=>

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] 1111111111=>[1,1,1,1,1,1,1,1,1,1,1]=>[11] 1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10] 1111111101=>[1,1,1,1,1,1,1,1,2,1]=>[2,9] 1111111100=>[1,1,1,1,1,1,1,1,3]=>[1,1,9] 1111111011=>[1,1,1,1,1,1,1,2,1,1]=>[3,8] 1111111001=>[1,1,1,1,1,1,1,3,1]=>[2,1,8] 1111110110=>[1,1,1,1,1,1,2,1,2]=>[1,3,7] 1111110101=>[1,1,1,1,1,1,2,2,1]=>[2,2,7] 1111110011=>[1,1,1,1,1,1,3,1,1]=>[3,1,7] 1111110010=>[1,1,1,1,1,1,3,2]=>[1,2,1,7] 1111110001=>[1,1,1,1,1,1,4,1]=>[2,1,1,7] 1111101110=>[1,1,1,1,1,2,1,1,2]=>[1,4,6] 1111101101=>[1,1,1,1,1,2,1,2,1]=>[2,3,6] 1111101011=>[1,1,1,1,1,2,2,1,1]=>[3,2,6] 1111101010=>[1,1,1,1,1,2,2,2]=>[1,2,2,6] 1111101001=>[1,1,1,1,1,2,3,1]=>[2,1,2,6] 1111100111=>[1,1,1,1,1,3,1,1,1]=>[4,1,6] 1111100001=>[1,1,1,1,1,5,1]=>[2,1,1,1,6] 1111011110=>[1,1,1,1,2,1,1,1,2]=>[1,5,5] 1111011011=>[1,1,1,1,2,1,2,1,1]=>[3,3,5] 1111010101=>[1,1,1,1,2,2,2,1]=>[2,2,2,5] 1111010100=>[1,1,1,1,2,2,3]=>[1,1,2,2,5] 1111010010=>[1,1,1,1,2,3,2]=>[1,2,1,2,5] 1111010001=>[1,1,1,1,2,4,1]=>[2,1,1,2,5] 1111001111=>[1,1,1,1,3,1,1,1,1]=>[5,1,5] 1111001100=>[1,1,1,1,3,1,3]=>[1,1,3,1,5] 1111000110=>[1,1,1,1,4,1,2]=>[1,3,1,1,5] 1111000001=>[1,1,1,1,6,1]=>[2,1,1,1,1,5] 1110111111=>[1,1,1,2,1,1,1,1,1,1]=>[7,4] 1110111110=>[1,1,1,2,1,1,1,1,2]=>[1,6,4] 1110111101=>[1,1,1,2,1,1,1,2,1]=>[2,5,4] 1110110111=>[1,1,1,2,1,2,1,1,1]=>[4,3,4] 1110110001=>[1,1,1,2,1,4,1]=>[2,1,1,3,4] 1110101011=>[1,1,1,2,2,2,1,1]=>[3,2,2,4] 1110101010=>[1,1,1,2,2,2,2]=>[1,2,2,2,4] 1110100101=>[1,1,1,2,3,2,1]=>[2,2,1,2,4] 1110100001=>[1,1,1,2,5,1]=>[2,1,1,1,2,4] 1110011111=>[1,1,1,3,1,1,1,1,1]=>[6,1,4] 1110011110=>[1,1,1,3,1,1,1,2]=>[1,5,1,4] 1110011001=>[1,1,1,3,1,3,1]=>[2,1,3,1,4] 1110010001=>[1,1,1,3,4,1]=>[2,1,1,2,1,4] 1110001101=>[1,1,1,4,1,2,1]=>[2,3,1,1,4] 1110001001=>[1,1,1,4,3,1]=>[2,1,2,1,1,4] 1110000111=>[1,1,1,5,1,1,1]=>[4,1,1,1,4] 1110000110=>[1,1,1,5,1,2]=>[1,3,1,1,1,4] 1110000101=>[1,1,1,5,2,1]=>[2,2,1,1,1,4] 1110000011=>[1,1,1,6,1,1]=>[3,1,1,1,1,4] 1110000001=>[1,1,1,7,1]=>[2,1,1,1,1,1,4] 1101111111=>[1,1,2,1,1,1,1,1,1,1]=>[8,3] 1101111110=>[1,1,2,1,1,1,1,1,2]=>[1,7,3] 1101111011=>[1,1,2,1,1,1,2,1,1]=>[3,5,3] 1101111001=>[1,1,2,1,1,1,3,1]=>[2,1,5,3] 1101101111=>[1,1,2,1,2,1,1,1,1]=>[5,3,3] 1101101100=>[1,1,2,1,2,1,3]=>[1,1,3,3,3] 1101101011=>[1,1,2,1,2,2,1,1]=>[3,2,3,3] 1101100110=>[1,1,2,1,3,1,2]=>[1,3,1,3,3] 1101100011=>[1,1,2,1,4,1,1]=>[3,1,1,3,3] 1101100001=>[1,1,2,1,5,1]=>[2,1,1,1,3,3] 1101011111=>[1,1,2,2,1,1,1,1,1]=>[6,2,3] 1101011011=>[1,1,2,2,1,2,1,1]=>[3,3,2,3] 1101010111=>[1,1,2,2,2,1,1,1]=>[4,2,2,3] 1101010101=>[1,1,2,2,2,2,1]=>[2,2,2,2,3] 1101010011=>[1,1,2,2,3,1,1]=>[3,1,2,2,3] 1101010001=>[1,1,2,2,4,1]=>[2,1,1,2,2,3] 1101001110=>[1,1,2,3,1,1,2]=>[1,4,1,2,3] 1101001101=>[1,1,2,3,1,2,1]=>[2,3,1,2,3] 1101001011=>[1,1,2,3,2,1,1]=>[3,2,1,2,3] 1101001001=>[1,1,2,3,3,1]=>[2,1,2,1,2,3] 1101001000=>[1,1,2,3,4]=>[1,1,1,2,1,2,3] 1101000111=>[1,1,2,4,1,1,1]=>[4,1,1,2,3] 1101000110=>[1,1,2,4,1,2]=>[1,3,1,1,2,3] 1101000101=>[1,1,2,4,2,1]=>[2,2,1,1,2,3] 1101000011=>[1,1,2,5,1,1]=>[3,1,1,1,2,3] 1101000001=>[1,1,2,6,1]=>[2,1,1,1,1,2,3] 1100111111=>[1,1,3,1,1,1,1,1,1]=>[7,1,3] 1100111100=>[1,1,3,1,1,1,3]=>[1,1,5,1,3] 1100110110=>[1,1,3,1,2,1,2]=>[1,3,3,1,3] 1100110101=>[1,1,3,1,2,2,1]=>[2,2,3,1,3] 1100110011=>[1,1,3,1,3,1,1]=>[3,1,3,1,3] 1100110001=>[1,1,3,1,4,1]=>[2,1,1,3,1,3] 1100101101=>[1,1,3,2,1,2,1]=>[2,3,2,1,3] 1100101011=>[1,1,3,2,2,1,1]=>[3,2,2,1,3] 1100101001=>[1,1,3,2,3,1]=>[2,1,2,2,1,3] 1100100111=>[1,1,3,3,1,1,1]=>[4,1,2,1,3] 1100100110=>[1,1,3,3,1,2]=>[1,3,1,2,1,3] 1100100101=>[1,1,3,3,2,1]=>[2,2,1,2,1,3] 1100011110=>[1,1,4,1,1,1,2]=>[1,5,1,1,3] 1100011101=>[1,1,4,1,1,2,1]=>[2,4,1,1,3] 1100011011=>[1,1,4,1,2,1,1]=>[3,3,1,1,3] 1100011001=>[1,1,4,1,3,1]=>[2,1,3,1,1,3] 1100011000=>[1,1,4,1,4]=>[1,1,1,3,1,1,3] 1100010111=>[1,1,4,2,1,1,1]=>[4,2,1,1,3] 1100010101=>[1,1,4,2,2,1]=>[2,2,2,1,1,3] 1100010011=>[1,1,4,3,1,1]=>[3,1,2,1,1,3] 1100010010=>[1,1,4,3,2]=>[1,2,1,2,1,1,3] 1100001111=>[1,1,5,1,1,1,1]=>[5,1,1,1,3] 1100001101=>[1,1,5,1,2,1]=>[2,3,1,1,1,3] 1100001100=>[1,1,5,1,3]=>[1,1,3,1,1,1,3] 1100001011=>[1,1,5,2,1,1]=>[3,2,1,1,1,3] 1100001000=>[1,1,5,4]=>[1,1,1,2,1,1,1,3] 1100000111=>[1,1,6,1,1,1]=>[4,1,1,1,1,3] 1100000110=>[1,1,6,1,2]=>[1,3,1,1,1,1,3] 1100000011=>[1,1,7,1,1]=>[3,1,1,1,1,1,3] 1100000010=>[1,1,7,2]=>[1,2,1,1,1,1,1,3] 1100000001=>[1,1,8,1]=>[2,1,1,1,1,1,1,3] 1100000000=>[1,1,9]=>[1,1,1,1,1,1,1,1,3] 1011111111=>[1,2,1,1,1,1,1,1,1,1]=>[9,2] 1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1011111101=>[1,2,1,1,1,1,1,2,1]=>[2,7,2] 1011111011=>[1,2,1,1,1,1,2,1,1]=>[3,6,2] 1011111010=>[1,2,1,1,1,1,2,2]=>[1,2,6,2] 1011110111=>[1,2,1,1,1,2,1,1,1]=>[4,5,2] 1011110001=>[1,2,1,1,1,4,1]=>[2,1,1,5,2] 1011101011=>[1,2,1,1,2,2,1,1]=>[3,2,4,2] 1011100101=>[1,2,1,1,3,2,1]=>[2,2,1,4,2] 1011100001=>[1,2,1,1,5,1]=>[2,1,1,1,4,2] 1011011111=>[1,2,1,2,1,1,1,1,1]=>[6,3,2] 1011011001=>[1,2,1,2,1,3,1]=>[2,1,3,3,2] 1011010101=>[1,2,1,2,2,2,1]=>[2,2,2,3,2] 1011010011=>[1,2,1,2,3,1,1]=>[3,1,2,3,2] 1011010001=>[1,2,1,2,4,1]=>[2,1,1,2,3,2] 1011001101=>[1,2,1,3,1,2,1]=>[2,3,1,3,2] 1011001011=>[1,2,1,3,2,1,1]=>[3,2,1,3,2] 1011001001=>[1,2,1,3,3,1]=>[2,1,2,1,3,2] 1011000111=>[1,2,1,4,1,1,1]=>[4,1,1,3,2] 1011000101=>[1,2,1,4,2,1]=>[2,2,1,1,3,2] 1011000011=>[1,2,1,5,1,1]=>[3,1,1,1,3,2] 1011000001=>[1,2,1,6,1]=>[2,1,1,1,1,3,2] 1010111110=>[1,2,2,1,1,1,1,2]=>[1,6,2,2] 1010110101=>[1,2,2,1,2,2,1]=>[2,2,3,2,2] 1010110011=>[1,2,2,1,3,1,1]=>[3,1,3,2,2] 1010110001=>[1,2,2,1,4,1]=>[2,1,1,3,2,2] 1010101111=>[1,2,2,2,1,1,1,1]=>[5,2,2,2] 1010101101=>[1,2,2,2,1,2,1]=>[2,3,2,2,2] 1010101011=>[1,2,2,2,2,1,1]=>[3,2,2,2,2] 1010101001=>[1,2,2,2,3,1]=>[2,1,2,2,2,2] 1010100111=>[1,2,2,3,1,1,1]=>[4,1,2,2,2] 1010100101=>[1,2,2,3,2,1]=>[2,2,1,2,2,2] 1010011101=>[1,2,3,1,1,2,1]=>[2,4,1,2,2] 1010011011=>[1,2,3,1,2,1,1]=>[3,3,1,2,2] 1010011001=>[1,2,3,1,3,1]=>[2,1,3,1,2,2] 1010010111=>[1,2,3,2,1,1,1]=>[4,2,1,2,2] 1010010101=>[1,2,3,2,2,1]=>[2,2,2,1,2,2] 1010010011=>[1,2,3,3,1,1]=>[3,1,2,1,2,2] 1010010001=>[1,2,3,4,1]=>[2,1,1,2,1,2,2] 1010001111=>[1,2,4,1,1,1,1]=>[5,1,1,2,2] 1010001101=>[1,2,4,1,2,1]=>[2,3,1,1,2,2] 1010001011=>[1,2,4,2,1,1]=>[3,2,1,1,2,2] 1010000111=>[1,2,5,1,1,1]=>[4,1,1,1,2,2] 1010000101=>[1,2,5,2,1]=>[2,2,1,1,1,2,2] 1010000001=>[1,2,7,1]=>[2,1,1,1,1,1,2,2] 1001111111=>[1,3,1,1,1,1,1,1,1]=>[8,1,2] 1001111110=>[1,3,1,1,1,1,1,2]=>[1,7,1,2] 1001111011=>[1,3,1,1,1,2,1,1]=>[3,5,1,2] 1001111001=>[1,3,1,1,1,3,1]=>[2,1,5,1,2] 1001111000=>[1,3,1,1,1,4]=>[1,1,1,5,1,2] 1001110101=>[1,3,1,1,2,2,1]=>[2,2,4,1,2] 1001110100=>[1,3,1,1,2,3]=>[1,1,2,4,1,2] 1001110011=>[1,3,1,1,3,1,1]=>[3,1,4,1,2] 1001110001=>[1,3,1,1,4,1]=>[2,1,1,4,1,2] 1001101101=>[1,3,1,2,1,2,1]=>[2,3,3,1,2] 1001101100=>[1,3,1,2,1,3]=>[1,1,3,3,1,2] 1001101011=>[1,3,1,2,2,1,1]=>[3,2,3,1,2] 1001101001=>[1,3,1,2,3,1]=>[2,1,2,3,1,2] 1001100111=>[1,3,1,3,1,1,1]=>[4,1,3,1,2] 1001100110=>[1,3,1,3,1,2]=>[1,3,1,3,1,2] 1001100101=>[1,3,1,3,2,1]=>[2,2,1,3,1,2] 1001100011=>[1,3,1,4,1,1]=>[3,1,1,3,1,2] 1001100001=>[1,3,1,5,1]=>[2,1,1,1,3,1,2] 1001011110=>[1,3,2,1,1,1,2]=>[1,5,2,1,2] 1001011101=>[1,3,2,1,1,2,1]=>[2,4,2,1,2] 1001011011=>[1,3,2,1,2,1,1]=>[3,3,2,1,2] 1001011001=>[1,3,2,1,3,1]=>[2,1,3,2,1,2] 1001010111=>[1,3,2,2,1,1,1]=>[4,2,2,1,2] 1001010101=>[1,3,2,2,2,1]=>[2,2,2,2,1,2] 1001001111=>[1,3,3,1,1,1,1]=>[5,1,2,1,2] 1001001101=>[1,3,3,1,2,1]=>[2,3,1,2,1,2] 1001001011=>[1,3,3,2,1,1]=>[3,2,1,2,1,2] 1001000111=>[1,3,4,1,1,1]=>[4,1,1,2,1,2] 1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 1000111101=>[1,4,1,1,1,2,1]=>[2,5,1,1,2] 1000111100=>[1,4,1,1,1,3]=>[1,1,5,1,1,2] 1000111011=>[1,4,1,1,2,1,1]=>[3,4,1,1,2] 1000111001=>[1,4,1,1,3,1]=>[2,1,4,1,1,2] 1000110111=>[1,4,1,2,1,1,1]=>[4,3,1,1,2] 1000110110=>[1,4,1,2,1,2]=>[1,3,3,1,1,2] 1000110011=>[1,4,1,3,1,1]=>[3,1,3,1,1,2] 1000110001=>[1,4,1,4,1]=>[2,1,1,3,1,1,2] 1000101111=>[1,4,2,1,1,1,1]=>[5,2,1,1,2] 1000101110=>[1,4,2,1,1,2]=>[1,4,2,1,1,2] 1000101011=>[1,4,2,2,1,1]=>[3,2,2,1,1,2] 1000100101=>[1,4,3,2,1]=>[2,2,1,2,1,1,2] 1000011111=>[1,5,1,1,1,1,1]=>[6,1,1,1,2] 1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2] 1000011101=>[1,5,1,1,2,1]=>[2,4,1,1,1,2] 1000011011=>[1,5,1,2,1,1]=>[3,3,1,1,1,2] 1000011001=>[1,5,1,3,1]=>[2,1,3,1,1,1,2] 1000010111=>[1,5,2,1,1,1]=>[4,2,1,1,1,2] 1000010110=>[1,5,2,1,2]=>[1,3,2,1,1,1,2] 1000001111=>[1,6,1,1,1,1]=>[5,1,1,1,1,2] 1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2] 1000001101=>[1,6,1,2,1]=>[2,3,1,1,1,1,2] 1000001010=>[1,6,2,2]=>[1,2,2,1,1,1,1,2] 1000001001=>[1,6,3,1]=>[2,1,2,1,1,1,1,2] 1000000111=>[1,7,1,1,1]=>[4,1,1,1,1,1,2] 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] 1000000001=>[1,9,1]=>[2,1,1,1,1,1,1,1,2] 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] 10000000100=>[1,8,3]=>[1,1,2,1,1,1,1,1,1,2] 10000001010=>[1,7,2,2]=>[1,2,2,1,1,1,1,1,2] 10000010110=>[1,6,2,1,2]=>[1,3,2,1,1,1,1,2] 10000101110=>[1,5,2,1,1,2]=>[1,4,2,1,1,1,2] 10001011110=>[1,4,2,1,1,1,2]=>[1,5,2,1,1,2] 10010111110=>[1,3,2,1,1,1,1,2]=>[1,6,2,1,2] 10101111110=>[1,2,2,1,1,1,1,1,2]=>[1,7,2,2] 11011111110=>[1,1,2,1,1,1,1,1,1,2]=>[1,8,3] 10000010000=>[1,6,5]=>[1,1,1,1,2,1,1,1,1,2] 10000100010=>[1,5,4,2]=>[1,2,1,1,2,1,1,1,2] 10111011110=>[1,2,1,1,2,1,1,1,2]=>[1,5,4,2] 11110111110=>[1,1,1,1,2,1,1,1,1,2]=>[1,6,5] 10001000010=>[1,4,5,2]=>[1,2,1,1,1,2,1,1,2] 10000100100=>[1,5,3,3]=>[1,1,2,1,2,1,1,1,2] 10001001010=>[1,4,3,2,2]=>[1,2,2,1,2,1,1,2] 10101101110=>[1,2,2,1,2,1,1,2]=>[1,4,3,2,2] 11011011110=>[1,1,2,1,2,1,1,1,2]=>[1,5,3,3] 10111101110=>[1,2,1,1,1,2,1,1,2]=>[1,4,5,2] 10001000100=>[1,4,4,3]=>[1,1,2,1,1,2,1,1,2] 10000101000=>[1,5,2,4]=>[1,1,1,2,2,1,1,1,2] 10010001010=>[1,3,4,2,2]=>[1,2,2,1,1,2,1,2] 10001010010=>[1,4,2,3,2]=>[1,2,1,2,2,1,1,2] 10110101110=>[1,2,1,2,2,1,1,2]=>[1,4,2,3,2] 10101110110=>[1,2,2,1,1,2,1,2]=>[1,3,4,2,2] 11101011110=>[1,1,1,2,2,1,1,1,2]=>[1,5,2,4] 11011101110=>[1,1,2,1,1,2,1,1,2]=>[1,4,4,3] 11111101110=>[1,1,1,1,1,1,2,1,1,2]=>[1,4,7] 10010000000=>[1,3,8]=>[1,1,1,1,1,1,1,2,1,2] 10010000100=>[1,3,5,3]=>[1,1,2,1,1,1,2,1,2] 10001001000=>[1,4,3,4]=>[1,1,1,2,1,2,1,1,2] 11000000110=>[1,1,7,1,2]=>[1,3,1,1,1,1,1,3] 10010010010=>[1,3,3,3,2]=>[1,2,1,2,1,2,1,2] 10001010100=>[1,4,2,2,3]=>[1,1,2,2,2,1,1,2] 10010101010=>[1,3,2,2,2,2]=>[1,2,2,2,2,1,2] 100001111100=>[1,5,1,1,1,1,3]=>[1,1,6,1,1,1,2] 10101010110=>[1,2,2,2,2,1,2]=>[1,3,2,2,2,2] 11010101110=>[1,1,2,2,2,1,1,2]=>[1,4,2,2,3] 10110110110=>[1,2,1,2,1,2,1,2]=>[1,3,3,3,2] 11101101110=>[1,1,1,2,1,2,1,1,2]=>[1,4,3,4] 11011110110=>[1,1,2,1,1,1,2,1,2]=>[1,3,5,3] 10111111010=>[1,2,1,1,1,1,1,2,2]=>[1,2,7,2] 11111110110=>[1,1,1,1,1,1,1,2,1,2]=>[1,3,8] 10010001000=>[1,3,4,4]=>[1,1,1,2,1,1,2,1,2] 10100010010=>[1,2,4,3,2]=>[1,2,1,2,1,1,2,2] 10010100010=>[1,3,2,4,2]=>[1,2,1,1,2,2,1,2] 10010010100=>[1,3,3,2,3]=>[1,1,2,2,1,2,1,2] 10100101010=>[1,2,3,2,2,2]=>[1,2,2,2,1,2,2] 11010001110=>[1,1,2,4,1,1,2]=>[1,4,1,1,2,3] 10101011010=>[1,2,2,2,1,2,2]=>[1,2,3,2,2,2] 11010110110=>[1,1,2,2,1,2,1,2]=>[1,3,3,2,3] 10111010110=>[1,2,1,1,2,2,1,2]=>[1,3,2,4,2] 10110111010=>[1,2,1,2,1,1,2,2]=>[1,2,4,3,2] 11101110110=>[1,1,1,2,1,1,2,1,2]=>[1,3,4,4] 10111111100=>[1,2,1,1,1,1,1,1,3]=>[1,1,8,2] 11111111010=>[1,1,1,1,1,1,1,1,2,2]=>[1,2,9] =>[1]=>[1] 0111111111=>[2,1,1,1,1,1,1,1,1,1]=>[10,1] 0111111101=>[2,1,1,1,1,1,1,2,1]=>[2,8,1] 0111111001=>[2,1,1,1,1,1,3,1]=>[2,1,7,1] 0111100001=>[2,1,1,1,5,1]=>[2,1,1,1,5,1] 0110000001=>[2,1,7,1]=>[2,1,1,1,1,1,3,1] 0100000001=>[2,8,1]=>[2,1,1,1,1,1,1,2,1] 0000000001=>[10,1]=>[2,1,1,1,1,1,1,1,1,1] 01111111111=>[2,1,1,1,1,1,1,1,1,1,1]=>[11,1] 01111111101=>[2,1,1,1,1,1,1,1,2,1]=>[2,9,1] 0111111011=>[2,1,1,1,1,1,2,1,1]=>[3,7,1] 01111111001=>[2,1,1,1,1,1,1,3,1]=>[2,1,8,1] 0111010001=>[2,1,1,2,4,1]=>[2,1,1,2,4,1] 01100000001=>[2,1,8,1]=>[2,1,1,1,1,1,1,3,1] 0010000001=>[3,7,1]=>[2,1,1,1,1,1,2,1,1] 01000000001=>[2,9,1]=>[2,1,1,1,1,1,1,1,2,1] 00000000001=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1] 0101010101=>[2,2,2,2,2,1]=>[2,2,2,2,2,1] 0101001011=>[2,2,3,2,1,1]=>[3,2,1,2,2,1] 0101000111=>[2,2,4,1,1,1]=>[4,1,1,2,2,1] 0100011011=>[2,4,1,2,1,1]=>[3,3,1,1,2,1] 0100010111=>[2,4,2,1,1,1]=>[4,2,1,1,2,1] 0100001111=>[2,5,1,1,1,1]=>[5,1,1,1,2,1] 0011010101=>[3,1,2,2,2,1]=>[2,2,2,3,1,1] 0011001101=>[3,1,3,1,2,1]=>[2,3,1,3,1,1] 0011000111=>[3,1,4,1,1,1]=>[4,1,1,3,1,1] 0010110101=>[3,2,1,2,2,1]=>[2,2,3,2,1,1] 0010010111=>[3,3,2,1,1,1]=>[4,2,1,2,1,1] 0010001111=>[3,4,1,1,1,1]=>[5,1,1,2,1,1] 0001110101=>[4,1,1,2,2,1]=>[2,2,4,1,1,1] 0001110011=>[4,1,1,3,1,1]=>[3,1,4,1,1,1] 0001101101=>[4,1,2,1,2,1]=>[2,3,3,1,1,1] 0001101011=>[4,1,2,2,1,1]=>[3,2,3,1,1,1] 0001011101=>[4,2,1,1,2,1]=>[2,4,2,1,1,1] 0001001111=>[4,3,1,1,1,1]=>[5,1,2,1,1,1] 0000111101=>[5,1,1,1,2,1]=>[2,5,1,1,1,1] 0000111011=>[5,1,1,2,1,1]=>[3,4,1,1,1,1] 0000110111=>[5,1,2,1,1,1]=>[4,3,1,1,1,1] 0000011111=>[6,1,1,1,1,1]=>[6,1,1,1,1,1] 010101010101=>[2,2,2,2,2,2,1]=>[2,2,2,2,2,2,1] 010100101011=>[2,2,3,2,2,1,1]=>[3,2,2,1,2,2,1] 010100100111=>[2,2,3,3,1,1,1]=>[4,1,2,1,2,2,1] 010100011011=>[2,2,4,1,2,1,1]=>[3,3,1,1,2,2,1] 010100010111=>[2,2,4,2,1,1,1]=>[4,2,1,1,2,2,1] 010100001111=>[2,2,5,1,1,1,1]=>[5,1,1,1,2,2,1] 010010011011=>[2,3,3,1,2,1,1]=>[3,3,1,2,1,2,1] 010010010111=>[2,3,3,2,1,1,1]=>[4,2,1,2,1,2,1] 010010001111=>[2,3,4,1,1,1,1]=>[5,1,1,2,1,2,1] 010000111011=>[2,5,1,1,2,1,1]=>[3,4,1,1,1,2,1] 010000110111=>[2,5,1,2,1,1,1]=>[4,3,1,1,1,2,1] 010000101111=>[2,5,2,1,1,1,1]=>[5,2,1,1,1,2,1] 010000011111=>[2,6,1,1,1,1,1]=>[6,1,1,1,1,2,1] 001101010101=>[3,1,2,2,2,2,1]=>[2,2,2,2,3,1,1] 001101001011=>[3,1,2,3,2,1,1]=>[3,2,1,2,3,1,1] 001100100111=>[3,1,3,3,1,1,1]=>[4,1,2,1,3,1,1] 001100010111=>[3,1,4,2,1,1,1]=>[4,2,1,1,3,1,1] 001100001111=>[3,1,5,1,1,1,1]=>[5,1,1,1,3,1,1] 001010010111=>[3,2,3,2,1,1,1]=>[4,2,1,2,2,1,1] 001010001111=>[3,2,4,1,1,1,1]=>[5,1,1,2,2,1,1] 001000110111=>[3,4,1,2,1,1,1]=>[4,3,1,1,2,1,1] 001000101111=>[3,4,2,1,1,1,1]=>[5,2,1,1,2,1,1] 001000011111=>[3,5,1,1,1,1,1]=>[6,1,1,1,2,1,1] 000111010101=>[4,1,1,2,2,2,1]=>[2,2,2,4,1,1,1] 000111010011=>[4,1,1,2,3,1,1]=>[3,1,2,4,1,1,1] 000111001101=>[4,1,1,3,1,2,1]=>[2,3,1,4,1,1,1] 000111001011=>[4,1,1,3,2,1,1]=>[3,2,1,4,1,1,1] 000110110101=>[4,1,2,1,2,2,1]=>[2,2,3,3,1,1,1] 000110110011=>[4,1,2,1,3,1,1]=>[3,1,3,3,1,1,1] 000110101101=>[4,1,2,2,1,2,1]=>[2,3,2,3,1,1,1] 000110101011=>[4,1,2,2,2,1,1]=>[3,2,2,3,1,1,1] 000110001111=>[4,1,4,1,1,1,1]=>[5,1,1,3,1,1,1] 000100101111=>[4,3,2,1,1,1,1]=>[5,2,1,2,1,1,1] 000100011111=>[4,4,1,1,1,1,1]=>[6,1,1,2,1,1,1] 000011110101=>[5,1,1,1,2,2,1]=>[2,2,5,1,1,1,1] 000011110011=>[5,1,1,1,3,1,1]=>[3,1,5,1,1,1,1] 000011101101=>[5,1,1,2,1,2,1]=>[2,3,4,1,1,1,1] 000011101011=>[5,1,1,2,2,1,1]=>[3,2,4,1,1,1,1] 000011100111=>[5,1,1,3,1,1,1]=>[4,1,4,1,1,1,1] 000011011101=>[5,1,2,1,1,2,1]=>[2,4,3,1,1,1,1] 000011011011=>[5,1,2,1,2,1,1]=>[3,3,3,1,1,1,1] 000011010111=>[5,1,2,2,1,1,1]=>[4,2,3,1,1,1,1] 000010011111=>[5,3,1,1,1,1,1]=>[6,1,2,1,1,1,1] 000001111101=>[6,1,1,1,1,2,1]=>[2,6,1,1,1,1,1] 000001111011=>[6,1,1,1,2,1,1]=>[3,5,1,1,1,1,1] 000001110111=>[6,1,1,2,1,1,1]=>[4,4,1,1,1,1,1] 000001101111=>[6,1,2,1,1,1,1]=>[5,3,1,1,1,1,1] 000000111111=>[7,1,1,1,1,1,1]=>[7,1,1,1,1,1,1] 11010101010=>[1,1,2,2,2,2,2]=>[1,2,2,2,2,3] 11010101000=>[1,1,2,2,2,4]=>[1,1,1,2,2,2,3] 11010101100=>[1,1,2,2,2,1,3]=>[1,1,3,2,2,3] 11010100100=>[1,1,2,2,3,3]=>[1,1,2,1,2,2,3] 11010110100=>[1,1,2,2,1,2,3]=>[1,1,2,3,2,3] 11010010100=>[1,1,2,3,2,3]=>[1,1,2,2,1,2,3] 11011010100=>[1,1,2,1,2,2,3]=>[1,1,2,2,3,3] 11001010100=>[1,1,3,2,2,3]=>[1,1,2,2,2,1,3] 11101010100=>[1,1,1,2,2,2,3]=>[1,1,2,2,2,4] 10101010100=>[1,2,2,2,2,3]=>[1,1,2,2,2,2,2] 111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>[13] 111111111001=>[1,1,1,1,1,1,1,1,1,3,1]=>[2,1,10] 111111100111=>[1,1,1,1,1,1,1,3,1,1,1]=>[4,1,8] 111111100001=>[1,1,1,1,1,1,1,5,1]=>[2,1,1,1,8] 111111101101=>[1,1,1,1,1,1,1,2,1,2,1]=>[2,3,8] 111110011111=>[1,1,1,1,1,3,1,1,1,1,1]=>[6,1,6] 111110011001=>[1,1,1,1,1,3,1,3,1]=>[2,1,3,1,6] 111110000111=>[1,1,1,1,1,5,1,1,1]=>[4,1,1,1,6] 111110000001=>[1,1,1,1,1,7,1]=>[2,1,1,1,1,1,6] 111110001101=>[1,1,1,1,1,4,1,2,1]=>[2,3,1,1,6] 111110110111=>[1,1,1,1,1,2,1,2,1,1,1]=>[4,3,6] 111110110001=>[1,1,1,1,1,2,1,4,1]=>[2,1,1,3,6] 111110111101=>[1,1,1,1,1,2,1,1,1,2,1]=>[2,5,6] 111110100101=>[1,1,1,1,1,2,3,2,1]=>[2,2,1,2,6] 111001111111=>[1,1,1,3,1,1,1,1,1,1,1]=>[8,1,4] 111001111001=>[1,1,1,3,1,1,1,3,1]=>[2,1,5,1,4] 111001100111=>[1,1,1,3,1,3,1,1,1]=>[4,1,3,1,4] 111001100001=>[1,1,1,3,1,5,1]=>[2,1,1,1,3,1,4] 111001101101=>[1,1,1,3,1,2,1,2,1]=>[2,3,3,1,4] 111000011111=>[1,1,1,5,1,1,1,1,1]=>[6,1,1,1,4] 111000011001=>[1,1,1,5,1,3,1]=>[2,1,3,1,1,1,4] 111000000111=>[1,1,1,7,1,1,1]=>[4,1,1,1,1,1,4] 111000000001=>[1,1,1,9,1]=>[2,1,1,1,1,1,1,1,4] 111000001101=>[1,1,1,6,1,2,1]=>[2,3,1,1,1,1,4] 111000110111=>[1,1,1,4,1,2,1,1,1]=>[4,3,1,1,4] 111000110001=>[1,1,1,4,1,4,1]=>[2,1,1,3,1,1,4] 111000111101=>[1,1,1,4,1,1,1,2,1]=>[2,5,1,1,4] 111000100101=>[1,1,1,4,3,2,1]=>[2,2,1,2,1,1,4] 111011011111=>[1,1,1,2,1,2,1,1,1,1,1]=>[6,3,4] 111011011001=>[1,1,1,2,1,2,1,3,1]=>[2,1,3,3,4] 111011000111=>[1,1,1,2,1,4,1,1,1]=>[4,1,1,3,4] 111011000001=>[1,1,1,2,1,6,1]=>[2,1,1,1,1,3,4] 111011001101=>[1,1,1,2,1,3,1,2,1]=>[2,3,1,3,4] 111011110111=>[1,1,1,2,1,1,1,2,1,1,1]=>[4,5,4] 111011110001=>[1,1,1,2,1,1,1,4,1]=>[2,1,1,5,4] 111011111101=>[1,1,1,2,1,1,1,1,1,2,1]=>[2,7,4] 111011100101=>[1,1,1,2,1,1,3,2,1]=>[2,2,1,4,4] 111010010111=>[1,1,1,2,3,2,1,1,1]=>[4,2,1,2,4] 111010010001=>[1,1,1,2,3,4,1]=>[2,1,1,2,1,2,4] 111010011101=>[1,1,1,2,3,1,1,2,1]=>[2,4,1,2,4] 111010000101=>[1,1,1,2,5,2,1]=>[2,2,1,1,1,2,4] 111010110101=>[1,1,1,2,2,1,2,2,1]=>[2,2,3,2,4] 100111111111=>[1,3,1,1,1,1,1,1,1,1,1]=>[10,1,2] 100111111001=>[1,3,1,1,1,1,1,3,1]=>[2,1,7,1,2] 100111100111=>[1,3,1,1,1,3,1,1,1]=>[4,1,5,1,2] 100111100001=>[1,3,1,1,1,5,1]=>[2,1,1,1,5,1,2] 100111101101=>[1,3,1,1,1,2,1,2,1]=>[2,3,5,1,2] 100110011111=>[1,3,1,3,1,1,1,1,1]=>[6,1,3,1,2] 100110011001=>[1,3,1,3,1,3,1]=>[2,1,3,1,3,1,2] 100110000111=>[1,3,1,5,1,1,1]=>[4,1,1,1,3,1,2] 100110000001=>[1,3,1,7,1]=>[2,1,1,1,1,1,3,1,2] 100110001101=>[1,3,1,4,1,2,1]=>[2,3,1,1,3,1,2] 100110110111=>[1,3,1,2,1,2,1,1,1]=>[4,3,3,1,2] 100110110001=>[1,3,1,2,1,4,1]=>[2,1,1,3,3,1,2] 100110111101=>[1,3,1,2,1,1,1,2,1]=>[2,5,3,1,2] 100110100101=>[1,3,1,2,3,2,1]=>[2,2,1,2,3,1,2] 100001111111=>[1,5,1,1,1,1,1,1,1]=>[8,1,1,1,2] 100001111001=>[1,5,1,1,1,3,1]=>[2,1,5,1,1,1,2] 100001100111=>[1,5,1,3,1,1,1]=>[4,1,3,1,1,1,2] 100001100001=>[1,5,1,5,1]=>[2,1,1,1,3,1,1,1,2] 100001101101=>[1,5,1,2,1,2,1]=>[2,3,3,1,1,1,2] 100000011111=>[1,7,1,1,1,1,1]=>[6,1,1,1,1,1,2] 100000011001=>[1,7,1,3,1]=>[2,1,3,1,1,1,1,1,2] 100000000111=>[1,9,1,1,1]=>[4,1,1,1,1,1,1,1,2] 100000000001=>[1,11,1]=>[2,1,1,1,1,1,1,1,1,1,2] 100000001101=>[1,8,1,2,1]=>[2,3,1,1,1,1,1,1,2] 100000110111=>[1,6,1,2,1,1,1]=>[4,3,1,1,1,1,2] 100000110001=>[1,6,1,4,1]=>[2,1,1,3,1,1,1,1,2] 100000111101=>[1,6,1,1,1,2,1]=>[2,5,1,1,1,1,2] 100000100101=>[1,6,3,2,1]=>[2,2,1,2,1,1,1,1,2] 100011011111=>[1,4,1,2,1,1,1,1,1]=>[6,3,1,1,2] 100011011001=>[1,4,1,2,1,3,1]=>[2,1,3,3,1,1,2] 100011000111=>[1,4,1,4,1,1,1]=>[4,1,1,3,1,1,2] 100011000001=>[1,4,1,6,1]=>[2,1,1,1,1,3,1,1,2] 100011001101=>[1,4,1,3,1,2,1]=>[2,3,1,3,1,1,2] 100011110111=>[1,4,1,1,1,2,1,1,1]=>[4,5,1,1,2] 100011110001=>[1,4,1,1,1,4,1]=>[2,1,1,5,1,1,2] 100011111101=>[1,4,1,1,1,1,1,2,1]=>[2,7,1,1,2] 100011100101=>[1,4,1,1,3,2,1]=>[2,2,1,4,1,1,2] 100010010111=>[1,4,3,2,1,1,1]=>[4,2,1,2,1,1,2] 100010010001=>[1,4,3,4,1]=>[2,1,1,2,1,2,1,1,2] 100010011101=>[1,4,3,1,1,2,1]=>[2,4,1,2,1,1,2] 100010000101=>[1,4,5,2,1]=>[2,2,1,1,1,2,1,1,2] 100010110101=>[1,4,2,1,2,2,1]=>[2,2,3,2,1,1,2] 101101111111=>[1,2,1,2,1,1,1,1,1,1,1]=>[8,3,2] 101101111001=>[1,2,1,2,1,1,1,3,1]=>[2,1,5,3,2] 101101100111=>[1,2,1,2,1,3,1,1,1]=>[4,1,3,3,2] 101101100001=>[1,2,1,2,1,5,1]=>[2,1,1,1,3,3,2] 101101101101=>[1,2,1,2,1,2,1,2,1]=>[2,3,3,3,2] 101100011111=>[1,2,1,4,1,1,1,1,1]=>[6,1,1,3,2] 101100011001=>[1,2,1,4,1,3,1]=>[2,1,3,1,1,3,2] 101100000111=>[1,2,1,6,1,1,1]=>[4,1,1,1,1,3,2] 101100000001=>[1,2,1,8,1]=>[2,1,1,1,1,1,1,3,2] 101100001101=>[1,2,1,5,1,2,1]=>[2,3,1,1,1,3,2] 101100110111=>[1,2,1,3,1,2,1,1,1]=>[4,3,1,3,2] 101100110001=>[1,2,1,3,1,4,1]=>[2,1,1,3,1,3,2] 101100111101=>[1,2,1,3,1,1,1,2,1]=>[2,5,1,3,2] 101100100101=>[1,2,1,3,3,2,1]=>[2,2,1,2,1,3,2] 101111011111=>[1,2,1,1,1,2,1,1,1,1,1]=>[6,5,2] 101111011001=>[1,2,1,1,1,2,1,3,1]=>[2,1,3,5,2] 101111000111=>[1,2,1,1,1,4,1,1,1]=>[4,1,1,5,2] 101111000001=>[1,2,1,1,1,6,1]=>[2,1,1,1,1,5,2] 101111001101=>[1,2,1,1,1,3,1,2,1]=>[2,3,1,5,2] 101111110111=>[1,2,1,1,1,1,1,2,1,1,1]=>[4,7,2] 101111110001=>[1,2,1,1,1,1,1,4,1]=>[2,1,1,7,2] 101111111101=>[1,2,1,1,1,1,1,1,1,2,1]=>[2,9,2] 101111100101=>[1,2,1,1,1,1,3,2,1]=>[2,2,1,6,2] 101110010111=>[1,2,1,1,3,2,1,1,1]=>[4,2,1,4,2] 101110010001=>[1,2,1,1,3,4,1]=>[2,1,1,2,1,4,2] 101110011101=>[1,2,1,1,3,1,1,2,1]=>[2,4,1,4,2] 101110000101=>[1,2,1,1,5,2,1]=>[2,2,1,1,1,4,2] 101110110101=>[1,2,1,1,2,1,2,2,1]=>[2,2,3,4,2] 101001011111=>[1,2,3,2,1,1,1,1,1]=>[6,2,1,2,2] 101001011001=>[1,2,3,2,1,3,1]=>[2,1,3,2,1,2,2] 101001000111=>[1,2,3,4,1,1,1]=>[4,1,1,2,1,2,2] 101001000001=>[1,2,3,6,1]=>[2,1,1,1,1,2,1,2,2] 101001001101=>[1,2,3,3,1,2,1]=>[2,3,1,2,1,2,2] 101001110111=>[1,2,3,1,1,2,1,1,1]=>[4,4,1,2,2] 101001110001=>[1,2,3,1,1,4,1]=>[2,1,1,4,1,2,2] 101001111101=>[1,2,3,1,1,1,1,2,1]=>[2,6,1,2,2] 101001100101=>[1,2,3,1,3,2,1]=>[2,2,1,3,1,2,2] 101000010111=>[1,2,5,2,1,1,1]=>[4,2,1,1,1,2,2] 101000010001=>[1,2,5,4,1]=>[2,1,1,2,1,1,1,2,2] 101000011101=>[1,2,5,1,1,2,1]=>[2,4,1,1,1,2,2] 101000000101=>[1,2,7,2,1]=>[2,2,1,1,1,1,1,2,2] 101000110101=>[1,2,4,1,2,2,1]=>[2,2,3,1,1,2,2] 101011010111=>[1,2,2,1,2,2,1,1,1]=>[4,2,3,2,2] 101011010001=>[1,2,2,1,2,4,1]=>[2,1,1,2,3,2,2] 101011011101=>[1,2,2,1,2,1,1,2,1]=>[2,4,3,2,2] 101011000101=>[1,2,2,1,4,2,1]=>[2,2,1,1,3,2,2] 101011110101=>[1,2,2,1,1,1,2,2,1]=>[2,2,5,2,2] 101010010101=>[1,2,2,3,2,2,1]=>[2,2,2,1,2,2,2] 0000000000=>[11]=>[1,1,1,1,1,1,1,1,1,1,1] 0000000110=>[8,1,2]=>[1,3,1,1,1,1,1,1,1] 0000011000=>[6,1,4]=>[1,1,1,3,1,1,1,1,1] 0000011110=>[6,1,1,1,2]=>[1,5,1,1,1,1,1] 0000010010=>[6,3,2]=>[1,2,1,2,1,1,1,1,1] 0001100000=>[4,1,6]=>[1,1,1,1,1,3,1,1,1] 0001100110=>[4,1,3,1,2]=>[1,3,1,3,1,1,1] 0001111000=>[4,1,1,1,4]=>[1,1,1,5,1,1,1] 0001111110=>[4,1,1,1,1,1,2]=>[1,7,1,1,1] 0001110010=>[4,1,1,3,2]=>[1,2,1,4,1,1,1] 0001001000=>[4,3,4]=>[1,1,1,2,1,2,1,1,1] 0001001110=>[4,3,1,1,2]=>[1,4,1,2,1,1,1] 0001000010=>[4,5,2]=>[1,2,1,1,1,2,1,1,1] 0001011010=>[4,2,1,2,2]=>[1,2,3,2,1,1,1] 0110000000=>[2,1,8]=>[1,1,1,1,1,1,1,3,1] 0110000110=>[2,1,5,1,2]=>[1,3,1,1,1,3,1] 0110011000=>[2,1,3,1,4]=>[1,1,1,3,1,3,1] 0110011110=>[2,1,3,1,1,1,2]=>[1,5,1,3,1] 0110010010=>[2,1,3,3,2]=>[1,2,1,2,1,3,1] 0111100000=>[2,1,1,1,6]=>[1,1,1,1,1,5,1] 0111100110=>[2,1,1,1,3,1,2]=>[1,3,1,5,1] 0111111000=>[2,1,1,1,1,1,4]=>[1,1,1,7,1] 0111111110=>[2,1,1,1,1,1,1,1,2]=>[1,9,1] 0111110010=>[2,1,1,1,1,3,2]=>[1,2,1,6,1] 0111001000=>[2,1,1,3,4]=>[1,1,1,2,1,4,1] 0111001110=>[2,1,1,3,1,1,2]=>[1,4,1,4,1] 0111000010=>[2,1,1,5,2]=>[1,2,1,1,1,4,1] 0111011010=>[2,1,1,2,1,2,2]=>[1,2,3,4,1] 0100100000=>[2,3,6]=>[1,1,1,1,1,2,1,2,1] 0100100110=>[2,3,3,1,2]=>[1,3,1,2,1,2,1] 0100111000=>[2,3,1,1,4]=>[1,1,1,4,1,2,1] 0100111110=>[2,3,1,1,1,1,2]=>[1,6,1,2,1] 0100110010=>[2,3,1,3,2]=>[1,2,1,3,1,2,1] 0100001000=>[2,5,4]=>[1,1,1,2,1,1,1,2,1] 0100001110=>[2,5,1,1,2]=>[1,4,1,1,1,2,1] 0100000010=>[2,7,2]=>[1,2,1,1,1,1,1,2,1] 0100011010=>[2,4,1,2,2]=>[1,2,3,1,1,2,1] 0101101000=>[2,2,1,2,4]=>[1,1,1,2,3,2,1] 0101101110=>[2,2,1,2,1,1,2]=>[1,4,3,2,1] 0101100010=>[2,2,1,4,2]=>[1,2,1,1,3,2,1] 0101111010=>[2,2,1,1,1,2,2]=>[1,2,5,2,1] 0101001010=>[2,2,3,2,2]=>[1,2,2,1,2,2,1] 000000000000=>[13]=>[1,1,1,1,1,1,1,1,1,1,1,1,1] 000000000110=>[10,1,2]=>[1,3,1,1,1,1,1,1,1,1,1] 000000011000=>[8,1,4]=>[1,1,1,3,1,1,1,1,1,1,1] 000000011110=>[8,1,1,1,2]=>[1,5,1,1,1,1,1,1,1] 000000010010=>[8,3,2]=>[1,2,1,2,1,1,1,1,1,1,1] 000001100000=>[6,1,6]=>[1,1,1,1,1,3,1,1,1,1,1] 000001100110=>[6,1,3,1,2]=>[1,3,1,3,1,1,1,1,1] 000001111000=>[6,1,1,1,4]=>[1,1,1,5,1,1,1,1,1] 000001111110=>[6,1,1,1,1,1,2]=>[1,7,1,1,1,1,1] 000001110010=>[6,1,1,3,2]=>[1,2,1,4,1,1,1,1,1] 000001001000=>[6,3,4]=>[1,1,1,2,1,2,1,1,1,1,1] 000001001110=>[6,3,1,1,2]=>[1,4,1,2,1,1,1,1,1] 000001000010=>[6,5,2]=>[1,2,1,1,1,2,1,1,1,1,1] 000001011010=>[6,2,1,2,2]=>[1,2,3,2,1,1,1,1,1] 000110000000=>[4,1,8]=>[1,1,1,1,1,1,1,3,1,1,1] 000110000110=>[4,1,5,1,2]=>[1,3,1,1,1,3,1,1,1] 000110011000=>[4,1,3,1,4]=>[1,1,1,3,1,3,1,1,1] 000110011110=>[4,1,3,1,1,1,2]=>[1,5,1,3,1,1,1] 000110010010=>[4,1,3,3,2]=>[1,2,1,2,1,3,1,1,1] 000111100000=>[4,1,1,1,6]=>[1,1,1,1,1,5,1,1,1] 000111100110=>[4,1,1,1,3,1,2]=>[1,3,1,5,1,1,1] 000111111000=>[4,1,1,1,1,1,4]=>[1,1,1,7,1,1,1] 000111111110=>[4,1,1,1,1,1,1,1,2]=>[1,9,1,1,1] 000111110010=>[4,1,1,1,1,3,2]=>[1,2,1,6,1,1,1] 000111001000=>[4,1,1,3,4]=>[1,1,1,2,1,4,1,1,1] 000111001110=>[4,1,1,3,1,1,2]=>[1,4,1,4,1,1,1] 000111000010=>[4,1,1,5,2]=>[1,2,1,1,1,4,1,1,1] 000111011010=>[4,1,1,2,1,2,2]=>[1,2,3,4,1,1,1] 000100100000=>[4,3,6]=>[1,1,1,1,1,2,1,2,1,1,1] 000100100110=>[4,3,3,1,2]=>[1,3,1,2,1,2,1,1,1] 000100111000=>[4,3,1,1,4]=>[1,1,1,4,1,2,1,1,1] 000100111110=>[4,3,1,1,1,1,2]=>[1,6,1,2,1,1,1] 000100110010=>[4,3,1,3,2]=>[1,2,1,3,1,2,1,1,1] 000100001000=>[4,5,4]=>[1,1,1,2,1,1,1,2,1,1,1] 000100001110=>[4,5,1,1,2]=>[1,4,1,1,1,2,1,1,1] 000100000010=>[4,7,2]=>[1,2,1,1,1,1,1,2,1,1,1] 000100011010=>[4,4,1,2,2]=>[1,2,3,1,1,2,1,1,1] 000101101000=>[4,2,1,2,4]=>[1,1,1,2,3,2,1,1,1] 000101101110=>[4,2,1,2,1,1,2]=>[1,4,3,2,1,1,1] 000101100010=>[4,2,1,4,2]=>[1,2,1,1,3,2,1,1,1] 000101111010=>[4,2,1,1,1,2,2]=>[1,2,5,2,1,1,1] 000101001010=>[4,2,3,2,2]=>[1,2,2,1,2,2,1,1,1] 011000000000=>[2,1,10]=>[1,1,1,1,1,1,1,1,1,3,1] 011000000110=>[2,1,7,1,2]=>[1,3,1,1,1,1,1,3,1] 011000011000=>[2,1,5,1,4]=>[1,1,1,3,1,1,1,3,1] 011000011110=>[2,1,5,1,1,1,2]=>[1,5,1,1,1,3,1] 011000010010=>[2,1,5,3,2]=>[1,2,1,2,1,1,1,3,1] 011001100000=>[2,1,3,1,6]=>[1,1,1,1,1,3,1,3,1] 011001100110=>[2,1,3,1,3,1,2]=>[1,3,1,3,1,3,1] 011001111000=>[2,1,3,1,1,1,4]=>[1,1,1,5,1,3,1] 011001111110=>[2,1,3,1,1,1,1,1,2]=>[1,7,1,3,1] 011001110010=>[2,1,3,1,1,3,2]=>[1,2,1,4,1,3,1] 011001001000=>[2,1,3,3,4]=>[1,1,1,2,1,2,1,3,1] 011001001110=>[2,1,3,3,1,1,2]=>[1,4,1,2,1,3,1] 011001000010=>[2,1,3,5,2]=>[1,2,1,1,1,2,1,3,1] 011001011010=>[2,1,3,2,1,2,2]=>[1,2,3,2,1,3,1] 011110000000=>[2,1,1,1,8]=>[1,1,1,1,1,1,1,5,1] 011110000110=>[2,1,1,1,5,1,2]=>[1,3,1,1,1,5,1] 011110011000=>[2,1,1,1,3,1,4]=>[1,1,1,3,1,5,1] 011110011110=>[2,1,1,1,3,1,1,1,2]=>[1,5,1,5,1] 011110010010=>[2,1,1,1,3,3,2]=>[1,2,1,2,1,5,1] 011111100000=>[2,1,1,1,1,1,6]=>[1,1,1,1,1,7,1] 011111100110=>[2,1,1,1,1,1,3,1,2]=>[1,3,1,7,1] 011111111000=>[2,1,1,1,1,1,1,1,4]=>[1,1,1,9,1] 011111111110=>[2,1,1,1,1,1,1,1,1,1,2]=>[1,11,1] 011111110010=>[2,1,1,1,1,1,1,3,2]=>[1,2,1,8,1] 011111001000=>[2,1,1,1,1,3,4]=>[1,1,1,2,1,6,1] 011111001110=>[2,1,1,1,1,3,1,1,2]=>[1,4,1,6,1] 011111000010=>[2,1,1,1,1,5,2]=>[1,2,1,1,1,6,1] 011111011010=>[2,1,1,1,1,2,1,2,2]=>[1,2,3,6,1] 011100100000=>[2,1,1,3,6]=>[1,1,1,1,1,2,1,4,1] 011100100110=>[2,1,1,3,3,1,2]=>[1,3,1,2,1,4,1] 011100111000=>[2,1,1,3,1,1,4]=>[1,1,1,4,1,4,1] 011100111110=>[2,1,1,3,1,1,1,1,2]=>[1,6,1,4,1] 011100110010=>[2,1,1,3,1,3,2]=>[1,2,1,3,1,4,1] 011100001000=>[2,1,1,5,4]=>[1,1,1,2,1,1,1,4,1] 011100001110=>[2,1,1,5,1,1,2]=>[1,4,1,1,1,4,1] 011100000010=>[2,1,1,7,2]=>[1,2,1,1,1,1,1,4,1] 011100011010=>[2,1,1,4,1,2,2]=>[1,2,3,1,1,4,1] 011101101000=>[2,1,1,2,1,2,4]=>[1,1,1,2,3,4,1] 011101101110=>[2,1,1,2,1,2,1,1,2]=>[1,4,3,4,1] 011101100010=>[2,1,1,2,1,4,2]=>[1,2,1,1,3,4,1] 011101111010=>[2,1,1,2,1,1,1,2,2]=>[1,2,5,4,1] 011101001010=>[2,1,1,2,3,2,2]=>[1,2,2,1,2,4,1] 010010000000=>[2,3,8]=>[1,1,1,1,1,1,1,2,1,2,1] 010010000110=>[2,3,5,1,2]=>[1,3,1,1,1,2,1,2,1] 010010011000=>[2,3,3,1,4]=>[1,1,1,3,1,2,1,2,1] 010010011110=>[2,3,3,1,1,1,2]=>[1,5,1,2,1,2,1] 010010010010=>[2,3,3,3,2]=>[1,2,1,2,1,2,1,2,1] 010011100000=>[2,3,1,1,6]=>[1,1,1,1,1,4,1,2,1] 010011100110=>[2,3,1,1,3,1,2]=>[1,3,1,4,1,2,1] 010011111000=>[2,3,1,1,1,1,4]=>[1,1,1,6,1,2,1] 010011111110=>[2,3,1,1,1,1,1,1,2]=>[1,8,1,2,1] 010011110010=>[2,3,1,1,1,3,2]=>[1,2,1,5,1,2,1] 010011001000=>[2,3,1,3,4]=>[1,1,1,2,1,3,1,2,1] 010011001110=>[2,3,1,3,1,1,2]=>[1,4,1,3,1,2,1] 010011000010=>[2,3,1,5,2]=>[1,2,1,1,1,3,1,2,1] 010011011010=>[2,3,1,2,1,2,2]=>[1,2,3,3,1,2,1] 010000100000=>[2,5,6]=>[1,1,1,1,1,2,1,1,1,2,1] 010000100110=>[2,5,3,1,2]=>[1,3,1,2,1,1,1,2,1] 010000111000=>[2,5,1,1,4]=>[1,1,1,4,1,1,1,2,1] 010000111110=>[2,5,1,1,1,1,2]=>[1,6,1,1,1,2,1] 010000110010=>[2,5,1,3,2]=>[1,2,1,3,1,1,1,2,1] 010000001000=>[2,7,4]=>[1,1,1,2,1,1,1,1,1,2,1] 010000001110=>[2,7,1,1,2]=>[1,4,1,1,1,1,1,2,1] 010000000010=>[2,9,2]=>[1,2,1,1,1,1,1,1,1,2,1] 010000011010=>[2,6,1,2,2]=>[1,2,3,1,1,1,1,2,1] 010001101000=>[2,4,1,2,4]=>[1,1,1,2,3,1,1,2,1] 010001101110=>[2,4,1,2,1,1,2]=>[1,4,3,1,1,2,1] 010001100010=>[2,4,1,4,2]=>[1,2,1,1,3,1,1,2,1] 010001111010=>[2,4,1,1,1,2,2]=>[1,2,5,1,1,2,1] 010001001010=>[2,4,3,2,2]=>[1,2,2,1,2,1,1,2,1] 010110100000=>[2,2,1,2,6]=>[1,1,1,1,1,2,3,2,1] 010110100110=>[2,2,1,2,3,1,2]=>[1,3,1,2,3,2,1] 010110111000=>[2,2,1,2,1,1,4]=>[1,1,1,4,3,2,1] 010110111110=>[2,2,1,2,1,1,1,1,2]=>[1,6,3,2,1] 010110110010=>[2,2,1,2,1,3,2]=>[1,2,1,3,3,2,1] 010110001000=>[2,2,1,4,4]=>[1,1,1,2,1,1,3,2,1] 010110001110=>[2,2,1,4,1,1,2]=>[1,4,1,1,3,2,1] 010110000010=>[2,2,1,6,2]=>[1,2,1,1,1,1,3,2,1] 010110011010=>[2,2,1,3,1,2,2]=>[1,2,3,1,3,2,1] 010111101000=>[2,2,1,1,1,2,4]=>[1,1,1,2,5,2,1] 010111101110=>[2,2,1,1,1,2,1,1,2]=>[1,4,5,2,1] 010111100010=>[2,2,1,1,1,4,2]=>[1,2,1,1,5,2,1] 010111111010=>[2,2,1,1,1,1,1,2,2]=>[1,2,7,2,1] 010111001010=>[2,2,1,1,3,2,2]=>[1,2,2,1,4,2,1] 010100101000=>[2,2,3,2,4]=>[1,1,1,2,2,1,2,2,1] 010100101110=>[2,2,3,2,1,1,2]=>[1,4,2,1,2,2,1] 010100100010=>[2,2,3,4,2]=>[1,2,1,1,2,1,2,2,1] 010100111010=>[2,2,3,1,1,2,2]=>[1,2,4,1,2,2,1] 010100001010=>[2,2,5,2,2]=>[1,2,2,1,1,1,2,2,1] 010101101010=>[2,2,2,1,2,2,2]=>[1,2,2,3,2,2,1] 0010101010=>[3,2,2,2,2]=>[1,2,2,2,2,1,1] 0010101000=>[3,2,2,4]=>[1,1,1,2,2,2,1,1] 0010101100=>[3,2,2,1,3]=>[1,1,3,2,2,1,1] 0010100100=>[3,2,3,3]=>[1,1,2,1,2,2,1,1] 0010110100=>[3,2,1,2,3]=>[1,1,2,3,2,1,1] 0010010100=>[3,3,2,3]=>[1,1,2,2,1,2,1,1] 0011010100=>[3,1,2,2,3]=>[1,1,2,2,3,1,1] 0001010100=>[4,2,2,3]=>[1,1,2,2,2,1,1,1] 0101010100=>[2,2,2,2,3]=>[1,1,2,2,2,2,1] 00101010101=>[3,2,2,2,2,1]=>[2,2,2,2,2,1,1] 00101010111=>[3,2,2,2,1,1,1]=>[4,2,2,2,1,1] 0010101110=>[3,2,2,1,1,2]=>[1,4,2,2,1,1] 00101010011=>[3,2,2,3,1,1]=>[3,1,2,2,2,1,1] 0010100000=>[3,2,6]=>[1,1,1,1,1,2,2,1,1] 00101011011=>[3,2,2,1,2,1,1]=>[3,3,2,2,1,1] 0010111100=>[3,2,1,1,1,3]=>[1,1,5,2,1,1] 00101001011=>[3,2,3,2,1,1]=>[3,2,1,2,2,1,1] 0010000100=>[3,5,3]=>[1,1,2,1,1,1,2,1,1] 00101101011=>[3,2,1,2,2,1,1]=>[3,2,3,2,1,1] 0011110100=>[3,1,1,1,2,3]=>[1,1,2,5,1,1] 00100101011=>[3,3,2,2,1,1]=>[3,2,2,1,2,1,1] 0000010100=>[6,2,3]=>[1,1,2,2,1,1,1,1,1] 00110101011=>[3,1,2,2,2,1,1]=>[3,2,2,3,1,1] 0111010100=>[2,1,1,2,2,3]=>[1,1,2,2,4,1] 00010101011=>[4,2,2,2,1,1]=>[3,2,2,2,1,1,1] 01010101011=>[2,2,2,2,2,1,1]=>[3,2,2,2,2,1] 0000000010=>[9,2]=>[1,2,1,1,1,1,1,1,1,1] 0000001110=>[7,1,1,2]=>[1,4,1,1,1,1,1,1] 0000111110=>[5,1,1,1,1,2]=>[1,6,1,1,1,1] 0011111110=>[3,1,1,1,1,1,1,2]=>[1,8,1,1] 00000000000=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1] 00000000010=>[10,2]=>[1,2,1,1,1,1,1,1,1,1,1] 0000000100=>[8,3]=>[1,1,2,1,1,1,1,1,1,1] 00000000110=>[9,1,2]=>[1,3,1,1,1,1,1,1,1,1] 0000001010=>[7,2,2]=>[1,2,2,1,1,1,1,1,1] 00000001110=>[8,1,1,2]=>[1,4,1,1,1,1,1,1,1] 0000010110=>[6,2,1,2]=>[1,3,2,1,1,1,1,1] 00000011110=>[7,1,1,1,2]=>[1,5,1,1,1,1,1,1] 0000101110=>[5,2,1,1,2]=>[1,4,2,1,1,1,1] 00000111110=>[6,1,1,1,1,2]=>[1,6,1,1,1,1,1] 0001011110=>[4,2,1,1,1,2]=>[1,5,2,1,1,1] 00001111110=>[5,1,1,1,1,1,2]=>[1,7,1,1,1,1] 0010111110=>[3,2,1,1,1,1,2]=>[1,6,2,1,1] 00011111110=>[4,1,1,1,1,1,1,2]=>[1,8,1,1,1] 0101111110=>[2,2,1,1,1,1,1,2]=>[1,7,2,1] 00111111110=>[3,1,1,1,1,1,1,1,2]=>[1,9,1,1] 01111111110=>[2,1,1,1,1,1,1,1,1,2]=>[1,10,1] 0010110010=>[3,2,1,3,2]=>[1,2,1,3,2,1,1] 0010111000=>[3,2,1,1,4]=>[1,1,1,4,2,1,1] 0011001010=>[3,1,3,2,2]=>[1,2,2,1,3,1,1] 0011001100=>[3,1,3,1,3]=>[1,1,3,1,3,1,1] 0011010010=>[3,1,2,3,2]=>[1,2,1,2,3,1,1] 0011011000=>[3,1,2,1,4]=>[1,1,1,3,3,1,1] 0011100010=>[3,1,1,4,2]=>[1,2,1,1,4,1,1] 0011100100=>[3,1,1,3,3]=>[1,1,2,1,4,1,1] 0011101000=>[3,1,1,2,4]=>[1,1,1,2,4,1,1] 0011110000=>[3,1,1,1,5]=>[1,1,1,1,5,1,1] 0100101010=>[2,3,2,2,2]=>[1,2,2,2,1,2,1] 0100101100=>[2,3,2,1,3]=>[1,1,3,2,1,2,1] 0100110100=>[2,3,1,2,3]=>[1,1,2,3,1,2,1] 0101001100=>[2,2,3,1,3]=>[1,1,3,1,2,2,1] 0101010010=>[2,2,2,3,2]=>[1,2,1,2,2,2,1] 0101011000=>[2,2,2,1,4]=>[1,1,1,3,2,2,1] 0101100100=>[2,2,1,3,3]=>[1,1,2,1,3,2,1] 0101110000=>[2,2,1,1,5]=>[1,1,1,1,4,2,1] 0110001010=>[2,1,4,2,2]=>[1,2,2,1,1,3,1] 0110001100=>[2,1,4,1,3]=>[1,1,3,1,1,3,1] 0110010100=>[2,1,3,2,3]=>[1,1,2,2,1,3,1] 0110100010=>[2,1,2,4,2]=>[1,2,1,1,2,3,1] 0110100100=>[2,1,2,3,3]=>[1,1,2,1,2,3,1] 0110101000=>[2,1,2,2,4]=>[1,1,1,2,2,3,1] 0110110000=>[2,1,2,1,5]=>[1,1,1,1,3,3,1] 0111000100=>[2,1,1,4,3]=>[1,1,2,1,1,4,1] 0111010000=>[2,1,1,2,5]=>[1,1,1,1,2,4,1] 001010101010=>[3,2,2,2,2,2]=>[1,2,2,2,2,2,1,1] 001010101100=>[3,2,2,2,1,3]=>[1,1,3,2,2,2,1,1] 001010110010=>[3,2,2,1,3,2]=>[1,2,1,3,2,2,1,1] 001010110100=>[3,2,2,1,2,3]=>[1,1,2,3,2,2,1,1] 001010111000=>[3,2,2,1,1,4]=>[1,1,1,4,2,2,1,1] 001011001010=>[3,2,1,3,2,2]=>[1,2,2,1,3,2,1,1] 001011001100=>[3,2,1,3,1,3]=>[1,1,3,1,3,2,1,1] 001011010010=>[3,2,1,2,3,2]=>[1,2,1,2,3,2,1,1] 001011010100=>[3,2,1,2,2,3]=>[1,1,2,2,3,2,1,1] 001011011000=>[3,2,1,2,1,4]=>[1,1,1,3,3,2,1,1] 001011100010=>[3,2,1,1,4,2]=>[1,2,1,1,4,2,1,1] 001011100100=>[3,2,1,1,3,3]=>[1,1,2,1,4,2,1,1] 001011101000=>[3,2,1,1,2,4]=>[1,1,1,2,4,2,1,1] 001011110000=>[3,2,1,1,1,5]=>[1,1,1,1,5,2,1,1] 001100101010=>[3,1,3,2,2,2]=>[1,2,2,2,1,3,1,1] 001100101100=>[3,1,3,2,1,3]=>[1,1,3,2,1,3,1,1] 001100110010=>[3,1,3,1,3,2]=>[1,2,1,3,1,3,1,1] 001100110100=>[3,1,3,1,2,3]=>[1,1,2,3,1,3,1,1] 001100111000=>[3,1,3,1,1,4]=>[1,1,1,4,1,3,1,1] 001101001010=>[3,1,2,3,2,2]=>[1,2,2,1,2,3,1,1] 001101001100=>[3,1,2,3,1,3]=>[1,1,3,1,2,3,1,1] 001101010010=>[3,1,2,2,3,2]=>[1,2,1,2,2,3,1,1] 001101010100=>[3,1,2,2,2,3]=>[1,1,2,2,2,3,1,1] 001101011000=>[3,1,2,2,1,4]=>[1,1,1,3,2,3,1,1] 001101100010=>[3,1,2,1,4,2]=>[1,2,1,1,3,3,1,1] 001101100100=>[3,1,2,1,3,3]=>[1,1,2,1,3,3,1,1] 001101101000=>[3,1,2,1,2,4]=>[1,1,1,2,3,3,1,1] 001101110000=>[3,1,2,1,1,5]=>[1,1,1,1,4,3,1,1] 001110001010=>[3,1,1,4,2,2]=>[1,2,2,1,1,4,1,1] 001110001100=>[3,1,1,4,1,3]=>[1,1,3,1,1,4,1,1] 001110010010=>[3,1,1,3,3,2]=>[1,2,1,2,1,4,1,1] 001110010100=>[3,1,1,3,2,3]=>[1,1,2,2,1,4,1,1] 001110011000=>[3,1,1,3,1,4]=>[1,1,1,3,1,4,1,1] 001110100010=>[3,1,1,2,4,2]=>[1,2,1,1,2,4,1,1] 001110100100=>[3,1,1,2,3,3]=>[1,1,2,1,2,4,1,1] 001110101000=>[3,1,1,2,2,4]=>[1,1,1,2,2,4,1,1] 001110110000=>[3,1,1,2,1,5]=>[1,1,1,1,3,4,1,1] 001111000010=>[3,1,1,1,5,2]=>[1,2,1,1,1,5,1,1] 001111000100=>[3,1,1,1,4,3]=>[1,1,2,1,1,5,1,1] 001111001000=>[3,1,1,1,3,4]=>[1,1,1,2,1,5,1,1] 001111010000=>[3,1,1,1,2,5]=>[1,1,1,1,2,5,1,1] 001111100000=>[3,1,1,1,1,6]=>[1,1,1,1,1,6,1,1] 010010101010=>[2,3,2,2,2,2]=>[1,2,2,2,2,1,2,1] 010010101100=>[2,3,2,2,1,3]=>[1,1,3,2,2,1,2,1] 010010110010=>[2,3,2,1,3,2]=>[1,2,1,3,2,1,2,1] 010010110100=>[2,3,2,1,2,3]=>[1,1,2,3,2,1,2,1] 010010111000=>[2,3,2,1,1,4]=>[1,1,1,4,2,1,2,1] 010011001010=>[2,3,1,3,2,2]=>[1,2,2,1,3,1,2,1] 010011001100=>[2,3,1,3,1,3]=>[1,1,3,1,3,1,2,1] 010011010010=>[2,3,1,2,3,2]=>[1,2,1,2,3,1,2,1] 010011010100=>[2,3,1,2,2,3]=>[1,1,2,2,3,1,2,1] 010011011000=>[2,3,1,2,1,4]=>[1,1,1,3,3,1,2,1] 010011100010=>[2,3,1,1,4,2]=>[1,2,1,1,4,1,2,1] 010011100100=>[2,3,1,1,3,3]=>[1,1,2,1,4,1,2,1] 010011101000=>[2,3,1,1,2,4]=>[1,1,1,2,4,1,2,1] 010011110000=>[2,3,1,1,1,5]=>[1,1,1,1,5,1,2,1] 010100101010=>[2,2,3,2,2,2]=>[1,2,2,2,1,2,2,1] 010100101100=>[2,2,3,2,1,3]=>[1,1,3,2,1,2,2,1] 010100110010=>[2,2,3,1,3,2]=>[1,2,1,3,1,2,2,1] 010100110100=>[2,2,3,1,2,3]=>[1,1,2,3,1,2,2,1] 010100111000=>[2,2,3,1,1,4]=>[1,1,1,4,1,2,2,1] 010101001010=>[2,2,2,3,2,2]=>[1,2,2,1,2,2,2,1] 010101001100=>[2,2,2,3,1,3]=>[1,1,3,1,2,2,2,1] 010101010010=>[2,2,2,2,3,2]=>[1,2,1,2,2,2,2,1] 010101010100=>[2,2,2,2,2,3]=>[1,1,2,2,2,2,2,1] 010101011000=>[2,2,2,2,1,4]=>[1,1,1,3,2,2,2,1] 010101100010=>[2,2,2,1,4,2]=>[1,2,1,1,3,2,2,1] 010101100100=>[2,2,2,1,3,3]=>[1,1,2,1,3,2,2,1] 010101101000=>[2,2,2,1,2,4]=>[1,1,1,2,3,2,2,1] 010101110000=>[2,2,2,1,1,5]=>[1,1,1,1,4,2,2,1] 010110001010=>[2,2,1,4,2,2]=>[1,2,2,1,1,3,2,1] 010110001100=>[2,2,1,4,1,3]=>[1,1,3,1,1,3,2,1] 010110010010=>[2,2,1,3,3,2]=>[1,2,1,2,1,3,2,1] 010110010100=>[2,2,1,3,2,3]=>[1,1,2,2,1,3,2,1] 010110011000=>[2,2,1,3,1,4]=>[1,1,1,3,1,3,2,1] 010110100010=>[2,2,1,2,4,2]=>[1,2,1,1,2,3,2,1] 010110100100=>[2,2,1,2,3,3]=>[1,1,2,1,2,3,2,1] 010110101000=>[2,2,1,2,2,4]=>[1,1,1,2,2,3,2,1] 010110110000=>[2,2,1,2,1,5]=>[1,1,1,1,3,3,2,1] 010111000010=>[2,2,1,1,5,2]=>[1,2,1,1,1,4,2,1] 010111000100=>[2,2,1,1,4,3]=>[1,1,2,1,1,4,2,1] 010111001000=>[2,2,1,1,3,4]=>[1,1,1,2,1,4,2,1] 010111010000=>[2,2,1,1,2,5]=>[1,1,1,1,2,4,2,1] 010111100000=>[2,2,1,1,1,6]=>[1,1,1,1,1,5,2,1] 011000101010=>[2,1,4,2,2,2]=>[1,2,2,2,1,1,3,1] 011000101100=>[2,1,4,2,1,3]=>[1,1,3,2,1,1,3,1] 011000110010=>[2,1,4,1,3,2]=>[1,2,1,3,1,1,3,1] 011000110100=>[2,1,4,1,2,3]=>[1,1,2,3,1,1,3,1] 011000111000=>[2,1,4,1,1,4]=>[1,1,1,4,1,1,3,1] 011001001010=>[2,1,3,3,2,2]=>[1,2,2,1,2,1,3,1] 011001001100=>[2,1,3,3,1,3]=>[1,1,3,1,2,1,3,1] 011001010010=>[2,1,3,2,3,2]=>[1,2,1,2,2,1,3,1] 011001010100=>[2,1,3,2,2,3]=>[1,1,2,2,2,1,3,1] 011001011000=>[2,1,3,2,1,4]=>[1,1,1,3,2,1,3,1] 011001100010=>[2,1,3,1,4,2]=>[1,2,1,1,3,1,3,1] 011001100100=>[2,1,3,1,3,3]=>[1,1,2,1,3,1,3,1] 011001101000=>[2,1,3,1,2,4]=>[1,1,1,2,3,1,3,1] 011001110000=>[2,1,3,1,1,5]=>[1,1,1,1,4,1,3,1] 011010001010=>[2,1,2,4,2,2]=>[1,2,2,1,1,2,3,1] 011010001100=>[2,1,2,4,1,3]=>[1,1,3,1,1,2,3,1] 011010010010=>[2,1,2,3,3,2]=>[1,2,1,2,1,2,3,1] 011010010100=>[2,1,2,3,2,3]=>[1,1,2,2,1,2,3,1] 011010011000=>[2,1,2,3,1,4]=>[1,1,1,3,1,2,3,1] 011010100010=>[2,1,2,2,4,2]=>[1,2,1,1,2,2,3,1] 011010100100=>[2,1,2,2,3,3]=>[1,1,2,1,2,2,3,1] 011010101000=>[2,1,2,2,2,4]=>[1,1,1,2,2,2,3,1] 011010110000=>[2,1,2,2,1,5]=>[1,1,1,1,3,2,3,1] 011011000010=>[2,1,2,1,5,2]=>[1,2,1,1,1,3,3,1] 011011000100=>[2,1,2,1,4,3]=>[1,1,2,1,1,3,3,1] 011011001000=>[2,1,2,1,3,4]=>[1,1,1,2,1,3,3,1] 011011010000=>[2,1,2,1,2,5]=>[1,1,1,1,2,3,3,1] 011011100000=>[2,1,2,1,1,6]=>[1,1,1,1,1,4,3,1] 011100001010=>[2,1,1,5,2,2]=>[1,2,2,1,1,1,4,1] 011100001100=>[2,1,1,5,1,3]=>[1,1,3,1,1,1,4,1] 011100010010=>[2,1,1,4,3,2]=>[1,2,1,2,1,1,4,1] 011100010100=>[2,1,1,4,2,3]=>[1,1,2,2,1,1,4,1] 011100011000=>[2,1,1,4,1,4]=>[1,1,1,3,1,1,4,1] 011100100010=>[2,1,1,3,4,2]=>[1,2,1,1,2,1,4,1] 011100100100=>[2,1,1,3,3,3]=>[1,1,2,1,2,1,4,1] 011100101000=>[2,1,1,3,2,4]=>[1,1,1,2,2,1,4,1] 011100110000=>[2,1,1,3,1,5]=>[1,1,1,1,3,1,4,1] 011101000010=>[2,1,1,2,5,2]=>[1,2,1,1,1,2,4,1] 011101000100=>[2,1,1,2,4,3]=>[1,1,2,1,1,2,4,1] 011101001000=>[2,1,1,2,3,4]=>[1,1,1,2,1,2,4,1] 011101010000=>[2,1,1,2,2,5]=>[1,1,1,1,2,2,4,1] 011101100000=>[2,1,1,2,1,6]=>[1,1,1,1,1,3,4,1] 011110000010=>[2,1,1,1,6,2]=>[1,2,1,1,1,1,5,1] 011110000100=>[2,1,1,1,5,3]=>[1,1,2,1,1,1,5,1] 011110001000=>[2,1,1,1,4,4]=>[1,1,1,2,1,1,5,1] 011110010000=>[2,1,1,1,3,5]=>[1,1,1,1,2,1,5,1] 011110100000=>[2,1,1,1,2,6]=>[1,1,1,1,1,2,5,1] 011111000000=>[2,1,1,1,1,7]=>[1,1,1,1,1,1,6,1] 10101010101=>[1,2,2,2,2,2,1]=>[2,2,2,2,2,2] 10101010010=>[1,2,2,2,3,2]=>[1,2,1,2,2,2,2] 10101001001=>[1,2,2,3,3,1]=>[2,1,2,1,2,2,2] 10101001010=>[1,2,2,3,2,2]=>[1,2,2,1,2,2,2] 10101000100=>[1,2,2,4,3]=>[1,1,2,1,1,2,2,2] 10100100101=>[1,2,3,3,2,1]=>[2,2,1,2,1,2,2] 10100100010=>[1,2,3,4,2]=>[1,2,1,1,2,1,2,2] 10100101001=>[1,2,3,2,3,1]=>[2,1,2,2,1,2,2] 10100100100=>[1,2,3,3,3]=>[1,1,2,1,2,1,2,2] 10100010001=>[1,2,4,4,1]=>[2,1,1,2,1,1,2,2] 10100010100=>[1,2,4,2,3]=>[1,1,2,2,1,1,2,2] 10100001000=>[1,2,5,4]=>[1,1,1,2,1,1,1,2,2] 10010010101=>[1,3,3,2,2,1]=>[2,2,2,1,2,1,2] 10010001001=>[1,3,4,3,1]=>[2,1,2,1,1,2,1,2] 10010100101=>[1,3,2,3,2,1]=>[2,2,1,2,2,1,2] 10010101001=>[1,3,2,2,3,1]=>[2,1,2,2,2,1,2] 10010100100=>[1,3,2,3,3]=>[1,1,2,1,2,2,1,2] 10010010001=>[1,3,3,4,1]=>[2,1,1,2,1,2,1,2] 10001000101=>[1,4,4,2,1]=>[2,2,1,1,2,1,1,2] 10001001001=>[1,4,3,3,1]=>[2,1,2,1,2,1,1,2] 10001010001=>[1,4,2,4,1]=>[2,1,1,2,2,1,1,2] 10000100001=>[1,5,5,1]=>[2,1,1,1,2,1,1,1,2] 01001010101=>[2,3,2,2,2,1]=>[2,2,2,2,1,2,1] 01001010010=>[2,3,2,3,2]=>[1,2,1,2,2,1,2,1] 01001001001=>[2,3,3,3,1]=>[2,1,2,1,2,1,2,1] 01001001010=>[2,3,3,2,2]=>[1,2,2,1,2,1,2,1] 01001000100=>[2,3,4,3]=>[1,1,2,1,1,2,1,2,1] 01000100101=>[2,4,3,2,1]=>[2,2,1,2,1,1,2,1] 01000100010=>[2,4,4,2]=>[1,2,1,1,2,1,1,2,1] 01000101001=>[2,4,2,3,1]=>[2,1,2,2,1,1,2,1] 01000101010=>[2,4,2,2,2]=>[1,2,2,2,1,1,2,1] 01000100100=>[2,4,3,3]=>[1,1,2,1,2,1,1,2,1] 01000010001=>[2,5,4,1]=>[2,1,1,2,1,1,1,2,1] 01000010010=>[2,5,3,2]=>[1,2,1,2,1,1,1,2,1] 01000010100=>[2,5,2,3]=>[1,1,2,2,1,1,1,2,1] 01000001000=>[2,6,4]=>[1,1,1,2,1,1,1,1,2,1] 01010010101=>[2,2,3,2,2,1]=>[2,2,2,1,2,2,1] 01010010010=>[2,2,3,3,2]=>[1,2,1,2,1,2,2,1] 01010001001=>[2,2,4,3,1]=>[2,1,2,1,1,2,2,1] 01010001010=>[2,2,4,2,2]=>[1,2,2,1,1,2,2,1] 01010000100=>[2,2,5,3]=>[1,1,2,1,1,1,2,2,1] 01010100101=>[2,2,2,3,2,1]=>[2,2,1,2,2,2,1] 01010100010=>[2,2,2,4,2]=>[1,2,1,1,2,2,2,1] 01010101001=>[2,2,2,2,3,1]=>[2,1,2,2,2,2,1] 01010101010=>[2,2,2,2,2,2]=>[1,2,2,2,2,2,1] 01010100100=>[2,2,2,3,3]=>[1,1,2,1,2,2,2,1] 01010010001=>[2,2,3,4,1]=>[2,1,1,2,1,2,2,1] 01010010100=>[2,2,3,2,3]=>[1,1,2,2,1,2,2,1] 01010001000=>[2,2,4,4]=>[1,1,1,2,1,1,2,2,1] 01001000101=>[2,3,4,2,1]=>[2,2,1,1,2,1,2,1] 01001000010=>[2,3,5,2]=>[1,2,1,1,1,2,1,2,1] 01001010001=>[2,3,2,4,1]=>[2,1,1,2,2,1,2,1] 01001010100=>[2,3,2,2,3]=>[1,1,2,2,2,1,2,1] 01001001000=>[2,3,3,4]=>[1,1,1,2,1,2,1,2,1] 01000100001=>[2,4,5,1]=>[2,1,1,1,2,1,1,2,1] 01000101000=>[2,4,2,4]=>[1,1,1,2,2,1,1,2,1] 01000010000=>[2,5,5]=>[1,1,1,1,2,1,1,1,2,1] 00100010101=>[3,4,2,2,1]=>[2,2,2,1,1,2,1,1] 00100010010=>[3,4,3,2]=>[1,2,1,2,1,1,2,1,1] 00100001001=>[3,5,3,1]=>[2,1,2,1,1,1,2,1,1] 00100001010=>[3,5,2,2]=>[1,2,2,1,1,1,2,1,1] 00100000100=>[3,6,3]=>[1,1,2,1,1,1,1,2,1,1] 00100100101=>[3,3,3,2,1]=>[2,2,1,2,1,2,1,1] 00100100010=>[3,3,4,2]=>[1,2,1,1,2,1,2,1,1] 00100101001=>[3,3,2,3,1]=>[2,1,2,2,1,2,1,1] 00100101010=>[3,3,2,2,2]=>[1,2,2,2,1,2,1,1] 00100100100=>[3,3,3,3]=>[1,1,2,1,2,1,2,1,1] 00100010001=>[3,4,4,1]=>[2,1,1,2,1,1,2,1,1] 00100010100=>[3,4,2,3]=>[1,1,2,2,1,1,2,1,1] 00100001000=>[3,5,4]=>[1,1,1,2,1,1,1,2,1,1] 00101000101=>[3,2,4,2,1]=>[2,2,1,1,2,2,1,1] 00101000010=>[3,2,5,2]=>[1,2,1,1,1,2,2,1,1] 00101001001=>[3,2,3,3,1]=>[2,1,2,1,2,2,1,1] 00101001010=>[3,2,3,2,2]=>[1,2,2,1,2,2,1,1] 00101000100=>[3,2,4,3]=>[1,1,2,1,1,2,2,1,1] 00101010001=>[3,2,2,4,1]=>[2,1,1,2,2,2,1,1] 00101010010=>[3,2,2,3,2]=>[1,2,1,2,2,2,1,1] 00101010100=>[3,2,2,2,3]=>[1,1,2,2,2,2,1,1] 00101001000=>[3,2,3,4]=>[1,1,1,2,1,2,2,1,1] 00100100001=>[3,3,5,1]=>[2,1,1,1,2,1,2,1,1] 00100101000=>[3,3,2,4]=>[1,1,1,2,2,1,2,1,1] 00100010000=>[3,4,5]=>[1,1,1,1,2,1,1,2,1,1] 00010000101=>[4,5,2,1]=>[2,2,1,1,1,2,1,1,1] 00010000010=>[4,6,2]=>[1,2,1,1,1,1,2,1,1,1] 00010001001=>[4,4,3,1]=>[2,1,2,1,1,2,1,1,1] 00010001010=>[4,4,2,2]=>[1,2,2,1,1,2,1,1,1] 00010000100=>[4,5,3]=>[1,1,2,1,1,1,2,1,1,1] 00010010001=>[4,3,4,1]=>[2,1,1,2,1,2,1,1,1] 00010010010=>[4,3,3,2]=>[1,2,1,2,1,2,1,1,1] 00010010100=>[4,3,2,3]=>[1,1,2,2,1,2,1,1,1] 00010001000=>[4,4,4]=>[1,1,1,2,1,1,2,1,1,1] 00010100001=>[4,2,5,1]=>[2,1,1,1,2,2,1,1,1] 00010100010=>[4,2,4,2]=>[1,2,1,1,2,2,1,1,1] 00010100100=>[4,2,3,3]=>[1,1,2,1,2,2,1,1,1] 00010101000=>[4,2,2,4]=>[1,1,1,2,2,2,1,1,1] 00010010000=>[4,3,5]=>[1,1,1,1,2,1,2,1,1,1] 00001000001=>[5,6,1]=>[2,1,1,1,1,2,1,1,1,1] 00001000010=>[5,5,2]=>[1,2,1,1,1,2,1,1,1,1] 00001000100=>[5,4,3]=>[1,1,2,1,1,2,1,1,1,1] 00001001000=>[5,3,4]=>[1,1,1,2,1,2,1,1,1,1] 00001010000=>[5,2,5]=>[1,1,1,1,2,2,1,1,1,1] 00000100000=>[6,6]=>[1,1,1,1,1,2,1,1,1,1,1] 0100000000=>[2,9]=>[1,1,1,1,1,1,1,1,2,1] 0100000011=>[2,7,1,1]=>[3,1,1,1,1,1,2,1] 0100000111=>[2,6,1,1,1]=>[4,1,1,1,1,2,1] 0100011111=>[2,4,1,1,1,1,1]=>[6,1,1,2,1] 0100111111=>[2,3,1,1,1,1,1,1]=>[7,1,2,1] 0101111111=>[2,2,1,1,1,1,1,1,1]=>[8,2,1] 01000000000=>[2,10]=>[1,1,1,1,1,1,1,1,1,2,1] 01000000011=>[2,8,1,1]=>[3,1,1,1,1,1,1,2,1] 0100000101=>[2,6,2,1]=>[2,2,1,1,1,1,2,1] 01000000111=>[2,7,1,1,1]=>[4,1,1,1,1,1,2,1] 0100001011=>[2,5,2,1,1]=>[3,2,1,1,1,2,1] 01000001111=>[2,6,1,1,1,1]=>[5,1,1,1,1,2,1] 01000011111=>[2,5,1,1,1,1,1]=>[6,1,1,1,2,1] 0100101111=>[2,3,2,1,1,1,1]=>[5,2,1,2,1] 01000111111=>[2,4,1,1,1,1,1,1]=>[7,1,1,2,1] 0101011111=>[2,2,2,1,1,1,1,1]=>[6,2,2,1] 01001111111=>[2,3,1,1,1,1,1,1,1]=>[8,1,2,1] 0110111111=>[2,1,2,1,1,1,1,1,1]=>[7,3,1] 01011111111=>[2,2,1,1,1,1,1,1,1,1]=>[9,2,1] 0101010110=>[2,2,2,2,1,2]=>[1,3,2,2,2,1] 0101011001=>[2,2,2,1,3,1]=>[2,1,3,2,2,1] 0101011010=>[2,2,2,1,2,2]=>[1,2,3,2,2,1] 0101011100=>[2,2,2,1,1,3]=>[1,1,4,2,2,1] 0101100101=>[2,2,1,3,2,1]=>[2,2,1,3,2,1] 0101100110=>[2,2,1,3,1,2]=>[1,3,1,3,2,1] 0101101001=>[2,2,1,2,3,1]=>[2,1,2,3,2,1] 0101101010=>[2,2,1,2,2,2]=>[1,2,2,3,2,1] 0101101100=>[2,2,1,2,1,3]=>[1,1,3,3,2,1] 0101110001=>[2,2,1,1,4,1]=>[2,1,1,4,2,1] 0101110010=>[2,2,1,1,3,2]=>[1,2,1,4,2,1] 0101110100=>[2,2,1,1,2,3]=>[1,1,2,4,2,1] 0101111000=>[2,2,1,1,1,4]=>[1,1,1,5,2,1] 0110010101=>[2,1,3,2,2,1]=>[2,2,2,1,3,1] 0110010110=>[2,1,3,2,1,2]=>[1,3,2,1,3,1] 0110011001=>[2,1,3,1,3,1]=>[2,1,3,1,3,1] 0110011010=>[2,1,3,1,2,2]=>[1,2,3,1,3,1] 0110011100=>[2,1,3,1,1,3]=>[1,1,4,1,3,1] 0110100101=>[2,1,2,3,2,1]=>[2,2,1,2,3,1] 0110100110=>[2,1,2,3,1,2]=>[1,3,1,2,3,1] 0110101001=>[2,1,2,2,3,1]=>[2,1,2,2,3,1] 0110101010=>[2,1,2,2,2,2]=>[1,2,2,2,3,1] 0110101100=>[2,1,2,2,1,3]=>[1,1,3,2,3,1] 0110110001=>[2,1,2,1,4,1]=>[2,1,1,3,3,1] 0110110010=>[2,1,2,1,3,2]=>[1,2,1,3,3,1] 0110110100=>[2,1,2,1,2,3]=>[1,1,2,3,3,1] 0110111000=>[2,1,2,1,1,4]=>[1,1,1,4,3,1] 0111000101=>[2,1,1,4,2,1]=>[2,2,1,1,4,1] 0111000110=>[2,1,1,4,1,2]=>[1,3,1,1,4,1] 0111001001=>[2,1,1,3,3,1]=>[2,1,2,1,4,1] 0111001010=>[2,1,1,3,2,2]=>[1,2,2,1,4,1] 0111001100=>[2,1,1,3,1,3]=>[1,1,3,1,4,1] 0111010010=>[2,1,1,2,3,2]=>[1,2,1,2,4,1] 0111011000=>[2,1,1,2,1,4]=>[1,1,1,3,4,1] 0111100010=>[2,1,1,1,4,2]=>[1,2,1,1,5,1] 0111100100=>[2,1,1,1,3,3]=>[1,1,2,1,5,1] 0111101000=>[2,1,1,1,2,4]=>[1,1,1,2,5,1] 0111110000=>[2,1,1,1,1,5]=>[1,1,1,1,6,1] 010101010110=>[2,2,2,2,2,1,2]=>[1,3,2,2,2,2,1] 010101011001=>[2,2,2,2,1,3,1]=>[2,1,3,2,2,2,1] 010101011010=>[2,2,2,2,1,2,2]=>[1,2,3,2,2,2,1] 010101011100=>[2,2,2,2,1,1,3]=>[1,1,4,2,2,2,1] 010101100101=>[2,2,2,1,3,2,1]=>[2,2,1,3,2,2,1] 010101100110=>[2,2,2,1,3,1,2]=>[1,3,1,3,2,2,1] 010101101001=>[2,2,2,1,2,3,1]=>[2,1,2,3,2,2,1] 010101101100=>[2,2,2,1,2,1,3]=>[1,1,3,3,2,2,1] 010101110001=>[2,2,2,1,1,4,1]=>[2,1,1,4,2,2,1] 010101110010=>[2,2,2,1,1,3,2]=>[1,2,1,4,2,2,1] 010101110100=>[2,2,2,1,1,2,3]=>[1,1,2,4,2,2,1] 010101111000=>[2,2,2,1,1,1,4]=>[1,1,1,5,2,2,1] 010110010101=>[2,2,1,3,2,2,1]=>[2,2,2,1,3,2,1] 010110010110=>[2,2,1,3,2,1,2]=>[1,3,2,1,3,2,1] 010110011001=>[2,2,1,3,1,3,1]=>[2,1,3,1,3,2,1] 010110011100=>[2,2,1,3,1,1,3]=>[1,1,4,1,3,2,1] 010110100101=>[2,2,1,2,3,2,1]=>[2,2,1,2,3,2,1] 010110101001=>[2,2,1,2,2,3,1]=>[2,1,2,2,3,2,1] 010110101010=>[2,2,1,2,2,2,2]=>[1,2,2,2,3,2,1] 010110101100=>[2,2,1,2,2,1,3]=>[1,1,3,2,3,2,1] 010110110001=>[2,2,1,2,1,4,1]=>[2,1,1,3,3,2,1] 010110110100=>[2,2,1,2,1,2,3]=>[1,1,2,3,3,2,1] 010111000101=>[2,2,1,1,4,2,1]=>[2,2,1,1,4,2,1] 010111000110=>[2,2,1,1,4,1,2]=>[1,3,1,1,4,2,1] 010111001001=>[2,2,1,1,3,3,1]=>[2,1,2,1,4,2,1] 010111001100=>[2,2,1,1,3,1,3]=>[1,1,3,1,4,2,1] 010111010001=>[2,2,1,1,2,4,1]=>[2,1,1,2,4,2,1] 010111010010=>[2,2,1,1,2,3,2]=>[1,2,1,2,4,2,1] 010111010100=>[2,2,1,1,2,2,3]=>[1,1,2,2,4,2,1] 010111011000=>[2,2,1,1,2,1,4]=>[1,1,1,3,4,2,1] 010111100001=>[2,2,1,1,1,5,1]=>[2,1,1,1,5,2,1] 010111100100=>[2,2,1,1,1,3,3]=>[1,1,2,1,5,2,1] 010111110000=>[2,2,1,1,1,1,5]=>[1,1,1,1,6,2,1] 011001010101=>[2,1,3,2,2,2,1]=>[2,2,2,2,1,3,1] 011001010110=>[2,1,3,2,2,1,2]=>[1,3,2,2,1,3,1] 011001011001=>[2,1,3,2,1,3,1]=>[2,1,3,2,1,3,1] 011001011100=>[2,1,3,2,1,1,3]=>[1,1,4,2,1,3,1] 011001100101=>[2,1,3,1,3,2,1]=>[2,2,1,3,1,3,1] 011001101001=>[2,1,3,1,2,3,1]=>[2,1,2,3,1,3,1] 011001101010=>[2,1,3,1,2,2,2]=>[1,2,2,3,1,3,1] 011001101100=>[2,1,3,1,2,1,3]=>[1,1,3,3,1,3,1] 011001110001=>[2,1,3,1,1,4,1]=>[2,1,1,4,1,3,1] 011001110100=>[2,1,3,1,1,2,3]=>[1,1,2,4,1,3,1] 011010010101=>[2,1,2,3,2,2,1]=>[2,2,2,1,2,3,1] 011010010110=>[2,1,2,3,2,1,2]=>[1,3,2,1,2,3,1] 011010011001=>[2,1,2,3,1,3,1]=>[2,1,3,1,2,3,1] 011010011010=>[2,1,2,3,1,2,2]=>[1,2,3,1,2,3,1] 011010011100=>[2,1,2,3,1,1,3]=>[1,1,4,1,2,3,1] 011010100101=>[2,1,2,2,3,2,1]=>[2,2,1,2,2,3,1] 011010100110=>[2,1,2,2,3,1,2]=>[1,3,1,2,2,3,1] 011010101001=>[2,1,2,2,2,3,1]=>[2,1,2,2,2,3,1] 011010101010=>[2,1,2,2,2,2,2]=>[1,2,2,2,2,3,1] 011010101100=>[2,1,2,2,2,1,3]=>[1,1,3,2,2,3,1] 011010110001=>[2,1,2,2,1,4,1]=>[2,1,1,3,2,3,1] 011010110010=>[2,1,2,2,1,3,2]=>[1,2,1,3,2,3,1] 011010110100=>[2,1,2,2,1,2,3]=>[1,1,2,3,2,3,1] 011010111000=>[2,1,2,2,1,1,4]=>[1,1,1,4,2,3,1] 011011000101=>[2,1,2,1,4,2,1]=>[2,2,1,1,3,3,1] 011011000110=>[2,1,2,1,4,1,2]=>[1,3,1,1,3,3,1] 011011001001=>[2,1,2,1,3,3,1]=>[2,1,2,1,3,3,1] 011011001010=>[2,1,2,1,3,2,2]=>[1,2,2,1,3,3,1] 011011001100=>[2,1,2,1,3,1,3]=>[1,1,3,1,3,3,1] 011011010001=>[2,1,2,1,2,4,1]=>[2,1,1,2,3,3,1] 011011010010=>[2,1,2,1,2,3,2]=>[1,2,1,2,3,3,1] 011011010100=>[2,1,2,1,2,2,3]=>[1,1,2,2,3,3,1] 011011011000=>[2,1,2,1,2,1,4]=>[1,1,1,3,3,3,1] 011011100001=>[2,1,2,1,1,5,1]=>[2,1,1,1,4,3,1] 011011100010=>[2,1,2,1,1,4,2]=>[1,2,1,1,4,3,1] 011011100100=>[2,1,2,1,1,3,3]=>[1,1,2,1,4,3,1] 011011101000=>[2,1,2,1,1,2,4]=>[1,1,1,2,4,3,1] 011011110000=>[2,1,2,1,1,1,5]=>[1,1,1,1,5,3,1] 011100010101=>[2,1,1,4,2,2,1]=>[2,2,2,1,1,4,1] 011100010110=>[2,1,1,4,2,1,2]=>[1,3,2,1,1,4,1] 011100011001=>[2,1,1,4,1,3,1]=>[2,1,3,1,1,4,1] 011100011100=>[2,1,1,4,1,1,3]=>[1,1,4,1,1,4,1] 011100100101=>[2,1,1,3,3,2,1]=>[2,2,1,2,1,4,1] 011100101001=>[2,1,1,3,2,3,1]=>[2,1,2,2,1,4,1] 011100101010=>[2,1,1,3,2,2,2]=>[1,2,2,2,1,4,1] 011100101100=>[2,1,1,3,2,1,3]=>[1,1,3,2,1,4,1] 011100110001=>[2,1,1,3,1,4,1]=>[2,1,1,3,1,4,1] 011100110100=>[2,1,1,3,1,2,3]=>[1,1,2,3,1,4,1] 011101000101=>[2,1,1,2,4,2,1]=>[2,2,1,1,2,4,1] 011101000110=>[2,1,1,2,4,1,2]=>[1,3,1,1,2,4,1] 011101001001=>[2,1,1,2,3,3,1]=>[2,1,2,1,2,4,1] 011101001100=>[2,1,1,2,3,1,3]=>[1,1,3,1,2,4,1] 011101010001=>[2,1,1,2,2,4,1]=>[2,1,1,2,2,4,1] 011101010010=>[2,1,1,2,2,3,2]=>[1,2,1,2,2,4,1] 011101010100=>[2,1,1,2,2,2,3]=>[1,1,2,2,2,4,1] 011101011000=>[2,1,1,2,2,1,4]=>[1,1,1,3,2,4,1] 011101100001=>[2,1,1,2,1,5,1]=>[2,1,1,1,3,4,1] 011101100100=>[2,1,1,2,1,3,3]=>[1,1,2,1,3,4,1] 011101110000=>[2,1,1,2,1,1,5]=>[1,1,1,1,4,4,1] 011110000101=>[2,1,1,1,5,2,1]=>[2,2,1,1,1,5,1] 011110001001=>[2,1,1,1,4,3,1]=>[2,1,2,1,1,5,1] 011110001010=>[2,1,1,1,4,2,2]=>[1,2,2,1,1,5,1] 011110001100=>[2,1,1,1,4,1,3]=>[1,1,3,1,1,5,1] 011110010001=>[2,1,1,1,3,4,1]=>[2,1,1,2,1,5,1] 011110010100=>[2,1,1,1,3,2,3]=>[1,1,2,2,1,5,1] 011110100001=>[2,1,1,1,2,5,1]=>[2,1,1,1,2,5,1] 011110100010=>[2,1,1,1,2,4,2]=>[1,2,1,1,2,5,1] 011110100100=>[2,1,1,1,2,3,3]=>[1,1,2,1,2,5,1] 011110101000=>[2,1,1,1,2,2,4]=>[1,1,1,2,2,5,1] 011110110000=>[2,1,1,1,2,1,5]=>[1,1,1,1,3,5,1] 011111000001=>[2,1,1,1,1,6,1]=>[2,1,1,1,1,6,1] 011111000100=>[2,1,1,1,1,4,3]=>[1,1,2,1,1,6,1] 011111010000=>[2,1,1,1,1,2,5]=>[1,1,1,1,2,6,1] 0100000100=>[2,6,3]=>[1,1,2,1,1,1,1,2,1] 0011100110=>[3,1,1,3,1,2]=>[1,3,1,4,1,1] 0011101010=>[3,1,1,2,2,2]=>[1,2,2,4,1,1] 0011101100=>[3,1,1,2,1,3]=>[1,1,3,4,1,1] 0001101110=>[4,1,2,1,1,2]=>[1,4,3,1,1,1] 0010110110=>[3,2,1,2,1,2]=>[1,3,3,2,1,1] 0011110010=>[3,1,1,1,3,2]=>[1,2,1,5,1,1] 0001110110=>[4,1,1,2,1,2]=>[1,3,4,1,1,1] 0100111010=>[2,3,1,1,2,2]=>[1,2,4,1,2,1] 0010111010=>[3,2,1,1,2,2]=>[1,2,4,2,1,1] 0011111000=>[3,1,1,1,1,4]=>[1,1,1,6,1,1] 0001111010=>[4,1,1,1,2,2]=>[1,2,5,1,1,1] 0100111100=>[2,3,1,1,1,3]=>[1,1,5,1,2,1] 0001111100=>[4,1,1,1,1,3]=>[1,1,6,1,1,1] 001111000110=>[3,1,1,1,4,1,2]=>[1,3,1,1,5,1,1] 001111001010=>[3,1,1,1,3,2,2]=>[1,2,2,1,5,1,1] 100111001100=>[1,3,1,1,3,1,3]=>[1,1,3,1,4,1,2] 001111001100=>[3,1,1,1,3,1,3]=>[1,1,3,1,5,1,1] 001011010110=>[3,2,1,2,2,1,2]=>[1,3,2,3,2,1,1] 001111010010=>[3,1,1,1,2,3,2]=>[1,2,1,2,5,1,1] 100111010100=>[1,3,1,1,2,2,3]=>[1,1,2,2,4,1,2] 001111010100=>[3,1,1,1,2,2,3]=>[1,1,2,2,5,1,1] 000111010110=>[4,1,1,2,2,1,2]=>[1,3,2,4,1,1,1] 001011011010=>[3,2,1,2,1,2,2]=>[1,2,3,3,2,1,1] 100111011000=>[1,3,1,1,2,1,4]=>[1,1,1,3,4,1,2] 001111011000=>[3,1,1,1,2,1,4]=>[1,1,1,3,5,1,1] 100011011100=>[1,4,1,2,1,1,3]=>[1,1,4,3,1,1,2] 010011011100=>[2,3,1,2,1,1,3]=>[1,1,4,3,1,2,1] 001011011100=>[3,2,1,2,1,1,3]=>[1,1,4,3,2,1,1] 000111011100=>[4,1,1,2,1,1,3]=>[1,1,4,4,1,1,1] 000011011110=>[5,1,2,1,1,1,2]=>[1,5,3,1,1,1,1] 001101100110=>[3,1,2,1,3,1,2]=>[1,3,1,3,3,1,1] 001101101010=>[3,1,2,1,2,2,2]=>[1,2,2,3,3,1,1] 100101101100=>[1,3,2,1,2,1,3]=>[1,1,3,3,2,1,2] 001101101100=>[3,1,2,1,2,1,3]=>[1,1,3,3,3,1,1] 001011100110=>[3,2,1,1,3,1,2]=>[1,3,1,4,2,1,1] 001111100010=>[3,1,1,1,1,4,2]=>[1,2,1,1,6,1,1] 100111100100=>[1,3,1,1,1,3,3]=>[1,1,2,1,5,1,2] 001111100100=>[3,1,1,1,1,3,3]=>[1,1,2,1,6,1,1] 010011101010=>[2,3,1,1,2,2,2]=>[1,2,2,4,1,2,1] 001011101010=>[3,2,1,1,2,2,2]=>[1,2,2,4,2,1,1] 100111101000=>[1,3,1,1,1,2,4]=>[1,1,1,2,5,1,2] 001111101000=>[3,1,1,1,1,2,4]=>[1,1,1,2,6,1,1] 000111101010=>[4,1,1,1,2,2,2]=>[1,2,2,5,1,1,1] 100011101100=>[1,4,1,1,2,1,3]=>[1,1,3,4,1,1,2] 010011101100=>[2,3,1,1,2,1,3]=>[1,1,3,4,1,2,1] 001011101100=>[3,2,1,1,2,1,3]=>[1,1,3,4,2,1,1] 000111101100=>[4,1,1,1,2,1,3]=>[1,1,3,5,1,1,1] 000011101110=>[5,1,1,2,1,1,2]=>[1,4,4,1,1,1,1] 101001110100=>[1,2,3,1,1,2,3]=>[1,1,2,4,1,2,2] 001001110110=>[3,3,1,1,2,1,2]=>[1,3,4,1,2,1,1] 001101110010=>[3,1,2,1,1,3,2]=>[1,2,1,4,3,1,1] 100101110100=>[1,3,2,1,1,2,3]=>[1,1,2,4,2,1,2] 001101110100=>[3,1,2,1,1,2,3]=>[1,1,2,4,3,1,1] 000101110110=>[4,2,1,1,2,1,2]=>[1,3,4,2,1,1,1] 001011110010=>[3,2,1,1,1,3,2]=>[1,2,1,5,2,1,1] 100111110000=>[1,3,1,1,1,1,5]=>[1,1,1,1,6,1,2] 001111110000=>[3,1,1,1,1,1,5]=>[1,1,1,1,7,1,1] 100011110100=>[1,4,1,1,1,2,3]=>[1,1,2,5,1,1,2] 010011110100=>[2,3,1,1,1,2,3]=>[1,1,2,5,1,2,1] 001011110100=>[3,2,1,1,1,2,3]=>[1,1,2,5,2,1,1] 000111110100=>[4,1,1,1,1,2,3]=>[1,1,2,6,1,1,1] 000011110110=>[5,1,1,1,2,1,2]=>[1,3,5,1,1,1,1] 110001111000=>[1,1,4,1,1,1,4]=>[1,1,1,5,1,1,3] 101001111000=>[1,2,3,1,1,1,4]=>[1,1,1,5,1,2,2] 001001111010=>[3,3,1,1,1,2,2]=>[1,2,5,1,2,1,1] 100101111000=>[1,3,2,1,1,1,4]=>[1,1,1,5,2,1,2] 001101111000=>[3,1,2,1,1,1,4]=>[1,1,1,5,3,1,1] 100011111000=>[1,4,1,1,1,1,4]=>[1,1,1,6,1,1,2] 001011111000=>[3,2,1,1,1,1,4]=>[1,1,1,6,2,1,1] 000011111010=>[5,1,1,1,1,2,2]=>[1,2,6,1,1,1,1] 010001111100=>[2,4,1,1,1,1,3]=>[1,1,6,1,1,2,1] 001001111100=>[3,3,1,1,1,1,3]=>[1,1,6,1,2,1,1] 000101111100=>[4,2,1,1,1,1,3]=>[1,1,6,2,1,1,1] 000011111100=>[5,1,1,1,1,1,3]=>[1,1,7,1,1,1,1] 0000000101=>[8,2,1]=>[2,2,1,1,1,1,1,1,1] 0000001101=>[7,1,2,1]=>[2,3,1,1,1,1,1,1] 0000011101=>[6,1,1,2,1]=>[2,4,1,1,1,1,1] 0001111101=>[4,1,1,1,1,2,1]=>[2,6,1,1,1] 0011111101=>[3,1,1,1,1,1,2,1]=>[2,7,1,1] 00000000101=>[9,2,1]=>[2,2,1,1,1,1,1,1,1,1] 0000001001=>[7,3,1]=>[2,1,2,1,1,1,1,1,1] 00000001101=>[8,1,2,1]=>[2,3,1,1,1,1,1,1,1] 0000010101=>[6,2,2,1]=>[2,2,2,1,1,1,1,1] 00000011101=>[7,1,1,2,1]=>[2,4,1,1,1,1,1,1] 0000101101=>[5,2,1,2,1]=>[2,3,2,1,1,1,1] 00000111101=>[6,1,1,1,2,1]=>[2,5,1,1,1,1,1] 00001111101=>[5,1,1,1,1,2,1]=>[2,6,1,1,1,1] 0010111101=>[3,2,1,1,1,2,1]=>[2,5,2,1,1] 00011111101=>[4,1,1,1,1,1,2,1]=>[2,7,1,1,1] 0101111101=>[2,2,1,1,1,1,2,1]=>[2,6,2,1] 00111111101=>[3,1,1,1,1,1,1,2,1]=>[2,8,1,1] 11111111101=>[1,1,1,1,1,1,1,1,1,2,1]=>[2,10] 100101010101=>[1,3,2,2,2,2,1]=>[2,2,2,2,2,1,2] 100101011001=>[1,3,2,2,1,3,1]=>[2,1,3,2,2,1,2] 100101100101=>[1,3,2,1,3,2,1]=>[2,2,1,3,2,1,2] 100101101001=>[1,3,2,1,2,3,1]=>[2,1,2,3,2,1,2] 100101110001=>[1,3,2,1,1,4,1]=>[2,1,1,4,2,1,2] 100110010101=>[1,3,1,3,2,2,1]=>[2,2,2,1,3,1,2] 100110101001=>[1,3,1,2,2,3,1]=>[2,1,2,2,3,1,2] 100111000101=>[1,3,1,1,4,2,1]=>[2,2,1,1,4,1,2] 100111001001=>[1,3,1,1,3,3,1]=>[2,1,2,1,4,1,2] 100111010001=>[1,3,1,1,2,4,1]=>[2,1,1,2,4,1,2] 101001010101=>[1,2,3,2,2,2,1]=>[2,2,2,2,1,2,2] 101001101001=>[1,2,3,1,2,3,1]=>[2,1,2,3,1,2,2] 101010011001=>[1,2,2,3,1,3,1]=>[2,1,3,1,2,2,2] 101010100101=>[1,2,2,2,3,2,1]=>[2,2,1,2,2,2,2] 101010101001=>[1,2,2,2,2,3,1]=>[2,1,2,2,2,2,2] 101010110001=>[1,2,2,2,1,4,1]=>[2,1,1,3,2,2,2] 101011001001=>[1,2,2,1,3,3,1]=>[2,1,2,1,3,2,2] 101011100001=>[1,2,2,1,1,5,1]=>[2,1,1,1,4,2,2] 101100010101=>[1,2,1,4,2,2,1]=>[2,2,2,1,1,3,2] 101100101001=>[1,2,1,3,2,3,1]=>[2,1,2,2,1,3,2] 101101000101=>[1,2,1,2,4,2,1]=>[2,2,1,1,2,3,2] 101101001001=>[1,2,1,2,3,3,1]=>[2,1,2,1,2,3,2] 101101010001=>[1,2,1,2,2,4,1]=>[2,1,1,2,2,3,2] 101110001001=>[1,2,1,1,4,3,1]=>[2,1,2,1,1,4,2] 101110100001=>[1,2,1,1,2,5,1]=>[2,1,1,1,2,4,2] 110001010101=>[1,1,4,2,2,2,1]=>[2,2,2,2,1,1,3] 110001011001=>[1,1,4,2,1,3,1]=>[2,1,3,2,1,1,3] 110001100101=>[1,1,4,1,3,2,1]=>[2,2,1,3,1,1,3] 110001101001=>[1,1,4,1,2,3,1]=>[2,1,2,3,1,1,3] 110001110001=>[1,1,4,1,1,4,1]=>[2,1,1,4,1,1,3] 110010010101=>[1,1,3,3,2,2,1]=>[2,2,2,1,2,1,3] 110010011001=>[1,1,3,3,1,3,1]=>[2,1,3,1,2,1,3] 110010100101=>[1,1,3,2,3,2,1]=>[2,2,1,2,2,1,3] 110010101001=>[1,1,3,2,2,3,1]=>[2,1,2,2,2,1,3] 110010110001=>[1,1,3,2,1,4,1]=>[2,1,1,3,2,1,3] 110011000101=>[1,1,3,1,4,2,1]=>[2,2,1,1,3,1,3] 110011001001=>[1,1,3,1,3,3,1]=>[2,1,2,1,3,1,3] 110011010001=>[1,1,3,1,2,4,1]=>[2,1,1,2,3,1,3] 110011100001=>[1,1,3,1,1,5,1]=>[2,1,1,1,4,1,3] 110100010101=>[1,1,2,4,2,2,1]=>[2,2,2,1,1,2,3] 110100011001=>[1,1,2,4,1,3,1]=>[2,1,3,1,1,2,3] 110100100101=>[1,1,2,3,3,2,1]=>[2,2,1,2,1,2,3] 110100101001=>[1,1,2,3,2,3,1]=>[2,1,2,2,1,2,3] 110100110001=>[1,1,2,3,1,4,1]=>[2,1,1,3,1,2,3] 110101000101=>[1,1,2,2,4,2,1]=>[2,2,1,1,2,2,3] 110101001001=>[1,1,2,2,3,3,1]=>[2,1,2,1,2,2,3] 110101010001=>[1,1,2,2,2,4,1]=>[2,1,1,2,2,2,3] 110101100001=>[1,1,2,2,1,5,1]=>[2,1,1,1,3,2,3] 110110000101=>[1,1,2,1,5,2,1]=>[2,2,1,1,1,3,3] 110110001001=>[1,1,2,1,4,3,1]=>[2,1,2,1,1,3,3] 110110010001=>[1,1,2,1,3,4,1]=>[2,1,1,2,1,3,3] 110110100001=>[1,1,2,1,2,5,1]=>[2,1,1,1,2,3,3] 110111000001=>[1,1,2,1,1,6,1]=>[2,1,1,1,1,4,3] 111000010101=>[1,1,1,5,2,2,1]=>[2,2,2,1,1,1,4] 111000101001=>[1,1,1,4,2,3,1]=>[2,1,2,2,1,1,4] 111001000101=>[1,1,1,3,4,2,1]=>[2,2,1,1,2,1,4] 111001001001=>[1,1,1,3,3,3,1]=>[2,1,2,1,2,1,4] 111001010001=>[1,1,1,3,2,4,1]=>[2,1,1,2,2,1,4] 111010001001=>[1,1,1,2,4,3,1]=>[2,1,2,1,1,2,4] 111010100001=>[1,1,1,2,2,5,1]=>[2,1,1,1,2,2,4] 111100000101=>[1,1,1,1,6,2,1]=>[2,2,1,1,1,1,5] 111100001001=>[1,1,1,1,5,3,1]=>[2,1,2,1,1,1,5] 111100010001=>[1,1,1,1,4,4,1]=>[2,1,1,2,1,1,5] 111100100001=>[1,1,1,1,3,5,1]=>[2,1,1,1,2,1,5] 111101000001=>[1,1,1,1,2,6,1]=>[2,1,1,1,1,2,5] 0111000011=>[2,1,1,5,1,1]=>[3,1,1,1,4,1] 0011110001=>[3,1,1,1,4,1]=>[2,1,1,5,1,1] 110100000111=>[1,1,2,6,1,1,1]=>[4,1,1,1,1,2,3] 110110000011=>[1,1,2,1,6,1,1]=>[3,1,1,1,1,3,3] 110000001111=>[1,1,7,1,1,1,1]=>[5,1,1,1,1,1,3] 011100000111=>[2,1,1,6,1,1,1]=>[4,1,1,1,1,4,1] 111010000011=>[1,1,1,2,6,1,1]=>[3,1,1,1,1,2,4] 001111010001=>[3,1,1,1,2,4,1]=>[2,1,1,2,5,1,1] 011110000011=>[2,1,1,1,6,1,1]=>[3,1,1,1,1,5,1] 111100000011=>[1,1,1,1,7,1,1]=>[3,1,1,1,1,1,5] 000111110001=>[4,1,1,1,1,4,1]=>[2,1,1,6,1,1,1] 001111100001=>[3,1,1,1,1,5,1]=>[2,1,1,1,6,1,1] 01111111011=>[2,1,1,1,1,1,1,2,1,1]=>[3,8,1] 01111010001=>[2,1,1,1,2,4,1]=>[2,1,1,2,5,1] 0011011001=>[3,1,2,1,3,1]=>[2,1,3,3,1,1] 0001100001=>[4,1,5,1]=>[2,1,1,1,3,1,1,1] 0001000001=>[4,6,1]=>[2,1,1,1,1,2,1,1,1] 0011110011=>[3,1,1,1,3,1,1]=>[3,1,5,1,1] 0111100011=>[2,1,1,1,4,1,1]=>[3,1,1,5,1] 110101010101=>[1,1,2,2,2,2,2,1]=>[2,2,2,2,2,3] 110101010011=>[1,1,2,2,2,3,1,1]=>[3,1,2,2,2,3] 110101001101=>[1,1,2,2,3,1,2,1]=>[2,3,1,2,2,3] 110101000111=>[1,1,2,2,4,1,1,1]=>[4,1,1,2,2,3] 110100110101=>[1,1,2,3,1,2,2,1]=>[2,2,3,1,2,3] 110100110011=>[1,1,2,3,1,3,1,1]=>[3,1,3,1,2,3] 110100011101=>[1,1,2,4,1,1,2,1]=>[2,4,1,1,2,3] 110100001111=>[1,1,2,5,1,1,1,1]=>[5,1,1,1,2,3] 110011010101=>[1,1,3,1,2,2,2,1]=>[2,2,2,3,1,3] 110011010011=>[1,1,3,1,2,3,1,1]=>[3,1,2,3,1,3] 110011001101=>[1,1,3,1,3,1,2,1]=>[2,3,1,3,1,3] 110011000111=>[1,1,3,1,4,1,1,1]=>[4,1,1,3,1,3] 110001110101=>[1,1,4,1,1,2,2,1]=>[2,2,4,1,1,3] 110001110011=>[1,1,4,1,1,3,1,1]=>[3,1,4,1,1,3] 110000111101=>[1,1,5,1,1,1,2,1]=>[2,5,1,1,1,3] 110000011111=>[1,1,6,1,1,1,1,1]=>[6,1,1,1,1,3] 111010101001=>[1,1,1,2,2,2,3,1]=>[2,1,2,2,2,4] 111101001001=>[1,1,1,1,2,3,3,1]=>[2,1,2,1,2,5] 11111110010=>[1,1,1,1,1,1,1,3,2]=>[1,2,1,8] 0001101100=>[4,1,2,1,3]=>[1,1,3,3,1,1,1] 0011000110=>[3,1,4,1,2]=>[1,3,1,1,3,1,1] 10111111101=>[1,2,1,1,1,1,1,1,2,1]=>[2,8,2] 01011111101=>[2,2,1,1,1,1,1,2,1]=>[2,7,2,1] 00101111101=>[3,2,1,1,1,1,2,1]=>[2,6,2,1,1] 0110111001=>[2,1,2,1,1,3,1]=>[2,1,4,3,1] 00010111101=>[4,2,1,1,1,2,1]=>[2,5,2,1,1,1] 00001011101=>[5,2,1,1,2,1]=>[2,4,2,1,1,1,1] 0001101001=>[4,1,2,3,1]=>[2,1,2,3,1,1,1] 00000101101=>[6,2,1,2,1]=>[2,3,2,1,1,1,1,1] 0000110001=>[5,1,4,1]=>[2,1,1,3,1,1,1,1] 00000010101=>[7,2,2,1]=>[2,2,2,1,1,1,1,1,1] 0000010001=>[6,4,1]=>[2,1,1,2,1,1,1,1,1] 00000001001=>[8,3,1]=>[2,1,2,1,1,1,1,1,1,1] 10000000001=>[1,10,1]=>[2,1,1,1,1,1,1,1,1,2] 11000000001=>[1,1,9,1]=>[2,1,1,1,1,1,1,1,3] 11100000001=>[1,1,1,8,1]=>[2,1,1,1,1,1,1,4] 11110000001=>[1,1,1,1,7,1]=>[2,1,1,1,1,1,5] 11111000001=>[1,1,1,1,1,6,1]=>[2,1,1,1,1,6] 11111100001=>[1,1,1,1,1,1,5,1]=>[2,1,1,1,7] 11111110001=>[1,1,1,1,1,1,1,4,1]=>[2,1,1,8] 11111111001=>[1,1,1,1,1,1,1,1,3,1]=>[2,1,9] 11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[12] 0110011011=>[2,1,3,1,2,1,1]=>[3,3,1,3,1] 0101111011=>[2,2,1,1,1,2,1,1]=>[3,5,2,1] 0110010011=>[2,1,3,3,1,1]=>[3,1,2,1,3,1] 0110110011=>[2,1,2,1,3,1,1]=>[3,1,3,3,1] 0110010111=>[2,1,3,2,1,1,1]=>[4,2,1,3,1] 0110110111=>[2,1,2,1,2,1,1,1]=>[4,3,3,1] 0101110111=>[2,2,1,1,2,1,1,1]=>[4,4,2,1] 0110101111=>[2,1,2,2,1,1,1,1]=>[5,2,3,1] 0101101111=>[2,2,1,2,1,1,1,1]=>[5,3,2,1] 100110011011=>[1,3,1,3,1,2,1,1]=>[3,3,1,3,1,2] 100100011011=>[1,3,4,1,2,1,1]=>[3,3,1,1,2,1,2] 101100011011=>[1,2,1,4,1,2,1,1]=>[3,3,1,1,3,2] 101000011011=>[1,2,5,1,2,1,1]=>[3,3,1,1,1,2,2] 100100111011=>[1,3,3,1,1,2,1,1]=>[3,4,1,2,1,2] 101000111011=>[1,2,4,1,1,2,1,1]=>[3,4,1,1,2,2] 101100010011=>[1,2,1,4,3,1,1]=>[3,1,2,1,1,3,2] 100110110011=>[1,3,1,2,1,3,1,1]=>[3,1,3,3,1,2] 101100110011=>[1,2,1,3,1,3,1,1]=>[3,1,3,1,3,2] 101000110011=>[1,2,4,1,3,1,1]=>[3,1,3,1,1,2,2] 100101110011=>[1,3,2,1,1,3,1,1]=>[3,1,4,2,1,2] 101001110011=>[1,2,3,1,1,3,1,1]=>[3,1,4,1,2,2] 101100100011=>[1,2,1,3,4,1,1]=>[3,1,1,2,1,3,2] 100110010111=>[1,3,1,3,2,1,1,1]=>[4,2,1,3,1,2] 100100010111=>[1,3,4,2,1,1,1]=>[4,2,1,1,2,1,2] 101100010111=>[1,2,1,4,2,1,1,1]=>[4,2,1,1,3,2] 100100110111=>[1,3,3,1,2,1,1,1]=>[4,3,1,2,1,2] 101000110111=>[1,2,4,1,2,1,1,1]=>[4,3,1,1,2,2] 100110100111=>[1,3,1,2,3,1,1,1]=>[4,1,2,3,1,2] 100100100111=>[1,3,3,3,1,1,1]=>[4,1,2,1,2,1,2] 101100100111=>[1,2,1,3,3,1,1,1]=>[4,1,2,1,3,2] 101000100111=>[1,2,4,3,1,1,1]=>[4,1,2,1,1,2,2] 100101100111=>[1,3,2,1,3,1,1,1]=>[4,1,3,2,1,2] 101001100111=>[1,2,3,1,3,1,1,1]=>[4,1,3,1,2,2] 101101000111=>[1,2,1,2,4,1,1,1]=>[4,1,1,2,3,2] 101011000111=>[1,2,2,1,4,1,1,1]=>[4,1,1,3,2,2] 101010000111=>[1,2,2,5,1,1,1]=>[4,1,1,1,2,2,2] 100100101111=>[1,3,3,2,1,1,1,1]=>[5,2,1,2,1,2] 101000101111=>[1,2,4,2,1,1,1,1]=>[5,2,1,1,2,2] 100101001111=>[1,3,2,3,1,1,1,1]=>[5,1,2,2,1,2] 101001001111=>[1,2,3,3,1,1,1,1]=>[5,1,2,1,2,2] 101010001111=>[1,2,2,4,1,1,1,1]=>[5,1,1,2,2,2] 101010001101=>[1,2,2,4,1,2,1]=>[2,3,1,1,2,2,2] 101000101101=>[1,2,4,2,1,2,1]=>[2,3,2,1,1,2,2] 100100101101=>[1,3,3,2,1,2,1]=>[2,3,2,1,2,1,2] 100100011101=>[1,3,4,1,1,2,1]=>[2,4,1,1,2,1,2] 101010010011=>[1,2,2,3,3,1,1]=>[3,1,2,1,2,2,2] 101010001011=>[1,2,2,4,2,1,1]=>[3,2,1,1,2,2,2] 100110001011=>[1,3,1,4,2,1,1]=>[3,2,1,1,3,1,2] 101000101011=>[1,2,4,2,2,1,1]=>[3,2,2,1,1,2,2] 100100101011=>[1,3,3,2,2,1,1]=>[3,2,2,1,2,1,2] 100010011011=>[1,4,3,1,2,1,1]=>[3,3,1,2,1,1,2] 100000111011=>[1,6,1,1,2,1,1]=>[3,4,1,1,1,1,2] 101000001111=>[1,2,6,1,1,1,1]=>[5,1,1,1,1,2,2] 100100001111=>[1,3,5,1,1,1,1]=>[5,1,1,1,2,1,2] 100010001111=>[1,4,4,1,1,1,1]=>[5,1,1,2,1,1,2] 100000101111=>[1,6,2,1,1,1,1]=>[5,2,1,1,1,1,2] 01010101101=>[2,2,2,2,1,2,1]=>[2,3,2,2,2,1] 01010110110=>[2,2,2,1,2,1,2]=>[1,3,3,2,2,1] 01010110101=>[2,2,2,1,2,2,1]=>[2,2,3,2,2,1] 01010111011=>[2,2,2,1,1,2,1,1]=>[3,4,2,2,1] 01011011010=>[2,2,1,2,1,2,2]=>[1,2,3,3,2,1] 01011011101=>[2,2,1,2,1,1,2,1]=>[2,4,3,2,1] 01011010110=>[2,2,1,2,2,1,2]=>[1,3,2,3,2,1] 01011010101=>[2,2,1,2,2,2,1]=>[2,2,2,3,2,1] 01011011011=>[2,2,1,2,1,2,1,1]=>[3,3,3,2,1] 01011101110=>[2,2,1,1,2,1,1,2]=>[1,4,4,2,1] 01011101101=>[2,2,1,1,2,1,2,1]=>[2,3,4,2,1] 01011101011=>[2,2,1,1,2,2,1,1]=>[3,2,4,2,1] 01011110111=>[2,2,1,1,1,2,1,1,1]=>[4,5,2,1] 01101101010=>[2,1,2,1,2,2,2]=>[1,2,2,3,3,1] 01101101101=>[2,1,2,1,2,1,2,1]=>[2,3,3,3,1] 01101110110=>[2,1,2,1,1,2,1,2]=>[1,3,4,3,1] 01101110101=>[2,1,2,1,1,2,2,1]=>[2,2,4,3,1] 01101111011=>[2,1,2,1,1,1,2,1,1]=>[3,5,3,1] 01101011010=>[2,1,2,2,1,2,2]=>[1,2,3,2,3,1] 01101011101=>[2,1,2,2,1,1,2,1]=>[2,4,2,3,1] 01101010110=>[2,1,2,2,2,1,2]=>[1,3,2,2,3,1] 01101010101=>[2,1,2,2,2,2,1]=>[2,2,2,2,3,1] 01101011011=>[2,1,2,2,1,2,1,1]=>[3,3,2,3,1] 01101101110=>[2,1,2,1,2,1,1,2]=>[1,4,3,3,1] 01101101011=>[2,1,2,1,2,2,1,1]=>[3,2,3,3,1] 01101110111=>[2,1,2,1,1,2,1,1,1]=>[4,4,3,1] 01110111010=>[2,1,1,2,1,1,2,2]=>[1,2,4,4,1] 01110111101=>[2,1,1,2,1,1,1,2,1]=>[2,5,4,1] 01110110110=>[2,1,1,2,1,2,1,2]=>[1,3,3,4,1] 01110110101=>[2,1,1,2,1,2,2,1]=>[2,2,3,4,1] 01110111011=>[2,1,1,2,1,1,2,1,1]=>[3,4,4,1] 01110101110=>[2,1,1,2,2,1,1,2]=>[1,4,2,4,1] 01110101101=>[2,1,1,2,2,1,2,1]=>[2,3,2,4,1] 01110101011=>[2,1,1,2,2,2,1,1]=>[3,2,2,4,1] 01110110111=>[2,1,1,2,1,2,1,1,1]=>[4,3,4,1] 01111011110=>[2,1,1,1,2,1,1,1,2]=>[1,5,5,1] 01111011101=>[2,1,1,1,2,1,1,2,1]=>[2,4,5,1] 01111011011=>[2,1,1,1,2,1,2,1,1]=>[3,3,5,1] 01111010111=>[2,1,1,1,2,2,1,1,1]=>[4,2,5,1] 01111101111=>[2,1,1,1,1,2,1,1,1,1]=>[5,6,1] 10110101010=>[1,2,1,2,2,2,2]=>[1,2,2,2,3,2] 10110101101=>[1,2,1,2,2,1,2,1]=>[2,3,2,3,2] 10110110101=>[1,2,1,2,1,2,2,1]=>[2,2,3,3,2] 10110111011=>[1,2,1,2,1,1,2,1,1]=>[3,4,3,2] 10111011010=>[1,2,1,1,2,1,2,2]=>[1,2,3,4,2] 10111011101=>[1,2,1,1,2,1,1,2,1]=>[2,4,4,2] 10111010101=>[1,2,1,1,2,2,2,1]=>[2,2,2,4,2] 10111011011=>[1,2,1,1,2,1,2,1,1]=>[3,3,4,2] 10111101101=>[1,2,1,1,1,2,1,2,1]=>[2,3,5,2] 10111101011=>[1,2,1,1,1,2,2,1,1]=>[3,2,5,2] 10111110111=>[1,2,1,1,1,1,2,1,1,1]=>[4,6,2] 10101101010=>[1,2,2,1,2,2,2]=>[1,2,2,3,2,2] 10101101101=>[1,2,2,1,2,1,2,1]=>[2,3,3,2,2] 10101110101=>[1,2,2,1,1,2,2,1]=>[2,2,4,2,2] 10101111011=>[1,2,2,1,1,1,2,1,1]=>[3,5,2,2] 10101011101=>[1,2,2,2,1,1,2,1]=>[2,4,2,2,2] 10101011011=>[1,2,2,2,1,2,1,1]=>[3,3,2,2,2] 10101101011=>[1,2,2,1,2,2,1,1]=>[3,2,3,2,2] 10101110111=>[1,2,2,1,1,2,1,1,1]=>[4,4,2,2] 10110111101=>[1,2,1,2,1,1,1,2,1]=>[2,5,3,2] 10110101011=>[1,2,1,2,2,2,1,1]=>[3,2,2,3,2] 10110110111=>[1,2,1,2,1,2,1,1,1]=>[4,3,3,2] 10111010111=>[1,2,1,1,2,2,1,1,1]=>[4,2,4,2] 10111101111=>[1,2,1,1,1,2,1,1,1,1]=>[5,5,2] 11011101010=>[1,1,2,1,1,2,2,2]=>[1,2,2,4,3] 11011101101=>[1,1,2,1,1,2,1,2,1]=>[2,3,4,3] 11011110101=>[1,1,2,1,1,1,2,2,1]=>[2,2,5,3] 11011111011=>[1,1,2,1,1,1,1,2,1,1]=>[3,6,3] 11011011010=>[1,1,2,1,2,1,2,2]=>[1,2,3,3,3] 11011011101=>[1,1,2,1,2,1,1,2,1]=>[2,4,3,3] 11011010110=>[1,1,2,1,2,2,1,2]=>[1,3,2,3,3] 11011010101=>[1,1,2,1,2,2,2,1]=>[2,2,2,3,3] 11011011011=>[1,1,2,1,2,1,2,1,1]=>[3,3,3,3] 11011101011=>[1,1,2,1,1,2,2,1,1]=>[3,2,4,3] 11011110111=>[1,1,2,1,1,1,2,1,1,1]=>[4,5,3] 11010111010=>[1,1,2,2,1,1,2,2]=>[1,2,4,2,3] 11010111101=>[1,1,2,2,1,1,1,2,1]=>[2,5,2,3] 11010110101=>[1,1,2,2,1,2,2,1]=>[2,2,3,2,3] 11010111011=>[1,1,2,2,1,1,2,1,1]=>[3,4,2,3] 11010101101=>[1,1,2,2,2,1,2,1]=>[2,3,2,2,3] 11010101011=>[1,1,2,2,2,2,1,1]=>[3,2,2,2,3] 11010110111=>[1,1,2,2,1,2,1,1,1]=>[4,3,2,3] 11011010111=>[1,1,2,1,2,2,1,1,1]=>[4,2,3,3] 11011101111=>[1,1,2,1,1,2,1,1,1,1]=>[5,4,3] 11101111010=>[1,1,1,2,1,1,1,2,2]=>[1,2,5,4] 11101111101=>[1,1,1,2,1,1,1,1,2,1]=>[2,6,4] 11101110101=>[1,1,1,2,1,1,2,2,1]=>[2,2,4,4] 11101111011=>[1,1,1,2,1,1,1,2,1,1]=>[3,5,4] 11101101101=>[1,1,1,2,1,2,1,2,1]=>[2,3,3,4] 11101101011=>[1,1,1,2,1,2,2,1,1]=>[3,2,3,4] 11101110111=>[1,1,1,2,1,1,2,1,1,1]=>[4,4,4] 11101011101=>[1,1,1,2,2,1,1,2,1]=>[2,4,2,4] 11101011011=>[1,1,1,2,2,1,2,1,1]=>[3,3,2,4] 11101010111=>[1,1,1,2,2,2,1,1,1]=>[4,2,2,4] 11101101111=>[1,1,1,2,1,2,1,1,1,1]=>[5,3,4] 11110111101=>[1,1,1,1,2,1,1,1,2,1]=>[2,5,5] 11110111011=>[1,1,1,1,2,1,1,2,1,1]=>[3,4,5] 11110110111=>[1,1,1,1,2,1,2,1,1,1]=>[4,3,5] 11110101111=>[1,1,1,1,2,2,1,1,1,1]=>[5,2,5] 11111011111=>[1,1,1,1,1,2,1,1,1,1,1]=>[6,6] 0000001100=>[7,1,3]=>[1,1,3,1,1,1,1,1,1] 0011001111=>[3,1,3,1,1,1,1]=>[5,1,3,1,1] 0110011111=>[2,1,3,1,1,1,1,1]=>[6,1,3,1] 00000001100=>[8,1,3]=>[1,1,3,1,1,1,1,1,1,1] 00011001111=>[4,1,3,1,1,1,1]=>[5,1,3,1,1,1] 01100111111=>[2,1,3,1,1,1,1,1,1]=>[7,1,3,1] 0000000011=>[9,1,1]=>[3,1,1,1,1,1,1,1,1] 00000000011=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1] 00001101111=>[5,1,2,1,1,1,1]=>[5,3,1,1,1,1] 01101111111=>[2,1,2,1,1,1,1,1,1,1]=>[8,3,1] 11011111111=>[1,1,2,1,1,1,1,1,1,1,1]=>[9,3] 01111010101=>[2,1,1,1,2,2,2,1]=>[2,2,2,5,1] 0001000011=>[4,5,1,1]=>[3,1,1,1,2,1,1,1] 0111100111=>[2,1,1,1,3,1,1,1]=>[4,1,5,1] 0111110111=>[2,1,1,1,1,2,1,1,1]=>[4,6,1] 11000000000=>[1,1,10]=>[1,1,1,1,1,1,1,1,1,3] 0110001011=>[2,1,4,2,1,1]=>[3,2,1,1,3,1] 0110000111=>[2,1,5,1,1,1]=>[4,1,1,1,3,1] 110000111001=>[1,1,5,1,1,3,1]=>[2,1,4,1,1,1,3] 110000110101=>[1,1,5,1,2,2,1]=>[2,2,3,1,1,1,3] 110010001101=>[1,1,3,4,1,2,1]=>[2,3,1,1,2,1,3] 110100001101=>[1,1,2,5,1,2,1]=>[2,3,1,1,1,2,3] 110000101101=>[1,1,5,2,1,2,1]=>[2,3,2,1,1,1,3] 110000011101=>[1,1,6,1,1,2,1]=>[2,4,1,1,1,1,3] 011100100011=>[2,1,1,3,4,1,1]=>[3,1,1,2,1,4,1] 011010010011=>[2,1,2,3,3,1,1]=>[3,1,2,1,2,3,1] 011100010011=>[2,1,1,4,3,1,1]=>[3,1,2,1,1,4,1] 011000110011=>[2,1,4,1,3,1,1]=>[3,1,3,1,1,3,1] 010110001011=>[2,2,1,4,2,1,1]=>[3,2,1,1,3,2,1] 011010001011=>[2,1,2,4,2,1,1]=>[3,2,1,1,2,3,1] 011100001011=>[2,1,1,5,2,1,1]=>[3,2,1,1,1,4,1] 011000101011=>[2,1,4,2,2,1,1]=>[3,2,2,1,1,3,1] 011000011011=>[2,1,5,1,2,1,1]=>[3,3,1,1,1,3,1] 101110000011=>[1,2,1,1,6,1,1]=>[3,1,1,1,1,4,2] 110100100011=>[1,1,2,3,4,1,1]=>[3,1,1,2,1,2,3] 111000100011=>[1,1,1,4,4,1,1]=>[3,1,1,2,1,1,4] 110010010011=>[1,1,3,3,3,1,1]=>[3,1,2,1,2,1,3] 110100010011=>[1,1,2,4,3,1,1]=>[3,1,2,1,1,2,3] 111000010011=>[1,1,1,5,3,1,1]=>[3,1,2,1,1,1,4] 110000110011=>[1,1,5,1,3,1,1]=>[3,1,3,1,1,1,3] 101100001011=>[1,2,1,5,2,1,1]=>[3,2,1,1,1,3,2] 110010001011=>[1,1,3,4,2,1,1]=>[3,2,1,1,2,1,3] 110100001011=>[1,1,2,5,2,1,1]=>[3,2,1,1,1,2,3] 111000001011=>[1,1,1,6,2,1,1]=>[3,2,1,1,1,1,4] 110000101011=>[1,1,5,2,2,1,1]=>[3,2,2,1,1,1,3] 110000011011=>[1,1,6,1,2,1,1]=>[3,3,1,1,1,1,3] 001110000111=>[3,1,1,5,1,1,1]=>[4,1,1,1,4,1,1] 010110000111=>[2,2,1,5,1,1,1]=>[4,1,1,1,3,2,1] 011010000111=>[2,1,2,5,1,1,1]=>[4,1,1,1,2,3,1] 011000100111=>[2,1,4,3,1,1,1]=>[4,1,2,1,1,3,1] 011000010111=>[2,1,5,2,1,1,1]=>[4,2,1,1,1,3,1] 110010000111=>[1,1,3,5,1,1,1]=>[4,1,1,1,2,1,3] 110000100111=>[1,1,5,3,1,1,1]=>[4,1,2,1,1,1,3] 110000010111=>[1,1,6,2,1,1,1]=>[4,2,1,1,1,1,3] 011000001111=>[2,1,6,1,1,1,1]=>[5,1,1,1,1,3,1] 0011011010=>[3,1,2,1,2,2]=>[1,2,3,3,1,1] 0011010110=>[3,1,2,2,1,2]=>[1,3,2,3,1,1] 0100110110=>[2,3,1,2,1,2]=>[1,3,3,1,2,1] 0101001110=>[2,2,3,1,1,2]=>[1,4,1,2,2,1] 0011001110=>[3,1,3,1,1,2]=>[1,4,1,3,1,1] 0100101110=>[2,3,2,1,1,2]=>[1,4,2,1,2,1] 0100011110=>[2,4,1,1,1,2]=>[1,5,1,1,2,1] 0010011110=>[3,3,1,1,1,2]=>[1,5,1,2,1,1] 001110101010=>[3,1,1,2,2,2,2]=>[1,2,2,2,4,1,1] 001110011010=>[3,1,1,3,1,2,2]=>[1,2,3,1,4,1,1] 001101011010=>[3,1,2,2,1,2,2]=>[1,2,3,2,3,1,1] 000110111010=>[4,1,2,1,1,2,2]=>[1,2,4,3,1,1,1] 001110100110=>[3,1,1,2,3,1,2]=>[1,3,1,2,4,1,1] 001110010110=>[3,1,1,3,2,1,2]=>[1,3,2,1,4,1,1] 001101010110=>[3,1,2,2,2,1,2]=>[1,3,2,2,3,1,1] 010011010110=>[2,3,1,2,2,1,2]=>[1,3,2,3,1,2,1] 010100110110=>[2,2,3,1,2,1,2]=>[1,3,3,1,2,2,1] 001100110110=>[3,1,3,1,2,1,2]=>[1,3,3,1,3,1,1] 010010110110=>[2,3,2,1,2,1,2]=>[1,3,3,2,1,2,1] 001010110110=>[3,2,2,1,2,1,2]=>[1,3,3,2,2,1,1] 000110110110=>[4,1,2,1,2,1,2]=>[1,3,3,3,1,1,1] 010001110110=>[2,4,1,1,2,1,2]=>[1,3,4,1,1,2,1] 010101001110=>[2,2,2,3,1,1,2]=>[1,4,1,2,2,2,1] 001101001110=>[3,1,2,3,1,1,2]=>[1,4,1,2,3,1,1] 001011001110=>[3,2,1,3,1,1,2]=>[1,4,1,3,2,1,1] 001100101110=>[3,1,3,2,1,1,2]=>[1,4,2,1,3,1,1] 010010101110=>[2,3,2,2,1,1,2]=>[1,4,2,2,1,2,1] 001010101110=>[3,2,2,2,1,1,2]=>[1,4,2,2,2,1,1] 000110101110=>[4,1,2,2,1,1,2]=>[1,4,2,3,1,1,1] 001001101110=>[3,3,1,2,1,1,2]=>[1,4,3,1,2,1,1] 010100011110=>[2,2,4,1,1,1,2]=>[1,5,1,1,2,2,1] 001100011110=>[3,1,4,1,1,1,2]=>[1,5,1,1,3,1,1] 001010011110=>[3,2,3,1,1,1,2]=>[1,5,1,2,2,1,1] 010001011110=>[2,4,2,1,1,1,2]=>[1,5,2,1,1,2,1] 001001011110=>[3,3,2,1,1,1,2]=>[1,5,2,1,2,1,1] 000101011110=>[4,2,2,1,1,1,2]=>[1,5,2,2,1,1,1] 001000111110=>[3,4,1,1,1,1,2]=>[1,6,1,1,2,1,1] 000010111110=>[5,2,1,1,1,1,2]=>[1,6,2,1,1,1,1] 0001000100=>[4,4,3]=>[1,1,2,1,1,2,1,1,1] 0001010101=>[4,2,2,2,1]=>[2,2,2,2,1,1,1] 0001001011=>[4,3,2,1,1]=>[3,2,1,2,1,1,1] 0001100011=>[4,1,4,1,1]=>[3,1,1,3,1,1,1] 0110000011=>[2,1,6,1,1]=>[3,1,1,1,1,3,1] 0111101111=>[2,1,1,1,2,1,1,1,1]=>[5,5,1] 000100010101=>[4,4,2,2,1]=>[2,2,2,1,1,2,1,1,1] 000111011001=>[4,1,1,2,1,3,1]=>[2,1,3,4,1,1,1] 01100000000=>[2,1,9]=>[1,1,1,1,1,1,1,1,3,1] 0111111010=>[2,1,1,1,1,1,2,2]=>[1,2,7,1] 101101010101=>[1,2,1,2,2,2,2,1]=>[2,2,2,2,3,2] 101011010101=>[1,2,2,1,2,2,2,1]=>[2,2,2,3,2,2] 100111010101=>[1,3,1,1,2,2,2,1]=>[2,2,2,4,1,2] 101100110101=>[1,2,1,3,1,2,2,1]=>[2,2,3,1,3,2] 110010110101=>[1,1,3,2,1,2,2,1]=>[2,2,3,2,1,3] 101010110101=>[1,2,2,2,1,2,2,1]=>[2,2,3,2,2,2] 100110110101=>[1,3,1,2,1,2,2,1]=>[2,2,3,3,1,2] 101001110101=>[1,2,3,1,1,2,2,1]=>[2,2,4,1,2,2] 100101110101=>[1,3,2,1,1,2,2,1]=>[2,2,4,2,1,2] 100011110101=>[1,4,1,1,1,2,2,1]=>[2,2,5,1,1,2] 101101001101=>[1,2,1,2,3,1,2,1]=>[2,3,1,2,3,2] 101011001101=>[1,2,2,1,3,1,2,1]=>[2,3,1,3,2,2] 100111001101=>[1,3,1,1,3,1,2,1]=>[2,3,1,4,1,2] 110100101101=>[1,1,2,3,2,1,2,1]=>[2,3,2,1,2,3] 101100101101=>[1,2,1,3,2,1,2,1]=>[2,3,2,1,3,2] 110010101101=>[1,1,3,2,2,1,2,1]=>[2,3,2,2,1,3] 101010101101=>[1,2,2,2,2,1,2,1]=>[2,3,2,2,2,2] 100110101101=>[1,3,1,2,2,1,2,1]=>[2,3,2,3,1,2] 110001101101=>[1,1,4,1,2,1,2,1]=>[2,3,3,1,1,3] 101001101101=>[1,2,3,1,2,1,2,1]=>[2,3,3,1,2,2] 100101101101=>[1,3,2,1,2,1,2,1]=>[2,3,3,2,1,2] 100011101101=>[1,4,1,1,2,1,2,1]=>[2,3,4,1,1,2] 101100011101=>[1,2,1,4,1,1,2,1]=>[2,4,1,1,3,2] 110010011101=>[1,1,3,3,1,1,2,1]=>[2,4,1,2,1,3] 101010011101=>[1,2,2,3,1,1,2,1]=>[2,4,1,2,2,2] 100110011101=>[1,3,1,3,1,1,2,1]=>[2,4,1,3,1,2] 110001011101=>[1,1,4,2,1,1,2,1]=>[2,4,2,1,1,3] 101001011101=>[1,2,3,2,1,1,2,1]=>[2,4,2,1,2,2] 100101011101=>[1,3,2,2,1,1,2,1]=>[2,4,2,2,1,2] 100011011101=>[1,4,1,2,1,1,2,1]=>[2,4,3,1,1,2] 101000111101=>[1,2,4,1,1,1,2,1]=>[2,5,1,1,2,2] 100100111101=>[1,3,3,1,1,1,2,1]=>[2,5,1,2,1,2] 100010111101=>[1,4,2,1,1,1,2,1]=>[2,5,2,1,1,2] 100001111101=>[1,5,1,1,1,1,2,1]=>[2,6,1,1,1,2] 101101010011=>[1,2,1,2,2,3,1,1]=>[3,1,2,2,3,2] 101011010011=>[1,2,2,1,2,3,1,1]=>[3,1,2,3,2,2] 100111010011=>[1,3,1,1,2,3,1,1]=>[3,1,2,4,1,2] 110010110011=>[1,1,3,2,1,3,1,1]=>[3,1,3,2,1,3] 101010110011=>[1,2,2,2,1,3,1,1]=>[3,1,3,2,2,2] 100011110011=>[1,4,1,1,1,3,1,1]=>[3,1,5,1,1,2] 110101001011=>[1,1,2,2,3,2,1,1]=>[3,2,1,2,2,3] 101101001011=>[1,2,1,2,3,2,1,1]=>[3,2,1,2,3,2] 110011001011=>[1,1,3,1,3,2,1,1]=>[3,2,1,3,1,3] 101011001011=>[1,2,2,1,3,2,1,1]=>[3,2,1,3,2,2] 100111001011=>[1,3,1,1,3,2,1,1]=>[3,2,1,4,1,2] 110100101011=>[1,1,2,3,2,2,1,1]=>[3,2,2,1,2,3] 101100101011=>[1,2,1,3,2,2,1,1]=>[3,2,2,1,3,2] 110010101011=>[1,1,3,2,2,2,1,1]=>[3,2,2,2,1,3] 101010101011=>[1,2,2,2,2,2,1,1]=>[3,2,2,2,2,2] 100110101011=>[1,3,1,2,2,2,1,1]=>[3,2,2,3,1,2] 110001101011=>[1,1,4,1,2,2,1,1]=>[3,2,3,1,1,3] 101001101011=>[1,2,3,1,2,2,1,1]=>[3,2,3,1,2,2] 100101101011=>[1,3,2,1,2,2,1,1]=>[3,2,3,2,1,2] 100011101011=>[1,4,1,1,2,2,1,1]=>[3,2,4,1,1,2] 110100011011=>[1,1,2,4,1,2,1,1]=>[3,3,1,1,2,3] 110010011011=>[1,1,3,3,1,2,1,1]=>[3,3,1,2,1,3] 101010011011=>[1,2,2,3,1,2,1,1]=>[3,3,1,2,2,2] 110001011011=>[1,1,4,2,1,2,1,1]=>[3,3,2,1,1,3] 101001011011=>[1,2,3,2,1,2,1,1]=>[3,3,2,1,2,2] 100101011011=>[1,3,2,2,1,2,1,1]=>[3,3,2,2,1,2] 100011011011=>[1,4,1,2,1,2,1,1]=>[3,3,3,1,1,2] 110000111011=>[1,1,5,1,1,2,1,1]=>[3,4,1,1,1,3] 100010111011=>[1,4,2,1,1,2,1,1]=>[3,4,2,1,1,2] 100001111011=>[1,5,1,1,1,2,1,1]=>[3,5,1,1,1,2] 100111000111=>[1,3,1,1,4,1,1,1]=>[4,1,1,4,1,2] 110100100111=>[1,1,2,3,3,1,1,1]=>[4,1,2,1,2,3] 110010100111=>[1,1,3,2,3,1,1,1]=>[4,1,2,2,1,3] 101010100111=>[1,2,2,2,3,1,1,1]=>[4,1,2,2,2,2] 110001100111=>[1,1,4,1,3,1,1,1]=>[4,1,3,1,1,3] 100011100111=>[1,4,1,1,3,1,1,1]=>[4,1,4,1,1,2] 110100010111=>[1,1,2,4,2,1,1,1]=>[4,2,1,1,2,3] 110010010111=>[1,1,3,3,2,1,1,1]=>[4,2,1,2,1,3] 101010010111=>[1,2,2,3,2,1,1,1]=>[4,2,1,2,2,2] 110001010111=>[1,1,4,2,2,1,1,1]=>[4,2,2,1,1,3] 101001010111=>[1,2,3,2,2,1,1,1]=>[4,2,2,1,2,2] 100101010111=>[1,3,2,2,2,1,1,1]=>[4,2,2,2,1,2] 100011010111=>[1,4,1,2,2,1,1,1]=>[4,2,3,1,1,2] 110000110111=>[1,1,5,1,2,1,1,1]=>[4,3,1,1,1,3] 100010110111=>[1,4,2,1,2,1,1,1]=>[4,3,2,1,1,2] 100001110111=>[1,5,1,1,2,1,1,1]=>[4,4,1,1,1,2] 101100001111=>[1,2,1,5,1,1,1,1]=>[5,1,1,1,3,2] 110010001111=>[1,1,3,4,1,1,1,1]=>[5,1,1,2,1,3] 100110001111=>[1,3,1,4,1,1,1,1]=>[5,1,1,3,1,2] 110001001111=>[1,1,4,3,1,1,1,1]=>[5,1,2,1,1,3] 100011001111=>[1,4,1,3,1,1,1,1]=>[5,1,3,1,1,2] 110000101111=>[1,1,5,2,1,1,1,1]=>[5,2,1,1,1,3] 100010101111=>[1,4,2,2,1,1,1,1]=>[5,2,2,1,1,2] 100001101111=>[1,5,1,2,1,1,1,1]=>[5,3,1,1,1,2] 101000011111=>[1,2,5,1,1,1,1,1]=>[6,1,1,1,2,2] 100100011111=>[1,3,4,1,1,1,1,1]=>[6,1,1,2,1,2] 100010011111=>[1,4,3,1,1,1,1,1]=>[6,1,2,1,1,2] 100001011111=>[1,5,2,1,1,1,1,1]=>[6,2,1,1,1,2] 100000111111=>[1,6,1,1,1,1,1,1]=>[7,1,1,1,1,2] 0000000111=>[8,1,1,1]=>[4,1,1,1,1,1,1,1] 0011111111=>[3,1,1,1,1,1,1,1,1]=>[9,1,1] 0000001011=>[7,2,1,1]=>[3,2,1,1,1,1,1,1] 00000111111=>[6,1,1,1,1,1,1]=>[7,1,1,1,1,1] 0010111111=>[3,2,1,1,1,1,1,1]=>[7,2,1,1] 10111000000=>[1,2,1,1,7]=>[1,1,1,1,1,1,4,2] 10111111111=>[1,2,1,1,1,1,1,1,1,1,1]=>[10,2] 10000101111=>[1,5,2,1,1,1,1]=>[5,2,1,1,1,2] 10010111111=>[1,3,2,1,1,1,1,1,1]=>[7,2,1,2] 10101111111=>[1,2,2,1,1,1,1,1,1,1]=>[8,2,2] 0011011110=>[3,1,2,1,1,1,2]=>[1,5,3,1,1] 0011110110=>[3,1,1,1,2,1,2]=>[1,3,5,1,1] 0011111100=>[3,1,1,1,1,1,3]=>[1,1,7,1,1] 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] 0011011100=>[3,1,2,1,1,3]=>[1,1,4,3,1,1] 0001111001=>[4,1,1,1,3,1]=>[2,1,5,1,1,1] 011000111100=>[2,1,4,1,1,1,3]=>[1,1,5,1,1,3,1] 010100111100=>[2,2,3,1,1,1,3]=>[1,1,5,1,2,2,1] 001100111100=>[3,1,3,1,1,1,3]=>[1,1,5,1,3,1,1] 010010111100=>[2,3,2,1,1,1,3]=>[1,1,5,2,1,2,1] 001010111100=>[3,2,2,1,1,1,3]=>[1,1,5,2,2,1,1] 000110111001=>[4,1,2,1,1,3,1]=>[2,1,4,3,1,1,1] 000110111100=>[4,1,2,1,1,1,3]=>[1,1,5,3,1,1,1] 001110110001=>[3,1,1,2,1,4,1]=>[2,1,1,3,4,1,1] 001110110010=>[3,1,1,2,1,3,2]=>[1,2,1,3,4,1,1] 001110110100=>[3,1,1,2,1,2,3]=>[1,1,2,3,4,1,1] 001110111000=>[3,1,1,2,1,1,4]=>[1,1,1,4,4,1,1] 001101101001=>[3,1,2,1,2,3,1]=>[2,1,2,3,3,1,1] 001101110001=>[3,1,2,1,1,4,1]=>[2,1,1,4,3,1,1] 000011111001=>[5,1,1,1,1,3,1]=>[2,1,6,1,1,1,1] 000111100011=>[4,1,1,1,4,1,1]=>[3,1,1,5,1,1,1] 000111100101=>[4,1,1,1,3,2,1]=>[2,2,1,5,1,1,1] 000111101001=>[4,1,1,1,2,3,1]=>[2,1,2,5,1,1,1] 0000101010=>[5,2,2,2]=>[1,2,2,2,1,1,1,1] 11000001111=>[1,1,6,1,1,1,1]=>[5,1,1,1,1,3] 0111101101=>[2,1,1,1,2,1,2,1]=>[2,3,5,1] 0110001101=>[2,1,4,1,2,1]=>[2,3,1,1,3,1] 0110111101=>[2,1,2,1,1,1,2,1]=>[2,5,3,1] 0000100101=>[5,3,2,1]=>[2,2,1,2,1,1,1,1] 0011100101=>[3,1,1,3,2,1]=>[2,2,1,4,1,1] 11010001000=>[1,1,2,4,4]=>[1,1,1,2,1,1,2,3] 11000100010=>[1,1,4,4,2]=>[1,2,1,1,2,1,1,3] 00010010101=>[4,3,2,2,1]=>[2,2,2,1,2,1,1,1] 00010100101=>[4,2,3,2,1]=>[2,2,1,2,2,1,1,1] 00010101001=>[4,2,2,3,1]=>[2,1,2,2,2,1,1,1] 00010101010=>[4,2,2,2,2]=>[1,2,2,2,2,1,1,1] 00000100010=>[6,4,2]=>[1,2,1,1,2,1,1,1,1,1] 001110011001=>[3,1,1,3,1,3,1]=>[2,1,3,1,4,1,1] 001110011100=>[3,1,1,3,1,1,3]=>[1,1,4,1,4,1,1] 001110100101=>[3,1,1,2,3,2,1]=>[2,2,1,2,4,1,1] 001111001001=>[3,1,1,1,3,3,1]=>[2,1,2,1,5,1,1] 11010100000=>[1,1,2,2,6]=>[1,1,1,1,1,2,2,3] 01000100000=>[2,4,6]=>[1,1,1,1,1,2,1,1,2,1] 100110011100=>[1,3,1,3,1,1,3]=>[1,1,4,1,3,1,2] 000010010101=>[5,3,2,2,1]=>[2,2,2,1,2,1,1,1,1] 0010010101=>[3,3,2,2,1]=>[2,2,2,1,2,1,1] 00001010101=>[5,2,2,2,1]=>[2,2,2,2,1,1,1,1] 000010010011=>[5,3,3,1,1]=>[3,1,2,1,2,1,1,1,1] 0010010011=>[3,3,3,1,1]=>[3,1,2,1,2,1,1] 00010001011=>[4,4,2,1,1]=>[3,2,1,1,2,1,1,1] 0000101011=>[5,2,2,1,1]=>[3,2,2,1,1,1,1] 0000100111=>[5,3,1,1,1]=>[4,1,2,1,1,1,1] 0001001010=>[4,3,2,2]=>[1,2,2,1,2,1,1,1] 0000100100=>[5,3,3]=>[1,1,2,1,2,1,1,1,1] 0011000000=>[3,1,7]=>[1,1,1,1,1,1,3,1,1] 0101010111=>[2,2,2,2,1,1,1]=>[4,2,2,2,1] 10101011001=>[1,2,2,2,1,3,1]=>[2,1,3,2,2,2] 10101101001=>[1,2,2,1,2,3,1]=>[2,1,2,3,2,2] 10110101001=>[1,2,1,2,2,3,1]=>[2,1,2,2,3,2] 11010101001=>[1,1,2,2,2,3,1]=>[2,1,2,2,2,3] 100100111100=>[1,3,3,1,1,1,3]=>[1,1,5,1,2,1,2] 01101010100=>[2,1,2,2,2,3]=>[1,1,2,2,2,3,1] 01101010010=>[2,1,2,2,3,2]=>[1,2,1,2,2,3,1] 01101001010=>[2,1,2,3,2,2]=>[1,2,2,1,2,3,1] 01100101010=>[2,1,3,2,2,2]=>[1,2,2,2,1,3,1] 01110101010=>[2,1,1,2,2,2,2]=>[1,2,2,2,4,1] 0101110101=>[2,2,1,1,2,2,1]=>[2,2,4,2,1] 01111100100=>[2,1,1,1,1,3,3]=>[1,1,2,1,6,1] 01000101111=>[2,4,2,1,1,1,1]=>[5,2,1,1,2,1] 10000011111=>[1,6,1,1,1,1,1]=>[6,1,1,1,1,2] 01010101000=>[2,2,2,2,4]=>[1,1,1,2,2,2,2,1] 01000000010=>[2,8,2]=>[1,2,1,1,1,1,1,1,2,1] 00010000000=>[4,8]=>[1,1,1,1,1,1,1,2,1,1,1] 00000001000=>[8,4]=>[1,1,1,2,1,1,1,1,1,1,1] 10000000111=>[1,8,1,1,1]=>[4,1,1,1,1,1,1,2] 01010100111=>[2,2,2,3,1,1,1]=>[4,1,2,2,2,1] 01010010111=>[2,2,3,2,1,1,1]=>[4,2,1,2,2,1] 01001010111=>[2,3,2,2,1,1,1]=>[4,2,2,1,2,1] 01000111011=>[2,4,1,1,2,1,1]=>[3,4,1,1,2,1] 00010111011=>[4,2,1,1,2,1,1]=>[3,4,2,1,1,1] 00010101101=>[4,2,2,1,2,1]=>[2,3,2,2,1,1,1] 00010110101=>[4,2,1,2,2,1]=>[2,2,3,2,1,1,1] 00011010101=>[4,1,2,2,2,1]=>[2,2,2,3,1,1,1] 01010101111=>[2,2,2,2,1,1,1,1]=>[5,2,2,2,1] 01010110111=>[2,2,2,1,2,1,1,1]=>[4,3,2,2,1] 01011010111=>[2,2,1,2,2,1,1,1]=>[4,2,3,2,1] 01101010111=>[2,1,2,2,2,1,1,1]=>[4,2,2,3,1] 10101010111=>[1,2,2,2,2,1,1,1]=>[4,2,2,2,2] 11000010100=>[1,1,5,2,3]=>[1,1,2,2,1,1,1,3] 11010000100=>[1,1,2,5,3]=>[1,1,2,1,1,1,2,3] 11011110100=>[1,1,2,1,1,1,2,3]=>[1,1,2,5,3] 0110001111=>[2,1,4,1,1,1,1]=>[5,1,1,3,1] 0101101011=>[2,2,1,2,2,1,1]=>[3,2,3,2,1] 0011000011=>[3,1,5,1,1]=>[3,1,1,1,3,1,1] 0011011011=>[3,1,2,1,2,1,1]=>[3,3,3,1,1] 111111001111=>[1,1,1,1,1,1,3,1,1,1,1]=>[5,1,7] 01010110100=>[2,2,2,1,2,3]=>[1,1,2,3,2,2,1] 0111011111=>[2,1,1,2,1,1,1,1,1]=>[6,4,1] 111101010101=>[1,1,1,1,2,2,2,2,1]=>[2,2,2,2,5] 01000001011=>[2,6,2,1,1]=>[3,2,1,1,1,1,2,1] 10111101000=>[1,2,1,1,1,2,4]=>[1,1,1,2,5,2] 11111101010=>[1,1,1,1,1,1,2,2,2]=>[1,2,2,7] 11111010010=>[1,1,1,1,1,2,3,2]=>[1,2,1,2,6] 11010000010=>[1,1,2,6,2]=>[1,2,1,1,1,1,2,3] 11111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[15] 11111111111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>[21] 01110111111=>[2,1,1,2,1,1,1,1,1,1]=>[7,4,1] 0000110000=>[5,1,5]=>[1,1,1,1,3,1,1,1,1] 101001011100=>[1,2,3,2,1,1,3]=>[1,1,4,2,1,2,2] 11110001000=>[1,1,1,1,4,4]=>[1,1,1,2,1,1,5] 11110000011=>[1,1,1,1,6,1,1]=>[3,1,1,1,1,5] 11000111000=>[1,1,4,1,1,4]=>[1,1,1,4,1,1,3] 11000100011=>[1,1,4,4,1,1]=>[3,1,1,2,1,1,3] 11010001011=>[1,1,2,4,2,1,1]=>[3,2,1,1,2,3] 00011111000=>[4,1,1,1,1,4]=>[1,1,1,6,1,1,1] 00011100011=>[4,1,1,4,1,1]=>[3,1,1,4,1,1,1] 00010001111=>[4,4,1,1,1,1]=>[5,1,1,2,1,1,1] 00010111010=>[4,2,1,1,2,2]=>[1,2,4,2,1,1,1] 01110001000=>[2,1,1,4,4]=>[1,1,1,2,1,1,4,1] 01110001110=>[2,1,1,4,1,1,2]=>[1,4,1,1,4,1] 01110111110=>[2,1,1,2,1,1,1,1,2]=>[1,6,4,1] 01111101110=>[2,1,1,1,1,2,1,1,2]=>[1,4,6,1] 01110001011=>[2,1,1,4,2,1,1]=>[3,2,1,1,4,1] 01000100011=>[2,4,4,1,1]=>[3,1,1,2,1,1,2,1] 01000111000=>[2,4,1,1,4]=>[1,1,1,4,1,1,2,1] 01000111110=>[2,4,1,1,1,1,2]=>[1,6,1,1,2,1] 01011111010=>[2,2,1,1,1,1,2,2]=>[1,2,6,2,1] 0000100001=>[5,5,1]=>[2,1,1,1,2,1,1,1,1]