=>

0=>1=>[1,1]=>[2] 1=>0=>[2]=>[1,1] 00=>11=>[1,1,1]=>[3] 01=>10=>[1,2]=>[1,2] 10=>01=>[2,1]=>[2,1] 11=>00=>[3]=>[1,1,1] 000=>111=>[1,1,1,1]=>[4] 001=>110=>[1,1,2]=>[1,3] 010=>101=>[1,2,1]=>[2,2] 011=>100=>[1,3]=>[1,1,2] 100=>011=>[2,1,1]=>[3,1] 101=>010=>[2,2]=>[1,2,1] 110=>001=>[3,1]=>[2,1,1] 111=>000=>[4]=>[1,1,1,1] 0000=>1111=>[1,1,1,1,1]=>[5] 0001=>1110=>[1,1,1,2]=>[1,4] 0010=>1101=>[1,1,2,1]=>[2,3] 0011=>1100=>[1,1,3]=>[1,1,3] 0100=>1011=>[1,2,1,1]=>[3,2] 0101=>1010=>[1,2,2]=>[1,2,2] 0110=>1001=>[1,3,1]=>[2,1,2] 0111=>1000=>[1,4]=>[1,1,1,2] 1000=>0111=>[2,1,1,1]=>[4,1] 1001=>0110=>[2,1,2]=>[1,3,1] 1010=>0101=>[2,2,1]=>[2,2,1] 1011=>0100=>[2,3]=>[1,1,2,1] 1100=>0011=>[3,1,1]=>[3,1,1] 1101=>0010=>[3,2]=>[1,2,1,1] 1110=>0001=>[4,1]=>[2,1,1,1] 1111=>0000=>[5]=>[1,1,1,1,1] 00000=>11111=>[1,1,1,1,1,1]=>[6] 00001=>11110=>[1,1,1,1,2]=>[1,5] 00010=>11101=>[1,1,1,2,1]=>[2,4] 00011=>11100=>[1,1,1,3]=>[1,1,4] 00100=>11011=>[1,1,2,1,1]=>[3,3] 00101=>11010=>[1,1,2,2]=>[1,2,3] 00110=>11001=>[1,1,3,1]=>[2,1,3] 00111=>11000=>[1,1,4]=>[1,1,1,3] 01000=>10111=>[1,2,1,1,1]=>[4,2] 01001=>10110=>[1,2,1,2]=>[1,3,2] 01010=>10101=>[1,2,2,1]=>[2,2,2] 01011=>10100=>[1,2,3]=>[1,1,2,2] 01100=>10011=>[1,3,1,1]=>[3,1,2] 01101=>10010=>[1,3,2]=>[1,2,1,2] 01110=>10001=>[1,4,1]=>[2,1,1,2] 01111=>10000=>[1,5]=>[1,1,1,1,2] 10000=>01111=>[2,1,1,1,1]=>[5,1] 10001=>01110=>[2,1,1,2]=>[1,4,1] 10010=>01101=>[2,1,2,1]=>[2,3,1] 10011=>01100=>[2,1,3]=>[1,1,3,1] 10100=>01011=>[2,2,1,1]=>[3,2,1] 10101=>01010=>[2,2,2]=>[1,2,2,1] 10110=>01001=>[2,3,1]=>[2,1,2,1] 10111=>01000=>[2,4]=>[1,1,1,2,1] 11000=>00111=>[3,1,1,1]=>[4,1,1] 11001=>00110=>[3,1,2]=>[1,3,1,1] 11010=>00101=>[3,2,1]=>[2,2,1,1] 11011=>00100=>[3,3]=>[1,1,2,1,1] 11100=>00011=>[4,1,1]=>[3,1,1,1] 11101=>00010=>[4,2]=>[1,2,1,1,1] 11110=>00001=>[5,1]=>[2,1,1,1,1] 11111=>00000=>[6]=>[1,1,1,1,1,1] 000000=>111111=>[1,1,1,1,1,1,1]=>[7] 000001=>111110=>[1,1,1,1,1,2]=>[1,6] 000010=>111101=>[1,1,1,1,2,1]=>[2,5] 000011=>111100=>[1,1,1,1,3]=>[1,1,5] 000100=>111011=>[1,1,1,2,1,1]=>[3,4] 000101=>111010=>[1,1,1,2,2]=>[1,2,4] 000110=>111001=>[1,1,1,3,1]=>[2,1,4] 000111=>111000=>[1,1,1,4]=>[1,1,1,4] 001000=>110111=>[1,1,2,1,1,1]=>[4,3] 001001=>110110=>[1,1,2,1,2]=>[1,3,3] 001010=>110101=>[1,1,2,2,1]=>[2,2,3] 001011=>110100=>[1,1,2,3]=>[1,1,2,3] 001100=>110011=>[1,1,3,1,1]=>[3,1,3] 001101=>110010=>[1,1,3,2]=>[1,2,1,3] 001110=>110001=>[1,1,4,1]=>[2,1,1,3] 001111=>110000=>[1,1,5]=>[1,1,1,1,3] 010000=>101111=>[1,2,1,1,1,1]=>[5,2] 010001=>101110=>[1,2,1,1,2]=>[1,4,2] 010010=>101101=>[1,2,1,2,1]=>[2,3,2] 010011=>101100=>[1,2,1,3]=>[1,1,3,2] 010100=>101011=>[1,2,2,1,1]=>[3,2,2] 010101=>101010=>[1,2,2,2]=>[1,2,2,2] 010110=>101001=>[1,2,3,1]=>[2,1,2,2] 010111=>101000=>[1,2,4]=>[1,1,1,2,2] 011000=>100111=>[1,3,1,1,1]=>[4,1,2] 011001=>100110=>[1,3,1,2]=>[1,3,1,2] 011010=>100101=>[1,3,2,1]=>[2,2,1,2] 011011=>100100=>[1,3,3]=>[1,1,2,1,2] 011100=>100011=>[1,4,1,1]=>[3,1,1,2] 011101=>100010=>[1,4,2]=>[1,2,1,1,2] 011110=>100001=>[1,5,1]=>[2,1,1,1,2] 011111=>100000=>[1,6]=>[1,1,1,1,1,2] 100000=>011111=>[2,1,1,1,1,1]=>[6,1] 100001=>011110=>[2,1,1,1,2]=>[1,5,1] 100010=>011101=>[2,1,1,2,1]=>[2,4,1] 100011=>011100=>[2,1,1,3]=>[1,1,4,1] 100100=>011011=>[2,1,2,1,1]=>[3,3,1] 100101=>011010=>[2,1,2,2]=>[1,2,3,1] 100110=>011001=>[2,1,3,1]=>[2,1,3,1] 100111=>011000=>[2,1,4]=>[1,1,1,3,1] 101000=>010111=>[2,2,1,1,1]=>[4,2,1] 101001=>010110=>[2,2,1,2]=>[1,3,2,1] 101010=>010101=>[2,2,2,1]=>[2,2,2,1] 101011=>010100=>[2,2,3]=>[1,1,2,2,1] 101100=>010011=>[2,3,1,1]=>[3,1,2,1] 101101=>010010=>[2,3,2]=>[1,2,1,2,1] 101110=>010001=>[2,4,1]=>[2,1,1,2,1] 101111=>010000=>[2,5]=>[1,1,1,1,2,1] 110000=>001111=>[3,1,1,1,1]=>[5,1,1] 110001=>001110=>[3,1,1,2]=>[1,4,1,1] 110010=>001101=>[3,1,2,1]=>[2,3,1,1] 110011=>001100=>[3,1,3]=>[1,1,3,1,1] 110100=>001011=>[3,2,1,1]=>[3,2,1,1] 110101=>001010=>[3,2,2]=>[1,2,2,1,1] 110110=>001001=>[3,3,1]=>[2,1,2,1,1] 110111=>001000=>[3,4]=>[1,1,1,2,1,1] 111000=>000111=>[4,1,1,1]=>[4,1,1,1] 111001=>000110=>[4,1,2]=>[1,3,1,1,1] 111010=>000101=>[4,2,1]=>[2,2,1,1,1] 111011=>000100=>[4,3]=>[1,1,2,1,1,1] 111100=>000011=>[5,1,1]=>[3,1,1,1,1] 111101=>000010=>[5,2]=>[1,2,1,1,1,1] 111110=>000001=>[6,1]=>[2,1,1,1,1,1] 111111=>000000=>[7]=>[1,1,1,1,1,1,1] 0000000=>1111111=>[1,1,1,1,1,1,1,1]=>[8] 0000001=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 0000010=>1111101=>[1,1,1,1,1,2,1]=>[2,6] 0000011=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 0000100=>1111011=>[1,1,1,1,2,1,1]=>[3,5] 0000101=>1111010=>[1,1,1,1,2,2]=>[1,2,5] 0000110=>1111001=>[1,1,1,1,3,1]=>[2,1,5] 0000111=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 0001000=>1110111=>[1,1,1,2,1,1,1]=>[4,4] 0001001=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 0001010=>1110101=>[1,1,1,2,2,1]=>[2,2,4] 0001011=>1110100=>[1,1,1,2,3]=>[1,1,2,4] 0001100=>1110011=>[1,1,1,3,1,1]=>[3,1,4] 0001101=>1110010=>[1,1,1,3,2]=>[1,2,1,4] 0001110=>1110001=>[1,1,1,4,1]=>[2,1,1,4] 0001111=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 0010000=>1101111=>[1,1,2,1,1,1,1]=>[5,3] 0010001=>1101110=>[1,1,2,1,1,2]=>[1,4,3] 0010010=>1101101=>[1,1,2,1,2,1]=>[2,3,3] 0010011=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 0010100=>1101011=>[1,1,2,2,1,1]=>[3,2,3] 0010101=>1101010=>[1,1,2,2,2]=>[1,2,2,3] 0010110=>1101001=>[1,1,2,3,1]=>[2,1,2,3] 0010111=>1101000=>[1,1,2,4]=>[1,1,1,2,3] 0011000=>1100111=>[1,1,3,1,1,1]=>[4,1,3] 0011001=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 0011010=>1100101=>[1,1,3,2,1]=>[2,2,1,3] 0011011=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 0011100=>1100011=>[1,1,4,1,1]=>[3,1,1,3] 0011101=>1100010=>[1,1,4,2]=>[1,2,1,1,3] 0011110=>1100001=>[1,1,5,1]=>[2,1,1,1,3] 0011111=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0100000=>1011111=>[1,2,1,1,1,1,1]=>[6,2] 0100001=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 0100010=>1011101=>[1,2,1,1,2,1]=>[2,4,2] 0100011=>1011100=>[1,2,1,1,3]=>[1,1,4,2] 0100100=>1011011=>[1,2,1,2,1,1]=>[3,3,2] 0100101=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 0100110=>1011001=>[1,2,1,3,1]=>[2,1,3,2] 0100111=>1011000=>[1,2,1,4]=>[1,1,1,3,2] 0101000=>1010111=>[1,2,2,1,1,1]=>[4,2,2] 0101001=>1010110=>[1,2,2,1,2]=>[1,3,2,2] 0101010=>1010101=>[1,2,2,2,1]=>[2,2,2,2] 0101011=>1010100=>[1,2,2,3]=>[1,1,2,2,2] 0101100=>1010011=>[1,2,3,1,1]=>[3,1,2,2] 0101101=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 0101110=>1010001=>[1,2,4,1]=>[2,1,1,2,2] 0101111=>1010000=>[1,2,5]=>[1,1,1,1,2,2] 0110000=>1001111=>[1,3,1,1,1,1]=>[5,1,2] 0110001=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 0110010=>1001101=>[1,3,1,2,1]=>[2,3,1,2] 0110011=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 0110100=>1001011=>[1,3,2,1,1]=>[3,2,1,2] 0110101=>1001010=>[1,3,2,2]=>[1,2,2,1,2] 0110110=>1001001=>[1,3,3,1]=>[2,1,2,1,2] 0110111=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0111000=>1000111=>[1,4,1,1,1]=>[4,1,1,2] 0111001=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 0111010=>1000101=>[1,4,2,1]=>[2,2,1,1,2] 0111011=>1000100=>[1,4,3]=>[1,1,2,1,1,2] 0111100=>1000011=>[1,5,1,1]=>[3,1,1,1,2] 0111101=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0111110=>1000001=>[1,6,1]=>[2,1,1,1,1,2] 0111111=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 1000000=>0111111=>[2,1,1,1,1,1,1]=>[7,1] 1000001=>0111110=>[2,1,1,1,1,2]=>[1,6,1] 1000010=>0111101=>[2,1,1,1,2,1]=>[2,5,1] 1000011=>0111100=>[2,1,1,1,3]=>[1,1,5,1] 1000100=>0111011=>[2,1,1,2,1,1]=>[3,4,1] 1000101=>0111010=>[2,1,1,2,2]=>[1,2,4,1] 1000110=>0111001=>[2,1,1,3,1]=>[2,1,4,1] 1000111=>0111000=>[2,1,1,4]=>[1,1,1,4,1] 1001000=>0110111=>[2,1,2,1,1,1]=>[4,3,1] 1001001=>0110110=>[2,1,2,1,2]=>[1,3,3,1] 1001010=>0110101=>[2,1,2,2,1]=>[2,2,3,1] 1001011=>0110100=>[2,1,2,3]=>[1,1,2,3,1] 1001100=>0110011=>[2,1,3,1,1]=>[3,1,3,1] 1001101=>0110010=>[2,1,3,2]=>[1,2,1,3,1] 1001110=>0110001=>[2,1,4,1]=>[2,1,1,3,1] 1001111=>0110000=>[2,1,5]=>[1,1,1,1,3,1] 1010000=>0101111=>[2,2,1,1,1,1]=>[5,2,1] 1010001=>0101110=>[2,2,1,1,2]=>[1,4,2,1] 1010010=>0101101=>[2,2,1,2,1]=>[2,3,2,1] 1010011=>0101100=>[2,2,1,3]=>[1,1,3,2,1] 1010100=>0101011=>[2,2,2,1,1]=>[3,2,2,1] 1010101=>0101010=>[2,2,2,2]=>[1,2,2,2,1] 1010110=>0101001=>[2,2,3,1]=>[2,1,2,2,1] 1010111=>0101000=>[2,2,4]=>[1,1,1,2,2,1] 1011000=>0100111=>[2,3,1,1,1]=>[4,1,2,1] 1011001=>0100110=>[2,3,1,2]=>[1,3,1,2,1] 1011010=>0100101=>[2,3,2,1]=>[2,2,1,2,1] 1011011=>0100100=>[2,3,3]=>[1,1,2,1,2,1] 1011100=>0100011=>[2,4,1,1]=>[3,1,1,2,1] 1011101=>0100010=>[2,4,2]=>[1,2,1,1,2,1] 1011110=>0100001=>[2,5,1]=>[2,1,1,1,2,1] 1011111=>0100000=>[2,6]=>[1,1,1,1,1,2,1] 1100000=>0011111=>[3,1,1,1,1,1]=>[6,1,1] 1100001=>0011110=>[3,1,1,1,2]=>[1,5,1,1] 1100010=>0011101=>[3,1,1,2,1]=>[2,4,1,1] 1100011=>0011100=>[3,1,1,3]=>[1,1,4,1,1] 1100100=>0011011=>[3,1,2,1,1]=>[3,3,1,1] 1100101=>0011010=>[3,1,2,2]=>[1,2,3,1,1] 1100110=>0011001=>[3,1,3,1]=>[2,1,3,1,1] 1100111=>0011000=>[3,1,4]=>[1,1,1,3,1,1] 1101000=>0010111=>[3,2,1,1,1]=>[4,2,1,1] 1101001=>0010110=>[3,2,1,2]=>[1,3,2,1,1] 1101010=>0010101=>[3,2,2,1]=>[2,2,2,1,1] 1101011=>0010100=>[3,2,3]=>[1,1,2,2,1,1] 1101100=>0010011=>[3,3,1,1]=>[3,1,2,1,1] 1101101=>0010010=>[3,3,2]=>[1,2,1,2,1,1] 1101110=>0010001=>[3,4,1]=>[2,1,1,2,1,1] 1101111=>0010000=>[3,5]=>[1,1,1,1,2,1,1] 1110000=>0001111=>[4,1,1,1,1]=>[5,1,1,1] 1110001=>0001110=>[4,1,1,2]=>[1,4,1,1,1] 1110010=>0001101=>[4,1,2,1]=>[2,3,1,1,1] 1110011=>0001100=>[4,1,3]=>[1,1,3,1,1,1] 1110100=>0001011=>[4,2,1,1]=>[3,2,1,1,1] 1110101=>0001010=>[4,2,2]=>[1,2,2,1,1,1] 1110110=>0001001=>[4,3,1]=>[2,1,2,1,1,1] 1110111=>0001000=>[4,4]=>[1,1,1,2,1,1,1] 1111000=>0000111=>[5,1,1,1]=>[4,1,1,1,1] 1111001=>0000110=>[5,1,2]=>[1,3,1,1,1,1] 1111010=>0000101=>[5,2,1]=>[2,2,1,1,1,1] 1111011=>0000100=>[5,3]=>[1,1,2,1,1,1,1] 1111100=>0000011=>[6,1,1]=>[3,1,1,1,1,1] 1111101=>0000010=>[6,2]=>[1,2,1,1,1,1,1] 1111110=>0000001=>[7,1]=>[2,1,1,1,1,1,1] 1111111=>0000000=>[8]=>[1,1,1,1,1,1,1,1] 00000000=>11111111=>[1,1,1,1,1,1,1,1,1]=>[9] 00000001=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 00000010=>11111101=>[1,1,1,1,1,1,2,1]=>[2,7] 00000011=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 00000100=>11111011=>[1,1,1,1,1,2,1,1]=>[3,6] 00000101=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 00000110=>11111001=>[1,1,1,1,1,3,1]=>[2,1,6] 00000111=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 00001000=>11110111=>[1,1,1,1,2,1,1,1]=>[4,5] 00001001=>11110110=>[1,1,1,1,2,1,2]=>[1,3,5] 00001010=>11110101=>[1,1,1,1,2,2,1]=>[2,2,5] 00001011=>11110100=>[1,1,1,1,2,3]=>[1,1,2,5] 00001100=>11110011=>[1,1,1,1,3,1,1]=>[3,1,5] 00001101=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 00001110=>11110001=>[1,1,1,1,4,1]=>[2,1,1,5] 00001111=>11110000=>[1,1,1,1,5]=>[1,1,1,1,5] 00010000=>11101111=>[1,1,1,2,1,1,1,1]=>[5,4] 00010001=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 00010010=>11101101=>[1,1,1,2,1,2,1]=>[2,3,4] 00010011=>11101100=>[1,1,1,2,1,3]=>[1,1,3,4] 00010100=>11101011=>[1,1,1,2,2,1,1]=>[3,2,4] 00010101=>11101010=>[1,1,1,2,2,2]=>[1,2,2,4] 00010110=>11101001=>[1,1,1,2,3,1]=>[2,1,2,4] 00010111=>11101000=>[1,1,1,2,4]=>[1,1,1,2,4] 00011000=>11100111=>[1,1,1,3,1,1,1]=>[4,1,4] 00011001=>11100110=>[1,1,1,3,1,2]=>[1,3,1,4] 00011010=>11100101=>[1,1,1,3,2,1]=>[2,2,1,4] 00011011=>11100100=>[1,1,1,3,3]=>[1,1,2,1,4] 00011100=>11100011=>[1,1,1,4,1,1]=>[3,1,1,4] 00011101=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 00011110=>11100001=>[1,1,1,5,1]=>[2,1,1,1,4] 00011111=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 00100000=>11011111=>[1,1,2,1,1,1,1,1]=>[6,3] 00100001=>11011110=>[1,1,2,1,1,1,2]=>[1,5,3] 00100010=>11011101=>[1,1,2,1,1,2,1]=>[2,4,3] 00100011=>11011100=>[1,1,2,1,1,3]=>[1,1,4,3] 00100100=>11011011=>[1,1,2,1,2,1,1]=>[3,3,3] 00100101=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 00100110=>11011001=>[1,1,2,1,3,1]=>[2,1,3,3] 00100111=>11011000=>[1,1,2,1,4]=>[1,1,1,3,3] 00101000=>11010111=>[1,1,2,2,1,1,1]=>[4,2,3] 00101001=>11010110=>[1,1,2,2,1,2]=>[1,3,2,3] 00101010=>11010101=>[1,1,2,2,2,1]=>[2,2,2,3] 00101011=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 00101100=>11010011=>[1,1,2,3,1,1]=>[3,1,2,3] 00101101=>11010010=>[1,1,2,3,2]=>[1,2,1,2,3] 00101110=>11010001=>[1,1,2,4,1]=>[2,1,1,2,3] 00101111=>11010000=>[1,1,2,5]=>[1,1,1,1,2,3] 00110000=>11001111=>[1,1,3,1,1,1,1]=>[5,1,3] 00110001=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 00110010=>11001101=>[1,1,3,1,2,1]=>[2,3,1,3] 00110011=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 00110100=>11001011=>[1,1,3,2,1,1]=>[3,2,1,3] 00110101=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 00110110=>11001001=>[1,1,3,3,1]=>[2,1,2,1,3] 00110111=>11001000=>[1,1,3,4]=>[1,1,1,2,1,3] 00111000=>11000111=>[1,1,4,1,1,1]=>[4,1,1,3] 00111001=>11000110=>[1,1,4,1,2]=>[1,3,1,1,3] 00111010=>11000101=>[1,1,4,2,1]=>[2,2,1,1,3] 00111011=>11000100=>[1,1,4,3]=>[1,1,2,1,1,3] 00111100=>11000011=>[1,1,5,1,1]=>[3,1,1,1,3] 00111101=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 00111110=>11000001=>[1,1,6,1]=>[2,1,1,1,1,3] 00111111=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 01000000=>10111111=>[1,2,1,1,1,1,1,1]=>[7,2] 01000001=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 01000010=>10111101=>[1,2,1,1,1,2,1]=>[2,5,2] 01000011=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 01000100=>10111011=>[1,2,1,1,2,1,1]=>[3,4,2] 01000101=>10111010=>[1,2,1,1,2,2]=>[1,2,4,2] 01000110=>10111001=>[1,2,1,1,3,1]=>[2,1,4,2] 01000111=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 01001000=>10110111=>[1,2,1,2,1,1,1]=>[4,3,2] 01001001=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 01001010=>10110101=>[1,2,1,2,2,1]=>[2,2,3,2] 01001011=>10110100=>[1,2,1,2,3]=>[1,1,2,3,2] 01001100=>10110011=>[1,2,1,3,1,1]=>[3,1,3,2] 01001101=>10110010=>[1,2,1,3,2]=>[1,2,1,3,2] 01001110=>10110001=>[1,2,1,4,1]=>[2,1,1,3,2] 01001111=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 01010000=>10101111=>[1,2,2,1,1,1,1]=>[5,2,2] 01010001=>10101110=>[1,2,2,1,1,2]=>[1,4,2,2] 01010010=>10101101=>[1,2,2,1,2,1]=>[2,3,2,2] 01010011=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 01010100=>10101011=>[1,2,2,2,1,1]=>[3,2,2,2] 01010101=>10101010=>[1,2,2,2,2]=>[1,2,2,2,2] 01010110=>10101001=>[1,2,2,3,1]=>[2,1,2,2,2] 01010111=>10101000=>[1,2,2,4]=>[1,1,1,2,2,2] 01011000=>10100111=>[1,2,3,1,1,1]=>[4,1,2,2] 01011001=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 01011010=>10100101=>[1,2,3,2,1]=>[2,2,1,2,2] 01011011=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 01011100=>10100011=>[1,2,4,1,1]=>[3,1,1,2,2] 01011101=>10100010=>[1,2,4,2]=>[1,2,1,1,2,2] 01011110=>10100001=>[1,2,5,1]=>[2,1,1,1,2,2] 01011111=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 01100000=>10011111=>[1,3,1,1,1,1,1]=>[6,1,2] 01100001=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 01100010=>10011101=>[1,3,1,1,2,1]=>[2,4,1,2] 01100011=>10011100=>[1,3,1,1,3]=>[1,1,4,1,2] 01100100=>10011011=>[1,3,1,2,1,1]=>[3,3,1,2] 01100101=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 01100110=>10011001=>[1,3,1,3,1]=>[2,1,3,1,2] 01100111=>10011000=>[1,3,1,4]=>[1,1,1,3,1,2] 01101000=>10010111=>[1,3,2,1,1,1]=>[4,2,1,2] 01101001=>10010110=>[1,3,2,1,2]=>[1,3,2,1,2] 01101010=>10010101=>[1,3,2,2,1]=>[2,2,2,1,2] 01101011=>10010100=>[1,3,2,3]=>[1,1,2,2,1,2] 01101100=>10010011=>[1,3,3,1,1]=>[3,1,2,1,2] 01101101=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 01101110=>10010001=>[1,3,4,1]=>[2,1,1,2,1,2] 01101111=>10010000=>[1,3,5]=>[1,1,1,1,2,1,2] 01110000=>10001111=>[1,4,1,1,1,1]=>[5,1,1,2] 01110001=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 01110010=>10001101=>[1,4,1,2,1]=>[2,3,1,1,2] 01110011=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 01110100=>10001011=>[1,4,2,1,1]=>[3,2,1,1,2] 01110101=>10001010=>[1,4,2,2]=>[1,2,2,1,1,2] 01110110=>10001001=>[1,4,3,1]=>[2,1,2,1,1,2] 01110111=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 01111000=>10000111=>[1,5,1,1,1]=>[4,1,1,1,2] 01111001=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 01111010=>10000101=>[1,5,2,1]=>[2,2,1,1,1,2] 01111011=>10000100=>[1,5,3]=>[1,1,2,1,1,1,2] 01111100=>10000011=>[1,6,1,1]=>[3,1,1,1,1,2] 01111101=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 01111110=>10000001=>[1,7,1]=>[2,1,1,1,1,1,2] 01111111=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 10000000=>01111111=>[2,1,1,1,1,1,1,1]=>[8,1] 10000001=>01111110=>[2,1,1,1,1,1,2]=>[1,7,1] 10000010=>01111101=>[2,1,1,1,1,2,1]=>[2,6,1] 10000011=>01111100=>[2,1,1,1,1,3]=>[1,1,6,1] 10000100=>01111011=>[2,1,1,1,2,1,1]=>[3,5,1] 10000101=>01111010=>[2,1,1,1,2,2]=>[1,2,5,1] 10000110=>01111001=>[2,1,1,1,3,1]=>[2,1,5,1] 10000111=>01111000=>[2,1,1,1,4]=>[1,1,1,5,1] 10001000=>01110111=>[2,1,1,2,1,1,1]=>[4,4,1] 10001001=>01110110=>[2,1,1,2,1,2]=>[1,3,4,1] 10001010=>01110101=>[2,1,1,2,2,1]=>[2,2,4,1] 10001011=>01110100=>[2,1,1,2,3]=>[1,1,2,4,1] 10001100=>01110011=>[2,1,1,3,1,1]=>[3,1,4,1] 10001101=>01110010=>[2,1,1,3,2]=>[1,2,1,4,1] 10001110=>01110001=>[2,1,1,4,1]=>[2,1,1,4,1] 10001111=>01110000=>[2,1,1,5]=>[1,1,1,1,4,1] 10010000=>01101111=>[2,1,2,1,1,1,1]=>[5,3,1] 10010001=>01101110=>[2,1,2,1,1,2]=>[1,4,3,1] 10010010=>01101101=>[2,1,2,1,2,1]=>[2,3,3,1] 10010011=>01101100=>[2,1,2,1,3]=>[1,1,3,3,1] 10010100=>01101011=>[2,1,2,2,1,1]=>[3,2,3,1] 10010101=>01101010=>[2,1,2,2,2]=>[1,2,2,3,1] 10010110=>01101001=>[2,1,2,3,1]=>[2,1,2,3,1] 10010111=>01101000=>[2,1,2,4]=>[1,1,1,2,3,1] 10011000=>01100111=>[2,1,3,1,1,1]=>[4,1,3,1] 10011001=>01100110=>[2,1,3,1,2]=>[1,3,1,3,1] 10011010=>01100101=>[2,1,3,2,1]=>[2,2,1,3,1] 10011011=>01100100=>[2,1,3,3]=>[1,1,2,1,3,1] 10011100=>01100011=>[2,1,4,1,1]=>[3,1,1,3,1] 10011101=>01100010=>[2,1,4,2]=>[1,2,1,1,3,1] 10011110=>01100001=>[2,1,5,1]=>[2,1,1,1,3,1] 10011111=>01100000=>[2,1,6]=>[1,1,1,1,1,3,1] 10100000=>01011111=>[2,2,1,1,1,1,1]=>[6,2,1] 10100001=>01011110=>[2,2,1,1,1,2]=>[1,5,2,1] 10100010=>01011101=>[2,2,1,1,2,1]=>[2,4,2,1] 10100011=>01011100=>[2,2,1,1,3]=>[1,1,4,2,1] 10100100=>01011011=>[2,2,1,2,1,1]=>[3,3,2,1] 10100101=>01011010=>[2,2,1,2,2]=>[1,2,3,2,1] 10100110=>01011001=>[2,2,1,3,1]=>[2,1,3,2,1] 10100111=>01011000=>[2,2,1,4]=>[1,1,1,3,2,1] 10101000=>01010111=>[2,2,2,1,1,1]=>[4,2,2,1] 10101001=>01010110=>[2,2,2,1,2]=>[1,3,2,2,1] 10101010=>01010101=>[2,2,2,2,1]=>[2,2,2,2,1] 10101011=>01010100=>[2,2,2,3]=>[1,1,2,2,2,1] 10101100=>01010011=>[2,2,3,1,1]=>[3,1,2,2,1] 10101101=>01010010=>[2,2,3,2]=>[1,2,1,2,2,1] 10101110=>01010001=>[2,2,4,1]=>[2,1,1,2,2,1] 10101111=>01010000=>[2,2,5]=>[1,1,1,1,2,2,1] 10110000=>01001111=>[2,3,1,1,1,1]=>[5,1,2,1] 10110001=>01001110=>[2,3,1,1,2]=>[1,4,1,2,1] 10110010=>01001101=>[2,3,1,2,1]=>[2,3,1,2,1] 10110011=>01001100=>[2,3,1,3]=>[1,1,3,1,2,1] 10110100=>01001011=>[2,3,2,1,1]=>[3,2,1,2,1] 10110101=>01001010=>[2,3,2,2]=>[1,2,2,1,2,1] 10110110=>01001001=>[2,3,3,1]=>[2,1,2,1,2,1] 10110111=>01001000=>[2,3,4]=>[1,1,1,2,1,2,1] 10111000=>01000111=>[2,4,1,1,1]=>[4,1,1,2,1] 10111001=>01000110=>[2,4,1,2]=>[1,3,1,1,2,1] 10111010=>01000101=>[2,4,2,1]=>[2,2,1,1,2,1] 10111011=>01000100=>[2,4,3]=>[1,1,2,1,1,2,1] 10111100=>01000011=>[2,5,1,1]=>[3,1,1,1,2,1] 10111101=>01000010=>[2,5,2]=>[1,2,1,1,1,2,1] 10111110=>01000001=>[2,6,1]=>[2,1,1,1,1,2,1] 10111111=>01000000=>[2,7]=>[1,1,1,1,1,1,2,1] 11000000=>00111111=>[3,1,1,1,1,1,1]=>[7,1,1] 11000001=>00111110=>[3,1,1,1,1,2]=>[1,6,1,1] 11000010=>00111101=>[3,1,1,1,2,1]=>[2,5,1,1] 11000011=>00111100=>[3,1,1,1,3]=>[1,1,5,1,1] 11000100=>00111011=>[3,1,1,2,1,1]=>[3,4,1,1] 11000101=>00111010=>[3,1,1,2,2]=>[1,2,4,1,1] 11000110=>00111001=>[3,1,1,3,1]=>[2,1,4,1,1] 11000111=>00111000=>[3,1,1,4]=>[1,1,1,4,1,1] 11001000=>00110111=>[3,1,2,1,1,1]=>[4,3,1,1] 11001001=>00110110=>[3,1,2,1,2]=>[1,3,3,1,1] 11001010=>00110101=>[3,1,2,2,1]=>[2,2,3,1,1] 11001011=>00110100=>[3,1,2,3]=>[1,1,2,3,1,1] 11001100=>00110011=>[3,1,3,1,1]=>[3,1,3,1,1] 11001101=>00110010=>[3,1,3,2]=>[1,2,1,3,1,1] 11001110=>00110001=>[3,1,4,1]=>[2,1,1,3,1,1] 11001111=>00110000=>[3,1,5]=>[1,1,1,1,3,1,1] 11010000=>00101111=>[3,2,1,1,1,1]=>[5,2,1,1] 11010001=>00101110=>[3,2,1,1,2]=>[1,4,2,1,1] 11010010=>00101101=>[3,2,1,2,1]=>[2,3,2,1,1] 11010011=>00101100=>[3,2,1,3]=>[1,1,3,2,1,1] 11010100=>00101011=>[3,2,2,1,1]=>[3,2,2,1,1] 11010101=>00101010=>[3,2,2,2]=>[1,2,2,2,1,1] 11010110=>00101001=>[3,2,3,1]=>[2,1,2,2,1,1] 11010111=>00101000=>[3,2,4]=>[1,1,1,2,2,1,1] 11011000=>00100111=>[3,3,1,1,1]=>[4,1,2,1,1] 11011001=>00100110=>[3,3,1,2]=>[1,3,1,2,1,1] 11011010=>00100101=>[3,3,2,1]=>[2,2,1,2,1,1] 11011011=>00100100=>[3,3,3]=>[1,1,2,1,2,1,1] 11011100=>00100011=>[3,4,1,1]=>[3,1,1,2,1,1] 11011101=>00100010=>[3,4,2]=>[1,2,1,1,2,1,1] 11011110=>00100001=>[3,5,1]=>[2,1,1,1,2,1,1] 11011111=>00100000=>[3,6]=>[1,1,1,1,1,2,1,1] 11100000=>00011111=>[4,1,1,1,1,1]=>[6,1,1,1] 11100001=>00011110=>[4,1,1,1,2]=>[1,5,1,1,1] 11100010=>00011101=>[4,1,1,2,1]=>[2,4,1,1,1] 11100011=>00011100=>[4,1,1,3]=>[1,1,4,1,1,1] 11100100=>00011011=>[4,1,2,1,1]=>[3,3,1,1,1] 11100101=>00011010=>[4,1,2,2]=>[1,2,3,1,1,1] 11100110=>00011001=>[4,1,3,1]=>[2,1,3,1,1,1] 11100111=>00011000=>[4,1,4]=>[1,1,1,3,1,1,1] 11101000=>00010111=>[4,2,1,1,1]=>[4,2,1,1,1] 11101001=>00010110=>[4,2,1,2]=>[1,3,2,1,1,1] 11101010=>00010101=>[4,2,2,1]=>[2,2,2,1,1,1] 11101011=>00010100=>[4,2,3]=>[1,1,2,2,1,1,1] 11101100=>00010011=>[4,3,1,1]=>[3,1,2,1,1,1] 11101101=>00010010=>[4,3,2]=>[1,2,1,2,1,1,1] 11101110=>00010001=>[4,4,1]=>[2,1,1,2,1,1,1] 11101111=>00010000=>[4,5]=>[1,1,1,1,2,1,1,1] 11110000=>00001111=>[5,1,1,1,1]=>[5,1,1,1,1] 11110001=>00001110=>[5,1,1,2]=>[1,4,1,1,1,1] 11110010=>00001101=>[5,1,2,1]=>[2,3,1,1,1,1] 11110011=>00001100=>[5,1,3]=>[1,1,3,1,1,1,1] 11110100=>00001011=>[5,2,1,1]=>[3,2,1,1,1,1] 11110101=>00001010=>[5,2,2]=>[1,2,2,1,1,1,1] 11110110=>00001001=>[5,3,1]=>[2,1,2,1,1,1,1] 11110111=>00001000=>[5,4]=>[1,1,1,2,1,1,1,1] 11111000=>00000111=>[6,1,1,1]=>[4,1,1,1,1,1] 11111001=>00000110=>[6,1,2]=>[1,3,1,1,1,1,1] 11111010=>00000101=>[6,2,1]=>[2,2,1,1,1,1,1] 11111011=>00000100=>[6,3]=>[1,1,2,1,1,1,1,1] 11111100=>00000011=>[7,1,1]=>[3,1,1,1,1,1,1] 11111101=>00000010=>[7,2]=>[1,2,1,1,1,1,1,1] 11111110=>00000001=>[8,1]=>[2,1,1,1,1,1,1,1] 11111111=>00000000=>[9]=>[1,1,1,1,1,1,1,1,1] 000000000=>111111111=>[1,1,1,1,1,1,1,1,1,1]=>[10] 000000001=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 000000010=>111111101=>[1,1,1,1,1,1,1,2,1]=>[2,8] 000000011=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 000000100=>111111011=>[1,1,1,1,1,1,2,1,1]=>[3,7] 000000101=>111111010=>[1,1,1,1,1,1,2,2]=>[1,2,7] 000000110=>111111001=>[1,1,1,1,1,1,3,1]=>[2,1,7] 000000111=>111111000=>[1,1,1,1,1,1,4]=>[1,1,1,7] 000001000=>111110111=>[1,1,1,1,1,2,1,1,1]=>[4,6] 000001001=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 000001010=>111110101=>[1,1,1,1,1,2,2,1]=>[2,2,6] 000001011=>111110100=>[1,1,1,1,1,2,3]=>[1,1,2,6] 000001100=>111110011=>[1,1,1,1,1,3,1,1]=>[3,1,6] 000001101=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 000001110=>111110001=>[1,1,1,1,1,4,1]=>[2,1,1,6] 000001111=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 000010000=>111101111=>[1,1,1,1,2,1,1,1,1]=>[5,5] 000010001=>111101110=>[1,1,1,1,2,1,1,2]=>[1,4,5] 000010010=>111101101=>[1,1,1,1,2,1,2,1]=>[2,3,5] 000010011=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 000010100=>111101011=>[1,1,1,1,2,2,1,1]=>[3,2,5] 000010101=>111101010=>[1,1,1,1,2,2,2]=>[1,2,2,5] 000010110=>111101001=>[1,1,1,1,2,3,1]=>[2,1,2,5] 000010111=>111101000=>[1,1,1,1,2,4]=>[1,1,1,2,5] 000011000=>111100111=>[1,1,1,1,3,1,1,1]=>[4,1,5] 000011001=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 000011010=>111100101=>[1,1,1,1,3,2,1]=>[2,2,1,5] 000011011=>111100100=>[1,1,1,1,3,3]=>[1,1,2,1,5] 000011100=>111100011=>[1,1,1,1,4,1,1]=>[3,1,1,5] 000011101=>111100010=>[1,1,1,1,4,2]=>[1,2,1,1,5] 000011110=>111100001=>[1,1,1,1,5,1]=>[2,1,1,1,5] 000011111=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 000100000=>111011111=>[1,1,1,2,1,1,1,1,1]=>[6,4] 000100001=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 000100010=>111011101=>[1,1,1,2,1,1,2,1]=>[2,4,4] 000100011=>111011100=>[1,1,1,2,1,1,3]=>[1,1,4,4] 000100100=>111011011=>[1,1,1,2,1,2,1,1]=>[3,3,4] 000100101=>111011010=>[1,1,1,2,1,2,2]=>[1,2,3,4] 000100110=>111011001=>[1,1,1,2,1,3,1]=>[2,1,3,4] 000100111=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 000101000=>111010111=>[1,1,1,2,2,1,1,1]=>[4,2,4] 000101001=>111010110=>[1,1,1,2,2,1,2]=>[1,3,2,4] 000101010=>111010101=>[1,1,1,2,2,2,1]=>[2,2,2,4] 000101011=>111010100=>[1,1,1,2,2,3]=>[1,1,2,2,4] 000101100=>111010011=>[1,1,1,2,3,1,1]=>[3,1,2,4] 000101101=>111010010=>[1,1,1,2,3,2]=>[1,2,1,2,4] 000101110=>111010001=>[1,1,1,2,4,1]=>[2,1,1,2,4] 000101111=>111010000=>[1,1,1,2,5]=>[1,1,1,1,2,4] 000110000=>111001111=>[1,1,1,3,1,1,1,1]=>[5,1,4] 000110001=>111001110=>[1,1,1,3,1,1,2]=>[1,4,1,4] 000110010=>111001101=>[1,1,1,3,1,2,1]=>[2,3,1,4] 000110011=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 000110100=>111001011=>[1,1,1,3,2,1,1]=>[3,2,1,4] 000110101=>111001010=>[1,1,1,3,2,2]=>[1,2,2,1,4] 000110110=>111001001=>[1,1,1,3,3,1]=>[2,1,2,1,4] 000110111=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 000111000=>111000111=>[1,1,1,4,1,1,1]=>[4,1,1,4] 000111001=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 000111010=>111000101=>[1,1,1,4,2,1]=>[2,2,1,1,4] 000111011=>111000100=>[1,1,1,4,3]=>[1,1,2,1,1,4] 000111100=>111000011=>[1,1,1,5,1,1]=>[3,1,1,1,4] 000111101=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 000111110=>111000001=>[1,1,1,6,1]=>[2,1,1,1,1,4] 000111111=>111000000=>[1,1,1,7]=>[1,1,1,1,1,1,4] 001000000=>110111111=>[1,1,2,1,1,1,1,1,1]=>[7,3] 001000001=>110111110=>[1,1,2,1,1,1,1,2]=>[1,6,3] 001000010=>110111101=>[1,1,2,1,1,1,2,1]=>[2,5,3] 001000011=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 001000100=>110111011=>[1,1,2,1,1,2,1,1]=>[3,4,3] 001000101=>110111010=>[1,1,2,1,1,2,2]=>[1,2,4,3] 001000110=>110111001=>[1,1,2,1,1,3,1]=>[2,1,4,3] 001000111=>110111000=>[1,1,2,1,1,4]=>[1,1,1,4,3] 001001000=>110110111=>[1,1,2,1,2,1,1,1]=>[4,3,3] 001001001=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 001001010=>110110101=>[1,1,2,1,2,2,1]=>[2,2,3,3] 001001011=>110110100=>[1,1,2,1,2,3]=>[1,1,2,3,3] 001001100=>110110011=>[1,1,2,1,3,1,1]=>[3,1,3,3] 001001101=>110110010=>[1,1,2,1,3,2]=>[1,2,1,3,3] 001001110=>110110001=>[1,1,2,1,4,1]=>[2,1,1,3,3] 001001111=>110110000=>[1,1,2,1,5]=>[1,1,1,1,3,3] 001010000=>110101111=>[1,1,2,2,1,1,1,1]=>[5,2,3] 001010001=>110101110=>[1,1,2,2,1,1,2]=>[1,4,2,3] 001010010=>110101101=>[1,1,2,2,1,2,1]=>[2,3,2,3] 001010011=>110101100=>[1,1,2,2,1,3]=>[1,1,3,2,3] 001010100=>110101011=>[1,1,2,2,2,1,1]=>[3,2,2,3] 001010101=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 001010110=>110101001=>[1,1,2,2,3,1]=>[2,1,2,2,3] 001010111=>110101000=>[1,1,2,2,4]=>[1,1,1,2,2,3] 001011000=>110100111=>[1,1,2,3,1,1,1]=>[4,1,2,3] 001011001=>110100110=>[1,1,2,3,1,2]=>[1,3,1,2,3] 001011010=>110100101=>[1,1,2,3,2,1]=>[2,2,1,2,3] 001011011=>110100100=>[1,1,2,3,3]=>[1,1,2,1,2,3] 001011100=>110100011=>[1,1,2,4,1,1]=>[3,1,1,2,3] 001011101=>110100010=>[1,1,2,4,2]=>[1,2,1,1,2,3] 001011110=>110100001=>[1,1,2,5,1]=>[2,1,1,1,2,3] 001011111=>110100000=>[1,1,2,6]=>[1,1,1,1,1,2,3] 001100000=>110011111=>[1,1,3,1,1,1,1,1]=>[6,1,3] 001100001=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 001100010=>110011101=>[1,1,3,1,1,2,1]=>[2,4,1,3] 001100011=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 001100100=>110011011=>[1,1,3,1,2,1,1]=>[3,3,1,3] 001100101=>110011010=>[1,1,3,1,2,2]=>[1,2,3,1,3] 001100110=>110011001=>[1,1,3,1,3,1]=>[2,1,3,1,3] 001100111=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 001101000=>110010111=>[1,1,3,2,1,1,1]=>[4,2,1,3] 001101001=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 001101010=>110010101=>[1,1,3,2,2,1]=>[2,2,2,1,3] 001101011=>110010100=>[1,1,3,2,3]=>[1,1,2,2,1,3] 001101100=>110010011=>[1,1,3,3,1,1]=>[3,1,2,1,3] 001101101=>110010010=>[1,1,3,3,2]=>[1,2,1,2,1,3] 001101110=>110010001=>[1,1,3,4,1]=>[2,1,1,2,1,3] 001101111=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 001110000=>110001111=>[1,1,4,1,1,1,1]=>[5,1,1,3] 001110001=>110001110=>[1,1,4,1,1,2]=>[1,4,1,1,3] 001110010=>110001101=>[1,1,4,1,2,1]=>[2,3,1,1,3] 001110011=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 001110100=>110001011=>[1,1,4,2,1,1]=>[3,2,1,1,3] 001110101=>110001010=>[1,1,4,2,2]=>[1,2,2,1,1,3] 001110110=>110001001=>[1,1,4,3,1]=>[2,1,2,1,1,3] 001110111=>110001000=>[1,1,4,4]=>[1,1,1,2,1,1,3] 001111000=>110000111=>[1,1,5,1,1,1]=>[4,1,1,1,3] 001111001=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 001111010=>110000101=>[1,1,5,2,1]=>[2,2,1,1,1,3] 001111011=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 001111100=>110000011=>[1,1,6,1,1]=>[3,1,1,1,1,3] 001111101=>110000010=>[1,1,6,2]=>[1,2,1,1,1,1,3] 001111110=>110000001=>[1,1,7,1]=>[2,1,1,1,1,1,3] 001111111=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 010000000=>101111111=>[1,2,1,1,1,1,1,1,1]=>[8,2] 010000001=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 010000010=>101111101=>[1,2,1,1,1,1,2,1]=>[2,6,2] 010000011=>101111100=>[1,2,1,1,1,1,3]=>[1,1,6,2] 010000100=>101111011=>[1,2,1,1,1,2,1,1]=>[3,5,2] 010000101=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 010000110=>101111001=>[1,2,1,1,1,3,1]=>[2,1,5,2] 010000111=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 010001000=>101110111=>[1,2,1,1,2,1,1,1]=>[4,4,2] 010001001=>101110110=>[1,2,1,1,2,1,2]=>[1,3,4,2] 010001010=>101110101=>[1,2,1,1,2,2,1]=>[2,2,4,2] 010001011=>101110100=>[1,2,1,1,2,3]=>[1,1,2,4,2] 010001100=>101110011=>[1,2,1,1,3,1,1]=>[3,1,4,2] 010001101=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 010001110=>101110001=>[1,2,1,1,4,1]=>[2,1,1,4,2] 010001111=>101110000=>[1,2,1,1,5]=>[1,1,1,1,4,2] 010010000=>101101111=>[1,2,1,2,1,1,1,1]=>[5,3,2] 010010001=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 010010010=>101101101=>[1,2,1,2,1,2,1]=>[2,3,3,2] 010010011=>101101100=>[1,2,1,2,1,3]=>[1,1,3,3,2] 010010100=>101101011=>[1,2,1,2,2,1,1]=>[3,2,3,2] 010010101=>101101010=>[1,2,1,2,2,2]=>[1,2,2,3,2] 010010110=>101101001=>[1,2,1,2,3,1]=>[2,1,2,3,2] 010010111=>101101000=>[1,2,1,2,4]=>[1,1,1,2,3,2] 010011000=>101100111=>[1,2,1,3,1,1,1]=>[4,1,3,2] 010011001=>101100110=>[1,2,1,3,1,2]=>[1,3,1,3,2] 010011010=>101100101=>[1,2,1,3,2,1]=>[2,2,1,3,2] 010011011=>101100100=>[1,2,1,3,3]=>[1,1,2,1,3,2] 010011100=>101100011=>[1,2,1,4,1,1]=>[3,1,1,3,2] 010011101=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 010011110=>101100001=>[1,2,1,5,1]=>[2,1,1,1,3,2] 010011111=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 010100000=>101011111=>[1,2,2,1,1,1,1,1]=>[6,2,2] 010100001=>101011110=>[1,2,2,1,1,1,2]=>[1,5,2,2] 010100010=>101011101=>[1,2,2,1,1,2,1]=>[2,4,2,2] 010100011=>101011100=>[1,2,2,1,1,3]=>[1,1,4,2,2] 010100100=>101011011=>[1,2,2,1,2,1,1]=>[3,3,2,2] 010100101=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 010100110=>101011001=>[1,2,2,1,3,1]=>[2,1,3,2,2] 010100111=>101011000=>[1,2,2,1,4]=>[1,1,1,3,2,2] 010101000=>101010111=>[1,2,2,2,1,1,1]=>[4,2,2,2] 010101001=>101010110=>[1,2,2,2,1,2]=>[1,3,2,2,2] 010101010=>101010101=>[1,2,2,2,2,1]=>[2,2,2,2,2] 010101011=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 010101100=>101010011=>[1,2,2,3,1,1]=>[3,1,2,2,2] 010101101=>101010010=>[1,2,2,3,2]=>[1,2,1,2,2,2] 010101110=>101010001=>[1,2,2,4,1]=>[2,1,1,2,2,2] 010101111=>101010000=>[1,2,2,5]=>[1,1,1,1,2,2,2] 010110000=>101001111=>[1,2,3,1,1,1,1]=>[5,1,2,2] 010110001=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 010110010=>101001101=>[1,2,3,1,2,1]=>[2,3,1,2,2] 010110011=>101001100=>[1,2,3,1,3]=>[1,1,3,1,2,2] 010110100=>101001011=>[1,2,3,2,1,1]=>[3,2,1,2,2] 010110101=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 010110110=>101001001=>[1,2,3,3,1]=>[2,1,2,1,2,2] 010110111=>101001000=>[1,2,3,4]=>[1,1,1,2,1,2,2] 010111000=>101000111=>[1,2,4,1,1,1]=>[4,1,1,2,2] 010111001=>101000110=>[1,2,4,1,2]=>[1,3,1,1,2,2] 010111010=>101000101=>[1,2,4,2,1]=>[2,2,1,1,2,2] 010111011=>101000100=>[1,2,4,3]=>[1,1,2,1,1,2,2] 010111100=>101000011=>[1,2,5,1,1]=>[3,1,1,1,2,2] 010111101=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 010111110=>101000001=>[1,2,6,1]=>[2,1,1,1,1,2,2] 010111111=>101000000=>[1,2,7]=>[1,1,1,1,1,1,2,2] 011000000=>100111111=>[1,3,1,1,1,1,1,1]=>[7,1,2] 011000001=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 011000010=>100111101=>[1,3,1,1,1,2,1]=>[2,5,1,2] 011000011=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 011000100=>100111011=>[1,3,1,1,2,1,1]=>[3,4,1,2] 011000101=>100111010=>[1,3,1,1,2,2]=>[1,2,4,1,2] 011000110=>100111001=>[1,3,1,1,3,1]=>[2,1,4,1,2] 011000111=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 011001000=>100110111=>[1,3,1,2,1,1,1]=>[4,3,1,2] 011001001=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 011001010=>100110101=>[1,3,1,2,2,1]=>[2,2,3,1,2] 011001011=>100110100=>[1,3,1,2,3]=>[1,1,2,3,1,2] 011001100=>100110011=>[1,3,1,3,1,1]=>[3,1,3,1,2] 011001101=>100110010=>[1,3,1,3,2]=>[1,2,1,3,1,2] 011001110=>100110001=>[1,3,1,4,1]=>[2,1,1,3,1,2] 011001111=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 011010000=>100101111=>[1,3,2,1,1,1,1]=>[5,2,1,2] 011010001=>100101110=>[1,3,2,1,1,2]=>[1,4,2,1,2] 011010010=>100101101=>[1,3,2,1,2,1]=>[2,3,2,1,2] 011010011=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 011010100=>100101011=>[1,3,2,2,1,1]=>[3,2,2,1,2] 011010101=>100101010=>[1,3,2,2,2]=>[1,2,2,2,1,2] 011010110=>100101001=>[1,3,2,3,1]=>[2,1,2,2,1,2] 011010111=>100101000=>[1,3,2,4]=>[1,1,1,2,2,1,2] 011011000=>100100111=>[1,3,3,1,1,1]=>[4,1,2,1,2] 011011001=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 011011010=>100100101=>[1,3,3,2,1]=>[2,2,1,2,1,2] 011011011=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 011011100=>100100011=>[1,3,4,1,1]=>[3,1,1,2,1,2] 011011101=>100100010=>[1,3,4,2]=>[1,2,1,1,2,1,2] 011011110=>100100001=>[1,3,5,1]=>[2,1,1,1,2,1,2] 011011111=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 011100000=>100011111=>[1,4,1,1,1,1,1]=>[6,1,1,2] 011100001=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 011100010=>100011101=>[1,4,1,1,2,1]=>[2,4,1,1,2] 011100011=>100011100=>[1,4,1,1,3]=>[1,1,4,1,1,2] 011100100=>100011011=>[1,4,1,2,1,1]=>[3,3,1,1,2] 011100101=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 011100110=>100011001=>[1,4,1,3,1]=>[2,1,3,1,1,2] 011100111=>100011000=>[1,4,1,4]=>[1,1,1,3,1,1,2] 011101000=>100010111=>[1,4,2,1,1,1]=>[4,2,1,1,2] 011101001=>100010110=>[1,4,2,1,2]=>[1,3,2,1,1,2] 011101010=>100010101=>[1,4,2,2,1]=>[2,2,2,1,1,2] 011101011=>100010100=>[1,4,2,3]=>[1,1,2,2,1,1,2] 011101100=>100010011=>[1,4,3,1,1]=>[3,1,2,1,1,2] 011101101=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 011101110=>100010001=>[1,4,4,1]=>[2,1,1,2,1,1,2] 011101111=>100010000=>[1,4,5]=>[1,1,1,1,2,1,1,2] 011110000=>100001111=>[1,5,1,1,1,1]=>[5,1,1,1,2] 011110001=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 011110010=>100001101=>[1,5,1,2,1]=>[2,3,1,1,1,2] 011110011=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 011110100=>100001011=>[1,5,2,1,1]=>[3,2,1,1,1,2] 011110101=>100001010=>[1,5,2,2]=>[1,2,2,1,1,1,2] 011110110=>100001001=>[1,5,3,1]=>[2,1,2,1,1,1,2] 011110111=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 011111000=>100000111=>[1,6,1,1,1]=>[4,1,1,1,1,2] 011111001=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 011111010=>100000101=>[1,6,2,1]=>[2,2,1,1,1,1,2] 011111011=>100000100=>[1,6,3]=>[1,1,2,1,1,1,1,2] 011111100=>100000011=>[1,7,1,1]=>[3,1,1,1,1,1,2] 011111101=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 011111110=>100000001=>[1,8,1]=>[2,1,1,1,1,1,1,2] 011111111=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 100000000=>011111111=>[2,1,1,1,1,1,1,1,1]=>[9,1] 100000001=>011111110=>[2,1,1,1,1,1,1,2]=>[1,8,1] 100000010=>011111101=>[2,1,1,1,1,1,2,1]=>[2,7,1] 100000011=>011111100=>[2,1,1,1,1,1,3]=>[1,1,7,1] 100000100=>011111011=>[2,1,1,1,1,2,1,1]=>[3,6,1] 100000101=>011111010=>[2,1,1,1,1,2,2]=>[1,2,6,1] 100000110=>011111001=>[2,1,1,1,1,3,1]=>[2,1,6,1] 100000111=>011111000=>[2,1,1,1,1,4]=>[1,1,1,6,1] 100001000=>011110111=>[2,1,1,1,2,1,1,1]=>[4,5,1] 100001001=>011110110=>[2,1,1,1,2,1,2]=>[1,3,5,1] 100001010=>011110101=>[2,1,1,1,2,2,1]=>[2,2,5,1] 100001011=>011110100=>[2,1,1,1,2,3]=>[1,1,2,5,1] 100001100=>011110011=>[2,1,1,1,3,1,1]=>[3,1,5,1] 100001101=>011110010=>[2,1,1,1,3,2]=>[1,2,1,5,1] 100001110=>011110001=>[2,1,1,1,4,1]=>[2,1,1,5,1] 100001111=>011110000=>[2,1,1,1,5]=>[1,1,1,1,5,1] 100010000=>011101111=>[2,1,1,2,1,1,1,1]=>[5,4,1] 100010001=>011101110=>[2,1,1,2,1,1,2]=>[1,4,4,1] 100010010=>011101101=>[2,1,1,2,1,2,1]=>[2,3,4,1] 100010011=>011101100=>[2,1,1,2,1,3]=>[1,1,3,4,1] 100010100=>011101011=>[2,1,1,2,2,1,1]=>[3,2,4,1] 100010101=>011101010=>[2,1,1,2,2,2]=>[1,2,2,4,1] 100010110=>011101001=>[2,1,1,2,3,1]=>[2,1,2,4,1] 100010111=>011101000=>[2,1,1,2,4]=>[1,1,1,2,4,1] 100011000=>011100111=>[2,1,1,3,1,1,1]=>[4,1,4,1] 100011001=>011100110=>[2,1,1,3,1,2]=>[1,3,1,4,1] 100011010=>011100101=>[2,1,1,3,2,1]=>[2,2,1,4,1] 100011011=>011100100=>[2,1,1,3,3]=>[1,1,2,1,4,1] 100011100=>011100011=>[2,1,1,4,1,1]=>[3,1,1,4,1] 100011101=>011100010=>[2,1,1,4,2]=>[1,2,1,1,4,1] 100011110=>011100001=>[2,1,1,5,1]=>[2,1,1,1,4,1] 100011111=>011100000=>[2,1,1,6]=>[1,1,1,1,1,4,1] 100100000=>011011111=>[2,1,2,1,1,1,1,1]=>[6,3,1] 100100001=>011011110=>[2,1,2,1,1,1,2]=>[1,5,3,1] 100100010=>011011101=>[2,1,2,1,1,2,1]=>[2,4,3,1] 100100011=>011011100=>[2,1,2,1,1,3]=>[1,1,4,3,1] 100100100=>011011011=>[2,1,2,1,2,1,1]=>[3,3,3,1] 100100101=>011011010=>[2,1,2,1,2,2]=>[1,2,3,3,1] 100100110=>011011001=>[2,1,2,1,3,1]=>[2,1,3,3,1] 100100111=>011011000=>[2,1,2,1,4]=>[1,1,1,3,3,1] 100101000=>011010111=>[2,1,2,2,1,1,1]=>[4,2,3,1] 100101001=>011010110=>[2,1,2,2,1,2]=>[1,3,2,3,1] 100101010=>011010101=>[2,1,2,2,2,1]=>[2,2,2,3,1] 100101011=>011010100=>[2,1,2,2,3]=>[1,1,2,2,3,1] 100101100=>011010011=>[2,1,2,3,1,1]=>[3,1,2,3,1] 100101101=>011010010=>[2,1,2,3,2]=>[1,2,1,2,3,1] 100101110=>011010001=>[2,1,2,4,1]=>[2,1,1,2,3,1] 100101111=>011010000=>[2,1,2,5]=>[1,1,1,1,2,3,1] 100110000=>011001111=>[2,1,3,1,1,1,1]=>[5,1,3,1] 100110001=>011001110=>[2,1,3,1,1,2]=>[1,4,1,3,1] 100110010=>011001101=>[2,1,3,1,2,1]=>[2,3,1,3,1] 100110011=>011001100=>[2,1,3,1,3]=>[1,1,3,1,3,1] 100110100=>011001011=>[2,1,3,2,1,1]=>[3,2,1,3,1] 100110101=>011001010=>[2,1,3,2,2]=>[1,2,2,1,3,1] 100110110=>011001001=>[2,1,3,3,1]=>[2,1,2,1,3,1] 100110111=>011001000=>[2,1,3,4]=>[1,1,1,2,1,3,1] 100111000=>011000111=>[2,1,4,1,1,1]=>[4,1,1,3,1] 100111001=>011000110=>[2,1,4,1,2]=>[1,3,1,1,3,1] 100111010=>011000101=>[2,1,4,2,1]=>[2,2,1,1,3,1] 100111011=>011000100=>[2,1,4,3]=>[1,1,2,1,1,3,1] 100111100=>011000011=>[2,1,5,1,1]=>[3,1,1,1,3,1] 100111101=>011000010=>[2,1,5,2]=>[1,2,1,1,1,3,1] 100111110=>011000001=>[2,1,6,1]=>[2,1,1,1,1,3,1] 100111111=>011000000=>[2,1,7]=>[1,1,1,1,1,1,3,1] 101000000=>010111111=>[2,2,1,1,1,1,1,1]=>[7,2,1] 101000001=>010111110=>[2,2,1,1,1,1,2]=>[1,6,2,1] 101000010=>010111101=>[2,2,1,1,1,2,1]=>[2,5,2,1] 101000011=>010111100=>[2,2,1,1,1,3]=>[1,1,5,2,1] 101000100=>010111011=>[2,2,1,1,2,1,1]=>[3,4,2,1] 101000101=>010111010=>[2,2,1,1,2,2]=>[1,2,4,2,1] 101000110=>010111001=>[2,2,1,1,3,1]=>[2,1,4,2,1] 101000111=>010111000=>[2,2,1,1,4]=>[1,1,1,4,2,1] 101001000=>010110111=>[2,2,1,2,1,1,1]=>[4,3,2,1] 101001001=>010110110=>[2,2,1,2,1,2]=>[1,3,3,2,1] 101001010=>010110101=>[2,2,1,2,2,1]=>[2,2,3,2,1] 101001011=>010110100=>[2,2,1,2,3]=>[1,1,2,3,2,1] 101001100=>010110011=>[2,2,1,3,1,1]=>[3,1,3,2,1] 101001101=>010110010=>[2,2,1,3,2]=>[1,2,1,3,2,1] 101001110=>010110001=>[2,2,1,4,1]=>[2,1,1,3,2,1] 101001111=>010110000=>[2,2,1,5]=>[1,1,1,1,3,2,1] 101010000=>010101111=>[2,2,2,1,1,1,1]=>[5,2,2,1] 101010001=>010101110=>[2,2,2,1,1,2]=>[1,4,2,2,1] 101010010=>010101101=>[2,2,2,1,2,1]=>[2,3,2,2,1] 101010011=>010101100=>[2,2,2,1,3]=>[1,1,3,2,2,1] 101010100=>010101011=>[2,2,2,2,1,1]=>[3,2,2,2,1] 101010101=>010101010=>[2,2,2,2,2]=>[1,2,2,2,2,1] 101010110=>010101001=>[2,2,2,3,1]=>[2,1,2,2,2,1] 101010111=>010101000=>[2,2,2,4]=>[1,1,1,2,2,2,1] 101011000=>010100111=>[2,2,3,1,1,1]=>[4,1,2,2,1] 101011001=>010100110=>[2,2,3,1,2]=>[1,3,1,2,2,1] 101011010=>010100101=>[2,2,3,2,1]=>[2,2,1,2,2,1] 101011011=>010100100=>[2,2,3,3]=>[1,1,2,1,2,2,1] 101011100=>010100011=>[2,2,4,1,1]=>[3,1,1,2,2,1] 101011101=>010100010=>[2,2,4,2]=>[1,2,1,1,2,2,1] 101011110=>010100001=>[2,2,5,1]=>[2,1,1,1,2,2,1] 101011111=>010100000=>[2,2,6]=>[1,1,1,1,1,2,2,1] 101100000=>010011111=>[2,3,1,1,1,1,1]=>[6,1,2,1] 101100001=>010011110=>[2,3,1,1,1,2]=>[1,5,1,2,1] 101100010=>010011101=>[2,3,1,1,2,1]=>[2,4,1,2,1] 101100011=>010011100=>[2,3,1,1,3]=>[1,1,4,1,2,1] 101100100=>010011011=>[2,3,1,2,1,1]=>[3,3,1,2,1] 101100101=>010011010=>[2,3,1,2,2]=>[1,2,3,1,2,1] 101100110=>010011001=>[2,3,1,3,1]=>[2,1,3,1,2,1] 101100111=>010011000=>[2,3,1,4]=>[1,1,1,3,1,2,1] 101101000=>010010111=>[2,3,2,1,1,1]=>[4,2,1,2,1] 101101001=>010010110=>[2,3,2,1,2]=>[1,3,2,1,2,1] 101101010=>010010101=>[2,3,2,2,1]=>[2,2,2,1,2,1] 101101011=>010010100=>[2,3,2,3]=>[1,1,2,2,1,2,1] 101101100=>010010011=>[2,3,3,1,1]=>[3,1,2,1,2,1] 101101101=>010010010=>[2,3,3,2]=>[1,2,1,2,1,2,1] 101101110=>010010001=>[2,3,4,1]=>[2,1,1,2,1,2,1] 101101111=>010010000=>[2,3,5]=>[1,1,1,1,2,1,2,1] 101110000=>010001111=>[2,4,1,1,1,1]=>[5,1,1,2,1] 101110001=>010001110=>[2,4,1,1,2]=>[1,4,1,1,2,1] 101110010=>010001101=>[2,4,1,2,1]=>[2,3,1,1,2,1] 101110011=>010001100=>[2,4,1,3]=>[1,1,3,1,1,2,1] 101110100=>010001011=>[2,4,2,1,1]=>[3,2,1,1,2,1] 101110101=>010001010=>[2,4,2,2]=>[1,2,2,1,1,2,1] 101110110=>010001001=>[2,4,3,1]=>[2,1,2,1,1,2,1] 101110111=>010001000=>[2,4,4]=>[1,1,1,2,1,1,2,1] 101111000=>010000111=>[2,5,1,1,1]=>[4,1,1,1,2,1] 101111001=>010000110=>[2,5,1,2]=>[1,3,1,1,1,2,1] 101111010=>010000101=>[2,5,2,1]=>[2,2,1,1,1,2,1] 101111011=>010000100=>[2,5,3]=>[1,1,2,1,1,1,2,1] 101111100=>010000011=>[2,6,1,1]=>[3,1,1,1,1,2,1] 101111101=>010000010=>[2,6,2]=>[1,2,1,1,1,1,2,1] 101111110=>010000001=>[2,7,1]=>[2,1,1,1,1,1,2,1] 101111111=>010000000=>[2,8]=>[1,1,1,1,1,1,1,2,1] 110000000=>001111111=>[3,1,1,1,1,1,1,1]=>[8,1,1] 110000001=>001111110=>[3,1,1,1,1,1,2]=>[1,7,1,1] 110000010=>001111101=>[3,1,1,1,1,2,1]=>[2,6,1,1] 110000011=>001111100=>[3,1,1,1,1,3]=>[1,1,6,1,1] 110000100=>001111011=>[3,1,1,1,2,1,1]=>[3,5,1,1] 110000101=>001111010=>[3,1,1,1,2,2]=>[1,2,5,1,1] 110000110=>001111001=>[3,1,1,1,3,1]=>[2,1,5,1,1] 110000111=>001111000=>[3,1,1,1,4]=>[1,1,1,5,1,1] 110001000=>001110111=>[3,1,1,2,1,1,1]=>[4,4,1,1] 110001001=>001110110=>[3,1,1,2,1,2]=>[1,3,4,1,1] 110001010=>001110101=>[3,1,1,2,2,1]=>[2,2,4,1,1] 110001011=>001110100=>[3,1,1,2,3]=>[1,1,2,4,1,1] 110001100=>001110011=>[3,1,1,3,1,1]=>[3,1,4,1,1] 110001101=>001110010=>[3,1,1,3,2]=>[1,2,1,4,1,1] 110001110=>001110001=>[3,1,1,4,1]=>[2,1,1,4,1,1] 110001111=>001110000=>[3,1,1,5]=>[1,1,1,1,4,1,1] 110010000=>001101111=>[3,1,2,1,1,1,1]=>[5,3,1,1] 110010001=>001101110=>[3,1,2,1,1,2]=>[1,4,3,1,1] 110010010=>001101101=>[3,1,2,1,2,1]=>[2,3,3,1,1] 110010011=>001101100=>[3,1,2,1,3]=>[1,1,3,3,1,1] 110010100=>001101011=>[3,1,2,2,1,1]=>[3,2,3,1,1] 110010101=>001101010=>[3,1,2,2,2]=>[1,2,2,3,1,1] 110010110=>001101001=>[3,1,2,3,1]=>[2,1,2,3,1,1] 110010111=>001101000=>[3,1,2,4]=>[1,1,1,2,3,1,1] 110011000=>001100111=>[3,1,3,1,1,1]=>[4,1,3,1,1] 110011001=>001100110=>[3,1,3,1,2]=>[1,3,1,3,1,1] 110011010=>001100101=>[3,1,3,2,1]=>[2,2,1,3,1,1] 110011011=>001100100=>[3,1,3,3]=>[1,1,2,1,3,1,1] 110011100=>001100011=>[3,1,4,1,1]=>[3,1,1,3,1,1] 110011101=>001100010=>[3,1,4,2]=>[1,2,1,1,3,1,1] 110011110=>001100001=>[3,1,5,1]=>[2,1,1,1,3,1,1] 110011111=>001100000=>[3,1,6]=>[1,1,1,1,1,3,1,1] 110100000=>001011111=>[3,2,1,1,1,1,1]=>[6,2,1,1] 110100001=>001011110=>[3,2,1,1,1,2]=>[1,5,2,1,1] 110100010=>001011101=>[3,2,1,1,2,1]=>[2,4,2,1,1] 110100011=>001011100=>[3,2,1,1,3]=>[1,1,4,2,1,1] 110100100=>001011011=>[3,2,1,2,1,1]=>[3,3,2,1,1] 110100101=>001011010=>[3,2,1,2,2]=>[1,2,3,2,1,1] 110100110=>001011001=>[3,2,1,3,1]=>[2,1,3,2,1,1] 110100111=>001011000=>[3,2,1,4]=>[1,1,1,3,2,1,1] 110101000=>001010111=>[3,2,2,1,1,1]=>[4,2,2,1,1] 110101001=>001010110=>[3,2,2,1,2]=>[1,3,2,2,1,1] 110101010=>001010101=>[3,2,2,2,1]=>[2,2,2,2,1,1] 110101011=>001010100=>[3,2,2,3]=>[1,1,2,2,2,1,1] 110101100=>001010011=>[3,2,3,1,1]=>[3,1,2,2,1,1] 110101101=>001010010=>[3,2,3,2]=>[1,2,1,2,2,1,1] 110101110=>001010001=>[3,2,4,1]=>[2,1,1,2,2,1,1] 110101111=>001010000=>[3,2,5]=>[1,1,1,1,2,2,1,1] 110110000=>001001111=>[3,3,1,1,1,1]=>[5,1,2,1,1] 110110001=>001001110=>[3,3,1,1,2]=>[1,4,1,2,1,1] 110110010=>001001101=>[3,3,1,2,1]=>[2,3,1,2,1,1] 110110011=>001001100=>[3,3,1,3]=>[1,1,3,1,2,1,1] 110110100=>001001011=>[3,3,2,1,1]=>[3,2,1,2,1,1] 110110101=>001001010=>[3,3,2,2]=>[1,2,2,1,2,1,1] 110110110=>001001001=>[3,3,3,1]=>[2,1,2,1,2,1,1] 110110111=>001001000=>[3,3,4]=>[1,1,1,2,1,2,1,1] 110111000=>001000111=>[3,4,1,1,1]=>[4,1,1,2,1,1] 110111001=>001000110=>[3,4,1,2]=>[1,3,1,1,2,1,1] 110111010=>001000101=>[3,4,2,1]=>[2,2,1,1,2,1,1] 110111011=>001000100=>[3,4,3]=>[1,1,2,1,1,2,1,1] 110111100=>001000011=>[3,5,1,1]=>[3,1,1,1,2,1,1] 110111101=>001000010=>[3,5,2]=>[1,2,1,1,1,2,1,1] 110111110=>001000001=>[3,6,1]=>[2,1,1,1,1,2,1,1] 110111111=>001000000=>[3,7]=>[1,1,1,1,1,1,2,1,1] 111000000=>000111111=>[4,1,1,1,1,1,1]=>[7,1,1,1] 111000001=>000111110=>[4,1,1,1,1,2]=>[1,6,1,1,1] 111000010=>000111101=>[4,1,1,1,2,1]=>[2,5,1,1,1] 111000011=>000111100=>[4,1,1,1,3]=>[1,1,5,1,1,1] 111000100=>000111011=>[4,1,1,2,1,1]=>[3,4,1,1,1] 111000101=>000111010=>[4,1,1,2,2]=>[1,2,4,1,1,1] 111000110=>000111001=>[4,1,1,3,1]=>[2,1,4,1,1,1] 111000111=>000111000=>[4,1,1,4]=>[1,1,1,4,1,1,1] 111001000=>000110111=>[4,1,2,1,1,1]=>[4,3,1,1,1] 111001001=>000110110=>[4,1,2,1,2]=>[1,3,3,1,1,1] 111001010=>000110101=>[4,1,2,2,1]=>[2,2,3,1,1,1] 111001011=>000110100=>[4,1,2,3]=>[1,1,2,3,1,1,1] 111001100=>000110011=>[4,1,3,1,1]=>[3,1,3,1,1,1] 111001101=>000110010=>[4,1,3,2]=>[1,2,1,3,1,1,1] 111001110=>000110001=>[4,1,4,1]=>[2,1,1,3,1,1,1] 111001111=>000110000=>[4,1,5]=>[1,1,1,1,3,1,1,1] 111010000=>000101111=>[4,2,1,1,1,1]=>[5,2,1,1,1] 111010001=>000101110=>[4,2,1,1,2]=>[1,4,2,1,1,1] 111010010=>000101101=>[4,2,1,2,1]=>[2,3,2,1,1,1] 111010011=>000101100=>[4,2,1,3]=>[1,1,3,2,1,1,1] 111010100=>000101011=>[4,2,2,1,1]=>[3,2,2,1,1,1] 111010101=>000101010=>[4,2,2,2]=>[1,2,2,2,1,1,1] 111010110=>000101001=>[4,2,3,1]=>[2,1,2,2,1,1,1] 111010111=>000101000=>[4,2,4]=>[1,1,1,2,2,1,1,1] 111011000=>000100111=>[4,3,1,1,1]=>[4,1,2,1,1,1] 111011001=>000100110=>[4,3,1,2]=>[1,3,1,2,1,1,1] 111011010=>000100101=>[4,3,2,1]=>[2,2,1,2,1,1,1] 111011011=>000100100=>[4,3,3]=>[1,1,2,1,2,1,1,1] 111011100=>000100011=>[4,4,1,1]=>[3,1,1,2,1,1,1] 111011101=>000100010=>[4,4,2]=>[1,2,1,1,2,1,1,1] 111011110=>000100001=>[4,5,1]=>[2,1,1,1,2,1,1,1] 111011111=>000100000=>[4,6]=>[1,1,1,1,1,2,1,1,1] 111100000=>000011111=>[5,1,1,1,1,1]=>[6,1,1,1,1] 111100001=>000011110=>[5,1,1,1,2]=>[1,5,1,1,1,1] 111100010=>000011101=>[5,1,1,2,1]=>[2,4,1,1,1,1] 111100011=>000011100=>[5,1,1,3]=>[1,1,4,1,1,1,1] 111100100=>000011011=>[5,1,2,1,1]=>[3,3,1,1,1,1] 111100101=>000011010=>[5,1,2,2]=>[1,2,3,1,1,1,1] 111100110=>000011001=>[5,1,3,1]=>[2,1,3,1,1,1,1] 111100111=>000011000=>[5,1,4]=>[1,1,1,3,1,1,1,1] 111101000=>000010111=>[5,2,1,1,1]=>[4,2,1,1,1,1] 111101001=>000010110=>[5,2,1,2]=>[1,3,2,1,1,1,1] 111101010=>000010101=>[5,2,2,1]=>[2,2,2,1,1,1,1] 111101011=>000010100=>[5,2,3]=>[1,1,2,2,1,1,1,1] 111101100=>000010011=>[5,3,1,1]=>[3,1,2,1,1,1,1] 111101101=>000010010=>[5,3,2]=>[1,2,1,2,1,1,1,1] 111101110=>000010001=>[5,4,1]=>[2,1,1,2,1,1,1,1] 111101111=>000010000=>[5,5]=>[1,1,1,1,2,1,1,1,1] 111110000=>000001111=>[6,1,1,1,1]=>[5,1,1,1,1,1] 111110001=>000001110=>[6,1,1,2]=>[1,4,1,1,1,1,1] 111110010=>000001101=>[6,1,2,1]=>[2,3,1,1,1,1,1] 111110011=>000001100=>[6,1,3]=>[1,1,3,1,1,1,1,1] 111110100=>000001011=>[6,2,1,1]=>[3,2,1,1,1,1,1] 111110101=>000001010=>[6,2,2]=>[1,2,2,1,1,1,1,1] 111110110=>000001001=>[6,3,1]=>[2,1,2,1,1,1,1,1] 111110111=>000001000=>[6,4]=>[1,1,1,2,1,1,1,1,1] 111111000=>000000111=>[7,1,1,1]=>[4,1,1,1,1,1,1] 111111001=>000000110=>[7,1,2]=>[1,3,1,1,1,1,1,1] 111111010=>000000101=>[7,2,1]=>[2,2,1,1,1,1,1,1] 111111011=>000000100=>[7,3]=>[1,1,2,1,1,1,1,1,1] 111111100=>000000011=>[8,1,1]=>[3,1,1,1,1,1,1,1] 111111101=>000000010=>[8,2]=>[1,2,1,1,1,1,1,1,1] 111111110=>000000001=>[9,1]=>[2,1,1,1,1,1,1,1,1] 111111111=>000000000=>[10]=>[1,1,1,1,1,1,1,1,1,1] 1111111111=>0000000000=>[11]=>[1,1,1,1,1,1,1,1,1,1,1] 1111111110=>0000000001=>[10,1]=>[2,1,1,1,1,1,1,1,1,1] 0111111111=>1000000000=>[1,10]=>[1,1,1,1,1,1,1,1,1,2] 0111111101=>1000000010=>[1,8,2]=>[1,2,1,1,1,1,1,1,2] 0111111001=>1000000110=>[1,7,1,2]=>[1,3,1,1,1,1,1,2] 0111110001=>1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2] 0111100001=>1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2] 0111000001=>1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 0110000001=>1001111110=>[1,3,1,1,1,1,1,2]=>[1,7,1,2] 0100000001=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 0000000001=>1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10] 01111111111=>10000000000=>[1,11]=>[1,1,1,1,1,1,1,1,1,1,2] 01111111101=>10000000010=>[1,9,2]=>[1,2,1,1,1,1,1,1,1,2] 0111111011=>1000000100=>[1,7,3]=>[1,1,2,1,1,1,1,1,2] 01111111001=>10000000110=>[1,8,1,2]=>[1,3,1,1,1,1,1,1,2] 0111110101=>1000001010=>[1,6,2,2]=>[1,2,2,1,1,1,1,2] 01111110001=>10000001110=>[1,7,1,1,2]=>[1,4,1,1,1,1,1,2] 0111101001=>1000010110=>[1,5,2,1,2]=>[1,3,2,1,1,1,2] 01111100001=>10000011110=>[1,6,1,1,1,2]=>[1,5,1,1,1,1,2] 0111010001=>1000101110=>[1,4,2,1,1,2]=>[1,4,2,1,1,2] 01111000001=>10000111110=>[1,5,1,1,1,1,2]=>[1,6,1,1,1,2] 0110100001=>1001011110=>[1,3,2,1,1,1,2]=>[1,5,2,1,2] 01110000001=>10001111110=>[1,4,1,1,1,1,1,2]=>[1,7,1,1,2] 0101000001=>1010111110=>[1,2,2,1,1,1,1,2]=>[1,6,2,2] 01100000001=>10011111110=>[1,3,1,1,1,1,1,1,2]=>[1,8,1,2] 0010000001=>1101111110=>[1,1,2,1,1,1,1,1,2]=>[1,7,3] 01000000001=>10111111110=>[1,2,1,1,1,1,1,1,1,2]=>[1,9,2] 00000000001=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2]=>[1,11] 0101010101=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 0101010011=>1010101100=>[1,2,2,2,1,3]=>[1,1,3,2,2,2] 0101001101=>1010110010=>[1,2,2,1,3,2]=>[1,2,1,3,2,2] 0101001011=>1010110100=>[1,2,2,1,2,3]=>[1,1,2,3,2,2] 0101000111=>1010111000=>[1,2,2,1,1,4]=>[1,1,1,4,2,2] 0100110101=>1011001010=>[1,2,1,3,2,2]=>[1,2,2,1,3,2] 0100110011=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] 0100101101=>1011010010=>[1,2,1,2,3,2]=>[1,2,1,2,3,2] 0100101011=>1011010100=>[1,2,1,2,2,3]=>[1,1,2,2,3,2] 0100100111=>1011011000=>[1,2,1,2,1,4]=>[1,1,1,3,3,2] 0100011101=>1011100010=>[1,2,1,1,4,2]=>[1,2,1,1,4,2] 0100011011=>1011100100=>[1,2,1,1,3,3]=>[1,1,2,1,4,2] 0100010111=>1011101000=>[1,2,1,1,2,4]=>[1,1,1,2,4,2] 0100001111=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 0011010101=>1100101010=>[1,1,3,2,2,2]=>[1,2,2,2,1,3] 0011010011=>1100101100=>[1,1,3,2,1,3]=>[1,1,3,2,1,3] 0011001101=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] 0011001011=>1100110100=>[1,1,3,1,2,3]=>[1,1,2,3,1,3] 0011000111=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 0010110101=>1101001010=>[1,1,2,3,2,2]=>[1,2,2,1,2,3] 0010110011=>1101001100=>[1,1,2,3,1,3]=>[1,1,3,1,2,3] 0010101101=>1101010010=>[1,1,2,2,3,2]=>[1,2,1,2,2,3] 0010101011=>1101010100=>[1,1,2,2,2,3]=>[1,1,2,2,2,3] 0010100111=>1101011000=>[1,1,2,2,1,4]=>[1,1,1,3,2,3] 0010011101=>1101100010=>[1,1,2,1,4,2]=>[1,2,1,1,3,3] 0010011011=>1101100100=>[1,1,2,1,3,3]=>[1,1,2,1,3,3] 0010010111=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 0010001111=>1101110000=>[1,1,2,1,1,5]=>[1,1,1,1,4,3] 0001110101=>1110001010=>[1,1,1,4,2,2]=>[1,2,2,1,1,4] 0001110011=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 0001101101=>1110010010=>[1,1,1,3,3,2]=>[1,2,1,2,1,4] 0001101011=>1110010100=>[1,1,1,3,2,3]=>[1,1,2,2,1,4] 0001100111=>1110011000=>[1,1,1,3,1,4]=>[1,1,1,3,1,4] 0001011101=>1110100010=>[1,1,1,2,4,2]=>[1,2,1,1,2,4] 0001011011=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 0001010111=>1110101000=>[1,1,1,2,2,4]=>[1,1,1,2,2,4] 0001001111=>1110110000=>[1,1,1,2,1,5]=>[1,1,1,1,3,4] 0000111101=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 0000111011=>1111000100=>[1,1,1,1,4,3]=>[1,1,2,1,1,5] 0000110111=>1111001000=>[1,1,1,1,3,4]=>[1,1,1,2,1,5] 0000101111=>1111010000=>[1,1,1,1,2,5]=>[1,1,1,1,2,5] 0000011111=>1111100000=>[1,1,1,1,1,6]=>[1,1,1,1,1,6] 010101010101=>101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] 010101010011=>101010101100=>[1,2,2,2,2,1,3]=>[1,1,3,2,2,2,2] 010101001101=>101010110010=>[1,2,2,2,1,3,2]=>[1,2,1,3,2,2,2] 010101001011=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 010101000111=>101010111000=>[1,2,2,2,1,1,4]=>[1,1,1,4,2,2,2] 010100110101=>101011001010=>[1,2,2,1,3,2,2]=>[1,2,2,1,3,2,2] 010100110011=>101011001100=>[1,2,2,1,3,1,3]=>[1,1,3,1,3,2,2] 010100101101=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 010100101011=>101011010100=>[1,2,2,1,2,2,3]=>[1,1,2,2,3,2,2] 010100100111=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 010100011101=>101011100010=>[1,2,2,1,1,4,2]=>[1,2,1,1,4,2,2] 010100011011=>101011100100=>[1,2,2,1,1,3,3]=>[1,1,2,1,4,2,2] 010100010111=>101011101000=>[1,2,2,1,1,2,4]=>[1,1,1,2,4,2,2] 010100001111=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 010011010101=>101100101010=>[1,2,1,3,2,2,2]=>[1,2,2,2,1,3,2] 010011010011=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 010011001101=>101100110010=>[1,2,1,3,1,3,2]=>[1,2,1,3,1,3,2] 010011001011=>101100110100=>[1,2,1,3,1,2,3]=>[1,1,2,3,1,3,2] 010011000111=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 010010110101=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 010010110011=>101101001100=>[1,2,1,2,3,1,3]=>[1,1,3,1,2,3,2] 010010101101=>101101010010=>[1,2,1,2,2,3,2]=>[1,2,1,2,2,3,2] 010010101011=>101101010100=>[1,2,1,2,2,2,3]=>[1,1,2,2,2,3,2] 010010100111=>101101011000=>[1,2,1,2,2,1,4]=>[1,1,1,3,2,3,2] 010010011101=>101101100010=>[1,2,1,2,1,4,2]=>[1,2,1,1,3,3,2] 010010011011=>101101100100=>[1,2,1,2,1,3,3]=>[1,1,2,1,3,3,2] 010010010111=>101101101000=>[1,2,1,2,1,2,4]=>[1,1,1,2,3,3,2] 010010001111=>101101110000=>[1,2,1,2,1,1,5]=>[1,1,1,1,4,3,2] 010001110101=>101110001010=>[1,2,1,1,4,2,2]=>[1,2,2,1,1,4,2] 010001110011=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 010001101101=>101110010010=>[1,2,1,1,3,3,2]=>[1,2,1,2,1,4,2] 010001101011=>101110010100=>[1,2,1,1,3,2,3]=>[1,1,2,2,1,4,2] 010001100111=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 010001011101=>101110100010=>[1,2,1,1,2,4,2]=>[1,2,1,1,2,4,2] 010001011011=>101110100100=>[1,2,1,1,2,3,3]=>[1,1,2,1,2,4,2] 010001010111=>101110101000=>[1,2,1,1,2,2,4]=>[1,1,1,2,2,4,2] 010001001111=>101110110000=>[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] 010000111101=>101111000010=>[1,2,1,1,1,5,2]=>[1,2,1,1,1,5,2] 010000111011=>101111000100=>[1,2,1,1,1,4,3]=>[1,1,2,1,1,5,2] 010000110111=>101111001000=>[1,2,1,1,1,3,4]=>[1,1,1,2,1,5,2] 010000101111=>101111010000=>[1,2,1,1,1,2,5]=>[1,1,1,1,2,5,2] 010000011111=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 001101010101=>110010101010=>[1,1,3,2,2,2,2]=>[1,2,2,2,2,1,3] 001101010011=>110010101100=>[1,1,3,2,2,1,3]=>[1,1,3,2,2,1,3] 001101001101=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 001101001011=>110010110100=>[1,1,3,2,1,2,3]=>[1,1,2,3,2,1,3] 001101000111=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 001100110101=>110011001010=>[1,1,3,1,3,2,2]=>[1,2,2,1,3,1,3] 001100110011=>110011001100=>[1,1,3,1,3,1,3]=>[1,1,3,1,3,1,3] 001100101101=>110011010010=>[1,1,3,1,2,3,2]=>[1,2,1,2,3,1,3] 001100101011=>110011010100=>[1,1,3,1,2,2,3]=>[1,1,2,2,3,1,3] 001100100111=>110011011000=>[1,1,3,1,2,1,4]=>[1,1,1,3,3,1,3] 001100011101=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 001100011011=>110011100100=>[1,1,3,1,1,3,3]=>[1,1,2,1,4,1,3] 001100010111=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 001100001111=>110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] 001011010101=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 001011010011=>110100101100=>[1,1,2,3,2,1,3]=>[1,1,3,2,1,2,3] 001011001101=>110100110010=>[1,1,2,3,1,3,2]=>[1,2,1,3,1,2,3] 001011001011=>110100110100=>[1,1,2,3,1,2,3]=>[1,1,2,3,1,2,3] 001011000111=>110100111000=>[1,1,2,3,1,1,4]=>[1,1,1,4,1,2,3] 001010110101=>110101001010=>[1,1,2,2,3,2,2]=>[1,2,2,1,2,2,3] 001010110011=>110101001100=>[1,1,2,2,3,1,3]=>[1,1,3,1,2,2,3] 001010101101=>110101010010=>[1,1,2,2,2,3,2]=>[1,2,1,2,2,2,3] 001010101011=>110101010100=>[1,1,2,2,2,2,3]=>[1,1,2,2,2,2,3] 001010100111=>110101011000=>[1,1,2,2,2,1,4]=>[1,1,1,3,2,2,3] 001010011101=>110101100010=>[1,1,2,2,1,4,2]=>[1,2,1,1,3,2,3] 001010011011=>110101100100=>[1,1,2,2,1,3,3]=>[1,1,2,1,3,2,3] 001010010111=>110101101000=>[1,1,2,2,1,2,4]=>[1,1,1,2,3,2,3] 001010001111=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 001001110101=>110110001010=>[1,1,2,1,4,2,2]=>[1,2,2,1,1,3,3] 001001110011=>110110001100=>[1,1,2,1,4,1,3]=>[1,1,3,1,1,3,3] 001001101101=>110110010010=>[1,1,2,1,3,3,2]=>[1,2,1,2,1,3,3] 001001101011=>110110010100=>[1,1,2,1,3,2,3]=>[1,1,2,2,1,3,3] 001001100111=>110110011000=>[1,1,2,1,3,1,4]=>[1,1,1,3,1,3,3] 001001011101=>110110100010=>[1,1,2,1,2,4,2]=>[1,2,1,1,2,3,3] 001001011011=>110110100100=>[1,1,2,1,2,3,3]=>[1,1,2,1,2,3,3] 001001010111=>110110101000=>[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] 001001001111=>110110110000=>[1,1,2,1,2,1,5]=>[1,1,1,1,3,3,3] 001000111101=>110111000010=>[1,1,2,1,1,5,2]=>[1,2,1,1,1,4,3] 001000111011=>110111000100=>[1,1,2,1,1,4,3]=>[1,1,2,1,1,4,3] 001000110111=>110111001000=>[1,1,2,1,1,3,4]=>[1,1,1,2,1,4,3] 001000101111=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 001000011111=>110111100000=>[1,1,2,1,1,1,6]=>[1,1,1,1,1,5,3] 000111010101=>111000101010=>[1,1,1,4,2,2,2]=>[1,2,2,2,1,1,4] 000111010011=>111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] 000111001101=>111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] 000111001011=>111000110100=>[1,1,1,4,1,2,3]=>[1,1,2,3,1,1,4] 000111000111=>111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] 000110110101=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 000110110011=>111001001100=>[1,1,1,3,3,1,3]=>[1,1,3,1,2,1,4] 000110101101=>111001010010=>[1,1,1,3,2,3,2]=>[1,2,1,2,2,1,4] 000110101011=>111001010100=>[1,1,1,3,2,2,3]=>[1,1,2,2,2,1,4] 000110100111=>111001011000=>[1,1,1,3,2,1,4]=>[1,1,1,3,2,1,4] 000110011101=>111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] 000110011011=>111001100100=>[1,1,1,3,1,3,3]=>[1,1,2,1,3,1,4] 000110010111=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 000110001111=>111001110000=>[1,1,1,3,1,1,5]=>[1,1,1,1,4,1,4] 000101110101=>111010001010=>[1,1,1,2,4,2,2]=>[1,2,2,1,1,2,4] 000101110011=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 000101101101=>111010010010=>[1,1,1,2,3,3,2]=>[1,2,1,2,1,2,4] 000101101011=>111010010100=>[1,1,1,2,3,2,3]=>[1,1,2,2,1,2,4] 000101100111=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 000101011101=>111010100010=>[1,1,1,2,2,4,2]=>[1,2,1,1,2,2,4] 000101011011=>111010100100=>[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] 000101010111=>111010101000=>[1,1,1,2,2,2,4]=>[1,1,1,2,2,2,4] 000101001111=>111010110000=>[1,1,1,2,2,1,5]=>[1,1,1,1,3,2,4] 000100111101=>111011000010=>[1,1,1,2,1,5,2]=>[1,2,1,1,1,3,4] 000100111011=>111011000100=>[1,1,1,2,1,4,3]=>[1,1,2,1,1,3,4] 000100110111=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 000100101111=>111011010000=>[1,1,1,2,1,2,5]=>[1,1,1,1,2,3,4] 000100011111=>111011100000=>[1,1,1,2,1,1,6]=>[1,1,1,1,1,4,4] 000011110101=>111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] 000011110011=>111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] 000011101101=>111100010010=>[1,1,1,1,4,3,2]=>[1,2,1,2,1,1,5] 000011101011=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 000011100111=>111100011000=>[1,1,1,1,4,1,4]=>[1,1,1,3,1,1,5] 000011011101=>111100100010=>[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] 000011011011=>111100100100=>[1,1,1,1,3,3,3]=>[1,1,2,1,2,1,5] 000011010111=>111100101000=>[1,1,1,1,3,2,4]=>[1,1,1,2,2,1,5] 000011001111=>111100110000=>[1,1,1,1,3,1,5]=>[1,1,1,1,3,1,5] 000010111101=>111101000010=>[1,1,1,1,2,5,2]=>[1,2,1,1,1,2,5] 000010111011=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 000010110111=>111101001000=>[1,1,1,1,2,3,4]=>[1,1,1,2,1,2,5] 000010101111=>111101010000=>[1,1,1,1,2,2,5]=>[1,1,1,1,2,2,5] 000010011111=>111101100000=>[1,1,1,1,2,1,6]=>[1,1,1,1,1,3,5] 000001111101=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 000001111011=>111110000100=>[1,1,1,1,1,5,3]=>[1,1,2,1,1,1,6] 000001110111=>111110001000=>[1,1,1,1,1,4,4]=>[1,1,1,2,1,1,6] 000001101111=>111110010000=>[1,1,1,1,1,3,5]=>[1,1,1,1,2,1,6] 000001011111=>111110100000=>[1,1,1,1,1,2,6]=>[1,1,1,1,1,2,6] 000000111111=>111111000000=>[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7] 00000000000=>11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[12] 01010101010=>10101010101=>[1,2,2,2,2,2,1]=>[2,2,2,2,2,2] 10000000001=>01111111110=>[2,1,1,1,1,1,1,1,1,2]=>[1,10,1] 0111111100=>1000000011=>[1,8,1,1]=>[3,1,1,1,1,1,1,2] 0111111010=>1000000101=>[1,7,2,1]=>[2,2,1,1,1,1,1,2]