Identifier
Values
0 => [1] => 0
1 => [1] => 0
00 => [2] => 0
01 => [1,1] => 0
10 => [1,1] => 0
11 => [2] => 0
000 => [3] => 0
001 => [2,1] => 0
010 => [1,1,1] => 0
011 => [1,2] => 0
100 => [1,2] => 0
101 => [1,1,1] => 0
110 => [2,1] => 0
111 => [3] => 0
0000 => [4] => 0
0001 => [3,1] => 0
0010 => [2,1,1] => 0
0011 => [2,2] => 0
0100 => [1,1,2] => 0
0101 => [1,1,1,1] => 0
0110 => [1,2,1] => 1
0111 => [1,3] => 0
1000 => [1,3] => 0
1001 => [1,2,1] => 1
1010 => [1,1,1,1] => 0
1011 => [1,1,2] => 0
1100 => [2,2] => 0
1101 => [2,1,1] => 0
1110 => [3,1] => 0
1111 => [4] => 0
00000 => [5] => 0
00001 => [4,1] => 0
00010 => [3,1,1] => 0
00011 => [3,2] => 0
00100 => [2,1,2] => 0
00101 => [2,1,1,1] => 0
00110 => [2,2,1] => 0
00111 => [2,3] => 0
01000 => [1,1,3] => 0
01001 => [1,1,2,1] => 1
01010 => [1,1,1,1,1] => 0
01011 => [1,1,1,2] => 0
01100 => [1,2,2] => 0
01101 => [1,2,1,1] => 1
01110 => [1,3,1] => 1
01111 => [1,4] => 0
10000 => [1,4] => 0
10001 => [1,3,1] => 1
10010 => [1,2,1,1] => 1
10011 => [1,2,2] => 0
10100 => [1,1,1,2] => 0
10101 => [1,1,1,1,1] => 0
10110 => [1,1,2,1] => 1
10111 => [1,1,3] => 0
11000 => [2,3] => 0
11001 => [2,2,1] => 0
11010 => [2,1,1,1] => 0
11011 => [2,1,2] => 0
11100 => [3,2] => 0
11101 => [3,1,1] => 0
11110 => [4,1] => 0
11111 => [5] => 0
000000 => [6] => 0
000001 => [5,1] => 0
000010 => [4,1,1] => 0
000011 => [4,2] => 0
000100 => [3,1,2] => 0
000101 => [3,1,1,1] => 0
000110 => [3,2,1] => 0
000111 => [3,3] => 0
001000 => [2,1,3] => 0
001001 => [2,1,2,1] => 1
001010 => [2,1,1,1,1] => 0
001011 => [2,1,1,2] => 0
001100 => [2,2,2] => 0
001101 => [2,2,1,1] => 0
001110 => [2,3,1] => 1
001111 => [2,4] => 0
010000 => [1,1,4] => 0
010001 => [1,1,3,1] => 1
010010 => [1,1,2,1,1] => 1
010011 => [1,1,2,2] => 0
010100 => [1,1,1,1,2] => 0
010101 => [1,1,1,1,1,1] => 0
010110 => [1,1,1,2,1] => 1
010111 => [1,1,1,3] => 0
011000 => [1,2,3] => 0
011001 => [1,2,2,1] => 0
011010 => [1,2,1,1,1] => 1
011011 => [1,2,1,2] => 1
011100 => [1,3,2] => 1
011101 => [1,3,1,1] => 1
011110 => [1,4,1] => 1
011111 => [1,5] => 0
100000 => [1,5] => 0
100001 => [1,4,1] => 1
100010 => [1,3,1,1] => 1
100011 => [1,3,2] => 1
100100 => [1,2,1,2] => 1
100101 => [1,2,1,1,1] => 1
100110 => [1,2,2,1] => 0
>>> Load all 1345 entries. <<<
100111 => [1,2,3] => 0
101000 => [1,1,1,3] => 0
101001 => [1,1,1,2,1] => 1
101010 => [1,1,1,1,1,1] => 0
101011 => [1,1,1,1,2] => 0
101100 => [1,1,2,2] => 0
101101 => [1,1,2,1,1] => 1
101110 => [1,1,3,1] => 1
101111 => [1,1,4] => 0
110000 => [2,4] => 0
110001 => [2,3,1] => 1
110010 => [2,2,1,1] => 0
110011 => [2,2,2] => 0
110100 => [2,1,1,2] => 0
110101 => [2,1,1,1,1] => 0
110110 => [2,1,2,1] => 1
110111 => [2,1,3] => 0
111000 => [3,3] => 0
111001 => [3,2,1] => 0
111010 => [3,1,1,1] => 0
111011 => [3,1,2] => 0
111100 => [4,2] => 0
111101 => [4,1,1] => 0
111110 => [5,1] => 0
111111 => [6] => 0
0000000 => [7] => 0
0000001 => [6,1] => 0
0000010 => [5,1,1] => 0
0000011 => [5,2] => 0
0000100 => [4,1,2] => 0
0000101 => [4,1,1,1] => 0
0000110 => [4,2,1] => 0
0000111 => [4,3] => 0
0001000 => [3,1,3] => 0
0001001 => [3,1,2,1] => 1
0001010 => [3,1,1,1,1] => 0
0001011 => [3,1,1,2] => 0
0001100 => [3,2,2] => 0
0001101 => [3,2,1,1] => 0
0001110 => [3,3,1] => 0
0001111 => [3,4] => 0
0010000 => [2,1,4] => 0
0010001 => [2,1,3,1] => 1
0010010 => [2,1,2,1,1] => 1
0010011 => [2,1,2,2] => 0
0010100 => [2,1,1,1,2] => 0
0010101 => [2,1,1,1,1,1] => 0
0010110 => [2,1,1,2,1] => 1
0010111 => [2,1,1,3] => 0
0011000 => [2,2,3] => 0
0011001 => [2,2,2,1] => 0
0011010 => [2,2,1,1,1] => 0
0011011 => [2,2,1,2] => 0
0011100 => [2,3,2] => 1
0011101 => [2,3,1,1] => 1
0011110 => [2,4,1] => 1
0011111 => [2,5] => 0
0100000 => [1,1,5] => 0
0100001 => [1,1,4,1] => 1
0100010 => [1,1,3,1,1] => 1
0100011 => [1,1,3,2] => 1
0100100 => [1,1,2,1,2] => 1
0100101 => [1,1,2,1,1,1] => 1
0100110 => [1,1,2,2,1] => 0
0100111 => [1,1,2,3] => 0
0101000 => [1,1,1,1,3] => 0
0101001 => [1,1,1,1,2,1] => 1
0101010 => [1,1,1,1,1,1,1] => 0
0101011 => [1,1,1,1,1,2] => 0
0101100 => [1,1,1,2,2] => 0
0101101 => [1,1,1,2,1,1] => 1
0101110 => [1,1,1,3,1] => 1
0101111 => [1,1,1,4] => 0
0110000 => [1,2,4] => 0
0110001 => [1,2,3,1] => 1
0110010 => [1,2,2,1,1] => 0
0110011 => [1,2,2,2] => 0
0110100 => [1,2,1,1,2] => 1
0110101 => [1,2,1,1,1,1] => 1
0110110 => [1,2,1,2,1] => 2
0110111 => [1,2,1,3] => 1
0111000 => [1,3,3] => 0
0111001 => [1,3,2,1] => 1
0111010 => [1,3,1,1,1] => 1
0111011 => [1,3,1,2] => 1
0111100 => [1,4,2] => 1
0111101 => [1,4,1,1] => 1
0111110 => [1,5,1] => 1
0111111 => [1,6] => 0
1000000 => [1,6] => 0
1000001 => [1,5,1] => 1
1000010 => [1,4,1,1] => 1
1000011 => [1,4,2] => 1
1000100 => [1,3,1,2] => 1
1000101 => [1,3,1,1,1] => 1
1000110 => [1,3,2,1] => 1
1000111 => [1,3,3] => 0
1001000 => [1,2,1,3] => 1
1001001 => [1,2,1,2,1] => 2
1001010 => [1,2,1,1,1,1] => 1
1001011 => [1,2,1,1,2] => 1
1001100 => [1,2,2,2] => 0
1001101 => [1,2,2,1,1] => 0
1001110 => [1,2,3,1] => 1
1001111 => [1,2,4] => 0
1010000 => [1,1,1,4] => 0
1010001 => [1,1,1,3,1] => 1
1010010 => [1,1,1,2,1,1] => 1
1010011 => [1,1,1,2,2] => 0
1010100 => [1,1,1,1,1,2] => 0
1010101 => [1,1,1,1,1,1,1] => 0
1010110 => [1,1,1,1,2,1] => 1
1010111 => [1,1,1,1,3] => 0
1011000 => [1,1,2,3] => 0
1011001 => [1,1,2,2,1] => 0
1011010 => [1,1,2,1,1,1] => 1
1011011 => [1,1,2,1,2] => 1
1011100 => [1,1,3,2] => 1
1011101 => [1,1,3,1,1] => 1
1011110 => [1,1,4,1] => 1
1011111 => [1,1,5] => 0
1100000 => [2,5] => 0
1100001 => [2,4,1] => 1
1100010 => [2,3,1,1] => 1
1100011 => [2,3,2] => 1
1100100 => [2,2,1,2] => 0
1100101 => [2,2,1,1,1] => 0
1100110 => [2,2,2,1] => 0
1100111 => [2,2,3] => 0
1101000 => [2,1,1,3] => 0
1101001 => [2,1,1,2,1] => 1
1101010 => [2,1,1,1,1,1] => 0
1101011 => [2,1,1,1,2] => 0
1101100 => [2,1,2,2] => 0
1101101 => [2,1,2,1,1] => 1
1101110 => [2,1,3,1] => 1
1101111 => [2,1,4] => 0
1110000 => [3,4] => 0
1110001 => [3,3,1] => 0
1110010 => [3,2,1,1] => 0
1110011 => [3,2,2] => 0
1110100 => [3,1,1,2] => 0
1110101 => [3,1,1,1,1] => 0
1110110 => [3,1,2,1] => 1
1110111 => [3,1,3] => 0
1111000 => [4,3] => 0
1111001 => [4,2,1] => 0
1111010 => [4,1,1,1] => 0
1111011 => [4,1,2] => 0
1111100 => [5,2] => 0
1111101 => [5,1,1] => 0
1111110 => [6,1] => 0
1111111 => [7] => 0
00000000 => [8] => 0
00000001 => [7,1] => 0
00000010 => [6,1,1] => 0
00000011 => [6,2] => 0
00000100 => [5,1,2] => 0
00000101 => [5,1,1,1] => 0
00000110 => [5,2,1] => 0
00000111 => [5,3] => 0
00001000 => [4,1,3] => 0
00001001 => [4,1,2,1] => 1
00001010 => [4,1,1,1,1] => 0
00001011 => [4,1,1,2] => 0
00001100 => [4,2,2] => 0
00001101 => [4,2,1,1] => 0
00001110 => [4,3,1] => 0
00001111 => [4,4] => 0
00010000 => [3,1,4] => 0
00010001 => [3,1,3,1] => 1
00010010 => [3,1,2,1,1] => 1
00010011 => [3,1,2,2] => 0
00010100 => [3,1,1,1,2] => 0
00010101 => [3,1,1,1,1,1] => 0
00010110 => [3,1,1,2,1] => 1
00010111 => [3,1,1,3] => 0
00011000 => [3,2,3] => 0
00011001 => [3,2,2,1] => 0
00011010 => [3,2,1,1,1] => 0
00011011 => [3,2,1,2] => 0
00011100 => [3,3,2] => 0
00011101 => [3,3,1,1] => 0
00011110 => [3,4,1] => 1
00011111 => [3,5] => 0
00100000 => [2,1,5] => 0
00100001 => [2,1,4,1] => 1
00100010 => [2,1,3,1,1] => 1
00100011 => [2,1,3,2] => 1
00100100 => [2,1,2,1,2] => 1
00100101 => [2,1,2,1,1,1] => 1
00100110 => [2,1,2,2,1] => 0
00100111 => [2,1,2,3] => 0
00101000 => [2,1,1,1,3] => 0
00101001 => [2,1,1,1,2,1] => 1
00101010 => [2,1,1,1,1,1,1] => 0
00101011 => [2,1,1,1,1,2] => 0
00101100 => [2,1,1,2,2] => 0
00101101 => [2,1,1,2,1,1] => 1
00101110 => [2,1,1,3,1] => 1
00101111 => [2,1,1,4] => 0
00110000 => [2,2,4] => 0
00110001 => [2,2,3,1] => 1
00110010 => [2,2,2,1,1] => 0
00110011 => [2,2,2,2] => 0
00110100 => [2,2,1,1,2] => 0
00110101 => [2,2,1,1,1,1] => 0
00110110 => [2,2,1,2,1] => 1
00110111 => [2,2,1,3] => 0
00111000 => [2,3,3] => 0
00111001 => [2,3,2,1] => 1
00111010 => [2,3,1,1,1] => 1
00111011 => [2,3,1,2] => 1
00111100 => [2,4,2] => 1
00111101 => [2,4,1,1] => 1
00111110 => [2,5,1] => 1
00111111 => [2,6] => 0
01000000 => [1,1,6] => 0
01000001 => [1,1,5,1] => 1
01000010 => [1,1,4,1,1] => 1
01000011 => [1,1,4,2] => 1
01000100 => [1,1,3,1,2] => 1
01000101 => [1,1,3,1,1,1] => 1
01000110 => [1,1,3,2,1] => 1
01000111 => [1,1,3,3] => 0
01001000 => [1,1,2,1,3] => 1
01001001 => [1,1,2,1,2,1] => 2
01001010 => [1,1,2,1,1,1,1] => 1
01001011 => [1,1,2,1,1,2] => 1
01001100 => [1,1,2,2,2] => 0
01001101 => [1,1,2,2,1,1] => 0
01001110 => [1,1,2,3,1] => 1
01001111 => [1,1,2,4] => 0
01010000 => [1,1,1,1,4] => 0
01010001 => [1,1,1,1,3,1] => 1
01010010 => [1,1,1,1,2,1,1] => 1
01010011 => [1,1,1,1,2,2] => 0
01010100 => [1,1,1,1,1,1,2] => 0
01010101 => [1,1,1,1,1,1,1,1] => 0
01010110 => [1,1,1,1,1,2,1] => 1
01010111 => [1,1,1,1,1,3] => 0
01011000 => [1,1,1,2,3] => 0
01011001 => [1,1,1,2,2,1] => 0
01011010 => [1,1,1,2,1,1,1] => 1
01011011 => [1,1,1,2,1,2] => 1
01011100 => [1,1,1,3,2] => 1
01011101 => [1,1,1,3,1,1] => 1
01011110 => [1,1,1,4,1] => 1
01011111 => [1,1,1,5] => 0
01100000 => [1,2,5] => 0
01100001 => [1,2,4,1] => 1
01100010 => [1,2,3,1,1] => 1
01100011 => [1,2,3,2] => 1
01100100 => [1,2,2,1,2] => 0
01100101 => [1,2,2,1,1,1] => 0
01100110 => [1,2,2,2,1] => 0
01100111 => [1,2,2,3] => 0
01101000 => [1,2,1,1,3] => 1
01101001 => [1,2,1,1,2,1] => 2
01101010 => [1,2,1,1,1,1,1] => 1
01101011 => [1,2,1,1,1,2] => 1
01101100 => [1,2,1,2,2] => 1
01101101 => [1,2,1,2,1,1] => 2
01101110 => [1,2,1,3,1] => 2
01101111 => [1,2,1,4] => 1
01110000 => [1,3,4] => 0
01110001 => [1,3,3,1] => 0
01110010 => [1,3,2,1,1] => 1
01110011 => [1,3,2,2] => 1
01110100 => [1,3,1,1,2] => 1
01110101 => [1,3,1,1,1,1] => 1
01110110 => [1,3,1,2,1] => 2
01110111 => [1,3,1,3] => 1
01111000 => [1,4,3] => 1
01111001 => [1,4,2,1] => 1
01111010 => [1,4,1,1,1] => 1
01111011 => [1,4,1,2] => 1
01111100 => [1,5,2] => 1
01111101 => [1,5,1,1] => 1
01111110 => [1,6,1] => 1
01111111 => [1,7] => 0
10000000 => [1,7] => 0
10000001 => [1,6,1] => 1
10000010 => [1,5,1,1] => 1
10000011 => [1,5,2] => 1
10000100 => [1,4,1,2] => 1
10000101 => [1,4,1,1,1] => 1
10000110 => [1,4,2,1] => 1
10000111 => [1,4,3] => 1
10001000 => [1,3,1,3] => 1
10001001 => [1,3,1,2,1] => 2
10001010 => [1,3,1,1,1,1] => 1
10001011 => [1,3,1,1,2] => 1
10001100 => [1,3,2,2] => 1
10001101 => [1,3,2,1,1] => 1
10001110 => [1,3,3,1] => 0
10001111 => [1,3,4] => 0
10010000 => [1,2,1,4] => 1
10010001 => [1,2,1,3,1] => 2
10010010 => [1,2,1,2,1,1] => 2
10010011 => [1,2,1,2,2] => 1
10010100 => [1,2,1,1,1,2] => 1
10010101 => [1,2,1,1,1,1,1] => 1
10010110 => [1,2,1,1,2,1] => 2
10010111 => [1,2,1,1,3] => 1
10011000 => [1,2,2,3] => 0
10011001 => [1,2,2,2,1] => 0
10011010 => [1,2,2,1,1,1] => 0
10011011 => [1,2,2,1,2] => 0
10011100 => [1,2,3,2] => 1
10011101 => [1,2,3,1,1] => 1
10011110 => [1,2,4,1] => 1
10011111 => [1,2,5] => 0
10100000 => [1,1,1,5] => 0
10100001 => [1,1,1,4,1] => 1
10100010 => [1,1,1,3,1,1] => 1
10100011 => [1,1,1,3,2] => 1
10100100 => [1,1,1,2,1,2] => 1
10100101 => [1,1,1,2,1,1,1] => 1
10100110 => [1,1,1,2,2,1] => 0
10100111 => [1,1,1,2,3] => 0
10101000 => [1,1,1,1,1,3] => 0
10101001 => [1,1,1,1,1,2,1] => 1
10101010 => [1,1,1,1,1,1,1,1] => 0
10101011 => [1,1,1,1,1,1,2] => 0
10101100 => [1,1,1,1,2,2] => 0
10101101 => [1,1,1,1,2,1,1] => 1
10101110 => [1,1,1,1,3,1] => 1
10101111 => [1,1,1,1,4] => 0
10110000 => [1,1,2,4] => 0
10110001 => [1,1,2,3,1] => 1
10110010 => [1,1,2,2,1,1] => 0
10110011 => [1,1,2,2,2] => 0
10110100 => [1,1,2,1,1,2] => 1
10110101 => [1,1,2,1,1,1,1] => 1
10110110 => [1,1,2,1,2,1] => 2
10110111 => [1,1,2,1,3] => 1
10111000 => [1,1,3,3] => 0
10111001 => [1,1,3,2,1] => 1
10111010 => [1,1,3,1,1,1] => 1
10111011 => [1,1,3,1,2] => 1
10111100 => [1,1,4,2] => 1
10111101 => [1,1,4,1,1] => 1
10111110 => [1,1,5,1] => 1
10111111 => [1,1,6] => 0
11000000 => [2,6] => 0
11000001 => [2,5,1] => 1
11000010 => [2,4,1,1] => 1
11000011 => [2,4,2] => 1
11000100 => [2,3,1,2] => 1
11000101 => [2,3,1,1,1] => 1
11000110 => [2,3,2,1] => 1
11000111 => [2,3,3] => 0
11001000 => [2,2,1,3] => 0
11001001 => [2,2,1,2,1] => 1
11001010 => [2,2,1,1,1,1] => 0
11001011 => [2,2,1,1,2] => 0
11001100 => [2,2,2,2] => 0
11001101 => [2,2,2,1,1] => 0
11001110 => [2,2,3,1] => 1
11001111 => [2,2,4] => 0
11010000 => [2,1,1,4] => 0
11010001 => [2,1,1,3,1] => 1
11010010 => [2,1,1,2,1,1] => 1
11010011 => [2,1,1,2,2] => 0
11010100 => [2,1,1,1,1,2] => 0
11010101 => [2,1,1,1,1,1,1] => 0
11010110 => [2,1,1,1,2,1] => 1
11010111 => [2,1,1,1,3] => 0
11011000 => [2,1,2,3] => 0
11011001 => [2,1,2,2,1] => 0
11011010 => [2,1,2,1,1,1] => 1
11011011 => [2,1,2,1,2] => 1
11011100 => [2,1,3,2] => 1
11011101 => [2,1,3,1,1] => 1
11011110 => [2,1,4,1] => 1
11011111 => [2,1,5] => 0
11100000 => [3,5] => 0
11100001 => [3,4,1] => 1
11100010 => [3,3,1,1] => 0
11100011 => [3,3,2] => 0
11100100 => [3,2,1,2] => 0
11100101 => [3,2,1,1,1] => 0
11100110 => [3,2,2,1] => 0
11100111 => [3,2,3] => 0
11101000 => [3,1,1,3] => 0
11101001 => [3,1,1,2,1] => 1
11101010 => [3,1,1,1,1,1] => 0
11101011 => [3,1,1,1,2] => 0
11101100 => [3,1,2,2] => 0
11101101 => [3,1,2,1,1] => 1
11101110 => [3,1,3,1] => 1
11101111 => [3,1,4] => 0
11110000 => [4,4] => 0
11110001 => [4,3,1] => 0
11110010 => [4,2,1,1] => 0
11110011 => [4,2,2] => 0
11110100 => [4,1,1,2] => 0
11110101 => [4,1,1,1,1] => 0
11110110 => [4,1,2,1] => 1
11110111 => [4,1,3] => 0
11111000 => [5,3] => 0
11111001 => [5,2,1] => 0
11111010 => [5,1,1,1] => 0
11111011 => [5,1,2] => 0
11111100 => [6,2] => 0
11111101 => [6,1,1] => 0
11111110 => [7,1] => 0
11111111 => [8] => 0
000000000 => [9] => 0
000000001 => [8,1] => 0
000000010 => [7,1,1] => 0
000000011 => [7,2] => 0
000000100 => [6,1,2] => 0
000000101 => [6,1,1,1] => 0
000000110 => [6,2,1] => 0
000000111 => [6,3] => 0
000001000 => [5,1,3] => 0
000001001 => [5,1,2,1] => 1
000001010 => [5,1,1,1,1] => 0
000001011 => [5,1,1,2] => 0
000001100 => [5,2,2] => 0
000001101 => [5,2,1,1] => 0
000001110 => [5,3,1] => 0
000001111 => [5,4] => 0
000010000 => [4,1,4] => 0
000010001 => [4,1,3,1] => 1
000010010 => [4,1,2,1,1] => 1
000010011 => [4,1,2,2] => 0
000010100 => [4,1,1,1,2] => 0
000010101 => [4,1,1,1,1,1] => 0
000010110 => [4,1,1,2,1] => 1
000010111 => [4,1,1,3] => 0
000011000 => [4,2,3] => 0
000011001 => [4,2,2,1] => 0
000011010 => [4,2,1,1,1] => 0
000011011 => [4,2,1,2] => 0
000011100 => [4,3,2] => 0
000011101 => [4,3,1,1] => 0
000011110 => [4,4,1] => 0
000011111 => [4,5] => 0
000100000 => [3,1,5] => 0
000100001 => [3,1,4,1] => 1
000100010 => [3,1,3,1,1] => 1
000100011 => [3,1,3,2] => 1
000100100 => [3,1,2,1,2] => 1
000100101 => [3,1,2,1,1,1] => 1
000100110 => [3,1,2,2,1] => 0
000100111 => [3,1,2,3] => 0
000101000 => [3,1,1,1,3] => 0
000101001 => [3,1,1,1,2,1] => 1
000101010 => [3,1,1,1,1,1,1] => 0
000101011 => [3,1,1,1,1,2] => 0
000101100 => [3,1,1,2,2] => 0
000101101 => [3,1,1,2,1,1] => 1
000101110 => [3,1,1,3,1] => 1
000101111 => [3,1,1,4] => 0
000110000 => [3,2,4] => 0
000110001 => [3,2,3,1] => 1
000110010 => [3,2,2,1,1] => 0
000110011 => [3,2,2,2] => 0
000110100 => [3,2,1,1,2] => 0
000110101 => [3,2,1,1,1,1] => 0
000110110 => [3,2,1,2,1] => 1
000110111 => [3,2,1,3] => 0
000111000 => [3,3,3] => 0
000111001 => [3,3,2,1] => 0
000111010 => [3,3,1,1,1] => 0
000111011 => [3,3,1,2] => 0
000111100 => [3,4,2] => 1
000111101 => [3,4,1,1] => 1
000111110 => [3,5,1] => 1
000111111 => [3,6] => 0
001000000 => [2,1,6] => 0
001000001 => [2,1,5,1] => 1
001000010 => [2,1,4,1,1] => 1
001000011 => [2,1,4,2] => 1
001000100 => [2,1,3,1,2] => 1
001000101 => [2,1,3,1,1,1] => 1
001000110 => [2,1,3,2,1] => 1
001000111 => [2,1,3,3] => 0
001001000 => [2,1,2,1,3] => 1
001001001 => [2,1,2,1,2,1] => 2
001001010 => [2,1,2,1,1,1,1] => 1
001001011 => [2,1,2,1,1,2] => 1
001001100 => [2,1,2,2,2] => 0
001001101 => [2,1,2,2,1,1] => 0
001001110 => [2,1,2,3,1] => 1
001001111 => [2,1,2,4] => 0
001010000 => [2,1,1,1,4] => 0
001010001 => [2,1,1,1,3,1] => 1
001010010 => [2,1,1,1,2,1,1] => 1
001010011 => [2,1,1,1,2,2] => 0
001010100 => [2,1,1,1,1,1,2] => 0
001010101 => [2,1,1,1,1,1,1,1] => 0
001010110 => [2,1,1,1,1,2,1] => 1
001010111 => [2,1,1,1,1,3] => 0
001011000 => [2,1,1,2,3] => 0
001011001 => [2,1,1,2,2,1] => 0
001011010 => [2,1,1,2,1,1,1] => 1
001011011 => [2,1,1,2,1,2] => 1
001011100 => [2,1,1,3,2] => 1
001011101 => [2,1,1,3,1,1] => 1
001011110 => [2,1,1,4,1] => 1
001011111 => [2,1,1,5] => 0
001100000 => [2,2,5] => 0
001100001 => [2,2,4,1] => 1
001100010 => [2,2,3,1,1] => 1
001100011 => [2,2,3,2] => 1
001100100 => [2,2,2,1,2] => 0
001100101 => [2,2,2,1,1,1] => 0
001100110 => [2,2,2,2,1] => 0
001100111 => [2,2,2,3] => 0
001101000 => [2,2,1,1,3] => 0
001101001 => [2,2,1,1,2,1] => 1
001101010 => [2,2,1,1,1,1,1] => 0
001101011 => [2,2,1,1,1,2] => 0
001101100 => [2,2,1,2,2] => 0
001101101 => [2,2,1,2,1,1] => 1
001101110 => [2,2,1,3,1] => 1
001101111 => [2,2,1,4] => 0
001110000 => [2,3,4] => 0
001110001 => [2,3,3,1] => 0
001110010 => [2,3,2,1,1] => 1
001110011 => [2,3,2,2] => 1
001110100 => [2,3,1,1,2] => 1
001110101 => [2,3,1,1,1,1] => 1
001110110 => [2,3,1,2,1] => 2
001110111 => [2,3,1,3] => 1
001111000 => [2,4,3] => 1
001111001 => [2,4,2,1] => 1
001111010 => [2,4,1,1,1] => 1
001111011 => [2,4,1,2] => 1
001111100 => [2,5,2] => 1
001111101 => [2,5,1,1] => 1
001111110 => [2,6,1] => 1
001111111 => [2,7] => 0
010000000 => [1,1,7] => 0
010000001 => [1,1,6,1] => 1
010000010 => [1,1,5,1,1] => 1
010000011 => [1,1,5,2] => 1
010000100 => [1,1,4,1,2] => 1
010000101 => [1,1,4,1,1,1] => 1
010000110 => [1,1,4,2,1] => 1
010000111 => [1,1,4,3] => 1
010001000 => [1,1,3,1,3] => 1
010001001 => [1,1,3,1,2,1] => 2
010001010 => [1,1,3,1,1,1,1] => 1
010001011 => [1,1,3,1,1,2] => 1
010001100 => [1,1,3,2,2] => 1
010001101 => [1,1,3,2,1,1] => 1
010001110 => [1,1,3,3,1] => 0
010001111 => [1,1,3,4] => 0
010010000 => [1,1,2,1,4] => 1
010010001 => [1,1,2,1,3,1] => 2
010010010 => [1,1,2,1,2,1,1] => 2
010010011 => [1,1,2,1,2,2] => 1
010010100 => [1,1,2,1,1,1,2] => 1
010010101 => [1,1,2,1,1,1,1,1] => 1
010010110 => [1,1,2,1,1,2,1] => 2
010010111 => [1,1,2,1,1,3] => 1
010011000 => [1,1,2,2,3] => 0
010011001 => [1,1,2,2,2,1] => 0
010011010 => [1,1,2,2,1,1,1] => 0
010011011 => [1,1,2,2,1,2] => 0
010011100 => [1,1,2,3,2] => 1
010011101 => [1,1,2,3,1,1] => 1
010011110 => [1,1,2,4,1] => 1
010011111 => [1,1,2,5] => 0
010100000 => [1,1,1,1,5] => 0
010100001 => [1,1,1,1,4,1] => 1
010100010 => [1,1,1,1,3,1,1] => 1
010100011 => [1,1,1,1,3,2] => 1
010100100 => [1,1,1,1,2,1,2] => 1
010100101 => [1,1,1,1,2,1,1,1] => 1
010100110 => [1,1,1,1,2,2,1] => 0
010100111 => [1,1,1,1,2,3] => 0
010101000 => [1,1,1,1,1,1,3] => 0
010101001 => [1,1,1,1,1,1,2,1] => 1
010101010 => [1,1,1,1,1,1,1,1,1] => 0
010101011 => [1,1,1,1,1,1,1,2] => 0
010101100 => [1,1,1,1,1,2,2] => 0
010101101 => [1,1,1,1,1,2,1,1] => 1
010101110 => [1,1,1,1,1,3,1] => 1
010101111 => [1,1,1,1,1,4] => 0
010110000 => [1,1,1,2,4] => 0
010110001 => [1,1,1,2,3,1] => 1
010110010 => [1,1,1,2,2,1,1] => 0
010110011 => [1,1,1,2,2,2] => 0
010110100 => [1,1,1,2,1,1,2] => 1
010110101 => [1,1,1,2,1,1,1,1] => 1
010110110 => [1,1,1,2,1,2,1] => 2
010110111 => [1,1,1,2,1,3] => 1
010111000 => [1,1,1,3,3] => 0
010111001 => [1,1,1,3,2,1] => 1
010111010 => [1,1,1,3,1,1,1] => 1
010111011 => [1,1,1,3,1,2] => 1
010111100 => [1,1,1,4,2] => 1
010111101 => [1,1,1,4,1,1] => 1
010111110 => [1,1,1,5,1] => 1
010111111 => [1,1,1,6] => 0
011000000 => [1,2,6] => 0
011000001 => [1,2,5,1] => 1
011000010 => [1,2,4,1,1] => 1
011000011 => [1,2,4,2] => 1
011000100 => [1,2,3,1,2] => 1
011000101 => [1,2,3,1,1,1] => 1
011000110 => [1,2,3,2,1] => 1
011000111 => [1,2,3,3] => 0
011001000 => [1,2,2,1,3] => 0
011001001 => [1,2,2,1,2,1] => 1
011001010 => [1,2,2,1,1,1,1] => 0
011001011 => [1,2,2,1,1,2] => 0
011001100 => [1,2,2,2,2] => 0
011001101 => [1,2,2,2,1,1] => 0
011001110 => [1,2,2,3,1] => 1
011001111 => [1,2,2,4] => 0
011010000 => [1,2,1,1,4] => 1
011010001 => [1,2,1,1,3,1] => 2
011010010 => [1,2,1,1,2,1,1] => 2
011010011 => [1,2,1,1,2,2] => 1
011010100 => [1,2,1,1,1,1,2] => 1
011010101 => [1,2,1,1,1,1,1,1] => 1
011010110 => [1,2,1,1,1,2,1] => 2
011010111 => [1,2,1,1,1,3] => 1
011011000 => [1,2,1,2,3] => 1
011011001 => [1,2,1,2,2,1] => 1
011011010 => [1,2,1,2,1,1,1] => 2
011011011 => [1,2,1,2,1,2] => 2
011011100 => [1,2,1,3,2] => 2
011011101 => [1,2,1,3,1,1] => 2
011011110 => [1,2,1,4,1] => 2
011011111 => [1,2,1,5] => 1
011100000 => [1,3,5] => 0
011100001 => [1,3,4,1] => 1
011100010 => [1,3,3,1,1] => 0
011100011 => [1,3,3,2] => 0
011100100 => [1,3,2,1,2] => 1
011100101 => [1,3,2,1,1,1] => 1
011100110 => [1,3,2,2,1] => 1
011100111 => [1,3,2,3] => 1
011101000 => [1,3,1,1,3] => 1
011101001 => [1,3,1,1,2,1] => 2
011101010 => [1,3,1,1,1,1,1] => 1
011101011 => [1,3,1,1,1,2] => 1
011101100 => [1,3,1,2,2] => 1
011101101 => [1,3,1,2,1,1] => 2
011101110 => [1,3,1,3,1] => 2
011101111 => [1,3,1,4] => 1
011110000 => [1,4,4] => 0
011110001 => [1,4,3,1] => 1
011110010 => [1,4,2,1,1] => 1
011110011 => [1,4,2,2] => 1
011110100 => [1,4,1,1,2] => 1
011110101 => [1,4,1,1,1,1] => 1
011110110 => [1,4,1,2,1] => 2
011110111 => [1,4,1,3] => 1
011111000 => [1,5,3] => 1
011111001 => [1,5,2,1] => 1
011111010 => [1,5,1,1,1] => 1
011111011 => [1,5,1,2] => 1
011111100 => [1,6,2] => 1
011111101 => [1,6,1,1] => 1
011111110 => [1,7,1] => 1
011111111 => [1,8] => 0
100000000 => [1,8] => 0
100000001 => [1,7,1] => 1
100000010 => [1,6,1,1] => 1
100000011 => [1,6,2] => 1
100000100 => [1,5,1,2] => 1
100000101 => [1,5,1,1,1] => 1
100000110 => [1,5,2,1] => 1
100000111 => [1,5,3] => 1
100001000 => [1,4,1,3] => 1
100001001 => [1,4,1,2,1] => 2
100001010 => [1,4,1,1,1,1] => 1
100001011 => [1,4,1,1,2] => 1
100001100 => [1,4,2,2] => 1
100001101 => [1,4,2,1,1] => 1
100001110 => [1,4,3,1] => 1
100001111 => [1,4,4] => 0
100010000 => [1,3,1,4] => 1
100010001 => [1,3,1,3,1] => 2
100010010 => [1,3,1,2,1,1] => 2
100010011 => [1,3,1,2,2] => 1
100010100 => [1,3,1,1,1,2] => 1
100010101 => [1,3,1,1,1,1,1] => 1
100010110 => [1,3,1,1,2,1] => 2
100010111 => [1,3,1,1,3] => 1
100011000 => [1,3,2,3] => 1
100011001 => [1,3,2,2,1] => 1
100011010 => [1,3,2,1,1,1] => 1
100011011 => [1,3,2,1,2] => 1
100011100 => [1,3,3,2] => 0
100011101 => [1,3,3,1,1] => 0
100011110 => [1,3,4,1] => 1
100011111 => [1,3,5] => 0
100100000 => [1,2,1,5] => 1
100100001 => [1,2,1,4,1] => 2
100100010 => [1,2,1,3,1,1] => 2
100100011 => [1,2,1,3,2] => 2
100100100 => [1,2,1,2,1,2] => 2
100100101 => [1,2,1,2,1,1,1] => 2
100100110 => [1,2,1,2,2,1] => 1
100100111 => [1,2,1,2,3] => 1
100101000 => [1,2,1,1,1,3] => 1
100101001 => [1,2,1,1,1,2,1] => 2
100101010 => [1,2,1,1,1,1,1,1] => 1
100101011 => [1,2,1,1,1,1,2] => 1
100101100 => [1,2,1,1,2,2] => 1
100101101 => [1,2,1,1,2,1,1] => 2
100101110 => [1,2,1,1,3,1] => 2
100101111 => [1,2,1,1,4] => 1
100110000 => [1,2,2,4] => 0
100110001 => [1,2,2,3,1] => 1
100110010 => [1,2,2,2,1,1] => 0
100110011 => [1,2,2,2,2] => 0
100110100 => [1,2,2,1,1,2] => 0
100110101 => [1,2,2,1,1,1,1] => 0
100110110 => [1,2,2,1,2,1] => 1
100110111 => [1,2,2,1,3] => 0
100111000 => [1,2,3,3] => 0
100111001 => [1,2,3,2,1] => 1
100111010 => [1,2,3,1,1,1] => 1
100111011 => [1,2,3,1,2] => 1
100111100 => [1,2,4,2] => 1
100111101 => [1,2,4,1,1] => 1
100111110 => [1,2,5,1] => 1
100111111 => [1,2,6] => 0
101000000 => [1,1,1,6] => 0
101000001 => [1,1,1,5,1] => 1
101000010 => [1,1,1,4,1,1] => 1
101000011 => [1,1,1,4,2] => 1
101000100 => [1,1,1,3,1,2] => 1
101000101 => [1,1,1,3,1,1,1] => 1
101000110 => [1,1,1,3,2,1] => 1
101000111 => [1,1,1,3,3] => 0
101001000 => [1,1,1,2,1,3] => 1
101001001 => [1,1,1,2,1,2,1] => 2
101001010 => [1,1,1,2,1,1,1,1] => 1
101001011 => [1,1,1,2,1,1,2] => 1
101001100 => [1,1,1,2,2,2] => 0
101001101 => [1,1,1,2,2,1,1] => 0
101001110 => [1,1,1,2,3,1] => 1
101001111 => [1,1,1,2,4] => 0
101010000 => [1,1,1,1,1,4] => 0
101010001 => [1,1,1,1,1,3,1] => 1
101010010 => [1,1,1,1,1,2,1,1] => 1
101010011 => [1,1,1,1,1,2,2] => 0
101010100 => [1,1,1,1,1,1,1,2] => 0
101010101 => [1,1,1,1,1,1,1,1,1] => 0
101010110 => [1,1,1,1,1,1,2,1] => 1
101010111 => [1,1,1,1,1,1,3] => 0
101011000 => [1,1,1,1,2,3] => 0
101011001 => [1,1,1,1,2,2,1] => 0
101011010 => [1,1,1,1,2,1,1,1] => 1
101011011 => [1,1,1,1,2,1,2] => 1
101011100 => [1,1,1,1,3,2] => 1
101011101 => [1,1,1,1,3,1,1] => 1
101011110 => [1,1,1,1,4,1] => 1
101011111 => [1,1,1,1,5] => 0
101100000 => [1,1,2,5] => 0
101100001 => [1,1,2,4,1] => 1
101100010 => [1,1,2,3,1,1] => 1
101100011 => [1,1,2,3,2] => 1
101100100 => [1,1,2,2,1,2] => 0
101100101 => [1,1,2,2,1,1,1] => 0
101100110 => [1,1,2,2,2,1] => 0
101100111 => [1,1,2,2,3] => 0
101101000 => [1,1,2,1,1,3] => 1
101101001 => [1,1,2,1,1,2,1] => 2
101101010 => [1,1,2,1,1,1,1,1] => 1
101101011 => [1,1,2,1,1,1,2] => 1
101101100 => [1,1,2,1,2,2] => 1
101101101 => [1,1,2,1,2,1,1] => 2
101101110 => [1,1,2,1,3,1] => 2
101101111 => [1,1,2,1,4] => 1
101110000 => [1,1,3,4] => 0
101110001 => [1,1,3,3,1] => 0
101110010 => [1,1,3,2,1,1] => 1
101110011 => [1,1,3,2,2] => 1
101110100 => [1,1,3,1,1,2] => 1
101110101 => [1,1,3,1,1,1,1] => 1
101110110 => [1,1,3,1,2,1] => 2
101110111 => [1,1,3,1,3] => 1
101111000 => [1,1,4,3] => 1
101111001 => [1,1,4,2,1] => 1
101111010 => [1,1,4,1,1,1] => 1
101111011 => [1,1,4,1,2] => 1
101111100 => [1,1,5,2] => 1
101111101 => [1,1,5,1,1] => 1
101111110 => [1,1,6,1] => 1
101111111 => [1,1,7] => 0
110000000 => [2,7] => 0
110000001 => [2,6,1] => 1
110000010 => [2,5,1,1] => 1
110000011 => [2,5,2] => 1
110000100 => [2,4,1,2] => 1
110000101 => [2,4,1,1,1] => 1
110000110 => [2,4,2,1] => 1
110000111 => [2,4,3] => 1
110001000 => [2,3,1,3] => 1
110001001 => [2,3,1,2,1] => 2
110001010 => [2,3,1,1,1,1] => 1
110001011 => [2,3,1,1,2] => 1
110001100 => [2,3,2,2] => 1
110001101 => [2,3,2,1,1] => 1
110001110 => [2,3,3,1] => 0
110001111 => [2,3,4] => 0
110010000 => [2,2,1,4] => 0
110010001 => [2,2,1,3,1] => 1
110010010 => [2,2,1,2,1,1] => 1
110010011 => [2,2,1,2,2] => 0
110010100 => [2,2,1,1,1,2] => 0
110010101 => [2,2,1,1,1,1,1] => 0
110010110 => [2,2,1,1,2,1] => 1
110010111 => [2,2,1,1,3] => 0
110011000 => [2,2,2,3] => 0
110011001 => [2,2,2,2,1] => 0
110011010 => [2,2,2,1,1,1] => 0
110011011 => [2,2,2,1,2] => 0
110011100 => [2,2,3,2] => 1
110011101 => [2,2,3,1,1] => 1
110011110 => [2,2,4,1] => 1
110011111 => [2,2,5] => 0
110100000 => [2,1,1,5] => 0
110100001 => [2,1,1,4,1] => 1
110100010 => [2,1,1,3,1,1] => 1
110100011 => [2,1,1,3,2] => 1
110100100 => [2,1,1,2,1,2] => 1
110100101 => [2,1,1,2,1,1,1] => 1
110100110 => [2,1,1,2,2,1] => 0
110100111 => [2,1,1,2,3] => 0
110101000 => [2,1,1,1,1,3] => 0
110101001 => [2,1,1,1,1,2,1] => 1
110101010 => [2,1,1,1,1,1,1,1] => 0
110101011 => [2,1,1,1,1,1,2] => 0
110101100 => [2,1,1,1,2,2] => 0
110101101 => [2,1,1,1,2,1,1] => 1
110101110 => [2,1,1,1,3,1] => 1
110101111 => [2,1,1,1,4] => 0
110110000 => [2,1,2,4] => 0
110110001 => [2,1,2,3,1] => 1
110110010 => [2,1,2,2,1,1] => 0
110110011 => [2,1,2,2,2] => 0
110110100 => [2,1,2,1,1,2] => 1
110110101 => [2,1,2,1,1,1,1] => 1
110110110 => [2,1,2,1,2,1] => 2
110110111 => [2,1,2,1,3] => 1
110111000 => [2,1,3,3] => 0
110111001 => [2,1,3,2,1] => 1
110111010 => [2,1,3,1,1,1] => 1
110111011 => [2,1,3,1,2] => 1
110111100 => [2,1,4,2] => 1
110111101 => [2,1,4,1,1] => 1
110111110 => [2,1,5,1] => 1
110111111 => [2,1,6] => 0
111000000 => [3,6] => 0
111000001 => [3,5,1] => 1
111000010 => [3,4,1,1] => 1
111000011 => [3,4,2] => 1
111000100 => [3,3,1,2] => 0
111000101 => [3,3,1,1,1] => 0
111000110 => [3,3,2,1] => 0
111000111 => [3,3,3] => 0
111001000 => [3,2,1,3] => 0
111001001 => [3,2,1,2,1] => 1
111001010 => [3,2,1,1,1,1] => 0
111001011 => [3,2,1,1,2] => 0
111001100 => [3,2,2,2] => 0
111001101 => [3,2,2,1,1] => 0
111001110 => [3,2,3,1] => 1
111001111 => [3,2,4] => 0
111010000 => [3,1,1,4] => 0
111010001 => [3,1,1,3,1] => 1
111010010 => [3,1,1,2,1,1] => 1
111010011 => [3,1,1,2,2] => 0
111010100 => [3,1,1,1,1,2] => 0
111010101 => [3,1,1,1,1,1,1] => 0
111010110 => [3,1,1,1,2,1] => 1
111010111 => [3,1,1,1,3] => 0
111011000 => [3,1,2,3] => 0
111011001 => [3,1,2,2,1] => 0
111011010 => [3,1,2,1,1,1] => 1
111011011 => [3,1,2,1,2] => 1
111011100 => [3,1,3,2] => 1
111011101 => [3,1,3,1,1] => 1
111011110 => [3,1,4,1] => 1
111011111 => [3,1,5] => 0
111100000 => [4,5] => 0
111100001 => [4,4,1] => 0
111100010 => [4,3,1,1] => 0
111100011 => [4,3,2] => 0
111100100 => [4,2,1,2] => 0
111100101 => [4,2,1,1,1] => 0
111100110 => [4,2,2,1] => 0
111100111 => [4,2,3] => 0
111101000 => [4,1,1,3] => 0
111101001 => [4,1,1,2,1] => 1
111101010 => [4,1,1,1,1,1] => 0
111101011 => [4,1,1,1,2] => 0
111101100 => [4,1,2,2] => 0
111101101 => [4,1,2,1,1] => 1
111101110 => [4,1,3,1] => 1
111101111 => [4,1,4] => 0
111110000 => [5,4] => 0
111110001 => [5,3,1] => 0
111110010 => [5,2,1,1] => 0
111110011 => [5,2,2] => 0
111110100 => [5,1,1,2] => 0
111110101 => [5,1,1,1,1] => 0
111110110 => [5,1,2,1] => 1
111110111 => [5,1,3] => 0
111111000 => [6,3] => 0
111111001 => [6,2,1] => 0
111111010 => [6,1,1,1] => 0
111111011 => [6,1,2] => 0
111111100 => [7,2] => 0
111111101 => [7,1,1] => 0
111111110 => [8,1] => 0
111111111 => [9] => 0
1010101010 => [1,1,1,1,1,1,1,1,1,1] => 0
1010101100 => [1,1,1,1,1,1,2,2] => 0
1010110010 => [1,1,1,1,2,2,1,1] => 0
1010110100 => [1,1,1,1,2,1,1,2] => 1
1010111000 => [1,1,1,1,3,3] => 0
1011001010 => [1,1,2,2,1,1,1,1] => 0
1011001100 => [1,1,2,2,2,2] => 0
1011010010 => [1,1,2,1,1,2,1,1] => 2
1011010100 => [1,1,2,1,1,1,1,2] => 1
1011011000 => [1,1,2,1,2,3] => 1
1011100010 => [1,1,3,3,1,1] => 0
1011100100 => [1,1,3,2,1,2] => 1
1011101000 => [1,1,3,1,1,3] => 1
1011110000 => [1,1,4,4] => 0
1100101010 => [2,2,1,1,1,1,1,1] => 0
1100101100 => [2,2,1,1,2,2] => 0
1100110010 => [2,2,2,2,1,1] => 0
1100110100 => [2,2,2,1,1,2] => 0
1100111000 => [2,2,3,3] => 0
1101001010 => [2,1,1,2,1,1,1,1] => 1
1101001100 => [2,1,1,2,2,2] => 0
1101010010 => [2,1,1,1,1,2,1,1] => 1
1101010100 => [2,1,1,1,1,1,1,2] => 0
1101011000 => [2,1,1,1,2,3] => 0
1101100010 => [2,1,2,3,1,1] => 1
1101100100 => [2,1,2,2,1,2] => 0
1101101000 => [2,1,2,1,1,3] => 1
1101110000 => [2,1,3,4] => 0
1110001010 => [3,3,1,1,1,1] => 0
1110001100 => [3,3,2,2] => 0
1110010010 => [3,2,1,2,1,1] => 1
1110010100 => [3,2,1,1,1,2] => 0
1110011000 => [3,2,2,3] => 0
1110100010 => [3,1,1,3,1,1] => 1
1110100100 => [3,1,1,2,1,2] => 1
1110101000 => [3,1,1,1,1,3] => 0
1110110000 => [3,1,2,4] => 0
1111000010 => [4,4,1,1] => 0
1111000100 => [4,3,1,2] => 0
1111001000 => [4,2,1,3] => 0
1111010000 => [4,1,1,4] => 0
1111100000 => [5,5] => 0
101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
101010101100 => [1,1,1,1,1,1,1,1,2,2] => 0
101010110010 => [1,1,1,1,1,1,2,2,1,1] => 0
101010110100 => [1,1,1,1,1,1,2,1,1,2] => 1
101010111000 => [1,1,1,1,1,1,3,3] => 0
101011001010 => [1,1,1,1,2,2,1,1,1,1] => 0
101011001100 => [1,1,1,1,2,2,2,2] => 0
101011010010 => [1,1,1,1,2,1,1,2,1,1] => 2
101011010100 => [1,1,1,1,2,1,1,1,1,2] => 1
101011011000 => [1,1,1,1,2,1,2,3] => 1
101011100010 => [1,1,1,1,3,3,1,1] => 0
101011100100 => [1,1,1,1,3,2,1,2] => 1
101011101000 => [1,1,1,1,3,1,1,3] => 1
101011110000 => [1,1,1,1,4,4] => 0
101100101010 => [1,1,2,2,1,1,1,1,1,1] => 0
101100101100 => [1,1,2,2,1,1,2,2] => 0
101100110010 => [1,1,2,2,2,2,1,1] => 0
101100110100 => [1,1,2,2,2,1,1,2] => 0
101100111000 => [1,1,2,2,3,3] => 0
101101001010 => [1,1,2,1,1,2,1,1,1,1] => 2
101101001100 => [1,1,2,1,1,2,2,2] => 1
101101010010 => [1,1,2,1,1,1,1,2,1,1] => 2
101101010100 => [1,1,2,1,1,1,1,1,1,2] => 1
101101011000 => [1,1,2,1,1,1,2,3] => 1
101101100010 => [1,1,2,1,2,3,1,1] => 2
101101100100 => [1,1,2,1,2,2,1,2] => 1
101101101000 => [1,1,2,1,2,1,1,3] => 2
101101110000 => [1,1,2,1,3,4] => 1
101110001010 => [1,1,3,3,1,1,1,1] => 0
101110001100 => [1,1,3,3,2,2] => 0
101110010010 => [1,1,3,2,1,2,1,1] => 2
101110010100 => [1,1,3,2,1,1,1,2] => 1
101110011000 => [1,1,3,2,2,3] => 1
101110100010 => [1,1,3,1,1,3,1,1] => 2
101110100100 => [1,1,3,1,1,2,1,2] => 2
101110101000 => [1,1,3,1,1,1,1,3] => 1
101110110000 => [1,1,3,1,2,4] => 1
101111000010 => [1,1,4,4,1,1] => 0
101111000100 => [1,1,4,3,1,2] => 1
101111001000 => [1,1,4,2,1,3] => 1
101111010000 => [1,1,4,1,1,4] => 1
101111100000 => [1,1,5,5] => 0
110010101010 => [2,2,1,1,1,1,1,1,1,1] => 0
110010101100 => [2,2,1,1,1,1,2,2] => 0
110010110010 => [2,2,1,1,2,2,1,1] => 0
110010110100 => [2,2,1,1,2,1,1,2] => 1
110010111000 => [2,2,1,1,3,3] => 0
110011001010 => [2,2,2,2,1,1,1,1] => 0
110011001100 => [2,2,2,2,2,2] => 0
110011010010 => [2,2,2,1,1,2,1,1] => 1
110011010100 => [2,2,2,1,1,1,1,2] => 0
110011011000 => [2,2,2,1,2,3] => 0
110011100010 => [2,2,3,3,1,1] => 0
110011100100 => [2,2,3,2,1,2] => 1
110011101000 => [2,2,3,1,1,3] => 1
110011110000 => [2,2,4,4] => 0
110100101010 => [2,1,1,2,1,1,1,1,1,1] => 1
110100101100 => [2,1,1,2,1,1,2,2] => 1
110100110010 => [2,1,1,2,2,2,1,1] => 0
110100110100 => [2,1,1,2,2,1,1,2] => 0
110100111000 => [2,1,1,2,3,3] => 0
110101001010 => [2,1,1,1,1,2,1,1,1,1] => 1
110101001100 => [2,1,1,1,1,2,2,2] => 0
110101010010 => [2,1,1,1,1,1,1,2,1,1] => 1
110101010100 => [2,1,1,1,1,1,1,1,1,2] => 0
110101011000 => [2,1,1,1,1,1,2,3] => 0
110101100010 => [2,1,1,1,2,3,1,1] => 1
110101100100 => [2,1,1,1,2,2,1,2] => 0
110101101000 => [2,1,1,1,2,1,1,3] => 1
110101110000 => [2,1,1,1,3,4] => 0
110110001010 => [2,1,2,3,1,1,1,1] => 1
110110001100 => [2,1,2,3,2,2] => 1
110110010010 => [2,1,2,2,1,2,1,1] => 1
110110010100 => [2,1,2,2,1,1,1,2] => 0
110110011000 => [2,1,2,2,2,3] => 0
110110100010 => [2,1,2,1,1,3,1,1] => 2
110110100100 => [2,1,2,1,1,2,1,2] => 2
110110101000 => [2,1,2,1,1,1,1,3] => 1
110110110000 => [2,1,2,1,2,4] => 1
110111000010 => [2,1,3,4,1,1] => 1
110111000100 => [2,1,3,3,1,2] => 0
110111001000 => [2,1,3,2,1,3] => 1
110111010000 => [2,1,3,1,1,4] => 1
110111100000 => [2,1,4,5] => 0
111000101010 => [3,3,1,1,1,1,1,1] => 0
111000101100 => [3,3,1,1,2,2] => 0
111000110010 => [3,3,2,2,1,1] => 0
111000110100 => [3,3,2,1,1,2] => 0
111000111000 => [3,3,3,3] => 0
111001001010 => [3,2,1,2,1,1,1,1] => 1
111001001100 => [3,2,1,2,2,2] => 0
111001010010 => [3,2,1,1,1,2,1,1] => 1
111001010100 => [3,2,1,1,1,1,1,2] => 0
111001011000 => [3,2,1,1,2,3] => 0
111001100010 => [3,2,2,3,1,1] => 1
111001100100 => [3,2,2,2,1,2] => 0
111001101000 => [3,2,2,1,1,3] => 0
111001110000 => [3,2,3,4] => 0
111010001010 => [3,1,1,3,1,1,1,1] => 1
111010001100 => [3,1,1,3,2,2] => 1
111010010010 => [3,1,1,2,1,2,1,1] => 2
111010010100 => [3,1,1,2,1,1,1,2] => 1
111010011000 => [3,1,1,2,2,3] => 0
111010100010 => [3,1,1,1,1,3,1,1] => 1
111010100100 => [3,1,1,1,1,2,1,2] => 1
111010101000 => [3,1,1,1,1,1,1,3] => 0
111010110000 => [3,1,1,1,2,4] => 0
111011000010 => [3,1,2,4,1,1] => 1
111011000100 => [3,1,2,3,1,2] => 1
111011001000 => [3,1,2,2,1,3] => 0
111011010000 => [3,1,2,1,1,4] => 1
111011100000 => [3,1,3,5] => 0
111100001010 => [4,4,1,1,1,1] => 0
111100001100 => [4,4,2,2] => 0
111100010010 => [4,3,1,2,1,1] => 1
111100010100 => [4,3,1,1,1,2] => 0
111100011000 => [4,3,2,3] => 0
111100100010 => [4,2,1,3,1,1] => 1
111100100100 => [4,2,1,2,1,2] => 1
111100101000 => [4,2,1,1,1,3] => 0
111100110000 => [4,2,2,4] => 0
111101000010 => [4,1,1,4,1,1] => 1
111101000100 => [4,1,1,3,1,2] => 1
111101001000 => [4,1,1,2,1,3] => 1
111101010000 => [4,1,1,1,1,4] => 0
111101100000 => [4,1,2,5] => 0
111110000010 => [5,5,1,1] => 0
111110000100 => [5,4,1,2] => 0
111110001000 => [5,3,1,3] => 0
111110010000 => [5,2,1,4] => 0
111110100000 => [5,1,1,5] => 0
111111000000 => [6,6] => 0
1111111110 => [9,1] => 0
1111111101 => [8,1,1] => 0
1101111110 => [2,1,6,1] => 1
1011111110 => [1,1,7,1] => 1
1010111110 => [1,1,1,1,5,1] => 1
1001111110 => [1,2,6,1] => 1
1001011110 => [1,2,1,1,4,1] => 2
1000111110 => [1,3,5,1] => 1
1000101110 => [1,3,1,1,3,1] => 2
1000011110 => [1,4,4,1] => 0
1000010110 => [1,4,1,1,2,1] => 2
1000001110 => [1,5,3,1] => 1
1000001010 => [1,5,1,1,1,1] => 1
1000000110 => [1,6,2,1] => 1
1000000100 => [1,6,1,2] => 1
1000000010 => [1,7,1,1] => 1
1000000001 => [1,8,1] => 1
1000000000 => [1,9] => 0
10000000000 => [1,10] => 0
10000000010 => [1,8,1,1] => 1
10000000110 => [1,7,2,1] => 1
10000001110 => [1,6,3,1] => 1
10000011110 => [1,5,4,1] => 1
10000111110 => [1,4,5,1] => 1
10001111110 => [1,3,6,1] => 1
10011111110 => [1,2,7,1] => 1
10111111110 => [1,1,8,1] => 1
11111111110 => [10,1] => 0
0111111111 => [1,9] => 0
0111111101 => [1,7,1,1] => 1
0111111001 => [1,6,2,1] => 1
0111110001 => [1,5,3,1] => 1
0111100001 => [1,4,4,1] => 0
0100000001 => [1,1,7,1] => 1
0000000001 => [9,1] => 0
01111111111 => [1,10] => 0
01111111101 => [1,8,1,1] => 1
0111111011 => [1,6,1,2] => 1
0111110101 => [1,5,1,1,1,1] => 1
0111101001 => [1,4,1,1,2,1] => 2
0111010001 => [1,3,1,1,3,1] => 2
0110100001 => [1,2,1,1,4,1] => 2
0101000001 => [1,1,1,1,5,1] => 1
01000000001 => [1,1,8,1] => 1
00000000001 => [10,1] => 0
0101010101 => [1,1,1,1,1,1,1,1,1,1] => 0
0101001011 => [1,1,1,1,2,1,1,2] => 1
0101000111 => [1,1,1,1,3,3] => 0
0100110011 => [1,1,2,2,2,2] => 0
0100100111 => [1,1,2,1,2,3] => 1
0100011011 => [1,1,3,2,1,2] => 1
0100010111 => [1,1,3,1,1,3] => 1
0100001111 => [1,1,4,4] => 0
0011010011 => [2,2,1,1,2,2] => 0
0011000111 => [2,2,3,3] => 0
0010101011 => [2,1,1,1,1,1,1,2] => 0
0010010111 => [2,1,2,1,1,3] => 1
0010001111 => [2,1,3,4] => 0
0001110011 => [3,3,2,2] => 0
0001101011 => [3,2,1,1,1,2] => 0
0001100111 => [3,2,2,3] => 0
0001011101 => [3,1,1,3,1,1] => 1
0001010111 => [3,1,1,1,1,3] => 0
0001001111 => [3,1,2,4] => 0
0000111101 => [4,4,1,1] => 0
0000110111 => [4,2,1,3] => 0
0000101111 => [4,1,1,4] => 0
0000011111 => [5,5] => 0
010101010101 => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
010101001011 => [1,1,1,1,1,1,2,1,1,2] => 1
010100101011 => [1,1,1,1,2,1,1,1,1,2] => 1
010100100111 => [1,1,1,1,2,1,2,3] => 1
010100011011 => [1,1,1,1,3,2,1,2] => 1
010100010111 => [1,1,1,1,3,1,1,3] => 1
010100001111 => [1,1,1,1,4,4] => 0
010011010101 => [1,1,2,2,1,1,1,1,1,1] => 0
010011010011 => [1,1,2,2,1,1,2,2] => 0
010011001011 => [1,1,2,2,2,1,1,2] => 0
010011000111 => [1,1,2,2,3,3] => 0
010010110101 => [1,1,2,1,1,2,1,1,1,1] => 2
010010110011 => [1,1,2,1,1,2,2,2] => 1
010010101011 => [1,1,2,1,1,1,1,1,1,2] => 1
010010011011 => [1,1,2,1,2,2,1,2] => 1
010010010111 => [1,1,2,1,2,1,1,3] => 2
010010001111 => [1,1,2,1,3,4] => 1
010001110101 => [1,1,3,3,1,1,1,1] => 0
010001101011 => [1,1,3,2,1,1,1,2] => 1
010001011101 => [1,1,3,1,1,3,1,1] => 2
010001011011 => [1,1,3,1,1,2,1,2] => 2
010001010111 => [1,1,3,1,1,1,1,3] => 1
010000111011 => [1,1,4,3,1,2] => 1
010000110111 => [1,1,4,2,1,3] => 1
010000101111 => [1,1,4,1,1,4] => 1
010000011111 => [1,1,5,5] => 0
001101010101 => [2,2,1,1,1,1,1,1,1,1] => 0
001101001011 => [2,2,1,1,2,1,1,2] => 1
001100110011 => [2,2,2,2,2,2] => 0
001100100111 => [2,2,2,1,2,3] => 0
001100011011 => [2,2,3,2,1,2] => 1
001100010111 => [2,2,3,1,1,3] => 1
001100001111 => [2,2,4,4] => 0
001011010101 => [2,1,1,2,1,1,1,1,1,1] => 1
001011001101 => [2,1,1,2,2,2,1,1] => 0
001011000111 => [2,1,1,2,3,3] => 0
001010101011 => [2,1,1,1,1,1,1,1,1,2] => 0
001010010111 => [2,1,1,1,2,1,1,3] => 1
001010001111 => [2,1,1,1,3,4] => 0
001001110101 => [2,1,2,3,1,1,1,1] => 1
001001011101 => [2,1,2,1,1,3,1,1] => 2
001001010111 => [2,1,2,1,1,1,1,3] => 1
001000110111 => [2,1,3,2,1,3] => 1
001000101111 => [2,1,3,1,1,4] => 1
001000011111 => [2,1,4,5] => 0
000111010101 => [3,3,1,1,1,1,1,1] => 0
000111010011 => [3,3,1,1,2,2] => 0
000111001011 => [3,3,2,1,1,2] => 0
000111000111 => [3,3,3,3] => 0
000110110101 => [3,2,1,2,1,1,1,1] => 1
000110110011 => [3,2,1,2,2,2] => 0
000110101011 => [3,2,1,1,1,1,1,2] => 0
000110011011 => [3,2,2,2,1,2] => 0
000110010111 => [3,2,2,1,1,3] => 0
000110001111 => [3,2,3,4] => 0
000101110101 => [3,1,1,3,1,1,1,1] => 1
000101101011 => [3,1,1,2,1,1,1,2] => 1
000101011101 => [3,1,1,1,1,3,1,1] => 1
000101011011 => [3,1,1,1,1,2,1,2] => 1
000101010111 => [3,1,1,1,1,1,1,3] => 0
000100111011 => [3,1,2,3,1,2] => 1
000100110111 => [3,1,2,2,1,3] => 0
000100101111 => [3,1,2,1,1,4] => 1
000100011111 => [3,1,3,5] => 0
000011110101 => [4,4,1,1,1,1] => 0
000011110011 => [4,4,2,2] => 0
000011011101 => [4,2,1,3,1,1] => 1
000011011011 => [4,2,1,2,1,2] => 1
000011010111 => [4,2,1,1,1,3] => 0
000011001111 => [4,2,2,4] => 0
000010110111 => [4,1,1,2,1,3] => 1
000010101111 => [4,1,1,1,1,4] => 0
000010011111 => [4,1,2,5] => 0
000001111101 => [5,5,1,1] => 0
000001111011 => [5,4,1,2] => 0
000001110111 => [5,3,1,3] => 0
000001101111 => [5,2,1,4] => 0
000001011111 => [5,1,1,5] => 0
000000111111 => [6,6] => 0
0111111110 => [1,8,1] => 1
0000000010 => [8,1,1] => 0
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Description
The number of peaks in an integer composition.
A peak is an ascent followed by a descent, i.e., a subsequence $c_{i-1} c_i c_{i+1}$ with $c_i > \max(c_{i-1}, c_{i+1})$.
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 $w$.