Identifier
Values
00 => [2] => 3
01 => [1,1] => 3
10 => [1,1] => 3
11 => [2] => 3
000 => [3] => 4
001 => [2,1] => 4
010 => [1,1,1] => 4
011 => [1,2] => 4
100 => [1,2] => 4
101 => [1,1,1] => 4
110 => [2,1] => 4
111 => [3] => 4
0000 => [4] => 5
0001 => [3,1] => 5
0010 => [2,1,1] => 5
0011 => [2,2] => 4
0100 => [1,1,2] => 5
0101 => [1,1,1,1] => 5
0110 => [1,2,1] => 5
0111 => [1,3] => 5
1000 => [1,3] => 5
1001 => [1,2,1] => 5
1010 => [1,1,1,1] => 5
1011 => [1,1,2] => 5
1100 => [2,2] => 4
1101 => [2,1,1] => 5
1110 => [3,1] => 5
1111 => [4] => 5
00000 => [5] => 6
00001 => [4,1] => 6
00010 => [3,1,1] => 6
00011 => [3,2] => 5
00100 => [2,1,2] => 6
00101 => [2,1,1,1] => 6
00110 => [2,2,1] => 5
00111 => [2,3] => 5
01000 => [1,1,3] => 6
01001 => [1,1,2,1] => 6
01010 => [1,1,1,1,1] => 6
01011 => [1,1,1,2] => 6
01100 => [1,2,2] => 5
01101 => [1,2,1,1] => 6
01110 => [1,3,1] => 6
01111 => [1,4] => 6
10000 => [1,4] => 6
10001 => [1,3,1] => 6
10010 => [1,2,1,1] => 6
10011 => [1,2,2] => 5
10100 => [1,1,1,2] => 6
10101 => [1,1,1,1,1] => 6
10110 => [1,1,2,1] => 6
10111 => [1,1,3] => 6
11000 => [2,3] => 5
11001 => [2,2,1] => 5
11010 => [2,1,1,1] => 6
11011 => [2,1,2] => 6
11100 => [3,2] => 5
11101 => [3,1,1] => 6
11110 => [4,1] => 6
11111 => [5] => 6
000000 => [6] => 7
000001 => [5,1] => 7
000010 => [4,1,1] => 7
000011 => [4,2] => 6
000100 => [3,1,2] => 7
000101 => [3,1,1,1] => 7
000110 => [3,2,1] => 6
000111 => [3,3] => 5
001000 => [2,1,3] => 7
001001 => [2,1,2,1] => 7
001010 => [2,1,1,1,1] => 7
001011 => [2,1,1,2] => 7
001100 => [2,2,2] => 5
001101 => [2,2,1,1] => 6
001110 => [2,3,1] => 6
001111 => [2,4] => 6
010000 => [1,1,4] => 7
010001 => [1,1,3,1] => 7
010010 => [1,1,2,1,1] => 7
010011 => [1,1,2,2] => 6
010100 => [1,1,1,1,2] => 7
010101 => [1,1,1,1,1,1] => 7
010110 => [1,1,1,2,1] => 7
010111 => [1,1,1,3] => 7
011000 => [1,2,3] => 6
011001 => [1,2,2,1] => 6
011010 => [1,2,1,1,1] => 7
011011 => [1,2,1,2] => 7
011100 => [1,3,2] => 6
011101 => [1,3,1,1] => 7
011110 => [1,4,1] => 7
011111 => [1,5] => 7
100000 => [1,5] => 7
100001 => [1,4,1] => 7
100010 => [1,3,1,1] => 7
100011 => [1,3,2] => 6
100100 => [1,2,1,2] => 7
100101 => [1,2,1,1,1] => 7
100110 => [1,2,2,1] => 6
100111 => [1,2,3] => 6
101000 => [1,1,1,3] => 7
>>> Load all 1020 entries. <<<
101001 => [1,1,1,2,1] => 7
101010 => [1,1,1,1,1,1] => 7
101011 => [1,1,1,1,2] => 7
101100 => [1,1,2,2] => 6
101101 => [1,1,2,1,1] => 7
101110 => [1,1,3,1] => 7
101111 => [1,1,4] => 7
110000 => [2,4] => 6
110001 => [2,3,1] => 6
110010 => [2,2,1,1] => 6
110011 => [2,2,2] => 5
110100 => [2,1,1,2] => 7
110101 => [2,1,1,1,1] => 7
110110 => [2,1,2,1] => 7
110111 => [2,1,3] => 7
111000 => [3,3] => 5
111001 => [3,2,1] => 6
111010 => [3,1,1,1] => 7
111011 => [3,1,2] => 7
111100 => [4,2] => 6
111101 => [4,1,1] => 7
111110 => [5,1] => 7
111111 => [6] => 7
0000000 => [7] => 8
0000001 => [6,1] => 8
0000010 => [5,1,1] => 8
0000011 => [5,2] => 7
0000100 => [4,1,2] => 8
0000101 => [4,1,1,1] => 8
0000110 => [4,2,1] => 7
0000111 => [4,3] => 6
0001000 => [3,1,3] => 8
0001001 => [3,1,2,1] => 8
0001010 => [3,1,1,1,1] => 8
0001011 => [3,1,1,2] => 8
0001100 => [3,2,2] => 6
0001101 => [3,2,1,1] => 7
0001110 => [3,3,1] => 6
0001111 => [3,4] => 6
0010000 => [2,1,4] => 8
0010001 => [2,1,3,1] => 8
0010010 => [2,1,2,1,1] => 8
0010011 => [2,1,2,2] => 7
0010100 => [2,1,1,1,2] => 8
0010101 => [2,1,1,1,1,1] => 8
0010110 => [2,1,1,2,1] => 8
0010111 => [2,1,1,3] => 8
0011000 => [2,2,3] => 6
0011001 => [2,2,2,1] => 6
0011010 => [2,2,1,1,1] => 7
0011011 => [2,2,1,2] => 7
0011100 => [2,3,2] => 6
0011101 => [2,3,1,1] => 7
0011110 => [2,4,1] => 7
0011111 => [2,5] => 7
0100000 => [1,1,5] => 8
0100001 => [1,1,4,1] => 8
0100010 => [1,1,3,1,1] => 8
0100011 => [1,1,3,2] => 7
0100100 => [1,1,2,1,2] => 8
0100101 => [1,1,2,1,1,1] => 8
0100110 => [1,1,2,2,1] => 7
0100111 => [1,1,2,3] => 7
0101000 => [1,1,1,1,3] => 8
0101001 => [1,1,1,1,2,1] => 8
0101010 => [1,1,1,1,1,1,1] => 8
0101011 => [1,1,1,1,1,2] => 8
0101100 => [1,1,1,2,2] => 7
0101101 => [1,1,1,2,1,1] => 8
0101110 => [1,1,1,3,1] => 8
0101111 => [1,1,1,4] => 8
0110000 => [1,2,4] => 7
0110001 => [1,2,3,1] => 7
0110010 => [1,2,2,1,1] => 7
0110011 => [1,2,2,2] => 6
0110100 => [1,2,1,1,2] => 8
0110101 => [1,2,1,1,1,1] => 8
0110110 => [1,2,1,2,1] => 8
0110111 => [1,2,1,3] => 8
0111000 => [1,3,3] => 6
0111001 => [1,3,2,1] => 7
0111010 => [1,3,1,1,1] => 8
0111011 => [1,3,1,2] => 8
0111100 => [1,4,2] => 7
0111101 => [1,4,1,1] => 8
0111110 => [1,5,1] => 8
0111111 => [1,6] => 8
1000000 => [1,6] => 8
1000001 => [1,5,1] => 8
1000010 => [1,4,1,1] => 8
1000011 => [1,4,2] => 7
1000100 => [1,3,1,2] => 8
1000101 => [1,3,1,1,1] => 8
1000110 => [1,3,2,1] => 7
1000111 => [1,3,3] => 6
1001000 => [1,2,1,3] => 8
1001001 => [1,2,1,2,1] => 8
1001010 => [1,2,1,1,1,1] => 8
1001011 => [1,2,1,1,2] => 8
1001100 => [1,2,2,2] => 6
1001101 => [1,2,2,1,1] => 7
1001110 => [1,2,3,1] => 7
1001111 => [1,2,4] => 7
1010000 => [1,1,1,4] => 8
1010001 => [1,1,1,3,1] => 8
1010010 => [1,1,1,2,1,1] => 8
1010011 => [1,1,1,2,2] => 7
1010100 => [1,1,1,1,1,2] => 8
1010101 => [1,1,1,1,1,1,1] => 8
1010110 => [1,1,1,1,2,1] => 8
1010111 => [1,1,1,1,3] => 8
1011000 => [1,1,2,3] => 7
1011001 => [1,1,2,2,1] => 7
1011010 => [1,1,2,1,1,1] => 8
1011011 => [1,1,2,1,2] => 8
1011100 => [1,1,3,2] => 7
1011101 => [1,1,3,1,1] => 8
1011110 => [1,1,4,1] => 8
1011111 => [1,1,5] => 8
1100000 => [2,5] => 7
1100001 => [2,4,1] => 7
1100010 => [2,3,1,1] => 7
1100011 => [2,3,2] => 6
1100100 => [2,2,1,2] => 7
1100101 => [2,2,1,1,1] => 7
1100110 => [2,2,2,1] => 6
1100111 => [2,2,3] => 6
1101000 => [2,1,1,3] => 8
1101001 => [2,1,1,2,1] => 8
1101010 => [2,1,1,1,1,1] => 8
1101011 => [2,1,1,1,2] => 8
1101100 => [2,1,2,2] => 7
1101101 => [2,1,2,1,1] => 8
1101110 => [2,1,3,1] => 8
1101111 => [2,1,4] => 8
1110000 => [3,4] => 6
1110001 => [3,3,1] => 6
1110010 => [3,2,1,1] => 7
1110011 => [3,2,2] => 6
1110100 => [3,1,1,2] => 8
1110101 => [3,1,1,1,1] => 8
1110110 => [3,1,2,1] => 8
1110111 => [3,1,3] => 8
1111000 => [4,3] => 6
1111001 => [4,2,1] => 7
1111010 => [4,1,1,1] => 8
1111011 => [4,1,2] => 8
1111100 => [5,2] => 7
1111101 => [5,1,1] => 8
1111110 => [6,1] => 8
1111111 => [7] => 8
00000000 => [8] => 9
00000001 => [7,1] => 9
00000010 => [6,1,1] => 9
00000011 => [6,2] => 8
00000100 => [5,1,2] => 9
00000101 => [5,1,1,1] => 9
00000110 => [5,2,1] => 8
00000111 => [5,3] => 7
00001000 => [4,1,3] => 9
00001001 => [4,1,2,1] => 9
00001010 => [4,1,1,1,1] => 9
00001011 => [4,1,1,2] => 9
00001100 => [4,2,2] => 7
00001101 => [4,2,1,1] => 8
00001110 => [4,3,1] => 7
00001111 => [4,4] => 6
00010000 => [3,1,4] => 9
00010001 => [3,1,3,1] => 9
00010010 => [3,1,2,1,1] => 9
00010011 => [3,1,2,2] => 8
00010100 => [3,1,1,1,2] => 9
00010101 => [3,1,1,1,1,1] => 9
00010110 => [3,1,1,2,1] => 9
00010111 => [3,1,1,3] => 9
00011000 => [3,2,3] => 7
00011001 => [3,2,2,1] => 7
00011010 => [3,2,1,1,1] => 8
00011011 => [3,2,1,2] => 8
00011100 => [3,3,2] => 6
00011101 => [3,3,1,1] => 7
00011110 => [3,4,1] => 7
00011111 => [3,5] => 7
00100000 => [2,1,5] => 9
00100001 => [2,1,4,1] => 9
00100010 => [2,1,3,1,1] => 9
00100011 => [2,1,3,2] => 8
00100100 => [2,1,2,1,2] => 9
00100101 => [2,1,2,1,1,1] => 9
00100110 => [2,1,2,2,1] => 8
00100111 => [2,1,2,3] => 8
00101000 => [2,1,1,1,3] => 9
00101001 => [2,1,1,1,2,1] => 9
00101010 => [2,1,1,1,1,1,1] => 9
00101011 => [2,1,1,1,1,2] => 9
00101100 => [2,1,1,2,2] => 8
00101101 => [2,1,1,2,1,1] => 9
00101110 => [2,1,1,3,1] => 9
00101111 => [2,1,1,4] => 9
00110000 => [2,2,4] => 7
00110001 => [2,2,3,1] => 7
00110010 => [2,2,2,1,1] => 7
00110011 => [2,2,2,2] => 6
00110100 => [2,2,1,1,2] => 8
00110101 => [2,2,1,1,1,1] => 8
00110110 => [2,2,1,2,1] => 8
00110111 => [2,2,1,3] => 8
00111000 => [2,3,3] => 6
00111001 => [2,3,2,1] => 7
00111010 => [2,3,1,1,1] => 8
00111011 => [2,3,1,2] => 8
00111100 => [2,4,2] => 7
00111101 => [2,4,1,1] => 8
00111110 => [2,5,1] => 8
00111111 => [2,6] => 8
01000000 => [1,1,6] => 9
01000001 => [1,1,5,1] => 9
01000010 => [1,1,4,1,1] => 9
01000011 => [1,1,4,2] => 8
01000100 => [1,1,3,1,2] => 9
01000101 => [1,1,3,1,1,1] => 9
01000110 => [1,1,3,2,1] => 8
01000111 => [1,1,3,3] => 7
01001000 => [1,1,2,1,3] => 9
01001001 => [1,1,2,1,2,1] => 9
01001010 => [1,1,2,1,1,1,1] => 9
01001011 => [1,1,2,1,1,2] => 9
01001100 => [1,1,2,2,2] => 7
01001101 => [1,1,2,2,1,1] => 8
01001110 => [1,1,2,3,1] => 8
01001111 => [1,1,2,4] => 8
01010000 => [1,1,1,1,4] => 9
01010001 => [1,1,1,1,3,1] => 9
01010010 => [1,1,1,1,2,1,1] => 9
01010011 => [1,1,1,1,2,2] => 8
01010100 => [1,1,1,1,1,1,2] => 9
01010101 => [1,1,1,1,1,1,1,1] => 9
01010110 => [1,1,1,1,1,2,1] => 9
01010111 => [1,1,1,1,1,3] => 9
01011000 => [1,1,1,2,3] => 8
01011001 => [1,1,1,2,2,1] => 8
01011010 => [1,1,1,2,1,1,1] => 9
01011011 => [1,1,1,2,1,2] => 9
01011100 => [1,1,1,3,2] => 8
01011101 => [1,1,1,3,1,1] => 9
01011110 => [1,1,1,4,1] => 9
01011111 => [1,1,1,5] => 9
01100000 => [1,2,5] => 8
01100001 => [1,2,4,1] => 8
01100010 => [1,2,3,1,1] => 8
01100011 => [1,2,3,2] => 7
01100100 => [1,2,2,1,2] => 8
01100101 => [1,2,2,1,1,1] => 8
01100110 => [1,2,2,2,1] => 7
01100111 => [1,2,2,3] => 7
01101000 => [1,2,1,1,3] => 9
01101001 => [1,2,1,1,2,1] => 9
01101010 => [1,2,1,1,1,1,1] => 9
01101011 => [1,2,1,1,1,2] => 9
01101100 => [1,2,1,2,2] => 8
01101101 => [1,2,1,2,1,1] => 9
01101110 => [1,2,1,3,1] => 9
01101111 => [1,2,1,4] => 9
01110000 => [1,3,4] => 7
01110001 => [1,3,3,1] => 7
01110010 => [1,3,2,1,1] => 8
01110011 => [1,3,2,2] => 7
01110100 => [1,3,1,1,2] => 9
01110101 => [1,3,1,1,1,1] => 9
01110110 => [1,3,1,2,1] => 9
01110111 => [1,3,1,3] => 9
01111000 => [1,4,3] => 7
01111001 => [1,4,2,1] => 8
01111010 => [1,4,1,1,1] => 9
01111011 => [1,4,1,2] => 9
01111100 => [1,5,2] => 8
01111101 => [1,5,1,1] => 9
01111110 => [1,6,1] => 9
01111111 => [1,7] => 9
10000000 => [1,7] => 9
10000001 => [1,6,1] => 9
10000010 => [1,5,1,1] => 9
10000011 => [1,5,2] => 8
10000100 => [1,4,1,2] => 9
10000101 => [1,4,1,1,1] => 9
10000110 => [1,4,2,1] => 8
10000111 => [1,4,3] => 7
10001000 => [1,3,1,3] => 9
10001001 => [1,3,1,2,1] => 9
10001010 => [1,3,1,1,1,1] => 9
10001011 => [1,3,1,1,2] => 9
10001100 => [1,3,2,2] => 7
10001101 => [1,3,2,1,1] => 8
10001110 => [1,3,3,1] => 7
10001111 => [1,3,4] => 7
10010000 => [1,2,1,4] => 9
10010001 => [1,2,1,3,1] => 9
10010010 => [1,2,1,2,1,1] => 9
10010011 => [1,2,1,2,2] => 8
10010100 => [1,2,1,1,1,2] => 9
10010101 => [1,2,1,1,1,1,1] => 9
10010110 => [1,2,1,1,2,1] => 9
10010111 => [1,2,1,1,3] => 9
10011000 => [1,2,2,3] => 7
10011001 => [1,2,2,2,1] => 7
10011010 => [1,2,2,1,1,1] => 8
10011011 => [1,2,2,1,2] => 8
10011100 => [1,2,3,2] => 7
10011101 => [1,2,3,1,1] => 8
10011110 => [1,2,4,1] => 8
10011111 => [1,2,5] => 8
10100000 => [1,1,1,5] => 9
10100001 => [1,1,1,4,1] => 9
10100010 => [1,1,1,3,1,1] => 9
10100011 => [1,1,1,3,2] => 8
10100100 => [1,1,1,2,1,2] => 9
10100101 => [1,1,1,2,1,1,1] => 9
10100110 => [1,1,1,2,2,1] => 8
10100111 => [1,1,1,2,3] => 8
10101000 => [1,1,1,1,1,3] => 9
10101001 => [1,1,1,1,1,2,1] => 9
10101010 => [1,1,1,1,1,1,1,1] => 9
10101011 => [1,1,1,1,1,1,2] => 9
10101100 => [1,1,1,1,2,2] => 8
10101101 => [1,1,1,1,2,1,1] => 9
10101110 => [1,1,1,1,3,1] => 9
10101111 => [1,1,1,1,4] => 9
10110000 => [1,1,2,4] => 8
10110001 => [1,1,2,3,1] => 8
10110010 => [1,1,2,2,1,1] => 8
10110011 => [1,1,2,2,2] => 7
10110100 => [1,1,2,1,1,2] => 9
10110101 => [1,1,2,1,1,1,1] => 9
10110110 => [1,1,2,1,2,1] => 9
10110111 => [1,1,2,1,3] => 9
10111000 => [1,1,3,3] => 7
10111001 => [1,1,3,2,1] => 8
10111010 => [1,1,3,1,1,1] => 9
10111011 => [1,1,3,1,2] => 9
10111100 => [1,1,4,2] => 8
10111101 => [1,1,4,1,1] => 9
10111110 => [1,1,5,1] => 9
10111111 => [1,1,6] => 9
11000000 => [2,6] => 8
11000001 => [2,5,1] => 8
11000010 => [2,4,1,1] => 8
11000011 => [2,4,2] => 7
11000100 => [2,3,1,2] => 8
11000101 => [2,3,1,1,1] => 8
11000110 => [2,3,2,1] => 7
11000111 => [2,3,3] => 6
11001000 => [2,2,1,3] => 8
11001001 => [2,2,1,2,1] => 8
11001010 => [2,2,1,1,1,1] => 8
11001011 => [2,2,1,1,2] => 8
11001100 => [2,2,2,2] => 6
11001101 => [2,2,2,1,1] => 7
11001110 => [2,2,3,1] => 7
11001111 => [2,2,4] => 7
11010000 => [2,1,1,4] => 9
11010001 => [2,1,1,3,1] => 9
11010010 => [2,1,1,2,1,1] => 9
11010011 => [2,1,1,2,2] => 8
11010100 => [2,1,1,1,1,2] => 9
11010101 => [2,1,1,1,1,1,1] => 9
11010110 => [2,1,1,1,2,1] => 9
11010111 => [2,1,1,1,3] => 9
11011000 => [2,1,2,3] => 8
11011001 => [2,1,2,2,1] => 8
11011010 => [2,1,2,1,1,1] => 9
11011011 => [2,1,2,1,2] => 9
11011100 => [2,1,3,2] => 8
11011101 => [2,1,3,1,1] => 9
11011110 => [2,1,4,1] => 9
11011111 => [2,1,5] => 9
11100000 => [3,5] => 7
11100001 => [3,4,1] => 7
11100010 => [3,3,1,1] => 7
11100011 => [3,3,2] => 6
11100100 => [3,2,1,2] => 8
11100101 => [3,2,1,1,1] => 8
11100110 => [3,2,2,1] => 7
11100111 => [3,2,3] => 7
11101000 => [3,1,1,3] => 9
11101001 => [3,1,1,2,1] => 9
11101010 => [3,1,1,1,1,1] => 9
11101011 => [3,1,1,1,2] => 9
11101100 => [3,1,2,2] => 8
11101101 => [3,1,2,1,1] => 9
11101110 => [3,1,3,1] => 9
11101111 => [3,1,4] => 9
11110000 => [4,4] => 6
11110001 => [4,3,1] => 7
11110010 => [4,2,1,1] => 8
11110011 => [4,2,2] => 7
11110100 => [4,1,1,2] => 9
11110101 => [4,1,1,1,1] => 9
11110110 => [4,1,2,1] => 9
11110111 => [4,1,3] => 9
11111000 => [5,3] => 7
11111001 => [5,2,1] => 8
11111010 => [5,1,1,1] => 9
11111011 => [5,1,2] => 9
11111100 => [6,2] => 8
11111101 => [6,1,1] => 9
11111110 => [7,1] => 9
11111111 => [8] => 9
000000000 => [9] => 10
000000001 => [8,1] => 10
000000010 => [7,1,1] => 10
000000011 => [7,2] => 9
000000100 => [6,1,2] => 10
000000101 => [6,1,1,1] => 10
000000110 => [6,2,1] => 9
000000111 => [6,3] => 8
000001000 => [5,1,3] => 10
000001001 => [5,1,2,1] => 10
000001010 => [5,1,1,1,1] => 10
000001011 => [5,1,1,2] => 10
000001100 => [5,2,2] => 8
000001101 => [5,2,1,1] => 9
000001110 => [5,3,1] => 8
000001111 => [5,4] => 7
000010000 => [4,1,4] => 10
000010001 => [4,1,3,1] => 10
000010010 => [4,1,2,1,1] => 10
000010011 => [4,1,2,2] => 9
000010100 => [4,1,1,1,2] => 10
000010101 => [4,1,1,1,1,1] => 10
000010110 => [4,1,1,2,1] => 10
000010111 => [4,1,1,3] => 10
000011000 => [4,2,3] => 8
000011001 => [4,2,2,1] => 8
000011010 => [4,2,1,1,1] => 9
000011011 => [4,2,1,2] => 9
000011100 => [4,3,2] => 7
000011101 => [4,3,1,1] => 8
000011110 => [4,4,1] => 7
000011111 => [4,5] => 7
000100000 => [3,1,5] => 10
000100001 => [3,1,4,1] => 10
000100010 => [3,1,3,1,1] => 10
000100011 => [3,1,3,2] => 9
000100100 => [3,1,2,1,2] => 10
000100101 => [3,1,2,1,1,1] => 10
000100110 => [3,1,2,2,1] => 9
000100111 => [3,1,2,3] => 9
000101000 => [3,1,1,1,3] => 10
000101001 => [3,1,1,1,2,1] => 10
000101010 => [3,1,1,1,1,1,1] => 10
000101011 => [3,1,1,1,1,2] => 10
000101100 => [3,1,1,2,2] => 9
000101101 => [3,1,1,2,1,1] => 10
000101110 => [3,1,1,3,1] => 10
000101111 => [3,1,1,4] => 10
000110000 => [3,2,4] => 8
000110001 => [3,2,3,1] => 8
000110010 => [3,2,2,1,1] => 8
000110011 => [3,2,2,2] => 7
000110100 => [3,2,1,1,2] => 9
000110101 => [3,2,1,1,1,1] => 9
000110110 => [3,2,1,2,1] => 9
000110111 => [3,2,1,3] => 9
000111000 => [3,3,3] => 6
000111001 => [3,3,2,1] => 7
000111010 => [3,3,1,1,1] => 8
000111011 => [3,3,1,2] => 8
000111100 => [3,4,2] => 7
000111101 => [3,4,1,1] => 8
000111110 => [3,5,1] => 8
000111111 => [3,6] => 8
001000000 => [2,1,6] => 10
001000001 => [2,1,5,1] => 10
001000010 => [2,1,4,1,1] => 10
001000011 => [2,1,4,2] => 9
001000100 => [2,1,3,1,2] => 10
001000101 => [2,1,3,1,1,1] => 10
001000110 => [2,1,3,2,1] => 9
001000111 => [2,1,3,3] => 8
001001000 => [2,1,2,1,3] => 10
001001001 => [2,1,2,1,2,1] => 10
001001010 => [2,1,2,1,1,1,1] => 10
001001011 => [2,1,2,1,1,2] => 10
001001100 => [2,1,2,2,2] => 8
001001101 => [2,1,2,2,1,1] => 9
001001110 => [2,1,2,3,1] => 9
001001111 => [2,1,2,4] => 9
001010000 => [2,1,1,1,4] => 10
001010001 => [2,1,1,1,3,1] => 10
001010010 => [2,1,1,1,2,1,1] => 10
001010011 => [2,1,1,1,2,2] => 9
001010100 => [2,1,1,1,1,1,2] => 10
001010101 => [2,1,1,1,1,1,1,1] => 10
001010110 => [2,1,1,1,1,2,1] => 10
001010111 => [2,1,1,1,1,3] => 10
001011000 => [2,1,1,2,3] => 9
001011001 => [2,1,1,2,2,1] => 9
001011010 => [2,1,1,2,1,1,1] => 10
001011011 => [2,1,1,2,1,2] => 10
001011100 => [2,1,1,3,2] => 9
001011101 => [2,1,1,3,1,1] => 10
001011110 => [2,1,1,4,1] => 10
001011111 => [2,1,1,5] => 10
001100000 => [2,2,5] => 8
001100001 => [2,2,4,1] => 8
001100010 => [2,2,3,1,1] => 8
001100011 => [2,2,3,2] => 7
001100100 => [2,2,2,1,2] => 8
001100101 => [2,2,2,1,1,1] => 8
001100110 => [2,2,2,2,1] => 7
001100111 => [2,2,2,3] => 7
001101000 => [2,2,1,1,3] => 9
001101001 => [2,2,1,1,2,1] => 9
001101010 => [2,2,1,1,1,1,1] => 9
001101011 => [2,2,1,1,1,2] => 9
001101100 => [2,2,1,2,2] => 8
001101101 => [2,2,1,2,1,1] => 9
001101110 => [2,2,1,3,1] => 9
001101111 => [2,2,1,4] => 9
001110000 => [2,3,4] => 7
001110001 => [2,3,3,1] => 7
001110010 => [2,3,2,1,1] => 8
001110011 => [2,3,2,2] => 7
001110100 => [2,3,1,1,2] => 9
001110101 => [2,3,1,1,1,1] => 9
001110110 => [2,3,1,2,1] => 9
001110111 => [2,3,1,3] => 9
001111000 => [2,4,3] => 7
001111001 => [2,4,2,1] => 8
001111010 => [2,4,1,1,1] => 9
001111011 => [2,4,1,2] => 9
001111100 => [2,5,2] => 8
001111101 => [2,5,1,1] => 9
001111110 => [2,6,1] => 9
001111111 => [2,7] => 9
010000000 => [1,1,7] => 10
010000001 => [1,1,6,1] => 10
010000010 => [1,1,5,1,1] => 10
010000011 => [1,1,5,2] => 9
010000100 => [1,1,4,1,2] => 10
010000101 => [1,1,4,1,1,1] => 10
010000110 => [1,1,4,2,1] => 9
010000111 => [1,1,4,3] => 8
010001000 => [1,1,3,1,3] => 10
010001001 => [1,1,3,1,2,1] => 10
010001010 => [1,1,3,1,1,1,1] => 10
010001011 => [1,1,3,1,1,2] => 10
010001100 => [1,1,3,2,2] => 8
010001101 => [1,1,3,2,1,1] => 9
010001110 => [1,1,3,3,1] => 8
010001111 => [1,1,3,4] => 8
010010000 => [1,1,2,1,4] => 10
010010001 => [1,1,2,1,3,1] => 10
010010010 => [1,1,2,1,2,1,1] => 10
010010011 => [1,1,2,1,2,2] => 9
010010100 => [1,1,2,1,1,1,2] => 10
010010101 => [1,1,2,1,1,1,1,1] => 10
010010110 => [1,1,2,1,1,2,1] => 10
010010111 => [1,1,2,1,1,3] => 10
010011000 => [1,1,2,2,3] => 8
010011001 => [1,1,2,2,2,1] => 8
010011010 => [1,1,2,2,1,1,1] => 9
010011011 => [1,1,2,2,1,2] => 9
010011100 => [1,1,2,3,2] => 8
010011101 => [1,1,2,3,1,1] => 9
010011110 => [1,1,2,4,1] => 9
010011111 => [1,1,2,5] => 9
010100000 => [1,1,1,1,5] => 10
010100001 => [1,1,1,1,4,1] => 10
010100010 => [1,1,1,1,3,1,1] => 10
010100011 => [1,1,1,1,3,2] => 9
010100100 => [1,1,1,1,2,1,2] => 10
010100101 => [1,1,1,1,2,1,1,1] => 10
010100110 => [1,1,1,1,2,2,1] => 9
010100111 => [1,1,1,1,2,3] => 9
010101000 => [1,1,1,1,1,1,3] => 10
010101001 => [1,1,1,1,1,1,2,1] => 10
010101010 => [1,1,1,1,1,1,1,1,1] => 10
010101011 => [1,1,1,1,1,1,1,2] => 10
010101100 => [1,1,1,1,1,2,2] => 9
010101101 => [1,1,1,1,1,2,1,1] => 10
010101110 => [1,1,1,1,1,3,1] => 10
010101111 => [1,1,1,1,1,4] => 10
010110000 => [1,1,1,2,4] => 9
010110001 => [1,1,1,2,3,1] => 9
010110010 => [1,1,1,2,2,1,1] => 9
010110011 => [1,1,1,2,2,2] => 8
010110100 => [1,1,1,2,1,1,2] => 10
010110101 => [1,1,1,2,1,1,1,1] => 10
010110110 => [1,1,1,2,1,2,1] => 10
010110111 => [1,1,1,2,1,3] => 10
010111000 => [1,1,1,3,3] => 8
010111001 => [1,1,1,3,2,1] => 9
010111010 => [1,1,1,3,1,1,1] => 10
010111011 => [1,1,1,3,1,2] => 10
010111100 => [1,1,1,4,2] => 9
010111101 => [1,1,1,4,1,1] => 10
010111110 => [1,1,1,5,1] => 10
010111111 => [1,1,1,6] => 10
011000000 => [1,2,6] => 9
011000001 => [1,2,5,1] => 9
011000010 => [1,2,4,1,1] => 9
011000011 => [1,2,4,2] => 8
011000100 => [1,2,3,1,2] => 9
011000101 => [1,2,3,1,1,1] => 9
011000110 => [1,2,3,2,1] => 8
011000111 => [1,2,3,3] => 7
011001000 => [1,2,2,1,3] => 9
011001001 => [1,2,2,1,2,1] => 9
011001010 => [1,2,2,1,1,1,1] => 9
011001011 => [1,2,2,1,1,2] => 9
011001100 => [1,2,2,2,2] => 7
011001101 => [1,2,2,2,1,1] => 8
011001110 => [1,2,2,3,1] => 8
011001111 => [1,2,2,4] => 8
011010000 => [1,2,1,1,4] => 10
011010001 => [1,2,1,1,3,1] => 10
011010010 => [1,2,1,1,2,1,1] => 10
011010011 => [1,2,1,1,2,2] => 9
011010100 => [1,2,1,1,1,1,2] => 10
011010101 => [1,2,1,1,1,1,1,1] => 10
011010110 => [1,2,1,1,1,2,1] => 10
011010111 => [1,2,1,1,1,3] => 10
011011000 => [1,2,1,2,3] => 9
011011001 => [1,2,1,2,2,1] => 9
011011010 => [1,2,1,2,1,1,1] => 10
011011011 => [1,2,1,2,1,2] => 10
011011100 => [1,2,1,3,2] => 9
011011101 => [1,2,1,3,1,1] => 10
011011110 => [1,2,1,4,1] => 10
011011111 => [1,2,1,5] => 10
011100000 => [1,3,5] => 8
011100001 => [1,3,4,1] => 8
011100010 => [1,3,3,1,1] => 8
011100011 => [1,3,3,2] => 7
011100100 => [1,3,2,1,2] => 9
011100101 => [1,3,2,1,1,1] => 9
011100110 => [1,3,2,2,1] => 8
011100111 => [1,3,2,3] => 8
011101000 => [1,3,1,1,3] => 10
011101001 => [1,3,1,1,2,1] => 10
011101010 => [1,3,1,1,1,1,1] => 10
011101011 => [1,3,1,1,1,2] => 10
011101100 => [1,3,1,2,2] => 9
011101101 => [1,3,1,2,1,1] => 10
011101110 => [1,3,1,3,1] => 10
011101111 => [1,3,1,4] => 10
011110000 => [1,4,4] => 7
011110001 => [1,4,3,1] => 8
011110010 => [1,4,2,1,1] => 9
011110011 => [1,4,2,2] => 8
011110100 => [1,4,1,1,2] => 10
011110101 => [1,4,1,1,1,1] => 10
011110110 => [1,4,1,2,1] => 10
011110111 => [1,4,1,3] => 10
011111000 => [1,5,3] => 8
011111001 => [1,5,2,1] => 9
011111010 => [1,5,1,1,1] => 10
011111011 => [1,5,1,2] => 10
011111100 => [1,6,2] => 9
011111101 => [1,6,1,1] => 10
011111110 => [1,7,1] => 10
011111111 => [1,8] => 10
100000000 => [1,8] => 10
100000001 => [1,7,1] => 10
100000010 => [1,6,1,1] => 10
100000011 => [1,6,2] => 9
100000100 => [1,5,1,2] => 10
100000101 => [1,5,1,1,1] => 10
100000110 => [1,5,2,1] => 9
100000111 => [1,5,3] => 8
100001000 => [1,4,1,3] => 10
100001001 => [1,4,1,2,1] => 10
100001010 => [1,4,1,1,1,1] => 10
100001011 => [1,4,1,1,2] => 10
100001100 => [1,4,2,2] => 8
100001101 => [1,4,2,1,1] => 9
100001110 => [1,4,3,1] => 8
100001111 => [1,4,4] => 7
100010000 => [1,3,1,4] => 10
100010001 => [1,3,1,3,1] => 10
100010010 => [1,3,1,2,1,1] => 10
100010011 => [1,3,1,2,2] => 9
100010100 => [1,3,1,1,1,2] => 10
100010101 => [1,3,1,1,1,1,1] => 10
100010110 => [1,3,1,1,2,1] => 10
100010111 => [1,3,1,1,3] => 10
100011000 => [1,3,2,3] => 8
100011001 => [1,3,2,2,1] => 8
100011010 => [1,3,2,1,1,1] => 9
100011011 => [1,3,2,1,2] => 9
100011100 => [1,3,3,2] => 7
100011101 => [1,3,3,1,1] => 8
100011110 => [1,3,4,1] => 8
100011111 => [1,3,5] => 8
100100000 => [1,2,1,5] => 10
100100001 => [1,2,1,4,1] => 10
100100010 => [1,2,1,3,1,1] => 10
100100011 => [1,2,1,3,2] => 9
100100100 => [1,2,1,2,1,2] => 10
100100101 => [1,2,1,2,1,1,1] => 10
100100110 => [1,2,1,2,2,1] => 9
100100111 => [1,2,1,2,3] => 9
100101000 => [1,2,1,1,1,3] => 10
100101001 => [1,2,1,1,1,2,1] => 10
100101010 => [1,2,1,1,1,1,1,1] => 10
100101011 => [1,2,1,1,1,1,2] => 10
100101100 => [1,2,1,1,2,2] => 9
100101101 => [1,2,1,1,2,1,1] => 10
100101110 => [1,2,1,1,3,1] => 10
100101111 => [1,2,1,1,4] => 10
100110000 => [1,2,2,4] => 8
100110001 => [1,2,2,3,1] => 8
100110010 => [1,2,2,2,1,1] => 8
100110011 => [1,2,2,2,2] => 7
100110100 => [1,2,2,1,1,2] => 9
100110101 => [1,2,2,1,1,1,1] => 9
100110110 => [1,2,2,1,2,1] => 9
100110111 => [1,2,2,1,3] => 9
100111000 => [1,2,3,3] => 7
100111001 => [1,2,3,2,1] => 8
100111010 => [1,2,3,1,1,1] => 9
100111011 => [1,2,3,1,2] => 9
100111100 => [1,2,4,2] => 8
100111101 => [1,2,4,1,1] => 9
100111110 => [1,2,5,1] => 9
100111111 => [1,2,6] => 9
101000000 => [1,1,1,6] => 10
101000001 => [1,1,1,5,1] => 10
101000010 => [1,1,1,4,1,1] => 10
101000011 => [1,1,1,4,2] => 9
101000100 => [1,1,1,3,1,2] => 10
101000101 => [1,1,1,3,1,1,1] => 10
101000110 => [1,1,1,3,2,1] => 9
101000111 => [1,1,1,3,3] => 8
101001000 => [1,1,1,2,1,3] => 10
101001001 => [1,1,1,2,1,2,1] => 10
101001010 => [1,1,1,2,1,1,1,1] => 10
101001011 => [1,1,1,2,1,1,2] => 10
101001100 => [1,1,1,2,2,2] => 8
101001101 => [1,1,1,2,2,1,1] => 9
101001110 => [1,1,1,2,3,1] => 9
101001111 => [1,1,1,2,4] => 9
101010000 => [1,1,1,1,1,4] => 10
101010001 => [1,1,1,1,1,3,1] => 10
101010010 => [1,1,1,1,1,2,1,1] => 10
101010011 => [1,1,1,1,1,2,2] => 9
101010100 => [1,1,1,1,1,1,1,2] => 10
101010101 => [1,1,1,1,1,1,1,1,1] => 10
101010110 => [1,1,1,1,1,1,2,1] => 10
101010111 => [1,1,1,1,1,1,3] => 10
101011000 => [1,1,1,1,2,3] => 9
101011001 => [1,1,1,1,2,2,1] => 9
101011010 => [1,1,1,1,2,1,1,1] => 10
101011011 => [1,1,1,1,2,1,2] => 10
101011100 => [1,1,1,1,3,2] => 9
101011101 => [1,1,1,1,3,1,1] => 10
101011110 => [1,1,1,1,4,1] => 10
101011111 => [1,1,1,1,5] => 10
101100000 => [1,1,2,5] => 9
101100001 => [1,1,2,4,1] => 9
101100010 => [1,1,2,3,1,1] => 9
101100011 => [1,1,2,3,2] => 8
101100100 => [1,1,2,2,1,2] => 9
101100101 => [1,1,2,2,1,1,1] => 9
101100110 => [1,1,2,2,2,1] => 8
101100111 => [1,1,2,2,3] => 8
101101000 => [1,1,2,1,1,3] => 10
101101001 => [1,1,2,1,1,2,1] => 10
101101010 => [1,1,2,1,1,1,1,1] => 10
101101011 => [1,1,2,1,1,1,2] => 10
101101100 => [1,1,2,1,2,2] => 9
101101101 => [1,1,2,1,2,1,1] => 10
101101110 => [1,1,2,1,3,1] => 10
101101111 => [1,1,2,1,4] => 10
101110000 => [1,1,3,4] => 8
101110001 => [1,1,3,3,1] => 8
101110010 => [1,1,3,2,1,1] => 9
101110011 => [1,1,3,2,2] => 8
101110100 => [1,1,3,1,1,2] => 10
101110101 => [1,1,3,1,1,1,1] => 10
101110110 => [1,1,3,1,2,1] => 10
101110111 => [1,1,3,1,3] => 10
101111000 => [1,1,4,3] => 8
101111001 => [1,1,4,2,1] => 9
101111010 => [1,1,4,1,1,1] => 10
101111011 => [1,1,4,1,2] => 10
101111100 => [1,1,5,2] => 9
101111101 => [1,1,5,1,1] => 10
101111110 => [1,1,6,1] => 10
101111111 => [1,1,7] => 10
110000000 => [2,7] => 9
110000001 => [2,6,1] => 9
110000010 => [2,5,1,1] => 9
110000011 => [2,5,2] => 8
110000100 => [2,4,1,2] => 9
110000101 => [2,4,1,1,1] => 9
110000110 => [2,4,2,1] => 8
110000111 => [2,4,3] => 7
110001000 => [2,3,1,3] => 9
110001001 => [2,3,1,2,1] => 9
110001010 => [2,3,1,1,1,1] => 9
110001011 => [2,3,1,1,2] => 9
110001100 => [2,3,2,2] => 7
110001101 => [2,3,2,1,1] => 8
110001110 => [2,3,3,1] => 7
110001111 => [2,3,4] => 7
110010000 => [2,2,1,4] => 9
110010001 => [2,2,1,3,1] => 9
110010010 => [2,2,1,2,1,1] => 9
110010011 => [2,2,1,2,2] => 8
110010100 => [2,2,1,1,1,2] => 9
110010101 => [2,2,1,1,1,1,1] => 9
110010110 => [2,2,1,1,2,1] => 9
110010111 => [2,2,1,1,3] => 9
110011000 => [2,2,2,3] => 7
110011001 => [2,2,2,2,1] => 7
110011010 => [2,2,2,1,1,1] => 8
110011011 => [2,2,2,1,2] => 8
110011100 => [2,2,3,2] => 7
110011101 => [2,2,3,1,1] => 8
110011110 => [2,2,4,1] => 8
110011111 => [2,2,5] => 8
110100000 => [2,1,1,5] => 10
110100001 => [2,1,1,4,1] => 10
110100010 => [2,1,1,3,1,1] => 10
110100011 => [2,1,1,3,2] => 9
110100100 => [2,1,1,2,1,2] => 10
110100101 => [2,1,1,2,1,1,1] => 10
110100110 => [2,1,1,2,2,1] => 9
110100111 => [2,1,1,2,3] => 9
110101000 => [2,1,1,1,1,3] => 10
110101001 => [2,1,1,1,1,2,1] => 10
110101010 => [2,1,1,1,1,1,1,1] => 10
110101011 => [2,1,1,1,1,1,2] => 10
110101100 => [2,1,1,1,2,2] => 9
110101101 => [2,1,1,1,2,1,1] => 10
110101110 => [2,1,1,1,3,1] => 10
110101111 => [2,1,1,1,4] => 10
110110000 => [2,1,2,4] => 9
110110001 => [2,1,2,3,1] => 9
110110010 => [2,1,2,2,1,1] => 9
110110011 => [2,1,2,2,2] => 8
110110100 => [2,1,2,1,1,2] => 10
110110101 => [2,1,2,1,1,1,1] => 10
110110110 => [2,1,2,1,2,1] => 10
110110111 => [2,1,2,1,3] => 10
110111000 => [2,1,3,3] => 8
110111001 => [2,1,3,2,1] => 9
110111010 => [2,1,3,1,1,1] => 10
110111011 => [2,1,3,1,2] => 10
110111100 => [2,1,4,2] => 9
110111101 => [2,1,4,1,1] => 10
110111110 => [2,1,5,1] => 10
110111111 => [2,1,6] => 10
111000000 => [3,6] => 8
111000001 => [3,5,1] => 8
111000010 => [3,4,1,1] => 8
111000011 => [3,4,2] => 7
111000100 => [3,3,1,2] => 8
111000101 => [3,3,1,1,1] => 8
111000110 => [3,3,2,1] => 7
111000111 => [3,3,3] => 6
111001000 => [3,2,1,3] => 9
111001001 => [3,2,1,2,1] => 9
111001010 => [3,2,1,1,1,1] => 9
111001011 => [3,2,1,1,2] => 9
111001100 => [3,2,2,2] => 7
111001101 => [3,2,2,1,1] => 8
111001110 => [3,2,3,1] => 8
111001111 => [3,2,4] => 8
111010000 => [3,1,1,4] => 10
111010001 => [3,1,1,3,1] => 10
111010010 => [3,1,1,2,1,1] => 10
111010011 => [3,1,1,2,2] => 9
111010100 => [3,1,1,1,1,2] => 10
111010101 => [3,1,1,1,1,1,1] => 10
111010110 => [3,1,1,1,2,1] => 10
111010111 => [3,1,1,1,3] => 10
111011000 => [3,1,2,3] => 9
111011001 => [3,1,2,2,1] => 9
111011010 => [3,1,2,1,1,1] => 10
111011011 => [3,1,2,1,2] => 10
111011100 => [3,1,3,2] => 9
111011101 => [3,1,3,1,1] => 10
111011110 => [3,1,4,1] => 10
111011111 => [3,1,5] => 10
111100000 => [4,5] => 7
111100001 => [4,4,1] => 7
111100010 => [4,3,1,1] => 8
111100011 => [4,3,2] => 7
111100100 => [4,2,1,2] => 9
111100101 => [4,2,1,1,1] => 9
111100110 => [4,2,2,1] => 8
111100111 => [4,2,3] => 8
111101000 => [4,1,1,3] => 10
111101001 => [4,1,1,2,1] => 10
111101010 => [4,1,1,1,1,1] => 10
111101011 => [4,1,1,1,2] => 10
111101100 => [4,1,2,2] => 9
111101101 => [4,1,2,1,1] => 10
111101110 => [4,1,3,1] => 10
111101111 => [4,1,4] => 10
111110000 => [5,4] => 7
111110001 => [5,3,1] => 8
111110010 => [5,2,1,1] => 9
111110011 => [5,2,2] => 8
111110100 => [5,1,1,2] => 10
111110101 => [5,1,1,1,1] => 10
111110110 => [5,1,2,1] => 10
111110111 => [5,1,3] => 10
111111000 => [6,3] => 8
111111001 => [6,2,1] => 9
111111010 => [6,1,1,1] => 10
111111011 => [6,1,2] => 10
111111100 => [7,2] => 9
111111101 => [7,1,1] => 10
111111110 => [8,1] => 10
111111111 => [9] => 10
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Description
The semiperimeter of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the semiperimeter of the polygon determined by the axis and the bargraph. Put differently, it is the sum of the number of up steps and the number of horizontal steps when regarding the bargraph as a path with up, horizontal and down steps.
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 $w$.