=>

0=>1=>1=>[1,1] 1=>0=>0=>[2] 00=>11=>11=>[1,1,1] 01=>10=>10=>[1,2] 10=>01=>10=>[1,2] 11=>00=>00=>[3] 000=>111=>111=>[1,1,1,1] 001=>110=>110=>[1,1,2] 010=>101=>110=>[1,1,2] 011=>100=>100=>[1,3] 100=>011=>110=>[1,1,2] 101=>010=>100=>[1,3] 110=>001=>100=>[1,3] 111=>000=>000=>[4] 0000=>1111=>1111=>[1,1,1,1,1] 0001=>1110=>1110=>[1,1,1,2] 0010=>1101=>1110=>[1,1,1,2] 0011=>1100=>1010=>[1,2,2] 0100=>1011=>1110=>[1,1,1,2] 0101=>1010=>1100=>[1,1,3] 0110=>1001=>1010=>[1,2,2] 0111=>1000=>1000=>[1,4] 1000=>0111=>1110=>[1,1,1,2] 1001=>0110=>1010=>[1,2,2] 1010=>0101=>1100=>[1,1,3] 1011=>0100=>1000=>[1,4] 1100=>0011=>1010=>[1,2,2] 1101=>0010=>1000=>[1,4] 1110=>0001=>1000=>[1,4] 1111=>0000=>0000=>[5] 00000=>11111=>11111=>[1,1,1,1,1,1] 00001=>11110=>11110=>[1,1,1,1,2] 00010=>11101=>11110=>[1,1,1,1,2] 00011=>11100=>10110=>[1,2,1,2] 00100=>11011=>11110=>[1,1,1,1,2] 00101=>11010=>11100=>[1,1,1,3] 00110=>11001=>10110=>[1,2,1,2] 00111=>11000=>10010=>[1,3,2] 01000=>10111=>11110=>[1,1,1,1,2] 01001=>10110=>11100=>[1,1,1,3] 01010=>10101=>11100=>[1,1,1,3] 01011=>10100=>11000=>[1,1,4] 01100=>10011=>10110=>[1,2,1,2] 01101=>10010=>11000=>[1,1,4] 01110=>10001=>10010=>[1,3,2] 01111=>10000=>10000=>[1,5] 10000=>01111=>11110=>[1,1,1,1,2] 10001=>01110=>10110=>[1,2,1,2] 10010=>01101=>11100=>[1,1,1,3] 10011=>01100=>10010=>[1,3,2] 10100=>01011=>11100=>[1,1,1,3] 10101=>01010=>11000=>[1,1,4] 10110=>01001=>11000=>[1,1,4] 10111=>01000=>10000=>[1,5] 11000=>00111=>10110=>[1,2,1,2] 11001=>00110=>10010=>[1,3,2] 11010=>00101=>11000=>[1,1,4] 11011=>00100=>10000=>[1,5] 11100=>00011=>10010=>[1,3,2] 11101=>00010=>10000=>[1,5] 11110=>00001=>10000=>[1,5] 11111=>00000=>00000=>[6] 000000=>111111=>111111=>[1,1,1,1,1,1,1] 000001=>111110=>111110=>[1,1,1,1,1,2] 000010=>111101=>111110=>[1,1,1,1,1,2] 000011=>111100=>101110=>[1,2,1,1,2] 000100=>111011=>111110=>[1,1,1,1,1,2] 000101=>111010=>111010=>[1,1,1,2,2] 000110=>111001=>101110=>[1,2,1,1,2] 000111=>111000=>100110=>[1,3,1,2] 001000=>110111=>111110=>[1,1,1,1,1,2] 001001=>110110=>111100=>[1,1,1,1,3] 001010=>110101=>111010=>[1,1,1,2,2] 001011=>110100=>110010=>[1,1,3,2] 001100=>110011=>101110=>[1,2,1,1,2] 001101=>110010=>101100=>[1,2,1,3] 001110=>110001=>100110=>[1,3,1,2] 001111=>110000=>100010=>[1,4,2] 010000=>101111=>111110=>[1,1,1,1,1,2] 010001=>101110=>111010=>[1,1,1,2,2] 010010=>101101=>111100=>[1,1,1,1,3] 010011=>101100=>101100=>[1,2,1,3] 010100=>101011=>111010=>[1,1,1,2,2] 010101=>101010=>111000=>[1,1,1,4] 010110=>101001=>110010=>[1,1,3,2] 010111=>101000=>101000=>[1,2,4] 011000=>100111=>101110=>[1,2,1,1,2] 011001=>100110=>110010=>[1,1,3,2] 011010=>100101=>101100=>[1,2,1,3] 011011=>100100=>110000=>[1,1,5] 011100=>100011=>100110=>[1,3,1,2] 011101=>100010=>101000=>[1,2,4] 011110=>100001=>100010=>[1,4,2] 011111=>100000=>100000=>[1,6] 100000=>011111=>111110=>[1,1,1,1,1,2] 100001=>011110=>101110=>[1,2,1,1,2] 100010=>011101=>111010=>[1,1,1,2,2] 100011=>011100=>100110=>[1,3,1,2] 100100=>011011=>111100=>[1,1,1,1,3] 100101=>011010=>110010=>[1,1,3,2] 100110=>011001=>101100=>[1,2,1,3] 100111=>011000=>100010=>[1,4,2] 101000=>010111=>111010=>[1,1,1,2,2] 101001=>010110=>101100=>[1,2,1,3] 101010=>010101=>111000=>[1,1,1,4] 101011=>010100=>101000=>[1,2,4] 101100=>010011=>110010=>[1,1,3,2] 101101=>010010=>110000=>[1,1,5] 101110=>010001=>101000=>[1,2,4] 101111=>010000=>100000=>[1,6] 110000=>001111=>101110=>[1,2,1,1,2] 110001=>001110=>100110=>[1,3,1,2] 110010=>001101=>110010=>[1,1,3,2] 110011=>001100=>100010=>[1,4,2] 110100=>001011=>101100=>[1,2,1,3] 110101=>001010=>101000=>[1,2,4] 110110=>001001=>110000=>[1,1,5] 110111=>001000=>100000=>[1,6] 111000=>000111=>100110=>[1,3,1,2] 111001=>000110=>100010=>[1,4,2] 111010=>000101=>101000=>[1,2,4] 111011=>000100=>100000=>[1,6] 111100=>000011=>100010=>[1,4,2] 111101=>000010=>100000=>[1,6] 111110=>000001=>100000=>[1,6] 111111=>000000=>000000=>[7] 0000000=>1111111=>1111111=>[1,1,1,1,1,1,1,1] 0000001=>1111110=>1111110=>[1,1,1,1,1,1,2] 0000010=>1111101=>1111110=>[1,1,1,1,1,1,2] 0000011=>1111100=>1011110=>[1,2,1,1,1,2] 0000100=>1111011=>1111110=>[1,1,1,1,1,1,2] 0000101=>1111010=>1110110=>[1,1,1,2,1,2] 0000110=>1111001=>1011110=>[1,2,1,1,1,2] 0000111=>1111000=>1001110=>[1,3,1,1,2] 0001000=>1110111=>1111110=>[1,1,1,1,1,1,2] 0001001=>1110110=>1111100=>[1,1,1,1,1,3] 0001010=>1110101=>1110110=>[1,1,1,2,1,2] 0001011=>1110100=>1100110=>[1,1,3,1,2] 0001100=>1110011=>1011110=>[1,2,1,1,1,2] 0001101=>1110010=>1011010=>[1,2,1,2,2] 0001110=>1110001=>1001110=>[1,3,1,1,2] 0001111=>1110000=>1000110=>[1,4,1,2] 0010000=>1101111=>1111110=>[1,1,1,1,1,1,2] 0010001=>1101110=>1111100=>[1,1,1,1,1,3] 0010010=>1101101=>1111100=>[1,1,1,1,1,3] 0010011=>1101100=>1101100=>[1,1,2,1,3] 0010100=>1101011=>1110110=>[1,1,1,2,1,2] 0010101=>1101010=>1111000=>[1,1,1,1,4] 0010110=>1101001=>1100110=>[1,1,3,1,2] 0010111=>1101000=>1010010=>[1,2,3,2] 0011000=>1100111=>1011110=>[1,2,1,1,1,2] 0011001=>1100110=>1101100=>[1,1,2,1,3] 0011010=>1100101=>1011010=>[1,2,1,2,2] 0011011=>1100100=>1100100=>[1,1,3,3] 0011100=>1100011=>1001110=>[1,3,1,1,2] 0011101=>1100010=>1001100=>[1,3,1,3] 0011110=>1100001=>1000110=>[1,4,1,2] 0011111=>1100000=>1000010=>[1,5,2] 0100000=>1011111=>1111110=>[1,1,1,1,1,1,2] 0100001=>1011110=>1110110=>[1,1,1,2,1,2] 0100010=>1011101=>1111100=>[1,1,1,1,1,3] 0100011=>1011100=>1011010=>[1,2,1,2,2] 0100100=>1011011=>1111100=>[1,1,1,1,1,3] 0100101=>1011010=>1111000=>[1,1,1,1,4] 0100110=>1011001=>1101100=>[1,1,2,1,3] 0100111=>1011000=>1001100=>[1,3,1,3] 0101000=>1010111=>1110110=>[1,1,1,2,1,2] 0101001=>1010110=>1111000=>[1,1,1,1,4] 0101010=>1010101=>1111000=>[1,1,1,1,4] 0101011=>1010100=>1110000=>[1,1,1,5] 0101100=>1010011=>1100110=>[1,1,3,1,2] 0101101=>1010010=>1110000=>[1,1,1,5] 0101110=>1010001=>1010010=>[1,2,3,2] 0101111=>1010000=>1001000=>[1,3,4] 0110000=>1001111=>1011110=>[1,2,1,1,1,2] 0110001=>1001110=>1100110=>[1,1,3,1,2] 0110010=>1001101=>1101100=>[1,1,2,1,3] 0110011=>1001100=>1100100=>[1,1,3,3] 0110100=>1001011=>1011010=>[1,2,1,2,2] 0110101=>1001010=>1110000=>[1,1,1,5] 0110110=>1001001=>1100100=>[1,1,3,3] 0110111=>1001000=>1100000=>[1,1,6] 0111000=>1000111=>1001110=>[1,3,1,1,2] 0111001=>1000110=>1010010=>[1,2,3,2] 0111010=>1000101=>1001100=>[1,3,1,3] 0111011=>1000100=>1100000=>[1,1,6] 0111100=>1000011=>1000110=>[1,4,1,2] 0111101=>1000010=>1001000=>[1,3,4] 0111110=>1000001=>1000010=>[1,5,2] 0111111=>1000000=>1000000=>[1,7] 1000000=>0111111=>1111110=>[1,1,1,1,1,1,2] 1000001=>0111110=>1011110=>[1,2,1,1,1,2] 1000010=>0111101=>1110110=>[1,1,1,2,1,2] 1000011=>0111100=>1001110=>[1,3,1,1,2] 1000100=>0111011=>1111100=>[1,1,1,1,1,3] 1000101=>0111010=>1100110=>[1,1,3,1,2] 1000110=>0111001=>1011010=>[1,2,1,2,2] 1000111=>0111000=>1000110=>[1,4,1,2] 1001000=>0110111=>1111100=>[1,1,1,1,1,3] 1001001=>0110110=>1101100=>[1,1,2,1,3] 1001010=>0110101=>1111000=>[1,1,1,1,4] 1001011=>0110100=>1010010=>[1,2,3,2] 1001100=>0110011=>1101100=>[1,1,2,1,3] 1001101=>0110010=>1100100=>[1,1,3,3] 1001110=>0110001=>1001100=>[1,3,1,3] 1001111=>0110000=>1000010=>[1,5,2] 1010000=>0101111=>1110110=>[1,1,1,2,1,2] 1010001=>0101110=>1011010=>[1,2,1,2,2] 1010010=>0101101=>1111000=>[1,1,1,1,4] 1010011=>0101100=>1001100=>[1,3,1,3] 1010100=>0101011=>1111000=>[1,1,1,1,4] 1010101=>0101010=>1110000=>[1,1,1,5] 1010110=>0101001=>1110000=>[1,1,1,5] 1010111=>0101000=>1001000=>[1,3,4] 1011000=>0100111=>1100110=>[1,1,3,1,2] 1011001=>0100110=>1100100=>[1,1,3,3] 1011010=>0100101=>1110000=>[1,1,1,5] 1011011=>0100100=>1100000=>[1,1,6] 1011100=>0100011=>1010010=>[1,2,3,2] 1011101=>0100010=>1100000=>[1,1,6] 1011110=>0100001=>1001000=>[1,3,4] 1011111=>0100000=>1000000=>[1,7] 1100000=>0011111=>1011110=>[1,2,1,1,1,2] 1100001=>0011110=>1001110=>[1,3,1,1,2] 1100010=>0011101=>1100110=>[1,1,3,1,2] 1100011=>0011100=>1000110=>[1,4,1,2] 1100100=>0011011=>1101100=>[1,1,2,1,3] 1100101=>0011010=>1010010=>[1,2,3,2] 1100110=>0011001=>1100100=>[1,1,3,3] 1100111=>0011000=>1000010=>[1,5,2] 1101000=>0010111=>1011010=>[1,2,1,2,2] 1101001=>0010110=>1001100=>[1,3,1,3] 1101010=>0010101=>1110000=>[1,1,1,5] 1101011=>0010100=>1001000=>[1,3,4] 1101100=>0010011=>1100100=>[1,1,3,3] 1101101=>0010010=>1100000=>[1,1,6] 1101110=>0010001=>1100000=>[1,1,6] 1101111=>0010000=>1000000=>[1,7] 1110000=>0001111=>1001110=>[1,3,1,1,2] 1110001=>0001110=>1000110=>[1,4,1,2] 1110010=>0001101=>1010010=>[1,2,3,2] 1110011=>0001100=>1000010=>[1,5,2] 1110100=>0001011=>1001100=>[1,3,1,3] 1110101=>0001010=>1001000=>[1,3,4] 1110110=>0001001=>1100000=>[1,1,6] 1110111=>0001000=>1000000=>[1,7] 1111000=>0000111=>1000110=>[1,4,1,2] 1111001=>0000110=>1000010=>[1,5,2] 1111010=>0000101=>1001000=>[1,3,4] 1111011=>0000100=>1000000=>[1,7] 1111100=>0000011=>1000010=>[1,5,2] 1111101=>0000010=>1000000=>[1,7] 1111110=>0000001=>1000000=>[1,7] 1111111=>0000000=>0000000=>[8] 00000000=>11111111=>11111111=>[1,1,1,1,1,1,1,1,1] 00000001=>11111110=>11111110=>[1,1,1,1,1,1,1,2] 00000010=>11111101=>11111110=>[1,1,1,1,1,1,1,2] 00000011=>11111100=>10111110=>[1,2,1,1,1,1,2] 00000100=>11111011=>11111110=>[1,1,1,1,1,1,1,2] 00000101=>11111010=>11101110=>[1,1,1,2,1,1,2] 00000110=>11111001=>10111110=>[1,2,1,1,1,1,2] 00000111=>11111000=>10011110=>[1,3,1,1,1,2] 00001000=>11110111=>11111110=>[1,1,1,1,1,1,1,2] 00001001=>11110110=>11111010=>[1,1,1,1,1,2,2] 00001010=>11110101=>11101110=>[1,1,1,2,1,1,2] 00001011=>11110100=>11001110=>[1,1,3,1,1,2] 00001100=>11110011=>10111110=>[1,2,1,1,1,1,2] 00001101=>11110010=>10110110=>[1,2,1,2,1,2] 00001110=>11110001=>10011110=>[1,3,1,1,1,2] 00001111=>11110000=>10001110=>[1,4,1,1,2] 00010000=>11101111=>11111110=>[1,1,1,1,1,1,1,2] 00010001=>11101110=>11111100=>[1,1,1,1,1,1,3] 00010010=>11101101=>11111010=>[1,1,1,1,1,2,2] 00010011=>11101100=>11011010=>[1,1,2,1,2,2] 00010100=>11101011=>11101110=>[1,1,1,2,1,1,2] 00010101=>11101010=>11110010=>[1,1,1,1,3,2] 00010110=>11101001=>11001110=>[1,1,3,1,1,2] 00010111=>11101000=>10100110=>[1,2,3,1,2] 00011000=>11100111=>10111110=>[1,2,1,1,1,1,2] 00011001=>11100110=>10111100=>[1,2,1,1,1,3] 00011010=>11100101=>10110110=>[1,2,1,2,1,2] 00011011=>11100100=>11001010=>[1,1,3,2,2] 00011100=>11100011=>10011110=>[1,3,1,1,1,2] 00011101=>11100010=>10011010=>[1,3,1,2,2] 00011110=>11100001=>10001110=>[1,4,1,1,2] 00011111=>11100000=>10000110=>[1,5,1,2] 00100000=>11011111=>11111110=>[1,1,1,1,1,1,1,2] 00100001=>11011110=>11111010=>[1,1,1,1,1,2,2] 00100010=>11011101=>11111100=>[1,1,1,1,1,1,3] 00100011=>11011100=>10111100=>[1,2,1,1,1,3] 00100100=>11011011=>11111010=>[1,1,1,1,1,2,2] 00100101=>11011010=>11111000=>[1,1,1,1,1,4] 00100110=>11011001=>11011010=>[1,1,2,1,2,2] 00100111=>11011000=>10101100=>[1,2,2,1,3] 00101000=>11010111=>11101110=>[1,1,1,2,1,1,2] 00101001=>11010110=>11111000=>[1,1,1,1,1,4] 00101010=>11010101=>11110010=>[1,1,1,1,3,2] 00101011=>11010100=>11100010=>[1,1,1,4,2] 00101100=>11010011=>11001110=>[1,1,3,1,1,2] 00101101=>11010010=>11010100=>[1,1,2,2,3] 00101110=>11010001=>10100110=>[1,2,3,1,2] 00101111=>11010000=>10010010=>[1,3,3,2] 00110000=>11001111=>10111110=>[1,2,1,1,1,1,2] 00110001=>11001110=>11011010=>[1,1,2,1,2,2] 00110010=>11001101=>10111100=>[1,2,1,1,1,3] 00110011=>11001100=>11001100=>[1,1,3,1,3] 00110100=>11001011=>10110110=>[1,2,1,2,1,2] 00110101=>11001010=>10111000=>[1,2,1,1,4] 00110110=>11001001=>11001010=>[1,1,3,2,2] 00110111=>11001000=>11000010=>[1,1,5,2] 00111000=>11000111=>10011110=>[1,3,1,1,1,2] 00111001=>11000110=>10101100=>[1,2,2,1,3] 00111010=>11000101=>10011010=>[1,3,1,2,2] 00111011=>11000100=>10100100=>[1,2,3,3] 00111100=>11000011=>10001110=>[1,4,1,1,2] 00111101=>11000010=>10001100=>[1,4,1,3] 00111110=>11000001=>10000110=>[1,5,1,2] 00111111=>11000000=>10000010=>[1,6,2] 01000000=>10111111=>11111110=>[1,1,1,1,1,1,1,2] 01000001=>10111110=>11101110=>[1,1,1,2,1,1,2] 01000010=>10111101=>11111010=>[1,1,1,1,1,2,2] 01000011=>10111100=>10110110=>[1,2,1,2,1,2] 01000100=>10111011=>11111100=>[1,1,1,1,1,1,3] 01000101=>10111010=>11110010=>[1,1,1,1,3,2] 01000110=>10111001=>10111100=>[1,2,1,1,1,3] 01000111=>10111000=>10011010=>[1,3,1,2,2] 01001000=>10110111=>11111010=>[1,1,1,1,1,2,2] 01001001=>10110110=>11111000=>[1,1,1,1,1,4] 01001010=>10110101=>11111000=>[1,1,1,1,1,4] 01001011=>10110100=>11010100=>[1,1,2,2,3] 01001100=>10110011=>11011010=>[1,1,2,1,2,2] 01001101=>10110010=>10111000=>[1,2,1,1,4] 01001110=>10110001=>10101100=>[1,2,2,1,3] 01001111=>10110000=>10001100=>[1,4,1,3] 01010000=>10101111=>11101110=>[1,1,1,2,1,1,2] 01010001=>10101110=>11110010=>[1,1,1,1,3,2] 01010010=>10101101=>11111000=>[1,1,1,1,1,4] 01010011=>10101100=>10111000=>[1,2,1,1,4] 01010100=>10101011=>11110010=>[1,1,1,1,3,2] 01010101=>10101010=>11110000=>[1,1,1,1,5] 01010110=>10101001=>11100010=>[1,1,1,4,2] 01010111=>10101000=>10110000=>[1,2,1,5] 01011000=>10100111=>11001110=>[1,1,3,1,1,2] 01011001=>10100110=>11100010=>[1,1,1,4,2] 01011010=>10100101=>11010100=>[1,1,2,2,3] 01011011=>10100100=>11100000=>[1,1,1,6] 01011100=>10100011=>10100110=>[1,2,3,1,2] 01011101=>10100010=>10110000=>[1,2,1,5] 01011110=>10100001=>10010010=>[1,3,3,2] 01011111=>10100000=>10001000=>[1,4,4] 01100000=>10011111=>10111110=>[1,2,1,1,1,1,2] 01100001=>10011110=>11001110=>[1,1,3,1,1,2] 01100010=>10011101=>11011010=>[1,1,2,1,2,2] 01100011=>10011100=>11001010=>[1,1,3,2,2] 01100100=>10011011=>10111100=>[1,2,1,1,1,3] 01100101=>10011010=>11100010=>[1,1,1,4,2] 01100110=>10011001=>11001100=>[1,1,3,1,3] 01100111=>10011000=>10100100=>[1,2,3,3] 01101000=>10010111=>10110110=>[1,2,1,2,1,2] 01101001=>10010110=>11010100=>[1,1,2,2,3] 01101010=>10010101=>10111000=>[1,2,1,1,4] 01101011=>10010100=>11100000=>[1,1,1,6] 01101100=>10010011=>11001010=>[1,1,3,2,2] 01101101=>10010010=>11100000=>[1,1,1,6] 01101110=>10010001=>11000010=>[1,1,5,2] 01101111=>10010000=>10100000=>[1,2,6] 01110000=>10001111=>10011110=>[1,3,1,1,1,2] 01110001=>10001110=>10100110=>[1,2,3,1,2] 01110010=>10001101=>10101100=>[1,2,2,1,3] 01110011=>10001100=>11000010=>[1,1,5,2] 01110100=>10001011=>10011010=>[1,3,1,2,2] 01110101=>10001010=>10110000=>[1,2,1,5] 01110110=>10001001=>10100100=>[1,2,3,3] 01110111=>10001000=>11000000=>[1,1,7] 01111000=>10000111=>10001110=>[1,4,1,1,2] 01111001=>10000110=>10010010=>[1,3,3,2] 01111010=>10000101=>10001100=>[1,4,1,3] 01111011=>10000100=>10100000=>[1,2,6] 01111100=>10000011=>10000110=>[1,5,1,2] 01111101=>10000010=>10001000=>[1,4,4] 01111110=>10000001=>10000010=>[1,6,2] 01111111=>10000000=>10000000=>[1,8] 10000000=>01111111=>11111110=>[1,1,1,1,1,1,1,2] 10000001=>01111110=>10111110=>[1,2,1,1,1,1,2] 10000010=>01111101=>11101110=>[1,1,1,2,1,1,2] 10000011=>01111100=>10011110=>[1,3,1,1,1,2] 10000100=>01111011=>11111010=>[1,1,1,1,1,2,2] 10000101=>01111010=>11001110=>[1,1,3,1,1,2] 10000110=>01111001=>10110110=>[1,2,1,2,1,2] 10000111=>01111000=>10001110=>[1,4,1,1,2] 10001000=>01110111=>11111100=>[1,1,1,1,1,1,3] 10001001=>01110110=>11011010=>[1,1,2,1,2,2] 10001010=>01110101=>11110010=>[1,1,1,1,3,2] 10001011=>01110100=>10100110=>[1,2,3,1,2] 10001100=>01110011=>10111100=>[1,2,1,1,1,3] 10001101=>01110010=>11001010=>[1,1,3,2,2] 10001110=>01110001=>10011010=>[1,3,1,2,2] 10001111=>01110000=>10000110=>[1,5,1,2] 10010000=>01101111=>11111010=>[1,1,1,1,1,2,2] 10010001=>01101110=>10111100=>[1,2,1,1,1,3] 10010010=>01101101=>11111000=>[1,1,1,1,1,4] 10010011=>01101100=>10101100=>[1,2,2,1,3] 10010100=>01101011=>11111000=>[1,1,1,1,1,4] 10010101=>01101010=>11100010=>[1,1,1,4,2] 10010110=>01101001=>11010100=>[1,1,2,2,3] 10010111=>01101000=>10010010=>[1,3,3,2] 10011000=>01100111=>11011010=>[1,1,2,1,2,2] 10011001=>01100110=>11001100=>[1,1,3,1,3] 10011010=>01100101=>10111000=>[1,2,1,1,4] 10011011=>01100100=>11000010=>[1,1,5,2] 10011100=>01100011=>10101100=>[1,2,2,1,3] 10011101=>01100010=>10100100=>[1,2,3,3] 10011110=>01100001=>10001100=>[1,4,1,3] 10011111=>01100000=>10000010=>[1,6,2] 10100000=>01011111=>11101110=>[1,1,1,2,1,1,2] 10100001=>01011110=>10110110=>[1,2,1,2,1,2] 10100010=>01011101=>11110010=>[1,1,1,1,3,2] 10100011=>01011100=>10011010=>[1,3,1,2,2] 10100100=>01011011=>11111000=>[1,1,1,1,1,4] 10100101=>01011010=>11010100=>[1,1,2,2,3] 10100110=>01011001=>10111000=>[1,2,1,1,4] 10100111=>01011000=>10001100=>[1,4,1,3] 10101000=>01010111=>11110010=>[1,1,1,1,3,2] 10101001=>01010110=>10111000=>[1,2,1,1,4] 10101010=>01010101=>11110000=>[1,1,1,1,5] 10101011=>01010100=>10110000=>[1,2,1,5] 10101100=>01010011=>11100010=>[1,1,1,4,2] 10101101=>01010010=>11100000=>[1,1,1,6] 10101110=>01010001=>10110000=>[1,2,1,5] 10101111=>01010000=>10001000=>[1,4,4] 10110000=>01001111=>11001110=>[1,1,3,1,1,2] 10110001=>01001110=>11001010=>[1,1,3,2,2] 10110010=>01001101=>11100010=>[1,1,1,4,2] 10110011=>01001100=>10100100=>[1,2,3,3] 10110100=>01001011=>11010100=>[1,1,2,2,3] 10110101=>01001010=>11100000=>[1,1,1,6] 10110110=>01001001=>11100000=>[1,1,1,6] 10110111=>01001000=>10100000=>[1,2,6] 10111000=>01000111=>10100110=>[1,2,3,1,2] 10111001=>01000110=>11000010=>[1,1,5,2] 10111010=>01000101=>10110000=>[1,2,1,5] 10111011=>01000100=>11000000=>[1,1,7] 10111100=>01000011=>10010010=>[1,3,3,2] 10111101=>01000010=>10100000=>[1,2,6] 10111110=>01000001=>10001000=>[1,4,4] 10111111=>01000000=>10000000=>[1,8] 11000000=>00111111=>10111110=>[1,2,1,1,1,1,2] 11000001=>00111110=>10011110=>[1,3,1,1,1,2] 11000010=>00111101=>11001110=>[1,1,3,1,1,2] 11000011=>00111100=>10001110=>[1,4,1,1,2] 11000100=>00111011=>11011010=>[1,1,2,1,2,2] 11000101=>00111010=>10100110=>[1,2,3,1,2] 11000110=>00111001=>11001010=>[1,1,3,2,2] 11000111=>00111000=>10000110=>[1,5,1,2] 11001000=>00110111=>10111100=>[1,2,1,1,1,3] 11001001=>00110110=>10101100=>[1,2,2,1,3] 11001010=>00110101=>11100010=>[1,1,1,4,2] 11001011=>00110100=>10010010=>[1,3,3,2] 11001100=>00110011=>11001100=>[1,1,3,1,3] 11001101=>00110010=>11000010=>[1,1,5,2] 11001110=>00110001=>10100100=>[1,2,3,3] 11001111=>00110000=>10000010=>[1,6,2] 11010000=>00101111=>10110110=>[1,2,1,2,1,2] 11010001=>00101110=>10011010=>[1,3,1,2,2] 11010010=>00101101=>11010100=>[1,1,2,2,3] 11010011=>00101100=>10001100=>[1,4,1,3] 11010100=>00101011=>10111000=>[1,2,1,1,4] 11010101=>00101010=>10110000=>[1,2,1,5] 11010110=>00101001=>11100000=>[1,1,1,6] 11010111=>00101000=>10001000=>[1,4,4] 11011000=>00100111=>11001010=>[1,1,3,2,2] 11011001=>00100110=>10100100=>[1,2,3,3] 11011010=>00100101=>11100000=>[1,1,1,6] 11011011=>00100100=>10100000=>[1,2,6] 11011100=>00100011=>11000010=>[1,1,5,2] 11011101=>00100010=>11000000=>[1,1,7] 11011110=>00100001=>10100000=>[1,2,6] 11011111=>00100000=>10000000=>[1,8] 11100000=>00011111=>10011110=>[1,3,1,1,1,2] 11100001=>00011110=>10001110=>[1,4,1,1,2] 11100010=>00011101=>10100110=>[1,2,3,1,2] 11100011=>00011100=>10000110=>[1,5,1,2] 11100100=>00011011=>10101100=>[1,2,2,1,3] 11100101=>00011010=>10010010=>[1,3,3,2] 11100110=>00011001=>11000010=>[1,1,5,2] 11100111=>00011000=>10000010=>[1,6,2] 11101000=>00010111=>10011010=>[1,3,1,2,2] 11101001=>00010110=>10001100=>[1,4,1,3] 11101010=>00010101=>10110000=>[1,2,1,5] 11101011=>00010100=>10001000=>[1,4,4] 11101100=>00010011=>10100100=>[1,2,3,3] 11101101=>00010010=>10100000=>[1,2,6] 11101110=>00010001=>11000000=>[1,1,7] 11101111=>00010000=>10000000=>[1,8] 11110000=>00001111=>10001110=>[1,4,1,1,2] 11110001=>00001110=>10000110=>[1,5,1,2] 11110010=>00001101=>10010010=>[1,3,3,2] 11110011=>00001100=>10000010=>[1,6,2] 11110100=>00001011=>10001100=>[1,4,1,3] 11110101=>00001010=>10001000=>[1,4,4] 11110110=>00001001=>10100000=>[1,2,6] 11110111=>00001000=>10000000=>[1,8] 11111000=>00000111=>10000110=>[1,5,1,2] 11111001=>00000110=>10000010=>[1,6,2] 11111010=>00000101=>10001000=>[1,4,4] 11111011=>00000100=>10000000=>[1,8] 11111100=>00000011=>10000010=>[1,6,2] 11111101=>00000010=>10000000=>[1,8] 11111110=>00000001=>10000000=>[1,8] 11111111=>00000000=>00000000=>[9] 000000000=>111111111=>111111111=>[1,1,1,1,1,1,1,1,1,1] 000000001=>111111110=>111111110=>[1,1,1,1,1,1,1,1,2] 000000010=>111111101=>111111110=>[1,1,1,1,1,1,1,1,2] 000000011=>111111100=>101111110=>[1,2,1,1,1,1,1,2] 000000100=>111111011=>111111110=>[1,1,1,1,1,1,1,1,2] 000000101=>111111010=>111011110=>[1,1,1,2,1,1,1,2] 000000110=>111111001=>101111110=>[1,2,1,1,1,1,1,2] 000000111=>111111000=>100111110=>[1,3,1,1,1,1,2] 000001000=>111110111=>111111110=>[1,1,1,1,1,1,1,1,2] 000001001=>111110110=>111110110=>[1,1,1,1,1,2,1,2] 000001010=>111110101=>111011110=>[1,1,1,2,1,1,1,2] 000001011=>111110100=>110011110=>[1,1,3,1,1,1,2] 000001100=>111110011=>101111110=>[1,2,1,1,1,1,1,2] 000001101=>111110010=>101101110=>[1,2,1,2,1,1,2] 000001110=>111110001=>100111110=>[1,3,1,1,1,1,2] 000001111=>111110000=>100011110=>[1,4,1,1,1,2] 000010000=>111101111=>111111110=>[1,1,1,1,1,1,1,1,2] 000010001=>111101110=>111111100=>[1,1,1,1,1,1,1,3] 000010010=>111101101=>111110110=>[1,1,1,1,1,2,1,2] 000010011=>111101100=>110110110=>[1,1,2,1,2,1,2] 000010100=>111101011=>111011110=>[1,1,1,2,1,1,1,2] 000010101=>111101010=>111100110=>[1,1,1,1,3,1,2] 000010110=>111101001=>110011110=>[1,1,3,1,1,1,2] 000010111=>111101000=>101001110=>[1,2,3,1,1,2] 000011000=>111100111=>101111110=>[1,2,1,1,1,1,1,2] 000011001=>111100110=>101111010=>[1,2,1,1,1,2,2] 000011010=>111100101=>101101110=>[1,2,1,2,1,1,2] 000011011=>111100100=>110010110=>[1,1,3,2,1,2] 000011100=>111100011=>100111110=>[1,3,1,1,1,1,2] 000011101=>111100010=>100110110=>[1,3,1,2,1,2] 000011110=>111100001=>100011110=>[1,4,1,1,1,2] 000011111=>111100000=>100001110=>[1,5,1,1,2] 000100000=>111011111=>111111110=>[1,1,1,1,1,1,1,1,2] 000100001=>111011110=>111111100=>[1,1,1,1,1,1,1,3] 000100010=>111011101=>111111100=>[1,1,1,1,1,1,1,3] 000100011=>111011100=>110111100=>[1,1,2,1,1,1,3] 000100100=>111011011=>111110110=>[1,1,1,1,1,2,1,2] 000100101=>111011010=>111110010=>[1,1,1,1,1,3,2] 000100110=>111011001=>110110110=>[1,1,2,1,2,1,2] 000100111=>111011000=>101011010=>[1,2,2,1,2,2] 000101000=>111010111=>111011110=>[1,1,1,2,1,1,1,2] 000101001=>111010110=>111101100=>[1,1,1,1,2,1,3] 000101010=>111010101=>111100110=>[1,1,1,1,3,1,2] 000101011=>111010100=>111000110=>[1,1,1,4,1,2] 000101100=>111010011=>110011110=>[1,1,3,1,1,1,2] 000101101=>111010010=>110101010=>[1,1,2,2,2,2] 000101110=>111010001=>101001110=>[1,2,3,1,1,2] 000101111=>111010000=>100100110=>[1,3,3,1,2] 000110000=>111001111=>101111110=>[1,2,1,1,1,1,1,2] 000110001=>111001110=>110111100=>[1,1,2,1,1,1,3] 000110010=>111001101=>101111010=>[1,2,1,1,1,2,2] 000110011=>111001100=>110011100=>[1,1,3,1,1,3] 000110100=>111001011=>101101110=>[1,2,1,2,1,1,2] 000110101=>111001010=>101110010=>[1,2,1,1,3,2] 000110110=>111001001=>110010110=>[1,1,3,2,1,2] 000110111=>111001000=>110000110=>[1,1,5,1,2] 000111000=>111000111=>100111110=>[1,3,1,1,1,1,2] 000111001=>111000110=>100111100=>[1,3,1,1,1,3] 000111010=>111000101=>100110110=>[1,3,1,2,1,2] 000111011=>111000100=>101001010=>[1,2,3,2,2] 000111100=>111000011=>100011110=>[1,4,1,1,1,2] 000111101=>111000010=>100011010=>[1,4,1,2,2] 000111110=>111000001=>100001110=>[1,5,1,1,2] 000111111=>111000000=>100000110=>[1,6,1,2] 001000000=>110111111=>111111110=>[1,1,1,1,1,1,1,1,2] 001000001=>110111110=>111110110=>[1,1,1,1,1,2,1,2] 001000010=>110111101=>111111100=>[1,1,1,1,1,1,1,3] 001000011=>110111100=>101111010=>[1,2,1,1,1,2,2] 001000100=>110111011=>111111100=>[1,1,1,1,1,1,1,3] 001000101=>110111010=>111101100=>[1,1,1,1,2,1,3] 001000110=>110111001=>110111100=>[1,1,2,1,1,1,3] 001000111=>110111000=>100111100=>[1,3,1,1,1,3] 001001000=>110110111=>111110110=>[1,1,1,1,1,2,1,2] 001001001=>110110110=>111111000=>[1,1,1,1,1,1,4] 001001010=>110110101=>111110010=>[1,1,1,1,1,3,2] 001001011=>110110100=>111001100=>[1,1,1,3,1,3] 001001100=>110110011=>110110110=>[1,1,2,1,2,1,2] 001001101=>110110010=>101111000=>[1,2,1,1,1,4] 001001110=>110110001=>101011010=>[1,2,2,1,2,2] 001001111=>110110000=>100101100=>[1,3,2,1,3] 001010000=>110101111=>111011110=>[1,1,1,2,1,1,1,2] 001010001=>110101110=>111110010=>[1,1,1,1,1,3,2] 001010010=>110101101=>111101100=>[1,1,1,1,2,1,3] 001010011=>110101100=>111011000=>[1,1,1,2,1,4] 001010100=>110101011=>111100110=>[1,1,1,1,3,1,2] 001010101=>110101010=>111110000=>[1,1,1,1,1,5] 001010110=>110101001=>111000110=>[1,1,1,4,1,2] 001010111=>110101000=>101100010=>[1,2,1,4,2] 001011000=>110100111=>110011110=>[1,1,3,1,1,1,2] 001011001=>110100110=>111001100=>[1,1,1,3,1,3] 001011010=>110100101=>110101010=>[1,1,2,2,2,2] 001011011=>110100100=>111000010=>[1,1,1,5,2] 001011100=>110100011=>101001110=>[1,2,3,1,1,2] 001011101=>110100010=>101010100=>[1,2,2,2,3] 001011110=>110100001=>100100110=>[1,3,3,1,2] 001011111=>110100000=>100010010=>[1,4,3,2] 001100000=>110011111=>101111110=>[1,2,1,1,1,1,1,2] 001100001=>110011110=>110110110=>[1,1,2,1,2,1,2] 001100010=>110011101=>110111100=>[1,1,2,1,1,1,3] 001100011=>110011100=>110011100=>[1,1,3,1,1,3] 001100100=>110011011=>101111010=>[1,2,1,1,1,2,2] 001100101=>110011010=>111011000=>[1,1,1,2,1,4] 001100110=>110011001=>110011100=>[1,1,3,1,1,3] 001100111=>110011000=>110001100=>[1,1,4,1,3] 001101000=>110010111=>101101110=>[1,2,1,2,1,1,2] 001101001=>110010110=>101111000=>[1,2,1,1,1,4] 001101010=>110010101=>101110010=>[1,2,1,1,3,2] 001101011=>110010100=>111001000=>[1,1,1,3,4] 001101100=>110010011=>110010110=>[1,1,3,2,1,2] 001101101=>110010010=>110011000=>[1,1,3,1,4] 001101110=>110010001=>110000110=>[1,1,5,1,2] 001101111=>110010000=>101000010=>[1,2,5,2] 001110000=>110001111=>100111110=>[1,3,1,1,1,1,2] 001110001=>110001110=>101011010=>[1,2,2,1,2,2] 001110010=>110001101=>100111100=>[1,3,1,1,1,3] 001110011=>110001100=>110001100=>[1,1,4,1,3] 001110100=>110001011=>100110110=>[1,3,1,2,1,2] 001110101=>110001010=>100111000=>[1,3,1,1,4] 001110110=>110001001=>101001010=>[1,2,3,2,2] 001110111=>110001000=>110000100=>[1,1,5,3] 001111000=>110000111=>100011110=>[1,4,1,1,1,2] 001111001=>110000110=>100101100=>[1,3,2,1,3] 001111010=>110000101=>100011010=>[1,4,1,2,2] 001111011=>110000100=>100100100=>[1,3,3,3] 001111100=>110000011=>100001110=>[1,5,1,1,2] 001111101=>110000010=>100001100=>[1,5,1,3] 001111110=>110000001=>100000110=>[1,6,1,2] 001111111=>110000000=>100000010=>[1,7,2] 010000000=>101111111=>111111110=>[1,1,1,1,1,1,1,1,2] 010000001=>101111110=>111011110=>[1,1,1,2,1,1,1,2] 010000010=>101111101=>111110110=>[1,1,1,1,1,2,1,2] 010000011=>101111100=>101101110=>[1,2,1,2,1,1,2] 010000100=>101111011=>111111100=>[1,1,1,1,1,1,1,3] 010000101=>101111010=>111100110=>[1,1,1,1,3,1,2] 010000110=>101111001=>101111010=>[1,2,1,1,1,2,2] 010000111=>101111000=>100110110=>[1,3,1,2,1,2] 010001000=>101110111=>111111100=>[1,1,1,1,1,1,1,3] 010001001=>101110110=>111110010=>[1,1,1,1,1,3,2] 010001010=>101110101=>111101100=>[1,1,1,1,2,1,3] 010001011=>101110100=>110101010=>[1,1,2,2,2,2] 010001100=>101110011=>110111100=>[1,1,2,1,1,1,3] 010001101=>101110010=>101110010=>[1,2,1,1,3,2] 010001110=>101110001=>100111100=>[1,3,1,1,1,3] 010001111=>101110000=>100011010=>[1,4,1,2,2] 010010000=>101101111=>111110110=>[1,1,1,1,1,2,1,2] 010010001=>101101110=>111101100=>[1,1,1,1,2,1,3] 010010010=>101101101=>111111000=>[1,1,1,1,1,1,4] 010010011=>101101100=>101111000=>[1,2,1,1,1,4] 010010100=>101101011=>111110010=>[1,1,1,1,1,3,2] 010010101=>101101010=>111110000=>[1,1,1,1,1,5] 010010110=>101101001=>111001100=>[1,1,1,3,1,3] 010010111=>101101000=>101010100=>[1,2,2,2,3] 010011000=>101100111=>110110110=>[1,1,2,1,2,1,2] 010011001=>101100110=>111011000=>[1,1,1,2,1,4] 010011010=>101100101=>101111000=>[1,2,1,1,1,4] 010011011=>101100100=>110011000=>[1,1,3,1,4] 010011100=>101100011=>101011010=>[1,2,2,1,2,2] 010011101=>101100010=>100111000=>[1,3,1,1,4] 010011110=>101100001=>100101100=>[1,3,2,1,3] 010011111=>101100000=>100001100=>[1,5,1,3] 010100000=>101011111=>111011110=>[1,1,1,2,1,1,1,2] 010100001=>101011110=>111100110=>[1,1,1,1,3,1,2] 010100010=>101011101=>111110010=>[1,1,1,1,1,3,2] 010100011=>101011100=>101110010=>[1,2,1,1,3,2] 010100100=>101011011=>111101100=>[1,1,1,1,2,1,3] 010100101=>101011010=>111110000=>[1,1,1,1,1,5] 010100110=>101011001=>111011000=>[1,1,1,2,1,4] 010100111=>101011000=>100111000=>[1,3,1,1,4] 010101000=>101010111=>111100110=>[1,1,1,1,3,1,2] 010101001=>101010110=>111110000=>[1,1,1,1,1,5] 010101010=>101010101=>111110000=>[1,1,1,1,1,5] 010101011=>101010100=>111100000=>[1,1,1,1,6] 010101100=>101010011=>111000110=>[1,1,1,4,1,2] 010101101=>101010010=>111100000=>[1,1,1,1,6] 010101110=>101010001=>101100010=>[1,2,1,4,2] 010101111=>101010000=>100110000=>[1,3,1,5] 010110000=>101001111=>110011110=>[1,1,3,1,1,1,2] 010110001=>101001110=>111000110=>[1,1,1,4,1,2] 010110010=>101001101=>111001100=>[1,1,1,3,1,3] 010110011=>101001100=>111001000=>[1,1,1,3,4] 010110100=>101001011=>110101010=>[1,1,2,2,2,2] 010110101=>101001010=>111100000=>[1,1,1,1,6] 010110110=>101001001=>111000010=>[1,1,1,5,2] 010110111=>101001000=>110010000=>[1,1,3,5] 010111000=>101000111=>101001110=>[1,2,3,1,1,2] 010111001=>101000110=>101100010=>[1,2,1,4,2] 010111010=>101000101=>101010100=>[1,2,2,2,3] 010111011=>101000100=>101100000=>[1,2,1,6] 010111100=>101000011=>100100110=>[1,3,3,1,2] 010111101=>101000010=>100110000=>[1,3,1,5] 010111110=>101000001=>100010010=>[1,4,3,2] 010111111=>101000000=>100001000=>[1,5,4] 011000000=>100111111=>101111110=>[1,2,1,1,1,1,1,2] 011000001=>100111110=>110011110=>[1,1,3,1,1,1,2] 011000010=>100111101=>110110110=>[1,1,2,1,2,1,2] 011000011=>100111100=>110010110=>[1,1,3,2,1,2] 011000100=>100111011=>110111100=>[1,1,2,1,1,1,3] 011000101=>100111010=>111000110=>[1,1,1,4,1,2] 011000110=>100111001=>110011100=>[1,1,3,1,1,3] 011000111=>100111000=>101001010=>[1,2,3,2,2] 011001000=>100110111=>101111010=>[1,2,1,1,1,2,2] 011001001=>100110110=>111001100=>[1,1,1,3,1,3] 011001010=>100110101=>111011000=>[1,1,1,2,1,4] 011001011=>100110100=>111000010=>[1,1,1,5,2] 011001100=>100110011=>110011100=>[1,1,3,1,1,3] 011001101=>100110010=>111001000=>[1,1,1,3,4] 011001110=>100110001=>110001100=>[1,1,4,1,3] 011001111=>100110000=>100100100=>[1,3,3,3] 011010000=>100101111=>101101110=>[1,2,1,2,1,1,2] 011010001=>100101110=>110101010=>[1,1,2,2,2,2] 011010010=>100101101=>101111000=>[1,2,1,1,1,4] 011010011=>100101100=>110011000=>[1,1,3,1,4] 011010100=>100101011=>101110010=>[1,2,1,1,3,2] 011010101=>100101010=>111100000=>[1,1,1,1,6] 011010110=>100101001=>111001000=>[1,1,1,3,4] 011010111=>100101000=>101100000=>[1,2,1,6] 011011000=>100100111=>110010110=>[1,1,3,2,1,2] 011011001=>100100110=>111000010=>[1,1,1,5,2] 011011010=>100100101=>110011000=>[1,1,3,1,4] 011011011=>100100100=>111000000=>[1,1,1,7] 011011100=>100100011=>110000110=>[1,1,5,1,2] 011011101=>100100010=>110010000=>[1,1,3,5] 011011110=>100100001=>101000010=>[1,2,5,2] 011011111=>100100000=>100100000=>[1,3,6] 011100000=>100011111=>100111110=>[1,3,1,1,1,1,2] 011100001=>100011110=>101001110=>[1,2,3,1,1,2] 011100010=>100011101=>101011010=>[1,2,2,1,2,2] 011100011=>100011100=>110000110=>[1,1,5,1,2] 011100100=>100011011=>100111100=>[1,3,1,1,1,3] 011100101=>100011010=>101100010=>[1,2,1,4,2] 011100110=>100011001=>110001100=>[1,1,4,1,3] 011100111=>100011000=>110000100=>[1,1,5,3] 011101000=>100010111=>100110110=>[1,3,1,2,1,2] 011101001=>100010110=>101010100=>[1,2,2,2,3] 011101010=>100010101=>100111000=>[1,3,1,1,4] 011101011=>100010100=>110010000=>[1,1,3,5] 011101100=>100010011=>101001010=>[1,2,3,2,2] 011101101=>100010010=>101100000=>[1,2,1,6] 011101110=>100010001=>110000100=>[1,1,5,3] 011101111=>100010000=>110000000=>[1,1,8] 011110000=>100001111=>100011110=>[1,4,1,1,1,2] 011110001=>100001110=>100100110=>[1,3,3,1,2] 011110010=>100001101=>100101100=>[1,3,2,1,3] 011110011=>100001100=>101000010=>[1,2,5,2] 011110100=>100001011=>100011010=>[1,4,1,2,2] 011110101=>100001010=>100110000=>[1,3,1,5] 011110110=>100001001=>100100100=>[1,3,3,3] 011110111=>100001000=>110000000=>[1,1,8] 011111000=>100000111=>100001110=>[1,5,1,1,2] 011111001=>100000110=>100010010=>[1,4,3,2] 011111010=>100000101=>100001100=>[1,5,1,3] 011111011=>100000100=>100100000=>[1,3,6] 011111100=>100000011=>100000110=>[1,6,1,2] 011111101=>100000010=>100001000=>[1,5,4] 011111110=>100000001=>100000010=>[1,7,2] 011111111=>100000000=>100000000=>[1,9] 100000000=>011111111=>111111110=>[1,1,1,1,1,1,1,1,2] 100000001=>011111110=>101111110=>[1,2,1,1,1,1,1,2] 100000010=>011111101=>111011110=>[1,1,1,2,1,1,1,2] 100000011=>011111100=>100111110=>[1,3,1,1,1,1,2] 100000100=>011111011=>111110110=>[1,1,1,1,1,2,1,2] 100000101=>011111010=>110011110=>[1,1,3,1,1,1,2] 100000110=>011111001=>101101110=>[1,2,1,2,1,1,2] 100000111=>011111000=>100011110=>[1,4,1,1,1,2] 100001000=>011110111=>111111100=>[1,1,1,1,1,1,1,3] 100001001=>011110110=>110110110=>[1,1,2,1,2,1,2] 100001010=>011110101=>111100110=>[1,1,1,1,3,1,2] 100001011=>011110100=>101001110=>[1,2,3,1,1,2] 100001100=>011110011=>101111010=>[1,2,1,1,1,2,2] 100001101=>011110010=>110010110=>[1,1,3,2,1,2] 100001110=>011110001=>100110110=>[1,3,1,2,1,2] 100001111=>011110000=>100001110=>[1,5,1,1,2] 100010000=>011101111=>111111100=>[1,1,1,1,1,1,1,3] 100010001=>011101110=>110111100=>[1,1,2,1,1,1,3] 100010010=>011101101=>111110010=>[1,1,1,1,1,3,2] 100010011=>011101100=>101011010=>[1,2,2,1,2,2] 100010100=>011101011=>111101100=>[1,1,1,1,2,1,3] 100010101=>011101010=>111000110=>[1,1,1,4,1,2] 100010110=>011101001=>110101010=>[1,1,2,2,2,2] 100010111=>011101000=>100100110=>[1,3,3,1,2] 100011000=>011100111=>110111100=>[1,1,2,1,1,1,3] 100011001=>011100110=>110011100=>[1,1,3,1,1,3] 100011010=>011100101=>101110010=>[1,2,1,1,3,2] 100011011=>011100100=>110000110=>[1,1,5,1,2] 100011100=>011100011=>100111100=>[1,3,1,1,1,3] 100011101=>011100010=>101001010=>[1,2,3,2,2] 100011110=>011100001=>100011010=>[1,4,1,2,2] 100011111=>011100000=>100000110=>[1,6,1,2] 100100000=>011011111=>111110110=>[1,1,1,1,1,2,1,2] 100100001=>011011110=>101111010=>[1,2,1,1,1,2,2] 100100010=>011011101=>111101100=>[1,1,1,1,2,1,3] 100100011=>011011100=>100111100=>[1,3,1,1,1,3] 100100100=>011011011=>111111000=>[1,1,1,1,1,1,4] 100100101=>011011010=>111001100=>[1,1,1,3,1,3] 100100110=>011011001=>101111000=>[1,2,1,1,1,4] 100100111=>011011000=>100101100=>[1,3,2,1,3] 100101000=>011010111=>111110010=>[1,1,1,1,1,3,2] 100101001=>011010110=>111011000=>[1,1,1,2,1,4] 100101010=>011010101=>111110000=>[1,1,1,1,1,5] 100101011=>011010100=>101100010=>[1,2,1,4,2] 100101100=>011010011=>111001100=>[1,1,1,3,1,3] 100101101=>011010010=>111000010=>[1,1,1,5,2] 100101110=>011010001=>101010100=>[1,2,2,2,3] 100101111=>011010000=>100010010=>[1,4,3,2] 100110000=>011001111=>110110110=>[1,1,2,1,2,1,2] 100110001=>011001110=>110011100=>[1,1,3,1,1,3] 100110010=>011001101=>111011000=>[1,1,1,2,1,4] 100110011=>011001100=>110001100=>[1,1,4,1,3] 100110100=>011001011=>101111000=>[1,2,1,1,1,4] 100110101=>011001010=>111001000=>[1,1,1,3,4] 100110110=>011001001=>110011000=>[1,1,3,1,4] 100110111=>011001000=>101000010=>[1,2,5,2] 100111000=>011000111=>101011010=>[1,2,2,1,2,2] 100111001=>011000110=>110001100=>[1,1,4,1,3] 100111010=>011000101=>100111000=>[1,3,1,1,4] 100111011=>011000100=>110000100=>[1,1,5,3] 100111100=>011000011=>100101100=>[1,3,2,1,3] 100111101=>011000010=>100100100=>[1,3,3,3] 100111110=>011000001=>100001100=>[1,5,1,3] 100111111=>011000000=>100000010=>[1,7,2] 101000000=>010111111=>111011110=>[1,1,1,2,1,1,1,2] 101000001=>010111110=>101101110=>[1,2,1,2,1,1,2] 101000010=>010111101=>111100110=>[1,1,1,1,3,1,2] 101000011=>010111100=>100110110=>[1,3,1,2,1,2] 101000100=>010111011=>111110010=>[1,1,1,1,1,3,2] 101000101=>010111010=>110101010=>[1,1,2,2,2,2] 101000110=>010111001=>101110010=>[1,2,1,1,3,2] 101000111=>010111000=>100011010=>[1,4,1,2,2] 101001000=>010110111=>111101100=>[1,1,1,1,2,1,3] 101001001=>010110110=>101111000=>[1,2,1,1,1,4] 101001010=>010110101=>111110000=>[1,1,1,1,1,5] 101001011=>010110100=>101010100=>[1,2,2,2,3] 101001100=>010110011=>111011000=>[1,1,1,2,1,4] 101001101=>010110010=>110011000=>[1,1,3,1,4] 101001110=>010110001=>100111000=>[1,3,1,1,4] 101001111=>010110000=>100001100=>[1,5,1,3] 101010000=>010101111=>111100110=>[1,1,1,1,3,1,2] 101010001=>010101110=>101110010=>[1,2,1,1,3,2] 101010010=>010101101=>111110000=>[1,1,1,1,1,5] 101010011=>010101100=>100111000=>[1,3,1,1,4] 101010100=>010101011=>111110000=>[1,1,1,1,1,5] 101010101=>010101010=>111100000=>[1,1,1,1,6] 101010110=>010101001=>111100000=>[1,1,1,1,6] 101010111=>010101000=>100110000=>[1,3,1,5] 101011000=>010100111=>111000110=>[1,1,1,4,1,2] 101011001=>010100110=>111001000=>[1,1,1,3,4] 101011010=>010100101=>111100000=>[1,1,1,1,6] 101011011=>010100100=>110010000=>[1,1,3,5] 101011100=>010100011=>101100010=>[1,2,1,4,2] 101011101=>010100010=>101100000=>[1,2,1,6] 101011110=>010100001=>100110000=>[1,3,1,5] 101011111=>010100000=>100001000=>[1,5,4] 101100000=>010011111=>110011110=>[1,1,3,1,1,1,2] 101100001=>010011110=>110010110=>[1,1,3,2,1,2] 101100010=>010011101=>111000110=>[1,1,1,4,1,2] 101100011=>010011100=>101001010=>[1,2,3,2,2] 101100100=>010011011=>111001100=>[1,1,1,3,1,3] 101100101=>010011010=>111000010=>[1,1,1,5,2] 101100110=>010011001=>111001000=>[1,1,1,3,4] 101100111=>010011000=>100100100=>[1,3,3,3] 101101000=>010010111=>110101010=>[1,1,2,2,2,2] 101101001=>010010110=>110011000=>[1,1,3,1,4] 101101010=>010010101=>111100000=>[1,1,1,1,6] 101101011=>010010100=>101100000=>[1,2,1,6] 101101100=>010010011=>111000010=>[1,1,1,5,2] 101101101=>010010010=>111000000=>[1,1,1,7] 101101110=>010010001=>110010000=>[1,1,3,5] 101101111=>010010000=>100100000=>[1,3,6] 101110000=>010001111=>101001110=>[1,2,3,1,1,2] 101110001=>010001110=>110000110=>[1,1,5,1,2] 101110010=>010001101=>101100010=>[1,2,1,4,2] 101110011=>010001100=>110000100=>[1,1,5,3] 101110100=>010001011=>101010100=>[1,2,2,2,3] 101110101=>010001010=>110010000=>[1,1,3,5] 101110110=>010001001=>101100000=>[1,2,1,6] 101110111=>010001000=>110000000=>[1,1,8] 101111000=>010000111=>100100110=>[1,3,3,1,2] 101111001=>010000110=>101000010=>[1,2,5,2] 101111010=>010000101=>100110000=>[1,3,1,5] 101111011=>010000100=>110000000=>[1,1,8] 101111100=>010000011=>100010010=>[1,4,3,2] 101111101=>010000010=>100100000=>[1,3,6] 101111110=>010000001=>100001000=>[1,5,4] 101111111=>010000000=>100000000=>[1,9] 110000000=>001111111=>101111110=>[1,2,1,1,1,1,1,2] 110000001=>001111110=>100111110=>[1,3,1,1,1,1,2] 110000010=>001111101=>110011110=>[1,1,3,1,1,1,2] 110000011=>001111100=>100011110=>[1,4,1,1,1,2] 110000100=>001111011=>110110110=>[1,1,2,1,2,1,2] 110000101=>001111010=>101001110=>[1,2,3,1,1,2] 110000110=>001111001=>110010110=>[1,1,3,2,1,2] 110000111=>001111000=>100001110=>[1,5,1,1,2] 110001000=>001110111=>110111100=>[1,1,2,1,1,1,3] 110001001=>001110110=>101011010=>[1,2,2,1,2,2] 110001010=>001110101=>111000110=>[1,1,1,4,1,2] 110001011=>001110100=>100100110=>[1,3,3,1,2] 110001100=>001110011=>110011100=>[1,1,3,1,1,3] 110001101=>001110010=>110000110=>[1,1,5,1,2] 110001110=>001110001=>101001010=>[1,2,3,2,2] 110001111=>001110000=>100000110=>[1,6,1,2] 110010000=>001101111=>101111010=>[1,2,1,1,1,2,2] 110010001=>001101110=>100111100=>[1,3,1,1,1,3] 110010010=>001101101=>111001100=>[1,1,1,3,1,3] 110010011=>001101100=>100101100=>[1,3,2,1,3] 110010100=>001101011=>111011000=>[1,1,1,2,1,4] 110010101=>001101010=>101100010=>[1,2,1,4,2] 110010110=>001101001=>111000010=>[1,1,1,5,2] 110010111=>001101000=>100010010=>[1,4,3,2] 110011000=>001100111=>110011100=>[1,1,3,1,1,3] 110011001=>001100110=>110001100=>[1,1,4,1,3] 110011010=>001100101=>111001000=>[1,1,1,3,4] 110011011=>001100100=>101000010=>[1,2,5,2] 110011100=>001100011=>110001100=>[1,1,4,1,3] 110011101=>001100010=>110000100=>[1,1,5,3] 110011110=>001100001=>100100100=>[1,3,3,3] 110011111=>001100000=>100000010=>[1,7,2] 110100000=>001011111=>101101110=>[1,2,1,2,1,1,2] 110100001=>001011110=>100110110=>[1,3,1,2,1,2] 110100010=>001011101=>110101010=>[1,1,2,2,2,2] 110100011=>001011100=>100011010=>[1,4,1,2,2] 110100100=>001011011=>101111000=>[1,2,1,1,1,4] 110100101=>001011010=>101010100=>[1,2,2,2,3] 110100110=>001011001=>110011000=>[1,1,3,1,4] 110100111=>001011000=>100001100=>[1,5,1,3] 110101000=>001010111=>101110010=>[1,2,1,1,3,2] 110101001=>001010110=>100111000=>[1,3,1,1,4] 110101010=>001010101=>111100000=>[1,1,1,1,6] 110101011=>001010100=>100110000=>[1,3,1,5] 110101100=>001010011=>111001000=>[1,1,1,3,4] 110101101=>001010010=>110010000=>[1,1,3,5] 110101110=>001010001=>101100000=>[1,2,1,6] 110101111=>001010000=>100001000=>[1,5,4] 110110000=>001001111=>110010110=>[1,1,3,2,1,2] 110110001=>001001110=>101001010=>[1,2,3,2,2] 110110010=>001001101=>111000010=>[1,1,1,5,2] 110110011=>001001100=>100100100=>[1,3,3,3] 110110100=>001001011=>110011000=>[1,1,3,1,4] 110110101=>001001010=>101100000=>[1,2,1,6] 110110110=>001001001=>111000000=>[1,1,1,7] 110110111=>001001000=>100100000=>[1,3,6] 110111000=>001000111=>110000110=>[1,1,5,1,2] 110111001=>001000110=>110000100=>[1,1,5,3] 110111010=>001000101=>110010000=>[1,1,3,5] 110111011=>001000100=>110000000=>[1,1,8] 110111100=>001000011=>101000010=>[1,2,5,2] 110111101=>001000010=>110000000=>[1,1,8] 110111110=>001000001=>100100000=>[1,3,6] 110111111=>001000000=>100000000=>[1,9] 111000000=>000111111=>100111110=>[1,3,1,1,1,1,2] 111000001=>000111110=>100011110=>[1,4,1,1,1,2] 111000010=>000111101=>101001110=>[1,2,3,1,1,2] 111000011=>000111100=>100001110=>[1,5,1,1,2] 111000100=>000111011=>101011010=>[1,2,2,1,2,2] 111000101=>000111010=>100100110=>[1,3,3,1,2] 111000110=>000111001=>110000110=>[1,1,5,1,2] 111000111=>000111000=>100000110=>[1,6,1,2] 111001000=>000110111=>100111100=>[1,3,1,1,1,3] 111001001=>000110110=>100101100=>[1,3,2,1,3] 111001010=>000110101=>101100010=>[1,2,1,4,2] 111001011=>000110100=>100010010=>[1,4,3,2] 111001100=>000110011=>110001100=>[1,1,4,1,3] 111001101=>000110010=>101000010=>[1,2,5,2] 111001110=>000110001=>110000100=>[1,1,5,3] 111001111=>000110000=>100000010=>[1,7,2] 111010000=>000101111=>100110110=>[1,3,1,2,1,2] 111010001=>000101110=>100011010=>[1,4,1,2,2] 111010010=>000101101=>101010100=>[1,2,2,2,3] 111010011=>000101100=>100001100=>[1,5,1,3] 111010100=>000101011=>100111000=>[1,3,1,1,4] 111010101=>000101010=>100110000=>[1,3,1,5] 111010110=>000101001=>110010000=>[1,1,3,5] 111010111=>000101000=>100001000=>[1,5,4] 111011000=>000100111=>101001010=>[1,2,3,2,2] 111011001=>000100110=>100100100=>[1,3,3,3] 111011010=>000100101=>101100000=>[1,2,1,6] 111011011=>000100100=>100100000=>[1,3,6] 111011100=>000100011=>110000100=>[1,1,5,3] 111011101=>000100010=>110000000=>[1,1,8] 111011110=>000100001=>110000000=>[1,1,8] 111011111=>000100000=>100000000=>[1,9] 111100000=>000011111=>100011110=>[1,4,1,1,1,2] 111100001=>000011110=>100001110=>[1,5,1,1,2] 111100010=>000011101=>100100110=>[1,3,3,1,2] 111100011=>000011100=>100000110=>[1,6,1,2] 111100100=>000011011=>100101100=>[1,3,2,1,3] 111100101=>000011010=>100010010=>[1,4,3,2] 111100110=>000011001=>101000010=>[1,2,5,2] 111100111=>000011000=>100000010=>[1,7,2] 111101000=>000010111=>100011010=>[1,4,1,2,2] 111101001=>000010110=>100001100=>[1,5,1,3] 111101010=>000010101=>100110000=>[1,3,1,5] 111101011=>000010100=>100001000=>[1,5,4] 111101100=>000010011=>100100100=>[1,3,3,3] 111101101=>000010010=>100100000=>[1,3,6] 111101110=>000010001=>110000000=>[1,1,8] 111101111=>000010000=>100000000=>[1,9] 111110000=>000001111=>100001110=>[1,5,1,1,2] 111110001=>000001110=>100000110=>[1,6,1,2] 111110010=>000001101=>100010010=>[1,4,3,2] 111110011=>000001100=>100000010=>[1,7,2] 111110100=>000001011=>100001100=>[1,5,1,3] 111110101=>000001010=>100001000=>[1,5,4] 111110110=>000001001=>100100000=>[1,3,6] 111110111=>000001000=>100000000=>[1,9] 111111000=>000000111=>100000110=>[1,6,1,2] 111111001=>000000110=>100000010=>[1,7,2] 111111010=>000000101=>100001000=>[1,5,4] 111111011=>000000100=>100000000=>[1,9] 111111100=>000000011=>100000010=>[1,7,2] 111111101=>000000010=>100000000=>[1,9] 111111110=>000000001=>100000000=>[1,9] 111111111=>000000000=>000000000=>[10] 1010101010=>0101010101=>1111100000=>[1,1,1,1,1,6] 1010101100=>0101010011=>1111000010=>[1,1,1,1,5,2] 1010110010=>0101001101=>1111000010=>[1,1,1,1,5,2] 1010110100=>0101001011=>1110100100=>[1,1,1,2,3,3] 1011001010=>0100110101=>1111000010=>[1,1,1,1,5,2] 1011001100=>0100110011=>1110001100=>[1,1,1,4,1,3] 1011010010=>0100101101=>1110100100=>[1,1,1,2,3,3] 1011010100=>0100101011=>1101101000=>[1,1,2,1,2,4] 1011100100=>0100011011=>1011001100=>[1,2,1,3,1,3] 1011101000=>0100010111=>1010101010=>[1,2,2,2,2,2] 1100101010=>0011010101=>1111000010=>[1,1,1,1,5,2] 1100101100=>0011010011=>1110001100=>[1,1,1,4,1,3] 1100110010=>0011001101=>1110001100=>[1,1,1,4,1,3] 1100110100=>0011001011=>1100111000=>[1,1,3,1,1,4] 1101001010=>0010110101=>1110100100=>[1,1,1,2,3,3] 1101001100=>0010110011=>1100111000=>[1,1,3,1,1,4] 1101010010=>0010101101=>1101101000=>[1,1,2,1,2,4] 1101010100=>0010101011=>1011110000=>[1,2,1,1,1,5] 1101011000=>0010100111=>1110010010=>[1,1,1,3,3,2] 1101100100=>0010011011=>1101010100=>[1,1,2,2,2,3] 1101101000=>0010010111=>1100110010=>[1,1,3,1,3,2] 1110010010=>0001101101=>1011001100=>[1,2,1,3,1,3] 1110010100=>0001101011=>1011011000=>[1,2,1,2,1,4] 1110100010=>0001011101=>1010101010=>[1,2,2,2,2,2] 1111100000=>0000011111=>1000011110=>[1,5,1,1,1,2] 101010101010=>010101010101=>111111000000=>[1,1,1,1,1,1,7] 101010101100=>010101010011=>111110000010=>[1,1,1,1,1,6,2] 101010110010=>010101001101=>111110000010=>[1,1,1,1,1,6,2] 101010110100=>010101001011=>111101000100=>[1,1,1,1,2,4,3] 101011001010=>010100110101=>111110000010=>[1,1,1,1,1,6,2] 101011001100=>010100110011=>111100010100=>[1,1,1,1,4,2,3] 101011010010=>010100101101=>111101000100=>[1,1,1,1,2,4,3] 101011010100=>010100101011=>111011001000=>[1,1,1,2,1,3,4] 101011100100=>010100011011=>101110001100=>[1,2,1,1,4,1,3] 101011101000=>010100010111=>101101001010=>[1,2,1,2,3,2,2] 101100101010=>010011010101=>111110000010=>[1,1,1,1,1,6,2] 101100101100=>010011010011=>111100001100=>[1,1,1,1,5,1,3] 101100110010=>010011001101=>111100010100=>[1,1,1,1,4,2,3] 101100110100=>010011001011=>111001101000=>[1,1,1,3,1,2,4] 101100111000=>010011000111=>110100101010=>[1,1,2,3,2,2,2] 101101001010=>010010110101=>111101000100=>[1,1,1,1,2,4,3] 101101001100=>010010110011=>111010011000=>[1,1,1,2,3,1,4] 101101010010=>010010101101=>111011001000=>[1,1,1,2,1,3,4] 101101010100=>010010101011=>110111010000=>[1,1,2,1,1,2,5] 101101011000=>010010100111=>111100001010=>[1,1,1,1,5,2,2] 101101100100=>010010011011=>111010001100=>[1,1,1,2,4,1,3] 101101101000=>010010010111=>111001001010=>[1,1,1,3,3,2,2] 101110001100=>010001110011=>110100011100=>[1,1,2,4,1,1,3] 101110010010=>010001101101=>101110001100=>[1,2,1,1,4,1,3] 101110010100=>010001101011=>101110011000=>[1,2,1,1,3,1,4] 101110100010=>010001011101=>101101001010=>[1,2,1,2,3,2,2] 101110100100=>010001011011=>101011011000=>[1,2,2,1,2,1,4] 101110101000=>010001010111=>101011010010=>[1,2,2,1,2,3,2] 110010101010=>001101010101=>111110000010=>[1,1,1,1,1,6,2] 110010101100=>001101010011=>111100010100=>[1,1,1,1,4,2,3] 110010110010=>001101001101=>111100001100=>[1,1,1,1,5,1,3] 110010110100=>001101001011=>111010011000=>[1,1,1,2,3,1,4] 110010111000=>001101000111=>110100011100=>[1,1,2,4,1,1,3] 110011001010=>001100110101=>111100010100=>[1,1,1,1,4,2,3] 110011001100=>001100110011=>111000111000=>[1,1,1,4,1,1,4] 110011010010=>001100101101=>111001101000=>[1,1,1,3,1,2,4] 110011010100=>001100101011=>110101110000=>[1,1,2,2,1,1,5] 110011011000=>001100100111=>111000110010=>[1,1,1,4,1,3,2] 110011100010=>001100011101=>110100101010=>[1,1,2,3,2,2,2] 110011100100=>001100011011=>110010111000=>[1,1,3,2,1,1,4] 110100101010=>001011010101=>111101000100=>[1,1,1,1,2,4,3] 110100101100=>001011010011=>111001101000=>[1,1,1,3,1,2,4] 110100110010=>001011001101=>111010011000=>[1,1,1,2,3,1,4] 110100110100=>001011001011=>110011110000=>[1,1,3,1,1,1,5] 110100111000=>001011000111=>110010110010=>[1,1,3,2,1,3,2] 110101001010=>001010110101=>111011001000=>[1,1,1,2,1,3,4] 110101001100=>001010110011=>110101110000=>[1,1,2,2,1,1,5] 110101010010=>001010101101=>110111010000=>[1,1,2,1,1,2,5] 110101010100=>001010101011=>101111100000=>[1,2,1,1,1,1,6] 110101011000=>001010100111=>111100100010=>[1,1,1,1,3,4,2] 110101100010=>001010011101=>111100001010=>[1,1,1,1,5,2,2] 110101100100=>001010011011=>111010100100=>[1,1,1,2,2,3,3] 110101101000=>001010010111=>111001100010=>[1,1,1,3,1,4,2] 110110001100=>001001110011=>111000110010=>[1,1,1,4,1,3,2] 110110010010=>001001101101=>111010001100=>[1,1,1,2,4,1,3] 110110010100=>001001101011=>110110101000=>[1,1,2,1,2,2,4] 110110011000=>001001100111=>111000101100=>[1,1,1,4,2,1,3] 110110100010=>001001011101=>111001001010=>[1,1,1,3,3,2,2] 110110100100=>001001011011=>110011101000=>[1,1,3,1,1,2,4] 110110101000=>001001010111=>110011100010=>[1,1,3,1,1,4,2] 111000101100=>000111010011=>110100101010=>[1,1,2,3,2,2,2] 111000110010=>000111001101=>110100011100=>[1,1,2,4,1,1,3] 111000110100=>000111001011=>110010110010=>[1,1,3,2,1,3,2] 111000111000=>000111000111=>110000111100=>[1,1,5,1,1,1,3] 111001001010=>000110110101=>101110001100=>[1,2,1,1,4,1,3] 111001001100=>000110110011=>110010111000=>[1,1,3,2,1,1,4] 111001010010=>000110101101=>101110011000=>[1,2,1,1,3,1,4] 111001010100=>000110101011=>101110110000=>[1,2,1,1,2,1,5] 111001011000=>000110100111=>101100101100=>[1,2,1,3,2,1,3] 111001100100=>000110011011=>101100111000=>[1,2,1,3,1,1,4] 111001101000=>000110010111=>110001110100=>[1,1,4,1,1,2,3] 111010001010=>000101110101=>101101001010=>[1,2,1,2,3,2,2] 111010010010=>000101101101=>101011011000=>[1,2,2,1,2,1,4] 111010010100=>000101101011=>101011110000=>[1,2,2,1,1,1,5] 111010011000=>000101100111=>101010110100=>[1,2,2,2,1,2,3] 111010100010=>000101011101=>101011010010=>[1,2,2,1,2,3,2] 111011000100=>000100111011=>101010101010=>[1,2,2,2,2,2,2] 1111111110=>0000000001=>1000000000=>[1,10] 1001011110=>0110100001=>1001010100=>[1,3,2,2,3] 1000101110=>0111010001=>1010101010=>[1,2,2,2,2,2] 1000000010=>0111111101=>1110111110=>[1,1,1,2,1,1,1,1,2] 1000000000=>0111111111=>1111111110=>[1,1,1,1,1,1,1,1,1,2] 10000000000=>01111111111=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2] 11111111110=>00000000001=>10000000000=>[1,11] 0111111111=>1000000000=>1000000000=>[1,10] 0100000001=>1011111110=>1110111110=>[1,1,1,2,1,1,1,1,2] 0000000001=>1111111110=>1111111110=>[1,1,1,1,1,1,1,1,1,2] 01111111111=>10000000000=>10000000000=>[1,11] 0111101001=>1000010110=>1001010100=>[1,3,2,2,3] 0111010001=>1000101110=>1010101010=>[1,2,2,2,2,2] 01100000001=>10011111110=>11001111110=>[1,1,3,1,1,1,1,1,2] 00000000001=>11111111110=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2] 0101010101=>1010101010=>1111100000=>[1,1,1,1,1,6] 0101010011=>1010101100=>1011110000=>[1,2,1,1,1,5] 0101001101=>1010110010=>1011110000=>[1,2,1,1,1,5] 0101001011=>1010110100=>1101101000=>[1,1,2,1,2,4] 0100110101=>1011001010=>1011110000=>[1,2,1,1,1,5] 0100110011=>1011001100=>1100111000=>[1,1,3,1,1,4] 0100101101=>1011010010=>1101101000=>[1,1,2,1,2,4] 0100101011=>1011010100=>1110100100=>[1,1,1,2,3,3] 0100011011=>1011100100=>1100110010=>[1,1,3,1,3,2] 0100010111=>1011101000=>1010101010=>[1,2,2,2,2,2] 0011010101=>1100101010=>1011110000=>[1,2,1,1,1,5] 0011010011=>1100101100=>1100111000=>[1,1,3,1,1,4] 0011001101=>1100110010=>1100111000=>[1,1,3,1,1,4] 0011001011=>1100110100=>1110001100=>[1,1,1,4,1,3] 0010110101=>1101001010=>1101101000=>[1,1,2,1,2,4] 0010110011=>1101001100=>1110001100=>[1,1,1,4,1,3] 0010101101=>1101010010=>1110100100=>[1,1,1,2,3,3] 0010101011=>1101010100=>1111000010=>[1,1,1,1,5,2] 0010100111=>1101011000=>1011011000=>[1,2,1,2,1,4] 0010011011=>1101100100=>1101010100=>[1,1,2,2,2,3] 0010010111=>1101101000=>1011001100=>[1,2,1,3,1,3] 0001101101=>1110010010=>1100110010=>[1,1,3,1,3,2] 0001101011=>1110010100=>1110010010=>[1,1,1,3,3,2] 0001011101=>1110100010=>1010101010=>[1,2,2,2,2,2] 0000011111=>1111100000=>1000011110=>[1,5,1,1,1,2] 010101010101=>101010101010=>111111000000=>[1,1,1,1,1,1,7] 010101010011=>101010101100=>101111100000=>[1,2,1,1,1,1,6] 010101001101=>101010110010=>101111100000=>[1,2,1,1,1,1,6] 010101001011=>101010110100=>110111010000=>[1,1,2,1,1,2,5] 010100110101=>101011001010=>101111100000=>[1,2,1,1,1,1,6] 010100110011=>101011001100=>110101110000=>[1,1,2,2,1,1,5] 010100101101=>101011010010=>110111010000=>[1,1,2,1,1,2,5] 010100101011=>101011010100=>111011001000=>[1,1,1,2,1,3,4] 010100011011=>101011100100=>110011100010=>[1,1,3,1,1,4,2] 010100010111=>101011101000=>101011010010=>[1,2,2,1,2,3,2] 010011010101=>101100101010=>101111100000=>[1,2,1,1,1,1,6] 010011010011=>101100101100=>110011110000=>[1,1,3,1,1,1,5] 010011001101=>101100110010=>110101110000=>[1,1,2,2,1,1,5] 010011001011=>101100110100=>111010011000=>[1,1,1,2,3,1,4] 010011000111=>101100111000=>101010110100=>[1,2,2,2,1,2,3] 010010110101=>101101001010=>110111010000=>[1,1,2,1,1,2,5] 010010110011=>101101001100=>111001101000=>[1,1,1,3,1,2,4] 010010101101=>101101010010=>111011001000=>[1,1,1,2,1,3,4] 010010101011=>101101010100=>111101000100=>[1,1,1,1,2,4,3] 010010100111=>101101011000=>101011110000=>[1,2,2,1,1,1,5] 010010011011=>101101100100=>110011101000=>[1,1,3,1,1,2,4] 010010010111=>101101101000=>101011011000=>[1,2,2,1,2,1,4] 010001110011=>101110001100=>110001110100=>[1,1,4,1,1,2,3] 010001101101=>101110010010=>110011100010=>[1,1,3,1,1,4,2] 010001101011=>101110010100=>111001100010=>[1,1,1,3,1,4,2] 010001011101=>101110100010=>101011010010=>[1,2,2,1,2,3,2] 010001011011=>101110100100=>111001001010=>[1,1,1,3,3,2,2] 010001010111=>101110101000=>101101001010=>[1,2,1,2,3,2,2] 001101010101=>110010101010=>101111100000=>[1,2,1,1,1,1,6] 001101010011=>110010101100=>110101110000=>[1,1,2,2,1,1,5] 001101001101=>110010110010=>110011110000=>[1,1,3,1,1,1,5] 001101001011=>110010110100=>111001101000=>[1,1,1,3,1,2,4] 001101000111=>110010111000=>110001110100=>[1,1,4,1,1,2,3] 001100110101=>110011001010=>110101110000=>[1,1,2,2,1,1,5] 001100110011=>110011001100=>111000111000=>[1,1,1,4,1,1,4] 001100101101=>110011010010=>111010011000=>[1,1,1,2,3,1,4] 001100101011=>110011010100=>111100010100=>[1,1,1,1,4,2,3] 001100100111=>110011011000=>101100111000=>[1,2,1,3,1,1,4] 001100011101=>110011100010=>101010110100=>[1,2,2,2,1,2,3] 001100011011=>110011100100=>111000101100=>[1,1,1,4,2,1,3] 001011010101=>110100101010=>110111010000=>[1,1,2,1,1,2,5] 001011010011=>110100101100=>111010011000=>[1,1,1,2,3,1,4] 001011001101=>110100110010=>111001101000=>[1,1,1,3,1,2,4] 001011001011=>110100110100=>111100001100=>[1,1,1,1,5,1,3] 001011000111=>110100111000=>101100101100=>[1,2,1,3,2,1,3] 001010110101=>110101001010=>111011001000=>[1,1,1,2,1,3,4] 001010110011=>110101001100=>111100010100=>[1,1,1,1,4,2,3] 001010101101=>110101010010=>111101000100=>[1,1,1,1,2,4,3] 001010101011=>110101010100=>111110000010=>[1,1,1,1,1,6,2] 001010100111=>110101011000=>101110110000=>[1,2,1,1,2,1,5] 001010011101=>110101100010=>101011110000=>[1,2,2,1,1,1,5] 001010011011=>110101100100=>110110101000=>[1,1,2,1,2,2,4] 001010010111=>110101101000=>101110011000=>[1,2,1,1,3,1,4] 001001110011=>110110001100=>101100111000=>[1,2,1,3,1,1,4] 001001101101=>110110010010=>110011101000=>[1,1,3,1,1,2,4] 001001101011=>110110010100=>111010100100=>[1,1,1,2,2,3,3] 001001100111=>110110011000=>110010111000=>[1,1,3,2,1,1,4] 001001011101=>110110100010=>101011011000=>[1,2,2,1,2,1,4] 001001011011=>110110100100=>111010001100=>[1,1,1,2,4,1,3] 001001010111=>110110101000=>101110001100=>[1,2,1,1,4,1,3] 000111010011=>111000101100=>101010110100=>[1,2,2,2,1,2,3] 000111001101=>111000110010=>110001110100=>[1,1,4,1,1,2,3] 000111001011=>111000110100=>101100101100=>[1,2,1,3,2,1,3] 000111000111=>111000111000=>110000111100=>[1,1,5,1,1,1,3] 000110110101=>111001001010=>110011100010=>[1,1,3,1,1,4,2] 000110110011=>111001001100=>111000101100=>[1,1,1,4,2,1,3] 000110101101=>111001010010=>111001100010=>[1,1,1,3,1,4,2] 000110101011=>111001010100=>111100100010=>[1,1,1,1,3,4,2] 000110100111=>111001011000=>110010110010=>[1,1,3,2,1,3,2] 000110011011=>111001100100=>111000110010=>[1,1,1,4,1,3,2] 000110010111=>111001101000=>110100011100=>[1,1,2,4,1,1,3] 000101110101=>111010001010=>101011010010=>[1,2,2,1,2,3,2] 000101101101=>111010010010=>111001001010=>[1,1,1,3,3,2,2] 000101101011=>111010010100=>111100001010=>[1,1,1,1,5,2,2] 000101100111=>111010011000=>110100101010=>[1,1,2,3,2,2,2] 000101011101=>111010100010=>101101001010=>[1,2,1,2,3,2,2] 000100111011=>111011000100=>101010101010=>[1,2,2,2,2,2,2] 0000000000=>1111111111=>1111111111=>[1,1,1,1,1,1,1,1,1,1,1] 0000000110=>1111111001=>1011111110=>[1,2,1,1,1,1,1,1,2] 0000011000=>1111100111=>1011111110=>[1,2,1,1,1,1,1,1,2] 0000011110=>1111100001=>1000111110=>[1,4,1,1,1,1,2] 0001100000=>1110011111=>1011111110=>[1,2,1,1,1,1,1,1,2] 0001111000=>1110000111=>1000111110=>[1,4,1,1,1,1,2] 0001111110=>1110000001=>1000001110=>[1,6,1,1,2] 0110000000=>1001111111=>1011111110=>[1,2,1,1,1,1,1,1,2] 0110011110=>1001100001=>1010001100=>[1,2,4,1,3] 0110010010=>1001101101=>1110111000=>[1,1,1,2,1,1,4] 0111100000=>1000011111=>1000111110=>[1,4,1,1,1,1,2] 0111100110=>1000011001=>1010001100=>[1,2,4,1,3] 0111111000=>1000000111=>1000001110=>[1,6,1,1,2] 0111111110=>1000000001=>1000000010=>[1,8,2] 0111110010=>1000001101=>1000101100=>[1,4,2,1,3] 0100100110=>1011011001=>1110111000=>[1,1,1,2,1,1,4] 0100111110=>1011000001=>1000101100=>[1,4,2,1,3] 0100110010=>1011001101=>1110111000=>[1,1,1,2,1,1,4] 0101001010=>1010110101=>1111110000=>[1,1,1,1,1,1,5] 000000000000=>111111111111=>111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1] 011001100110=>100110011001=>111000111000=>[1,1,1,4,1,1,4] 011001110010=>100110001101=>110010111000=>[1,1,3,2,1,1,4] 011101100010=>100010011101=>101010101010=>[1,2,2,2,2,2,2] 011101001010=>100010110101=>101011110000=>[1,2,2,1,1,1,5] 010011100110=>101100011001=>101100111000=>[1,2,1,3,1,1,4] 010011011010=>101100100101=>110011101000=>[1,1,3,1,1,2,4] 010110110010=>101001001101=>111010001100=>[1,1,1,2,4,1,3] 010111001010=>101000110101=>101110011000=>[1,2,1,1,3,1,4] 010100101110=>101011010001=>101110011000=>[1,2,1,1,3,1,4] 010100111010=>101011000101=>101011110000=>[1,2,2,1,1,1,5] 010101101010=>101010010101=>111011001000=>[1,1,1,2,1,3,4] 0010101010=>1101010101=>1111100010=>[1,1,1,1,1,4,2] 0101010100=>1010101011=>1111100010=>[1,1,1,1,1,4,2] 0010100000=>1101011111=>1110111110=>[1,1,1,2,1,1,1,1,2] 0000010100=>1111101011=>1110111110=>[1,1,1,2,1,1,1,1,2]