=>

0=>0=>[2]=>[1,1] 1=>1=>[1,1]=>[2] 00=>00=>[3]=>[1,1,1] 01=>10=>[1,2]=>[1,2] 10=>10=>[1,2]=>[1,2] 11=>11=>[1,1,1]=>[3] 000=>000=>[4]=>[1,1,1,1] 001=>100=>[1,3]=>[1,1,2] 010=>100=>[1,3]=>[1,1,2] 011=>110=>[1,1,2]=>[1,3] 100=>100=>[1,3]=>[1,1,2] 101=>110=>[1,1,2]=>[1,3] 110=>110=>[1,1,2]=>[1,3] 111=>111=>[1,1,1,1]=>[4] 0000=>0000=>[5]=>[1,1,1,1,1] 0001=>1000=>[1,4]=>[1,1,1,2] 0010=>1000=>[1,4]=>[1,1,1,2] 0011=>1010=>[1,2,2]=>[1,2,2] 0100=>1000=>[1,4]=>[1,1,1,2] 0101=>1100=>[1,1,3]=>[1,1,3] 0110=>1010=>[1,2,2]=>[1,2,2] 0111=>1110=>[1,1,1,2]=>[1,4] 1000=>1000=>[1,4]=>[1,1,1,2] 1001=>1010=>[1,2,2]=>[1,2,2] 1010=>1100=>[1,1,3]=>[1,1,3] 1011=>1110=>[1,1,1,2]=>[1,4] 1100=>1010=>[1,2,2]=>[1,2,2] 1101=>1110=>[1,1,1,2]=>[1,4] 1110=>1110=>[1,1,1,2]=>[1,4] 1111=>1111=>[1,1,1,1,1]=>[5] 00000=>00000=>[6]=>[1,1,1,1,1,1] 00001=>10000=>[1,5]=>[1,1,1,1,2] 00010=>10000=>[1,5]=>[1,1,1,1,2] 00011=>10010=>[1,3,2]=>[1,2,1,2] 00100=>10000=>[1,5]=>[1,1,1,1,2] 00101=>11000=>[1,1,4]=>[1,1,1,3] 00110=>10010=>[1,3,2]=>[1,2,1,2] 00111=>10110=>[1,2,1,2]=>[1,3,2] 01000=>10000=>[1,5]=>[1,1,1,1,2] 01001=>11000=>[1,1,4]=>[1,1,1,3] 01010=>11000=>[1,1,4]=>[1,1,1,3] 01011=>11100=>[1,1,1,3]=>[1,1,4] 01100=>10010=>[1,3,2]=>[1,2,1,2] 01101=>11100=>[1,1,1,3]=>[1,1,4] 01110=>10110=>[1,2,1,2]=>[1,3,2] 01111=>11110=>[1,1,1,1,2]=>[1,5] 10000=>10000=>[1,5]=>[1,1,1,1,2] 10001=>10010=>[1,3,2]=>[1,2,1,2] 10010=>11000=>[1,1,4]=>[1,1,1,3] 10011=>10110=>[1,2,1,2]=>[1,3,2] 10100=>11000=>[1,1,4]=>[1,1,1,3] 10101=>11100=>[1,1,1,3]=>[1,1,4] 10110=>11100=>[1,1,1,3]=>[1,1,4] 10111=>11110=>[1,1,1,1,2]=>[1,5] 11000=>10010=>[1,3,2]=>[1,2,1,2] 11001=>10110=>[1,2,1,2]=>[1,3,2] 11010=>11100=>[1,1,1,3]=>[1,1,4] 11011=>11110=>[1,1,1,1,2]=>[1,5] 11100=>10110=>[1,2,1,2]=>[1,3,2] 11101=>11110=>[1,1,1,1,2]=>[1,5] 11110=>11110=>[1,1,1,1,2]=>[1,5] 11111=>11111=>[1,1,1,1,1,1]=>[6] 000000=>000000=>[7]=>[1,1,1,1,1,1,1] 000001=>100000=>[1,6]=>[1,1,1,1,1,2] 000010=>100000=>[1,6]=>[1,1,1,1,1,2] 000011=>100010=>[1,4,2]=>[1,2,1,1,2] 000100=>100000=>[1,6]=>[1,1,1,1,1,2] 000101=>101000=>[1,2,4]=>[1,1,1,2,2] 000110=>100010=>[1,4,2]=>[1,2,1,1,2] 000111=>100110=>[1,3,1,2]=>[1,3,1,2] 001000=>100000=>[1,6]=>[1,1,1,1,1,2] 001001=>110000=>[1,1,5]=>[1,1,1,1,3] 001010=>101000=>[1,2,4]=>[1,1,1,2,2] 001011=>101100=>[1,2,1,3]=>[1,1,3,2] 001100=>100010=>[1,4,2]=>[1,2,1,1,2] 001101=>110010=>[1,1,3,2]=>[1,2,1,3] 001110=>100110=>[1,3,1,2]=>[1,3,1,2] 001111=>101110=>[1,2,1,1,2]=>[1,4,2] 010000=>100000=>[1,6]=>[1,1,1,1,1,2] 010001=>101000=>[1,2,4]=>[1,1,1,2,2] 010010=>110000=>[1,1,5]=>[1,1,1,1,3] 010011=>110010=>[1,1,3,2]=>[1,2,1,3] 010100=>101000=>[1,2,4]=>[1,1,1,2,2] 010101=>111000=>[1,1,1,4]=>[1,1,1,4] 010110=>101100=>[1,2,1,3]=>[1,1,3,2] 010111=>111010=>[1,1,1,2,2]=>[1,2,4] 011000=>100010=>[1,4,2]=>[1,2,1,1,2] 011001=>101100=>[1,2,1,3]=>[1,1,3,2] 011010=>110010=>[1,1,3,2]=>[1,2,1,3] 011011=>111100=>[1,1,1,1,3]=>[1,1,5] 011100=>100110=>[1,3,1,2]=>[1,3,1,2] 011101=>111010=>[1,1,1,2,2]=>[1,2,4] 011110=>101110=>[1,2,1,1,2]=>[1,4,2] 011111=>111110=>[1,1,1,1,1,2]=>[1,6] 100000=>100000=>[1,6]=>[1,1,1,1,1,2] 100001=>100010=>[1,4,2]=>[1,2,1,1,2] 100010=>101000=>[1,2,4]=>[1,1,1,2,2] 100011=>100110=>[1,3,1,2]=>[1,3,1,2] 100100=>110000=>[1,1,5]=>[1,1,1,1,3] 100101=>101100=>[1,2,1,3]=>[1,1,3,2] 100110=>110010=>[1,1,3,2]=>[1,2,1,3] 100111=>101110=>[1,2,1,1,2]=>[1,4,2] 101000=>101000=>[1,2,4]=>[1,1,1,2,2] 101001=>110010=>[1,1,3,2]=>[1,2,1,3] 101010=>111000=>[1,1,1,4]=>[1,1,1,4] 101011=>111010=>[1,1,1,2,2]=>[1,2,4] 101100=>101100=>[1,2,1,3]=>[1,1,3,2] 101101=>111100=>[1,1,1,1,3]=>[1,1,5] 101110=>111010=>[1,1,1,2,2]=>[1,2,4] 101111=>111110=>[1,1,1,1,1,2]=>[1,6] 110000=>100010=>[1,4,2]=>[1,2,1,1,2] 110001=>100110=>[1,3,1,2]=>[1,3,1,2] 110010=>101100=>[1,2,1,3]=>[1,1,3,2] 110011=>101110=>[1,2,1,1,2]=>[1,4,2] 110100=>110010=>[1,1,3,2]=>[1,2,1,3] 110101=>111010=>[1,1,1,2,2]=>[1,2,4] 110110=>111100=>[1,1,1,1,3]=>[1,1,5] 110111=>111110=>[1,1,1,1,1,2]=>[1,6] 111000=>100110=>[1,3,1,2]=>[1,3,1,2] 111001=>101110=>[1,2,1,1,2]=>[1,4,2] 111010=>111010=>[1,1,1,2,2]=>[1,2,4] 111011=>111110=>[1,1,1,1,1,2]=>[1,6] 111100=>101110=>[1,2,1,1,2]=>[1,4,2] 111101=>111110=>[1,1,1,1,1,2]=>[1,6] 111110=>111110=>[1,1,1,1,1,2]=>[1,6] 111111=>111111=>[1,1,1,1,1,1,1]=>[7] 0000000=>0000000=>[8]=>[1,1,1,1,1,1,1,1] 0000001=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0000010=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0000011=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0000100=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0000101=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0000110=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0000111=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 0001000=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0001001=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0001010=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0001011=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 0001100=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0001101=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 0001110=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 0001111=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 0010000=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0010001=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0010010=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0010011=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 0010100=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0010101=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 0010110=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 0010111=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 0011000=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0011001=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 0011010=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 0011011=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 0011100=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 0011101=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 0011110=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 0011111=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 0100000=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 0100001=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0100010=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0100011=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 0100100=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 0100101=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 0100110=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 0100111=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 0101000=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 0101001=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 0101010=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 0101011=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 0101100=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 0101101=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 0101110=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 0101111=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 0110000=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 0110001=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 0110010=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 0110011=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 0110100=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 0110101=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 0110110=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 0110111=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 0111000=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 0111001=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 0111010=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 0111011=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 0111100=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 0111101=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 0111110=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 0111111=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1000000=>1000000=>[1,7]=>[1,1,1,1,1,1,2] 1000001=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 1000010=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 1000011=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 1000100=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 1000101=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 1000110=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 1000111=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 1001000=>1100000=>[1,1,6]=>[1,1,1,1,1,3] 1001001=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 1001010=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 1001011=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 1001100=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 1001101=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 1001110=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 1001111=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 1010000=>1001000=>[1,3,4]=>[1,1,1,2,1,2] 1010001=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 1010010=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 1010011=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 1010100=>1110000=>[1,1,1,5]=>[1,1,1,1,4] 1010101=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 1010110=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 1010111=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 1011000=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 1011001=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 1011010=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 1011011=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 1011100=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 1011101=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 1011110=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 1011111=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1100000=>1000010=>[1,5,2]=>[1,2,1,1,1,2] 1100001=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 1100010=>1001100=>[1,3,1,3]=>[1,1,3,1,2] 1100011=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 1100100=>1100100=>[1,1,3,3]=>[1,1,2,1,3] 1100101=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 1100110=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 1100111=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 1101000=>1010010=>[1,2,3,2]=>[1,2,1,2,2] 1101001=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 1101010=>1111000=>[1,1,1,1,4]=>[1,1,1,5] 1101011=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 1101100=>1101100=>[1,1,2,1,3]=>[1,1,3,3] 1101101=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 1101110=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 1101111=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1110000=>1000110=>[1,4,1,2]=>[1,3,1,1,2] 1110001=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 1110010=>1011010=>[1,2,1,2,2]=>[1,2,3,2] 1110011=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 1110100=>1100110=>[1,1,3,1,2]=>[1,3,1,3] 1110101=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 1110110=>1111100=>[1,1,1,1,1,3]=>[1,1,6] 1110111=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1111000=>1001110=>[1,3,1,1,2]=>[1,4,1,2] 1111001=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 1111010=>1110110=>[1,1,1,2,1,2]=>[1,3,4] 1111011=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1111100=>1011110=>[1,2,1,1,1,2]=>[1,5,2] 1111101=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1111110=>1111110=>[1,1,1,1,1,1,2]=>[1,7] 1111111=>1111111=>[1,1,1,1,1,1,1,1]=>[8] 00000000=>00000000=>[9]=>[1,1,1,1,1,1,1,1,1] 00000001=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00000010=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00000011=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 00000100=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00000101=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 00000110=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 00000111=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 00001000=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00001001=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 00001010=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 00001011=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 00001100=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 00001101=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 00001110=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 00001111=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 00010000=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00010001=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 00010010=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 00010011=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 00010100=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 00010101=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 00010110=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 00010111=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 00011000=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 00011001=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 00011010=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 00011011=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 00011100=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 00011101=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 00011110=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 00011111=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 00100000=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 00100001=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 00100010=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 00100011=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 00100100=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 00100101=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 00100110=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 00100111=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 00101000=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 00101001=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 00101010=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 00101011=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 00101100=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 00101101=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 00101110=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 00101111=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 00110000=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 00110001=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 00110010=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 00110011=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 00110100=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 00110101=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 00110110=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 00110111=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 00111000=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 00111001=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 00111010=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 00111011=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 00111100=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 00111101=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 00111110=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 00111111=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 01000000=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 01000001=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 01000010=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 01000011=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 01000100=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 01000101=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 01000110=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 01000111=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 01001000=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 01001001=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 01001010=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 01001011=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 01001100=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 01001101=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 01001110=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 01001111=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 01010000=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 01010001=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 01010010=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 01010011=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 01010100=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 01010101=>11110000=>[1,1,1,1,5]=>[1,1,1,1,5] 01010110=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 01010111=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 01011000=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 01011001=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 01011010=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 01011011=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 01011100=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 01011101=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 01011110=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 01011111=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 01100000=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 01100001=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 01100010=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 01100011=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 01100100=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 01100101=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 01100110=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 01100111=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 01101000=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 01101001=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 01101010=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 01101011=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 01101100=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 01101101=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 01101110=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 01101111=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 01110000=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 01110001=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 01110010=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 01110011=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 01110100=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 01110101=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 01110110=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 01110111=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 01111000=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 01111001=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 01111010=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 01111011=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 01111100=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 01111101=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 01111110=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 01111111=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 10000000=>10000000=>[1,8]=>[1,1,1,1,1,1,1,2] 10000001=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 10000010=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 10000011=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 10000100=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 10000101=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 10000110=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 10000111=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 10001000=>11000000=>[1,1,7]=>[1,1,1,1,1,1,3] 10001001=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 10001010=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 10001011=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 10001100=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 10001101=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 10001110=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 10001111=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 10010000=>10100000=>[1,2,6]=>[1,1,1,1,1,2,2] 10010001=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 10010010=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 10010011=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 10010100=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 10010101=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 10010110=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 10010111=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 10011000=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 10011001=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 10011010=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 10011011=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 10011100=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 10011101=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 10011110=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 10011111=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 10100000=>10001000=>[1,4,4]=>[1,1,1,2,1,1,2] 10100001=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 10100010=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 10100011=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 10100100=>11100000=>[1,1,1,6]=>[1,1,1,1,1,4] 10100101=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 10100110=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 10100111=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 10101000=>10110000=>[1,2,1,5]=>[1,1,1,1,3,2] 10101001=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 10101010=>11110000=>[1,1,1,1,5]=>[1,1,1,1,5] 10101011=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 10101100=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 10101101=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 10101110=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 10101111=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 10110000=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 10110001=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 10110010=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 10110011=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 10110100=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 10110101=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 10110110=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 10110111=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 10111000=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 10111001=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 10111010=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 10111011=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 10111100=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 10111101=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 10111110=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 10111111=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11000000=>10000010=>[1,6,2]=>[1,2,1,1,1,1,2] 11000001=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 11000010=>10001100=>[1,4,1,3]=>[1,1,3,1,1,2] 11000011=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 11000100=>10100100=>[1,2,3,3]=>[1,1,2,1,2,2] 11000101=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 11000110=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 11000111=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 11001000=>11000010=>[1,1,5,2]=>[1,2,1,1,1,3] 11001001=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 11001010=>10111000=>[1,2,1,1,4]=>[1,1,1,4,2] 11001011=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 11001100=>11001100=>[1,1,3,1,3]=>[1,1,3,1,3] 11001101=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 11001110=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 11001111=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 11010000=>10010010=>[1,3,3,2]=>[1,2,1,2,1,2] 11010001=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 11010010=>11010100=>[1,1,2,2,3]=>[1,1,2,2,3] 11010011=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 11010100=>11100010=>[1,1,1,4,2]=>[1,2,1,1,4] 11010101=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 11010110=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 11010111=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 11011000=>10101100=>[1,2,2,1,3]=>[1,1,3,2,2] 11011001=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 11011010=>11111000=>[1,1,1,1,1,4]=>[1,1,1,6] 11011011=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 11011100=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 11011101=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 11011110=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 11011111=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11100000=>10000110=>[1,5,1,2]=>[1,3,1,1,1,2] 11100001=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 11100010=>10011010=>[1,3,1,2,2]=>[1,2,3,1,2] 11100011=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 11100100=>11001010=>[1,1,3,2,2]=>[1,2,2,1,3] 11100101=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 11100110=>10111100=>[1,2,1,1,1,3]=>[1,1,5,2] 11100111=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 11101000=>10100110=>[1,2,3,1,2]=>[1,3,1,2,2] 11101001=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 11101010=>11110010=>[1,1,1,1,3,2]=>[1,2,1,5] 11101011=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 11101100=>11011010=>[1,1,2,1,2,2]=>[1,2,3,3] 11101101=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 11101110=>11111100=>[1,1,1,1,1,1,3]=>[1,1,7] 11101111=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11110000=>10001110=>[1,4,1,1,2]=>[1,4,1,1,2] 11110001=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 11110010=>10110110=>[1,2,1,2,1,2]=>[1,3,3,2] 11110011=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 11110100=>11001110=>[1,1,3,1,1,2]=>[1,4,1,3] 11110101=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 11110110=>11111010=>[1,1,1,1,1,2,2]=>[1,2,6] 11110111=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11111000=>10011110=>[1,3,1,1,1,2]=>[1,5,1,2] 11111001=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 11111010=>11101110=>[1,1,1,2,1,1,2]=>[1,4,4] 11111011=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11111100=>10111110=>[1,2,1,1,1,1,2]=>[1,6,2] 11111101=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11111110=>11111110=>[1,1,1,1,1,1,1,2]=>[1,8] 11111111=>11111111=>[1,1,1,1,1,1,1,1,1]=>[9] 000000000=>000000000=>[10]=>[1,1,1,1,1,1,1,1,1,1] 000000001=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000000010=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000000011=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 000000100=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000000101=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 000000110=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 000000111=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 000001000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000001001=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 000001010=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 000001011=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 000001100=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 000001101=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 000001110=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 000001111=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 000010000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000010001=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 000010010=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 000010011=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 000010100=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 000010101=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 000010110=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 000010111=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 000011000=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 000011001=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 000011010=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 000011011=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 000011100=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 000011101=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 000011110=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 000011111=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 000100000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 000100001=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 000100010=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 000100011=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 000100100=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 000100101=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 000100110=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 000100111=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 000101000=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 000101001=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 000101010=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 000101011=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 000101100=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 000101101=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 000101110=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 000101111=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 000110000=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 000110001=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 000110010=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 000110011=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 000110100=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 000110101=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 000110110=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 000110111=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 000111000=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 000111001=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 000111010=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 000111011=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 000111100=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 000111101=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 000111110=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 000111111=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 001000000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 001000001=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 001000010=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 001000011=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 001000100=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 001000101=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 001000110=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 001000111=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 001001000=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 001001001=>111000000=>[1,1,1,7]=>[1,1,1,1,1,1,4] 001001010=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 001001011=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 001001100=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 001001101=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 001001110=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 001001111=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 001010000=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 001010001=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 001010010=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 001010011=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 001010100=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 001010101=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 001010110=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 001010111=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 001011000=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 001011001=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 001011010=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 001011011=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 001011100=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 001011101=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 001011110=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 001011111=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 001100000=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 001100001=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 001100010=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 001100011=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 001100100=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 001100101=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 001100110=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 001100111=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 001101000=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 001101001=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 001101010=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 001101011=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 001101100=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 001101101=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 001101110=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 001101111=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 001110000=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 001110001=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 001110010=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 001110011=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 001110100=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 001110101=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 001110110=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 001110111=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 001111000=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 001111001=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 001111010=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 001111011=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 001111100=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 001111101=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 001111110=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 001111111=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 010000000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 010000001=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 010000010=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 010000011=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 010000100=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 010000101=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 010000110=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 010000111=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 010001000=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 010001001=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 010001010=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 010001011=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 010001100=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 010001101=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 010001110=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 010001111=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 010010000=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 010010001=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 010010010=>111000000=>[1,1,1,7]=>[1,1,1,1,1,1,4] 010010011=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 010010100=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 010010101=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 010010110=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 010010111=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 010011000=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 010011001=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 010011010=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 010011011=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 010011100=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 010011101=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 010011110=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 010011111=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 010100000=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 010100001=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 010100010=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 010100011=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 010100100=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 010100101=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 010100110=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 010100111=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 010101000=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 010101001=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 010101010=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 010101011=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 010101100=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 010101101=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 010101110=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 010101111=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 010110000=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 010110001=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 010110010=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 010110011=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 010110100=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 010110101=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 010110110=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 010110111=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 010111000=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 010111001=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 010111010=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 010111011=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 010111100=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 010111101=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 010111110=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 010111111=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 011000000=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 011000001=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 011000010=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 011000011=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 011000100=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 011000101=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 011000110=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 011000111=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 011001000=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 011001001=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 011001010=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 011001011=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 011001100=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 011001101=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 011001110=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 011001111=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 011010000=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 011010001=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 011010010=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 011010011=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 011010100=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 011010101=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 011010110=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 011010111=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 011011000=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 011011001=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 011011010=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 011011011=>111111000=>[1,1,1,1,1,1,4]=>[1,1,1,7] 011011100=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 011011101=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 011011110=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 011011111=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 011100000=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 011100001=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 011100010=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 011100011=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 011100100=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 011100101=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 011100110=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 011100111=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 011101000=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 011101001=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 011101010=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 011101011=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 011101100=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 011101101=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 011101110=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 011101111=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 011110000=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 011110001=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 011110010=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 011110011=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 011110100=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 011110101=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 011110110=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 011110111=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 011111000=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 011111001=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 011111010=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 011111011=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 011111100=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 011111101=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 011111110=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 011111111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 100000000=>100000000=>[1,9]=>[1,1,1,1,1,1,1,1,2] 100000001=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 100000010=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 100000011=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 100000100=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 100000101=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 100000110=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 100000111=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 100001000=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 100001001=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 100001010=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 100001011=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 100001100=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 100001101=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 100001110=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 100001111=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 100010000=>110000000=>[1,1,8]=>[1,1,1,1,1,1,1,3] 100010001=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 100010010=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 100010011=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 100010100=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 100010101=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 100010110=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 100010111=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 100011000=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 100011001=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 100011010=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 100011011=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 100011100=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 100011101=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 100011110=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 100011111=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 100100000=>100100000=>[1,3,6]=>[1,1,1,1,1,2,1,2] 100100001=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 100100010=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 100100011=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 100100100=>111000000=>[1,1,1,7]=>[1,1,1,1,1,1,4] 100100101=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 100100110=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 100100111=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 100101000=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 100101001=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 100101010=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 100101011=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 100101100=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 100101101=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 100101110=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 100101111=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 100110000=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 100110001=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 100110010=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 100110011=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 100110100=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 100110101=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 100110110=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 100110111=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 100111000=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 100111001=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 100111010=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 100111011=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 100111100=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 100111101=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 100111110=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 100111111=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 101000000=>100001000=>[1,5,4]=>[1,1,1,2,1,1,1,2] 101000001=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 101000010=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 101000011=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 101000100=>101100000=>[1,2,1,6]=>[1,1,1,1,1,3,2] 101000101=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 101000110=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 101000111=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 101001000=>110010000=>[1,1,3,5]=>[1,1,1,1,2,1,3] 101001001=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 101001010=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 101001011=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 101001100=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 101001101=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 101001110=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 101001111=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 101010000=>100110000=>[1,3,1,5]=>[1,1,1,1,3,1,2] 101010001=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 101010010=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 101010011=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 101010100=>111100000=>[1,1,1,1,6]=>[1,1,1,1,1,5] 101010101=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 101010110=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 101010111=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 101011000=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 101011001=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 101011010=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 101011011=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 101011100=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 101011101=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 101011110=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 101011111=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 101100000=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 101100001=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 101100010=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 101100011=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 101100100=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 101100101=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 101100110=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 101100111=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 101101000=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 101101001=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 101101010=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 101101011=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 101101100=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 101101101=>111111000=>[1,1,1,1,1,1,4]=>[1,1,1,7] 101101110=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 101101111=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 101110000=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 101110001=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 101110010=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 101110011=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 101110100=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 101110101=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 101110110=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 101110111=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 101111000=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 101111001=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 101111010=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 101111011=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 101111100=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 101111101=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 101111110=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 101111111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 110000000=>100000010=>[1,7,2]=>[1,2,1,1,1,1,1,2] 110000001=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 110000010=>100001100=>[1,5,1,3]=>[1,1,3,1,1,1,2] 110000011=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 110000100=>100100100=>[1,3,3,3]=>[1,1,2,1,2,1,2] 110000101=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 110000110=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 110000111=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 110001000=>110000100=>[1,1,5,3]=>[1,1,2,1,1,1,3] 110001001=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 110001010=>100111000=>[1,3,1,1,4]=>[1,1,1,4,1,2] 110001011=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 110001100=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 110001101=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 110001110=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 110001111=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 110010000=>101000010=>[1,2,5,2]=>[1,2,1,1,1,2,2] 110010001=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 110010010=>110011000=>[1,1,3,1,4]=>[1,1,1,3,1,3] 110010011=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 110010100=>111001000=>[1,1,1,3,4]=>[1,1,1,2,1,4] 110010101=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 110010110=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 110010111=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 110011000=>110001100=>[1,1,4,1,3]=>[1,1,3,1,1,3] 110011001=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 110011010=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 110011011=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 110011100=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 110011101=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 110011110=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 110011111=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 110100000=>100010010=>[1,4,3,2]=>[1,2,1,2,1,1,2] 110100001=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 110100010=>101010100=>[1,2,2,2,3]=>[1,1,2,2,2,2] 110100011=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 110100100=>111000010=>[1,1,1,5,2]=>[1,2,1,1,1,4] 110100101=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 110100110=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 110100111=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 110101000=>101100010=>[1,2,1,4,2]=>[1,2,1,1,3,2] 110101001=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 110101010=>111110000=>[1,1,1,1,1,5]=>[1,1,1,1,6] 110101011=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 110101100=>111011000=>[1,1,1,2,1,4]=>[1,1,1,3,4] 110101101=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 110101110=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 110101111=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 110110000=>100101100=>[1,3,2,1,3]=>[1,1,3,2,1,2] 110110001=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 110110010=>101111000=>[1,2,1,1,1,4]=>[1,1,1,5,2] 110110011=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 110110100=>111001100=>[1,1,1,3,1,3]=>[1,1,3,1,4] 110110101=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 110110110=>111111000=>[1,1,1,1,1,1,4]=>[1,1,1,7] 110110111=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 110111000=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 110111001=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 110111010=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 110111011=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 110111100=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 110111101=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 110111110=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 110111111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111000000=>100000110=>[1,6,1,2]=>[1,3,1,1,1,1,2] 111000001=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 111000010=>100011010=>[1,4,1,2,2]=>[1,2,3,1,1,2] 111000011=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 111000100=>101001010=>[1,2,3,2,2]=>[1,2,2,1,2,2] 111000101=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 111000110=>100111100=>[1,3,1,1,1,3]=>[1,1,5,1,2] 111000111=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 111001000=>110000110=>[1,1,5,1,2]=>[1,3,1,1,1,3] 111001001=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 111001010=>101110010=>[1,2,1,1,3,2]=>[1,2,1,4,2] 111001011=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 111001100=>110011100=>[1,1,3,1,1,3]=>[1,1,4,1,3] 111001101=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 111001110=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 111001111=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 111010000=>100100110=>[1,3,3,1,2]=>[1,3,1,2,1,2] 111010001=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 111010010=>110101010=>[1,1,2,2,2,2]=>[1,2,2,2,3] 111010011=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 111010100=>111000110=>[1,1,1,4,1,2]=>[1,3,1,1,4] 111010101=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 111010110=>111101100=>[1,1,1,1,2,1,3]=>[1,1,3,5] 111010111=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 111011000=>101011010=>[1,2,2,1,2,2]=>[1,2,3,2,2] 111011001=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 111011010=>111110010=>[1,1,1,1,1,3,2]=>[1,2,1,6] 111011011=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 111011100=>110111100=>[1,1,2,1,1,1,3]=>[1,1,5,3] 111011101=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 111011110=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 111011111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111100000=>100001110=>[1,5,1,1,2]=>[1,4,1,1,1,2] 111100001=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 111100010=>100110110=>[1,3,1,2,1,2]=>[1,3,3,1,2] 111100011=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 111100100=>110010110=>[1,1,3,2,1,2]=>[1,3,2,1,3] 111100101=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 111100110=>101111010=>[1,2,1,1,1,2,2]=>[1,2,5,2] 111100111=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 111101000=>101001110=>[1,2,3,1,1,2]=>[1,4,1,2,2] 111101001=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 111101010=>111100110=>[1,1,1,1,3,1,2]=>[1,3,1,5] 111101011=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 111101100=>110110110=>[1,1,2,1,2,1,2]=>[1,3,3,3] 111101101=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 111101110=>111111100=>[1,1,1,1,1,1,1,3]=>[1,1,8] 111101111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111110000=>100011110=>[1,4,1,1,1,2]=>[1,5,1,1,2] 111110001=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 111110010=>101101110=>[1,2,1,2,1,1,2]=>[1,4,3,2] 111110011=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 111110100=>110011110=>[1,1,3,1,1,1,2]=>[1,5,1,3] 111110101=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 111110110=>111110110=>[1,1,1,1,1,2,1,2]=>[1,3,6] 111110111=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111111000=>100111110=>[1,3,1,1,1,1,2]=>[1,6,1,2] 111111001=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 111111010=>111011110=>[1,1,1,2,1,1,1,2]=>[1,5,4] 111111011=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111111100=>101111110=>[1,2,1,1,1,1,1,2]=>[1,7,2] 111111101=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111111110=>111111110=>[1,1,1,1,1,1,1,1,2]=>[1,9] 111111111=>111111111=>[1,1,1,1,1,1,1,1,1,1]=>[10] 1010101010=>1111100000=>[1,1,1,1,1,6]=>[1,1,1,1,1,6] 1010101100=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 1010110010=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 1010110100=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 1011001010=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 1011001100=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 1011010010=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 1011010100=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 1011100100=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] 1011101000=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 1100101010=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 1100101100=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 1100110010=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 1100110100=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 1101001010=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 1101001100=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 1101010010=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 1101010100=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 1101011000=>1011011000=>[1,2,1,2,1,4]=>[1,1,1,3,3,2] 1101100100=>1101010100=>[1,1,2,2,2,3]=>[1,1,2,2,2,3] 1101101000=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] 1110010010=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] 1110010100=>1110010010=>[1,1,1,3,3,2]=>[1,2,1,2,1,4] 1110100010=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 1111100000=>1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2] 101010101010=>111111000000=>[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7] 101010101100=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 101010110010=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 101010110100=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 101011001010=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 101011001100=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 101011010010=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 101011010100=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 101011100100=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 101011101000=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 101100101010=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 101100101100=>110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] 101100110010=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 101100110100=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 101100111000=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 101101001010=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 101101001100=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 101101010010=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 101101010100=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 101101011000=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 101101100100=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 101101101000=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 101110010010=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 101110010100=>111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] 101110100010=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 101110100100=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 101110101000=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 110010101010=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 110010101100=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 110010110010=>110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] 110010110100=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 110011001010=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 110011001100=>111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] 110011010010=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 110011010100=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 110011011000=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 110011100010=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 110011100100=>111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] 110100101010=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 110100101100=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 110100110010=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 110100110100=>111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] 110100111000=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 110101001010=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 110101001100=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 110101010010=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 110101010100=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 110101011000=>101110110000=>[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] 110101100010=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 110101100100=>110110101000=>[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] 110101101000=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 110110001100=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 110110010010=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 110110010100=>111010100100=>[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] 110110011000=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 110110100010=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 110110100100=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 110110101000=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 111000101100=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 111000110100=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 111001001010=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 111001001100=>111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] 111001010010=>111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] 111001010100=>111100100010=>[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] 111001011000=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 111001100100=>111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] 111010001010=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 111010010010=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 111010010100=>111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] 111010011000=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 111010100010=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 111011000100=>101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] 1111111110=>1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10] 1111111001=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1111100111=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1111100001=>1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 1110011111=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1110000111=>1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 1110000001=>1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2] 1001111111=>1011111110=>[1,2,1,1,1,1,1,1,2]=>[1,8,2] 1000101110=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 1000011111=>1000111110=>[1,4,1,1,1,1,2]=>[1,6,1,1,2] 1000000111=>1000001110=>[1,6,1,1,2]=>[1,4,1,1,1,1,2] 1000000001=>1000000010=>[1,8,2]=>[1,2,1,1,1,1,1,1,2] 1000000000=>1000000000=>[1,10]=>[1,1,1,1,1,1,1,1,1,2] 10000000000=>10000000000=>[1,11]=>[1,1,1,1,1,1,1,1,1,1,2] 11111111110=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2]=>[1,11] 0111111111=>1111111110=>[1,1,1,1,1,1,1,1,1,2]=>[1,10] 0000000001=>1000000000=>[1,10]=>[1,1,1,1,1,1,1,1,1,2] 01111111111=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2]=>[1,11] 0111010001=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 00000000001=>10000000000=>[1,11]=>[1,1,1,1,1,1,1,1,1,1,2] 0101010101=>1111100000=>[1,1,1,1,1,6]=>[1,1,1,1,1,6] 0101010011=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 0101001101=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 0101001011=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 0100110101=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 0100110011=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 0100101101=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 0100101011=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 0100011011=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] 0100010111=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 0011010101=>1111000010=>[1,1,1,1,5,2]=>[1,2,1,1,1,5] 0011010011=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 0011001101=>1110001100=>[1,1,1,4,1,3]=>[1,1,3,1,1,4] 0011001011=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 0010110101=>1110100100=>[1,1,1,2,3,3]=>[1,1,2,1,2,4] 0010110011=>1100111000=>[1,1,3,1,1,4]=>[1,1,1,4,1,3] 0010101101=>1101101000=>[1,1,2,1,2,4]=>[1,1,1,2,3,3] 0010101011=>1011110000=>[1,2,1,1,1,5]=>[1,1,1,1,5,2] 0010100111=>1110010010=>[1,1,1,3,3,2]=>[1,2,1,2,1,4] 0010011011=>1101010100=>[1,1,2,2,2,3]=>[1,1,2,2,2,3] 0010010111=>1100110010=>[1,1,3,1,3,2]=>[1,2,1,3,1,3] 0001101101=>1011001100=>[1,2,1,3,1,3]=>[1,1,3,1,3,2] 0001101011=>1011011000=>[1,2,1,2,1,4]=>[1,1,1,3,3,2] 0001011101=>1010101010=>[1,2,2,2,2,2]=>[1,2,2,2,2,2] 0000011111=>1000011110=>[1,5,1,1,1,2]=>[1,5,1,1,1,2] 010101010101=>111111000000=>[1,1,1,1,1,1,7]=>[1,1,1,1,1,1,7] 010101010011=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 010101001101=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 010101001011=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 010100110101=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 010100110011=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 010100101101=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 010100101011=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 010100011011=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 010100010111=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 010011010101=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 010011010011=>111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] 010011001101=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 010011001011=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 010011000111=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 010010110101=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 010010110011=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 010010101101=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 010010101011=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 010010100111=>111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] 010010011011=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 010010010111=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 010001101101=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 010001101011=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 010001011101=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 010001011011=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 010001010111=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 001101010101=>111110000010=>[1,1,1,1,1,6,2]=>[1,2,1,1,1,1,6] 001101010011=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 001101001101=>111100001100=>[1,1,1,1,5,1,3]=>[1,1,3,1,1,1,5] 001101001011=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 001100110101=>111100010100=>[1,1,1,1,4,2,3]=>[1,1,2,2,1,1,5] 001100110011=>111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] 001100101101=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 001100101011=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 001100100111=>111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] 001100011101=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 001100011011=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 001011010101=>111101000100=>[1,1,1,1,2,4,3]=>[1,1,2,1,1,2,5] 001011010011=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 001011001101=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 001011001011=>110011110000=>[1,1,3,1,1,1,5]=>[1,1,1,1,5,1,3] 001011000111=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 001010110101=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4] 001010110011=>110101110000=>[1,1,2,2,1,1,5]=>[1,1,1,1,4,2,3] 001010101101=>110111010000=>[1,1,2,1,1,2,5]=>[1,1,1,1,2,4,3] 001010101011=>101111100000=>[1,2,1,1,1,1,6]=>[1,1,1,1,1,6,2] 001010100111=>111100100010=>[1,1,1,1,3,4,2]=>[1,2,1,1,2,1,5] 001010011101=>111100001010=>[1,1,1,1,5,2,2]=>[1,2,2,1,1,1,5] 001010011011=>111010100100=>[1,1,1,2,2,3,3]=>[1,1,2,1,2,2,4] 001010010111=>111001100010=>[1,1,1,3,1,4,2]=>[1,2,1,1,3,1,4] 001001110011=>111000110010=>[1,1,1,4,1,3,2]=>[1,2,1,3,1,1,4] 001001101101=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 001001101011=>110110101000=>[1,1,2,1,2,2,4]=>[1,1,1,2,2,3,3] 001001100111=>111000101100=>[1,1,1,4,2,1,3]=>[1,1,3,2,1,1,4] 001001011101=>111001001010=>[1,1,1,3,3,2,2]=>[1,2,2,1,2,1,4] 001001011011=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 001001010111=>110011100010=>[1,1,3,1,1,4,2]=>[1,2,1,1,4,1,3] 000111010011=>110100101010=>[1,1,2,3,2,2,2]=>[1,2,2,2,1,2,3] 000111001011=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 000110110101=>101110001100=>[1,2,1,1,4,1,3]=>[1,1,3,1,1,4,2] 000110110011=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 000110101101=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 000110101011=>101110110000=>[1,2,1,1,2,1,5]=>[1,1,1,1,3,4,2] 000110100111=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 000110011011=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 000101110101=>101101001010=>[1,2,1,2,3,2,2]=>[1,2,2,1,2,3,2] 000101101101=>101011011000=>[1,2,2,1,2,1,4]=>[1,1,1,3,3,2,2] 000101101011=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 000101100111=>101010110100=>[1,2,2,2,1,2,3]=>[1,1,2,3,2,2,2] 000101011101=>101011010010=>[1,2,2,1,2,3,2]=>[1,2,1,2,3,2,2] 000100111011=>101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] 100110011001=>111000111000=>[1,1,1,4,1,1,4]=>[1,1,1,4,1,1,4] 100110001101=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 100110110001=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 100110100101=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 100011011001=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 100011001101=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 100011100101=>110010110010=>[1,1,3,2,1,3,2]=>[1,2,1,3,2,1,3] 100010011101=>101010101010=>[1,2,2,2,2,2,2]=>[1,2,2,2,2,2,2] 100010110101=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 101100011001=>101100111000=>[1,2,1,3,1,1,4]=>[1,1,1,4,1,3,2] 101100110001=>110010111000=>[1,1,3,2,1,1,4]=>[1,1,1,4,2,1,3] 101100100101=>110011101000=>[1,1,3,1,1,2,4]=>[1,1,1,2,4,1,3] 101001011001=>111010011000=>[1,1,1,2,3,1,4]=>[1,1,1,3,1,2,4] 101001001101=>111010001100=>[1,1,1,2,4,1,3]=>[1,1,3,1,1,2,4] 101001110001=>101100101100=>[1,2,1,3,2,1,3]=>[1,1,3,2,1,3,2] 101001100101=>111001101000=>[1,1,1,3,1,2,4]=>[1,1,1,2,3,1,4] 101000110101=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 101011010001=>101110011000=>[1,2,1,1,3,1,4]=>[1,1,1,3,1,4,2] 101011000101=>101011110000=>[1,2,2,1,1,1,5]=>[1,1,1,1,5,2,2] 101010010101=>111011001000=>[1,1,1,2,1,3,4]=>[1,1,1,2,1,3,4]