=>

0=>[2]=>[1,1] 1=>[1,1]=>[2] 00=>[3]=>[1,1,1] 01=>[2,1]=>[2,1] 10=>[1,2]=>[1,2] 11=>[1,1,1]=>[3] 000=>[4]=>[1,1,1,1] 001=>[3,1]=>[2,1,1] 010=>[2,2]=>[1,2,1] 011=>[2,1,1]=>[3,1] 100=>[1,3]=>[1,1,2] 101=>[1,2,1]=>[2,2] 110=>[1,1,2]=>[1,3] 111=>[1,1,1,1]=>[4] 0000=>[5]=>[1,1,1,1,1] 0001=>[4,1]=>[2,1,1,1] 0010=>[3,2]=>[1,2,1,1] 0011=>[3,1,1]=>[3,1,1] 0100=>[2,3]=>[1,1,2,1] 0101=>[2,2,1]=>[2,2,1] 0110=>[2,1,2]=>[1,3,1] 0111=>[2,1,1,1]=>[4,1] 1000=>[1,4]=>[1,1,1,2] 1001=>[1,3,1]=>[2,1,2] 1010=>[1,2,2]=>[1,2,2] 1011=>[1,2,1,1]=>[3,2] 1100=>[1,1,3]=>[1,1,3] 1101=>[1,1,2,1]=>[2,3] 1110=>[1,1,1,2]=>[1,4] 1111=>[1,1,1,1,1]=>[5] 00000=>[6]=>[1,1,1,1,1,1] 00001=>[5,1]=>[2,1,1,1,1] 00010=>[4,2]=>[1,2,1,1,1] 00011=>[4,1,1]=>[3,1,1,1] 00100=>[3,3]=>[1,1,2,1,1] 00101=>[3,2,1]=>[2,2,1,1] 00110=>[3,1,2]=>[1,3,1,1] 00111=>[3,1,1,1]=>[4,1,1] 01000=>[2,4]=>[1,1,1,2,1] 01001=>[2,3,1]=>[2,1,2,1] 01010=>[2,2,2]=>[1,2,2,1] 01011=>[2,2,1,1]=>[3,2,1] 01100=>[2,1,3]=>[1,1,3,1] 01101=>[2,1,2,1]=>[2,3,1] 01110=>[2,1,1,2]=>[1,4,1] 01111=>[2,1,1,1,1]=>[5,1] 10000=>[1,5]=>[1,1,1,1,2] 10001=>[1,4,1]=>[2,1,1,2] 10010=>[1,3,2]=>[1,2,1,2] 10011=>[1,3,1,1]=>[3,1,2] 10100=>[1,2,3]=>[1,1,2,2] 10101=>[1,2,2,1]=>[2,2,2] 10110=>[1,2,1,2]=>[1,3,2] 10111=>[1,2,1,1,1]=>[4,2] 11000=>[1,1,4]=>[1,1,1,3] 11001=>[1,1,3,1]=>[2,1,3] 11010=>[1,1,2,2]=>[1,2,3] 11011=>[1,1,2,1,1]=>[3,3] 11100=>[1,1,1,3]=>[1,1,4] 11101=>[1,1,1,2,1]=>[2,4] 11110=>[1,1,1,1,2]=>[1,5] 11111=>[1,1,1,1,1,1]=>[6] 000000=>[7]=>[1,1,1,1,1,1,1] 000001=>[6,1]=>[2,1,1,1,1,1] 000010=>[5,2]=>[1,2,1,1,1,1] 000011=>[5,1,1]=>[3,1,1,1,1] 000100=>[4,3]=>[1,1,2,1,1,1] 000101=>[4,2,1]=>[2,2,1,1,1] 000110=>[4,1,2]=>[1,3,1,1,1] 000111=>[4,1,1,1]=>[4,1,1,1] 001000=>[3,4]=>[1,1,1,2,1,1] 001001=>[3,3,1]=>[2,1,2,1,1] 001010=>[3,2,2]=>[1,2,2,1,1] 001011=>[3,2,1,1]=>[3,2,1,1] 001100=>[3,1,3]=>[1,1,3,1,1] 001101=>[3,1,2,1]=>[2,3,1,1] 001110=>[3,1,1,2]=>[1,4,1,1] 001111=>[3,1,1,1,1]=>[5,1,1] 010000=>[2,5]=>[1,1,1,1,2,1] 010001=>[2,4,1]=>[2,1,1,2,1] 010010=>[2,3,2]=>[1,2,1,2,1] 010011=>[2,3,1,1]=>[3,1,2,1] 010100=>[2,2,3]=>[1,1,2,2,1] 010101=>[2,2,2,1]=>[2,2,2,1] 010110=>[2,2,1,2]=>[1,3,2,1] 010111=>[2,2,1,1,1]=>[4,2,1] 011000=>[2,1,4]=>[1,1,1,3,1] 011001=>[2,1,3,1]=>[2,1,3,1] 011010=>[2,1,2,2]=>[1,2,3,1] 011011=>[2,1,2,1,1]=>[3,3,1] 011100=>[2,1,1,3]=>[1,1,4,1] 011101=>[2,1,1,2,1]=>[2,4,1] 011110=>[2,1,1,1,2]=>[1,5,1] 011111=>[2,1,1,1,1,1]=>[6,1] 100000=>[1,6]=>[1,1,1,1,1,2] 100001=>[1,5,1]=>[2,1,1,1,2] 100010=>[1,4,2]=>[1,2,1,1,2] 100011=>[1,4,1,1]=>[3,1,1,2] 100100=>[1,3,3]=>[1,1,2,1,2] 100101=>[1,3,2,1]=>[2,2,1,2] 100110=>[1,3,1,2]=>[1,3,1,2] 100111=>[1,3,1,1,1]=>[4,1,2] 101000=>[1,2,4]=>[1,1,1,2,2] 101001=>[1,2,3,1]=>[2,1,2,2] 101010=>[1,2,2,2]=>[1,2,2,2] 101011=>[1,2,2,1,1]=>[3,2,2] 101100=>[1,2,1,3]=>[1,1,3,2] 101101=>[1,2,1,2,1]=>[2,3,2] 101110=>[1,2,1,1,2]=>[1,4,2] 101111=>[1,2,1,1,1,1]=>[5,2] 110000=>[1,1,5]=>[1,1,1,1,3] 110001=>[1,1,4,1]=>[2,1,1,3] 110010=>[1,1,3,2]=>[1,2,1,3] 110011=>[1,1,3,1,1]=>[3,1,3] 110100=>[1,1,2,3]=>[1,1,2,3] 110101=>[1,1,2,2,1]=>[2,2,3] 110110=>[1,1,2,1,2]=>[1,3,3] 110111=>[1,1,2,1,1,1]=>[4,3] 111000=>[1,1,1,4]=>[1,1,1,4] 111001=>[1,1,1,3,1]=>[2,1,4] 111010=>[1,1,1,2,2]=>[1,2,4] 111011=>[1,1,1,2,1,1]=>[3,4] 111100=>[1,1,1,1,3]=>[1,1,5] 111101=>[1,1,1,1,2,1]=>[2,5] 111110=>[1,1,1,1,1,2]=>[1,6] 111111=>[1,1,1,1,1,1,1]=>[7] 0000000=>[8]=>[1,1,1,1,1,1,1,1] 0000001=>[7,1]=>[2,1,1,1,1,1,1] 0000010=>[6,2]=>[1,2,1,1,1,1,1] 0000011=>[6,1,1]=>[3,1,1,1,1,1] 0000100=>[5,3]=>[1,1,2,1,1,1,1] 0000101=>[5,2,1]=>[2,2,1,1,1,1] 0000110=>[5,1,2]=>[1,3,1,1,1,1] 0000111=>[5,1,1,1]=>[4,1,1,1,1] 0001000=>[4,4]=>[1,1,1,2,1,1,1] 0001001=>[4,3,1]=>[2,1,2,1,1,1] 0001010=>[4,2,2]=>[1,2,2,1,1,1] 0001011=>[4,2,1,1]=>[3,2,1,1,1] 0001100=>[4,1,3]=>[1,1,3,1,1,1] 0001101=>[4,1,2,1]=>[2,3,1,1,1] 0001110=>[4,1,1,2]=>[1,4,1,1,1] 0001111=>[4,1,1,1,1]=>[5,1,1,1] 0010000=>[3,5]=>[1,1,1,1,2,1,1] 0010001=>[3,4,1]=>[2,1,1,2,1,1] 0010010=>[3,3,2]=>[1,2,1,2,1,1] 0010011=>[3,3,1,1]=>[3,1,2,1,1] 0010100=>[3,2,3]=>[1,1,2,2,1,1] 0010101=>[3,2,2,1]=>[2,2,2,1,1] 0010110=>[3,2,1,2]=>[1,3,2,1,1] 0010111=>[3,2,1,1,1]=>[4,2,1,1] 0011000=>[3,1,4]=>[1,1,1,3,1,1] 0011001=>[3,1,3,1]=>[2,1,3,1,1] 0011010=>[3,1,2,2]=>[1,2,3,1,1] 0011011=>[3,1,2,1,1]=>[3,3,1,1] 0011100=>[3,1,1,3]=>[1,1,4,1,1] 0011101=>[3,1,1,2,1]=>[2,4,1,1] 0011110=>[3,1,1,1,2]=>[1,5,1,1] 0011111=>[3,1,1,1,1,1]=>[6,1,1] 0100000=>[2,6]=>[1,1,1,1,1,2,1] 0100001=>[2,5,1]=>[2,1,1,1,2,1] 0100010=>[2,4,2]=>[1,2,1,1,2,1] 0100011=>[2,4,1,1]=>[3,1,1,2,1] 0100100=>[2,3,3]=>[1,1,2,1,2,1] 0100101=>[2,3,2,1]=>[2,2,1,2,1] 0100110=>[2,3,1,2]=>[1,3,1,2,1] 0100111=>[2,3,1,1,1]=>[4,1,2,1] 0101000=>[2,2,4]=>[1,1,1,2,2,1] 0101001=>[2,2,3,1]=>[2,1,2,2,1] 0101010=>[2,2,2,2]=>[1,2,2,2,1] 0101011=>[2,2,2,1,1]=>[3,2,2,1] 0101100=>[2,2,1,3]=>[1,1,3,2,1] 0101101=>[2,2,1,2,1]=>[2,3,2,1] 0101110=>[2,2,1,1,2]=>[1,4,2,1] 0101111=>[2,2,1,1,1,1]=>[5,2,1] 0110000=>[2,1,5]=>[1,1,1,1,3,1] 0110001=>[2,1,4,1]=>[2,1,1,3,1] 0110010=>[2,1,3,2]=>[1,2,1,3,1] 0110011=>[2,1,3,1,1]=>[3,1,3,1] 0110100=>[2,1,2,3]=>[1,1,2,3,1] 0110101=>[2,1,2,2,1]=>[2,2,3,1] 0110110=>[2,1,2,1,2]=>[1,3,3,1] 0110111=>[2,1,2,1,1,1]=>[4,3,1] 0111000=>[2,1,1,4]=>[1,1,1,4,1] 0111001=>[2,1,1,3,1]=>[2,1,4,1] 0111010=>[2,1,1,2,2]=>[1,2,4,1] 0111011=>[2,1,1,2,1,1]=>[3,4,1] 0111100=>[2,1,1,1,3]=>[1,1,5,1] 0111101=>[2,1,1,1,2,1]=>[2,5,1] 0111110=>[2,1,1,1,1,2]=>[1,6,1] 0111111=>[2,1,1,1,1,1,1]=>[7,1] 1000000=>[1,7]=>[1,1,1,1,1,1,2] 1000001=>[1,6,1]=>[2,1,1,1,1,2] 1000010=>[1,5,2]=>[1,2,1,1,1,2] 1000011=>[1,5,1,1]=>[3,1,1,1,2] 1000100=>[1,4,3]=>[1,1,2,1,1,2] 1000101=>[1,4,2,1]=>[2,2,1,1,2] 1000110=>[1,4,1,2]=>[1,3,1,1,2] 1000111=>[1,4,1,1,1]=>[4,1,1,2] 1001000=>[1,3,4]=>[1,1,1,2,1,2] 1001001=>[1,3,3,1]=>[2,1,2,1,2] 1001010=>[1,3,2,2]=>[1,2,2,1,2] 1001011=>[1,3,2,1,1]=>[3,2,1,2] 1001100=>[1,3,1,3]=>[1,1,3,1,2] 1001101=>[1,3,1,2,1]=>[2,3,1,2] 1001110=>[1,3,1,1,2]=>[1,4,1,2] 1001111=>[1,3,1,1,1,1]=>[5,1,2] 1010000=>[1,2,5]=>[1,1,1,1,2,2] 1010001=>[1,2,4,1]=>[2,1,1,2,2] 1010010=>[1,2,3,2]=>[1,2,1,2,2] 1010011=>[1,2,3,1,1]=>[3,1,2,2] 1010100=>[1,2,2,3]=>[1,1,2,2,2] 1010101=>[1,2,2,2,1]=>[2,2,2,2] 1010110=>[1,2,2,1,2]=>[1,3,2,2] 1010111=>[1,2,2,1,1,1]=>[4,2,2] 1011000=>[1,2,1,4]=>[1,1,1,3,2] 1011001=>[1,2,1,3,1]=>[2,1,3,2] 1011010=>[1,2,1,2,2]=>[1,2,3,2] 1011011=>[1,2,1,2,1,1]=>[3,3,2] 1011100=>[1,2,1,1,3]=>[1,1,4,2] 1011101=>[1,2,1,1,2,1]=>[2,4,2] 1011110=>[1,2,1,1,1,2]=>[1,5,2] 1011111=>[1,2,1,1,1,1,1]=>[6,2] 1100000=>[1,1,6]=>[1,1,1,1,1,3] 1100001=>[1,1,5,1]=>[2,1,1,1,3] 1100010=>[1,1,4,2]=>[1,2,1,1,3] 1100011=>[1,1,4,1,1]=>[3,1,1,3] 1100100=>[1,1,3,3]=>[1,1,2,1,3] 1100101=>[1,1,3,2,1]=>[2,2,1,3] 1100110=>[1,1,3,1,2]=>[1,3,1,3] 1100111=>[1,1,3,1,1,1]=>[4,1,3] 1101000=>[1,1,2,4]=>[1,1,1,2,3] 1101001=>[1,1,2,3,1]=>[2,1,2,3] 1101010=>[1,1,2,2,2]=>[1,2,2,3] 1101011=>[1,1,2,2,1,1]=>[3,2,3] 1101100=>[1,1,2,1,3]=>[1,1,3,3] 1101101=>[1,1,2,1,2,1]=>[2,3,3] 1101110=>[1,1,2,1,1,2]=>[1,4,3] 1101111=>[1,1,2,1,1,1,1]=>[5,3] 1110000=>[1,1,1,5]=>[1,1,1,1,4] 1110001=>[1,1,1,4,1]=>[2,1,1,4] 1110010=>[1,1,1,3,2]=>[1,2,1,4] 1110011=>[1,1,1,3,1,1]=>[3,1,4] 1110100=>[1,1,1,2,3]=>[1,1,2,4] 1110101=>[1,1,1,2,2,1]=>[2,2,4] 1110110=>[1,1,1,2,1,2]=>[1,3,4] 1110111=>[1,1,1,2,1,1,1]=>[4,4] 1111000=>[1,1,1,1,4]=>[1,1,1,5] 1111001=>[1,1,1,1,3,1]=>[2,1,5] 1111010=>[1,1,1,1,2,2]=>[1,2,5] 1111011=>[1,1,1,1,2,1,1]=>[3,5] 1111100=>[1,1,1,1,1,3]=>[1,1,6] 1111101=>[1,1,1,1,1,2,1]=>[2,6] 1111110=>[1,1,1,1,1,1,2]=>[1,7] 1111111=>[1,1,1,1,1,1,1,1]=>[8] 00000000=>[9]=>[1,1,1,1,1,1,1,1,1] 00000001=>[8,1]=>[2,1,1,1,1,1,1,1] 00000010=>[7,2]=>[1,2,1,1,1,1,1,1] 00000011=>[7,1,1]=>[3,1,1,1,1,1,1] 00000100=>[6,3]=>[1,1,2,1,1,1,1,1] 00000101=>[6,2,1]=>[2,2,1,1,1,1,1] 00000110=>[6,1,2]=>[1,3,1,1,1,1,1] 00000111=>[6,1,1,1]=>[4,1,1,1,1,1] 00001000=>[5,4]=>[1,1,1,2,1,1,1,1] 00001001=>[5,3,1]=>[2,1,2,1,1,1,1] 00001010=>[5,2,2]=>[1,2,2,1,1,1,1] 00001011=>[5,2,1,1]=>[3,2,1,1,1,1] 00001100=>[5,1,3]=>[1,1,3,1,1,1,1] 00001101=>[5,1,2,1]=>[2,3,1,1,1,1] 00001110=>[5,1,1,2]=>[1,4,1,1,1,1] 00001111=>[5,1,1,1,1]=>[5,1,1,1,1] 00010000=>[4,5]=>[1,1,1,1,2,1,1,1] 00010001=>[4,4,1]=>[2,1,1,2,1,1,1] 00010010=>[4,3,2]=>[1,2,1,2,1,1,1] 00010011=>[4,3,1,1]=>[3,1,2,1,1,1] 00010100=>[4,2,3]=>[1,1,2,2,1,1,1] 00010101=>[4,2,2,1]=>[2,2,2,1,1,1] 00010110=>[4,2,1,2]=>[1,3,2,1,1,1] 00010111=>[4,2,1,1,1]=>[4,2,1,1,1] 00011000=>[4,1,4]=>[1,1,1,3,1,1,1] 00011001=>[4,1,3,1]=>[2,1,3,1,1,1] 00011010=>[4,1,2,2]=>[1,2,3,1,1,1] 00011011=>[4,1,2,1,1]=>[3,3,1,1,1] 00011100=>[4,1,1,3]=>[1,1,4,1,1,1] 00011101=>[4,1,1,2,1]=>[2,4,1,1,1] 00011110=>[4,1,1,1,2]=>[1,5,1,1,1] 00011111=>[4,1,1,1,1,1]=>[6,1,1,1] 00100000=>[3,6]=>[1,1,1,1,1,2,1,1] 00100001=>[3,5,1]=>[2,1,1,1,2,1,1] 00100010=>[3,4,2]=>[1,2,1,1,2,1,1] 00100011=>[3,4,1,1]=>[3,1,1,2,1,1] 00100100=>[3,3,3]=>[1,1,2,1,2,1,1] 00100101=>[3,3,2,1]=>[2,2,1,2,1,1] 00100110=>[3,3,1,2]=>[1,3,1,2,1,1] 00100111=>[3,3,1,1,1]=>[4,1,2,1,1] 00101000=>[3,2,4]=>[1,1,1,2,2,1,1] 00101001=>[3,2,3,1]=>[2,1,2,2,1,1] 00101010=>[3,2,2,2]=>[1,2,2,2,1,1] 00101011=>[3,2,2,1,1]=>[3,2,2,1,1] 00101100=>[3,2,1,3]=>[1,1,3,2,1,1] 00101101=>[3,2,1,2,1]=>[2,3,2,1,1] 00101110=>[3,2,1,1,2]=>[1,4,2,1,1] 00101111=>[3,2,1,1,1,1]=>[5,2,1,1] 00110000=>[3,1,5]=>[1,1,1,1,3,1,1] 00110001=>[3,1,4,1]=>[2,1,1,3,1,1] 00110010=>[3,1,3,2]=>[1,2,1,3,1,1] 00110011=>[3,1,3,1,1]=>[3,1,3,1,1] 00110100=>[3,1,2,3]=>[1,1,2,3,1,1] 00110101=>[3,1,2,2,1]=>[2,2,3,1,1] 00110110=>[3,1,2,1,2]=>[1,3,3,1,1] 00110111=>[3,1,2,1,1,1]=>[4,3,1,1] 00111000=>[3,1,1,4]=>[1,1,1,4,1,1] 00111001=>[3,1,1,3,1]=>[2,1,4,1,1] 00111010=>[3,1,1,2,2]=>[1,2,4,1,1] 00111011=>[3,1,1,2,1,1]=>[3,4,1,1] 00111100=>[3,1,1,1,3]=>[1,1,5,1,1] 00111101=>[3,1,1,1,2,1]=>[2,5,1,1] 00111110=>[3,1,1,1,1,2]=>[1,6,1,1] 00111111=>[3,1,1,1,1,1,1]=>[7,1,1] 01000000=>[2,7]=>[1,1,1,1,1,1,2,1] 01000001=>[2,6,1]=>[2,1,1,1,1,2,1] 01000010=>[2,5,2]=>[1,2,1,1,1,2,1] 01000011=>[2,5,1,1]=>[3,1,1,1,2,1] 01000100=>[2,4,3]=>[1,1,2,1,1,2,1] 01000101=>[2,4,2,1]=>[2,2,1,1,2,1] 01000110=>[2,4,1,2]=>[1,3,1,1,2,1] 01000111=>[2,4,1,1,1]=>[4,1,1,2,1] 01001000=>[2,3,4]=>[1,1,1,2,1,2,1] 01001001=>[2,3,3,1]=>[2,1,2,1,2,1] 01001010=>[2,3,2,2]=>[1,2,2,1,2,1] 01001011=>[2,3,2,1,1]=>[3,2,1,2,1] 01001100=>[2,3,1,3]=>[1,1,3,1,2,1] 01001101=>[2,3,1,2,1]=>[2,3,1,2,1] 01001110=>[2,3,1,1,2]=>[1,4,1,2,1] 01001111=>[2,3,1,1,1,1]=>[5,1,2,1] 01010000=>[2,2,5]=>[1,1,1,1,2,2,1] 01010001=>[2,2,4,1]=>[2,1,1,2,2,1] 01010010=>[2,2,3,2]=>[1,2,1,2,2,1] 01010011=>[2,2,3,1,1]=>[3,1,2,2,1] 01010100=>[2,2,2,3]=>[1,1,2,2,2,1] 01010101=>[2,2,2,2,1]=>[2,2,2,2,1] 01010110=>[2,2,2,1,2]=>[1,3,2,2,1] 01010111=>[2,2,2,1,1,1]=>[4,2,2,1] 01011000=>[2,2,1,4]=>[1,1,1,3,2,1] 01011001=>[2,2,1,3,1]=>[2,1,3,2,1] 01011010=>[2,2,1,2,2]=>[1,2,3,2,1] 01011011=>[2,2,1,2,1,1]=>[3,3,2,1] 01011100=>[2,2,1,1,3]=>[1,1,4,2,1] 01011101=>[2,2,1,1,2,1]=>[2,4,2,1] 01011110=>[2,2,1,1,1,2]=>[1,5,2,1] 01011111=>[2,2,1,1,1,1,1]=>[6,2,1] 01100000=>[2,1,6]=>[1,1,1,1,1,3,1] 01100001=>[2,1,5,1]=>[2,1,1,1,3,1] 01100010=>[2,1,4,2]=>[1,2,1,1,3,1] 01100011=>[2,1,4,1,1]=>[3,1,1,3,1] 01100100=>[2,1,3,3]=>[1,1,2,1,3,1] 01100101=>[2,1,3,2,1]=>[2,2,1,3,1] 01100110=>[2,1,3,1,2]=>[1,3,1,3,1] 01100111=>[2,1,3,1,1,1]=>[4,1,3,1] 01101000=>[2,1,2,4]=>[1,1,1,2,3,1] 01101001=>[2,1,2,3,1]=>[2,1,2,3,1] 01101010=>[2,1,2,2,2]=>[1,2,2,3,1] 01101011=>[2,1,2,2,1,1]=>[3,2,3,1] 01101100=>[2,1,2,1,3]=>[1,1,3,3,1] 01101101=>[2,1,2,1,2,1]=>[2,3,3,1] 01101110=>[2,1,2,1,1,2]=>[1,4,3,1] 01101111=>[2,1,2,1,1,1,1]=>[5,3,1] 01110000=>[2,1,1,5]=>[1,1,1,1,4,1] 01110001=>[2,1,1,4,1]=>[2,1,1,4,1] 01110010=>[2,1,1,3,2]=>[1,2,1,4,1] 01110011=>[2,1,1,3,1,1]=>[3,1,4,1] 01110100=>[2,1,1,2,3]=>[1,1,2,4,1] 01110101=>[2,1,1,2,2,1]=>[2,2,4,1] 01110110=>[2,1,1,2,1,2]=>[1,3,4,1] 01110111=>[2,1,1,2,1,1,1]=>[4,4,1] 01111000=>[2,1,1,1,4]=>[1,1,1,5,1] 01111001=>[2,1,1,1,3,1]=>[2,1,5,1] 01111010=>[2,1,1,1,2,2]=>[1,2,5,1] 01111011=>[2,1,1,1,2,1,1]=>[3,5,1] 01111100=>[2,1,1,1,1,3]=>[1,1,6,1] 01111101=>[2,1,1,1,1,2,1]=>[2,6,1] 01111110=>[2,1,1,1,1,1,2]=>[1,7,1] 01111111=>[2,1,1,1,1,1,1,1]=>[8,1] 10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 10000001=>[1,7,1]=>[2,1,1,1,1,1,2] 10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 10000011=>[1,6,1,1]=>[3,1,1,1,1,2] 10000100=>[1,5,3]=>[1,1,2,1,1,1,2] 10000101=>[1,5,2,1]=>[2,2,1,1,1,2] 10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 10000111=>[1,5,1,1,1]=>[4,1,1,1,2] 10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 10001001=>[1,4,3,1]=>[2,1,2,1,1,2] 10001010=>[1,4,2,2]=>[1,2,2,1,1,2] 10001011=>[1,4,2,1,1]=>[3,2,1,1,2] 10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 10001101=>[1,4,1,2,1]=>[2,3,1,1,2] 10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 10001111=>[1,4,1,1,1,1]=>[5,1,1,2] 10010000=>[1,3,5]=>[1,1,1,1,2,1,2] 10010001=>[1,3,4,1]=>[2,1,1,2,1,2] 10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 10010011=>[1,3,3,1,1]=>[3,1,2,1,2] 10010100=>[1,3,2,3]=>[1,1,2,2,1,2] 10010101=>[1,3,2,2,1]=>[2,2,2,1,2] 10010110=>[1,3,2,1,2]=>[1,3,2,1,2] 10010111=>[1,3,2,1,1,1]=>[4,2,1,2] 10011000=>[1,3,1,4]=>[1,1,1,3,1,2] 10011001=>[1,3,1,3,1]=>[2,1,3,1,2] 10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 10011011=>[1,3,1,2,1,1]=>[3,3,1,2] 10011100=>[1,3,1,1,3]=>[1,1,4,1,2] 10011101=>[1,3,1,1,2,1]=>[2,4,1,2] 10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 10011111=>[1,3,1,1,1,1,1]=>[6,1,2] 10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 10100001=>[1,2,5,1]=>[2,1,1,1,2,2] 10100010=>[1,2,4,2]=>[1,2,1,1,2,2] 10100011=>[1,2,4,1,1]=>[3,1,1,2,2] 10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 10100101=>[1,2,3,2,1]=>[2,2,1,2,2] 10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 10100111=>[1,2,3,1,1,1]=>[4,1,2,2] 10101000=>[1,2,2,4]=>[1,1,1,2,2,2] 10101001=>[1,2,2,3,1]=>[2,1,2,2,2] 10101010=>[1,2,2,2,2]=>[1,2,2,2,2] 10101011=>[1,2,2,2,1,1]=>[3,2,2,2] 10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 10101101=>[1,2,2,1,2,1]=>[2,3,2,2] 10101110=>[1,2,2,1,1,2]=>[1,4,2,2] 10101111=>[1,2,2,1,1,1,1]=>[5,2,2] 10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 10110001=>[1,2,1,4,1]=>[2,1,1,3,2] 10110010=>[1,2,1,3,2]=>[1,2,1,3,2] 10110011=>[1,2,1,3,1,1]=>[3,1,3,2] 10110100=>[1,2,1,2,3]=>[1,1,2,3,2] 10110101=>[1,2,1,2,2,1]=>[2,2,3,2] 10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 10110111=>[1,2,1,2,1,1,1]=>[4,3,2] 10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 10111001=>[1,2,1,1,3,1]=>[2,1,4,2] 10111010=>[1,2,1,1,2,2]=>[1,2,4,2] 10111011=>[1,2,1,1,2,1,1]=>[3,4,2] 10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 10111101=>[1,2,1,1,1,2,1]=>[2,5,2] 10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 10111111=>[1,2,1,1,1,1,1,1]=>[7,2] 11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 11000001=>[1,1,6,1]=>[2,1,1,1,1,3] 11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 11000011=>[1,1,5,1,1]=>[3,1,1,1,3] 11000100=>[1,1,4,3]=>[1,1,2,1,1,3] 11000101=>[1,1,4,2,1]=>[2,2,1,1,3] 11000110=>[1,1,4,1,2]=>[1,3,1,1,3] 11000111=>[1,1,4,1,1,1]=>[4,1,1,3] 11001000=>[1,1,3,4]=>[1,1,1,2,1,3] 11001001=>[1,1,3,3,1]=>[2,1,2,1,3] 11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 11001011=>[1,1,3,2,1,1]=>[3,2,1,3] 11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 11001101=>[1,1,3,1,2,1]=>[2,3,1,3] 11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 11001111=>[1,1,3,1,1,1,1]=>[5,1,3] 11010000=>[1,1,2,5]=>[1,1,1,1,2,3] 11010001=>[1,1,2,4,1]=>[2,1,1,2,3] 11010010=>[1,1,2,3,2]=>[1,2,1,2,3] 11010011=>[1,1,2,3,1,1]=>[3,1,2,3] 11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 11010101=>[1,1,2,2,2,1]=>[2,2,2,3] 11010110=>[1,1,2,2,1,2]=>[1,3,2,3] 11010111=>[1,1,2,2,1,1,1]=>[4,2,3] 11011000=>[1,1,2,1,4]=>[1,1,1,3,3] 11011001=>[1,1,2,1,3,1]=>[2,1,3,3] 11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 11011011=>[1,1,2,1,2,1,1]=>[3,3,3] 11011100=>[1,1,2,1,1,3]=>[1,1,4,3] 11011101=>[1,1,2,1,1,2,1]=>[2,4,3] 11011110=>[1,1,2,1,1,1,2]=>[1,5,3] 11011111=>[1,1,2,1,1,1,1,1]=>[6,3] 11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 11100001=>[1,1,1,5,1]=>[2,1,1,1,4] 11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 11100011=>[1,1,1,4,1,1]=>[3,1,1,4] 11100100=>[1,1,1,3,3]=>[1,1,2,1,4] 11100101=>[1,1,1,3,2,1]=>[2,2,1,4] 11100110=>[1,1,1,3,1,2]=>[1,3,1,4] 11100111=>[1,1,1,3,1,1,1]=>[4,1,4] 11101000=>[1,1,1,2,4]=>[1,1,1,2,4] 11101001=>[1,1,1,2,3,1]=>[2,1,2,4] 11101010=>[1,1,1,2,2,2]=>[1,2,2,4] 11101011=>[1,1,1,2,2,1,1]=>[3,2,4] 11101100=>[1,1,1,2,1,3]=>[1,1,3,4] 11101101=>[1,1,1,2,1,2,1]=>[2,3,4] 11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 11101111=>[1,1,1,2,1,1,1,1]=>[5,4] 11110000=>[1,1,1,1,5]=>[1,1,1,1,5] 11110001=>[1,1,1,1,4,1]=>[2,1,1,5] 11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 11110011=>[1,1,1,1,3,1,1]=>[3,1,5] 11110100=>[1,1,1,1,2,3]=>[1,1,2,5] 11110101=>[1,1,1,1,2,2,1]=>[2,2,5] 11110110=>[1,1,1,1,2,1,2]=>[1,3,5] 11110111=>[1,1,1,1,2,1,1,1]=>[4,5] 11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 11111001=>[1,1,1,1,1,3,1]=>[2,1,6] 11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 11111011=>[1,1,1,1,1,2,1,1]=>[3,6] 11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 11111101=>[1,1,1,1,1,1,2,1]=>[2,7] 11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11111111=>[1,1,1,1,1,1,1,1,1]=>[9] 000000000=>[10]=>[1,1,1,1,1,1,1,1,1,1] 000000001=>[9,1]=>[2,1,1,1,1,1,1,1,1] 000000010=>[8,2]=>[1,2,1,1,1,1,1,1,1] 000000011=>[8,1,1]=>[3,1,1,1,1,1,1,1] 000000100=>[7,3]=>[1,1,2,1,1,1,1,1,1] 000000101=>[7,2,1]=>[2,2,1,1,1,1,1,1] 000000110=>[7,1,2]=>[1,3,1,1,1,1,1,1] 000000111=>[7,1,1,1]=>[4,1,1,1,1,1,1] 000001000=>[6,4]=>[1,1,1,2,1,1,1,1,1] 000001001=>[6,3,1]=>[2,1,2,1,1,1,1,1] 000001010=>[6,2,2]=>[1,2,2,1,1,1,1,1] 000001011=>[6,2,1,1]=>[3,2,1,1,1,1,1] 000001100=>[6,1,3]=>[1,1,3,1,1,1,1,1] 000001101=>[6,1,2,1]=>[2,3,1,1,1,1,1] 000001110=>[6,1,1,2]=>[1,4,1,1,1,1,1] 000001111=>[6,1,1,1,1]=>[5,1,1,1,1,1] 000010000=>[5,5]=>[1,1,1,1,2,1,1,1,1] 000010001=>[5,4,1]=>[2,1,1,2,1,1,1,1] 000010010=>[5,3,2]=>[1,2,1,2,1,1,1,1] 000010011=>[5,3,1,1]=>[3,1,2,1,1,1,1] 000010100=>[5,2,3]=>[1,1,2,2,1,1,1,1] 000010101=>[5,2,2,1]=>[2,2,2,1,1,1,1] 000010110=>[5,2,1,2]=>[1,3,2,1,1,1,1] 000010111=>[5,2,1,1,1]=>[4,2,1,1,1,1] 000011000=>[5,1,4]=>[1,1,1,3,1,1,1,1] 000011001=>[5,1,3,1]=>[2,1,3,1,1,1,1] 000011010=>[5,1,2,2]=>[1,2,3,1,1,1,1] 000011011=>[5,1,2,1,1]=>[3,3,1,1,1,1] 000011100=>[5,1,1,3]=>[1,1,4,1,1,1,1] 000011101=>[5,1,1,2,1]=>[2,4,1,1,1,1] 000011110=>[5,1,1,1,2]=>[1,5,1,1,1,1] 000011111=>[5,1,1,1,1,1]=>[6,1,1,1,1] 000100000=>[4,6]=>[1,1,1,1,1,2,1,1,1] 000100001=>[4,5,1]=>[2,1,1,1,2,1,1,1] 000100010=>[4,4,2]=>[1,2,1,1,2,1,1,1] 000100011=>[4,4,1,1]=>[3,1,1,2,1,1,1] 000100100=>[4,3,3]=>[1,1,2,1,2,1,1,1] 000100101=>[4,3,2,1]=>[2,2,1,2,1,1,1] 000100110=>[4,3,1,2]=>[1,3,1,2,1,1,1] 000100111=>[4,3,1,1,1]=>[4,1,2,1,1,1] 000101000=>[4,2,4]=>[1,1,1,2,2,1,1,1] 000101001=>[4,2,3,1]=>[2,1,2,2,1,1,1] 000101010=>[4,2,2,2]=>[1,2,2,2,1,1,1] 000101011=>[4,2,2,1,1]=>[3,2,2,1,1,1] 000101100=>[4,2,1,3]=>[1,1,3,2,1,1,1] 000101101=>[4,2,1,2,1]=>[2,3,2,1,1,1] 000101110=>[4,2,1,1,2]=>[1,4,2,1,1,1] 000101111=>[4,2,1,1,1,1]=>[5,2,1,1,1] 000110000=>[4,1,5]=>[1,1,1,1,3,1,1,1] 000110001=>[4,1,4,1]=>[2,1,1,3,1,1,1] 000110010=>[4,1,3,2]=>[1,2,1,3,1,1,1] 000110011=>[4,1,3,1,1]=>[3,1,3,1,1,1] 000110100=>[4,1,2,3]=>[1,1,2,3,1,1,1] 000110101=>[4,1,2,2,1]=>[2,2,3,1,1,1] 000110110=>[4,1,2,1,2]=>[1,3,3,1,1,1] 000110111=>[4,1,2,1,1,1]=>[4,3,1,1,1] 000111000=>[4,1,1,4]=>[1,1,1,4,1,1,1] 000111001=>[4,1,1,3,1]=>[2,1,4,1,1,1] 000111010=>[4,1,1,2,2]=>[1,2,4,1,1,1] 000111011=>[4,1,1,2,1,1]=>[3,4,1,1,1] 000111100=>[4,1,1,1,3]=>[1,1,5,1,1,1] 000111101=>[4,1,1,1,2,1]=>[2,5,1,1,1] 000111110=>[4,1,1,1,1,2]=>[1,6,1,1,1] 000111111=>[4,1,1,1,1,1,1]=>[7,1,1,1] 001000000=>[3,7]=>[1,1,1,1,1,1,2,1,1] 001000001=>[3,6,1]=>[2,1,1,1,1,2,1,1] 001000010=>[3,5,2]=>[1,2,1,1,1,2,1,1] 001000011=>[3,5,1,1]=>[3,1,1,1,2,1,1] 001000100=>[3,4,3]=>[1,1,2,1,1,2,1,1] 001000101=>[3,4,2,1]=>[2,2,1,1,2,1,1] 001000110=>[3,4,1,2]=>[1,3,1,1,2,1,1] 001000111=>[3,4,1,1,1]=>[4,1,1,2,1,1] 001001000=>[3,3,4]=>[1,1,1,2,1,2,1,1] 001001001=>[3,3,3,1]=>[2,1,2,1,2,1,1] 001001010=>[3,3,2,2]=>[1,2,2,1,2,1,1] 001001011=>[3,3,2,1,1]=>[3,2,1,2,1,1] 001001100=>[3,3,1,3]=>[1,1,3,1,2,1,1] 001001101=>[3,3,1,2,1]=>[2,3,1,2,1,1] 001001110=>[3,3,1,1,2]=>[1,4,1,2,1,1] 001001111=>[3,3,1,1,1,1]=>[5,1,2,1,1] 001010000=>[3,2,5]=>[1,1,1,1,2,2,1,1] 001010001=>[3,2,4,1]=>[2,1,1,2,2,1,1] 001010010=>[3,2,3,2]=>[1,2,1,2,2,1,1] 001010011=>[3,2,3,1,1]=>[3,1,2,2,1,1] 001010100=>[3,2,2,3]=>[1,1,2,2,2,1,1] 001010101=>[3,2,2,2,1]=>[2,2,2,2,1,1] 001010110=>[3,2,2,1,2]=>[1,3,2,2,1,1] 001010111=>[3,2,2,1,1,1]=>[4,2,2,1,1] 001011000=>[3,2,1,4]=>[1,1,1,3,2,1,1] 001011001=>[3,2,1,3,1]=>[2,1,3,2,1,1] 001011010=>[3,2,1,2,2]=>[1,2,3,2,1,1] 001011011=>[3,2,1,2,1,1]=>[3,3,2,1,1] 001011100=>[3,2,1,1,3]=>[1,1,4,2,1,1] 001011101=>[3,2,1,1,2,1]=>[2,4,2,1,1] 001011110=>[3,2,1,1,1,2]=>[1,5,2,1,1] 001011111=>[3,2,1,1,1,1,1]=>[6,2,1,1] 001100000=>[3,1,6]=>[1,1,1,1,1,3,1,1] 001100001=>[3,1,5,1]=>[2,1,1,1,3,1,1] 001100010=>[3,1,4,2]=>[1,2,1,1,3,1,1] 001100011=>[3,1,4,1,1]=>[3,1,1,3,1,1] 001100100=>[3,1,3,3]=>[1,1,2,1,3,1,1] 001100101=>[3,1,3,2,1]=>[2,2,1,3,1,1] 001100110=>[3,1,3,1,2]=>[1,3,1,3,1,1] 001100111=>[3,1,3,1,1,1]=>[4,1,3,1,1] 001101000=>[3,1,2,4]=>[1,1,1,2,3,1,1] 001101001=>[3,1,2,3,1]=>[2,1,2,3,1,1] 001101010=>[3,1,2,2,2]=>[1,2,2,3,1,1] 001101011=>[3,1,2,2,1,1]=>[3,2,3,1,1] 001101100=>[3,1,2,1,3]=>[1,1,3,3,1,1] 001101101=>[3,1,2,1,2,1]=>[2,3,3,1,1] 001101110=>[3,1,2,1,1,2]=>[1,4,3,1,1] 001101111=>[3,1,2,1,1,1,1]=>[5,3,1,1] 001110000=>[3,1,1,5]=>[1,1,1,1,4,1,1] 001110001=>[3,1,1,4,1]=>[2,1,1,4,1,1] 001110010=>[3,1,1,3,2]=>[1,2,1,4,1,1] 001110011=>[3,1,1,3,1,1]=>[3,1,4,1,1] 001110100=>[3,1,1,2,3]=>[1,1,2,4,1,1] 001110101=>[3,1,1,2,2,1]=>[2,2,4,1,1] 001110110=>[3,1,1,2,1,2]=>[1,3,4,1,1] 001110111=>[3,1,1,2,1,1,1]=>[4,4,1,1] 001111000=>[3,1,1,1,4]=>[1,1,1,5,1,1] 001111001=>[3,1,1,1,3,1]=>[2,1,5,1,1] 001111010=>[3,1,1,1,2,2]=>[1,2,5,1,1] 001111011=>[3,1,1,1,2,1,1]=>[3,5,1,1] 001111100=>[3,1,1,1,1,3]=>[1,1,6,1,1] 001111101=>[3,1,1,1,1,2,1]=>[2,6,1,1] 001111110=>[3,1,1,1,1,1,2]=>[1,7,1,1] 001111111=>[3,1,1,1,1,1,1,1]=>[8,1,1] 010000000=>[2,8]=>[1,1,1,1,1,1,1,2,1] 010000001=>[2,7,1]=>[2,1,1,1,1,1,2,1] 010000010=>[2,6,2]=>[1,2,1,1,1,1,2,1] 010000011=>[2,6,1,1]=>[3,1,1,1,1,2,1] 010000100=>[2,5,3]=>[1,1,2,1,1,1,2,1] 010000101=>[2,5,2,1]=>[2,2,1,1,1,2,1] 010000110=>[2,5,1,2]=>[1,3,1,1,1,2,1] 010000111=>[2,5,1,1,1]=>[4,1,1,1,2,1] 010001000=>[2,4,4]=>[1,1,1,2,1,1,2,1] 010001001=>[2,4,3,1]=>[2,1,2,1,1,2,1] 010001010=>[2,4,2,2]=>[1,2,2,1,1,2,1] 010001011=>[2,4,2,1,1]=>[3,2,1,1,2,1] 010001100=>[2,4,1,3]=>[1,1,3,1,1,2,1] 010001101=>[2,4,1,2,1]=>[2,3,1,1,2,1] 010001110=>[2,4,1,1,2]=>[1,4,1,1,2,1] 010001111=>[2,4,1,1,1,1]=>[5,1,1,2,1] 010010000=>[2,3,5]=>[1,1,1,1,2,1,2,1] 010010001=>[2,3,4,1]=>[2,1,1,2,1,2,1] 010010010=>[2,3,3,2]=>[1,2,1,2,1,2,1] 010010011=>[2,3,3,1,1]=>[3,1,2,1,2,1] 010010100=>[2,3,2,3]=>[1,1,2,2,1,2,1] 010010101=>[2,3,2,2,1]=>[2,2,2,1,2,1] 010010110=>[2,3,2,1,2]=>[1,3,2,1,2,1] 010010111=>[2,3,2,1,1,1]=>[4,2,1,2,1] 010011000=>[2,3,1,4]=>[1,1,1,3,1,2,1] 010011001=>[2,3,1,3,1]=>[2,1,3,1,2,1] 010011010=>[2,3,1,2,2]=>[1,2,3,1,2,1] 010011011=>[2,3,1,2,1,1]=>[3,3,1,2,1] 010011100=>[2,3,1,1,3]=>[1,1,4,1,2,1] 010011101=>[2,3,1,1,2,1]=>[2,4,1,2,1] 010011110=>[2,3,1,1,1,2]=>[1,5,1,2,1] 010011111=>[2,3,1,1,1,1,1]=>[6,1,2,1] 010100000=>[2,2,6]=>[1,1,1,1,1,2,2,1] 010100001=>[2,2,5,1]=>[2,1,1,1,2,2,1] 010100010=>[2,2,4,2]=>[1,2,1,1,2,2,1] 010100011=>[2,2,4,1,1]=>[3,1,1,2,2,1] 010100100=>[2,2,3,3]=>[1,1,2,1,2,2,1] 010100101=>[2,2,3,2,1]=>[2,2,1,2,2,1] 010100110=>[2,2,3,1,2]=>[1,3,1,2,2,1] 010100111=>[2,2,3,1,1,1]=>[4,1,2,2,1] 010101000=>[2,2,2,4]=>[1,1,1,2,2,2,1] 010101001=>[2,2,2,3,1]=>[2,1,2,2,2,1] 010101010=>[2,2,2,2,2]=>[1,2,2,2,2,1] 010101011=>[2,2,2,2,1,1]=>[3,2,2,2,1] 010101100=>[2,2,2,1,3]=>[1,1,3,2,2,1] 010101101=>[2,2,2,1,2,1]=>[2,3,2,2,1] 010101110=>[2,2,2,1,1,2]=>[1,4,2,2,1] 010101111=>[2,2,2,1,1,1,1]=>[5,2,2,1] 010110000=>[2,2,1,5]=>[1,1,1,1,3,2,1] 010110001=>[2,2,1,4,1]=>[2,1,1,3,2,1] 010110010=>[2,2,1,3,2]=>[1,2,1,3,2,1] 010110011=>[2,2,1,3,1,1]=>[3,1,3,2,1] 010110100=>[2,2,1,2,3]=>[1,1,2,3,2,1] 010110101=>[2,2,1,2,2,1]=>[2,2,3,2,1] 010110110=>[2,2,1,2,1,2]=>[1,3,3,2,1] 010110111=>[2,2,1,2,1,1,1]=>[4,3,2,1] 010111000=>[2,2,1,1,4]=>[1,1,1,4,2,1] 010111001=>[2,2,1,1,3,1]=>[2,1,4,2,1] 010111010=>[2,2,1,1,2,2]=>[1,2,4,2,1] 010111011=>[2,2,1,1,2,1,1]=>[3,4,2,1] 010111100=>[2,2,1,1,1,3]=>[1,1,5,2,1] 010111101=>[2,2,1,1,1,2,1]=>[2,5,2,1] 010111110=>[2,2,1,1,1,1,2]=>[1,6,2,1] 010111111=>[2,2,1,1,1,1,1,1]=>[7,2,1] 011000000=>[2,1,7]=>[1,1,1,1,1,1,3,1] 011000001=>[2,1,6,1]=>[2,1,1,1,1,3,1] 011000010=>[2,1,5,2]=>[1,2,1,1,1,3,1] 011000011=>[2,1,5,1,1]=>[3,1,1,1,3,1] 011000100=>[2,1,4,3]=>[1,1,2,1,1,3,1] 011000101=>[2,1,4,2,1]=>[2,2,1,1,3,1] 011000110=>[2,1,4,1,2]=>[1,3,1,1,3,1] 011000111=>[2,1,4,1,1,1]=>[4,1,1,3,1] 011001000=>[2,1,3,4]=>[1,1,1,2,1,3,1] 011001001=>[2,1,3,3,1]=>[2,1,2,1,3,1] 011001010=>[2,1,3,2,2]=>[1,2,2,1,3,1] 011001011=>[2,1,3,2,1,1]=>[3,2,1,3,1] 011001100=>[2,1,3,1,3]=>[1,1,3,1,3,1] 011001101=>[2,1,3,1,2,1]=>[2,3,1,3,1] 011001110=>[2,1,3,1,1,2]=>[1,4,1,3,1] 011001111=>[2,1,3,1,1,1,1]=>[5,1,3,1] 011010000=>[2,1,2,5]=>[1,1,1,1,2,3,1] 011010001=>[2,1,2,4,1]=>[2,1,1,2,3,1] 011010010=>[2,1,2,3,2]=>[1,2,1,2,3,1] 011010011=>[2,1,2,3,1,1]=>[3,1,2,3,1] 011010100=>[2,1,2,2,3]=>[1,1,2,2,3,1] 011010101=>[2,1,2,2,2,1]=>[2,2,2,3,1] 011010110=>[2,1,2,2,1,2]=>[1,3,2,3,1] 011010111=>[2,1,2,2,1,1,1]=>[4,2,3,1] 011011000=>[2,1,2,1,4]=>[1,1,1,3,3,1] 011011001=>[2,1,2,1,3,1]=>[2,1,3,3,1] 011011010=>[2,1,2,1,2,2]=>[1,2,3,3,1] 011011011=>[2,1,2,1,2,1,1]=>[3,3,3,1] 011011100=>[2,1,2,1,1,3]=>[1,1,4,3,1] 011011101=>[2,1,2,1,1,2,1]=>[2,4,3,1] 011011110=>[2,1,2,1,1,1,2]=>[1,5,3,1] 011011111=>[2,1,2,1,1,1,1,1]=>[6,3,1] 011100000=>[2,1,1,6]=>[1,1,1,1,1,4,1] 011100001=>[2,1,1,5,1]=>[2,1,1,1,4,1] 011100010=>[2,1,1,4,2]=>[1,2,1,1,4,1] 011100011=>[2,1,1,4,1,1]=>[3,1,1,4,1] 011100100=>[2,1,1,3,3]=>[1,1,2,1,4,1] 011100101=>[2,1,1,3,2,1]=>[2,2,1,4,1] 011100110=>[2,1,1,3,1,2]=>[1,3,1,4,1] 011100111=>[2,1,1,3,1,1,1]=>[4,1,4,1] 011101000=>[2,1,1,2,4]=>[1,1,1,2,4,1] 011101001=>[2,1,1,2,3,1]=>[2,1,2,4,1] 011101010=>[2,1,1,2,2,2]=>[1,2,2,4,1] 011101011=>[2,1,1,2,2,1,1]=>[3,2,4,1] 011101100=>[2,1,1,2,1,3]=>[1,1,3,4,1] 011101101=>[2,1,1,2,1,2,1]=>[2,3,4,1] 011101110=>[2,1,1,2,1,1,2]=>[1,4,4,1] 011101111=>[2,1,1,2,1,1,1,1]=>[5,4,1] 011110000=>[2,1,1,1,5]=>[1,1,1,1,5,1] 011110001=>[2,1,1,1,4,1]=>[2,1,1,5,1] 011110010=>[2,1,1,1,3,2]=>[1,2,1,5,1] 011110011=>[2,1,1,1,3,1,1]=>[3,1,5,1] 011110100=>[2,1,1,1,2,3]=>[1,1,2,5,1] 011110101=>[2,1,1,1,2,2,1]=>[2,2,5,1] 011110110=>[2,1,1,1,2,1,2]=>[1,3,5,1] 011110111=>[2,1,1,1,2,1,1,1]=>[4,5,1] 011111000=>[2,1,1,1,1,4]=>[1,1,1,6,1] 011111001=>[2,1,1,1,1,3,1]=>[2,1,6,1] 011111010=>[2,1,1,1,1,2,2]=>[1,2,6,1] 011111011=>[2,1,1,1,1,2,1,1]=>[3,6,1] 011111100=>[2,1,1,1,1,1,3]=>[1,1,7,1] 011111101=>[2,1,1,1,1,1,2,1]=>[2,7,1] 011111110=>[2,1,1,1,1,1,1,2]=>[1,8,1] 011111111=>[2,1,1,1,1,1,1,1,1]=>[9,1] 100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 100000001=>[1,8,1]=>[2,1,1,1,1,1,1,2] 100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 100000011=>[1,7,1,1]=>[3,1,1,1,1,1,2] 100000100=>[1,6,3]=>[1,1,2,1,1,1,1,2] 100000101=>[1,6,2,1]=>[2,2,1,1,1,1,2] 100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 100000111=>[1,6,1,1,1]=>[4,1,1,1,1,2] 100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 100001001=>[1,5,3,1]=>[2,1,2,1,1,1,2] 100001010=>[1,5,2,2]=>[1,2,2,1,1,1,2] 100001011=>[1,5,2,1,1]=>[3,2,1,1,1,2] 100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 100001101=>[1,5,1,2,1]=>[2,3,1,1,1,2] 100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 100001111=>[1,5,1,1,1,1]=>[5,1,1,1,2] 100010000=>[1,4,5]=>[1,1,1,1,2,1,1,2] 100010001=>[1,4,4,1]=>[2,1,1,2,1,1,2] 100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 100010011=>[1,4,3,1,1]=>[3,1,2,1,1,2] 100010100=>[1,4,2,3]=>[1,1,2,2,1,1,2] 100010101=>[1,4,2,2,1]=>[2,2,2,1,1,2] 100010110=>[1,4,2,1,2]=>[1,3,2,1,1,2] 100010111=>[1,4,2,1,1,1]=>[4,2,1,1,2] 100011000=>[1,4,1,4]=>[1,1,1,3,1,1,2] 100011001=>[1,4,1,3,1]=>[2,1,3,1,1,2] 100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 100011011=>[1,4,1,2,1,1]=>[3,3,1,1,2] 100011100=>[1,4,1,1,3]=>[1,1,4,1,1,2] 100011101=>[1,4,1,1,2,1]=>[2,4,1,1,2] 100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 100011111=>[1,4,1,1,1,1,1]=>[6,1,1,2] 100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 100100001=>[1,3,5,1]=>[2,1,1,1,2,1,2] 100100010=>[1,3,4,2]=>[1,2,1,1,2,1,2] 100100011=>[1,3,4,1,1]=>[3,1,1,2,1,2] 100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 100100101=>[1,3,3,2,1]=>[2,2,1,2,1,2] 100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 100100111=>[1,3,3,1,1,1]=>[4,1,2,1,2] 100101000=>[1,3,2,4]=>[1,1,1,2,2,1,2] 100101001=>[1,3,2,3,1]=>[2,1,2,2,1,2] 100101010=>[1,3,2,2,2]=>[1,2,2,2,1,2] 100101011=>[1,3,2,2,1,1]=>[3,2,2,1,2] 100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 100101101=>[1,3,2,1,2,1]=>[2,3,2,1,2] 100101110=>[1,3,2,1,1,2]=>[1,4,2,1,2] 100101111=>[1,3,2,1,1,1,1]=>[5,2,1,2] 100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 100110001=>[1,3,1,4,1]=>[2,1,1,3,1,2] 100110010=>[1,3,1,3,2]=>[1,2,1,3,1,2] 100110011=>[1,3,1,3,1,1]=>[3,1,3,1,2] 100110100=>[1,3,1,2,3]=>[1,1,2,3,1,2] 100110101=>[1,3,1,2,2,1]=>[2,2,3,1,2] 100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 100110111=>[1,3,1,2,1,1,1]=>[4,3,1,2] 100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 100111001=>[1,3,1,1,3,1]=>[2,1,4,1,2] 100111010=>[1,3,1,1,2,2]=>[1,2,4,1,2] 100111011=>[1,3,1,1,2,1,1]=>[3,4,1,2] 100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 100111101=>[1,3,1,1,1,2,1]=>[2,5,1,2] 100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 100111111=>[1,3,1,1,1,1,1,1]=>[7,1,2] 101000000=>[1,2,7]=>[1,1,1,1,1,1,2,2] 101000001=>[1,2,6,1]=>[2,1,1,1,1,2,2] 101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 101000011=>[1,2,5,1,1]=>[3,1,1,1,2,2] 101000100=>[1,2,4,3]=>[1,1,2,1,1,2,2] 101000101=>[1,2,4,2,1]=>[2,2,1,1,2,2] 101000110=>[1,2,4,1,2]=>[1,3,1,1,2,2] 101000111=>[1,2,4,1,1,1]=>[4,1,1,2,2] 101001000=>[1,2,3,4]=>[1,1,1,2,1,2,2] 101001001=>[1,2,3,3,1]=>[2,1,2,1,2,2] 101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 101001011=>[1,2,3,2,1,1]=>[3,2,1,2,2] 101001100=>[1,2,3,1,3]=>[1,1,3,1,2,2] 101001101=>[1,2,3,1,2,1]=>[2,3,1,2,2] 101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 101001111=>[1,2,3,1,1,1,1]=>[5,1,2,2] 101010000=>[1,2,2,5]=>[1,1,1,1,2,2,2] 101010001=>[1,2,2,4,1]=>[2,1,1,2,2,2] 101010010=>[1,2,2,3,2]=>[1,2,1,2,2,2] 101010011=>[1,2,2,3,1,1]=>[3,1,2,2,2] 101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 101010101=>[1,2,2,2,2,1]=>[2,2,2,2,2] 101010110=>[1,2,2,2,1,2]=>[1,3,2,2,2] 101010111=>[1,2,2,2,1,1,1]=>[4,2,2,2] 101011000=>[1,2,2,1,4]=>[1,1,1,3,2,2] 101011001=>[1,2,2,1,3,1]=>[2,1,3,2,2] 101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 101011011=>[1,2,2,1,2,1,1]=>[3,3,2,2] 101011100=>[1,2,2,1,1,3]=>[1,1,4,2,2] 101011101=>[1,2,2,1,1,2,1]=>[2,4,2,2] 101011110=>[1,2,2,1,1,1,2]=>[1,5,2,2] 101011111=>[1,2,2,1,1,1,1,1]=>[6,2,2] 101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 101100001=>[1,2,1,5,1]=>[2,1,1,1,3,2] 101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 101100011=>[1,2,1,4,1,1]=>[3,1,1,3,2] 101100100=>[1,2,1,3,3]=>[1,1,2,1,3,2] 101100101=>[1,2,1,3,2,1]=>[2,2,1,3,2] 101100110=>[1,2,1,3,1,2]=>[1,3,1,3,2] 101100111=>[1,2,1,3,1,1,1]=>[4,1,3,2] 101101000=>[1,2,1,2,4]=>[1,1,1,2,3,2] 101101001=>[1,2,1,2,3,1]=>[2,1,2,3,2] 101101010=>[1,2,1,2,2,2]=>[1,2,2,3,2] 101101011=>[1,2,1,2,2,1,1]=>[3,2,3,2] 101101100=>[1,2,1,2,1,3]=>[1,1,3,3,2] 101101101=>[1,2,1,2,1,2,1]=>[2,3,3,2] 101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 101101111=>[1,2,1,2,1,1,1,1]=>[5,3,2] 101110000=>[1,2,1,1,5]=>[1,1,1,1,4,2] 101110001=>[1,2,1,1,4,1]=>[2,1,1,4,2] 101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 101110011=>[1,2,1,1,3,1,1]=>[3,1,4,2] 101110100=>[1,2,1,1,2,3]=>[1,1,2,4,2] 101110101=>[1,2,1,1,2,2,1]=>[2,2,4,2] 101110110=>[1,2,1,1,2,1,2]=>[1,3,4,2] 101110111=>[1,2,1,1,2,1,1,1]=>[4,4,2] 101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 101111001=>[1,2,1,1,1,3,1]=>[2,1,5,2] 101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 101111011=>[1,2,1,1,1,2,1,1]=>[3,5,2] 101111100=>[1,2,1,1,1,1,3]=>[1,1,6,2] 101111101=>[1,2,1,1,1,1,2,1]=>[2,6,2] 101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 101111111=>[1,2,1,1,1,1,1,1,1]=>[8,2] 110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 110000001=>[1,1,7,1]=>[2,1,1,1,1,1,3] 110000010=>[1,1,6,2]=>[1,2,1,1,1,1,3] 110000011=>[1,1,6,1,1]=>[3,1,1,1,1,3] 110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 110000101=>[1,1,5,2,1]=>[2,2,1,1,1,3] 110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 110000111=>[1,1,5,1,1,1]=>[4,1,1,1,3] 110001000=>[1,1,4,4]=>[1,1,1,2,1,1,3] 110001001=>[1,1,4,3,1]=>[2,1,2,1,1,3] 110001010=>[1,1,4,2,2]=>[1,2,2,1,1,3] 110001011=>[1,1,4,2,1,1]=>[3,2,1,1,3] 110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 110001101=>[1,1,4,1,2,1]=>[2,3,1,1,3] 110001110=>[1,1,4,1,1,2]=>[1,4,1,1,3] 110001111=>[1,1,4,1,1,1,1]=>[5,1,1,3] 110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 110010001=>[1,1,3,4,1]=>[2,1,1,2,1,3] 110010010=>[1,1,3,3,2]=>[1,2,1,2,1,3] 110010011=>[1,1,3,3,1,1]=>[3,1,2,1,3] 110010100=>[1,1,3,2,3]=>[1,1,2,2,1,3] 110010101=>[1,1,3,2,2,1]=>[2,2,2,1,3] 110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 110010111=>[1,1,3,2,1,1,1]=>[4,2,1,3] 110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 110011001=>[1,1,3,1,3,1]=>[2,1,3,1,3] 110011010=>[1,1,3,1,2,2]=>[1,2,3,1,3] 110011011=>[1,1,3,1,2,1,1]=>[3,3,1,3] 110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 110011101=>[1,1,3,1,1,2,1]=>[2,4,1,3] 110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 110011111=>[1,1,3,1,1,1,1,1]=>[6,1,3] 110100000=>[1,1,2,6]=>[1,1,1,1,1,2,3] 110100001=>[1,1,2,5,1]=>[2,1,1,1,2,3] 110100010=>[1,1,2,4,2]=>[1,2,1,1,2,3] 110100011=>[1,1,2,4,1,1]=>[3,1,1,2,3] 110100100=>[1,1,2,3,3]=>[1,1,2,1,2,3] 110100101=>[1,1,2,3,2,1]=>[2,2,1,2,3] 110100110=>[1,1,2,3,1,2]=>[1,3,1,2,3] 110100111=>[1,1,2,3,1,1,1]=>[4,1,2,3] 110101000=>[1,1,2,2,4]=>[1,1,1,2,2,3] 110101001=>[1,1,2,2,3,1]=>[2,1,2,2,3] 110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 110101011=>[1,1,2,2,2,1,1]=>[3,2,2,3] 110101100=>[1,1,2,2,1,3]=>[1,1,3,2,3] 110101101=>[1,1,2,2,1,2,1]=>[2,3,2,3] 110101110=>[1,1,2,2,1,1,2]=>[1,4,2,3] 110101111=>[1,1,2,2,1,1,1,1]=>[5,2,3] 110110000=>[1,1,2,1,5]=>[1,1,1,1,3,3] 110110001=>[1,1,2,1,4,1]=>[2,1,1,3,3] 110110010=>[1,1,2,1,3,2]=>[1,2,1,3,3] 110110011=>[1,1,2,1,3,1,1]=>[3,1,3,3] 110110100=>[1,1,2,1,2,3]=>[1,1,2,3,3] 110110101=>[1,1,2,1,2,2,1]=>[2,2,3,3] 110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 110110111=>[1,1,2,1,2,1,1,1]=>[4,3,3] 110111000=>[1,1,2,1,1,4]=>[1,1,1,4,3] 110111001=>[1,1,2,1,1,3,1]=>[2,1,4,3] 110111010=>[1,1,2,1,1,2,2]=>[1,2,4,3] 110111011=>[1,1,2,1,1,2,1,1]=>[3,4,3] 110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 110111101=>[1,1,2,1,1,1,2,1]=>[2,5,3] 110111110=>[1,1,2,1,1,1,1,2]=>[1,6,3] 110111111=>[1,1,2,1,1,1,1,1,1]=>[7,3] 111000000=>[1,1,1,7]=>[1,1,1,1,1,1,4] 111000001=>[1,1,1,6,1]=>[2,1,1,1,1,4] 111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 111000011=>[1,1,1,5,1,1]=>[3,1,1,1,4] 111000100=>[1,1,1,4,3]=>[1,1,2,1,1,4] 111000101=>[1,1,1,4,2,1]=>[2,2,1,1,4] 111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 111000111=>[1,1,1,4,1,1,1]=>[4,1,1,4] 111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 111001001=>[1,1,1,3,3,1]=>[2,1,2,1,4] 111001010=>[1,1,1,3,2,2]=>[1,2,2,1,4] 111001011=>[1,1,1,3,2,1,1]=>[3,2,1,4] 111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 111001101=>[1,1,1,3,1,2,1]=>[2,3,1,4] 111001110=>[1,1,1,3,1,1,2]=>[1,4,1,4] 111001111=>[1,1,1,3,1,1,1,1]=>[5,1,4] 111010000=>[1,1,1,2,5]=>[1,1,1,1,2,4] 111010001=>[1,1,1,2,4,1]=>[2,1,1,2,4] 111010010=>[1,1,1,2,3,2]=>[1,2,1,2,4] 111010011=>[1,1,1,2,3,1,1]=>[3,1,2,4] 111010100=>[1,1,1,2,2,3]=>[1,1,2,2,4] 111010101=>[1,1,1,2,2,2,1]=>[2,2,2,4] 111010110=>[1,1,1,2,2,1,2]=>[1,3,2,4] 111010111=>[1,1,1,2,2,1,1,1]=>[4,2,4] 111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 111011001=>[1,1,1,2,1,3,1]=>[2,1,3,4] 111011010=>[1,1,1,2,1,2,2]=>[1,2,3,4] 111011011=>[1,1,1,2,1,2,1,1]=>[3,3,4] 111011100=>[1,1,1,2,1,1,3]=>[1,1,4,4] 111011101=>[1,1,1,2,1,1,2,1]=>[2,4,4] 111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 111011111=>[1,1,1,2,1,1,1,1,1]=>[6,4] 111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 111100001=>[1,1,1,1,5,1]=>[2,1,1,1,5] 111100010=>[1,1,1,1,4,2]=>[1,2,1,1,5] 111100011=>[1,1,1,1,4,1,1]=>[3,1,1,5] 111100100=>[1,1,1,1,3,3]=>[1,1,2,1,5] 111100101=>[1,1,1,1,3,2,1]=>[2,2,1,5] 111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 111100111=>[1,1,1,1,3,1,1,1]=>[4,1,5] 111101000=>[1,1,1,1,2,4]=>[1,1,1,2,5] 111101001=>[1,1,1,1,2,3,1]=>[2,1,2,5] 111101010=>[1,1,1,1,2,2,2]=>[1,2,2,5] 111101011=>[1,1,1,1,2,2,1,1]=>[3,2,5] 111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 111101101=>[1,1,1,1,2,1,2,1]=>[2,3,5] 111101110=>[1,1,1,1,2,1,1,2]=>[1,4,5] 111101111=>[1,1,1,1,2,1,1,1,1]=>[5,5] 111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 111110001=>[1,1,1,1,1,4,1]=>[2,1,1,6] 111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 111110011=>[1,1,1,1,1,3,1,1]=>[3,1,6] 111110100=>[1,1,1,1,1,2,3]=>[1,1,2,6] 111110101=>[1,1,1,1,1,2,2,1]=>[2,2,6] 111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 111110111=>[1,1,1,1,1,2,1,1,1]=>[4,6] 111111000=>[1,1,1,1,1,1,4]=>[1,1,1,7] 111111001=>[1,1,1,1,1,1,3,1]=>[2,1,7] 111111010=>[1,1,1,1,1,1,2,2]=>[1,2,7] 111111011=>[1,1,1,1,1,1,2,1,1]=>[3,7] 111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 111111101=>[1,1,1,1,1,1,1,2,1]=>[2,8] 111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111111111=>[1,1,1,1,1,1,1,1,1,1]=>[10] 1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 1010101100=>[1,2,2,2,1,3]=>[1,1,3,2,2,2] 1010110010=>[1,2,2,1,3,2]=>[1,2,1,3,2,2] 1010110100=>[1,2,2,1,2,3]=>[1,1,2,3,2,2] 1010111000=>[1,2,2,1,1,4]=>[1,1,1,4,2,2] 1011001010=>[1,2,1,3,2,2]=>[1,2,2,1,3,2] 1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] 1011010010=>[1,2,1,2,3,2]=>[1,2,1,2,3,2] 1011010100=>[1,2,1,2,2,3]=>[1,1,2,2,3,2] 1011011000=>[1,2,1,2,1,4]=>[1,1,1,3,3,2] 1011100010=>[1,2,1,1,4,2]=>[1,2,1,1,4,2] 1011100100=>[1,2,1,1,3,3]=>[1,1,2,1,4,2] 1011101000=>[1,2,1,1,2,4]=>[1,1,1,2,4,2] 1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 1100101010=>[1,1,3,2,2,2]=>[1,2,2,2,1,3] 1100101100=>[1,1,3,2,1,3]=>[1,1,3,2,1,3] 1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] 1100110100=>[1,1,3,1,2,3]=>[1,1,2,3,1,3] 1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 1101001010=>[1,1,2,3,2,2]=>[1,2,2,1,2,3] 1101001100=>[1,1,2,3,1,3]=>[1,1,3,1,2,3] 1101010010=>[1,1,2,2,3,2]=>[1,2,1,2,2,3] 1101010100=>[1,1,2,2,2,3]=>[1,1,2,2,2,3] 1101011000=>[1,1,2,2,1,4]=>[1,1,1,3,2,3] 1101100010=>[1,1,2,1,4,2]=>[1,2,1,1,3,3] 1101100100=>[1,1,2,1,3,3]=>[1,1,2,1,3,3] 1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 1101110000=>[1,1,2,1,1,5]=>[1,1,1,1,4,3] 1110001010=>[1,1,1,4,2,2]=>[1,2,2,1,1,4] 1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 1110010010=>[1,1,1,3,3,2]=>[1,2,1,2,1,4] 1110010100=>[1,1,1,3,2,3]=>[1,1,2,2,1,4] 1110011000=>[1,1,1,3,1,4]=>[1,1,1,3,1,4] 1110100010=>[1,1,1,2,4,2]=>[1,2,1,1,2,4] 1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 1110101000=>[1,1,1,2,2,4]=>[1,1,1,2,2,4] 1110110000=>[1,1,1,2,1,5]=>[1,1,1,1,3,4] 1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 1111000100=>[1,1,1,1,4,3]=>[1,1,2,1,1,5] 1111001000=>[1,1,1,1,3,4]=>[1,1,1,2,1,5] 1111010000=>[1,1,1,1,2,5]=>[1,1,1,1,2,5] 1111100000=>[1,1,1,1,1,6]=>[1,1,1,1,1,6] 101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] 101010101100=>[1,2,2,2,2,1,3]=>[1,1,3,2,2,2,2] 101010110010=>[1,2,2,2,1,3,2]=>[1,2,1,3,2,2,2] 101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 101010111000=>[1,2,2,2,1,1,4]=>[1,1,1,4,2,2,2] 101011001010=>[1,2,2,1,3,2,2]=>[1,2,2,1,3,2,2] 101011001100=>[1,2,2,1,3,1,3]=>[1,1,3,1,3,2,2] 101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 101011010100=>[1,2,2,1,2,2,3]=>[1,1,2,2,3,2,2] 101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 101011100010=>[1,2,2,1,1,4,2]=>[1,2,1,1,4,2,2] 101011100100=>[1,2,2,1,1,3,3]=>[1,1,2,1,4,2,2] 101011101000=>[1,2,2,1,1,2,4]=>[1,1,1,2,4,2,2] 101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 101100101010=>[1,2,1,3,2,2,2]=>[1,2,2,2,1,3,2] 101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 101100110010=>[1,2,1,3,1,3,2]=>[1,2,1,3,1,3,2] 101100110100=>[1,2,1,3,1,2,3]=>[1,1,2,3,1,3,2] 101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 101101001100=>[1,2,1,2,3,1,3]=>[1,1,3,1,2,3,2] 101101010010=>[1,2,1,2,2,3,2]=>[1,2,1,2,2,3,2] 101101010100=>[1,2,1,2,2,2,3]=>[1,1,2,2,2,3,2] 101101011000=>[1,2,1,2,2,1,4]=>[1,1,1,3,2,3,2] 101101100010=>[1,2,1,2,1,4,2]=>[1,2,1,1,3,3,2] 101101100100=>[1,2,1,2,1,3,3]=>[1,1,2,1,3,3,2] 101101101000=>[1,2,1,2,1,2,4]=>[1,1,1,2,3,3,2] 101101110000=>[1,2,1,2,1,1,5]=>[1,1,1,1,4,3,2] 101110001010=>[1,2,1,1,4,2,2]=>[1,2,2,1,1,4,2] 101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 101110010010=>[1,2,1,1,3,3,2]=>[1,2,1,2,1,4,2] 101110010100=>[1,2,1,1,3,2,3]=>[1,1,2,2,1,4,2] 101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 101110100010=>[1,2,1,1,2,4,2]=>[1,2,1,1,2,4,2] 101110100100=>[1,2,1,1,2,3,3]=>[1,1,2,1,2,4,2] 101110101000=>[1,2,1,1,2,2,4]=>[1,1,1,2,2,4,2] 101110110000=>[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] 101111000010=>[1,2,1,1,1,5,2]=>[1,2,1,1,1,5,2] 101111000100=>[1,2,1,1,1,4,3]=>[1,1,2,1,1,5,2] 101111001000=>[1,2,1,1,1,3,4]=>[1,1,1,2,1,5,2] 101111010000=>[1,2,1,1,1,2,5]=>[1,1,1,1,2,5,2] 101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 110010101010=>[1,1,3,2,2,2,2]=>[1,2,2,2,2,1,3] 110010101100=>[1,1,3,2,2,1,3]=>[1,1,3,2,2,1,3] 110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 110010110100=>[1,1,3,2,1,2,3]=>[1,1,2,3,2,1,3] 110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 110011001010=>[1,1,3,1,3,2,2]=>[1,2,2,1,3,1,3] 110011001100=>[1,1,3,1,3,1,3]=>[1,1,3,1,3,1,3] 110011010010=>[1,1,3,1,2,3,2]=>[1,2,1,2,3,1,3] 110011010100=>[1,1,3,1,2,2,3]=>[1,1,2,2,3,1,3] 110011011000=>[1,1,3,1,2,1,4]=>[1,1,1,3,3,1,3] 110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 110011100100=>[1,1,3,1,1,3,3]=>[1,1,2,1,4,1,3] 110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] 110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 110100101100=>[1,1,2,3,2,1,3]=>[1,1,3,2,1,2,3] 110100110010=>[1,1,2,3,1,3,2]=>[1,2,1,3,1,2,3] 110100110100=>[1,1,2,3,1,2,3]=>[1,1,2,3,1,2,3] 110100111000=>[1,1,2,3,1,1,4]=>[1,1,1,4,1,2,3] 110101001010=>[1,1,2,2,3,2,2]=>[1,2,2,1,2,2,3] 110101001100=>[1,1,2,2,3,1,3]=>[1,1,3,1,2,2,3] 110101010010=>[1,1,2,2,2,3,2]=>[1,2,1,2,2,2,3] 110101010100=>[1,1,2,2,2,2,3]=>[1,1,2,2,2,2,3] 110101011000=>[1,1,2,2,2,1,4]=>[1,1,1,3,2,2,3] 110101100010=>[1,1,2,2,1,4,2]=>[1,2,1,1,3,2,3] 110101100100=>[1,1,2,2,1,3,3]=>[1,1,2,1,3,2,3] 110101101000=>[1,1,2,2,1,2,4]=>[1,1,1,2,3,2,3] 110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 110110001010=>[1,1,2,1,4,2,2]=>[1,2,2,1,1,3,3] 110110001100=>[1,1,2,1,4,1,3]=>[1,1,3,1,1,3,3] 110110010010=>[1,1,2,1,3,3,2]=>[1,2,1,2,1,3,3] 110110010100=>[1,1,2,1,3,2,3]=>[1,1,2,2,1,3,3] 110110011000=>[1,1,2,1,3,1,4]=>[1,1,1,3,1,3,3] 110110100010=>[1,1,2,1,2,4,2]=>[1,2,1,1,2,3,3] 110110100100=>[1,1,2,1,2,3,3]=>[1,1,2,1,2,3,3] 110110101000=>[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] 110110110000=>[1,1,2,1,2,1,5]=>[1,1,1,1,3,3,3] 110111000010=>[1,1,2,1,1,5,2]=>[1,2,1,1,1,4,3] 110111000100=>[1,1,2,1,1,4,3]=>[1,1,2,1,1,4,3] 110111001000=>[1,1,2,1,1,3,4]=>[1,1,1,2,1,4,3] 110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 110111100000=>[1,1,2,1,1,1,6]=>[1,1,1,1,1,5,3] 111000101010=>[1,1,1,4,2,2,2]=>[1,2,2,2,1,1,4] 111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] 111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] 111000110100=>[1,1,1,4,1,2,3]=>[1,1,2,3,1,1,4] 111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] 111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 111001001100=>[1,1,1,3,3,1,3]=>[1,1,3,1,2,1,4] 111001010010=>[1,1,1,3,2,3,2]=>[1,2,1,2,2,1,4] 111001010100=>[1,1,1,3,2,2,3]=>[1,1,2,2,2,1,4] 111001011000=>[1,1,1,3,2,1,4]=>[1,1,1,3,2,1,4] 111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] 111001100100=>[1,1,1,3,1,3,3]=>[1,1,2,1,3,1,4] 111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 111001110000=>[1,1,1,3,1,1,5]=>[1,1,1,1,4,1,4] 111010001010=>[1,1,1,2,4,2,2]=>[1,2,2,1,1,2,4] 111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 111010010010=>[1,1,1,2,3,3,2]=>[1,2,1,2,1,2,4] 111010010100=>[1,1,1,2,3,2,3]=>[1,1,2,2,1,2,4] 111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 111010100010=>[1,1,1,2,2,4,2]=>[1,2,1,1,2,2,4] 111010100100=>[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] 111010101000=>[1,1,1,2,2,2,4]=>[1,1,1,2,2,2,4] 111010110000=>[1,1,1,2,2,1,5]=>[1,1,1,1,3,2,4] 111011000010=>[1,1,1,2,1,5,2]=>[1,2,1,1,1,3,4] 111011000100=>[1,1,1,2,1,4,3]=>[1,1,2,1,1,3,4] 111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 111011010000=>[1,1,1,2,1,2,5]=>[1,1,1,1,2,3,4] 111011100000=>[1,1,1,2,1,1,6]=>[1,1,1,1,1,4,4] 111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] 111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] 111100010010=>[1,1,1,1,4,3,2]=>[1,2,1,2,1,1,5] 111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 111100011000=>[1,1,1,1,4,1,4]=>[1,1,1,3,1,1,5] 111100100010=>[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] 111100100100=>[1,1,1,1,3,3,3]=>[1,1,2,1,2,1,5] 111100101000=>[1,1,1,1,3,2,4]=>[1,1,1,2,2,1,5] 111100110000=>[1,1,1,1,3,1,5]=>[1,1,1,1,3,1,5] 111101000010=>[1,1,1,1,2,5,2]=>[1,2,1,1,1,2,5] 111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 111101001000=>[1,1,1,1,2,3,4]=>[1,1,1,2,1,2,5] 111101010000=>[1,1,1,1,2,2,5]=>[1,1,1,1,2,2,5] 111101100000=>[1,1,1,1,2,1,6]=>[1,1,1,1,1,3,5] 111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 111110000100=>[1,1,1,1,1,5,3]=>[1,1,2,1,1,1,6] 111110001000=>[1,1,1,1,1,4,4]=>[1,1,1,2,1,1,6] 111110010000=>[1,1,1,1,1,3,5]=>[1,1,1,1,2,1,6] 111110100000=>[1,1,1,1,1,2,6]=>[1,1,1,1,1,2,6] 111111000000=>[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7] 1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10] 1101111110=>[1,1,2,1,1,1,1,1,2]=>[1,7,3] 1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1010111110=>[1,2,2,1,1,1,1,2]=>[1,6,2,2] 1001111110=>[1,3,1,1,1,1,1,2]=>[1,7,1,2] 1001011110=>[1,3,2,1,1,1,2]=>[1,5,2,1,2] 1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 1000101110=>[1,4,2,1,1,2]=>[1,4,2,1,1,2] 1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2] 1000010110=>[1,5,2,1,2]=>[1,3,2,1,1,1,2] 1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2] 1000001010=>[1,6,2,2]=>[1,2,2,1,1,1,1,2] 1000000110=>[1,7,1,2]=>[1,3,1,1,1,1,1,2] 1000000101=>[1,7,2,1]=>[2,2,1,1,1,1,1,2] 1000000100=>[1,7,3]=>[1,1,2,1,1,1,1,1,2] 1000000011=>[1,8,1,1]=>[3,1,1,1,1,1,1,2] 1000000010=>[1,8,2]=>[1,2,1,1,1,1,1,1,2] 1000000000=>[1,10]=>[1,1,1,1,1,1,1,1,1,2] 10000000000=>[1,11]=>[1,1,1,1,1,1,1,1,1,1,2] 10000000010=>[1,9,2]=>[1,2,1,1,1,1,1,1,1,2] 10000000110=>[1,8,1,2]=>[1,3,1,1,1,1,1,1,2] 10000001110=>[1,7,1,1,2]=>[1,4,1,1,1,1,1,2] 10000011110=>[1,6,1,1,1,2]=>[1,5,1,1,1,1,2] 10000111110=>[1,5,1,1,1,1,2]=>[1,6,1,1,1,2] 10001111110=>[1,4,1,1,1,1,1,2]=>[1,7,1,1,2] 10011111110=>[1,3,1,1,1,1,1,1,2]=>[1,8,1,2] 10111111110=>[1,2,1,1,1,1,1,1,1,2]=>[1,9,2] 11111111110=>[1,1,1,1,1,1,1,1,1,1,2]=>[1,11] 0000000001=>[10,1]=>[2,1,1,1,1,1,1,1,1,1] 0000000000=>[11]=>[1,1,1,1,1,1,1,1,1,1,1] 01111111110=>[2,1,1,1,1,1,1,1,1,2]=>[1,10,1] 10101010101=>[1,2,2,2,2,2,1]=>[2,2,2,2,2,2] 11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[12] 00101111110=>[3,2,1,1,1,1,1,2]=>[1,7,2,1,1] 00111011110=>[3,1,1,2,1,1,1,2]=>[1,5,4,1,1] 00111110110=>[3,1,1,1,1,2,1,2]=>[1,3,6,1,1] 00111111100=>[3,1,1,1,1,1,1,3]=>[1,1,8,1,1]