Identifier
Images
=>
0=>[2]
1=>[1,1]
00=>[3]
01=>[2,1]
10=>[1,2]
11=>[1,1,1]
000=>[4]
001=>[3,1]
010=>[2,2]
011=>[2,1,1]
100=>[1,3]
101=>[1,2,1]
110=>[1,1,2]
111=>[1,1,1,1]
0000=>[5]
0001=>[4,1]
0010=>[3,2]
0011=>[3,1,1]
0100=>[2,3]
0101=>[2,2,1]
0110=>[2,1,2]
0111=>[2,1,1,1]
1000=>[1,4]
1001=>[1,3,1]
1010=>[1,2,2]
1011=>[1,2,1,1]
1100=>[1,1,3]
1101=>[1,1,2,1]
1110=>[1,1,1,2]
1111=>[1,1,1,1,1]
00000=>[6]
00001=>[5,1]
00010=>[4,2]
00011=>[4,1,1]
00100=>[3,3]
00101=>[3,2,1]
00110=>[3,1,2]
00111=>[3,1,1,1]
01000=>[2,4]
01001=>[2,3,1]
01010=>[2,2,2]
01011=>[2,2,1,1]
01100=>[2,1,3]
01101=>[2,1,2,1]
01110=>[2,1,1,2]
01111=>[2,1,1,1,1]
10000=>[1,5]
10001=>[1,4,1]
10010=>[1,3,2]
10011=>[1,3,1,1]
10100=>[1,2,3]
10101=>[1,2,2,1]
10110=>[1,2,1,2]
10111=>[1,2,1,1,1]
11000=>[1,1,4]
11001=>[1,1,3,1]
11010=>[1,1,2,2]
11011=>[1,1,2,1,1]
11100=>[1,1,1,3]
11101=>[1,1,1,2,1]
11110=>[1,1,1,1,2]
11111=>[1,1,1,1,1,1]
000000=>[7]
000001=>[6,1]
000010=>[5,2]
000011=>[5,1,1]
000100=>[4,3]
000101=>[4,2,1]
000110=>[4,1,2]
000111=>[4,1,1,1]
001000=>[3,4]
001001=>[3,3,1]
001010=>[3,2,2]
001011=>[3,2,1,1]
001100=>[3,1,3]
001101=>[3,1,2,1]
001110=>[3,1,1,2]
001111=>[3,1,1,1,1]
010000=>[2,5]
010001=>[2,4,1]
010010=>[2,3,2]
010011=>[2,3,1,1]
010100=>[2,2,3]
010101=>[2,2,2,1]
010110=>[2,2,1,2]
010111=>[2,2,1,1,1]
011000=>[2,1,4]
011001=>[2,1,3,1]
011010=>[2,1,2,2]
011011=>[2,1,2,1,1]
011100=>[2,1,1,3]
011101=>[2,1,1,2,1]
011110=>[2,1,1,1,2]
011111=>[2,1,1,1,1,1]
100000=>[1,6]
100001=>[1,5,1]
100010=>[1,4,2]
100011=>[1,4,1,1]
100100=>[1,3,3]
100101=>[1,3,2,1]
100110=>[1,3,1,2]
100111=>[1,3,1,1,1]
101000=>[1,2,4]
101001=>[1,2,3,1]
101010=>[1,2,2,2]
101011=>[1,2,2,1,1]
101100=>[1,2,1,3]
101101=>[1,2,1,2,1]
101110=>[1,2,1,1,2]
101111=>[1,2,1,1,1,1]
110000=>[1,1,5]
110001=>[1,1,4,1]
110010=>[1,1,3,2]
110011=>[1,1,3,1,1]
110100=>[1,1,2,3]
110101=>[1,1,2,2,1]
110110=>[1,1,2,1,2]
110111=>[1,1,2,1,1,1]
111000=>[1,1,1,4]
111001=>[1,1,1,3,1]
111010=>[1,1,1,2,2]
111011=>[1,1,1,2,1,1]
111100=>[1,1,1,1,3]
111101=>[1,1,1,1,2,1]
111110=>[1,1,1,1,1,2]
111111=>[1,1,1,1,1,1,1]
0000000=>[8]
0000001=>[7,1]
0000010=>[6,2]
0000011=>[6,1,1]
0000100=>[5,3]
0000101=>[5,2,1]
0000110=>[5,1,2]
0000111=>[5,1,1,1]
0001000=>[4,4]
0001001=>[4,3,1]
0001010=>[4,2,2]
0001011=>[4,2,1,1]
0001100=>[4,1,3]
0001101=>[4,1,2,1]
0001110=>[4,1,1,2]
0001111=>[4,1,1,1,1]
0010000=>[3,5]
0010001=>[3,4,1]
0010010=>[3,3,2]
0010011=>[3,3,1,1]
0010100=>[3,2,3]
0010101=>[3,2,2,1]
0010110=>[3,2,1,2]
0010111=>[3,2,1,1,1]
0011000=>[3,1,4]
0011001=>[3,1,3,1]
0011010=>[3,1,2,2]
0011011=>[3,1,2,1,1]
0011100=>[3,1,1,3]
0011101=>[3,1,1,2,1]
0011110=>[3,1,1,1,2]
0011111=>[3,1,1,1,1,1]
0100000=>[2,6]
0100001=>[2,5,1]
0100010=>[2,4,2]
0100011=>[2,4,1,1]
0100100=>[2,3,3]
0100101=>[2,3,2,1]
0100110=>[2,3,1,2]
0100111=>[2,3,1,1,1]
0101000=>[2,2,4]
0101001=>[2,2,3,1]
0101010=>[2,2,2,2]
0101011=>[2,2,2,1,1]
0101100=>[2,2,1,3]
0101101=>[2,2,1,2,1]
0101110=>[2,2,1,1,2]
0101111=>[2,2,1,1,1,1]
0110000=>[2,1,5]
0110001=>[2,1,4,1]
0110010=>[2,1,3,2]
0110011=>[2,1,3,1,1]
0110100=>[2,1,2,3]
0110101=>[2,1,2,2,1]
0110110=>[2,1,2,1,2]
0110111=>[2,1,2,1,1,1]
0111000=>[2,1,1,4]
0111001=>[2,1,1,3,1]
0111010=>[2,1,1,2,2]
0111011=>[2,1,1,2,1,1]
0111100=>[2,1,1,1,3]
0111101=>[2,1,1,1,2,1]
0111110=>[2,1,1,1,1,2]
0111111=>[2,1,1,1,1,1,1]
1000000=>[1,7]
1000001=>[1,6,1]
1000010=>[1,5,2]
1000011=>[1,5,1,1]
1000100=>[1,4,3]
1000101=>[1,4,2,1]
1000110=>[1,4,1,2]
1000111=>[1,4,1,1,1]
1001000=>[1,3,4]
1001001=>[1,3,3,1]
1001010=>[1,3,2,2]
1001011=>[1,3,2,1,1]
1001100=>[1,3,1,3]
1001101=>[1,3,1,2,1]
1001110=>[1,3,1,1,2]
1001111=>[1,3,1,1,1,1]
1010000=>[1,2,5]
1010001=>[1,2,4,1]
1010010=>[1,2,3,2]
1010011=>[1,2,3,1,1]
1010100=>[1,2,2,3]
1010101=>[1,2,2,2,1]
1010110=>[1,2,2,1,2]
1010111=>[1,2,2,1,1,1]
1011000=>[1,2,1,4]
1011001=>[1,2,1,3,1]
1011010=>[1,2,1,2,2]
1011011=>[1,2,1,2,1,1]
1011100=>[1,2,1,1,3]
1011101=>[1,2,1,1,2,1]
1011110=>[1,2,1,1,1,2]
1011111=>[1,2,1,1,1,1,1]
1100000=>[1,1,6]
1100001=>[1,1,5,1]
1100010=>[1,1,4,2]
1100011=>[1,1,4,1,1]
1100100=>[1,1,3,3]
1100101=>[1,1,3,2,1]
1100110=>[1,1,3,1,2]
1100111=>[1,1,3,1,1,1]
1101000=>[1,1,2,4]
1101001=>[1,1,2,3,1]
1101010=>[1,1,2,2,2]
1101011=>[1,1,2,2,1,1]
1101100=>[1,1,2,1,3]
1101101=>[1,1,2,1,2,1]
1101110=>[1,1,2,1,1,2]
1101111=>[1,1,2,1,1,1,1]
1110000=>[1,1,1,5]
1110001=>[1,1,1,4,1]
1110010=>[1,1,1,3,2]
1110011=>[1,1,1,3,1,1]
1110100=>[1,1,1,2,3]
1110101=>[1,1,1,2,2,1]
1110110=>[1,1,1,2,1,2]
1110111=>[1,1,1,2,1,1,1]
1111000=>[1,1,1,1,4]
1111001=>[1,1,1,1,3,1]
1111010=>[1,1,1,1,2,2]
1111011=>[1,1,1,1,2,1,1]
1111100=>[1,1,1,1,1,3]
1111101=>[1,1,1,1,1,2,1]
1111110=>[1,1,1,1,1,1,2]
1111111=>[1,1,1,1,1,1,1,1]
00000000=>[9]
00000001=>[8,1]
00000010=>[7,2]
00000011=>[7,1,1]
00000100=>[6,3]
00000101=>[6,2,1]
00000110=>[6,1,2]
00000111=>[6,1,1,1]
00001000=>[5,4]
00001001=>[5,3,1]
00001010=>[5,2,2]
00001011=>[5,2,1,1]
00001100=>[5,1,3]
00001101=>[5,1,2,1]
00001110=>[5,1,1,2]
00001111=>[5,1,1,1,1]
00010000=>[4,5]
00010001=>[4,4,1]
00010010=>[4,3,2]
00010011=>[4,3,1,1]
00010100=>[4,2,3]
00010101=>[4,2,2,1]
00010110=>[4,2,1,2]
00010111=>[4,2,1,1,1]
00011000=>[4,1,4]
00011001=>[4,1,3,1]
00011010=>[4,1,2,2]
00011011=>[4,1,2,1,1]
00011100=>[4,1,1,3]
00011101=>[4,1,1,2,1]
00011110=>[4,1,1,1,2]
00011111=>[4,1,1,1,1,1]
00100000=>[3,6]
00100001=>[3,5,1]
00100010=>[3,4,2]
00100011=>[3,4,1,1]
00100100=>[3,3,3]
00100101=>[3,3,2,1]
00100110=>[3,3,1,2]
00100111=>[3,3,1,1,1]
00101000=>[3,2,4]
00101001=>[3,2,3,1]
00101010=>[3,2,2,2]
00101011=>[3,2,2,1,1]
00101100=>[3,2,1,3]
00101101=>[3,2,1,2,1]
00101110=>[3,2,1,1,2]
00101111=>[3,2,1,1,1,1]
00110000=>[3,1,5]
00110001=>[3,1,4,1]
00110010=>[3,1,3,2]
00110011=>[3,1,3,1,1]
00110100=>[3,1,2,3]
00110101=>[3,1,2,2,1]
00110110=>[3,1,2,1,2]
00110111=>[3,1,2,1,1,1]
00111000=>[3,1,1,4]
00111001=>[3,1,1,3,1]
00111010=>[3,1,1,2,2]
00111011=>[3,1,1,2,1,1]
00111100=>[3,1,1,1,3]
00111101=>[3,1,1,1,2,1]
00111110=>[3,1,1,1,1,2]
00111111=>[3,1,1,1,1,1,1]
01000000=>[2,7]
01000001=>[2,6,1]
01000010=>[2,5,2]
01000011=>[2,5,1,1]
01000100=>[2,4,3]
01000101=>[2,4,2,1]
01000110=>[2,4,1,2]
01000111=>[2,4,1,1,1]
01001000=>[2,3,4]
01001001=>[2,3,3,1]
01001010=>[2,3,2,2]
01001011=>[2,3,2,1,1]
01001100=>[2,3,1,3]
01001101=>[2,3,1,2,1]
01001110=>[2,3,1,1,2]
01001111=>[2,3,1,1,1,1]
01010000=>[2,2,5]
01010001=>[2,2,4,1]
01010010=>[2,2,3,2]
01010011=>[2,2,3,1,1]
01010100=>[2,2,2,3]
01010101=>[2,2,2,2,1]
01010110=>[2,2,2,1,2]
01010111=>[2,2,2,1,1,1]
01011000=>[2,2,1,4]
01011001=>[2,2,1,3,1]
01011010=>[2,2,1,2,2]
01011011=>[2,2,1,2,1,1]
01011100=>[2,2,1,1,3]
01011101=>[2,2,1,1,2,1]
01011110=>[2,2,1,1,1,2]
01011111=>[2,2,1,1,1,1,1]
01100000=>[2,1,6]
01100001=>[2,1,5,1]
01100010=>[2,1,4,2]
01100011=>[2,1,4,1,1]
01100100=>[2,1,3,3]
01100101=>[2,1,3,2,1]
01100110=>[2,1,3,1,2]
01100111=>[2,1,3,1,1,1]
01101000=>[2,1,2,4]
01101001=>[2,1,2,3,1]
01101010=>[2,1,2,2,2]
01101011=>[2,1,2,2,1,1]
01101100=>[2,1,2,1,3]
01101101=>[2,1,2,1,2,1]
01101110=>[2,1,2,1,1,2]
01101111=>[2,1,2,1,1,1,1]
01110000=>[2,1,1,5]
01110001=>[2,1,1,4,1]
01110010=>[2,1,1,3,2]
01110011=>[2,1,1,3,1,1]
01110100=>[2,1,1,2,3]
01110101=>[2,1,1,2,2,1]
01110110=>[2,1,1,2,1,2]
01110111=>[2,1,1,2,1,1,1]
01111000=>[2,1,1,1,4]
01111001=>[2,1,1,1,3,1]
01111010=>[2,1,1,1,2,2]
01111011=>[2,1,1,1,2,1,1]
01111100=>[2,1,1,1,1,3]
01111101=>[2,1,1,1,1,2,1]
01111110=>[2,1,1,1,1,1,2]
01111111=>[2,1,1,1,1,1,1,1]
10000000=>[1,8]
10000001=>[1,7,1]
10000010=>[1,6,2]
10000011=>[1,6,1,1]
10000100=>[1,5,3]
10000101=>[1,5,2,1]
10000110=>[1,5,1,2]
10000111=>[1,5,1,1,1]
10001000=>[1,4,4]
10001001=>[1,4,3,1]
10001010=>[1,4,2,2]
10001011=>[1,4,2,1,1]
10001100=>[1,4,1,3]
10001101=>[1,4,1,2,1]
10001110=>[1,4,1,1,2]
10001111=>[1,4,1,1,1,1]
10010000=>[1,3,5]
10010001=>[1,3,4,1]
10010010=>[1,3,3,2]
10010011=>[1,3,3,1,1]
10010100=>[1,3,2,3]
10010101=>[1,3,2,2,1]
10010110=>[1,3,2,1,2]
10010111=>[1,3,2,1,1,1]
10011000=>[1,3,1,4]
10011001=>[1,3,1,3,1]
10011010=>[1,3,1,2,2]
10011011=>[1,3,1,2,1,1]
10011100=>[1,3,1,1,3]
10011101=>[1,3,1,1,2,1]
10011110=>[1,3,1,1,1,2]
10011111=>[1,3,1,1,1,1,1]
10100000=>[1,2,6]
10100001=>[1,2,5,1]
10100010=>[1,2,4,2]
10100011=>[1,2,4,1,1]
10100100=>[1,2,3,3]
10100101=>[1,2,3,2,1]
10100110=>[1,2,3,1,2]
10100111=>[1,2,3,1,1,1]
10101000=>[1,2,2,4]
10101001=>[1,2,2,3,1]
10101010=>[1,2,2,2,2]
10101011=>[1,2,2,2,1,1]
10101100=>[1,2,2,1,3]
10101101=>[1,2,2,1,2,1]
10101110=>[1,2,2,1,1,2]
10101111=>[1,2,2,1,1,1,1]
10110000=>[1,2,1,5]
10110001=>[1,2,1,4,1]
10110010=>[1,2,1,3,2]
10110011=>[1,2,1,3,1,1]
10110100=>[1,2,1,2,3]
10110101=>[1,2,1,2,2,1]
10110110=>[1,2,1,2,1,2]
10110111=>[1,2,1,2,1,1,1]
10111000=>[1,2,1,1,4]
10111001=>[1,2,1,1,3,1]
10111010=>[1,2,1,1,2,2]
10111011=>[1,2,1,1,2,1,1]
10111100=>[1,2,1,1,1,3]
10111101=>[1,2,1,1,1,2,1]
10111110=>[1,2,1,1,1,1,2]
10111111=>[1,2,1,1,1,1,1,1]
11000000=>[1,1,7]
11000001=>[1,1,6,1]
11000010=>[1,1,5,2]
11000011=>[1,1,5,1,1]
11000100=>[1,1,4,3]
11000101=>[1,1,4,2,1]
11000110=>[1,1,4,1,2]
11000111=>[1,1,4,1,1,1]
11001000=>[1,1,3,4]
11001001=>[1,1,3,3,1]
11001010=>[1,1,3,2,2]
11001011=>[1,1,3,2,1,1]
11001100=>[1,1,3,1,3]
11001101=>[1,1,3,1,2,1]
11001110=>[1,1,3,1,1,2]
11001111=>[1,1,3,1,1,1,1]
11010000=>[1,1,2,5]
11010001=>[1,1,2,4,1]
11010010=>[1,1,2,3,2]
11010011=>[1,1,2,3,1,1]
11010100=>[1,1,2,2,3]
11010101=>[1,1,2,2,2,1]
11010110=>[1,1,2,2,1,2]
11010111=>[1,1,2,2,1,1,1]
11011000=>[1,1,2,1,4]
11011001=>[1,1,2,1,3,1]
11011010=>[1,1,2,1,2,2]
11011011=>[1,1,2,1,2,1,1]
11011100=>[1,1,2,1,1,3]
11011101=>[1,1,2,1,1,2,1]
11011110=>[1,1,2,1,1,1,2]
11011111=>[1,1,2,1,1,1,1,1]
11100000=>[1,1,1,6]
11100001=>[1,1,1,5,1]
11100010=>[1,1,1,4,2]
11100011=>[1,1,1,4,1,1]
11100100=>[1,1,1,3,3]
11100101=>[1,1,1,3,2,1]
11100110=>[1,1,1,3,1,2]
11100111=>[1,1,1,3,1,1,1]
11101000=>[1,1,1,2,4]
11101001=>[1,1,1,2,3,1]
11101010=>[1,1,1,2,2,2]
11101011=>[1,1,1,2,2,1,1]
11101100=>[1,1,1,2,1,3]
11101101=>[1,1,1,2,1,2,1]
11101110=>[1,1,1,2,1,1,2]
11101111=>[1,1,1,2,1,1,1,1]
11110000=>[1,1,1,1,5]
11110001=>[1,1,1,1,4,1]
11110010=>[1,1,1,1,3,2]
11110011=>[1,1,1,1,3,1,1]
11110100=>[1,1,1,1,2,3]
11110101=>[1,1,1,1,2,2,1]
11110110=>[1,1,1,1,2,1,2]
11110111=>[1,1,1,1,2,1,1,1]
11111000=>[1,1,1,1,1,4]
11111001=>[1,1,1,1,1,3,1]
11111010=>[1,1,1,1,1,2,2]
11111011=>[1,1,1,1,1,2,1,1]
11111100=>[1,1,1,1,1,1,3]
11111101=>[1,1,1,1,1,1,2,1]
11111110=>[1,1,1,1,1,1,1,2]
11111111=>[1,1,1,1,1,1,1,1,1]
000000000=>[10]
000000001=>[9,1]
000000010=>[8,2]
000000011=>[8,1,1]
000000100=>[7,3]
000000101=>[7,2,1]
000000110=>[7,1,2]
000000111=>[7,1,1,1]
000001000=>[6,4]
000001001=>[6,3,1]
000001010=>[6,2,2]
000001011=>[6,2,1,1]
000001100=>[6,1,3]
000001101=>[6,1,2,1]
000001110=>[6,1,1,2]
000001111=>[6,1,1,1,1]
000010000=>[5,5]
000010001=>[5,4,1]
000010010=>[5,3,2]
000010011=>[5,3,1,1]
000010100=>[5,2,3]
000010101=>[5,2,2,1]
000010110=>[5,2,1,2]
000010111=>[5,2,1,1,1]
000011000=>[5,1,4]
000011001=>[5,1,3,1]
000011010=>[5,1,2,2]
000011011=>[5,1,2,1,1]
000011100=>[5,1,1,3]
000011101=>[5,1,1,2,1]
000011110=>[5,1,1,1,2]
000011111=>[5,1,1,1,1,1]
000100000=>[4,6]
000100001=>[4,5,1]
000100010=>[4,4,2]
000100011=>[4,4,1,1]
000100100=>[4,3,3]
000100101=>[4,3,2,1]
000100110=>[4,3,1,2]
000100111=>[4,3,1,1,1]
000101000=>[4,2,4]
000101001=>[4,2,3,1]
000101010=>[4,2,2,2]
000101011=>[4,2,2,1,1]
000101100=>[4,2,1,3]
000101101=>[4,2,1,2,1]
000101110=>[4,2,1,1,2]
000101111=>[4,2,1,1,1,1]
000110000=>[4,1,5]
000110001=>[4,1,4,1]
000110010=>[4,1,3,2]
000110011=>[4,1,3,1,1]
000110100=>[4,1,2,3]
000110101=>[4,1,2,2,1]
000110110=>[4,1,2,1,2]
000110111=>[4,1,2,1,1,1]
000111000=>[4,1,1,4]
000111001=>[4,1,1,3,1]
000111010=>[4,1,1,2,2]
000111011=>[4,1,1,2,1,1]
000111100=>[4,1,1,1,3]
000111101=>[4,1,1,1,2,1]
000111110=>[4,1,1,1,1,2]
000111111=>[4,1,1,1,1,1,1]
001000000=>[3,7]
001000001=>[3,6,1]
001000010=>[3,5,2]
001000011=>[3,5,1,1]
001000100=>[3,4,3]
001000101=>[3,4,2,1]
001000110=>[3,4,1,2]
001000111=>[3,4,1,1,1]
001001000=>[3,3,4]
001001001=>[3,3,3,1]
001001010=>[3,3,2,2]
001001011=>[3,3,2,1,1]
001001100=>[3,3,1,3]
001001101=>[3,3,1,2,1]
001001110=>[3,3,1,1,2]
001001111=>[3,3,1,1,1,1]
001010000=>[3,2,5]
001010001=>[3,2,4,1]
001010010=>[3,2,3,2]
001010011=>[3,2,3,1,1]
001010100=>[3,2,2,3]
001010101=>[3,2,2,2,1]
001010110=>[3,2,2,1,2]
001010111=>[3,2,2,1,1,1]
001011000=>[3,2,1,4]
001011001=>[3,2,1,3,1]
001011010=>[3,2,1,2,2]
001011011=>[3,2,1,2,1,1]
001011100=>[3,2,1,1,3]
001011101=>[3,2,1,1,2,1]
001011110=>[3,2,1,1,1,2]
001011111=>[3,2,1,1,1,1,1]
001100000=>[3,1,6]
001100001=>[3,1,5,1]
001100010=>[3,1,4,2]
001100011=>[3,1,4,1,1]
001100100=>[3,1,3,3]
001100101=>[3,1,3,2,1]
001100110=>[3,1,3,1,2]
001100111=>[3,1,3,1,1,1]
001101000=>[3,1,2,4]
001101001=>[3,1,2,3,1]
001101010=>[3,1,2,2,2]
001101011=>[3,1,2,2,1,1]
001101100=>[3,1,2,1,3]
001101101=>[3,1,2,1,2,1]
001101110=>[3,1,2,1,1,2]
001101111=>[3,1,2,1,1,1,1]
001110000=>[3,1,1,5]
001110001=>[3,1,1,4,1]
001110010=>[3,1,1,3,2]
001110011=>[3,1,1,3,1,1]
001110100=>[3,1,1,2,3]
001110101=>[3,1,1,2,2,1]
001110110=>[3,1,1,2,1,2]
001110111=>[3,1,1,2,1,1,1]
001111000=>[3,1,1,1,4]
001111001=>[3,1,1,1,3,1]
001111010=>[3,1,1,1,2,2]
001111011=>[3,1,1,1,2,1,1]
001111100=>[3,1,1,1,1,3]
001111101=>[3,1,1,1,1,2,1]
001111110=>[3,1,1,1,1,1,2]
001111111=>[3,1,1,1,1,1,1,1]
010000000=>[2,8]
010000001=>[2,7,1]
010000010=>[2,6,2]
010000011=>[2,6,1,1]
010000100=>[2,5,3]
010000101=>[2,5,2,1]
010000110=>[2,5,1,2]
010000111=>[2,5,1,1,1]
010001000=>[2,4,4]
010001001=>[2,4,3,1]
010001010=>[2,4,2,2]
010001011=>[2,4,2,1,1]
010001100=>[2,4,1,3]
010001101=>[2,4,1,2,1]
010001110=>[2,4,1,1,2]
010001111=>[2,4,1,1,1,1]
010010000=>[2,3,5]
010010001=>[2,3,4,1]
010010010=>[2,3,3,2]
010010011=>[2,3,3,1,1]
010010100=>[2,3,2,3]
010010101=>[2,3,2,2,1]
010010110=>[2,3,2,1,2]
010010111=>[2,3,2,1,1,1]
010011000=>[2,3,1,4]
010011001=>[2,3,1,3,1]
010011010=>[2,3,1,2,2]
010011011=>[2,3,1,2,1,1]
010011100=>[2,3,1,1,3]
010011101=>[2,3,1,1,2,1]
010011110=>[2,3,1,1,1,2]
010011111=>[2,3,1,1,1,1,1]
010100000=>[2,2,6]
010100001=>[2,2,5,1]
010100010=>[2,2,4,2]
010100011=>[2,2,4,1,1]
010100100=>[2,2,3,3]
010100101=>[2,2,3,2,1]
010100110=>[2,2,3,1,2]
010100111=>[2,2,3,1,1,1]
010101000=>[2,2,2,4]
010101001=>[2,2,2,3,1]
010101010=>[2,2,2,2,2]
010101011=>[2,2,2,2,1,1]
010101100=>[2,2,2,1,3]
010101101=>[2,2,2,1,2,1]
010101110=>[2,2,2,1,1,2]
010101111=>[2,2,2,1,1,1,1]
010110000=>[2,2,1,5]
010110001=>[2,2,1,4,1]
010110010=>[2,2,1,3,2]
010110011=>[2,2,1,3,1,1]
010110100=>[2,2,1,2,3]
010110101=>[2,2,1,2,2,1]
010110110=>[2,2,1,2,1,2]
010110111=>[2,2,1,2,1,1,1]
010111000=>[2,2,1,1,4]
010111001=>[2,2,1,1,3,1]
010111010=>[2,2,1,1,2,2]
010111011=>[2,2,1,1,2,1,1]
010111100=>[2,2,1,1,1,3]
010111101=>[2,2,1,1,1,2,1]
010111110=>[2,2,1,1,1,1,2]
010111111=>[2,2,1,1,1,1,1,1]
011000000=>[2,1,7]
011000001=>[2,1,6,1]
011000010=>[2,1,5,2]
011000011=>[2,1,5,1,1]
011000100=>[2,1,4,3]
011000101=>[2,1,4,2,1]
011000110=>[2,1,4,1,2]
011000111=>[2,1,4,1,1,1]
011001000=>[2,1,3,4]
011001001=>[2,1,3,3,1]
011001010=>[2,1,3,2,2]
011001011=>[2,1,3,2,1,1]
011001100=>[2,1,3,1,3]
011001101=>[2,1,3,1,2,1]
011001110=>[2,1,3,1,1,2]
011001111=>[2,1,3,1,1,1,1]
011010000=>[2,1,2,5]
011010001=>[2,1,2,4,1]
011010010=>[2,1,2,3,2]
011010011=>[2,1,2,3,1,1]
011010100=>[2,1,2,2,3]
011010101=>[2,1,2,2,2,1]
011010110=>[2,1,2,2,1,2]
011010111=>[2,1,2,2,1,1,1]
011011000=>[2,1,2,1,4]
011011001=>[2,1,2,1,3,1]
011011010=>[2,1,2,1,2,2]
011011011=>[2,1,2,1,2,1,1]
011011100=>[2,1,2,1,1,3]
011011101=>[2,1,2,1,1,2,1]
011011110=>[2,1,2,1,1,1,2]
011011111=>[2,1,2,1,1,1,1,1]
011100000=>[2,1,1,6]
011100001=>[2,1,1,5,1]
011100010=>[2,1,1,4,2]
011100011=>[2,1,1,4,1,1]
011100100=>[2,1,1,3,3]
011100101=>[2,1,1,3,2,1]
011100110=>[2,1,1,3,1,2]
011100111=>[2,1,1,3,1,1,1]
011101000=>[2,1,1,2,4]
011101001=>[2,1,1,2,3,1]
011101010=>[2,1,1,2,2,2]
011101011=>[2,1,1,2,2,1,1]
011101100=>[2,1,1,2,1,3]
011101101=>[2,1,1,2,1,2,1]
011101110=>[2,1,1,2,1,1,2]
011101111=>[2,1,1,2,1,1,1,1]
011110000=>[2,1,1,1,5]
011110001=>[2,1,1,1,4,1]
011110010=>[2,1,1,1,3,2]
011110011=>[2,1,1,1,3,1,1]
011110100=>[2,1,1,1,2,3]
011110101=>[2,1,1,1,2,2,1]
011110110=>[2,1,1,1,2,1,2]
011110111=>[2,1,1,1,2,1,1,1]
011111000=>[2,1,1,1,1,4]
011111001=>[2,1,1,1,1,3,1]
011111010=>[2,1,1,1,1,2,2]
011111011=>[2,1,1,1,1,2,1,1]
011111100=>[2,1,1,1,1,1,3]
011111101=>[2,1,1,1,1,1,2,1]
011111110=>[2,1,1,1,1,1,1,2]
011111111=>[2,1,1,1,1,1,1,1,1]
100000000=>[1,9]
100000001=>[1,8,1]
100000010=>[1,7,2]
100000011=>[1,7,1,1]
100000100=>[1,6,3]
100000101=>[1,6,2,1]
100000110=>[1,6,1,2]
100000111=>[1,6,1,1,1]
100001000=>[1,5,4]
100001001=>[1,5,3,1]
100001010=>[1,5,2,2]
100001011=>[1,5,2,1,1]
100001100=>[1,5,1,3]
100001101=>[1,5,1,2,1]
100001110=>[1,5,1,1,2]
100001111=>[1,5,1,1,1,1]
100010000=>[1,4,5]
100010001=>[1,4,4,1]
100010010=>[1,4,3,2]
100010011=>[1,4,3,1,1]
100010100=>[1,4,2,3]
100010101=>[1,4,2,2,1]
100010110=>[1,4,2,1,2]
100010111=>[1,4,2,1,1,1]
100011000=>[1,4,1,4]
100011001=>[1,4,1,3,1]
100011010=>[1,4,1,2,2]
100011011=>[1,4,1,2,1,1]
100011100=>[1,4,1,1,3]
100011101=>[1,4,1,1,2,1]
100011110=>[1,4,1,1,1,2]
100011111=>[1,4,1,1,1,1,1]
100100000=>[1,3,6]
100100001=>[1,3,5,1]
100100010=>[1,3,4,2]
100100011=>[1,3,4,1,1]
100100100=>[1,3,3,3]
100100101=>[1,3,3,2,1]
100100110=>[1,3,3,1,2]
100100111=>[1,3,3,1,1,1]
100101000=>[1,3,2,4]
100101001=>[1,3,2,3,1]
100101010=>[1,3,2,2,2]
100101011=>[1,3,2,2,1,1]
100101100=>[1,3,2,1,3]
100101101=>[1,3,2,1,2,1]
100101110=>[1,3,2,1,1,2]
100101111=>[1,3,2,1,1,1,1]
100110000=>[1,3,1,5]
100110001=>[1,3,1,4,1]
100110010=>[1,3,1,3,2]
100110011=>[1,3,1,3,1,1]
100110100=>[1,3,1,2,3]
100110101=>[1,3,1,2,2,1]
100110110=>[1,3,1,2,1,2]
100110111=>[1,3,1,2,1,1,1]
100111000=>[1,3,1,1,4]
100111001=>[1,3,1,1,3,1]
100111010=>[1,3,1,1,2,2]
100111011=>[1,3,1,1,2,1,1]
100111100=>[1,3,1,1,1,3]
100111101=>[1,3,1,1,1,2,1]
100111110=>[1,3,1,1,1,1,2]
100111111=>[1,3,1,1,1,1,1,1]
101000000=>[1,2,7]
101000001=>[1,2,6,1]
101000010=>[1,2,5,2]
101000011=>[1,2,5,1,1]
101000100=>[1,2,4,3]
101000101=>[1,2,4,2,1]
101000110=>[1,2,4,1,2]
101000111=>[1,2,4,1,1,1]
101001000=>[1,2,3,4]
101001001=>[1,2,3,3,1]
101001010=>[1,2,3,2,2]
101001011=>[1,2,3,2,1,1]
101001100=>[1,2,3,1,3]
101001101=>[1,2,3,1,2,1]
101001110=>[1,2,3,1,1,2]
101001111=>[1,2,3,1,1,1,1]
101010000=>[1,2,2,5]
101010001=>[1,2,2,4,1]
101010010=>[1,2,2,3,2]
101010011=>[1,2,2,3,1,1]
101010100=>[1,2,2,2,3]
101010101=>[1,2,2,2,2,1]
101010110=>[1,2,2,2,1,2]
101010111=>[1,2,2,2,1,1,1]
101011000=>[1,2,2,1,4]
101011001=>[1,2,2,1,3,1]
101011010=>[1,2,2,1,2,2]
101011011=>[1,2,2,1,2,1,1]
101011100=>[1,2,2,1,1,3]
101011101=>[1,2,2,1,1,2,1]
101011110=>[1,2,2,1,1,1,2]
101011111=>[1,2,2,1,1,1,1,1]
101100000=>[1,2,1,6]
101100001=>[1,2,1,5,1]
101100010=>[1,2,1,4,2]
101100011=>[1,2,1,4,1,1]
101100100=>[1,2,1,3,3]
101100101=>[1,2,1,3,2,1]
101100110=>[1,2,1,3,1,2]
101100111=>[1,2,1,3,1,1,1]
101101000=>[1,2,1,2,4]
101101001=>[1,2,1,2,3,1]
101101010=>[1,2,1,2,2,2]
101101011=>[1,2,1,2,2,1,1]
101101100=>[1,2,1,2,1,3]
101101101=>[1,2,1,2,1,2,1]
101101110=>[1,2,1,2,1,1,2]
101101111=>[1,2,1,2,1,1,1,1]
101110000=>[1,2,1,1,5]
101110001=>[1,2,1,1,4,1]
101110010=>[1,2,1,1,3,2]
101110011=>[1,2,1,1,3,1,1]
101110100=>[1,2,1,1,2,3]
101110101=>[1,2,1,1,2,2,1]
101110110=>[1,2,1,1,2,1,2]
101110111=>[1,2,1,1,2,1,1,1]
101111000=>[1,2,1,1,1,4]
101111001=>[1,2,1,1,1,3,1]
101111010=>[1,2,1,1,1,2,2]
101111011=>[1,2,1,1,1,2,1,1]
101111100=>[1,2,1,1,1,1,3]
101111101=>[1,2,1,1,1,1,2,1]
101111110=>[1,2,1,1,1,1,1,2]
101111111=>[1,2,1,1,1,1,1,1,1]
110000000=>[1,1,8]
110000001=>[1,1,7,1]
110000010=>[1,1,6,2]
110000011=>[1,1,6,1,1]
110000100=>[1,1,5,3]
110000101=>[1,1,5,2,1]
110000110=>[1,1,5,1,2]
110000111=>[1,1,5,1,1,1]
110001000=>[1,1,4,4]
110001001=>[1,1,4,3,1]
110001010=>[1,1,4,2,2]
110001011=>[1,1,4,2,1,1]
110001100=>[1,1,4,1,3]
110001101=>[1,1,4,1,2,1]
110001110=>[1,1,4,1,1,2]
110001111=>[1,1,4,1,1,1,1]
110010000=>[1,1,3,5]
110010001=>[1,1,3,4,1]
110010010=>[1,1,3,3,2]
110010011=>[1,1,3,3,1,1]
110010100=>[1,1,3,2,3]
110010101=>[1,1,3,2,2,1]
110010110=>[1,1,3,2,1,2]
110010111=>[1,1,3,2,1,1,1]
110011000=>[1,1,3,1,4]
110011001=>[1,1,3,1,3,1]
110011010=>[1,1,3,1,2,2]
110011011=>[1,1,3,1,2,1,1]
110011100=>[1,1,3,1,1,3]
110011101=>[1,1,3,1,1,2,1]
110011110=>[1,1,3,1,1,1,2]
110011111=>[1,1,3,1,1,1,1,1]
110100000=>[1,1,2,6]
110100001=>[1,1,2,5,1]
110100010=>[1,1,2,4,2]
110100011=>[1,1,2,4,1,1]
110100100=>[1,1,2,3,3]
110100101=>[1,1,2,3,2,1]
110100110=>[1,1,2,3,1,2]
110100111=>[1,1,2,3,1,1,1]
110101000=>[1,1,2,2,4]
110101001=>[1,1,2,2,3,1]
110101010=>[1,1,2,2,2,2]
110101011=>[1,1,2,2,2,1,1]
110101100=>[1,1,2,2,1,3]
110101101=>[1,1,2,2,1,2,1]
110101110=>[1,1,2,2,1,1,2]
110101111=>[1,1,2,2,1,1,1,1]
110110000=>[1,1,2,1,5]
110110001=>[1,1,2,1,4,1]
110110010=>[1,1,2,1,3,2]
110110011=>[1,1,2,1,3,1,1]
110110100=>[1,1,2,1,2,3]
110110101=>[1,1,2,1,2,2,1]
110110110=>[1,1,2,1,2,1,2]
110110111=>[1,1,2,1,2,1,1,1]
110111000=>[1,1,2,1,1,4]
110111001=>[1,1,2,1,1,3,1]
110111010=>[1,1,2,1,1,2,2]
110111011=>[1,1,2,1,1,2,1,1]
110111100=>[1,1,2,1,1,1,3]
110111101=>[1,1,2,1,1,1,2,1]
110111110=>[1,1,2,1,1,1,1,2]
110111111=>[1,1,2,1,1,1,1,1,1]
111000000=>[1,1,1,7]
111000001=>[1,1,1,6,1]
111000010=>[1,1,1,5,2]
111000011=>[1,1,1,5,1,1]
111000100=>[1,1,1,4,3]
111000101=>[1,1,1,4,2,1]
111000110=>[1,1,1,4,1,2]
111000111=>[1,1,1,4,1,1,1]
111001000=>[1,1,1,3,4]
111001001=>[1,1,1,3,3,1]
111001010=>[1,1,1,3,2,2]
111001011=>[1,1,1,3,2,1,1]
111001100=>[1,1,1,3,1,3]
111001101=>[1,1,1,3,1,2,1]
111001110=>[1,1,1,3,1,1,2]
111001111=>[1,1,1,3,1,1,1,1]
111010000=>[1,1,1,2,5]
111010001=>[1,1,1,2,4,1]
111010010=>[1,1,1,2,3,2]
111010011=>[1,1,1,2,3,1,1]
111010100=>[1,1,1,2,2,3]
111010101=>[1,1,1,2,2,2,1]
111010110=>[1,1,1,2,2,1,2]
111010111=>[1,1,1,2,2,1,1,1]
111011000=>[1,1,1,2,1,4]
111011001=>[1,1,1,2,1,3,1]
111011010=>[1,1,1,2,1,2,2]
111011011=>[1,1,1,2,1,2,1,1]
111011100=>[1,1,1,2,1,1,3]
111011101=>[1,1,1,2,1,1,2,1]
111011110=>[1,1,1,2,1,1,1,2]
111011111=>[1,1,1,2,1,1,1,1,1]
111100000=>[1,1,1,1,6]
111100001=>[1,1,1,1,5,1]
111100010=>[1,1,1,1,4,2]
111100011=>[1,1,1,1,4,1,1]
111100100=>[1,1,1,1,3,3]
111100101=>[1,1,1,1,3,2,1]
111100110=>[1,1,1,1,3,1,2]
111100111=>[1,1,1,1,3,1,1,1]
111101000=>[1,1,1,1,2,4]
111101001=>[1,1,1,1,2,3,1]
111101010=>[1,1,1,1,2,2,2]
111101011=>[1,1,1,1,2,2,1,1]
111101100=>[1,1,1,1,2,1,3]
111101101=>[1,1,1,1,2,1,2,1]
111101110=>[1,1,1,1,2,1,1,2]
111101111=>[1,1,1,1,2,1,1,1,1]
111110000=>[1,1,1,1,1,5]
111110001=>[1,1,1,1,1,4,1]
111110010=>[1,1,1,1,1,3,2]
111110011=>[1,1,1,1,1,3,1,1]
111110100=>[1,1,1,1,1,2,3]
111110101=>[1,1,1,1,1,2,2,1]
111110110=>[1,1,1,1,1,2,1,2]
111110111=>[1,1,1,1,1,2,1,1,1]
111111000=>[1,1,1,1,1,1,4]
111111001=>[1,1,1,1,1,1,3,1]
111111010=>[1,1,1,1,1,1,2,2]
111111011=>[1,1,1,1,1,1,2,1,1]
111111100=>[1,1,1,1,1,1,1,3]
111111101=>[1,1,1,1,1,1,1,2,1]
111111110=>[1,1,1,1,1,1,1,1,2]
111111111=>[1,1,1,1,1,1,1,1,1,1]
1010101010=>[1,2,2,2,2,2]
1010101100=>[1,2,2,2,1,3]
1010110010=>[1,2,2,1,3,2]
1010110100=>[1,2,2,1,2,3]
1010111000=>[1,2,2,1,1,4]
1011001010=>[1,2,1,3,2,2]
1011001100=>[1,2,1,3,1,3]
1011010010=>[1,2,1,2,3,2]
1011010100=>[1,2,1,2,2,3]
1011011000=>[1,2,1,2,1,4]
1011100010=>[1,2,1,1,4,2]
1011100100=>[1,2,1,1,3,3]
1011101000=>[1,2,1,1,2,4]
1011110000=>[1,2,1,1,1,5]
1100101010=>[1,1,3,2,2,2]
1100101100=>[1,1,3,2,1,3]
1100110010=>[1,1,3,1,3,2]
1100110100=>[1,1,3,1,2,3]
1100111000=>[1,1,3,1,1,4]
1101001010=>[1,1,2,3,2,2]
1101001100=>[1,1,2,3,1,3]
1101010010=>[1,1,2,2,3,2]
1101010100=>[1,1,2,2,2,3]
1101011000=>[1,1,2,2,1,4]
1101100010=>[1,1,2,1,4,2]
1101100100=>[1,1,2,1,3,3]
1101101000=>[1,1,2,1,2,4]
1101110000=>[1,1,2,1,1,5]
1110001010=>[1,1,1,4,2,2]
1110001100=>[1,1,1,4,1,3]
1110010010=>[1,1,1,3,3,2]
1110010100=>[1,1,1,3,2,3]
1110011000=>[1,1,1,3,1,4]
1110100010=>[1,1,1,2,4,2]
1110100100=>[1,1,1,2,3,3]
1110101000=>[1,1,1,2,2,4]
1110110000=>[1,1,1,2,1,5]
1111000010=>[1,1,1,1,5,2]
1111000100=>[1,1,1,1,4,3]
1111001000=>[1,1,1,1,3,4]
1111010000=>[1,1,1,1,2,5]
1111100000=>[1,1,1,1,1,6]
1111111111=>[1,1,1,1,1,1,1,1,1,1,1]
1111111110=>[1,1,1,1,1,1,1,1,1,2]
1111111001=>[1,1,1,1,1,1,1,3,1]
1111110000=>[1,1,1,1,1,1,5]
1111101101=>[1,1,1,1,1,2,1,2,1]
1111101000=>[1,1,1,1,1,2,4]
1111100111=>[1,1,1,1,1,3,1,1,1]
1111100100=>[1,1,1,1,1,3,3]
1111100010=>[1,1,1,1,1,4,2]
1111100001=>[1,1,1,1,1,5,1]
1111011000=>[1,1,1,1,2,1,4]
1111010100=>[1,1,1,1,2,2,3]
1111010010=>[1,1,1,1,2,3,2]
1111010001=>[1,1,1,1,2,4,1]
1111001100=>[1,1,1,1,3,1,3]
1111001010=>[1,1,1,1,3,2,2]
1111001001=>[1,1,1,1,3,3,1]
1111000101=>[1,1,1,1,4,2,1]
1111000011=>[1,1,1,1,5,1,1]
1111000001=>[1,1,1,1,6,1]
1110111111=>[1,1,1,2,1,1,1,1,1,1]
1110111110=>[1,1,1,2,1,1,1,1,2]
1110111101=>[1,1,1,2,1,1,1,2,1]
1110111000=>[1,1,1,2,1,1,4]
1110110111=>[1,1,1,2,1,2,1,1,1]
1110110100=>[1,1,1,2,1,2,3]
1110110010=>[1,1,1,2,1,3,2]
1110110001=>[1,1,1,2,1,4,1]
1110101100=>[1,1,1,2,2,1,3]
1110101010=>[1,1,1,2,2,2,2]
1110101001=>[1,1,1,2,2,3,1]
1110100101=>[1,1,1,2,3,2,1]
1110100011=>[1,1,1,2,4,1,1]
1110100001=>[1,1,1,2,5,1]
1110011111=>[1,1,1,3,1,1,1,1,1]
1110011001=>[1,1,1,3,1,3,1]
1110010101=>[1,1,1,3,2,2,1]
1110010011=>[1,1,1,3,3,1,1]
1110010001=>[1,1,1,3,4,1]
1110001101=>[1,1,1,4,1,2,1]
1110000111=>[1,1,1,5,1,1,1]
1110000011=>[1,1,1,6,1,1]
1110000001=>[1,1,1,7,1]
1101111111=>[1,1,2,1,1,1,1,1,1,1]
1101111110=>[1,1,2,1,1,1,1,1,2]
1101110001=>[1,1,2,1,1,4,1]
1101101001=>[1,1,2,1,2,3,1]
1101100101=>[1,1,2,1,3,2,1]
1101100011=>[1,1,2,1,4,1,1]
1101100001=>[1,1,2,1,5,1]
1101011111=>[1,1,2,2,1,1,1,1,1]
1101011001=>[1,1,2,2,1,3,1]
1101010101=>[1,1,2,2,2,2,1]
1101010011=>[1,1,2,2,3,1,1]
1101010001=>[1,1,2,2,4,1]
1101001111=>[1,1,2,3,1,1,1,1]
1101001101=>[1,1,2,3,1,2,1]
1101000111=>[1,1,2,4,1,1,1]
1101000011=>[1,1,2,5,1,1]
1100111111=>[1,1,3,1,1,1,1,1,1]
1100111001=>[1,1,3,1,1,3,1]
1100110101=>[1,1,3,1,2,2,1]
1100110011=>[1,1,3,1,3,1,1]
1100110001=>[1,1,3,1,4,1]
1100101110=>[1,1,3,2,1,1,2]
1100011110=>[1,1,4,1,1,1,2]
1100011101=>[1,1,4,1,1,2,1]
1100011100=>[1,1,4,1,1,3]
1100001111=>[1,1,5,1,1,1,1]
1100001010=>[1,1,5,2,2]
1100000111=>[1,1,6,1,1,1]
1100000110=>[1,1,6,1,2]
1100000000=>[1,1,9]
1011111110=>[1,2,1,1,1,1,1,1,2]
1011111101=>[1,2,1,1,1,1,1,2,1]
1011110111=>[1,2,1,1,1,2,1,1,1]
1011110001=>[1,2,1,1,1,4,1]
1011100101=>[1,2,1,1,3,2,1]
1011100000=>[1,2,1,1,6]
1011011111=>[1,2,1,2,1,1,1,1,1]
1011011001=>[1,2,1,2,1,3,1]
1011010101=>[1,2,1,2,2,2,1]
1011010000=>[1,2,1,2,5]
1011001101=>[1,2,1,3,1,2,1]
1011001000=>[1,2,1,3,4]
1011000111=>[1,2,1,4,1,1,1]
1011000100=>[1,2,1,4,3]
1011000010=>[1,2,1,5,2]
1011000001=>[1,2,1,6,1]
1010111110=>[1,2,2,1,1,1,1,2]
1010110101=>[1,2,2,1,2,2,1]
1010110000=>[1,2,2,1,5]
1010101000=>[1,2,2,2,4]
1010100100=>[1,2,2,3,3]
1010100010=>[1,2,2,4,2]
1010011101=>[1,2,3,1,1,2,1]
1010011000=>[1,2,3,1,4]
1010010111=>[1,2,3,2,1,1,1]
1010010100=>[1,2,3,2,3]
1010010010=>[1,2,3,3,2]
1010010001=>[1,2,3,4,1]
1010001100=>[1,2,4,1,3]
1010001010=>[1,2,4,2,2]
1010000101=>[1,2,5,2,1]
1001111111=>[1,3,1,1,1,1,1,1,1]
1001111110=>[1,3,1,1,1,1,1,2]
1001111001=>[1,3,1,1,1,3,1]
1001110000=>[1,3,1,1,5]
1001101101=>[1,3,1,2,1,2,1]
1001101000=>[1,3,1,2,4]
1001100111=>[1,3,1,3,1,1,1]
1001100100=>[1,3,1,3,3]
1001100010=>[1,3,1,4,2]
1001100001=>[1,3,1,5,1]
1001011110=>[1,3,2,1,1,1,2]
1001011000=>[1,3,2,1,4]
1001010101=>[1,3,2,2,2,1]
1001010100=>[1,3,2,2,3]
1001010010=>[1,3,2,3,2]
1001001100=>[1,3,3,1,3]
1001001010=>[1,3,3,2,2]
1000111110=>[1,4,1,1,1,1,2]
1000111101=>[1,4,1,1,1,2,1]
1000111000=>[1,4,1,1,4]
1000110111=>[1,4,1,2,1,1,1]
1000110101=>[1,4,1,2,2,1]
1000110100=>[1,4,1,2,3]
1000110010=>[1,4,1,3,2]
1000110001=>[1,4,1,4,1]
1000101110=>[1,4,2,1,1,2]
1000101100=>[1,4,2,1,3]
1000101010=>[1,4,2,2,2]
1000100101=>[1,4,3,2,1]
1000011111=>[1,5,1,1,1,1,1]
1000011110=>[1,5,1,1,1,2]
1000011001=>[1,5,1,3,1]
1000010110=>[1,5,2,1,2]
1000010101=>[1,5,2,2,1]
1000001110=>[1,6,1,1,2]
1000001101=>[1,6,1,2,1]
1000001010=>[1,6,2,2]
1000000111=>[1,7,1,1,1]
1000000110=>[1,7,1,2]
1000000101=>[1,7,2,1]
1000000100=>[1,7,3]
1000000011=>[1,8,1,1]
1000000010=>[1,8,2]
1000000001=>[1,9,1]
1000000000=>[1,10]
0111111111=>[2,1,1,1,1,1,1,1,1,1]
0111111101=>[2,1,1,1,1,1,1,2,1]
0111111001=>[2,1,1,1,1,1,3,1]
0111110001=>[2,1,1,1,1,4,1]
0111100001=>[2,1,1,1,5,1]
0111000001=>[2,1,1,6,1]
0110000001=>[2,1,7,1]
0100000001=>[2,8,1]
0000000001=>[10,1]
0111111011=>[2,1,1,1,1,1,2,1,1]
0111110101=>[2,1,1,1,1,2,2,1]
0111101001=>[2,1,1,1,2,3,1]
0111010001=>[2,1,1,2,4,1]
0110100001=>[2,1,2,5,1]
0101000001=>[2,2,6,1]
0010000001=>[3,7,1]
0101010101=>[2,2,2,2,2,1]
0101010011=>[2,2,2,3,1,1]
0101001101=>[2,2,3,1,2,1]
0101001011=>[2,2,3,2,1,1]
0101000111=>[2,2,4,1,1,1]
0100110101=>[2,3,1,2,2,1]
0100110011=>[2,3,1,3,1,1]
0100101101=>[2,3,2,1,2,1]
0100101011=>[2,3,2,2,1,1]
0100100111=>[2,3,3,1,1,1]
0100011101=>[2,4,1,1,2,1]
0100011011=>[2,4,1,2,1,1]
0100010111=>[2,4,2,1,1,1]
0100001111=>[2,5,1,1,1,1]
0011010101=>[3,1,2,2,2,1]
0011010011=>[3,1,2,3,1,1]
0011001101=>[3,1,3,1,2,1]
0011001011=>[3,1,3,2,1,1]
0011000111=>[3,1,4,1,1,1]
0010110101=>[3,2,1,2,2,1]
0010110011=>[3,2,1,3,1,1]
0010101101=>[3,2,2,1,2,1]
0010101011=>[3,2,2,2,1,1]
0010100111=>[3,2,3,1,1,1]
0010011101=>[3,3,1,1,2,1]
0010011011=>[3,3,1,2,1,1]
0010010111=>[3,3,2,1,1,1]
0010001111=>[3,4,1,1,1,1]
0001110101=>[4,1,1,2,2,1]
0001110011=>[4,1,1,3,1,1]
0001101101=>[4,1,2,1,2,1]
0001101011=>[4,1,2,2,1,1]
0001100111=>[4,1,3,1,1,1]
0001011101=>[4,2,1,1,2,1]
0001011011=>[4,2,1,2,1,1]
0001010111=>[4,2,2,1,1,1]
0001001111=>[4,3,1,1,1,1]
0000111101=>[5,1,1,1,2,1]
0000111011=>[5,1,1,2,1,1]
0000110111=>[5,1,2,1,1,1]
0000101111=>[5,2,1,1,1,1]
0000011111=>[6,1,1,1,1,1]
0000000000=>[11]
0000011000=>[6,1,4]
0000011110=>[6,1,1,1,2]
0001111110=>[4,1,1,1,1,1,2]
0111111110=>[2,1,1,1,1,1,1,1,2]
0100111110=>[2,3,1,1,1,1,2]
0101010100=>[2,2,2,2,3]
0011110100=>[3,1,1,1,2,3]
0000010100=>[6,2,3]
0111010100=>[2,1,1,2,2,3]
0000000010=>[9,2]
0000001110=>[7,1,1,2]
0000111110=>[5,1,1,1,1,2]
0011111110=>[3,1,1,1,1,1,1,2]
0000000100=>[8,3]
0000010110=>[6,2,1,2]
0001011110=>[4,2,1,1,1,2]
0010111110=>[3,2,1,1,1,1,2]
0101111110=>[2,2,1,1,1,1,1,2]
0011100010=>[3,1,1,4,2]
0011110000=>[3,1,1,1,5]
0100101100=>[2,3,2,1,3]
0110001100=>[2,1,4,1,3]
0110100100=>[2,1,2,3,3]
0110110000=>[2,1,2,1,5]
0100001011=>[2,5,2,1,1]
0100101111=>[2,3,2,1,1,1,1]
0101011111=>[2,2,2,1,1,1,1,1]
0110111111=>[2,1,2,1,1,1,1,1,1]
0101110001=>[2,2,1,1,4,1]
0110010101=>[2,1,3,2,2,1]
0110011001=>[2,1,3,1,3,1]
0110110001=>[2,1,2,1,4,1]
0111001100=>[2,1,1,3,1,3]
0111011000=>[2,1,1,2,1,4]
0111100100=>[2,1,1,1,3,3]
0111101000=>[2,1,1,1,2,4]
0111110000=>[2,1,1,1,1,5]
0100000100=>[2,6,3]
0011111000=>[3,1,1,1,1,4]
0001111100=>[4,1,1,1,1,3]
0000000101=>[8,2,1]
0000001101=>[7,1,2,1]
0001111101=>[4,1,1,1,1,2,1]
0001000001=>[4,6,1]
0001101100=>[4,1,2,1,3]
0011000110=>[3,1,4,1,2]
0010001110=>[3,4,1,1,2]
0110111001=>[2,1,2,1,1,3,1]
0001101001=>[4,1,2,3,1]
0000010001=>[6,4,1]
0100100011=>[2,3,4,1,1]
0110010011=>[2,1,3,3,1,1]
0111000011=>[2,1,1,5,1,1]
0101000000=>[2,2,7]
0000000011=>[9,1,1]
0000111111=>[5,1,1,1,1,1,1]
0011111111=>[3,1,1,1,1,1,1,1,1]
0011110001=>[3,1,1,1,4,1]
0011111100=>[3,1,1,1,1,1,3]
0011111001=>[3,1,1,1,1,3,1]
0011110011=>[3,1,1,1,3,1,1]
0011001111=>[3,1,3,1,1,1,1]
0000001100=>[7,1,3]
0000110011=>[5,1,3,1,1]
0110100111=>[2,1,2,3,1,1,1]
0111100011=>[2,1,1,1,4,1,1]
0111101111=>[2,1,1,1,2,1,1,1,1]
0001101111=>[4,1,2,1,1,1,1]
0110110011=>[2,1,2,1,3,1,1]
0100101001=>[2,3,2,3,1]
0100111011=>[2,3,1,1,2,1,1]
0100010101=>[2,4,2,2,1]
0001010101=>[4,2,2,2,1]
0000110101=>[5,1,2,2,1]
0011010111=>[3,1,2,2,1,1,1]
0111010101=>[2,1,1,2,2,2,1]
0001110111=>[4,1,1,2,1,1,1]
0011110101=>[3,1,1,1,2,2,1]
0000011011=>[6,1,2,1,1]
0001100011=>[4,1,4,1,1]
0001001011=>[4,3,2,1,1]
0110000011=>[2,1,6,1,1]
0110011011=>[2,1,3,1,2,1,1]
0000011001=>[6,1,3,1]
0011011111=>[3,1,2,1,1,1,1,1]
0110011111=>[2,1,3,1,1,1,1,1]
0110110111=>[2,1,2,1,2,1,1,1]
0100100001=>[2,3,5,1]
0110010001=>[2,1,3,4,1]
0111100101=>[2,1,1,1,3,2,1]
0110101011=>[2,1,2,2,2,1,1]
0100111001=>[2,3,1,1,3,1]
0101100011=>[2,2,1,4,1,1]
0111011001=>[2,1,1,2,1,3,1]
0101100001=>[2,2,1,5,1]
0100011001=>[2,4,1,3,1]
0101111001=>[2,2,1,1,1,3,1]
0100010001=>[2,4,4,1]
0100110001=>[2,3,1,4,1]
0110111011=>[2,1,2,1,1,2,1,1]
0101111011=>[2,2,1,1,1,2,1,1]
0100010011=>[2,4,3,1,1]
0101110011=>[2,2,1,1,3,1,1]
0110100011=>[2,1,2,4,1,1]
0101000011=>[2,2,5,1,1]
0110010111=>[2,1,3,2,1,1,1]
0100110111=>[2,3,1,2,1,1,1]
0101110111=>[2,2,1,1,2,1,1,1]
0101100111=>[2,2,1,3,1,1,1]
0110101111=>[2,1,2,2,1,1,1,1]
0101101111=>[2,2,1,2,1,1,1,1]
0101001111=>[2,2,3,1,1,1,1]
0001010000=>[4,2,5]
0100010000=>[2,4,5]
0001000100=>[4,4,3]
0111011100=>[2,1,1,2,1,1,3]
0101000101=>[2,2,4,2,1]
0110110101=>[2,1,2,1,2,2,1]
0101010001=>[2,2,2,4,1]
0110001001=>[2,1,4,3,1]
0101011011=>[2,2,2,1,2,1,1]
0111010011=>[2,1,1,2,3,1,1]
0111000111=>[2,1,1,4,1,1,1]
0011011110=>[3,1,2,1,1,1,2]
0011101110=>[3,1,1,2,1,1,2]
0011110110=>[3,1,1,1,2,1,2]
0011111010=>[3,1,1,1,1,2,2]
0000110100=>[5,1,2,3]
0111001101=>[2,1,1,3,1,2,1]
10000000000=>[1,11]
10000000010=>[1,9,2]
10000000110=>[1,8,1,2]
10000001110=>[1,7,1,1,2]
10000011110=>[1,6,1,1,1,2]
10000111110=>[1,5,1,1,1,1,2]
10001111110=>[1,4,1,1,1,1,1,2]
10011111110=>[1,3,1,1,1,1,1,1,2]
10111111110=>[1,2,1,1,1,1,1,1,1,2]
11111111110=>[1,1,1,1,1,1,1,1,1,1,2]
11001111110=>[1,1,3,1,1,1,1,1,2]
11000011110=>[1,1,5,1,1,1,2]
11000000110=>[1,1,7,1,2]
01111111111=>[2,1,1,1,1,1,1,1,1,1,1]
01111111101=>[2,1,1,1,1,1,1,1,2,1]
01111111001=>[2,1,1,1,1,1,1,3,1]
01111110001=>[2,1,1,1,1,1,4,1]
01111100001=>[2,1,1,1,1,5,1]
01111000001=>[2,1,1,1,6,1]
01110000001=>[2,1,1,7,1]
01100000001=>[2,1,8,1]
01000000001=>[2,9,1]
00000000001=>[11,1]
00000000010=>[10,2]
00000001110=>[8,1,1,2]
00000111110=>[6,1,1,1,1,2]
00011111110=>[4,1,1,1,1,1,1,2]
01111111110=>[2,1,1,1,1,1,1,1,1,2]
10101010101=>[1,2,2,2,2,2,1]
00000001101=>[8,1,2,1]
01111110101=>[2,1,1,1,1,1,2,2,1]
10000000001=>[1,10,1]
11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1]
01101010101=>[2,1,2,2,2,2,1]
00000000011=>[10,1,1]
00111111111=>[3,1,1,1,1,1,1,1,1,1]
10000000101=>[1,8,2,1]
11011111111=>[1,1,2,1,1,1,1,1,1,1,1]
10001010101=>[1,4,2,2,2,1]
01111010101=>[2,1,1,1,2,2,2,1]
10000010101=>[1,6,2,2,1]
00101111110=>[3,2,1,1,1,1,1,2]
00110111110=>[3,1,2,1,1,1,1,2]
00111011110=>[3,1,1,2,1,1,1,2]
00111101110=>[3,1,1,1,2,1,1,2]
00111110110=>[3,1,1,1,1,2,1,2]
00111111010=>[3,1,1,1,1,1,2,2]
00111111100=>[3,1,1,1,1,1,1,3]
11000000000=>[1,1,10]
00011011111=>[4,1,2,1,1,1,1,1]
00000001100=>[8,1,3]
00000110011=>[6,1,3,1,1]
00110111111=>[3,1,2,1,1,1,1,1,1]
01100111111=>[2,1,3,1,1,1,1,1,1]
11001111111=>[1,1,3,1,1,1,1,1,1,1]
00000011001=>[7,1,3,1]
00001100111=>[5,1,3,1,1,1]
00011001111=>[4,1,3,1,1,1,1]
00110011111=>[3,1,3,1,1,1,1,1]
00000011011=>[7,1,2,1,1]
00000110111=>[6,1,2,1,1,1]
00001101111=>[5,1,2,1,1,1,1]
01101111111=>[2,1,2,1,1,1,1,1,1,1]
101010101010=>[1,2,2,2,2,2,2]
101010101100=>[1,2,2,2,2,1,3]
101010110010=>[1,2,2,2,1,3,2]
101010110100=>[1,2,2,2,1,2,3]
101010111000=>[1,2,2,2,1,1,4]
101011001010=>[1,2,2,1,3,2,2]
101011001100=>[1,2,2,1,3,1,3]
101011010010=>[1,2,2,1,2,3,2]
101011010100=>[1,2,2,1,2,2,3]
101011011000=>[1,2,2,1,2,1,4]
101011100010=>[1,2,2,1,1,4,2]
101011100100=>[1,2,2,1,1,3,3]
101011101000=>[1,2,2,1,1,2,4]
101011110000=>[1,2,2,1,1,1,5]
101100101010=>[1,2,1,3,2,2,2]
101100101100=>[1,2,1,3,2,1,3]
101100110010=>[1,2,1,3,1,3,2]
101100110100=>[1,2,1,3,1,2,3]
101100111000=>[1,2,1,3,1,1,4]
101101001010=>[1,2,1,2,3,2,2]
101101001100=>[1,2,1,2,3,1,3]
101101010010=>[1,2,1,2,2,3,2]
101101010100=>[1,2,1,2,2,2,3]
101101011000=>[1,2,1,2,2,1,4]
101101100010=>[1,2,1,2,1,4,2]
101101100100=>[1,2,1,2,1,3,3]
101101101000=>[1,2,1,2,1,2,4]
101101110000=>[1,2,1,2,1,1,5]
101110001010=>[1,2,1,1,4,2,2]
101110001100=>[1,2,1,1,4,1,3]
101110010010=>[1,2,1,1,3,3,2]
101110010100=>[1,2,1,1,3,2,3]
101110011000=>[1,2,1,1,3,1,4]
101110100010=>[1,2,1,1,2,4,2]
101110100100=>[1,2,1,1,2,3,3]
101110101000=>[1,2,1,1,2,2,4]
101110110000=>[1,2,1,1,2,1,5]
101111000010=>[1,2,1,1,1,5,2]
101111000100=>[1,2,1,1,1,4,3]
101111001000=>[1,2,1,1,1,3,4]
101111010000=>[1,2,1,1,1,2,5]
101111100000=>[1,2,1,1,1,1,6]
110010101010=>[1,1,3,2,2,2,2]
110010101100=>[1,1,3,2,2,1,3]
110010110010=>[1,1,3,2,1,3,2]
110010110100=>[1,1,3,2,1,2,3]
110010111000=>[1,1,3,2,1,1,4]
110011001010=>[1,1,3,1,3,2,2]
110011001100=>[1,1,3,1,3,1,3]
110011010010=>[1,1,3,1,2,3,2]
110011010100=>[1,1,3,1,2,2,3]
110011011000=>[1,1,3,1,2,1,4]
110011100010=>[1,1,3,1,1,4,2]
110011100100=>[1,1,3,1,1,3,3]
110011101000=>[1,1,3,1,1,2,4]
110011110000=>[1,1,3,1,1,1,5]
110100101010=>[1,1,2,3,2,2,2]
110100101100=>[1,1,2,3,2,1,3]
110100110010=>[1,1,2,3,1,3,2]
110100110100=>[1,1,2,3,1,2,3]
110100111000=>[1,1,2,3,1,1,4]
110101001010=>[1,1,2,2,3,2,2]
110101001100=>[1,1,2,2,3,1,3]
110101010010=>[1,1,2,2,2,3,2]
110101010100=>[1,1,2,2,2,2,3]
110101011000=>[1,1,2,2,2,1,4]
110101100010=>[1,1,2,2,1,4,2]
110101100100=>[1,1,2,2,1,3,3]
110101101000=>[1,1,2,2,1,2,4]
110101110000=>[1,1,2,2,1,1,5]
110110001010=>[1,1,2,1,4,2,2]
110110001100=>[1,1,2,1,4,1,3]
110110010010=>[1,1,2,1,3,3,2]
110110010100=>[1,1,2,1,3,2,3]
110110011000=>[1,1,2,1,3,1,4]
110110100010=>[1,1,2,1,2,4,2]
110110100100=>[1,1,2,1,2,3,3]
110110101000=>[1,1,2,1,2,2,4]
110110110000=>[1,1,2,1,2,1,5]
110111000010=>[1,1,2,1,1,5,2]
110111000100=>[1,1,2,1,1,4,3]
110111001000=>[1,1,2,1,1,3,4]
110111010000=>[1,1,2,1,1,2,5]
110111100000=>[1,1,2,1,1,1,6]
111000101010=>[1,1,1,4,2,2,2]
111000101100=>[1,1,1,4,2,1,3]
111000110010=>[1,1,1,4,1,3,2]
111000110100=>[1,1,1,4,1,2,3]
111000111000=>[1,1,1,4,1,1,4]
111001001010=>[1,1,1,3,3,2,2]
111001001100=>[1,1,1,3,3,1,3]
111001010010=>[1,1,1,3,2,3,2]
111001010100=>[1,1,1,3,2,2,3]
111001011000=>[1,1,1,3,2,1,4]
111001100010=>[1,1,1,3,1,4,2]
111001100100=>[1,1,1,3,1,3,3]
111001101000=>[1,1,1,3,1,2,4]
111001110000=>[1,1,1,3,1,1,5]
111010001010=>[1,1,1,2,4,2,2]
111010001100=>[1,1,1,2,4,1,3]
111010010010=>[1,1,1,2,3,3,2]
111010010100=>[1,1,1,2,3,2,3]
111010011000=>[1,1,1,2,3,1,4]
111010100010=>[1,1,1,2,2,4,2]
111010100100=>[1,1,1,2,2,3,3]
111010101000=>[1,1,1,2,2,2,4]
111010110000=>[1,1,1,2,2,1,5]
111011000010=>[1,1,1,2,1,5,2]
111011000100=>[1,1,1,2,1,4,3]
111011001000=>[1,1,1,2,1,3,4]
111011010000=>[1,1,1,2,1,2,5]
111011100000=>[1,1,1,2,1,1,6]
111100001010=>[1,1,1,1,5,2,2]
111100001100=>[1,1,1,1,5,1,3]
111100010010=>[1,1,1,1,4,3,2]
111100010100=>[1,1,1,1,4,2,3]
111100011000=>[1,1,1,1,4,1,4]
111100100010=>[1,1,1,1,3,4,2]
111100100100=>[1,1,1,1,3,3,3]
111100101000=>[1,1,1,1,3,2,4]
111100110000=>[1,1,1,1,3,1,5]
111101000010=>[1,1,1,1,2,5,2]
111101000100=>[1,1,1,1,2,4,3]
111101001000=>[1,1,1,1,2,3,4]
111101010000=>[1,1,1,1,2,2,5]
111101100000=>[1,1,1,1,2,1,6]
111110000010=>[1,1,1,1,1,6,2]
111110000100=>[1,1,1,1,1,5,3]
111110001000=>[1,1,1,1,1,4,4]
111110010000=>[1,1,1,1,1,3,5]
111110100000=>[1,1,1,1,1,2,6]
111111000000=>[1,1,1,1,1,1,7]
010101010101=>[2,2,2,2,2,2,1]
010101010011=>[2,2,2,2,3,1,1]
010101001101=>[2,2,2,3,1,2,1]
010101001011=>[2,2,2,3,2,1,1]
010101000111=>[2,2,2,4,1,1,1]
010100110101=>[2,2,3,1,2,2,1]
010100110011=>[2,2,3,1,3,1,1]
010100101101=>[2,2,3,2,1,2,1]
010100101011=>[2,2,3,2,2,1,1]
010100100111=>[2,2,3,3,1,1,1]
010100011101=>[2,2,4,1,1,2,1]
010100011011=>[2,2,4,1,2,1,1]
010100010111=>[2,2,4,2,1,1,1]
010100001111=>[2,2,5,1,1,1,1]
010011010101=>[2,3,1,2,2,2,1]
010011010011=>[2,3,1,2,3,1,1]
010011001101=>[2,3,1,3,1,2,1]
010011001011=>[2,3,1,3,2,1,1]
010011000111=>[2,3,1,4,1,1,1]
010010110101=>[2,3,2,1,2,2,1]
010010110011=>[2,3,2,1,3,1,1]
010010101101=>[2,3,2,2,1,2,1]
010010101011=>[2,3,2,2,2,1,1]
010010100111=>[2,3,2,3,1,1,1]
010010011101=>[2,3,3,1,1,2,1]
010010011011=>[2,3,3,1,2,1,1]
010010010111=>[2,3,3,2,1,1,1]
010010001111=>[2,3,4,1,1,1,1]
010001110101=>[2,4,1,1,2,2,1]
010001110011=>[2,4,1,1,3,1,1]
010001101101=>[2,4,1,2,1,2,1]
010001101011=>[2,4,1,2,2,1,1]
010001100111=>[2,4,1,3,1,1,1]
010001011101=>[2,4,2,1,1,2,1]
010001011011=>[2,4,2,1,2,1,1]
010001010111=>[2,4,2,2,1,1,1]
010001001111=>[2,4,3,1,1,1,1]
010000111101=>[2,5,1,1,1,2,1]
010000111011=>[2,5,1,1,2,1,1]
010000110111=>[2,5,1,2,1,1,1]
010000101111=>[2,5,2,1,1,1,1]
010000011111=>[2,6,1,1,1,1,1]
001101010101=>[3,1,2,2,2,2,1]
001101010011=>[3,1,2,2,3,1,1]
001101001101=>[3,1,2,3,1,2,1]
001101001011=>[3,1,2,3,2,1,1]
001101000111=>[3,1,2,4,1,1,1]
001100110101=>[3,1,3,1,2,2,1]
001100110011=>[3,1,3,1,3,1,1]
001100101101=>[3,1,3,2,1,2,1]
001100101011=>[3,1,3,2,2,1,1]
001100100111=>[3,1,3,3,1,1,1]
001100011101=>[3,1,4,1,1,2,1]
001100011011=>[3,1,4,1,2,1,1]
001100010111=>[3,1,4,2,1,1,1]
001100001111=>[3,1,5,1,1,1,1]
001011010101=>[3,2,1,2,2,2,1]
001011010011=>[3,2,1,2,3,1,1]
001011001101=>[3,2,1,3,1,2,1]
001011001011=>[3,2,1,3,2,1,1]
001011000111=>[3,2,1,4,1,1,1]
001010110101=>[3,2,2,1,2,2,1]
001010110011=>[3,2,2,1,3,1,1]
001010101101=>[3,2,2,2,1,2,1]
001010101011=>[3,2,2,2,2,1,1]
001010100111=>[3,2,2,3,1,1,1]
001010011101=>[3,2,3,1,1,2,1]
001010011011=>[3,2,3,1,2,1,1]
001010010111=>[3,2,3,2,1,1,1]
001010001111=>[3,2,4,1,1,1,1]
001001110101=>[3,3,1,1,2,2,1]
001001110011=>[3,3,1,1,3,1,1]
001001101101=>[3,3,1,2,1,2,1]
001001101011=>[3,3,1,2,2,1,1]
001001100111=>[3,3,1,3,1,1,1]
001001011101=>[3,3,2,1,1,2,1]
001001011011=>[3,3,2,1,2,1,1]
001001010111=>[3,3,2,2,1,1,1]
001001001111=>[3,3,3,1,1,1,1]
001000111101=>[3,4,1,1,1,2,1]
001000111011=>[3,4,1,1,2,1,1]
001000110111=>[3,4,1,2,1,1,1]
001000101111=>[3,4,2,1,1,1,1]
001000011111=>[3,5,1,1,1,1,1]
000111010101=>[4,1,1,2,2,2,1]
000111010011=>[4,1,1,2,3,1,1]
000111001101=>[4,1,1,3,1,2,1]
000111001011=>[4,1,1,3,2,1,1]
000111000111=>[4,1,1,4,1,1,1]
000110110101=>[4,1,2,1,2,2,1]
000110110011=>[4,1,2,1,3,1,1]
000110101101=>[4,1,2,2,1,2,1]
000110101011=>[4,1,2,2,2,1,1]
000110100111=>[4,1,2,3,1,1,1]
000110011101=>[4,1,3,1,1,2,1]
000110011011=>[4,1,3,1,2,1,1]
000110010111=>[4,1,3,2,1,1,1]
000110001111=>[4,1,4,1,1,1,1]
000101110101=>[4,2,1,1,2,2,1]
000101110011=>[4,2,1,1,3,1,1]
000101101101=>[4,2,1,2,1,2,1]
000101101011=>[4,2,1,2,2,1,1]
000101100111=>[4,2,1,3,1,1,1]
000101011101=>[4,2,2,1,1,2,1]
000101011011=>[4,2,2,1,2,1,1]
000101010111=>[4,2,2,2,1,1,1]
000101001111=>[4,2,3,1,1,1,1]
000100111101=>[4,3,1,1,1,2,1]
000100111011=>[4,3,1,1,2,1,1]
000100110111=>[4,3,1,2,1,1,1]
000100101111=>[4,3,2,1,1,1,1]
000100011111=>[4,4,1,1,1,1,1]
000011110101=>[5,1,1,1,2,2,1]
000011110011=>[5,1,1,1,3,1,1]
000011101101=>[5,1,1,2,1,2,1]
000011101011=>[5,1,1,2,2,1,1]
000011100111=>[5,1,1,3,1,1,1]
000011011101=>[5,1,2,1,1,2,1]
000011011011=>[5,1,2,1,2,1,1]
000011010111=>[5,1,2,2,1,1,1]
000011001111=>[5,1,3,1,1,1,1]
000010111101=>[5,2,1,1,1,2,1]
000010111011=>[5,2,1,1,2,1,1]
000010110111=>[5,2,1,2,1,1,1]
000010101111=>[5,2,2,1,1,1,1]
000010011111=>[5,3,1,1,1,1,1]
000001111101=>[6,1,1,1,1,2,1]
000001111011=>[6,1,1,1,2,1,1]
000001110111=>[6,1,1,2,1,1,1]
000001101111=>[6,1,2,1,1,1,1]
000001011111=>[6,2,1,1,1,1,1]
000000111111=>[7,1,1,1,1,1,1]
111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1]
111111111001=>[1,1,1,1,1,1,1,1,1,3,1]
111111100111=>[1,1,1,1,1,1,1,3,1,1,1]
111111100001=>[1,1,1,1,1,1,1,5,1]
111111101101=>[1,1,1,1,1,1,1,2,1,2,1]
111110011111=>[1,1,1,1,1,3,1,1,1,1,1]
111110011001=>[1,1,1,1,1,3,1,3,1]
111110000111=>[1,1,1,1,1,5,1,1,1]
111110000001=>[1,1,1,1,1,7,1]
111110001101=>[1,1,1,1,1,4,1,2,1]
111110110111=>[1,1,1,1,1,2,1,2,1,1,1]
111110110001=>[1,1,1,1,1,2,1,4,1]
111110111101=>[1,1,1,1,1,2,1,1,1,2,1]
111110100101=>[1,1,1,1,1,2,3,2,1]
111001111111=>[1,1,1,3,1,1,1,1,1,1,1]
111001111001=>[1,1,1,3,1,1,1,3,1]
111001100111=>[1,1,1,3,1,3,1,1,1]
111001100001=>[1,1,1,3,1,5,1]
111001101101=>[1,1,1,3,1,2,1,2,1]
111000011111=>[1,1,1,5,1,1,1,1,1]
111000011001=>[1,1,1,5,1,3,1]
111000000111=>[1,1,1,7,1,1,1]
111000000001=>[1,1,1,9,1]
111000001101=>[1,1,1,6,1,2,1]
111000110111=>[1,1,1,4,1,2,1,1,1]
111000110001=>[1,1,1,4,1,4,1]
111000111101=>[1,1,1,4,1,1,1,2,1]
111000100101=>[1,1,1,4,3,2,1]
111011011111=>[1,1,1,2,1,2,1,1,1,1,1]
111011011001=>[1,1,1,2,1,2,1,3,1]
111011000111=>[1,1,1,2,1,4,1,1,1]
111011000001=>[1,1,1,2,1,6,1]
111011001101=>[1,1,1,2,1,3,1,2,1]
111011110111=>[1,1,1,2,1,1,1,2,1,1,1]
111011110001=>[1,1,1,2,1,1,1,4,1]
111011111101=>[1,1,1,2,1,1,1,1,1,2,1]
111011100101=>[1,1,1,2,1,1,3,2,1]
111010010111=>[1,1,1,2,3,2,1,1,1]
111010010001=>[1,1,1,2,3,4,1]
111010011101=>[1,1,1,2,3,1,1,2,1]
111010000101=>[1,1,1,2,5,2,1]
111010110101=>[1,1,1,2,2,1,2,2,1]
100111111111=>[1,3,1,1,1,1,1,1,1,1,1]
100111111001=>[1,3,1,1,1,1,1,3,1]
100111100111=>[1,3,1,1,1,3,1,1,1]
100111100001=>[1,3,1,1,1,5,1]
100111101101=>[1,3,1,1,1,2,1,2,1]
100110011111=>[1,3,1,3,1,1,1,1,1]
100110011001=>[1,3,1,3,1,3,1]
100110000111=>[1,3,1,5,1,1,1]
100110000001=>[1,3,1,7,1]
100110001101=>[1,3,1,4,1,2,1]
100110110111=>[1,3,1,2,1,2,1,1,1]
100110110001=>[1,3,1,2,1,4,1]
100110111101=>[1,3,1,2,1,1,1,2,1]
100110100101=>[1,3,1,2,3,2,1]
100001111111=>[1,5,1,1,1,1,1,1,1]
100001111001=>[1,5,1,1,1,3,1]
100001100111=>[1,5,1,3,1,1,1]
100001100001=>[1,5,1,5,1]
100001101101=>[1,5,1,2,1,2,1]
100000011111=>[1,7,1,1,1,1,1]
100000011001=>[1,7,1,3,1]
100000000111=>[1,9,1,1,1]
100000000001=>[1,11,1]
100000001101=>[1,8,1,2,1]
100000110111=>[1,6,1,2,1,1,1]
100000110001=>[1,6,1,4,1]
100000111101=>[1,6,1,1,1,2,1]
100000100101=>[1,6,3,2,1]
100011011111=>[1,4,1,2,1,1,1,1,1]
100011011001=>[1,4,1,2,1,3,1]
100011000111=>[1,4,1,4,1,1,1]
100011000001=>[1,4,1,6,1]
100011001101=>[1,4,1,3,1,2,1]
100011110111=>[1,4,1,1,1,2,1,1,1]
100011110001=>[1,4,1,1,1,4,1]
100011111101=>[1,4,1,1,1,1,1,2,1]
100011100101=>[1,4,1,1,3,2,1]
100010010111=>[1,4,3,2,1,1,1]
100010010001=>[1,4,3,4,1]
100010011101=>[1,4,3,1,1,2,1]
100010000101=>[1,4,5,2,1]
100010110101=>[1,4,2,1,2,2,1]
101101111111=>[1,2,1,2,1,1,1,1,1,1,1]
101101111001=>[1,2,1,2,1,1,1,3,1]
101101100111=>[1,2,1,2,1,3,1,1,1]
101101100001=>[1,2,1,2,1,5,1]
101101101101=>[1,2,1,2,1,2,1,2,1]
101100011111=>[1,2,1,4,1,1,1,1,1]
101100011001=>[1,2,1,4,1,3,1]
101100000111=>[1,2,1,6,1,1,1]
101100000001=>[1,2,1,8,1]
101100001101=>[1,2,1,5,1,2,1]
101100110111=>[1,2,1,3,1,2,1,1,1]
101100110001=>[1,2,1,3,1,4,1]
101100111101=>[1,2,1,3,1,1,1,2,1]
101100100101=>[1,2,1,3,3,2,1]
101111011111=>[1,2,1,1,1,2,1,1,1,1,1]
101111011001=>[1,2,1,1,1,2,1,3,1]
101111000111=>[1,2,1,1,1,4,1,1,1]
101111000001=>[1,2,1,1,1,6,1]
101111001101=>[1,2,1,1,1,3,1,2,1]
101111110111=>[1,2,1,1,1,1,1,2,1,1,1]
101111110001=>[1,2,1,1,1,1,1,4,1]
101111111101=>[1,2,1,1,1,1,1,1,1,2,1]
101111100101=>[1,2,1,1,1,1,3,2,1]
101110010111=>[1,2,1,1,3,2,1,1,1]
101110010001=>[1,2,1,1,3,4,1]
101110011101=>[1,2,1,1,3,1,1,2,1]
101110000101=>[1,2,1,1,5,2,1]
101110110101=>[1,2,1,1,2,1,2,2,1]
101001011111=>[1,2,3,2,1,1,1,1,1]
101001011001=>[1,2,3,2,1,3,1]
101001000111=>[1,2,3,4,1,1,1]
101001000001=>[1,2,3,6,1]
101001001101=>[1,2,3,3,1,2,1]
101001110111=>[1,2,3,1,1,2,1,1,1]
101001110001=>[1,2,3,1,1,4,1]
101001111101=>[1,2,3,1,1,1,1,2,1]
101001100101=>[1,2,3,1,3,2,1]
101000010111=>[1,2,5,2,1,1,1]
101000010001=>[1,2,5,4,1]
101000011101=>[1,2,5,1,1,2,1]
101000000101=>[1,2,7,2,1]
101000110101=>[1,2,4,1,2,2,1]
101011010111=>[1,2,2,1,2,2,1,1,1]
101011010001=>[1,2,2,1,2,4,1]
101011011101=>[1,2,2,1,2,1,1,2,1]
101011000101=>[1,2,2,1,4,2,1]
101011110101=>[1,2,2,1,1,1,2,2,1]
101010010101=>[1,2,2,3,2,2,1]
000000000000=>[13]
000111111000=>[4,1,1,1,1,1,4]
011110011000=>[2,1,1,1,3,1,4]
011111100000=>[2,1,1,1,1,1,6]
011111001000=>[2,1,1,1,1,3,4]
011100111000=>[2,1,1,3,1,1,4]
011101101000=>[2,1,1,2,1,2,4]
001010101010=>[3,2,2,2,2,2]
001010101100=>[3,2,2,2,1,3]
001010110010=>[3,2,2,1,3,2]
001010110100=>[3,2,2,1,2,3]
001010111000=>[3,2,2,1,1,4]
001011001010=>[3,2,1,3,2,2]
001011001100=>[3,2,1,3,1,3]
001011010010=>[3,2,1,2,3,2]
001011010100=>[3,2,1,2,2,3]
001011011000=>[3,2,1,2,1,4]
001011100010=>[3,2,1,1,4,2]
001011100100=>[3,2,1,1,3,3]
001011101000=>[3,2,1,1,2,4]
001011110000=>[3,2,1,1,1,5]
001100101010=>[3,1,3,2,2,2]
001100101100=>[3,1,3,2,1,3]
001100110010=>[3,1,3,1,3,2]
001100110100=>[3,1,3,1,2,3]
001100111000=>[3,1,3,1,1,4]
001101001010=>[3,1,2,3,2,2]
001101001100=>[3,1,2,3,1,3]
001101010010=>[3,1,2,2,3,2]
001101010100=>[3,1,2,2,2,3]
001101011000=>[3,1,2,2,1,4]
001101100010=>[3,1,2,1,4,2]
001101100100=>[3,1,2,1,3,3]
001101101000=>[3,1,2,1,2,4]
001101110000=>[3,1,2,1,1,5]
001110001010=>[3,1,1,4,2,2]
001110001100=>[3,1,1,4,1,3]
001110010010=>[3,1,1,3,3,2]
001110010100=>[3,1,1,3,2,3]
001110011000=>[3,1,1,3,1,4]
001110100010=>[3,1,1,2,4,2]
001110100100=>[3,1,1,2,3,3]
001110101000=>[3,1,1,2,2,4]
001110110000=>[3,1,1,2,1,5]
001111000010=>[3,1,1,1,5,2]
001111000100=>[3,1,1,1,4,3]
001111001000=>[3,1,1,1,3,4]
001111010000=>[3,1,1,1,2,5]
001111100000=>[3,1,1,1,1,6]
010010101010=>[2,3,2,2,2,2]
010010101100=>[2,3,2,2,1,3]
010010110010=>[2,3,2,1,3,2]
010010110100=>[2,3,2,1,2,3]
010010111000=>[2,3,2,1,1,4]
010011001010=>[2,3,1,3,2,2]
010011001100=>[2,3,1,3,1,3]
010011010010=>[2,3,1,2,3,2]
010011010100=>[2,3,1,2,2,3]
010011011000=>[2,3,1,2,1,4]
010011100010=>[2,3,1,1,4,2]
010011100100=>[2,3,1,1,3,3]
010011101000=>[2,3,1,1,2,4]
010011110000=>[2,3,1,1,1,5]
010100101010=>[2,2,3,2,2,2]
010100101100=>[2,2,3,2,1,3]
010100110010=>[2,2,3,1,3,2]
010100110100=>[2,2,3,1,2,3]
010100111000=>[2,2,3,1,1,4]
010101001010=>[2,2,2,3,2,2]
010101001100=>[2,2,2,3,1,3]
010101010010=>[2,2,2,2,3,2]
010101010100=>[2,2,2,2,2,3]
010101011000=>[2,2,2,2,1,4]
010101100010=>[2,2,2,1,4,2]
010101100100=>[2,2,2,1,3,3]
010101101000=>[2,2,2,1,2,4]
010101110000=>[2,2,2,1,1,5]
010110001010=>[2,2,1,4,2,2]
010110001100=>[2,2,1,4,1,3]
010110010010=>[2,2,1,3,3,2]
010110010100=>[2,2,1,3,2,3]
010110011000=>[2,2,1,3,1,4]
010110100010=>[2,2,1,2,4,2]
010110100100=>[2,2,1,2,3,3]
010110101000=>[2,2,1,2,2,4]
010110110000=>[2,2,1,2,1,5]
010111000010=>[2,2,1,1,5,2]
010111000100=>[2,2,1,1,4,3]
010111001000=>[2,2,1,1,3,4]
010111010000=>[2,2,1,1,2,5]
010111100000=>[2,2,1,1,1,6]
011000101010=>[2,1,4,2,2,2]
011000101100=>[2,1,4,2,1,3]
011000110010=>[2,1,4,1,3,2]
011000110100=>[2,1,4,1,2,3]
011000111000=>[2,1,4,1,1,4]
011001001010=>[2,1,3,3,2,2]
011001001100=>[2,1,3,3,1,3]
011001010010=>[2,1,3,2,3,2]
011001010100=>[2,1,3,2,2,3]
011001011000=>[2,1,3,2,1,4]
011001100010=>[2,1,3,1,4,2]
011001100100=>[2,1,3,1,3,3]
011001101000=>[2,1,3,1,2,4]
011001110000=>[2,1,3,1,1,5]
011010001010=>[2,1,2,4,2,2]
011010001100=>[2,1,2,4,1,3]
011010010010=>[2,1,2,3,3,2]
011010010100=>[2,1,2,3,2,3]
011010011000=>[2,1,2,3,1,4]
011010100010=>[2,1,2,2,4,2]
011010100100=>[2,1,2,2,3,3]
011010101000=>[2,1,2,2,2,4]
011010110000=>[2,1,2,2,1,5]
011011000010=>[2,1,2,1,5,2]
011011000100=>[2,1,2,1,4,3]
011011001000=>[2,1,2,1,3,4]
011011010000=>[2,1,2,1,2,5]
011011100000=>[2,1,2,1,1,6]
011100001010=>[2,1,1,5,2,2]
011100001100=>[2,1,1,5,1,3]
011100010010=>[2,1,1,4,3,2]
011100010100=>[2,1,1,4,2,3]
011100011000=>[2,1,1,4,1,4]
011100100010=>[2,1,1,3,4,2]
011100100100=>[2,1,1,3,3,3]
011100101000=>[2,1,1,3,2,4]
011100110000=>[2,1,1,3,1,5]
011101000010=>[2,1,1,2,5,2]
011101000100=>[2,1,1,2,4,3]
011101001000=>[2,1,1,2,3,4]
011101010000=>[2,1,1,2,2,5]
011101100000=>[2,1,1,2,1,6]
011110000010=>[2,1,1,1,6,2]
011110000100=>[2,1,1,1,5,3]
011110001000=>[2,1,1,1,4,4]
011110010000=>[2,1,1,1,3,5]
011110100000=>[2,1,1,1,2,6]
011111000000=>[2,1,1,1,1,7]
010101101001=>[2,2,2,1,2,3,1]
010101101100=>[2,2,2,1,2,1,3]
011001011001=>[2,1,3,2,1,3,1]
011001011100=>[2,1,3,2,1,1,3]
011010010101=>[2,1,2,3,2,2,1]
011010101001=>[2,1,2,2,2,3,1]
011010101100=>[2,1,2,2,2,1,3]
011011000101=>[2,1,2,1,4,2,1]
011011010001=>[2,1,2,1,2,4,1]
011011010100=>[2,1,2,1,2,2,3]
011100011001=>[2,1,1,4,1,3,1]
011100011100=>[2,1,1,4,1,1,3]
011100110001=>[2,1,1,3,1,4,1]
011100110100=>[2,1,1,3,1,2,3]
011101001001=>[2,1,1,2,3,3,1]
011101001100=>[2,1,1,2,3,1,3]
011101010001=>[2,1,1,2,2,4,1]
011101010100=>[2,1,1,2,2,2,3]
011101011000=>[2,1,1,2,2,1,4]
011101100001=>[2,1,1,2,1,5,1]
011101100100=>[2,1,1,2,1,3,3]
011101110000=>[2,1,1,2,1,1,5]
011110001100=>[2,1,1,1,4,1,3]
011110010001=>[2,1,1,1,3,4,1]
011110010100=>[2,1,1,1,3,2,3]
011110100001=>[2,1,1,1,2,5,1]
011110100100=>[2,1,1,1,2,3,3]
011110101000=>[2,1,1,1,2,2,4]
011110110000=>[2,1,1,1,2,1,5]
011111000001=>[2,1,1,1,1,6,1]
011111000100=>[2,1,1,1,1,4,3]
011111010000=>[2,1,1,1,1,2,5]
001111001100=>[3,1,1,1,3,1,3]
001111010100=>[3,1,1,1,2,2,3]
001111011000=>[3,1,1,1,2,1,4]
010011011100=>[2,3,1,2,1,1,3]
000111011100=>[4,1,1,2,1,1,3]
001111100100=>[3,1,1,1,1,3,3]
001111101000=>[3,1,1,1,1,2,4]
001111110000=>[3,1,1,1,1,1,5]
000111110100=>[4,1,1,1,1,2,3]
110001111000=>[1,1,4,1,1,1,4]
000011111100=>[5,1,1,1,1,1,3]
100101110001=>[1,3,2,1,1,4,1]
101011100001=>[1,2,2,1,1,5,1]
101110100001=>[1,2,1,1,2,5,1]
110001110001=>[1,1,4,1,1,4,1]
110011010001=>[1,1,3,1,2,4,1]
110011100001=>[1,1,3,1,1,5,1]
110100110001=>[1,1,2,3,1,4,1]
110101010001=>[1,1,2,2,2,4,1]
110101100001=>[1,1,2,2,1,5,1]
110110010001=>[1,1,2,1,3,4,1]
110110100001=>[1,1,2,1,2,5,1]
110111000001=>[1,1,2,1,1,6,1]
111001010001=>[1,1,1,3,2,4,1]
111010100001=>[1,1,1,2,2,5,1]
111100010001=>[1,1,1,1,4,4,1]
111100100001=>[1,1,1,1,3,5,1]
111101000001=>[1,1,1,1,2,6,1]
101000111001=>[1,2,4,1,1,3,1]
100100111001=>[1,3,3,1,1,3,1]
100110100011=>[1,3,1,2,4,1,1]
101001100011=>[1,2,3,1,4,1,1]
100101100011=>[1,3,2,1,4,1,1]
100110010011=>[1,3,1,3,3,1,1]
101000110011=>[1,2,4,1,3,1,1]
100100110011=>[1,3,3,1,3,1,1]
101000011011=>[1,2,5,1,2,1,1]
100100011011=>[1,3,4,1,2,1,1]
101010000111=>[1,2,2,5,1,1,1]
100101000111=>[1,3,2,4,1,1,1]
101000100111=>[1,2,4,3,1,1,1]
100100100111=>[1,3,3,3,1,1,1]
100100010111=>[1,3,4,2,1,1,1]
110101010101=>[1,1,2,2,2,2,2,1]
110101011001=>[1,1,2,2,2,1,3,1]
110101100101=>[1,1,2,2,1,3,2,1]
110101101001=>[1,1,2,2,1,2,3,1]
110101110001=>[1,1,2,2,1,1,4,1]
110110010101=>[1,1,2,1,3,2,2,1]
110110100101=>[1,1,2,1,2,3,2,1]
110110101001=>[1,1,2,1,2,2,3,1]
110110110001=>[1,1,2,1,2,1,4,1]
110111000101=>[1,1,2,1,1,4,2,1]
110111001001=>[1,1,2,1,1,3,3,1]
110111010001=>[1,1,2,1,1,2,4,1]
110111100001=>[1,1,2,1,1,1,5,1]
111001010101=>[1,1,1,3,2,2,2,1]
111001011001=>[1,1,1,3,2,1,3,1]
111010010101=>[1,1,1,2,3,2,2,1]
111010100101=>[1,1,1,2,2,3,2,1]
111010101001=>[1,1,1,2,2,2,3,1]
111010110001=>[1,1,1,2,2,1,4,1]
111011000101=>[1,1,1,2,1,4,2,1]
111011001001=>[1,1,1,2,1,3,3,1]
111011010001=>[1,1,1,2,1,2,4,1]
111011100001=>[1,1,1,2,1,1,5,1]
111100010101=>[1,1,1,1,4,2,2,1]
111100100101=>[1,1,1,1,3,3,2,1]
111100101001=>[1,1,1,1,3,2,3,1]
111101000101=>[1,1,1,1,2,4,2,1]
111101001001=>[1,1,1,1,2,3,3,1]
111101010001=>[1,1,1,1,2,2,4,1]
111101100001=>[1,1,1,1,2,1,5,1]
111110000101=>[1,1,1,1,1,5,2,1]
111110001001=>[1,1,1,1,1,4,3,1]
111110010001=>[1,1,1,1,1,3,4,1]
111110100001=>[1,1,1,1,1,2,5,1]
111111000001=>[1,1,1,1,1,1,6,1]
011110000011=>[2,1,1,1,6,1,1]
011100010011=>[2,1,1,4,3,1,1]
011010001011=>[2,1,2,4,2,1,1]
011000101011=>[2,1,4,2,2,1,1]
101100100011=>[1,2,1,3,4,1,1]
101100010011=>[1,2,1,4,3,1,1]
110110000011=>[1,1,2,1,6,1,1]
111010000011=>[1,1,1,2,6,1,1]
111100000011=>[1,1,1,1,7,1,1]
011100000111=>[2,1,1,6,1,1,1]
011000010111=>[2,1,5,2,1,1,1]
110100000111=>[1,1,2,6,1,1,1]
110000001111=>[1,1,7,1,1,1,1]
110011010101=>[1,1,3,1,2,2,2,1]
110100110101=>[1,1,2,3,1,2,2,1]
110001110101=>[1,1,4,1,1,2,2,1]
110101001101=>[1,1,2,2,3,1,2,1]
110011001101=>[1,1,3,1,3,1,2,1]
110100011101=>[1,1,2,4,1,1,2,1]
110000111101=>[1,1,5,1,1,1,2,1]
110101010011=>[1,1,2,2,2,3,1,1]
110011010011=>[1,1,3,1,2,3,1,1]
110100110011=>[1,1,2,3,1,3,1,1]
101100110011=>[1,2,1,3,1,3,1,1]
100110110011=>[1,3,1,2,1,3,1,1]
110001110011=>[1,1,4,1,1,3,1,1]
101001110011=>[1,2,3,1,1,3,1,1]
100101110011=>[1,3,2,1,1,3,1,1]
101100011011=>[1,2,1,4,1,2,1,1]
100110011011=>[1,3,1,3,1,2,1,1]
101000111011=>[1,2,4,1,1,2,1,1]
100100111011=>[1,3,3,1,1,2,1,1]
110101000111=>[1,1,2,2,4,1,1,1]
101101000111=>[1,2,1,2,4,1,1,1]
110011000111=>[1,1,3,1,4,1,1,1]
101011000111=>[1,2,2,1,4,1,1,1]
101100100111=>[1,2,1,3,3,1,1,1]
100110100111=>[1,3,1,2,3,1,1,1]
101001100111=>[1,2,3,1,3,1,1,1]
100101100111=>[1,3,2,1,3,1,1,1]
101100010111=>[1,2,1,4,2,1,1,1]
100110010111=>[1,3,1,3,2,1,1,1]
101000110111=>[1,2,4,1,2,1,1,1]
100100110111=>[1,3,3,1,2,1,1,1]
110100001111=>[1,1,2,5,1,1,1,1]
101010001111=>[1,2,2,4,1,1,1,1]
101001001111=>[1,2,3,3,1,1,1,1]
100101001111=>[1,3,2,3,1,1,1,1]
101000101111=>[1,2,4,2,1,1,1,1]
100100101111=>[1,3,3,2,1,1,1,1]
110000011111=>[1,1,6,1,1,1,1,1]
000111110001=>[4,1,1,1,1,4,1]
001111100001=>[3,1,1,1,1,5,1]
001111000011=>[3,1,1,1,5,1,1]
011010110111=>[2,1,2,2,1,2,1,1,1]
011110110011=>[2,1,1,1,2,1,3,1,1]
011110111001=>[2,1,1,1,2,1,1,3,1]
011000100001=>[2,1,4,5,1]
010000100011=>[2,5,4,1,1]
011110100111=>[2,1,1,1,2,3,1,1,1]
000110100001=>[4,1,2,5,1]
010010100001=>[2,3,2,5,1]
011100101111=>[2,1,1,3,2,1,1,1,1]
011010000001=>[2,1,2,7,1]
010010000011=>[2,3,6,1,1]
000100101001=>[4,3,2,3,1]
010000101001=>[2,5,2,3,1]
011110001111=>[2,1,1,1,4,1,1,1,1]
000110001001=>[4,1,4,3,1]
010010001001=>[2,3,4,3,1]
101011000011=>[1,2,2,1,5,1,1]
110011000011=>[1,1,3,1,5,1,1]
111000011100=>[1,1,1,5,1,1,3]
101101000011=>[1,2,1,2,5,1,1]
110101000011=>[1,1,2,2,5,1,1]
111001000011=>[1,1,1,3,5,1,1]
110000111100=>[1,1,5,1,1,1,3]
000000000101=>[10,2,1]
010000010101=>[2,6,2,2,1]
000100010101=>[4,4,2,2,1]
100101011111=>[1,3,2,2,1,1,1,1,1]
100101110111=>[1,3,2,1,1,2,1,1,1]
010101110111=>[2,2,2,1,1,2,1,1,1]
000001010101=>[6,2,2,2,1]
011101010111=>[2,1,1,2,2,2,1,1,1]
011101110101=>[2,1,1,2,1,1,2,2,1]
011111011111=>[2,1,1,1,1,2,1,1,1,1,1]
000000011011=>[8,1,2,1,1]
000001100011=>[6,1,4,1,1]
000001001011=>[6,3,2,1,1]
000110000011=>[4,1,6,1,1]
000111101111=>[4,1,1,1,2,1,1,1,1]
000100100011=>[4,3,4,1,1]
000100001011=>[4,5,2,1,1]
011000000011=>[2,1,8,1,1]
011001101111=>[2,1,3,1,2,1,1,1,1]
011011011011=>[2,1,2,1,2,1,2,1,1]
011101101011=>[2,1,1,2,1,2,2,1,1]
010011101111=>[2,3,1,1,2,1,1,1,1]
010000001011=>[2,7,2,1,1]
110101100011=>[1,1,2,2,1,4,1,1]
110100111001=>[1,1,2,3,1,1,3,1]
110110010011=>[1,1,2,1,3,3,1,1]
110110011001=>[1,1,2,1,3,1,3,1]
110110001101=>[1,1,2,1,4,1,2,1]
110110100011=>[1,1,2,1,2,4,1,1]
110111000011=>[1,1,2,1,1,5,1,1]
110011011001=>[1,1,3,1,2,1,3,1]
110011100011=>[1,1,3,1,1,4,1,1]
110011100101=>[1,1,3,1,1,3,2,1]
110011101001=>[1,1,3,1,1,2,3,1]
110011110001=>[1,1,3,1,1,1,4,1]
111001010011=>[1,1,1,3,2,3,1,1]
111001001101=>[1,1,1,3,3,1,2,1]
111001100101=>[1,1,1,3,1,3,2,1]
111001100011=>[1,1,1,3,1,4,1,1]
111001101001=>[1,1,1,3,1,2,3,1]
111001110001=>[1,1,1,3,1,1,4,1]
111000110011=>[1,1,1,4,1,3,1,1]
111000110101=>[1,1,1,4,1,2,2,1]
111000111001=>[1,1,1,4,1,1,3,1]
111010010011=>[1,1,1,2,3,3,1,1]
111010011001=>[1,1,1,2,3,1,3,1]
111010001101=>[1,1,1,2,4,1,2,1]
111010100011=>[1,1,1,2,2,4,1,1]
111011000011=>[1,1,1,2,1,5,1,1]
101011100011=>[1,2,2,1,1,4,1,1]
101011110001=>[1,2,2,1,1,1,4,1]
111100010011=>[1,1,1,1,4,3,1,1]
111100011001=>[1,1,1,1,4,1,3,1]
111100001101=>[1,1,1,1,5,1,2,1]
111100100011=>[1,1,1,1,3,4,1,1]
111100110001=>[1,1,1,1,3,1,4,1]
101100111001=>[1,2,1,3,1,1,3,1]
111101000011=>[1,1,1,1,2,5,1,1]
101101100011=>[1,2,1,2,1,4,1,1]
101101110001=>[1,2,1,2,1,1,4,1]
111110000011=>[1,1,1,1,1,6,1,1]
101110010011=>[1,2,1,1,3,3,1,1]
101110011001=>[1,2,1,1,3,1,3,1]
101110100011=>[1,2,1,1,2,4,1,1]
101110110001=>[1,2,1,1,2,1,4,1]
000001111111=>[6,1,1,1,1,1,1,1]
000011111101=>[5,1,1,1,1,1,2,1]
000111111001=>[4,1,1,1,1,1,3,1]
001111000111=>[3,1,1,1,4,1,1,1]
001111001101=>[3,1,1,1,3,1,2,1]
001111011001=>[3,1,1,1,2,1,3,1]
001111110001=>[3,1,1,1,1,1,4,1]
001111100101=>[3,1,1,1,1,3,2,1]
011111100001=>[2,1,1,1,1,1,5,1]
011110011001=>[2,1,1,1,3,1,3,1]
011110000111=>[2,1,1,1,5,1,1,1]
011110001101=>[2,1,1,1,4,1,2,1]
011110110001=>[2,1,1,1,2,1,4,1]
011110100101=>[2,1,1,1,2,3,2,1]
110001110100=>[1,1,4,1,1,2,3]
110100011100=>[1,1,2,4,1,1,3]
011010100011=>[2,1,2,2,4,1,1]
000111011001=>[4,1,1,2,1,3,1]
010011011001=>[2,3,1,2,1,3,1]
001111010001=>[3,1,1,1,2,4,1]
011001000111=>[2,1,3,4,1,1,1]
011101000011=>[2,1,1,2,5,1,1]
100100100001=>[1,3,3,5,1]
100101101111=>[1,3,2,1,2,1,1,1,1]
101101110011=>[1,2,1,2,1,1,3,1,1]
100101111011=>[1,3,2,1,1,1,2,1,1]
100100011001=>[1,3,4,1,3,1]
101000011001=>[1,2,5,1,3,1]
100110111001=>[1,3,1,2,1,1,3,1]
101110111001=>[1,2,1,1,2,1,1,3,1]
100101111001=>[1,3,2,1,1,1,3,1]
101001111001=>[1,2,3,1,1,1,3,1]
101011111001=>[1,2,2,1,1,1,1,3,1]
100110010001=>[1,3,1,3,4,1]
100100010001=>[1,3,4,4,1]
101100010001=>[1,2,1,4,4,1]
100100110001=>[1,3,3,1,4,1]
101000110001=>[1,2,4,1,4,1]
100110100001=>[1,3,1,2,5,1]
101100100001=>[1,2,1,3,5,1]
101000100001=>[1,2,4,5,1]
100101100001=>[1,3,2,1,5,1]
101001100001=>[1,2,3,1,5,1]
100101000001=>[1,3,2,6,1]
101101000001=>[1,2,1,2,6,1]
101011000001=>[1,2,2,1,6,1]
101010000001=>[1,2,2,7,1]
101110011011=>[1,2,1,1,3,1,2,1,1]
100110111011=>[1,3,1,2,1,1,2,1,1]
101110111011=>[1,2,1,1,2,1,1,2,1,1]
101100111011=>[1,2,1,3,1,1,2,1,1]
101101111011=>[1,2,1,2,1,1,1,2,1,1]
101001111011=>[1,2,3,1,1,1,2,1,1]
101011111011=>[1,2,2,1,1,1,1,2,1,1]
100100010011=>[1,3,4,3,1,1]
101000010011=>[1,2,5,3,1,1]
101110110011=>[1,2,1,1,2,1,3,1,1]
101011110011=>[1,2,2,1,1,1,3,1,1]
100100100011=>[1,3,3,4,1,1]
101000100011=>[1,2,4,4,1,1]
100101000011=>[1,3,2,5,1,1]
101001000011=>[1,2,3,5,1,1]
101010000011=>[1,2,2,6,1,1]
101110110111=>[1,2,1,1,2,1,2,1,1,1]
101101110111=>[1,2,1,2,1,1,2,1,1,1]
101011110111=>[1,2,2,1,1,1,2,1,1,1]
101110100111=>[1,2,1,1,2,3,1,1,1]
101011100111=>[1,2,2,1,1,3,1,1,1]
100110101111=>[1,3,1,2,2,1,1,1,1]
101110101111=>[1,2,1,1,2,2,1,1,1,1]
101100101111=>[1,2,1,3,2,1,1,1,1]
101101101111=>[1,2,1,2,1,2,1,1,1,1]
101001101111=>[1,2,3,1,2,1,1,1,1]
101011101111=>[1,2,2,1,1,2,1,1,1,1]
101101001111=>[1,2,1,2,3,1,1,1,1]
101011001111=>[1,2,2,1,3,1,1,1,1]
101101011111=>[1,2,1,2,2,1,1,1,1,1]
101011011111=>[1,2,2,1,2,1,1,1,1,1]
101010011111=>[1,2,2,3,1,1,1,1,1]
101010111111=>[1,2,2,2,1,1,1,1,1,1]
010100000000=>[2,2,9]
000101000000=>[4,2,7]
010001000000=>[2,4,7]
011011000000=>[2,1,2,1,7]
000001010000=>[6,2,5]
010101010000=>[2,2,2,2,5]
000100010000=>[4,4,5]
010000010000=>[2,6,5]
011010010000=>[2,1,2,3,5]
000110110000=>[4,1,2,1,5]
010010110000=>[2,3,2,1,5]
011000110000=>[2,1,4,1,5]
000000010100=>[8,2,3]
010100010100=>[2,2,4,2,3]
000101010100=>[4,2,2,2,3]
010001010100=>[2,4,2,2,3]
000001000100=>[6,4,3]
010101000100=>[2,2,2,4,3]
000100000100=>[4,6,3]
010000000100=>[2,8,3]
011010000100=>[2,1,2,5,3]
000110100100=>[4,1,2,3,3]
010010100100=>[2,3,2,3,3]
011000100100=>[2,1,4,3,3]
000001101100=>[6,1,2,1,3]
000100101100=>[4,3,2,1,3]
010000101100=>[2,5,2,1,3]
000110001100=>[4,1,4,1,3]
010010001100=>[2,3,4,1,3]
011000001100=>[2,1,6,1,3]
011110111100=>[2,1,1,1,2,1,1,1,3]
010100000101=>[2,2,6,2,1]
000101000101=>[4,2,4,2,1]
010001000101=>[2,4,4,2,1]
011000110101=>[2,1,4,1,2,2,1]
000000010001=>[8,4,1]
010100010001=>[2,2,4,4,1]
000101010001=>[4,2,2,4,1]
010001010001=>[2,4,2,4,1]
000001000001=>[6,6,1]
010101000001=>[2,2,2,6,1]
000100000001=>[4,8,1]
010000000001=>[2,10,1]
000001101001=>[6,1,2,3,1]
011000001001=>[2,1,6,3,1]
010101100011=>[2,2,2,1,4,1,1]
011001010011=>[2,1,3,2,3,1,1]
111001000111=>[1,1,1,3,4,1,1,1]
111100000111=>[1,1,1,1,6,1,1,1]
011100110011=>[2,1,1,3,1,3,1,1]
011101100011=>[2,1,1,2,1,4,1,1]
011101000111=>[2,1,1,2,4,1,1,1]
111010000111=>[1,1,1,2,5,1,1,1]
111000001111=>[1,1,1,6,1,1,1,1]
001111010011=>[3,1,1,1,2,3,1,1]
001111101001=>[3,1,1,1,1,2,3,1]
000111110101=>[4,1,1,1,1,2,2,1]
011110010011=>[2,1,1,1,3,3,1,1]
000111110011=>[4,1,1,1,1,3,1,1]
110001111001=>[1,1,4,1,1,1,3,1]
011101110001=>[2,1,1,2,1,1,4,1]
011101100101=>[2,1,1,2,1,3,2,1]
011101001101=>[2,1,1,2,3,1,2,1]
011100011101=>[2,1,1,4,1,1,2,1]
011101010101=>[2,1,1,2,2,2,2,1]
011101010011=>[2,1,1,2,2,3,1,1]
011100110101=>[2,1,1,3,1,2,2,1]
011100001111=>[2,1,1,5,1,1,1,1]
001111010101=>[3,1,1,1,2,2,2,1]
110110000111=>[1,1,2,1,5,1,1,1]
111000011101=>[1,1,1,5,1,1,2,1]
011100111001=>[2,1,1,3,1,1,3,1]
011111001001=>[2,1,1,1,1,3,3,1]
011101101001=>[2,1,1,2,1,2,3,1]
011111000011=>[2,1,1,1,1,5,1,1]
011101011001=>[2,1,1,2,2,1,3,1]
011110010101=>[2,1,1,1,3,2,2,1]
011110101001=>[2,1,1,1,2,2,3,1]
011110100011=>[2,1,1,1,2,4,1,1]
001111100011=>[3,1,1,1,1,4,1,1]
011111000101=>[2,1,1,1,1,4,2,1]
011111010001=>[2,1,1,1,1,2,4,1]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Properties
injective, graded
Sage code
def mapping(w): return Compositions().from_code([1] + list(w))
Weight
26
Created
Sep 21, 2020 at 21:21 by Martin Rubey
Updated
Sep 21, 2020 at 21:21 by Martin Rubey
searching the database
Sorry, this map was not found in the database.