101 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
011010110 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
011010111 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011011000 => [1,2,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
011011001 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011011010 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
011011011 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
011011100 => [1,2,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
011011101 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011011110 => [1,2,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
011011111 => [1,2,1,5] => [5,2,1,1] => [2,1,1] => 6
011100000 => [1,3,5] => [5,3,1] => [3,1] => 10
011100001 => [1,3,4,1] => [4,3,1,1] => [3,1,1] => 13
011100010 => [1,3,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
011100011 => [1,3,3,2] => [3,3,2,1] => [3,2,1] => 15
011100100 => [1,3,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
011100101 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011100110 => [1,3,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
011100111 => [1,3,2,3] => [3,3,2,1] => [3,2,1] => 15
011101000 => [1,3,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
011101001 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011101010 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
011101011 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011101100 => [1,3,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
011101101 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
011101110 => [1,3,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
011101111 => [1,3,1,4] => [4,3,1,1] => [3,1,1] => 13
011110000 => [1,4,4] => [4,4,1] => [4,1] => 18
011110001 => [1,4,3,1] => [4,3,1,1] => [3,1,1] => 13
011110010 => [1,4,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
011110011 => [1,4,2,2] => [4,2,2,1] => [2,2,1] => 7
011110100 => [1,4,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
011110101 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
011110110 => [1,4,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
011110111 => [1,4,1,3] => [4,3,1,1] => [3,1,1] => 13
011111000 => [1,5,3] => [5,3,1] => [3,1] => 10
011111001 => [1,5,2,1] => [5,2,1,1] => [2,1,1] => 6
011111010 => [1,5,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
011111011 => [1,5,1,2] => [5,2,1,1] => [2,1,1] => 6
011111100 => [1,6,2] => [6,2,1] => [2,1] => 4
011111101 => [1,6,1,1] => [6,1,1,1] => [1,1,1] => 1
011111110 => [1,7,1] => [7,1,1] => [1,1] => 0
011111111 => [1,8] => [8,1] => [1] => 1
100000000 => [1,8] => [8,1] => [1] => 1
100000001 => [1,7,1] => [7,1,1] => [1,1] => 0
100000010 => [1,6,1,1] => [6,1,1,1] => [1,1,1] => 1
100000011 => [1,6,2] => [6,2,1] => [2,1] => 4
100000100 => [1,5,1,2] => [5,2,1,1] => [2,1,1] => 6
100000101 => [1,5,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
100000110 => [1,5,2,1] => [5,2,1,1] => [2,1,1] => 6
100000111 => [1,5,3] => [5,3,1] => [3,1] => 10
100001000 => [1,4,1,3] => [4,3,1,1] => [3,1,1] => 13
100001001 => [1,4,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
100001010 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
100001011 => [1,4,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
100001100 => [1,4,2,2] => [4,2,2,1] => [2,2,1] => 7
100001101 => [1,4,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
100001110 => [1,4,3,1] => [4,3,1,1] => [3,1,1] => 13
100001111 => [1,4,4] => [4,4,1] => [4,1] => 18
100010000 => [1,3,1,4] => [4,3,1,1] => [3,1,1] => 13
100010001 => [1,3,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
100010010 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100010011 => [1,3,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
100010100 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100010101 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
100010110 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100010111 => [1,3,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
100011000 => [1,3,2,3] => [3,3,2,1] => [3,2,1] => 15
100011001 => [1,3,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
100011010 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100011011 => [1,3,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
100011100 => [1,3,3,2] => [3,3,2,1] => [3,2,1] => 15
100011101 => [1,3,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
100011110 => [1,3,4,1] => [4,3,1,1] => [3,1,1] => 13
100011111 => [1,3,5] => [5,3,1] => [3,1] => 10
100100000 => [1,2,1,5] => [5,2,1,1] => [2,1,1] => 6
100100001 => [1,2,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
100100010 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100100011 => [1,2,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
100100100 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100100101 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100100110 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100100111 => [1,2,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
100101000 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100101001 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100101010 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
100101011 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100101100 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100101101 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100101110 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100101111 => [1,2,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
100110000 => [1,2,2,4] => [4,2,2,1] => [2,2,1] => 7
100110001 => [1,2,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
100110010 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100110011 => [1,2,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
100110100 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100110101 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100110110 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
100110111 => [1,2,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
100111000 => [1,2,3,3] => [3,3,2,1] => [3,2,1] => 15
100111001 => [1,2,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
100111010 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
100111011 => [1,2,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
100111100 => [1,2,4,2] => [4,2,2,1] => [2,2,1] => 7
100111101 => [1,2,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
100111110 => [1,2,5,1] => [5,2,1,1] => [2,1,1] => 6
100111111 => [1,2,6] => [6,2,1] => [2,1] => 4
101000000 => [1,1,1,6] => [6,1,1,1] => [1,1,1] => 1
101000001 => [1,1,1,5,1] => [5,1,1,1,1] => [1,1,1,1] => 0
101000010 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
101000011 => [1,1,1,4,2] => [4,2,1,1,1] => [2,1,1,1] => 6
101000100 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101000101 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101000110 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101000111 => [1,1,1,3,3] => [3,3,1,1,1] => [3,1,1,1] => 14
101001000 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101001001 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101001010 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101001011 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101001100 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
101001101 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101001110 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101001111 => [1,1,1,2,4] => [4,2,1,1,1] => [2,1,1,1] => 6
101010000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
101010001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101010010 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101010011 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101010100 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101010101 => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
101010110 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101010111 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101011000 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101011001 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101011010 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101011011 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101011100 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101011101 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101011110 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
101011111 => [1,1,1,1,5] => [5,1,1,1,1] => [1,1,1,1] => 0
101100000 => [1,1,2,5] => [5,2,1,1] => [2,1,1] => 6
101100001 => [1,1,2,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
101100010 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101100011 => [1,1,2,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
101100100 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
101100101 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101100110 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
101100111 => [1,1,2,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
101101000 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101101001 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101101010 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
101101011 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101101100 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
101101101 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101101110 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101101111 => [1,1,2,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
101110000 => [1,1,3,4] => [4,3,1,1] => [3,1,1] => 13
101110001 => [1,1,3,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
101110010 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101110011 => [1,1,3,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
101110100 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101110101 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
101110110 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
101110111 => [1,1,3,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
101111000 => [1,1,4,3] => [4,3,1,1] => [3,1,1] => 13
101111001 => [1,1,4,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
101111010 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
101111011 => [1,1,4,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
101111100 => [1,1,5,2] => [5,2,1,1] => [2,1,1] => 6
101111101 => [1,1,5,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
101111110 => [1,1,6,1] => [6,1,1,1] => [1,1,1] => 1
101111111 => [1,1,7] => [7,1,1] => [1,1] => 0
110000000 => [2,7] => [7,2] => [2] => 4
110000001 => [2,6,1] => [6,2,1] => [2,1] => 4
110000010 => [2,5,1,1] => [5,2,1,1] => [2,1,1] => 6
110000011 => [2,5,2] => [5,2,2] => [2,2] => 4
110000100 => [2,4,1,2] => [4,2,2,1] => [2,2,1] => 7
110000101 => [2,4,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
110000110 => [2,4,2,1] => [4,2,2,1] => [2,2,1] => 7
110000111 => [2,4,3] => [4,3,2] => [3,2] => 11
110001000 => [2,3,1,3] => [3,3,2,1] => [3,2,1] => 15
110001001 => [2,3,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110001010 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
110001011 => [2,3,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
110001100 => [2,3,2,2] => [3,2,2,2] => [2,2,2] => 8
110001101 => [2,3,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110001110 => [2,3,3,1] => [3,3,2,1] => [3,2,1] => 15
110001111 => [2,3,4] => [4,3,2] => [3,2] => 11
110010000 => [2,2,1,4] => [4,2,2,1] => [2,2,1] => 7
110010001 => [2,2,1,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110010010 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110010011 => [2,2,1,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
110010100 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110010101 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110010110 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110010111 => [2,2,1,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
110011000 => [2,2,2,3] => [3,2,2,2] => [2,2,2] => 8
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
110011010 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110011011 => [2,2,2,1,2] => [2,2,2,2,1] => [2,2,2,1] => 9
110011100 => [2,2,3,2] => [3,2,2,2] => [2,2,2] => 8
110011101 => [2,2,3,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110011110 => [2,2,4,1] => [4,2,2,1] => [2,2,1] => 7
110011111 => [2,2,5] => [5,2,2] => [2,2] => 4
110100000 => [2,1,1,5] => [5,2,1,1] => [2,1,1] => 6
110100001 => [2,1,1,4,1] => [4,2,1,1,1] => [2,1,1,1] => 6
110100010 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
110100011 => [2,1,1,3,2] => [3,2,2,1,1] => [2,2,1,1] => 8
110100100 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110100101 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110100110 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110100111 => [2,1,1,2,3] => [3,2,2,1,1] => [2,2,1,1] => 8
110101000 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
110101001 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110101010 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
110101011 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110101100 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110101101 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110101110 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
110101111 => [2,1,1,1,4] => [4,2,1,1,1] => [2,1,1,1] => 6
110110000 => [2,1,2,4] => [4,2,2,1] => [2,2,1] => 7
110110001 => [2,1,2,3,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110110010 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110110011 => [2,1,2,2,2] => [2,2,2,2,1] => [2,2,2,1] => 9
110110100 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110110101 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
110110110 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 9
110110111 => [2,1,2,1,3] => [3,2,2,1,1] => [2,2,1,1] => 8
110111000 => [2,1,3,3] => [3,3,2,1] => [3,2,1] => 15
110111001 => [2,1,3,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
110111010 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
110111011 => [2,1,3,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
110111100 => [2,1,4,2] => [4,2,2,1] => [2,2,1] => 7
110111101 => [2,1,4,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
110111110 => [2,1,5,1] => [5,2,1,1] => [2,1,1] => 6
110111111 => [2,1,6] => [6,2,1] => [2,1] => 4
111000000 => [3,6] => [6,3] => [3] => 9
111000001 => [3,5,1] => [5,3,1] => [3,1] => 10
111000010 => [3,4,1,1] => [4,3,1,1] => [3,1,1] => 13
111000011 => [3,4,2] => [4,3,2] => [3,2] => 11
111000100 => [3,3,1,2] => [3,3,2,1] => [3,2,1] => 15
111000101 => [3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
111000110 => [3,3,2,1] => [3,3,2,1] => [3,2,1] => 15
111000111 => [3,3,3] => [3,3,3] => [3,3] => 12
111001000 => [3,2,1,3] => [3,3,2,1] => [3,2,1] => 15
111001001 => [3,2,1,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
111001010 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
111001011 => [3,2,1,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
111001100 => [3,2,2,2] => [3,2,2,2] => [2,2,2] => 8
111001101 => [3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 8
111001110 => [3,2,3,1] => [3,3,2,1] => [3,2,1] => 15
111001111 => [3,2,4] => [4,3,2] => [3,2] => 11
111010000 => [3,1,1,4] => [4,3,1,1] => [3,1,1] => 13
111010001 => [3,1,1,3,1] => [3,3,1,1,1] => [3,1,1,1] => 14
111010010 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
111010011 => [3,1,1,2,2] => [3,2,2,1,1] => [2,2,1,1] => 8
111010100 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
111010101 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
111010110 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
111010111 => [3,1,1,1,3] => [3,3,1,1,1] => [3,1,1,1] => 14
111011000 => [3,1,2,3] => [3,3,2,1] => [3,2,1] => 15
111011001 => [3,1,2,2,1] => [3,2,2,1,1] => [2,2,1,1] => 8
111011010 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 8
111011011 => [3,1,2,1,2] => [3,2,2,1,1] => [2,2,1,1] => 8
111011100 => [3,1,3,2] => [3,3,2,1] => [3,2,1] => 15
111011101 => [3,1,3,1,1] => [3,3,1,1,1] => [3,1,1,1] => 14
111011110 => [3,1,4,1] => [4,3,1,1] => [3,1,1] => 13
111011111 => [3,1,5] => [5,3,1] => [3,1] => 10
111100000 => [4,5] => [5,4] => [4] => 16
111100001 => [4,4,1] => [4,4,1] => [4,1] => 18
111100010 => [4,3,1,1] => [4,3,1,1] => [3,1,1] => 13
111100011 => [4,3,2] => [4,3,2] => [3,2] => 11
111100100 => [4,2,1,2] => [4,2,2,1] => [2,2,1] => 7
111100101 => [4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
111100110 => [4,2,2,1] => [4,2,2,1] => [2,2,1] => 7
111100111 => [4,2,3] => [4,3,2] => [3,2] => 11
111101000 => [4,1,1,3] => [4,3,1,1] => [3,1,1] => 13
111101001 => [4,1,1,2,1] => [4,2,1,1,1] => [2,1,1,1] => 6
111101010 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
111101011 => [4,1,1,1,2] => [4,2,1,1,1] => [2,1,1,1] => 6
111101100 => [4,1,2,2] => [4,2,2,1] => [2,2,1] => 7
111101101 => [4,1,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => 6
111101110 => [4,1,3,1] => [4,3,1,1] => [3,1,1] => 13
111101111 => [4,1,4] => [4,4,1] => [4,1] => 18
111110000 => [5,4] => [5,4] => [4] => 16
111110001 => [5,3,1] => [5,3,1] => [3,1] => 10
111110010 => [5,2,1,1] => [5,2,1,1] => [2,1,1] => 6
111110011 => [5,2,2] => [5,2,2] => [2,2] => 4
111110100 => [5,1,1,2] => [5,2,1,1] => [2,1,1] => 6
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 0
111110110 => [5,1,2,1] => [5,2,1,1] => [2,1,1] => 6
111110111 => [5,1,3] => [5,3,1] => [3,1] => 10
111111000 => [6,3] => [6,3] => [3] => 9
111111001 => [6,2,1] => [6,2,1] => [2,1] => 4
111111010 => [6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
111111011 => [6,1,2] => [6,2,1] => [2,1] => 4
111111100 => [7,2] => [7,2] => [2] => 4
111111101 => [7,1,1] => [7,1,1] => [1,1] => 0
111111110 => [8,1] => [8,1] => [1] => 1
1010101100 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010110010 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010110100 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010111000 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1011001010 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1011001100 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1011010010 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1011010100 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1011011000 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1011100010 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1011100100 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1011101000 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1011110000 => [1,1,4,4] => [4,4,1,1] => [4,1,1] => 22
1100101010 => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1100101100 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1100110010 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1100110100 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1100111000 => [2,2,3,3] => [3,3,2,2] => [3,2,2] => 17
1101001010 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1101001100 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1101010010 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1101010100 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1101011000 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101100010 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101100100 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1101101000 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101110000 => [2,1,3,4] => [4,3,2,1] => [3,2,1] => 15
1110001010 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1110001100 => [3,3,2,2] => [3,3,2,2] => [3,2,2] => 17
1110010010 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110010100 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110011000 => [3,2,2,3] => [3,3,2,2] => [3,2,2] => 17
1110100010 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1110100100 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110101000 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1110110000 => [3,1,2,4] => [4,3,2,1] => [3,2,1] => 15
1111000010 => [4,4,1,1] => [4,4,1,1] => [4,1,1] => 22
1111000100 => [4,3,1,2] => [4,3,2,1] => [3,2,1] => 15
1111001000 => [4,2,1,3] => [4,3,2,1] => [3,2,1] => 15
1111010000 => [4,1,1,4] => [4,4,1,1] => [4,1,1] => 22
1111100000 => [5,5] => [5,5] => [5] => 25
101011110000 => [1,1,1,1,4,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
101101110000 => [1,1,2,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
101110110000 => [1,1,3,1,2,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
101111000010 => [1,1,4,4,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
101111000100 => [1,1,4,3,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
101111001000 => [1,1,4,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
101111010000 => [1,1,4,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
101111100000 => [1,1,5,5] => [5,5,1,1] => [5,1,1] => 33
110011110000 => [2,2,4,4] => [4,4,2,2] => [4,2,2] => 28
110101110000 => [2,1,1,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
110110110000 => [2,1,2,1,2,4] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
110111000010 => [2,1,3,4,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
110111010000 => [2,1,3,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
110111100000 => [2,1,4,5] => [5,4,2,1] => [4,2,1] => 25
111001110000 => [3,2,3,4] => [4,3,3,2] => [3,3,2] => 19
111010110000 => [3,1,1,1,2,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111011000010 => [3,1,2,4,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111011010000 => [3,1,2,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111011100000 => [3,1,3,5] => [5,3,3,1] => [3,3,1] => 17
111100001010 => [4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
111100001100 => [4,4,2,2] => [4,4,2,2] => [4,2,2] => 28
111100010010 => [4,3,1,2,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111100010100 => [4,3,1,1,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111100011000 => [4,3,2,3] => [4,3,3,2] => [3,3,2] => 19
111100100010 => [4,2,1,3,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111100100100 => [4,2,1,2,1,2] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
111100101000 => [4,2,1,1,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111100110000 => [4,2,2,4] => [4,4,2,2] => [4,2,2] => 28
111101000010 => [4,1,1,4,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
111101000100 => [4,1,1,3,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111101001000 => [4,1,1,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
111101010000 => [4,1,1,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
111101100000 => [4,1,2,5] => [5,4,2,1] => [4,2,1] => 25
111110000010 => [5,5,1,1] => [5,5,1,1] => [5,1,1] => 33
111110000100 => [5,4,1,2] => [5,4,2,1] => [4,2,1] => 25
111110001000 => [5,3,1,3] => [5,3,3,1] => [3,3,1] => 17
111110010000 => [5,2,1,4] => [5,4,2,1] => [4,2,1] => 25
111110100000 => [5,1,1,5] => [5,5,1,1] => [5,1,1] => 33
111111000000 => [6,6] => [6,6] => [6] => 36
1111111110 => [9,1] => [9,1] => [1] => 1
1111111101 => [8,1,1] => [8,1,1] => [1,1] => 0
1111111100 => [8,2] => [8,2] => [2] => 4
1111111011 => [7,1,2] => [7,2,1] => [2,1] => 4
1111111010 => [7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
1111111001 => [7,2,1] => [7,2,1] => [2,1] => 4
1111110110 => [6,1,2,1] => [6,2,1,1] => [2,1,1] => 6
1111110101 => [6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
1111110011 => [6,2,2] => [6,2,2] => [2,2] => 4
1111110010 => [6,2,1,1] => [6,2,1,1] => [2,1,1] => 6
1111110001 => [6,3,1] => [6,3,1] => [3,1] => 10
1111110000 => [6,4] => [6,4] => [4] => 16
1111101010 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1111101001 => [5,1,1,2,1] => [5,2,1,1,1] => [2,1,1,1] => 6
1111101000 => [5,1,1,3] => [5,3,1,1] => [3,1,1] => 13
1111100100 => [5,2,1,2] => [5,2,2,1] => [2,2,1] => 7
1111100011 => [5,3,2] => [5,3,2] => [3,2] => 11
1111100010 => [5,3,1,1] => [5,3,1,1] => [3,1,1] => 13
1111100001 => [5,4,1] => [5,4,1] => [4,1] => 18
1111011110 => [4,1,4,1] => [4,4,1,1] => [4,1,1] => 22
1111011101 => [4,1,3,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1111011011 => [4,1,2,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1111011000 => [4,1,2,3] => [4,3,2,1] => [3,2,1] => 15
1111010111 => [4,1,1,1,3] => [4,3,1,1,1] => [3,1,1,1] => 14
1111010101 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
1111010100 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1111010011 => [4,1,1,2,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1111010010 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1111010001 => [4,1,1,3,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1111001111 => [4,2,4] => [4,4,2] => [4,2] => 20
1111001100 => [4,2,2,2] => [4,2,2,2] => [2,2,2] => 8
1111001011 => [4,2,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1111001010 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1111001001 => [4,2,1,2,1] => [4,2,2,1,1] => [2,2,1,1] => 8
1111000111 => [4,3,3] => [4,3,3] => [3,3] => 12
1111000110 => [4,3,2,1] => [4,3,2,1] => [3,2,1] => 15
1111000101 => [4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1111000011 => [4,4,2] => [4,4,2] => [4,2] => 20
1111000001 => [4,5,1] => [5,4,1] => [4,1] => 18
1111000000 => [4,6] => [6,4] => [4] => 16
1110111111 => [3,1,6] => [6,3,1] => [3,1] => 10
1110111110 => [3,1,5,1] => [5,3,1,1] => [3,1,1] => 13
1110111101 => [3,1,4,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1110111011 => [3,1,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => 17
1110111000 => [3,1,3,3] => [3,3,3,1] => [3,3,1] => 17
1110110101 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110110100 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110110010 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110110001 => [3,1,2,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1110101111 => [3,1,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => 14
1110101101 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110101100 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1110101011 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110101010 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
1110101001 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110100101 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110100011 => [3,1,1,3,2] => [3,3,2,1,1] => [3,2,1,1] => 17
1110100001 => [3,1,1,4,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1110011111 => [3,2,5] => [5,3,2] => [3,2] => 11
1110011110 => [3,2,4,1] => [4,3,2,1] => [3,2,1] => 15
1110011001 => [3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
1110010101 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1110010011 => [3,2,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1110010001 => [3,2,1,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1110001101 => [3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1110001001 => [3,3,1,2,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1110000111 => [3,4,3] => [4,3,3] => [3,3] => 12
1110000101 => [3,4,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1110000011 => [3,5,2] => [5,3,2] => [3,2] => 11
1110000010 => [3,5,1,1] => [5,3,1,1] => [3,1,1] => 13
1110000001 => [3,6,1] => [6,3,1] => [3,1] => 10
1101111111 => [2,1,7] => [7,2,1] => [2,1] => 4
1101111110 => [2,1,6,1] => [6,2,1,1] => [2,1,1] => 6
1101111101 => [2,1,5,1,1] => [5,2,1,1,1] => [2,1,1,1] => 6
1101111011 => [2,1,4,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1101111001 => [2,1,4,2,1] => [4,2,2,1,1] => [2,2,1,1] => 8
1101111000 => [2,1,4,3] => [4,3,2,1] => [3,2,1] => 15
1101110111 => [2,1,3,1,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1101110010 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101110001 => [2,1,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1101101111 => [2,1,2,1,4] => [4,2,2,1,1] => [2,2,1,1] => 8
1101101100 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1101101001 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101100110 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1101100101 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101100011 => [2,1,2,3,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1101100001 => [2,1,2,4,1] => [4,2,2,1,1] => [2,2,1,1] => 8
1101100000 => [2,1,2,5] => [5,2,2,1] => [2,2,1] => 7
1101011111 => [2,1,1,1,5] => [5,2,1,1,1] => [2,1,1,1] => 6
1101011010 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1101011001 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101010111 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1101010101 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1101010011 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101010001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1101001111 => [2,1,1,2,4] => [4,2,2,1,1] => [2,2,1,1] => 8
1101001110 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101001101 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101001011 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101001001 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1101001000 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1101000111 => [2,1,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1101000101 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1101000011 => [2,1,1,4,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1101000010 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1101000001 => [2,1,1,5,1] => [5,2,1,1,1] => [2,1,1,1] => 6
1100111111 => [2,2,6] => [6,2,2] => [2,2] => 4
1100111100 => [2,2,4,2] => [4,2,2,2] => [2,2,2] => 8
1100111001 => [2,2,3,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
1100110110 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1100110101 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1100110011 => [2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 10
1100110001 => [2,2,2,3,1] => [3,2,2,2,1] => [2,2,2,1] => 9
1100110000 => [2,2,2,4] => [4,2,2,2] => [2,2,2] => 8
1100101110 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1100101101 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1100101011 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1100101001 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1100100111 => [2,2,1,2,3] => [3,2,2,2,1] => [2,2,2,1] => 9
1100100110 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1100100101 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1100100011 => [2,2,1,3,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1100011110 => [2,3,4,1] => [4,3,2,1] => [3,2,1] => 15
1100011101 => [2,3,3,1,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1100011100 => [2,3,3,2] => [3,3,2,2] => [3,2,2] => 17
1100011011 => [2,3,2,1,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1100011001 => [2,3,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
1100011000 => [2,3,2,3] => [3,3,2,2] => [3,2,2] => 17
1100010111 => [2,3,1,1,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1100010101 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1100010011 => [2,3,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1100010010 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1100001111 => [2,4,4] => [4,4,2] => [4,2] => 20
1100001101 => [2,4,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 8
1100001100 => [2,4,2,2] => [4,2,2,2] => [2,2,2] => 8
1100001011 => [2,4,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1100001010 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1100001000 => [2,4,1,3] => [4,3,2,1] => [3,2,1] => 15
1100000111 => [2,5,3] => [5,3,2] => [3,2] => 11
1100000110 => [2,5,2,1] => [5,2,2,1] => [2,2,1] => 7
1100000011 => [2,6,2] => [6,2,2] => [2,2] => 4
1100000010 => [2,6,1,1] => [6,2,1,1] => [2,1,1] => 6
1100000001 => [2,7,1] => [7,2,1] => [2,1] => 4
1100000000 => [2,8] => [8,2] => [2] => 4
1011111111 => [1,1,8] => [8,1,1] => [1,1] => 0
1011111110 => [1,1,7,1] => [7,1,1,1] => [1,1,1] => 1
1011111101 => [1,1,6,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
1011111100 => [1,1,6,2] => [6,2,1,1] => [2,1,1] => 6
1011111011 => [1,1,5,1,2] => [5,2,1,1,1] => [2,1,1,1] => 6
1011111010 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1011111000 => [1,1,5,3] => [5,3,1,1] => [3,1,1] => 13
1011110111 => [1,1,4,1,3] => [4,3,1,1,1] => [3,1,1,1] => 14
1011110100 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1011110001 => [1,1,4,3,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1011100011 => [1,1,3,3,2] => [3,3,2,1,1] => [3,2,1,1] => 17
1011100001 => [1,1,3,4,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1011100000 => [1,1,3,5] => [5,3,1,1] => [3,1,1] => 13
1011011001 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1011010111 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1011010101 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1011010011 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1011010001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1011010000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1011001101 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1011001011 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1011001001 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1011001000 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1011000111 => [1,1,2,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1011000101 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1011000100 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1011000011 => [1,1,2,4,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1011000010 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1011000000 => [1,1,2,6] => [6,2,1,1] => [2,1,1] => 6
1010111111 => [1,1,1,1,6] => [6,1,1,1,1] => [1,1,1,1] => 0
1010111110 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1010110111 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010110101 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010110011 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1010110001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010110000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1010101111 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
1010101101 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010101011 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010101001 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010101000 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
1010100111 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010100110 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010100101 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010100100 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010100011 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010100010 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
1010100000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1010011101 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010011011 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1010011010 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010011001 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1010011000 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1010010111 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010010110 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010010101 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1010010100 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010010011 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1010010010 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1010010001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010001111 => [1,1,1,3,4] => [4,3,1,1,1] => [3,1,1,1] => 14
1010001110 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1010001101 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010001100 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1010001011 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1010001010 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
1010000111 => [1,1,1,4,3] => [4,3,1,1,1] => [3,1,1,1] => 14
1010000010 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1010000001 => [1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1] => 0
1010000000 => [1,1,1,7] => [7,1,1,1] => [1,1,1] => 1
1001111110 => [1,2,6,1] => [6,2,1,1] => [2,1,1] => 6
1001111000 => [1,2,4,3] => [4,3,2,1] => [3,2,1] => 15
1001110101 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1001110100 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1001110011 => [1,2,3,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1001110001 => [1,2,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1001110000 => [1,2,3,4] => [4,3,2,1] => [3,2,1] => 15
1001101101 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001101100 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1001101011 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001101010 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001101001 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001101000 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1001100111 => [1,2,2,2,3] => [3,2,2,2,1] => [2,2,2,1] => 9
1001100110 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1001100101 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001100100 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1001100011 => [1,2,2,3,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1001100010 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1001011111 => [1,2,1,1,5] => [5,2,1,1,1] => [2,1,1,1] => 6
1001011110 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1001011101 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1001011011 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001011010 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001011001 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001011000 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1001010111 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1001010110 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001010101 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
1001010100 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001010011 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001010010 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001001111 => [1,2,1,2,4] => [4,2,2,1,1] => [2,2,1,1] => 8
1001001110 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1001001101 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001001100 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
1001001011 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
1001001010 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
1001000111 => [1,2,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1001000000 => [1,2,1,6] => [6,2,1,1] => [2,1,1] => 6
1000111110 => [1,3,5,1] => [5,3,1,1] => [3,1,1] => 13
1000111101 => [1,3,4,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1000111100 => [1,3,4,2] => [4,3,2,1] => [3,2,1] => 15
1000111011 => [1,3,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => 17
1000111010 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1000111001 => [1,3,3,2,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1000111000 => [1,3,3,3] => [3,3,3,1] => [3,3,1] => 17
1000110111 => [1,3,2,1,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1000110110 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1000110101 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1000110100 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1000110011 => [1,3,2,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
1000110010 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1000110001 => [1,3,2,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
1000101111 => [1,3,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => 14
1000101110 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
1000101101 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1000101100 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
1000101011 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
1000101010 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
1000100111 => [1,3,1,2,3] => [3,3,2,1,1] => [3,2,1,1] => 17
1000011111 => [1,4,5] => [5,4,1] => [4,1] => 18
1000011110 => [1,4,4,1] => [4,4,1,1] => [4,1,1] => 22
1000011101 => [1,4,3,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
1000011011 => [1,4,2,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
1000010111 => [1,4,1,1,3] => [4,3,1,1,1] => [3,1,1,1] => 14
1000010110 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
1000010101 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
1000001111 => [1,5,4] => [5,4,1] => [4,1] => 18
1000001110 => [1,5,3,1] => [5,3,1,1] => [3,1,1] => 13
1000001101 => [1,5,2,1,1] => [5,2,1,1,1] => [2,1,1,1] => 6
1000001011 => [1,5,1,1,2] => [5,2,1,1,1] => [2,1,1,1] => 6
1000001010 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
1000001001 => [1,5,1,2,1] => [5,2,1,1,1] => [2,1,1,1] => 6
1000000110 => [1,6,2,1] => [6,2,1,1] => [2,1,1] => 6
1000000101 => [1,6,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
1000000100 => [1,6,1,2] => [6,2,1,1] => [2,1,1] => 6
1000000011 => [1,7,2] => [7,2,1] => [2,1] => 4
1000000010 => [1,7,1,1] => [7,1,1,1] => [1,1,1] => 1
1000000001 => [1,8,1] => [8,1,1] => [1,1] => 0
1000000000 => [1,9] => [9,1] => [1] => 1
10000000000 => [1,10] => [10,1] => [1] => 1
10000000010 => [1,8,1,1] => [8,1,1,1] => [1,1,1] => 1
10000000110 => [1,7,2,1] => [7,2,1,1] => [2,1,1] => 6
10000001110 => [1,6,3,1] => [6,3,1,1] => [3,1,1] => 13
10000011110 => [1,5,4,1] => [5,4,1,1] => [4,1,1] => 22
10000111110 => [1,4,5,1] => [5,4,1,1] => [4,1,1] => 22
10001111110 => [1,3,6,1] => [6,3,1,1] => [3,1,1] => 13
10011111110 => [1,2,7,1] => [7,2,1,1] => [2,1,1] => 6
10111111110 => [1,1,8,1] => [8,1,1,1] => [1,1,1] => 1
11111111110 => [10,1] => [10,1] => [1] => 1
10000000100 => [1,7,1,2] => [7,2,1,1] => [2,1,1] => 6
100000111110 => [1,5,5,1] => [5,5,1,1] => [5,1,1] => 33
11011111110 => [2,1,7,1] => [7,2,1,1] => [2,1,1] => 6
11001111110 => [2,2,6,1] => [6,2,2,1] => [2,2,1] => 7
110111111110 => [2,1,8,1] => [8,2,1,1] => [2,1,1] => 6
10001010100 => [1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
110000011110 => [2,5,4,1] => [5,4,2,1] => [4,2,1] => 25
100001111100 => [1,4,5,2] => [5,4,2,1] => [4,2,1] => 25
10010001000 => [1,2,1,3,1,3] => [3,3,2,1,1,1] => [3,2,1,1,1] => 19
0111111111 => [1,9] => [9,1] => [1] => 1
0111111101 => [1,7,1,1] => [7,1,1,1] => [1,1,1] => 1
0111111001 => [1,6,2,1] => [6,2,1,1] => [2,1,1] => 6
0111110001 => [1,5,3,1] => [5,3,1,1] => [3,1,1] => 13
0111100001 => [1,4,4,1] => [4,4,1,1] => [4,1,1] => 22
0100000001 => [1,1,7,1] => [7,1,1,1] => [1,1,1] => 1
0000000001 => [9,1] => [9,1] => [1] => 1
01111111111 => [1,10] => [10,1] => [1] => 1
01111111101 => [1,8,1,1] => [8,1,1,1] => [1,1,1] => 1
0111111011 => [1,6,1,2] => [6,2,1,1] => [2,1,1] => 6
0111110101 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
0111101001 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0111010001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0110100001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101000001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
01000000001 => [1,1,8,1] => [8,1,1,1] => [1,1,1] => 1
00000000001 => [10,1] => [10,1] => [1] => 1
0101001011 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101000111 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0100110011 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0100100111 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100011011 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100010111 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0100001111 => [1,1,4,4] => [4,4,1,1] => [4,1,1] => 22
0011010011 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0011000111 => [2,2,3,3] => [3,3,2,2] => [3,2,2] => 17
0010101011 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0010010111 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0010001111 => [2,1,3,4] => [4,3,2,1] => [3,2,1] => 15
0001110011 => [3,3,2,2] => [3,3,2,2] => [3,2,2] => 17
0001101011 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0001100111 => [3,2,2,3] => [3,3,2,2] => [3,2,2] => 17
0001011101 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0001010111 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0001001111 => [3,1,2,4] => [4,3,2,1] => [3,2,1] => 15
0000111101 => [4,4,1,1] => [4,4,1,1] => [4,1,1] => 22
0000110111 => [4,2,1,3] => [4,3,2,1] => [3,2,1] => 15
0000101111 => [4,1,1,4] => [4,4,1,1] => [4,1,1] => 22
0000011111 => [5,5] => [5,5] => [5] => 25
010100001111 => [1,1,1,1,4,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
010010001111 => [1,1,2,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
010000111011 => [1,1,4,3,1,2] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
010000110111 => [1,1,4,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
010000101111 => [1,1,4,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
010000011111 => [1,1,5,5] => [5,5,1,1] => [5,1,1] => 33
001100001111 => [2,2,4,4] => [4,4,2,2] => [4,2,2] => 28
001010001111 => [2,1,1,1,3,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
001000101111 => [2,1,3,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
001000011111 => [2,1,4,5] => [5,4,2,1] => [4,2,1] => 25
000110001111 => [3,2,3,4] => [4,3,3,2] => [3,3,2] => 19
000100101111 => [3,1,2,1,1,4] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
000100011111 => [3,1,3,5] => [5,3,3,1] => [3,3,1] => 17
000011110101 => [4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
000011110011 => [4,4,2,2] => [4,4,2,2] => [4,2,2] => 28
000011011101 => [4,2,1,3,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
000011011011 => [4,2,1,2,1,2] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
000011010111 => [4,2,1,1,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
000011001111 => [4,2,2,4] => [4,4,2,2] => [4,2,2] => 28
000010110111 => [4,1,1,2,1,3] => [4,3,2,1,1,1] => [3,2,1,1,1] => 19
000010101111 => [4,1,1,1,1,4] => [4,4,1,1,1,1] => [4,1,1,1,1] => 28
000010011111 => [4,1,2,5] => [5,4,2,1] => [4,2,1] => 25
000001111101 => [5,5,1,1] => [5,5,1,1] => [5,1,1] => 33
000001111011 => [5,4,1,2] => [5,4,2,1] => [4,2,1] => 25
000001110111 => [5,3,1,3] => [5,3,3,1] => [3,3,1] => 17
000001101111 => [5,2,1,4] => [5,4,2,1] => [4,2,1] => 25
000001011111 => [5,1,1,5] => [5,5,1,1] => [5,1,1] => 33
000000111111 => [6,6] => [6,6] => [6] => 36
111110000001 => [5,6,1] => [6,5,1] => [5,1] => 28
111001100001 => [3,2,2,4,1] => [4,3,2,2,1] => [3,2,2,1] => 19
111000011001 => [3,4,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
111000000111 => [3,6,3] => [6,3,3] => [3,3] => 12
111000001101 => [3,5,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 17
111011000001 => [3,1,2,5,1] => [5,3,2,1,1] => [3,2,1,1] => 17
111010000101 => [3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
100111100001 => [1,2,4,4,1] => [4,4,2,1,1] => [4,2,1,1] => 28
100110000111 => [1,2,2,4,3] => [4,3,2,2,1] => [3,2,2,1] => 19
100001111001 => [1,4,4,2,1] => [4,4,2,1,1] => [4,2,1,1] => 28
100001100111 => [1,4,2,2,3] => [4,3,2,2,1] => [3,2,2,1] => 19
100001101101 => [1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
100000011111 => [1,6,5] => [6,5,1] => [5,1] => 28
100000110111 => [1,5,2,1,3] => [5,3,2,1,1] => [3,2,1,1] => 17
100000110001 => [1,5,2,3,1] => [5,3,2,1,1] => [3,2,1,1] => 17
100000111101 => [1,5,4,1,1] => [5,4,1,1,1] => [4,1,1,1] => 24
100011110001 => [1,3,4,3,1] => [4,3,3,1,1] => [3,3,1,1] => 19
101101111001 => [1,1,2,1,4,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101101100001 => [1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101100011111 => [1,1,2,3,5] => [5,3,2,1,1] => [3,2,1,1] => 17
101100000111 => [1,1,2,5,3] => [5,3,2,1,1] => [3,2,1,1] => 17
101100001101 => [1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101100111101 => [1,1,2,2,4,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101111011001 => [1,1,4,1,2,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101111000111 => [1,1,4,3,3] => [4,3,3,1,1] => [3,3,1,1] => 19
101111000001 => [1,1,4,5,1] => [5,4,1,1,1] => [4,1,1,1] => 24
101111001101 => [1,1,4,2,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
101111110001 => [1,1,6,3,1] => [6,3,1,1,1] => [3,1,1,1] => 14
101110000101 => [1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
101001011111 => [1,1,1,2,1,1,5] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101001000001 => [1,1,1,2,1,5,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
101000010111 => [1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
101000010001 => [1,1,1,4,1,3,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
101000011101 => [1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
0000000110 => [7,2,1] => [7,2,1] => [2,1] => 4
0000011000 => [5,2,3] => [5,3,2] => [3,2] => 11
0000011110 => [5,4,1] => [5,4,1] => [4,1] => 18
0001111110 => [3,6,1] => [6,3,1] => [3,1] => 10
0110011000 => [1,2,2,2,3] => [3,2,2,2,1] => [2,2,2,1] => 9
0110010010 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0111100000 => [1,4,5] => [5,4,1] => [4,1] => 18
0111111110 => [1,8,1] => [8,1,1] => [1,1] => 0
0111001000 => [1,3,2,1,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0111000010 => [1,3,4,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0100111000 => [1,1,2,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0100111110 => [1,1,2,5,1] => [5,2,1,1,1] => [2,1,1,1] => 6
0100110010 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0100000010 => [1,1,6,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
0101101000 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101100010 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101001010 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
000001111110 => [5,6,1] => [6,5,1] => [5,1] => 28
000110011110 => [3,2,2,4,1] => [4,3,2,2,1] => [3,2,2,1] => 19
000111100110 => [3,4,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
000111111000 => [3,6,3] => [6,3,3] => [3,3] => 12
000111110010 => [3,5,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 17
000100111110 => [3,1,2,5,1] => [5,3,2,1,1] => [3,2,1,1] => 17
000101111010 => [3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
011000011110 => [1,2,4,4,1] => [4,4,2,1,1] => [4,2,1,1] => 28
011001111000 => [1,2,2,4,3] => [4,3,2,2,1] => [3,2,2,1] => 19
011110000110 => [1,4,4,2,1] => [4,4,2,1,1] => [4,2,1,1] => 28
011110011000 => [1,4,2,2,3] => [4,3,2,2,1] => [3,2,2,1] => 19
011110010010 => [1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
011111100000 => [1,6,5] => [6,5,1] => [5,1] => 28
011111001000 => [1,5,2,1,3] => [5,3,2,1,1] => [3,2,1,1] => 17
011111000010 => [1,5,4,1,1] => [5,4,1,1,1] => [4,1,1,1] => 24
010010011110 => [1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
010011111000 => [1,1,2,5,3] => [5,3,2,1,1] => [3,2,1,1] => 17
010011110010 => [1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
010000111110 => [1,1,4,5,1] => [5,4,1,1,1] => [4,1,1,1] => 24
010001111010 => [1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
010111101000 => [1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
010111100010 => [1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
0010101010 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0010101100 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0010110100 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0011010100 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101010100 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0010101110 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0010111100 => [2,1,1,4,2] => [4,2,2,1,1] => [2,2,1,1] => 8
0011110100 => [2,4,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
0000010100 => [5,1,1,1,2] => [5,2,1,1,1] => [2,1,1,1] => 6
0111010100 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0000000010 => [8,1,1] => [8,1,1] => [1,1] => 0
0000001110 => [6,3,1] => [6,3,1] => [3,1] => 10
0000111110 => [4,5,1] => [5,4,1] => [4,1] => 18
0011111110 => [2,7,1] => [7,2,1] => [2,1] => 4
0000000100 => [7,1,2] => [7,2,1] => [2,1] => 4
0000001010 => [6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 0
0000010110 => [5,1,1,2,1] => [5,2,1,1,1] => [2,1,1,1] => 6
0000101110 => [4,1,1,3,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0001011110 => [3,1,1,4,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0010111110 => [2,1,1,5,1] => [5,2,1,1,1] => [2,1,1,1] => 6
00011111110 => [3,7,1] => [7,3,1] => [3,1] => 10
0101111110 => [1,1,1,6,1] => [6,1,1,1,1] => [1,1,1,1] => 0
00111111110 => [2,8,1] => [8,2,1] => [2,1] => 4
01111111110 => [1,9,1] => [9,1,1] => [1,1] => 0
0010110010 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0010111000 => [2,1,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0011001010 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0011001100 => [2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 10
0011010010 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0011011000 => [2,2,1,2,3] => [3,2,2,2,1] => [2,2,2,1] => 9
0011100010 => [2,3,3,1,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0011100100 => [2,3,2,1,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0011101000 => [2,3,1,1,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0011110000 => [2,4,4] => [4,4,2] => [4,2] => 20
0100101010 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0100101100 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0100110100 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101001100 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101010010 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0101011000 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101100100 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101110000 => [1,1,1,3,4] => [4,3,1,1,1] => [3,1,1,1] => 14
0110001010 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0110001100 => [1,2,3,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0110010100 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110100010 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0110100100 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110101000 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0110110000 => [1,2,1,2,4] => [4,2,2,1,1] => [2,2,1,1] => 8
0111000100 => [1,3,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => 17
0111010000 => [1,3,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => 14
001111100000 => [2,5,5] => [5,5,2] => [5,2] => 31
011100001010 => [1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
011100001100 => [1,3,4,2,2] => [4,3,2,2,1] => [3,2,2,1] => 19
10100010001 => [1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
10100001000 => [1,1,1,4,1,3] => [4,3,1,1,1,1] => [3,1,1,1,1] => 17
10010001001 => [1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
10010010001 => [1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
10001000101 => [1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
10001001001 => [1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
10001010001 => [1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
10000100001 => [1,4,1,4,1] => [4,4,1,1,1] => [4,1,1,1] => 24
00101010001 => [2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
00010000101 => [3,1,4,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 17
00010001001 => [3,1,3,1,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 19
0100000000 => [1,1,8] => [8,1,1] => [1,1] => 0
0100000011 => [1,1,6,2] => [6,2,1,1] => [2,1,1] => 6
0100000111 => [1,1,5,3] => [5,3,1,1] => [3,1,1] => 13
0100011111 => [1,1,3,5] => [5,3,1,1] => [3,1,1] => 13
0100111111 => [1,1,2,6] => [6,2,1,1] => [2,1,1] => 6
0101111111 => [1,1,1,7] => [7,1,1,1] => [1,1,1] => 1
01000000000 => [1,1,9] => [9,1,1] => [1,1] => 0
0100000101 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
0100001011 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0100101111 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101011111 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
0110111111 => [1,2,1,6] => [6,2,1,1] => [2,1,1] => 6
0101010110 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0101011001 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101011010 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0101011100 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101100101 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101100110 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101101001 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101101010 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0101101100 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0101110001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0101110010 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101110100 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0101111000 => [1,1,1,4,3] => [4,3,1,1,1] => [3,1,1,1] => 14
0110010101 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0110010110 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110011001 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0110011010 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110011100 => [1,2,2,3,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0110100101 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0110100110 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110101001 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0110101010 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0110101100 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110110001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110110010 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110110100 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110111000 => [1,2,1,3,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0111000101 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0111000110 => [1,3,3,2,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0111001001 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111001010 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0111001100 => [1,3,2,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0111010010 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0111011000 => [1,3,1,2,3] => [3,3,2,1,1] => [3,2,1,1] => 17
0111100010 => [1,4,3,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0111100100 => [1,4,2,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
0111101000 => [1,4,1,1,3] => [4,3,1,1,1] => [3,1,1,1] => 14
0111110000 => [1,5,4] => [5,4,1] => [4,1] => 18
011110001010 => [1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
011110001100 => [1,4,3,2,2] => [4,3,2,2,1] => [3,2,2,1] => 19
011110100010 => [1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
011111000001 => [1,5,5,1] => [5,5,1,1] => [5,1,1] => 33
0100000100 => [1,1,5,1,2] => [5,2,1,1,1] => [2,1,1,1] => 6
0011100110 => [2,3,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
0011101010 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0011101100 => [2,3,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0001101110 => [3,2,1,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0010110110 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0011110010 => [2,4,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 8
0001110110 => [3,3,1,2,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0100111010 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0010111010 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0011111000 => [2,5,3] => [5,3,2] => [3,2] => 11
0001111010 => [3,4,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0100111100 => [1,1,2,4,2] => [4,2,2,1,1] => [2,2,1,1] => 8
0001111100 => [3,5,2] => [5,3,2] => [3,2] => 11
001111000110 => [2,4,3,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
001111001010 => [2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
001111001100 => [2,4,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 10
001111010010 => [2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
000111101010 => [3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
100111110000 => [1,2,5,4] => [5,4,2,1] => [4,2,1] => 25
001111110000 => [2,6,4] => [6,4,2] => [4,2] => 20
110001111000 => [2,3,4,3] => [4,3,3,2] => [3,3,2] => 19
001001111010 => [2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
100011111000 => [1,3,5,3] => [5,3,3,1] => [3,3,1] => 17
000011111100 => [4,6,2] => [6,4,2] => [4,2] => 20
0000000101 => [7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
0000001101 => [6,2,1,1] => [6,2,1,1] => [2,1,1] => 6
0000011101 => [5,3,1,1] => [5,3,1,1] => [3,1,1] => 13
0001111101 => [3,5,1,1] => [5,3,1,1] => [3,1,1] => 13
0011111101 => [2,6,1,1] => [6,2,1,1] => [2,1,1] => 6
0000001001 => [6,1,2,1] => [6,2,1,1] => [2,1,1] => 6
0000010101 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
0000101101 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0010111101 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101111101 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
110011100001 => [2,2,3,4,1] => [4,3,2,2,1] => [3,2,2,1] => 19
110110000101 => [2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
111000010101 => [3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
0111000011 => [1,3,4,2] => [4,3,2,1] => [3,2,1] => 15
0011110001 => [2,4,3,1] => [4,3,2,1] => [3,2,1] => 15
110011000011 => [2,2,2,4,2] => [4,2,2,2,2] => [2,2,2,2] => 10
110000111100 => [2,4,4,2] => [4,4,2,2] => [4,2,2] => 28
110000001111 => [2,6,4] => [6,4,2] => [4,2] => 20
011100000111 => [1,3,5,3] => [5,3,3,1] => [3,3,1] => 17
111000011100 => [3,4,3,2] => [4,3,3,2] => [3,3,2] => 19
001111000011 => [2,4,4,2] => [4,4,2,2] => [4,2,2] => 28
011110000011 => [1,4,5,2] => [5,4,2,1] => [4,2,1] => 25
111100000011 => [4,6,2] => [6,4,2] => [4,2] => 20
000111110001 => [3,5,3,1] => [5,3,3,1] => [3,3,1] => 17
001111100001 => [2,5,4,1] => [5,4,2,1] => [4,2,1] => 25
0011011001 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0010110001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0001000001 => [3,1,5,1] => [5,3,1,1] => [3,1,1] => 13
0111010101 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0111010011 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111001101 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111011001 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111000111 => [1,3,3,3] => [3,3,3,1] => [3,3,1] => 17
0011110101 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0011110011 => [2,4,2,2] => [4,2,2,2] => [2,2,2] => 8
0111100101 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0111100011 => [1,4,3,2] => [4,3,2,1] => [3,2,1] => 15
0011111001 => [2,5,2,1] => [5,2,2,1] => [2,2,1] => 7
0000111111 => [4,6] => [6,4] => [4] => 16
110001111001 => [2,3,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
110011110001 => [2,2,4,3,1] => [4,3,2,2,1] => [3,2,2,1] => 19
110000011111 => [2,5,5] => [5,5,2] => [5,2] => 31
011100001111 => [1,3,4,4] => [4,4,3,1] => [4,3,1] => 28
111000001111 => [3,5,4] => [5,4,3] => [4,3] => 22
001111000111 => [2,4,3,3] => [4,3,3,2] => [3,3,2] => 19
011110011001 => [1,4,2,2,2,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 10
011110000111 => [1,4,4,3] => [4,4,3,1] => [4,3,1] => 28
111100010101 => [4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
111100100101 => [4,2,1,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
111100101001 => [4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
111101000101 => [4,1,1,3,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
111101001001 => [4,1,1,2,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
111100011001 => [4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
111100110001 => [4,2,2,3,1] => [4,3,2,2,1] => [3,2,2,1] => 19
111100000111 => [4,5,3] => [5,4,3] => [4,3] => 22
000111110011 => [3,5,2,2] => [5,3,2,2] => [3,2,2] => 17
001111100011 => [2,5,3,2] => [5,3,2,2] => [3,2,2] => 17
011111000011 => [1,5,4,2] => [5,4,2,1] => [4,2,1] => 25
111110000011 => [5,5,2] => [5,5,2] => [5,2] => 31
111111000001 => [6,5,1] => [6,5,1] => [5,1] => 28
0001101100 => [3,2,1,2,2] => [3,2,2,2,1] => [2,2,2,1] => 9
0011000110 => [2,2,3,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
0010001110 => [2,1,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0110111001 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
00001011101 => [4,1,1,3,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 17
0001101001 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
00000101101 => [5,1,1,2,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 8
0000110001 => [4,2,3,1] => [4,3,2,1] => [3,2,1] => 15
00000010101 => [6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
0000010001 => [5,1,3,1] => [5,3,1,1] => [3,1,1] => 13
10000000001 => [1,9,1] => [9,1,1] => [1,1] => 0
11000000001 => [2,8,1] => [8,2,1] => [2,1] => 4
11100000001 => [3,7,1] => [7,3,1] => [3,1] => 10
0100011001 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100111001 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101111001 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0110010001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100010001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0100110001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100100001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101100001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0110011011 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0110111011 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100111011 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101111011 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0110010011 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0100010011 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110110011 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0101110011 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110100011 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100100011 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101100011 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101000011 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0110010111 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110110111 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0100110111 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101110111 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => [3,1,1,1,1] => 17
0110100111 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101100111 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110101111 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101101111 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0101001111 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
100001110101 => [1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
100001011101 => [1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
100001110011 => [1,4,3,2,2] => [4,3,2,2,1] => [3,2,2,1] => 19
0000001100 => [6,2,2] => [6,2,2] => [2,2] => 4
0000011001 => [5,2,2,1] => [5,2,2,1] => [2,2,1] => 7
0000110011 => [4,2,2,2] => [4,2,2,2] => [2,2,2] => 8
0011001111 => [2,2,2,4] => [4,2,2,2] => [2,2,2] => 8
0110011111 => [1,2,2,5] => [5,2,2,1] => [2,2,1] => 7
0000110100 => [4,2,1,1,2] => [4,2,2,1,1] => [2,2,1,1] => 8
0000000011 => [8,2] => [8,2] => [2] => 4
0000011011 => [5,2,1,2] => [5,2,2,1] => [2,2,1] => 7
0001101111 => [3,2,1,4] => [4,3,2,1] => [3,2,1] => 15
0011011111 => [2,2,1,5] => [5,2,2,1] => [2,2,1] => 7
00000000011 => [9,2] => [9,2] => [2] => 4
0000110101 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 8
0011010111 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
10001010101 => [1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
10000010101 => [1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
10000000101 => [1,7,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 0
0111001011 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111110111 => [1,5,1,3] => [5,3,1,1] => [3,1,1] => 13
11000000000 => [2,9] => [9,2] => [2] => 4
0110001011 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110000111 => [1,2,4,3] => [4,3,2,1] => [3,2,1] => 15
110000111001 => [2,4,3,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
110000110101 => [2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
110000101101 => [2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
110000110011 => [2,4,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 10
001110000111 => [2,3,4,3] => [4,3,3,2] => [3,3,2] => 19
011000001111 => [1,2,5,4] => [5,4,2,1] => [4,2,1] => 25
0011011010 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0011010110 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0100110110 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
0110001110 => [1,2,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0101001110 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0011001110 => [2,2,2,3,1] => [3,2,2,2,1] => [2,2,2,1] => 9
0100101110 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
0100011110 => [1,1,3,4,1] => [4,3,1,1,1] => [3,1,1,1] => 14
0010011110 => [2,1,2,4,1] => [4,2,2,1,1] => [2,2,1,1] => 8
001100011110 => [2,2,3,4,1] => [4,3,2,2,1] => [3,2,2,1] => 19
0101000000 => [1,1,1,1,6] => [6,1,1,1,1] => [1,1,1,1] => 0
0001010000 => [3,1,1,1,4] => [4,3,1,1,1] => [3,1,1,1] => 14
0100010000 => [1,1,3,1,4] => [4,3,1,1,1] => [3,1,1,1] => 14
0001000100 => [3,1,3,1,2] => [3,3,2,1,1] => [3,2,1,1] => 17
0111011100 => [1,3,1,3,2] => [3,3,2,1,1] => [3,2,1,1] => 17
0101000101 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0001010101 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0100010101 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0110110101 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101010001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0100101001 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0110001001 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0101011011 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0001001011 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0110101011 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0001100011 => [3,2,3,2] => [3,3,2,2] => [3,2,2] => 17
0110000011 => [1,2,5,2] => [5,2,2,1] => [2,2,1] => 7
0001110111 => [3,3,1,3] => [3,3,3,1] => [3,3,1] => 17
0111101111 => [1,4,1,4] => [4,4,1,1] => [4,1,1] => 22
011000001100 => [1,2,5,2,2] => [5,2,2,2,1] => [2,2,2,1] => 9
000001100011 => [5,2,3,2] => [5,3,2,2] => [3,2,2] => 17
000110000011 => [3,2,5,2] => [5,3,2,2] => [3,2,2] => 17
011110001111 => [1,4,3,4] => [4,4,3,1] => [4,3,1] => 28
01111100000 => [1,5,5] => [5,5,1] => [5,1] => 28
01111110000 => [1,6,4] => [6,4,1] => [4,1] => 18
100011110101 => [1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 18
100011110011 => [1,3,4,2,2] => [4,3,2,2,1] => [3,2,2,1] => 19
0000000111 => [7,3] => [7,3] => [3] => 9
0000001111 => [6,4] => [6,4] => [4] => 16
0001111111 => [3,7] => [7,3] => [3] => 9
0011111111 => [2,8] => [8,2] => [2] => 4
0000001011 => [6,1,1,2] => [6,2,1,1] => [2,1,1] => 6
0000010111 => [5,1,1,3] => [5,3,1,1] => [3,1,1] => 13
0001011111 => [3,1,1,5] => [5,3,1,1] => [3,1,1] => 13
0010111111 => [2,1,1,6] => [6,2,1,1] => [2,1,1] => 6
00111111111 => [2,9] => [9,2] => [2] => 4
10111111111 => [1,1,9] => [9,1,1] => [1,1] => 0
10000001011 => [1,6,1,1,2] => [6,2,1,1,1] => [2,1,1,1] => 6
0011011110 => [2,2,1,4,1] => [4,2,2,1,1] => [2,2,1,1] => 8
0011101110 => [2,3,1,3,1] => [3,3,2,1,1] => [3,2,1,1] => 17
0011110110 => [2,4,1,2,1] => [4,2,2,1,1] => [2,2,1,1] => 8
0011111010 => [2,5,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 6
0011111100 => [2,6,2] => [6,2,2] => [2,2] => 4
00101111110 => [2,1,1,6,1] => [6,2,1,1,1] => [2,1,1,1] => 6
000111100011 => [3,4,3,2] => [4,3,3,2] => [3,3,2] => 19
0010010101 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101010111 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
10101010001 => [1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
01110101010 => [1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
0101110101 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
01111100100 => [1,5,2,1,2] => [5,2,2,1,1] => [2,2,1,1] => 8
100111110101 => [1,2,5,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 8
100000010101 => [1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
111101101001 => [4,1,2,1,1,2,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
111100101101 => [4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 10
110000011000 => [2,5,2,3] => [5,3,2,2] => [3,2,2] => 17
111100011110 => [4,3,4,1] => [4,4,3,1] => [4,3,1] => 28
111100000110 => [4,5,2,1] => [5,4,2,1] => [4,2,1] => 25
0110001111 => [1,2,3,4] => [4,3,2,1] => [3,2,1] => 15
0101101011 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 10
0101011101 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
0011000011 => [2,2,4,2] => [4,2,2,2] => [2,2,2] => 8
0011011011 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [2,2,2,1,1] => 10
0001111011 => [3,4,1,2] => [4,3,2,1] => [3,2,1] => 15
111111001111 => [6,2,4] => [6,4,2] => [4,2] => 20
111111000011 => [6,4,2] => [6,4,2] => [4,2] => 20
111100110011 => [4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 10
111100001111 => [4,4,4] => [4,4,4] => [4,4] => 24
110011110011 => [2,2,4,2,2] => [4,2,2,2,2] => [2,2,2,2] => 10
001111110011 => [2,6,2,2] => [6,2,2,2] => [2,2,2] => 8
001111001111 => [2,4,2,4] => [4,4,2,2] => [4,2,2] => 28
000011000011 => [4,2,4,2] => [4,4,2,2] => [4,2,2] => 28
000000110011 => [6,2,2,2] => [6,2,2,2] => [2,2,2] => 8
000000000011 => [10,2] => [10,2] => [2] => 4
011111111011 => [1,8,1,2] => [8,2,1,1] => [2,1,1] => 6
111111111100 => [10,2] => [10,2] => [2] => 4
111111001100 => [6,2,2,2] => [6,2,2,2] => [2,2,2] => 8
111100111100 => [4,2,4,2] => [4,4,2,2] => [4,2,2] => 28
110000110000 => [2,4,2,4] => [4,4,2,2] => [4,2,2] => 28
110000001100 => [2,6,2,2] => [6,2,2,2] => [2,2,2] => 8
0011011101 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 9
0111011111 => [1,3,1,5] => [5,3,1,1] => [3,1,1] => 13
111100111001 => [4,2,3,2,1] => [4,3,2,2,1] => [3,2,2,1] => 19
search for individual values
searching the database for the individual values of this statistic
Description
The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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 $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
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