=>

0=>0=>[1]=>[1] 1=>1=>[1]=>[1] 00=>00=>[2]=>[2] 01=>10=>[1,1]=>[1,1] 10=>01=>[1,1]=>[1,1] 11=>11=>[2]=>[2] 000=>000=>[3]=>[3] 001=>100=>[1,2]=>[2,1] 010=>001=>[2,1]=>[1,2] 011=>101=>[1,1,1]=>[1,1,1] 100=>010=>[1,1,1]=>[1,1,1] 101=>110=>[2,1]=>[1,2] 110=>011=>[1,2]=>[2,1] 111=>111=>[3]=>[3] 0000=>0000=>[4]=>[4] 0001=>1000=>[1,3]=>[3,1] 0010=>0001=>[3,1]=>[1,3] 0011=>1001=>[1,2,1]=>[1,2,1] 0100=>0010=>[2,1,1]=>[1,1,2] 0101=>1010=>[1,1,1,1]=>[1,1,1,1] 0110=>0011=>[2,2]=>[2,2] 0111=>1011=>[1,1,2]=>[2,1,1] 1000=>0100=>[1,1,2]=>[2,1,1] 1001=>1100=>[2,2]=>[2,2] 1010=>0101=>[1,1,1,1]=>[1,1,1,1] 1011=>1101=>[2,1,1]=>[1,1,2] 1100=>0110=>[1,2,1]=>[1,2,1] 1101=>1110=>[3,1]=>[1,3] 1110=>0111=>[1,3]=>[3,1] 1111=>1111=>[4]=>[4] 00000=>00000=>[5]=>[5] 00001=>10000=>[1,4]=>[4,1] 00010=>00001=>[4,1]=>[1,4] 00011=>10001=>[1,3,1]=>[1,3,1] 00100=>00010=>[3,1,1]=>[1,1,3] 00101=>10010=>[1,2,1,1]=>[1,1,2,1] 00110=>00011=>[3,2]=>[2,3] 00111=>10011=>[1,2,2]=>[2,2,1] 01000=>00100=>[2,1,2]=>[2,1,2] 01001=>10100=>[1,1,1,2]=>[2,1,1,1] 01010=>00101=>[2,1,1,1]=>[1,1,1,2] 01011=>10101=>[1,1,1,1,1]=>[1,1,1,1,1] 01100=>00110=>[2,2,1]=>[1,2,2] 01101=>10110=>[1,1,2,1]=>[1,2,1,1] 01110=>00111=>[2,3]=>[3,2] 01111=>10111=>[1,1,3]=>[3,1,1] 10000=>01000=>[1,1,3]=>[3,1,1] 10001=>11000=>[2,3]=>[3,2] 10010=>01001=>[1,1,2,1]=>[1,2,1,1] 10011=>11001=>[2,2,1]=>[1,2,2] 10100=>01010=>[1,1,1,1,1]=>[1,1,1,1,1] 10101=>11010=>[2,1,1,1]=>[1,1,1,2] 10110=>01011=>[1,1,1,2]=>[2,1,1,1] 10111=>11011=>[2,1,2]=>[2,1,2] 11000=>01100=>[1,2,2]=>[2,2,1] 11001=>11100=>[3,2]=>[2,3] 11010=>01101=>[1,2,1,1]=>[1,1,2,1] 11011=>11101=>[3,1,1]=>[1,1,3] 11100=>01110=>[1,3,1]=>[1,3,1] 11101=>11110=>[4,1]=>[1,4] 11110=>01111=>[1,4]=>[4,1] 11111=>11111=>[5]=>[5] 000000=>000000=>[6]=>[6] 000001=>100000=>[1,5]=>[5,1] 000010=>000001=>[5,1]=>[1,5] 000011=>100001=>[1,4,1]=>[1,4,1] 000100=>000010=>[4,1,1]=>[1,1,4] 000101=>100010=>[1,3,1,1]=>[1,1,3,1] 000110=>000011=>[4,2]=>[2,4] 000111=>100011=>[1,3,2]=>[2,3,1] 001000=>000100=>[3,1,2]=>[2,1,3] 001001=>100100=>[1,2,1,2]=>[2,1,2,1] 001010=>000101=>[3,1,1,1]=>[1,1,1,3] 001011=>100101=>[1,2,1,1,1]=>[1,1,1,2,1] 001100=>000110=>[3,2,1]=>[1,2,3] 001101=>100110=>[1,2,2,1]=>[1,2,2,1] 001110=>000111=>[3,3]=>[3,3] 001111=>100111=>[1,2,3]=>[3,2,1] 010000=>001000=>[2,1,3]=>[3,1,2] 010001=>101000=>[1,1,1,3]=>[3,1,1,1] 010010=>001001=>[2,1,2,1]=>[1,2,1,2] 010011=>101001=>[1,1,1,2,1]=>[1,2,1,1,1] 010100=>001010=>[2,1,1,1,1]=>[1,1,1,1,2] 010101=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1] 010110=>001011=>[2,1,1,2]=>[2,1,1,2] 010111=>101011=>[1,1,1,1,2]=>[2,1,1,1,1] 011000=>001100=>[2,2,2]=>[2,2,2] 011001=>101100=>[1,1,2,2]=>[2,2,1,1] 011010=>001101=>[2,2,1,1]=>[1,1,2,2] 011011=>101101=>[1,1,2,1,1]=>[1,1,2,1,1] 011100=>001110=>[2,3,1]=>[1,3,2] 011101=>101110=>[1,1,3,1]=>[1,3,1,1] 011110=>001111=>[2,4]=>[4,2] 011111=>101111=>[1,1,4]=>[4,1,1] 100000=>010000=>[1,1,4]=>[4,1,1] 100001=>110000=>[2,4]=>[4,2] 100010=>010001=>[1,1,3,1]=>[1,3,1,1] 100011=>110001=>[2,3,1]=>[1,3,2] 100100=>010010=>[1,1,2,1,1]=>[1,1,2,1,1] 100101=>110010=>[2,2,1,1]=>[1,1,2,2] 100110=>010011=>[1,1,2,2]=>[2,2,1,1] 100111=>110011=>[2,2,2]=>[2,2,2] 101000=>010100=>[1,1,1,1,2]=>[2,1,1,1,1] 101001=>110100=>[2,1,1,2]=>[2,1,1,2] 101010=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1] 101011=>110101=>[2,1,1,1,1]=>[1,1,1,1,2] 101100=>010110=>[1,1,1,2,1]=>[1,2,1,1,1] 101101=>110110=>[2,1,2,1]=>[1,2,1,2] 101110=>010111=>[1,1,1,3]=>[3,1,1,1] 101111=>110111=>[2,1,3]=>[3,1,2] 110000=>011000=>[1,2,3]=>[3,2,1] 110001=>111000=>[3,3]=>[3,3] 110010=>011001=>[1,2,2,1]=>[1,2,2,1] 110011=>111001=>[3,2,1]=>[1,2,3] 110100=>011010=>[1,2,1,1,1]=>[1,1,1,2,1] 110101=>111010=>[3,1,1,1]=>[1,1,1,3] 110110=>011011=>[1,2,1,2]=>[2,1,2,1] 110111=>111011=>[3,1,2]=>[2,1,3] 111000=>011100=>[1,3,2]=>[2,3,1] 111001=>111100=>[4,2]=>[2,4] 111010=>011101=>[1,3,1,1]=>[1,1,3,1] 111011=>111101=>[4,1,1]=>[1,1,4] 111100=>011110=>[1,4,1]=>[1,4,1] 111101=>111110=>[5,1]=>[1,5] 111110=>011111=>[1,5]=>[5,1] 111111=>111111=>[6]=>[6] 0000000=>0000000=>[7]=>[7] 0000001=>1000000=>[1,6]=>[6,1] 0000010=>0000001=>[6,1]=>[1,6] 0000011=>1000001=>[1,5,1]=>[1,5,1] 0000100=>0000010=>[5,1,1]=>[1,1,5] 0000101=>1000010=>[1,4,1,1]=>[1,1,4,1] 0000110=>0000011=>[5,2]=>[2,5] 0000111=>1000011=>[1,4,2]=>[2,4,1] 0001000=>0000100=>[4,1,2]=>[2,1,4] 0001001=>1000100=>[1,3,1,2]=>[2,1,3,1] 0001010=>0000101=>[4,1,1,1]=>[1,1,1,4] 0001011=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1] 0001100=>0000110=>[4,2,1]=>[1,2,4] 0001101=>1000110=>[1,3,2,1]=>[1,2,3,1] 0001110=>0000111=>[4,3]=>[3,4] 0001111=>1000111=>[1,3,3]=>[3,3,1] 0010000=>0001000=>[3,1,3]=>[3,1,3] 0010001=>1001000=>[1,2,1,3]=>[3,1,2,1] 0010010=>0001001=>[3,1,2,1]=>[1,2,1,3] 0010011=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1] 0010100=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3] 0010101=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1] 0010110=>0001011=>[3,1,1,2]=>[2,1,1,3] 0010111=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1] 0011000=>0001100=>[3,2,2]=>[2,2,3] 0011001=>1001100=>[1,2,2,2]=>[2,2,2,1] 0011010=>0001101=>[3,2,1,1]=>[1,1,2,3] 0011011=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1] 0011100=>0001110=>[3,3,1]=>[1,3,3] 0011101=>1001110=>[1,2,3,1]=>[1,3,2,1] 0011110=>0001111=>[3,4]=>[4,3] 0011111=>1001111=>[1,2,4]=>[4,2,1] 0100000=>0010000=>[2,1,4]=>[4,1,2] 0100001=>1010000=>[1,1,1,4]=>[4,1,1,1] 0100010=>0010001=>[2,1,3,1]=>[1,3,1,2] 0100011=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1] 0100100=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2] 0100101=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1] 0100110=>0010011=>[2,1,2,2]=>[2,2,1,2] 0100111=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1] 0101000=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2] 0101001=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1] 0101010=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2] 0101011=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1] 0101100=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2] 0101101=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1] 0101110=>0010111=>[2,1,1,3]=>[3,1,1,2] 0101111=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1] 0110000=>0011000=>[2,2,3]=>[3,2,2] 0110001=>1011000=>[1,1,2,3]=>[3,2,1,1] 0110010=>0011001=>[2,2,2,1]=>[1,2,2,2] 0110011=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1] 0110100=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2] 0110101=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1] 0110110=>0011011=>[2,2,1,2]=>[2,1,2,2] 0110111=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1] 0111000=>0011100=>[2,3,2]=>[2,3,2] 0111001=>1011100=>[1,1,3,2]=>[2,3,1,1] 0111010=>0011101=>[2,3,1,1]=>[1,1,3,2] 0111011=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1] 0111100=>0011110=>[2,4,1]=>[1,4,2] 0111101=>1011110=>[1,1,4,1]=>[1,4,1,1] 0111110=>0011111=>[2,5]=>[5,2] 0111111=>1011111=>[1,1,5]=>[5,1,1] 1000000=>0100000=>[1,1,5]=>[5,1,1] 1000001=>1100000=>[2,5]=>[5,2] 1000010=>0100001=>[1,1,4,1]=>[1,4,1,1] 1000011=>1100001=>[2,4,1]=>[1,4,2] 1000100=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1] 1000101=>1100010=>[2,3,1,1]=>[1,1,3,2] 1000110=>0100011=>[1,1,3,2]=>[2,3,1,1] 1000111=>1100011=>[2,3,2]=>[2,3,2] 1001000=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1] 1001001=>1100100=>[2,2,1,2]=>[2,1,2,2] 1001010=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1] 1001011=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2] 1001100=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1] 1001101=>1100110=>[2,2,2,1]=>[1,2,2,2] 1001110=>0100111=>[1,1,2,3]=>[3,2,1,1] 1001111=>1100111=>[2,2,3]=>[3,2,2] 1010000=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1] 1010001=>1101000=>[2,1,1,3]=>[3,1,1,2] 1010010=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1] 1010011=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2] 1010100=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1] 1010101=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2] 1010110=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1] 1010111=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2] 1011000=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1] 1011001=>1101100=>[2,1,2,2]=>[2,2,1,2] 1011010=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1] 1011011=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2] 1011100=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1] 1011101=>1101110=>[2,1,3,1]=>[1,3,1,2] 1011110=>0101111=>[1,1,1,4]=>[4,1,1,1] 1011111=>1101111=>[2,1,4]=>[4,1,2] 1100000=>0110000=>[1,2,4]=>[4,2,1] 1100001=>1110000=>[3,4]=>[4,3] 1100010=>0110001=>[1,2,3,1]=>[1,3,2,1] 1100011=>1110001=>[3,3,1]=>[1,3,3] 1100100=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1] 1100101=>1110010=>[3,2,1,1]=>[1,1,2,3] 1100110=>0110011=>[1,2,2,2]=>[2,2,2,1] 1100111=>1110011=>[3,2,2]=>[2,2,3] 1101000=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1] 1101001=>1110100=>[3,1,1,2]=>[2,1,1,3] 1101010=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1] 1101011=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3] 1101100=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1] 1101101=>1110110=>[3,1,2,1]=>[1,2,1,3] 1101110=>0110111=>[1,2,1,3]=>[3,1,2,1] 1101111=>1110111=>[3,1,3]=>[3,1,3] 1110000=>0111000=>[1,3,3]=>[3,3,1] 1110001=>1111000=>[4,3]=>[3,4] 1110010=>0111001=>[1,3,2,1]=>[1,2,3,1] 1110011=>1111001=>[4,2,1]=>[1,2,4] 1110100=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1] 1110101=>1111010=>[4,1,1,1]=>[1,1,1,4] 1110110=>0111011=>[1,3,1,2]=>[2,1,3,1] 1110111=>1111011=>[4,1,2]=>[2,1,4] 1111000=>0111100=>[1,4,2]=>[2,4,1] 1111001=>1111100=>[5,2]=>[2,5] 1111010=>0111101=>[1,4,1,1]=>[1,1,4,1] 1111011=>1111101=>[5,1,1]=>[1,1,5] 1111100=>0111110=>[1,5,1]=>[1,5,1] 1111101=>1111110=>[6,1]=>[1,6] 1111110=>0111111=>[1,6]=>[6,1] 1111111=>1111111=>[7]=>[7] 00000000=>00000000=>[8]=>[8] 00000001=>10000000=>[1,7]=>[7,1] 00000010=>00000001=>[7,1]=>[1,7] 00000011=>10000001=>[1,6,1]=>[1,6,1] 00000100=>00000010=>[6,1,1]=>[1,1,6] 00000101=>10000010=>[1,5,1,1]=>[1,1,5,1] 00000110=>00000011=>[6,2]=>[2,6] 00000111=>10000011=>[1,5,2]=>[2,5,1] 00001000=>00000100=>[5,1,2]=>[2,1,5] 00001001=>10000100=>[1,4,1,2]=>[2,1,4,1] 00001010=>00000101=>[5,1,1,1]=>[1,1,1,5] 00001011=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1] 00001100=>00000110=>[5,2,1]=>[1,2,5] 00001101=>10000110=>[1,4,2,1]=>[1,2,4,1] 00001110=>00000111=>[5,3]=>[3,5] 00001111=>10000111=>[1,4,3]=>[3,4,1] 00010000=>00001000=>[4,1,3]=>[3,1,4] 00010001=>10001000=>[1,3,1,3]=>[3,1,3,1] 00010010=>00001001=>[4,1,2,1]=>[1,2,1,4] 00010011=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1] 00010100=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4] 00010101=>10001010=>[1,3,1,1,1,1]=>[1,1,1,1,3,1] 00010110=>00001011=>[4,1,1,2]=>[2,1,1,4] 00010111=>10001011=>[1,3,1,1,2]=>[2,1,1,3,1] 00011000=>00001100=>[4,2,2]=>[2,2,4] 00011001=>10001100=>[1,3,2,2]=>[2,2,3,1] 00011010=>00001101=>[4,2,1,1]=>[1,1,2,4] 00011011=>10001101=>[1,3,2,1,1]=>[1,1,2,3,1] 00011100=>00001110=>[4,3,1]=>[1,3,4] 00011101=>10001110=>[1,3,3,1]=>[1,3,3,1] 00011110=>00001111=>[4,4]=>[4,4] 00011111=>10001111=>[1,3,4]=>[4,3,1] 00100000=>00010000=>[3,1,4]=>[4,1,3] 00100001=>10010000=>[1,2,1,4]=>[4,1,2,1] 00100010=>00010001=>[3,1,3,1]=>[1,3,1,3] 00100011=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1] 00100100=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3] 00100101=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1] 00100110=>00010011=>[3,1,2,2]=>[2,2,1,3] 00100111=>10010011=>[1,2,1,2,2]=>[2,2,1,2,1] 00101000=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3] 00101001=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1] 00101010=>00010101=>[3,1,1,1,1,1]=>[1,1,1,1,1,3] 00101011=>10010101=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1] 00101100=>00010110=>[3,1,1,2,1]=>[1,2,1,1,3] 00101101=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1] 00101110=>00010111=>[3,1,1,3]=>[3,1,1,3] 00101111=>10010111=>[1,2,1,1,3]=>[3,1,1,2,1] 00110000=>00011000=>[3,2,3]=>[3,2,3] 00110001=>10011000=>[1,2,2,3]=>[3,2,2,1] 00110010=>00011001=>[3,2,2,1]=>[1,2,2,3] 00110011=>10011001=>[1,2,2,2,1]=>[1,2,2,2,1] 00110100=>00011010=>[3,2,1,1,1]=>[1,1,1,2,3] 00110101=>10011010=>[1,2,2,1,1,1]=>[1,1,1,2,2,1] 00110110=>00011011=>[3,2,1,2]=>[2,1,2,3] 00110111=>10011011=>[1,2,2,1,2]=>[2,1,2,2,1] 00111000=>00011100=>[3,3,2]=>[2,3,3] 00111001=>10011100=>[1,2,3,2]=>[2,3,2,1] 00111010=>00011101=>[3,3,1,1]=>[1,1,3,3] 00111011=>10011101=>[1,2,3,1,1]=>[1,1,3,2,1] 00111100=>00011110=>[3,4,1]=>[1,4,3] 00111101=>10011110=>[1,2,4,1]=>[1,4,2,1] 00111110=>00011111=>[3,5]=>[5,3] 00111111=>10011111=>[1,2,5]=>[5,2,1] 01000000=>00100000=>[2,1,5]=>[5,1,2] 01000001=>10100000=>[1,1,1,5]=>[5,1,1,1] 01000010=>00100001=>[2,1,4,1]=>[1,4,1,2] 01000011=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1] 01000100=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2] 01000101=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1] 01000110=>00100011=>[2,1,3,2]=>[2,3,1,2] 01000111=>10100011=>[1,1,1,3,2]=>[2,3,1,1,1] 01001000=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2] 01001001=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1] 01001010=>00100101=>[2,1,2,1,1,1]=>[1,1,1,2,1,2] 01001011=>10100101=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1] 01001100=>00100110=>[2,1,2,2,1]=>[1,2,2,1,2] 01001101=>10100110=>[1,1,1,2,2,1]=>[1,2,2,1,1,1] 01001110=>00100111=>[2,1,2,3]=>[3,2,1,2] 01001111=>10100111=>[1,1,1,2,3]=>[3,2,1,1,1] 01010000=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2] 01010001=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1] 01010010=>00101001=>[2,1,1,1,2,1]=>[1,2,1,1,1,2] 01010011=>10101001=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1] 01010100=>00101010=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2] 01010101=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1] 01010110=>00101011=>[2,1,1,1,1,2]=>[2,1,1,1,1,2] 01010111=>10101011=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1] 01011000=>00101100=>[2,1,1,2,2]=>[2,2,1,1,2] 01011001=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1] 01011010=>00101101=>[2,1,1,2,1,1]=>[1,1,2,1,1,2] 01011011=>10101101=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1] 01011100=>00101110=>[2,1,1,3,1]=>[1,3,1,1,2] 01011101=>10101110=>[1,1,1,1,3,1]=>[1,3,1,1,1,1] 01011110=>00101111=>[2,1,1,4]=>[4,1,1,2] 01011111=>10101111=>[1,1,1,1,4]=>[4,1,1,1,1] 01100000=>00110000=>[2,2,4]=>[4,2,2] 01100001=>10110000=>[1,1,2,4]=>[4,2,1,1] 01100010=>00110001=>[2,2,3,1]=>[1,3,2,2] 01100011=>10110001=>[1,1,2,3,1]=>[1,3,2,1,1] 01100100=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2] 01100101=>10110010=>[1,1,2,2,1,1]=>[1,1,2,2,1,1] 01100110=>00110011=>[2,2,2,2]=>[2,2,2,2] 01100111=>10110011=>[1,1,2,2,2]=>[2,2,2,1,1] 01101000=>00110100=>[2,2,1,1,2]=>[2,1,1,2,2] 01101001=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1] 01101010=>00110101=>[2,2,1,1,1,1]=>[1,1,1,1,2,2] 01101011=>10110101=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1] 01101100=>00110110=>[2,2,1,2,1]=>[1,2,1,2,2] 01101101=>10110110=>[1,1,2,1,2,1]=>[1,2,1,2,1,1] 01101110=>00110111=>[2,2,1,3]=>[3,1,2,2] 01101111=>10110111=>[1,1,2,1,3]=>[3,1,2,1,1] 01110000=>00111000=>[2,3,3]=>[3,3,2] 01110001=>10111000=>[1,1,3,3]=>[3,3,1,1] 01110010=>00111001=>[2,3,2,1]=>[1,2,3,2] 01110011=>10111001=>[1,1,3,2,1]=>[1,2,3,1,1] 01110100=>00111010=>[2,3,1,1,1]=>[1,1,1,3,2] 01110101=>10111010=>[1,1,3,1,1,1]=>[1,1,1,3,1,1] 01110110=>00111011=>[2,3,1,2]=>[2,1,3,2] 01110111=>10111011=>[1,1,3,1,2]=>[2,1,3,1,1] 01111000=>00111100=>[2,4,2]=>[2,4,2] 01111001=>10111100=>[1,1,4,2]=>[2,4,1,1] 01111010=>00111101=>[2,4,1,1]=>[1,1,4,2] 01111011=>10111101=>[1,1,4,1,1]=>[1,1,4,1,1] 01111100=>00111110=>[2,5,1]=>[1,5,2] 01111101=>10111110=>[1,1,5,1]=>[1,5,1,1] 01111110=>00111111=>[2,6]=>[6,2] 01111111=>10111111=>[1,1,6]=>[6,1,1] 10000000=>01000000=>[1,1,6]=>[6,1,1] 10000001=>11000000=>[2,6]=>[6,2] 10000010=>01000001=>[1,1,5,1]=>[1,5,1,1] 10000011=>11000001=>[2,5,1]=>[1,5,2] 10000100=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1] 10000101=>11000010=>[2,4,1,1]=>[1,1,4,2] 10000110=>01000011=>[1,1,4,2]=>[2,4,1,1] 10000111=>11000011=>[2,4,2]=>[2,4,2] 10001000=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1] 10001001=>11000100=>[2,3,1,2]=>[2,1,3,2] 10001010=>01000101=>[1,1,3,1,1,1]=>[1,1,1,3,1,1] 10001011=>11000101=>[2,3,1,1,1]=>[1,1,1,3,2] 10001100=>01000110=>[1,1,3,2,1]=>[1,2,3,1,1] 10001101=>11000110=>[2,3,2,1]=>[1,2,3,2] 10001110=>01000111=>[1,1,3,3]=>[3,3,1,1] 10001111=>11000111=>[2,3,3]=>[3,3,2] 10010000=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1] 10010001=>11001000=>[2,2,1,3]=>[3,1,2,2] 10010010=>01001001=>[1,1,2,1,2,1]=>[1,2,1,2,1,1] 10010011=>11001001=>[2,2,1,2,1]=>[1,2,1,2,2] 10010100=>01001010=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1] 10010101=>11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2] 10010110=>01001011=>[1,1,2,1,1,2]=>[2,1,1,2,1,1] 10010111=>11001011=>[2,2,1,1,2]=>[2,1,1,2,2] 10011000=>01001100=>[1,1,2,2,2]=>[2,2,2,1,1] 10011001=>11001100=>[2,2,2,2]=>[2,2,2,2] 10011010=>01001101=>[1,1,2,2,1,1]=>[1,1,2,2,1,1] 10011011=>11001101=>[2,2,2,1,1]=>[1,1,2,2,2] 10011100=>01001110=>[1,1,2,3,1]=>[1,3,2,1,1] 10011101=>11001110=>[2,2,3,1]=>[1,3,2,2] 10011110=>01001111=>[1,1,2,4]=>[4,2,1,1] 10011111=>11001111=>[2,2,4]=>[4,2,2] 10100000=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1] 10100001=>11010000=>[2,1,1,4]=>[4,1,1,2] 10100010=>01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1] 10100011=>11010001=>[2,1,1,3,1]=>[1,3,1,1,2] 10100100=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1] 10100101=>11010010=>[2,1,1,2,1,1]=>[1,1,2,1,1,2] 10100110=>01010011=>[1,1,1,1,2,2]=>[2,2,1,1,1,1] 10100111=>11010011=>[2,1,1,2,2]=>[2,2,1,1,2] 10101000=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1] 10101001=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2] 10101010=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1] 10101011=>11010101=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2] 10101100=>01010110=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1] 10101101=>11010110=>[2,1,1,1,2,1]=>[1,2,1,1,1,2] 10101110=>01010111=>[1,1,1,1,1,3]=>[3,1,1,1,1,1] 10101111=>11010111=>[2,1,1,1,3]=>[3,1,1,1,2] 10110000=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1] 10110001=>11011000=>[2,1,2,3]=>[3,2,1,2] 10110010=>01011001=>[1,1,1,2,2,1]=>[1,2,2,1,1,1] 10110011=>11011001=>[2,1,2,2,1]=>[1,2,2,1,2] 10110100=>01011010=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1] 10110101=>11011010=>[2,1,2,1,1,1]=>[1,1,1,2,1,2] 10110110=>01011011=>[1,1,1,2,1,2]=>[2,1,2,1,1,1] 10110111=>11011011=>[2,1,2,1,2]=>[2,1,2,1,2] 10111000=>01011100=>[1,1,1,3,2]=>[2,3,1,1,1] 10111001=>11011100=>[2,1,3,2]=>[2,3,1,2] 10111010=>01011101=>[1,1,1,3,1,1]=>[1,1,3,1,1,1] 10111011=>11011101=>[2,1,3,1,1]=>[1,1,3,1,2] 10111100=>01011110=>[1,1,1,4,1]=>[1,4,1,1,1] 10111101=>11011110=>[2,1,4,1]=>[1,4,1,2] 10111110=>01011111=>[1,1,1,5]=>[5,1,1,1] 10111111=>11011111=>[2,1,5]=>[5,1,2] 11000000=>01100000=>[1,2,5]=>[5,2,1] 11000001=>11100000=>[3,5]=>[5,3] 11000010=>01100001=>[1,2,4,1]=>[1,4,2,1] 11000011=>11100001=>[3,4,1]=>[1,4,3] 11000100=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1] 11000101=>11100010=>[3,3,1,1]=>[1,1,3,3] 11000110=>01100011=>[1,2,3,2]=>[2,3,2,1] 11000111=>11100011=>[3,3,2]=>[2,3,3] 11001000=>01100100=>[1,2,2,1,2]=>[2,1,2,2,1] 11001001=>11100100=>[3,2,1,2]=>[2,1,2,3] 11001010=>01100101=>[1,2,2,1,1,1]=>[1,1,1,2,2,1] 11001011=>11100101=>[3,2,1,1,1]=>[1,1,1,2,3] 11001100=>01100110=>[1,2,2,2,1]=>[1,2,2,2,1] 11001101=>11100110=>[3,2,2,1]=>[1,2,2,3] 11001110=>01100111=>[1,2,2,3]=>[3,2,2,1] 11001111=>11100111=>[3,2,3]=>[3,2,3] 11010000=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1] 11010001=>11101000=>[3,1,1,3]=>[3,1,1,3] 11010010=>01101001=>[1,2,1,1,2,1]=>[1,2,1,1,2,1] 11010011=>11101001=>[3,1,1,2,1]=>[1,2,1,1,3] 11010100=>01101010=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1] 11010101=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3] 11010110=>01101011=>[1,2,1,1,1,2]=>[2,1,1,1,2,1] 11010111=>11101011=>[3,1,1,1,2]=>[2,1,1,1,3] 11011000=>01101100=>[1,2,1,2,2]=>[2,2,1,2,1] 11011001=>11101100=>[3,1,2,2]=>[2,2,1,3] 11011010=>01101101=>[1,2,1,2,1,1]=>[1,1,2,1,2,1] 11011011=>11101101=>[3,1,2,1,1]=>[1,1,2,1,3] 11011100=>01101110=>[1,2,1,3,1]=>[1,3,1,2,1] 11011101=>11101110=>[3,1,3,1]=>[1,3,1,3] 11011110=>01101111=>[1,2,1,4]=>[4,1,2,1] 11011111=>11101111=>[3,1,4]=>[4,1,3] 11100000=>01110000=>[1,3,4]=>[4,3,1] 11100001=>11110000=>[4,4]=>[4,4] 11100010=>01110001=>[1,3,3,1]=>[1,3,3,1] 11100011=>11110001=>[4,3,1]=>[1,3,4] 11100100=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1] 11100101=>11110010=>[4,2,1,1]=>[1,1,2,4] 11100110=>01110011=>[1,3,2,2]=>[2,2,3,1] 11100111=>11110011=>[4,2,2]=>[2,2,4] 11101000=>01110100=>[1,3,1,1,2]=>[2,1,1,3,1] 11101001=>11110100=>[4,1,1,2]=>[2,1,1,4] 11101010=>01110101=>[1,3,1,1,1,1]=>[1,1,1,1,3,1] 11101011=>11110101=>[4,1,1,1,1]=>[1,1,1,1,4] 11101100=>01110110=>[1,3,1,2,1]=>[1,2,1,3,1] 11101101=>11110110=>[4,1,2,1]=>[1,2,1,4] 11101110=>01110111=>[1,3,1,3]=>[3,1,3,1] 11101111=>11110111=>[4,1,3]=>[3,1,4] 11110000=>01111000=>[1,4,3]=>[3,4,1] 11110001=>11111000=>[5,3]=>[3,5] 11110010=>01111001=>[1,4,2,1]=>[1,2,4,1] 11110011=>11111001=>[5,2,1]=>[1,2,5] 11110100=>01111010=>[1,4,1,1,1]=>[1,1,1,4,1] 11110101=>11111010=>[5,1,1,1]=>[1,1,1,5] 11110110=>01111011=>[1,4,1,2]=>[2,1,4,1] 11110111=>11111011=>[5,1,2]=>[2,1,5] 11111000=>01111100=>[1,5,2]=>[2,5,1] 11111001=>11111100=>[6,2]=>[2,6] 11111010=>01111101=>[1,5,1,1]=>[1,1,5,1] 11111011=>11111101=>[6,1,1]=>[1,1,6] 11111100=>01111110=>[1,6,1]=>[1,6,1] 11111101=>11111110=>[7,1]=>[1,7] 11111110=>01111111=>[1,7]=>[7,1] 11111111=>11111111=>[8]=>[8] 000000000=>000000000=>[9]=>[9] 000000001=>100000000=>[1,8]=>[8,1] 000000010=>000000001=>[8,1]=>[1,8] 000000011=>100000001=>[1,7,1]=>[1,7,1] 000000100=>000000010=>[7,1,1]=>[1,1,7] 000000101=>100000010=>[1,6,1,1]=>[1,1,6,1] 000000110=>000000011=>[7,2]=>[2,7] 000000111=>100000011=>[1,6,2]=>[2,6,1] 000001000=>000000100=>[6,1,2]=>[2,1,6] 000001001=>100000100=>[1,5,1,2]=>[2,1,5,1] 000001010=>000000101=>[6,1,1,1]=>[1,1,1,6] 000001011=>100000101=>[1,5,1,1,1]=>[1,1,1,5,1] 000001100=>000000110=>[6,2,1]=>[1,2,6] 000001101=>100000110=>[1,5,2,1]=>[1,2,5,1] 000001110=>000000111=>[6,3]=>[3,6] 000001111=>100000111=>[1,5,3]=>[3,5,1] 000010000=>000001000=>[5,1,3]=>[3,1,5] 000010001=>100001000=>[1,4,1,3]=>[3,1,4,1] 000010010=>000001001=>[5,1,2,1]=>[1,2,1,5] 000010011=>100001001=>[1,4,1,2,1]=>[1,2,1,4,1] 000010100=>000001010=>[5,1,1,1,1]=>[1,1,1,1,5] 000010101=>100001010=>[1,4,1,1,1,1]=>[1,1,1,1,4,1] 000010110=>000001011=>[5,1,1,2]=>[2,1,1,5] 000010111=>100001011=>[1,4,1,1,2]=>[2,1,1,4,1] 000011000=>000001100=>[5,2,2]=>[2,2,5] 000011001=>100001100=>[1,4,2,2]=>[2,2,4,1] 000011010=>000001101=>[5,2,1,1]=>[1,1,2,5] 000011011=>100001101=>[1,4,2,1,1]=>[1,1,2,4,1] 000011100=>000001110=>[5,3,1]=>[1,3,5] 000011101=>100001110=>[1,4,3,1]=>[1,3,4,1] 000011110=>000001111=>[5,4]=>[4,5] 000011111=>100001111=>[1,4,4]=>[4,4,1] 000100000=>000010000=>[4,1,4]=>[4,1,4] 000100001=>100010000=>[1,3,1,4]=>[4,1,3,1] 000100010=>000010001=>[4,1,3,1]=>[1,3,1,4] 000100011=>100010001=>[1,3,1,3,1]=>[1,3,1,3,1] 000100100=>000010010=>[4,1,2,1,1]=>[1,1,2,1,4] 000100101=>100010010=>[1,3,1,2,1,1]=>[1,1,2,1,3,1] 000100110=>000010011=>[4,1,2,2]=>[2,2,1,4] 000100111=>100010011=>[1,3,1,2,2]=>[2,2,1,3,1] 000101000=>000010100=>[4,1,1,1,2]=>[2,1,1,1,4] 000101001=>100010100=>[1,3,1,1,1,2]=>[2,1,1,1,3,1] 000101010=>000010101=>[4,1,1,1,1,1]=>[1,1,1,1,1,4] 000101011=>100010101=>[1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1] 000101100=>000010110=>[4,1,1,2,1]=>[1,2,1,1,4] 000101101=>100010110=>[1,3,1,1,2,1]=>[1,2,1,1,3,1] 000101110=>000010111=>[4,1,1,3]=>[3,1,1,4] 000101111=>100010111=>[1,3,1,1,3]=>[3,1,1,3,1] 000110000=>000011000=>[4,2,3]=>[3,2,4] 000110001=>100011000=>[1,3,2,3]=>[3,2,3,1] 000110010=>000011001=>[4,2,2,1]=>[1,2,2,4] 000110011=>100011001=>[1,3,2,2,1]=>[1,2,2,3,1] 000110100=>000011010=>[4,2,1,1,1]=>[1,1,1,2,4] 000110101=>100011010=>[1,3,2,1,1,1]=>[1,1,1,2,3,1] 000110110=>000011011=>[4,2,1,2]=>[2,1,2,4] 000110111=>100011011=>[1,3,2,1,2]=>[2,1,2,3,1] 000111000=>000011100=>[4,3,2]=>[2,3,4] 000111001=>100011100=>[1,3,3,2]=>[2,3,3,1] 000111010=>000011101=>[4,3,1,1]=>[1,1,3,4] 000111011=>100011101=>[1,3,3,1,1]=>[1,1,3,3,1] 000111100=>000011110=>[4,4,1]=>[1,4,4] 000111101=>100011110=>[1,3,4,1]=>[1,4,3,1] 000111110=>000011111=>[4,5]=>[5,4] 000111111=>100011111=>[1,3,5]=>[5,3,1] 001000000=>000100000=>[3,1,5]=>[5,1,3] 001000001=>100100000=>[1,2,1,5]=>[5,1,2,1] 001000010=>000100001=>[3,1,4,1]=>[1,4,1,3] 001000011=>100100001=>[1,2,1,4,1]=>[1,4,1,2,1] 001000100=>000100010=>[3,1,3,1,1]=>[1,1,3,1,3] 001000101=>100100010=>[1,2,1,3,1,1]=>[1,1,3,1,2,1] 001000110=>000100011=>[3,1,3,2]=>[2,3,1,3] 001000111=>100100011=>[1,2,1,3,2]=>[2,3,1,2,1] 001001000=>000100100=>[3,1,2,1,2]=>[2,1,2,1,3] 001001001=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1] 001001010=>000100101=>[3,1,2,1,1,1]=>[1,1,1,2,1,3] 001001011=>100100101=>[1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1] 001001100=>000100110=>[3,1,2,2,1]=>[1,2,2,1,3] 001001101=>100100110=>[1,2,1,2,2,1]=>[1,2,2,1,2,1] 001001110=>000100111=>[3,1,2,3]=>[3,2,1,3] 001001111=>100100111=>[1,2,1,2,3]=>[3,2,1,2,1] 001010000=>000101000=>[3,1,1,1,3]=>[3,1,1,1,3] 001010001=>100101000=>[1,2,1,1,1,3]=>[3,1,1,1,2,1] 001010010=>000101001=>[3,1,1,1,2,1]=>[1,2,1,1,1,3] 001010011=>100101001=>[1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1] 001010100=>000101010=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3] 001010101=>100101010=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1] 001010110=>000101011=>[3,1,1,1,1,2]=>[2,1,1,1,1,3] 001010111=>100101011=>[1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1] 001011000=>000101100=>[3,1,1,2,2]=>[2,2,1,1,3] 001011001=>100101100=>[1,2,1,1,2,2]=>[2,2,1,1,2,1] 001011010=>000101101=>[3,1,1,2,1,1]=>[1,1,2,1,1,3] 001011011=>100101101=>[1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1] 001011100=>000101110=>[3,1,1,3,1]=>[1,3,1,1,3] 001011101=>100101110=>[1,2,1,1,3,1]=>[1,3,1,1,2,1] 001011110=>000101111=>[3,1,1,4]=>[4,1,1,3] 001011111=>100101111=>[1,2,1,1,4]=>[4,1,1,2,1] 001100000=>000110000=>[3,2,4]=>[4,2,3] 001100001=>100110000=>[1,2,2,4]=>[4,2,2,1] 001100010=>000110001=>[3,2,3,1]=>[1,3,2,3] 001100011=>100110001=>[1,2,2,3,1]=>[1,3,2,2,1] 001100100=>000110010=>[3,2,2,1,1]=>[1,1,2,2,3] 001100101=>100110010=>[1,2,2,2,1,1]=>[1,1,2,2,2,1] 001100110=>000110011=>[3,2,2,2]=>[2,2,2,3] 001100111=>100110011=>[1,2,2,2,2]=>[2,2,2,2,1] 001101000=>000110100=>[3,2,1,1,2]=>[2,1,1,2,3] 001101001=>100110100=>[1,2,2,1,1,2]=>[2,1,1,2,2,1] 001101010=>000110101=>[3,2,1,1,1,1]=>[1,1,1,1,2,3] 001101011=>100110101=>[1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1] 001101100=>000110110=>[3,2,1,2,1]=>[1,2,1,2,3] 001101101=>100110110=>[1,2,2,1,2,1]=>[1,2,1,2,2,1] 001101110=>000110111=>[3,2,1,3]=>[3,1,2,3] 001101111=>100110111=>[1,2,2,1,3]=>[3,1,2,2,1] 001110000=>000111000=>[3,3,3]=>[3,3,3] 001110001=>100111000=>[1,2,3,3]=>[3,3,2,1] 001110010=>000111001=>[3,3,2,1]=>[1,2,3,3] 001110011=>100111001=>[1,2,3,2,1]=>[1,2,3,2,1] 001110100=>000111010=>[3,3,1,1,1]=>[1,1,1,3,3] 001110101=>100111010=>[1,2,3,1,1,1]=>[1,1,1,3,2,1] 001110110=>000111011=>[3,3,1,2]=>[2,1,3,3] 001110111=>100111011=>[1,2,3,1,2]=>[2,1,3,2,1] 001111000=>000111100=>[3,4,2]=>[2,4,3] 001111001=>100111100=>[1,2,4,2]=>[2,4,2,1] 001111010=>000111101=>[3,4,1,1]=>[1,1,4,3] 001111011=>100111101=>[1,2,4,1,1]=>[1,1,4,2,1] 001111100=>000111110=>[3,5,1]=>[1,5,3] 001111101=>100111110=>[1,2,5,1]=>[1,5,2,1] 001111110=>000111111=>[3,6]=>[6,3] 001111111=>100111111=>[1,2,6]=>[6,2,1] 010000000=>001000000=>[2,1,6]=>[6,1,2] 010000001=>101000000=>[1,1,1,6]=>[6,1,1,1] 010000010=>001000001=>[2,1,5,1]=>[1,5,1,2] 010000011=>101000001=>[1,1,1,5,1]=>[1,5,1,1,1] 010000100=>001000010=>[2,1,4,1,1]=>[1,1,4,1,2] 010000101=>101000010=>[1,1,1,4,1,1]=>[1,1,4,1,1,1] 010000110=>001000011=>[2,1,4,2]=>[2,4,1,2] 010000111=>101000011=>[1,1,1,4,2]=>[2,4,1,1,1] 010001000=>001000100=>[2,1,3,1,2]=>[2,1,3,1,2] 010001001=>101000100=>[1,1,1,3,1,2]=>[2,1,3,1,1,1] 010001010=>001000101=>[2,1,3,1,1,1]=>[1,1,1,3,1,2] 010001011=>101000101=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1] 010001100=>001000110=>[2,1,3,2,1]=>[1,2,3,1,2] 010001101=>101000110=>[1,1,1,3,2,1]=>[1,2,3,1,1,1] 010001110=>001000111=>[2,1,3,3]=>[3,3,1,2] 010001111=>101000111=>[1,1,1,3,3]=>[3,3,1,1,1] 010010000=>001001000=>[2,1,2,1,3]=>[3,1,2,1,2] 010010001=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1] 010010010=>001001001=>[2,1,2,1,2,1]=>[1,2,1,2,1,2] 010010011=>101001001=>[1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1] 010010100=>001001010=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2] 010010101=>101001010=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1] 010010110=>001001011=>[2,1,2,1,1,2]=>[2,1,1,2,1,2] 010010111=>101001011=>[1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1] 010011000=>001001100=>[2,1,2,2,2]=>[2,2,2,1,2] 010011001=>101001100=>[1,1,1,2,2,2]=>[2,2,2,1,1,1] 010011010=>001001101=>[2,1,2,2,1,1]=>[1,1,2,2,1,2] 010011011=>101001101=>[1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1] 010011100=>001001110=>[2,1,2,3,1]=>[1,3,2,1,2] 010011101=>101001110=>[1,1,1,2,3,1]=>[1,3,2,1,1,1] 010011110=>001001111=>[2,1,2,4]=>[4,2,1,2] 010011111=>101001111=>[1,1,1,2,4]=>[4,2,1,1,1] 010100000=>001010000=>[2,1,1,1,4]=>[4,1,1,1,2] 010100001=>101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1] 010100010=>001010001=>[2,1,1,1,3,1]=>[1,3,1,1,1,2] 010100011=>101010001=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1] 010100100=>001010010=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2] 010100101=>101010010=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1] 010100110=>001010011=>[2,1,1,1,2,2]=>[2,2,1,1,1,2] 010100111=>101010011=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1] 010101000=>001010100=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2] 010101001=>101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1] 010101010=>001010101=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2] 010101011=>101010101=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1] 010101100=>001010110=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2] 010101101=>101010110=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1] 010101110=>001010111=>[2,1,1,1,1,3]=>[3,1,1,1,1,2] 010101111=>101010111=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1] 010110000=>001011000=>[2,1,1,2,3]=>[3,2,1,1,2] 010110001=>101011000=>[1,1,1,1,2,3]=>[3,2,1,1,1,1] 010110010=>001011001=>[2,1,1,2,2,1]=>[1,2,2,1,1,2] 010110011=>101011001=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1] 010110100=>001011010=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2] 010110101=>101011010=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1] 010110110=>001011011=>[2,1,1,2,1,2]=>[2,1,2,1,1,2] 010110111=>101011011=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1] 010111000=>001011100=>[2,1,1,3,2]=>[2,3,1,1,2] 010111001=>101011100=>[1,1,1,1,3,2]=>[2,3,1,1,1,1] 010111010=>001011101=>[2,1,1,3,1,1]=>[1,1,3,1,1,2] 010111011=>101011101=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1] 010111100=>001011110=>[2,1,1,4,1]=>[1,4,1,1,2] 010111101=>101011110=>[1,1,1,1,4,1]=>[1,4,1,1,1,1] 010111110=>001011111=>[2,1,1,5]=>[5,1,1,2] 010111111=>101011111=>[1,1,1,1,5]=>[5,1,1,1,1] 011000000=>001100000=>[2,2,5]=>[5,2,2] 011000001=>101100000=>[1,1,2,5]=>[5,2,1,1] 011000010=>001100001=>[2,2,4,1]=>[1,4,2,2] 011000011=>101100001=>[1,1,2,4,1]=>[1,4,2,1,1] 011000100=>001100010=>[2,2,3,1,1]=>[1,1,3,2,2] 011000101=>101100010=>[1,1,2,3,1,1]=>[1,1,3,2,1,1] 011000110=>001100011=>[2,2,3,2]=>[2,3,2,2] 011000111=>101100011=>[1,1,2,3,2]=>[2,3,2,1,1] 011001000=>001100100=>[2,2,2,1,2]=>[2,1,2,2,2] 011001001=>101100100=>[1,1,2,2,1,2]=>[2,1,2,2,1,1] 011001010=>001100101=>[2,2,2,1,1,1]=>[1,1,1,2,2,2] 011001011=>101100101=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1] 011001100=>001100110=>[2,2,2,2,1]=>[1,2,2,2,2] 011001101=>101100110=>[1,1,2,2,2,1]=>[1,2,2,2,1,1] 011001110=>001100111=>[2,2,2,3]=>[3,2,2,2] 011001111=>101100111=>[1,1,2,2,3]=>[3,2,2,1,1] 011010000=>001101000=>[2,2,1,1,3]=>[3,1,1,2,2] 011010001=>101101000=>[1,1,2,1,1,3]=>[3,1,1,2,1,1] 011010010=>001101001=>[2,2,1,1,2,1]=>[1,2,1,1,2,2] 011010011=>101101001=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1] 011010100=>001101010=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2] 011010101=>101101010=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1] 011010110=>001101011=>[2,2,1,1,1,2]=>[2,1,1,1,2,2] 011010111=>101101011=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1] 011011000=>001101100=>[2,2,1,2,2]=>[2,2,1,2,2] 011011001=>101101100=>[1,1,2,1,2,2]=>[2,2,1,2,1,1] 011011010=>001101101=>[2,2,1,2,1,1]=>[1,1,2,1,2,2] 011011011=>101101101=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1] 011011100=>001101110=>[2,2,1,3,1]=>[1,3,1,2,2] 011011101=>101101110=>[1,1,2,1,3,1]=>[1,3,1,2,1,1] 011011110=>001101111=>[2,2,1,4]=>[4,1,2,2] 011011111=>101101111=>[1,1,2,1,4]=>[4,1,2,1,1] 011100000=>001110000=>[2,3,4]=>[4,3,2] 011100001=>101110000=>[1,1,3,4]=>[4,3,1,1] 011100010=>001110001=>[2,3,3,1]=>[1,3,3,2] 011100011=>101110001=>[1,1,3,3,1]=>[1,3,3,1,1] 011100100=>001110010=>[2,3,2,1,1]=>[1,1,2,3,2] 011100101=>101110010=>[1,1,3,2,1,1]=>[1,1,2,3,1,1] 011100110=>001110011=>[2,3,2,2]=>[2,2,3,2] 011100111=>101110011=>[1,1,3,2,2]=>[2,2,3,1,1] 011101000=>001110100=>[2,3,1,1,2]=>[2,1,1,3,2] 011101001=>101110100=>[1,1,3,1,1,2]=>[2,1,1,3,1,1] 011101010=>001110101=>[2,3,1,1,1,1]=>[1,1,1,1,3,2] 011101011=>101110101=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1] 011101100=>001110110=>[2,3,1,2,1]=>[1,2,1,3,2] 011101101=>101110110=>[1,1,3,1,2,1]=>[1,2,1,3,1,1] 011101110=>001110111=>[2,3,1,3]=>[3,1,3,2] 011101111=>101110111=>[1,1,3,1,3]=>[3,1,3,1,1] 011110000=>001111000=>[2,4,3]=>[3,4,2] 011110001=>101111000=>[1,1,4,3]=>[3,4,1,1] 011110010=>001111001=>[2,4,2,1]=>[1,2,4,2] 011110011=>101111001=>[1,1,4,2,1]=>[1,2,4,1,1] 011110100=>001111010=>[2,4,1,1,1]=>[1,1,1,4,2] 011110101=>101111010=>[1,1,4,1,1,1]=>[1,1,1,4,1,1] 011110110=>001111011=>[2,4,1,2]=>[2,1,4,2] 011110111=>101111011=>[1,1,4,1,2]=>[2,1,4,1,1] 011111000=>001111100=>[2,5,2]=>[2,5,2] 011111001=>101111100=>[1,1,5,2]=>[2,5,1,1] 011111010=>001111101=>[2,5,1,1]=>[1,1,5,2] 011111011=>101111101=>[1,1,5,1,1]=>[1,1,5,1,1] 011111100=>001111110=>[2,6,1]=>[1,6,2] 011111101=>101111110=>[1,1,6,1]=>[1,6,1,1] 011111110=>001111111=>[2,7]=>[7,2] 011111111=>101111111=>[1,1,7]=>[7,1,1] 100000000=>010000000=>[1,1,7]=>[7,1,1] 100000001=>110000000=>[2,7]=>[7,2] 100000010=>010000001=>[1,1,6,1]=>[1,6,1,1] 100000011=>110000001=>[2,6,1]=>[1,6,2] 100000100=>010000010=>[1,1,5,1,1]=>[1,1,5,1,1] 100000101=>110000010=>[2,5,1,1]=>[1,1,5,2] 100000110=>010000011=>[1,1,5,2]=>[2,5,1,1] 100000111=>110000011=>[2,5,2]=>[2,5,2] 100001000=>010000100=>[1,1,4,1,2]=>[2,1,4,1,1] 100001001=>110000100=>[2,4,1,2]=>[2,1,4,2] 100001010=>010000101=>[1,1,4,1,1,1]=>[1,1,1,4,1,1] 100001011=>110000101=>[2,4,1,1,1]=>[1,1,1,4,2] 100001100=>010000110=>[1,1,4,2,1]=>[1,2,4,1,1] 100001101=>110000110=>[2,4,2,1]=>[1,2,4,2] 100001110=>010000111=>[1,1,4,3]=>[3,4,1,1] 100001111=>110000111=>[2,4,3]=>[3,4,2] 100010000=>010001000=>[1,1,3,1,3]=>[3,1,3,1,1] 100010001=>110001000=>[2,3,1,3]=>[3,1,3,2] 100010010=>010001001=>[1,1,3,1,2,1]=>[1,2,1,3,1,1] 100010011=>110001001=>[2,3,1,2,1]=>[1,2,1,3,2] 100010100=>010001010=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1] 100010101=>110001010=>[2,3,1,1,1,1]=>[1,1,1,1,3,2] 100010110=>010001011=>[1,1,3,1,1,2]=>[2,1,1,3,1,1] 100010111=>110001011=>[2,3,1,1,2]=>[2,1,1,3,2] 100011000=>010001100=>[1,1,3,2,2]=>[2,2,3,1,1] 100011001=>110001100=>[2,3,2,2]=>[2,2,3,2] 100011010=>010001101=>[1,1,3,2,1,1]=>[1,1,2,3,1,1] 100011011=>110001101=>[2,3,2,1,1]=>[1,1,2,3,2] 100011100=>010001110=>[1,1,3,3,1]=>[1,3,3,1,1] 100011101=>110001110=>[2,3,3,1]=>[1,3,3,2] 100011110=>010001111=>[1,1,3,4]=>[4,3,1,1] 100011111=>110001111=>[2,3,4]=>[4,3,2] 100100000=>010010000=>[1,1,2,1,4]=>[4,1,2,1,1] 100100001=>110010000=>[2,2,1,4]=>[4,1,2,2] 100100010=>010010001=>[1,1,2,1,3,1]=>[1,3,1,2,1,1] 100100011=>110010001=>[2,2,1,3,1]=>[1,3,1,2,2] 100100100=>010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1] 100100101=>110010010=>[2,2,1,2,1,1]=>[1,1,2,1,2,2] 100100110=>010010011=>[1,1,2,1,2,2]=>[2,2,1,2,1,1] 100100111=>110010011=>[2,2,1,2,2]=>[2,2,1,2,2] 100101000=>010010100=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1] 100101001=>110010100=>[2,2,1,1,1,2]=>[2,1,1,1,2,2] 100101010=>010010101=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1] 100101011=>110010101=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2] 100101100=>010010110=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1] 100101101=>110010110=>[2,2,1,1,2,1]=>[1,2,1,1,2,2] 100101110=>010010111=>[1,1,2,1,1,3]=>[3,1,1,2,1,1] 100101111=>110010111=>[2,2,1,1,3]=>[3,1,1,2,2] 100110000=>010011000=>[1,1,2,2,3]=>[3,2,2,1,1] 100110001=>110011000=>[2,2,2,3]=>[3,2,2,2] 100110010=>010011001=>[1,1,2,2,2,1]=>[1,2,2,2,1,1] 100110011=>110011001=>[2,2,2,2,1]=>[1,2,2,2,2] 100110100=>010011010=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1] 100110101=>110011010=>[2,2,2,1,1,1]=>[1,1,1,2,2,2] 100110110=>010011011=>[1,1,2,2,1,2]=>[2,1,2,2,1,1] 100110111=>110011011=>[2,2,2,1,2]=>[2,1,2,2,2] 100111000=>010011100=>[1,1,2,3,2]=>[2,3,2,1,1] 100111001=>110011100=>[2,2,3,2]=>[2,3,2,2] 100111010=>010011101=>[1,1,2,3,1,1]=>[1,1,3,2,1,1] 100111011=>110011101=>[2,2,3,1,1]=>[1,1,3,2,2] 100111100=>010011110=>[1,1,2,4,1]=>[1,4,2,1,1] 100111101=>110011110=>[2,2,4,1]=>[1,4,2,2] 100111110=>010011111=>[1,1,2,5]=>[5,2,1,1] 100111111=>110011111=>[2,2,5]=>[5,2,2] 101000000=>010100000=>[1,1,1,1,5]=>[5,1,1,1,1] 101000001=>110100000=>[2,1,1,5]=>[5,1,1,2] 101000010=>010100001=>[1,1,1,1,4,1]=>[1,4,1,1,1,1] 101000011=>110100001=>[2,1,1,4,1]=>[1,4,1,1,2] 101000100=>010100010=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1] 101000101=>110100010=>[2,1,1,3,1,1]=>[1,1,3,1,1,2] 101000110=>010100011=>[1,1,1,1,3,2]=>[2,3,1,1,1,1] 101000111=>110100011=>[2,1,1,3,2]=>[2,3,1,1,2] 101001000=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1] 101001001=>110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2] 101001010=>010100101=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1] 101001011=>110100101=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2] 101001100=>010100110=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1] 101001101=>110100110=>[2,1,1,2,2,1]=>[1,2,2,1,1,2] 101001110=>010100111=>[1,1,1,1,2,3]=>[3,2,1,1,1,1] 101001111=>110100111=>[2,1,1,2,3]=>[3,2,1,1,2] 101010000=>010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1] 101010001=>110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2] 101010010=>010101001=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1] 101010011=>110101001=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2] 101010100=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1] 101010101=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2] 101010110=>010101011=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1] 101010111=>110101011=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2] 101011000=>010101100=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1] 101011001=>110101100=>[2,1,1,1,2,2]=>[2,2,1,1,1,2] 101011010=>010101101=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1] 101011011=>110101101=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2] 101011100=>010101110=>[1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1] 101011101=>110101110=>[2,1,1,1,3,1]=>[1,3,1,1,1,2] 101011110=>010101111=>[1,1,1,1,1,4]=>[4,1,1,1,1,1] 101011111=>110101111=>[2,1,1,1,4]=>[4,1,1,1,2] 101100000=>010110000=>[1,1,1,2,4]=>[4,2,1,1,1] 101100001=>110110000=>[2,1,2,4]=>[4,2,1,2] 101100010=>010110001=>[1,1,1,2,3,1]=>[1,3,2,1,1,1] 101100011=>110110001=>[2,1,2,3,1]=>[1,3,2,1,2] 101100100=>010110010=>[1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1] 101100101=>110110010=>[2,1,2,2,1,1]=>[1,1,2,2,1,2] 101100110=>010110011=>[1,1,1,2,2,2]=>[2,2,2,1,1,1] 101100111=>110110011=>[2,1,2,2,2]=>[2,2,2,1,2] 101101000=>010110100=>[1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1] 101101001=>110110100=>[2,1,2,1,1,2]=>[2,1,1,2,1,2] 101101010=>010110101=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1] 101101011=>110110101=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2] 101101100=>010110110=>[1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1] 101101101=>110110110=>[2,1,2,1,2,1]=>[1,2,1,2,1,2] 101101110=>010110111=>[1,1,1,2,1,3]=>[3,1,2,1,1,1] 101101111=>110110111=>[2,1,2,1,3]=>[3,1,2,1,2] 101110000=>010111000=>[1,1,1,3,3]=>[3,3,1,1,1] 101110001=>110111000=>[2,1,3,3]=>[3,3,1,2] 101110010=>010111001=>[1,1,1,3,2,1]=>[1,2,3,1,1,1] 101110011=>110111001=>[2,1,3,2,1]=>[1,2,3,1,2] 101110100=>010111010=>[1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1] 101110101=>110111010=>[2,1,3,1,1,1]=>[1,1,1,3,1,2] 101110110=>010111011=>[1,1,1,3,1,2]=>[2,1,3,1,1,1] 101110111=>110111011=>[2,1,3,1,2]=>[2,1,3,1,2] 101111000=>010111100=>[1,1,1,4,2]=>[2,4,1,1,1] 101111001=>110111100=>[2,1,4,2]=>[2,4,1,2] 101111010=>010111101=>[1,1,1,4,1,1]=>[1,1,4,1,1,1] 101111011=>110111101=>[2,1,4,1,1]=>[1,1,4,1,2] 101111100=>010111110=>[1,1,1,5,1]=>[1,5,1,1,1] 101111101=>110111110=>[2,1,5,1]=>[1,5,1,2] 101111110=>010111111=>[1,1,1,6]=>[6,1,1,1] 101111111=>110111111=>[2,1,6]=>[6,1,2] 110000000=>011000000=>[1,2,6]=>[6,2,1] 110000001=>111000000=>[3,6]=>[6,3] 110000010=>011000001=>[1,2,5,1]=>[1,5,2,1] 110000011=>111000001=>[3,5,1]=>[1,5,3] 110000100=>011000010=>[1,2,4,1,1]=>[1,1,4,2,1] 110000101=>111000010=>[3,4,1,1]=>[1,1,4,3] 110000110=>011000011=>[1,2,4,2]=>[2,4,2,1] 110000111=>111000011=>[3,4,2]=>[2,4,3] 110001000=>011000100=>[1,2,3,1,2]=>[2,1,3,2,1] 110001001=>111000100=>[3,3,1,2]=>[2,1,3,3] 110001010=>011000101=>[1,2,3,1,1,1]=>[1,1,1,3,2,1] 110001011=>111000101=>[3,3,1,1,1]=>[1,1,1,3,3] 110001100=>011000110=>[1,2,3,2,1]=>[1,2,3,2,1] 110001101=>111000110=>[3,3,2,1]=>[1,2,3,3] 110001110=>011000111=>[1,2,3,3]=>[3,3,2,1] 110001111=>111000111=>[3,3,3]=>[3,3,3] 110010000=>011001000=>[1,2,2,1,3]=>[3,1,2,2,1] 110010001=>111001000=>[3,2,1,3]=>[3,1,2,3] 110010010=>011001001=>[1,2,2,1,2,1]=>[1,2,1,2,2,1] 110010011=>111001001=>[3,2,1,2,1]=>[1,2,1,2,3] 110010100=>011001010=>[1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1] 110010101=>111001010=>[3,2,1,1,1,1]=>[1,1,1,1,2,3] 110010110=>011001011=>[1,2,2,1,1,2]=>[2,1,1,2,2,1] 110010111=>111001011=>[3,2,1,1,2]=>[2,1,1,2,3] 110011000=>011001100=>[1,2,2,2,2]=>[2,2,2,2,1] 110011001=>111001100=>[3,2,2,2]=>[2,2,2,3] 110011010=>011001101=>[1,2,2,2,1,1]=>[1,1,2,2,2,1] 110011011=>111001101=>[3,2,2,1,1]=>[1,1,2,2,3] 110011100=>011001110=>[1,2,2,3,1]=>[1,3,2,2,1] 110011101=>111001110=>[3,2,3,1]=>[1,3,2,3] 110011110=>011001111=>[1,2,2,4]=>[4,2,2,1] 110011111=>111001111=>[3,2,4]=>[4,2,3] 110100000=>011010000=>[1,2,1,1,4]=>[4,1,1,2,1] 110100001=>111010000=>[3,1,1,4]=>[4,1,1,3] 110100010=>011010001=>[1,2,1,1,3,1]=>[1,3,1,1,2,1] 110100011=>111010001=>[3,1,1,3,1]=>[1,3,1,1,3] 110100100=>011010010=>[1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1] 110100101=>111010010=>[3,1,1,2,1,1]=>[1,1,2,1,1,3] 110100110=>011010011=>[1,2,1,1,2,2]=>[2,2,1,1,2,1] 110100111=>111010011=>[3,1,1,2,2]=>[2,2,1,1,3] 110101000=>011010100=>[1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1] 110101001=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3] 110101010=>011010101=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1] 110101011=>111010101=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3] 110101100=>011010110=>[1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1] 110101101=>111010110=>[3,1,1,1,2,1]=>[1,2,1,1,1,3] 110101110=>011010111=>[1,2,1,1,1,3]=>[3,1,1,1,2,1] 110101111=>111010111=>[3,1,1,1,3]=>[3,1,1,1,3] 110110000=>011011000=>[1,2,1,2,3]=>[3,2,1,2,1] 110110001=>111011000=>[3,1,2,3]=>[3,2,1,3] 110110010=>011011001=>[1,2,1,2,2,1]=>[1,2,2,1,2,1] 110110011=>111011001=>[3,1,2,2,1]=>[1,2,2,1,3] 110110100=>011011010=>[1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1] 110110101=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3] 110110110=>011011011=>[1,2,1,2,1,2]=>[2,1,2,1,2,1] 110110111=>111011011=>[3,1,2,1,2]=>[2,1,2,1,3] 110111000=>011011100=>[1,2,1,3,2]=>[2,3,1,2,1] 110111001=>111011100=>[3,1,3,2]=>[2,3,1,3] 110111010=>011011101=>[1,2,1,3,1,1]=>[1,1,3,1,2,1] 110111011=>111011101=>[3,1,3,1,1]=>[1,1,3,1,3] 110111100=>011011110=>[1,2,1,4,1]=>[1,4,1,2,1] 110111101=>111011110=>[3,1,4,1]=>[1,4,1,3] 110111110=>011011111=>[1,2,1,5]=>[5,1,2,1] 110111111=>111011111=>[3,1,5]=>[5,1,3] 111000000=>011100000=>[1,3,5]=>[5,3,1] 111000001=>111100000=>[4,5]=>[5,4] 111000010=>011100001=>[1,3,4,1]=>[1,4,3,1] 111000011=>111100001=>[4,4,1]=>[1,4,4] 111000100=>011100010=>[1,3,3,1,1]=>[1,1,3,3,1] 111000101=>111100010=>[4,3,1,1]=>[1,1,3,4] 111000110=>011100011=>[1,3,3,2]=>[2,3,3,1] 111000111=>111100011=>[4,3,2]=>[2,3,4] 111001000=>011100100=>[1,3,2,1,2]=>[2,1,2,3,1] 111001001=>111100100=>[4,2,1,2]=>[2,1,2,4] 111001010=>011100101=>[1,3,2,1,1,1]=>[1,1,1,2,3,1] 111001011=>111100101=>[4,2,1,1,1]=>[1,1,1,2,4] 111001100=>011100110=>[1,3,2,2,1]=>[1,2,2,3,1] 111001101=>111100110=>[4,2,2,1]=>[1,2,2,4] 111001110=>011100111=>[1,3,2,3]=>[3,2,3,1] 111001111=>111100111=>[4,2,3]=>[3,2,4] 111010000=>011101000=>[1,3,1,1,3]=>[3,1,1,3,1] 111010001=>111101000=>[4,1,1,3]=>[3,1,1,4] 111010010=>011101001=>[1,3,1,1,2,1]=>[1,2,1,1,3,1] 111010011=>111101001=>[4,1,1,2,1]=>[1,2,1,1,4] 111010100=>011101010=>[1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1] 111010101=>111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4] 111010110=>011101011=>[1,3,1,1,1,2]=>[2,1,1,1,3,1] 111010111=>111101011=>[4,1,1,1,2]=>[2,1,1,1,4] 111011000=>011101100=>[1,3,1,2,2]=>[2,2,1,3,1] 111011001=>111101100=>[4,1,2,2]=>[2,2,1,4] 111011010=>011101101=>[1,3,1,2,1,1]=>[1,1,2,1,3,1] 111011011=>111101101=>[4,1,2,1,1]=>[1,1,2,1,4] 111011100=>011101110=>[1,3,1,3,1]=>[1,3,1,3,1] 111011101=>111101110=>[4,1,3,1]=>[1,3,1,4] 111011110=>011101111=>[1,3,1,4]=>[4,1,3,1] 111011111=>111101111=>[4,1,4]=>[4,1,4] 111100000=>011110000=>[1,4,4]=>[4,4,1] 111100001=>111110000=>[5,4]=>[4,5] 111100010=>011110001=>[1,4,3,1]=>[1,3,4,1] 111100011=>111110001=>[5,3,1]=>[1,3,5] 111100100=>011110010=>[1,4,2,1,1]=>[1,1,2,4,1] 111100101=>111110010=>[5,2,1,1]=>[1,1,2,5] 111100110=>011110011=>[1,4,2,2]=>[2,2,4,1] 111100111=>111110011=>[5,2,2]=>[2,2,5] 111101000=>011110100=>[1,4,1,1,2]=>[2,1,1,4,1] 111101001=>111110100=>[5,1,1,2]=>[2,1,1,5] 111101010=>011110101=>[1,4,1,1,1,1]=>[1,1,1,1,4,1] 111101011=>111110101=>[5,1,1,1,1]=>[1,1,1,1,5] 111101100=>011110110=>[1,4,1,2,1]=>[1,2,1,4,1] 111101101=>111110110=>[5,1,2,1]=>[1,2,1,5] 111101110=>011110111=>[1,4,1,3]=>[3,1,4,1] 111101111=>111110111=>[5,1,3]=>[3,1,5] 111110000=>011111000=>[1,5,3]=>[3,5,1] 111110001=>111111000=>[6,3]=>[3,6] 111110010=>011111001=>[1,5,2,1]=>[1,2,5,1] 111110011=>111111001=>[6,2,1]=>[1,2,6] 111110100=>011111010=>[1,5,1,1,1]=>[1,1,1,5,1] 111110101=>111111010=>[6,1,1,1]=>[1,1,1,6] 111110110=>011111011=>[1,5,1,2]=>[2,1,5,1] 111110111=>111111011=>[6,1,2]=>[2,1,6] 111111000=>011111100=>[1,6,2]=>[2,6,1] 111111001=>111111100=>[7,2]=>[2,7] 111111010=>011111101=>[1,6,1,1]=>[1,1,6,1] 111111011=>111111101=>[7,1,1]=>[1,1,7] 111111100=>011111110=>[1,7,1]=>[1,7,1] 111111101=>111111110=>[8,1]=>[1,8] 111111110=>011111111=>[1,8]=>[8,1] 111111111=>111111111=>[9]=>[9] 1010101010=>0101010101=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1] 1011100010=>0101110001=>[1,1,1,3,3,1]=>[1,3,3,1,1,1] 1100101010=>0110010101=>[1,2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2,1] 1100110010=>0110011001=>[1,2,2,2,2,1]=>[1,2,2,2,2,1] 1101100010=>0110110001=>[1,2,1,2,3,1]=>[1,3,2,1,2,1] 1110011000=>0111001100=>[1,3,2,2,2]=>[2,2,2,3,1] 1110100010=>0111010001=>[1,3,1,1,3,1]=>[1,3,1,1,3,1] 1110101000=>0111010100=>[1,3,1,1,1,1,2]=>[2,1,1,1,1,3,1] 1110110000=>0111011000=>[1,3,1,2,3]=>[3,2,1,3,1] 1111000010=>0111100001=>[1,4,4,1]=>[1,4,4,1] 1111001000=>0111100100=>[1,4,2,1,2]=>[2,1,2,4,1] 1111010000=>0111101000=>[1,4,1,1,3]=>[3,1,1,4,1] 1111100000=>0111110000=>[1,5,4]=>[4,5,1] 101010101010=>010101010101=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1] 111000110010=>011100011001=>[1,3,3,2,2,1]=>[1,2,2,3,3,1] 111000111000=>011100011100=>[1,3,3,3,2]=>[2,3,3,3,1] 111001100010=>011100110001=>[1,3,2,2,3,1]=>[1,3,2,2,3,1] 111001110000=>011100111000=>[1,3,2,3,3]=>[3,3,2,3,1] 111100011000=>011110001100=>[1,4,3,2,2]=>[2,2,3,4,1] 111100110000=>011110011000=>[1,4,2,2,3]=>[3,2,2,4,1] 111110000010=>011111000001=>[1,5,5,1]=>[1,5,5,1] 111111000000=>011111100000=>[1,6,5]=>[5,6,1] 1111111111=>1111111111=>[10]=>[10] 1111111110=>0111111111=>[1,9]=>[9,1] 1111100010=>0111110001=>[1,5,3,1]=>[1,3,5,1] 1111100001=>1111110000=>[6,4]=>[4,6] 1111010010=>0111101001=>[1,4,1,1,2,1]=>[1,2,1,1,4,1] 1111010001=>1111101000=>[5,1,1,3]=>[3,1,1,5] 1111001010=>0111100101=>[1,4,2,1,1,1]=>[1,1,1,2,4,1] 1111001001=>1111100100=>[5,2,1,2]=>[2,1,2,5] 1111000101=>1111100010=>[5,3,1,1]=>[1,1,3,5] 1111000011=>1111100001=>[5,4,1]=>[1,4,5] 1111000001=>1111100000=>[5,5]=>[5,5] 1110111000=>0111011100=>[1,3,1,3,2]=>[2,3,1,3,1] 1110110010=>0111011001=>[1,3,1,2,2,1]=>[1,2,2,1,3,1] 1110110001=>1111011000=>[4,1,2,3]=>[3,2,1,4] 1110101010=>0111010101=>[1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1] 1110101001=>1111010100=>[4,1,1,1,1,2]=>[2,1,1,1,1,4] 1110100101=>1111010010=>[4,1,1,2,1,1]=>[1,1,2,1,1,4] 1110100011=>1111010001=>[4,1,1,3,1]=>[1,3,1,1,4] 1110100001=>1111010000=>[4,1,1,4]=>[4,1,1,4] 1110011001=>1111001100=>[4,2,2,2]=>[2,2,2,4] 1110010101=>1111001010=>[4,2,1,1,1,1]=>[1,1,1,1,2,4] 1110010011=>1111001001=>[4,2,1,2,1]=>[1,2,1,2,4] 1110010001=>1111001000=>[4,2,1,3]=>[3,1,2,4] 1110000111=>1111000011=>[4,4,2]=>[2,4,4] 1110000011=>1111000001=>[4,5,1]=>[1,5,4] 1101111111=>1110111111=>[3,1,6]=>[6,1,3] 1101111110=>0110111111=>[1,2,1,6]=>[6,1,2,1] 1101110001=>1110111000=>[3,1,3,3]=>[3,3,1,3] 1101101001=>1110110100=>[3,1,2,1,1,2]=>[2,1,1,2,1,3] 1101100101=>1110110010=>[3,1,2,2,1,1]=>[1,1,2,2,1,3] 1101100011=>1110110001=>[3,1,2,3,1]=>[1,3,2,1,3] 1101100001=>1110110000=>[3,1,2,4]=>[4,2,1,3] 1101011001=>1110101100=>[3,1,1,1,2,2]=>[2,2,1,1,1,3] 1101010101=>1110101010=>[3,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,3] 1101010011=>1110101001=>[3,1,1,1,1,2,1]=>[1,2,1,1,1,1,3] 1101010001=>1110101000=>[3,1,1,1,1,3]=>[3,1,1,1,1,3] 1101000111=>1110100011=>[3,1,1,3,2]=>[2,3,1,1,3] 1101000011=>1110100001=>[3,1,1,4,1]=>[1,4,1,1,3] 1100111111=>1110011111=>[3,2,5]=>[5,2,3] 1100110011=>1110011001=>[3,2,2,2,1]=>[1,2,2,2,3] 1100110001=>1110011000=>[3,2,2,3]=>[3,2,2,3] 1100101110=>0110010111=>[1,2,2,1,1,3]=>[3,1,1,2,2,1] 1100001111=>1110000111=>[3,4,3]=>[3,4,3] 1100000111=>1110000011=>[3,5,2]=>[2,5,3] 1100000110=>0110000011=>[1,2,5,2]=>[2,5,2,1] 1011111101=>1101111110=>[2,1,6,1]=>[1,6,1,2] 1011000111=>1101100011=>[2,1,2,3,2]=>[2,3,2,1,2] 1011000010=>0101100001=>[1,1,1,2,4,1]=>[1,4,2,1,1,1] 1010111110=>0101011111=>[1,1,1,1,1,5]=>[5,1,1,1,1,1] 1010101000=>0101010100=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1] 1010100010=>0101010001=>[1,1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1,1] 1010001010=>0101000101=>[1,1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1,1] 1001111111=>1100111111=>[2,2,6]=>[6,2,2] 1001100111=>1100110011=>[2,2,2,2,2]=>[2,2,2,2,2] 1001100010=>0100110001=>[1,1,2,2,3,1]=>[1,3,2,2,1,1] 1001011110=>0100101111=>[1,1,2,1,1,4]=>[4,1,1,2,1,1] 1001011000=>0100101100=>[1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1] 1001010101=>1100101010=>[2,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,2] 1001010010=>0100101001=>[1,1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1,1] 1000111101=>1100011110=>[2,3,4,1]=>[1,4,3,2] 1000110010=>0100011001=>[1,1,3,2,2,1]=>[1,2,2,3,1,1] 1000101110=>0100010111=>[1,1,3,1,1,3]=>[3,1,1,3,1,1] 1000101010=>0100010101=>[1,1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1,1] 1000011111=>1100001111=>[2,4,4]=>[4,4,2] 1000010110=>0100001011=>[1,1,4,1,1,2]=>[2,1,1,4,1,1] 1000010101=>1100001010=>[2,4,1,1,1,1]=>[1,1,1,1,4,2] 1000001101=>1100000110=>[2,5,2,1]=>[1,2,5,2] 1000000010=>0100000001=>[1,1,7,1]=>[1,7,1,1] 1000000001=>1100000000=>[2,8]=>[8,2] 11111111110=>01111111111=>[1,10]=>[10,1] 0111111101=>1011111110=>[1,1,7,1]=>[1,7,1,1] 0111100001=>1011110000=>[1,1,4,4]=>[4,4,1,1] 0111000001=>1011100000=>[1,1,3,5]=>[5,3,1,1] 0000000001=>1000000000=>[1,9]=>[9,1] 01111111101=>10111111110=>[1,1,8,1]=>[1,8,1,1] 0111010001=>1011101000=>[1,1,3,1,1,3]=>[3,1,1,3,1,1] 0110100001=>1011010000=>[1,1,2,1,1,4]=>[4,1,1,2,1,1] 00000000001=>10000000000=>[1,10]=>[10,1] 0101010101=>1010101010=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1] 0010101011=>1001010101=>[1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1] 0001101011=>1000110101=>[1,3,2,1,1,1,1]=>[1,1,1,1,2,3,1] 0001011101=>1000101110=>[1,3,1,1,3,1]=>[1,3,1,1,3,1] 0000111101=>1000011110=>[1,4,4,1]=>[1,4,4,1] 010101010101=>101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1,1] 001100110011=>100110011001=>[1,2,2,2,2,2,1]=>[1,2,2,2,2,2,1] 111110000001=>111111000000=>[6,6]=>[6,6] 111001100001=>111100110000=>[4,2,2,4]=>[4,2,2,4] 111000011001=>111100001100=>[4,4,2,2]=>[2,2,4,4] 111000000111=>111100000011=>[4,6,2]=>[2,6,4] 111000110001=>111100011000=>[4,3,2,3]=>[3,2,3,4] 111000100101=>111100010010=>[4,3,1,2,1,1]=>[1,1,2,1,3,4] 111011000001=>111101100000=>[4,1,2,5]=>[5,2,1,4] 111010010001=>111101001000=>[4,1,1,2,1,3]=>[3,1,2,1,1,4] 111010000101=>111101000010=>[4,1,1,4,1,1]=>[1,1,4,1,1,4] 100111100001=>110011110000=>[2,2,4,4]=>[4,4,2,2] 100110011001=>110011001100=>[2,2,2,2,2,2]=>[2,2,2,2,2,2] 100110000111=>110011000011=>[2,2,2,4,2]=>[2,4,2,2,2] 100110110001=>110011011000=>[2,2,2,1,2,3]=>[3,2,1,2,2,2] 100110100101=>110011010010=>[2,2,2,1,1,2,1,1]=>[1,1,2,1,1,2,2,2] 100001111001=>110000111100=>[2,4,4,2]=>[2,4,4,2] 100000011111=>110000001111=>[2,6,4]=>[4,6,2] 100011110001=>110001111000=>[2,3,4,3]=>[3,4,3,2] 101101100001=>110110110000=>[2,1,2,1,2,4]=>[4,2,1,2,1,2] 101100011001=>110110001100=>[2,1,2,3,2,2]=>[2,2,3,2,1,2] 101100110001=>110110011000=>[2,1,2,2,2,3]=>[3,2,2,2,1,2] 101100100101=>110110010010=>[2,1,2,2,1,2,1,1]=>[1,1,2,1,2,2,1,2] 101111000001=>110111100000=>[2,1,4,5]=>[5,4,1,2] 101110010001=>110111001000=>[2,1,3,2,1,3]=>[3,1,2,3,1,2] 101110000101=>110111000010=>[2,1,3,4,1,1]=>[1,1,4,3,1,2] 101001011001=>110100101100=>[2,1,1,2,1,1,2,2]=>[2,2,1,1,2,1,1,2] 101001110001=>110100111000=>[2,1,1,2,3,3]=>[3,3,2,1,1,2] 101001100101=>110100110010=>[2,1,1,2,2,2,1,1]=>[1,1,2,2,2,1,1,2] 101011010001=>110101101000=>[2,1,1,1,2,1,1,3]=>[3,1,1,2,1,1,1,2] 101011000101=>110101100010=>[2,1,1,1,2,3,1,1]=>[1,1,3,2,1,1,1,2] 101010010101=>110101001010=>[2,1,1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1,1,2] 0000000000=>0000000000=>[10]=>[10] 0000011000=>0000001100=>[6,2,2]=>[2,2,6] 0001111110=>0000111111=>[4,6]=>[6,4] 0111111110=>0011111111=>[2,8]=>[8,2] 000111111000=>000011111100=>[4,6,2]=>[2,6,4] 011110011000=>001111001100=>[2,4,2,2,2]=>[2,2,2,4,2] 011111100000=>001111110000=>[2,6,4]=>[4,6,2] 0000000010=>0000000001=>[9,1]=>[1,9] 0000111110=>0000011111=>[5,5]=>[5,5] 00000000010=>00000000001=>[10,1]=>[1,10] 0000000100=>0000000010=>[8,1,1]=>[1,1,8] 01111111110=>00111111111=>[2,9]=>[9,2] 0110001100=>0011000110=>[2,2,3,2,1]=>[1,2,3,2,2] 011001100100=>001100110010=>[2,2,2,2,2,1,1]=>[1,1,2,2,2,2,2] 011001110000=>001100111000=>[2,2,2,3,3]=>[3,3,2,2,2] 011011000100=>001101100010=>[2,2,1,2,3,1,1]=>[1,1,3,2,1,2,2] 011100010100=>001110001010=>[2,3,3,1,1,1,1]=>[1,1,1,1,3,3,2] 011100011000=>001110001100=>[2,3,3,2,2]=>[2,2,3,3,2] 011100100100=>001110010010=>[2,3,2,1,2,1,1]=>[1,1,2,1,2,3,2] 011100110000=>001110011000=>[2,3,2,2,3]=>[3,2,2,3,2] 011101000100=>001110100010=>[2,3,1,1,3,1,1]=>[1,1,3,1,1,3,2] 011111000000=>001111100000=>[2,5,5]=>[5,5,2] 0101110001=>1010111000=>[1,1,1,1,3,3]=>[3,3,1,1,1,1] 0110010101=>1011001010=>[1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1] 0110011001=>1011001100=>[1,1,2,2,2,2]=>[2,2,2,2,1,1] 0110110001=>1011011000=>[1,1,2,1,2,3]=>[3,2,1,2,1,1] 0111101000=>0011110100=>[2,4,1,1,2]=>[2,1,1,4,2] 0111110000=>0011111000=>[2,5,3]=>[3,5,2] 010101101001=>101010110100=>[1,1,1,1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1,1,1,1] 011001011001=>101100101100=>[1,1,2,2,1,1,2,2]=>[2,2,1,1,2,2,1,1] 011010010101=>101101001010=>[1,1,2,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,2,1,1] 011010101001=>101101010100=>[1,1,2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2,1,1] 011011000101=>101101100010=>[1,1,2,1,2,3,1,1]=>[1,1,3,2,1,2,1,1] 011011010001=>101101101000=>[1,1,2,1,2,1,1,3]=>[3,1,1,2,1,2,1,1] 011100011001=>101110001100=>[1,1,3,3,2,2]=>[2,2,3,3,1,1] 011100110001=>101110011000=>[1,1,3,2,2,3]=>[3,2,2,3,1,1] 011101001001=>101110100100=>[1,1,3,1,1,2,1,2]=>[2,1,2,1,1,3,1,1] 011101010001=>101110101000=>[1,1,3,1,1,1,1,3]=>[3,1,1,1,1,3,1,1] 011101100001=>101110110000=>[1,1,3,1,2,4]=>[4,2,1,3,1,1] 011110010001=>101111001000=>[1,1,4,2,1,3]=>[3,1,2,4,1,1] 011110100001=>101111010000=>[1,1,4,1,1,4]=>[4,1,1,4,1,1] 011111000001=>101111100000=>[1,1,5,5]=>[5,5,1,1] 0011111000=>0001111100=>[3,5,2]=>[2,5,3] 0001111100=>0000111110=>[4,5,1]=>[1,5,4] 001111110000=>000111111000=>[3,6,3]=>[3,6,3] 0000000101=>1000000010=>[1,7,1,1]=>[1,1,7,1] 0000001101=>1000000110=>[1,6,2,1]=>[1,2,6,1] 0001111101=>1000111110=>[1,3,5,1]=>[1,5,3,1] 00000001101=>10000000110=>[1,7,2,1]=>[1,2,7,1] 100101110001=>110010111000=>[2,2,1,1,3,3]=>[3,3,1,1,2,2] 101011100001=>110101110000=>[2,1,1,1,3,4]=>[4,3,1,1,1,2] 101110100001=>110111010000=>[2,1,3,1,1,4]=>[4,1,1,3,1,2] 110001110001=>111000111000=>[3,3,3,3]=>[3,3,3,3] 110011010001=>111001101000=>[3,2,2,1,1,3]=>[3,1,1,2,2,3] 110011100001=>111001110000=>[3,2,3,4]=>[4,3,2,3] 110100110001=>111010011000=>[3,1,1,2,2,3]=>[3,2,2,1,1,3] 110101010001=>111010101000=>[3,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,3] 110101100001=>111010110000=>[3,1,1,1,2,4]=>[4,2,1,1,1,3] 110110010001=>111011001000=>[3,1,2,2,1,3]=>[3,1,2,2,1,3] 110110100001=>111011010000=>[3,1,2,1,1,4]=>[4,1,1,2,1,3] 110111000001=>111011100000=>[3,1,3,5]=>[5,3,1,3] 111001010001=>111100101000=>[4,2,1,1,1,3]=>[3,1,1,1,2,4] 111010100001=>111101010000=>[4,1,1,1,1,4]=>[4,1,1,1,1,4] 111100010001=>111110001000=>[5,3,1,3]=>[3,1,3,5] 111100100001=>111110010000=>[5,2,1,4]=>[4,1,2,5] 111101000001=>111110100000=>[5,1,1,5]=>[5,1,1,5] 0011000110=>0001100011=>[3,2,3,2]=>[2,3,2,3] 0001101001=>1000110100=>[1,3,2,1,1,2]=>[2,1,1,2,3,1] 10000000001=>11000000000=>[2,9]=>[9,2] 11111111111=>11111111111=>[11]=>[11] 111100000011=>111110000001=>[5,6,1]=>[1,6,5] 110000001111=>111000000111=>[3,6,3]=>[3,6,3] 110011010011=>111001101001=>[3,2,2,1,1,2,1]=>[1,2,1,1,2,2,3] 110100110011=>111010011001=>[3,1,1,2,2,2,1]=>[1,2,2,2,1,1,3] 101100110011=>110110011001=>[2,1,2,2,2,2,1]=>[1,2,2,2,2,1,2] 100110110011=>110011011001=>[2,2,2,1,2,2,1]=>[1,2,2,1,2,2,2] 110001110011=>111000111001=>[3,3,3,2,1]=>[1,2,3,3,3] 101100011011=>110110001101=>[2,1,2,3,2,1,1]=>[1,1,2,3,2,1,2] 100110011011=>110011001101=>[2,2,2,2,2,1,1]=>[1,1,2,2,2,2,2] 110011000111=>111001100011=>[3,2,2,3,2]=>[2,3,2,2,3] 110000011111=>111000001111=>[3,5,4]=>[4,5,3] 0000000011=>1000000001=>[1,8,1]=>[1,8,1] 0011111100=>0001111110=>[3,6,1]=>[1,6,3] 0100101001=>1010010100=>[1,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,1] 110011000011=>111001100001=>[3,2,2,4,1]=>[1,4,2,2,3] 0100010101=>1010001010=>[1,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,1] 0001010101=>1000101010=>[1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1] 0000011011=>1000001101=>[1,5,2,1,1]=>[1,1,2,5,1] 110110010011=>111011001001=>[3,1,2,2,1,2,1]=>[1,2,1,2,2,1,3] 110011100011=>111001110001=>[3,2,3,3,1]=>[1,3,3,2,3] 111001010011=>111100101001=>[4,2,1,1,1,2,1]=>[1,2,1,1,1,2,4] 111010010011=>111101001001=>[4,1,1,2,1,2,1]=>[1,2,1,2,1,1,4] 101110010011=>110111001001=>[2,1,3,2,1,2,1]=>[1,2,1,2,3,1,2] 0110010001=>1011001000=>[1,1,2,2,1,3]=>[3,1,2,2,1,1] 0110101011=>1011010101=>[1,1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1,1] 0101100001=>1010110000=>[1,1,1,1,2,4]=>[4,2,1,1,1,1] 0100011001=>1010001100=>[1,1,1,3,2,2]=>[2,2,3,1,1,1] 0100110001=>1010011000=>[1,1,1,2,2,3]=>[3,2,2,1,1,1] 0111011100=>0011101110=>[2,3,1,3,1]=>[1,3,1,3,2] 0101000101=>1010100010=>[1,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,1] 0101010001=>1010101000=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1] 0110001001=>1011000100=>[1,1,2,3,1,2]=>[2,1,3,2,1,1] 0011011110=>0001101111=>[3,2,1,4]=>[4,1,2,3] 0011101110=>0001110111=>[3,3,1,3]=>[3,1,3,3] 0011111010=>0001111101=>[3,5,1,1]=>[1,1,5,3] 111100000111=>111110000011=>[5,5,2]=>[2,5,5] 111000001111=>111100000111=>[4,5,3]=>[3,5,4]