=>

0=>0=>1=>[1,1] 1=>1=>0=>[2] 00=>00=>11=>[1,1,1] 01=>10=>01=>[2,1] 10=>01=>10=>[1,2] 11=>11=>00=>[3] 000=>000=>111=>[1,1,1,1] 001=>100=>011=>[2,1,1] 010=>010=>101=>[1,2,1] 011=>110=>001=>[3,1] 100=>001=>110=>[1,1,2] 101=>101=>010=>[2,2] 110=>011=>100=>[1,3] 111=>111=>000=>[4] 0000=>0000=>1111=>[1,1,1,1,1] 0001=>1000=>0111=>[2,1,1,1] 0010=>0100=>1011=>[1,2,1,1] 0011=>1100=>0011=>[3,1,1] 0100=>0010=>1101=>[1,1,2,1] 0101=>1010=>0101=>[2,2,1] 0110=>0110=>1001=>[1,3,1] 0111=>1110=>0001=>[4,1] 1000=>0001=>1110=>[1,1,1,2] 1001=>1001=>0110=>[2,1,2] 1010=>0101=>1010=>[1,2,2] 1011=>1101=>0010=>[3,2] 1100=>0011=>1100=>[1,1,3] 1101=>1011=>0100=>[2,3] 1110=>0111=>1000=>[1,4] 1111=>1111=>0000=>[5] 00000=>00000=>11111=>[1,1,1,1,1,1] 00001=>10000=>01111=>[2,1,1,1,1] 00010=>01000=>10111=>[1,2,1,1,1] 00011=>11000=>00111=>[3,1,1,1] 00100=>00100=>11011=>[1,1,2,1,1] 00101=>10100=>01011=>[2,2,1,1] 00110=>01100=>10011=>[1,3,1,1] 00111=>11100=>00011=>[4,1,1] 01000=>00010=>11101=>[1,1,1,2,1] 01001=>10010=>01101=>[2,1,2,1] 01010=>01010=>10101=>[1,2,2,1] 01011=>11010=>00101=>[3,2,1] 01100=>00110=>11001=>[1,1,3,1] 01101=>10110=>01001=>[2,3,1] 01110=>01110=>10001=>[1,4,1] 01111=>11110=>00001=>[5,1] 10000=>00001=>11110=>[1,1,1,1,2] 10001=>10001=>01110=>[2,1,1,2] 10010=>01001=>10110=>[1,2,1,2] 10011=>11001=>00110=>[3,1,2] 10100=>00101=>11010=>[1,1,2,2] 10101=>10101=>01010=>[2,2,2] 10110=>01101=>10010=>[1,3,2] 10111=>11101=>00010=>[4,2] 11000=>00011=>11100=>[1,1,1,3] 11001=>10011=>01100=>[2,1,3] 11010=>01011=>10100=>[1,2,3] 11011=>11011=>00100=>[3,3] 11100=>00111=>11000=>[1,1,4] 11101=>10111=>01000=>[2,4] 11110=>01111=>10000=>[1,5] 11111=>11111=>00000=>[6] 000000=>000000=>111111=>[1,1,1,1,1,1,1] 000001=>100000=>011111=>[2,1,1,1,1,1] 000010=>010000=>101111=>[1,2,1,1,1,1] 000011=>110000=>001111=>[3,1,1,1,1] 000100=>001000=>110111=>[1,1,2,1,1,1] 000101=>101000=>010111=>[2,2,1,1,1] 000110=>011000=>100111=>[1,3,1,1,1] 000111=>111000=>000111=>[4,1,1,1] 001000=>000100=>111011=>[1,1,1,2,1,1] 001001=>100100=>011011=>[2,1,2,1,1] 001010=>010100=>101011=>[1,2,2,1,1] 001011=>110100=>001011=>[3,2,1,1] 001100=>001100=>110011=>[1,1,3,1,1] 001101=>101100=>010011=>[2,3,1,1] 001110=>011100=>100011=>[1,4,1,1] 001111=>111100=>000011=>[5,1,1] 010000=>000010=>111101=>[1,1,1,1,2,1] 010001=>100010=>011101=>[2,1,1,2,1] 010010=>010010=>101101=>[1,2,1,2,1] 010011=>110010=>001101=>[3,1,2,1] 010100=>001010=>110101=>[1,1,2,2,1] 010101=>101010=>010101=>[2,2,2,1] 010110=>011010=>100101=>[1,3,2,1] 010111=>111010=>000101=>[4,2,1] 011000=>000110=>111001=>[1,1,1,3,1] 011001=>100110=>011001=>[2,1,3,1] 011010=>010110=>101001=>[1,2,3,1] 011011=>110110=>001001=>[3,3,1] 011100=>001110=>110001=>[1,1,4,1] 011101=>101110=>010001=>[2,4,1] 011110=>011110=>100001=>[1,5,1] 011111=>111110=>000001=>[6,1] 100000=>000001=>111110=>[1,1,1,1,1,2] 100001=>100001=>011110=>[2,1,1,1,2] 100010=>010001=>101110=>[1,2,1,1,2] 100011=>110001=>001110=>[3,1,1,2] 100100=>001001=>110110=>[1,1,2,1,2] 100101=>101001=>010110=>[2,2,1,2] 100110=>011001=>100110=>[1,3,1,2] 100111=>111001=>000110=>[4,1,2] 101000=>000101=>111010=>[1,1,1,2,2] 101001=>100101=>011010=>[2,1,2,2] 101010=>010101=>101010=>[1,2,2,2] 101011=>110101=>001010=>[3,2,2] 101100=>001101=>110010=>[1,1,3,2] 101101=>101101=>010010=>[2,3,2] 101110=>011101=>100010=>[1,4,2] 101111=>111101=>000010=>[5,2] 110000=>000011=>111100=>[1,1,1,1,3] 110001=>100011=>011100=>[2,1,1,3] 110010=>010011=>101100=>[1,2,1,3] 110011=>110011=>001100=>[3,1,3] 110100=>001011=>110100=>[1,1,2,3] 110101=>101011=>010100=>[2,2,3] 110110=>011011=>100100=>[1,3,3] 110111=>111011=>000100=>[4,3] 111000=>000111=>111000=>[1,1,1,4] 111001=>100111=>011000=>[2,1,4] 111010=>010111=>101000=>[1,2,4] 111011=>110111=>001000=>[3,4] 111100=>001111=>110000=>[1,1,5] 111101=>101111=>010000=>[2,5] 111110=>011111=>100000=>[1,6] 111111=>111111=>000000=>[7] 0000000=>0000000=>1111111=>[1,1,1,1,1,1,1,1] 0000001=>1000000=>0111111=>[2,1,1,1,1,1,1] 0000010=>0100000=>1011111=>[1,2,1,1,1,1,1] 0000011=>1100000=>0011111=>[3,1,1,1,1,1] 0000100=>0010000=>1101111=>[1,1,2,1,1,1,1] 0000101=>1010000=>0101111=>[2,2,1,1,1,1] 0000110=>0110000=>1001111=>[1,3,1,1,1,1] 0000111=>1110000=>0001111=>[4,1,1,1,1] 0001000=>0001000=>1110111=>[1,1,1,2,1,1,1] 0001001=>1001000=>0110111=>[2,1,2,1,1,1] 0001010=>0101000=>1010111=>[1,2,2,1,1,1] 0001011=>1101000=>0010111=>[3,2,1,1,1] 0001100=>0011000=>1100111=>[1,1,3,1,1,1] 0001101=>1011000=>0100111=>[2,3,1,1,1] 0001110=>0111000=>1000111=>[1,4,1,1,1] 0001111=>1111000=>0000111=>[5,1,1,1] 0010000=>0000100=>1111011=>[1,1,1,1,2,1,1] 0010001=>1000100=>0111011=>[2,1,1,2,1,1] 0010010=>0100100=>1011011=>[1,2,1,2,1,1] 0010011=>1100100=>0011011=>[3,1,2,1,1] 0010100=>0010100=>1101011=>[1,1,2,2,1,1] 0010101=>1010100=>0101011=>[2,2,2,1,1] 0010110=>0110100=>1001011=>[1,3,2,1,1] 0010111=>1110100=>0001011=>[4,2,1,1] 0011000=>0001100=>1110011=>[1,1,1,3,1,1] 0011001=>1001100=>0110011=>[2,1,3,1,1] 0011010=>0101100=>1010011=>[1,2,3,1,1] 0011011=>1101100=>0010011=>[3,3,1,1] 0011100=>0011100=>1100011=>[1,1,4,1,1] 0011101=>1011100=>0100011=>[2,4,1,1] 0011110=>0111100=>1000011=>[1,5,1,1] 0011111=>1111100=>0000011=>[6,1,1] 0100000=>0000010=>1111101=>[1,1,1,1,1,2,1] 0100001=>1000010=>0111101=>[2,1,1,1,2,1] 0100010=>0100010=>1011101=>[1,2,1,1,2,1] 0100011=>1100010=>0011101=>[3,1,1,2,1] 0100100=>0010010=>1101101=>[1,1,2,1,2,1] 0100101=>1010010=>0101101=>[2,2,1,2,1] 0100110=>0110010=>1001101=>[1,3,1,2,1] 0100111=>1110010=>0001101=>[4,1,2,1] 0101000=>0001010=>1110101=>[1,1,1,2,2,1] 0101001=>1001010=>0110101=>[2,1,2,2,1] 0101010=>0101010=>1010101=>[1,2,2,2,1] 0101011=>1101010=>0010101=>[3,2,2,1] 0101100=>0011010=>1100101=>[1,1,3,2,1] 0101101=>1011010=>0100101=>[2,3,2,1] 0101110=>0111010=>1000101=>[1,4,2,1] 0101111=>1111010=>0000101=>[5,2,1] 0110000=>0000110=>1111001=>[1,1,1,1,3,1] 0110001=>1000110=>0111001=>[2,1,1,3,1] 0110010=>0100110=>1011001=>[1,2,1,3,1] 0110011=>1100110=>0011001=>[3,1,3,1] 0110100=>0010110=>1101001=>[1,1,2,3,1] 0110101=>1010110=>0101001=>[2,2,3,1] 0110110=>0110110=>1001001=>[1,3,3,1] 0110111=>1110110=>0001001=>[4,3,1] 0111000=>0001110=>1110001=>[1,1,1,4,1] 0111001=>1001110=>0110001=>[2,1,4,1] 0111010=>0101110=>1010001=>[1,2,4,1] 0111011=>1101110=>0010001=>[3,4,1] 0111100=>0011110=>1100001=>[1,1,5,1] 0111101=>1011110=>0100001=>[2,5,1] 0111110=>0111110=>1000001=>[1,6,1] 0111111=>1111110=>0000001=>[7,1] 1000000=>0000001=>1111110=>[1,1,1,1,1,1,2] 1000001=>1000001=>0111110=>[2,1,1,1,1,2] 1000010=>0100001=>1011110=>[1,2,1,1,1,2] 1000011=>1100001=>0011110=>[3,1,1,1,2] 1000100=>0010001=>1101110=>[1,1,2,1,1,2] 1000101=>1010001=>0101110=>[2,2,1,1,2] 1000110=>0110001=>1001110=>[1,3,1,1,2] 1000111=>1110001=>0001110=>[4,1,1,2] 1001000=>0001001=>1110110=>[1,1,1,2,1,2] 1001001=>1001001=>0110110=>[2,1,2,1,2] 1001010=>0101001=>1010110=>[1,2,2,1,2] 1001011=>1101001=>0010110=>[3,2,1,2] 1001100=>0011001=>1100110=>[1,1,3,1,2] 1001101=>1011001=>0100110=>[2,3,1,2] 1001110=>0111001=>1000110=>[1,4,1,2] 1001111=>1111001=>0000110=>[5,1,2] 1010000=>0000101=>1111010=>[1,1,1,1,2,2] 1010001=>1000101=>0111010=>[2,1,1,2,2] 1010010=>0100101=>1011010=>[1,2,1,2,2] 1010011=>1100101=>0011010=>[3,1,2,2] 1010100=>0010101=>1101010=>[1,1,2,2,2] 1010101=>1010101=>0101010=>[2,2,2,2] 1010110=>0110101=>1001010=>[1,3,2,2] 1010111=>1110101=>0001010=>[4,2,2] 1011000=>0001101=>1110010=>[1,1,1,3,2] 1011001=>1001101=>0110010=>[2,1,3,2] 1011010=>0101101=>1010010=>[1,2,3,2] 1011011=>1101101=>0010010=>[3,3,2] 1011100=>0011101=>1100010=>[1,1,4,2] 1011101=>1011101=>0100010=>[2,4,2] 1011110=>0111101=>1000010=>[1,5,2] 1011111=>1111101=>0000010=>[6,2] 1100000=>0000011=>1111100=>[1,1,1,1,1,3] 1100001=>1000011=>0111100=>[2,1,1,1,3] 1100010=>0100011=>1011100=>[1,2,1,1,3] 1100011=>1100011=>0011100=>[3,1,1,3] 1100100=>0010011=>1101100=>[1,1,2,1,3] 1100101=>1010011=>0101100=>[2,2,1,3] 1100110=>0110011=>1001100=>[1,3,1,3] 1100111=>1110011=>0001100=>[4,1,3] 1101000=>0001011=>1110100=>[1,1,1,2,3] 1101001=>1001011=>0110100=>[2,1,2,3] 1101010=>0101011=>1010100=>[1,2,2,3] 1101011=>1101011=>0010100=>[3,2,3] 1101100=>0011011=>1100100=>[1,1,3,3] 1101101=>1011011=>0100100=>[2,3,3] 1101110=>0111011=>1000100=>[1,4,3] 1101111=>1111011=>0000100=>[5,3] 1110000=>0000111=>1111000=>[1,1,1,1,4] 1110001=>1000111=>0111000=>[2,1,1,4] 1110010=>0100111=>1011000=>[1,2,1,4] 1110011=>1100111=>0011000=>[3,1,4] 1110100=>0010111=>1101000=>[1,1,2,4] 1110101=>1010111=>0101000=>[2,2,4] 1110110=>0110111=>1001000=>[1,3,4] 1110111=>1110111=>0001000=>[4,4] 1111000=>0001111=>1110000=>[1,1,1,5] 1111001=>1001111=>0110000=>[2,1,5] 1111010=>0101111=>1010000=>[1,2,5] 1111011=>1101111=>0010000=>[3,5] 1111100=>0011111=>1100000=>[1,1,6] 1111101=>1011111=>0100000=>[2,6] 1111110=>0111111=>1000000=>[1,7] 1111111=>1111111=>0000000=>[8] 00000000=>00000000=>11111111=>[1,1,1,1,1,1,1,1,1] 00000001=>10000000=>01111111=>[2,1,1,1,1,1,1,1] 00000010=>01000000=>10111111=>[1,2,1,1,1,1,1,1] 00000011=>11000000=>00111111=>[3,1,1,1,1,1,1] 00000100=>00100000=>11011111=>[1,1,2,1,1,1,1,1] 00000101=>10100000=>01011111=>[2,2,1,1,1,1,1] 00000110=>01100000=>10011111=>[1,3,1,1,1,1,1] 00000111=>11100000=>00011111=>[4,1,1,1,1,1] 00001000=>00010000=>11101111=>[1,1,1,2,1,1,1,1] 00001001=>10010000=>01101111=>[2,1,2,1,1,1,1] 00001010=>01010000=>10101111=>[1,2,2,1,1,1,1] 00001011=>11010000=>00101111=>[3,2,1,1,1,1] 00001100=>00110000=>11001111=>[1,1,3,1,1,1,1] 00001101=>10110000=>01001111=>[2,3,1,1,1,1] 00001110=>01110000=>10001111=>[1,4,1,1,1,1] 00001111=>11110000=>00001111=>[5,1,1,1,1] 00010000=>00001000=>11110111=>[1,1,1,1,2,1,1,1] 00010001=>10001000=>01110111=>[2,1,1,2,1,1,1] 00010010=>01001000=>10110111=>[1,2,1,2,1,1,1] 00010011=>11001000=>00110111=>[3,1,2,1,1,1] 00010100=>00101000=>11010111=>[1,1,2,2,1,1,1] 00010101=>10101000=>01010111=>[2,2,2,1,1,1] 00010110=>01101000=>10010111=>[1,3,2,1,1,1] 00010111=>11101000=>00010111=>[4,2,1,1,1] 00011000=>00011000=>11100111=>[1,1,1,3,1,1,1] 00011001=>10011000=>01100111=>[2,1,3,1,1,1] 00011010=>01011000=>10100111=>[1,2,3,1,1,1] 00011011=>11011000=>00100111=>[3,3,1,1,1] 00011100=>00111000=>11000111=>[1,1,4,1,1,1] 00011101=>10111000=>01000111=>[2,4,1,1,1] 00011110=>01111000=>10000111=>[1,5,1,1,1] 00011111=>11111000=>00000111=>[6,1,1,1] 00100000=>00000100=>11111011=>[1,1,1,1,1,2,1,1] 00100001=>10000100=>01111011=>[2,1,1,1,2,1,1] 00100010=>01000100=>10111011=>[1,2,1,1,2,1,1] 00100011=>11000100=>00111011=>[3,1,1,2,1,1] 00100100=>00100100=>11011011=>[1,1,2,1,2,1,1] 00100101=>10100100=>01011011=>[2,2,1,2,1,1] 00100110=>01100100=>10011011=>[1,3,1,2,1,1] 00100111=>11100100=>00011011=>[4,1,2,1,1] 00101000=>00010100=>11101011=>[1,1,1,2,2,1,1] 00101001=>10010100=>01101011=>[2,1,2,2,1,1] 00101010=>01010100=>10101011=>[1,2,2,2,1,1] 00101011=>11010100=>00101011=>[3,2,2,1,1] 00101100=>00110100=>11001011=>[1,1,3,2,1,1] 00101101=>10110100=>01001011=>[2,3,2,1,1] 00101110=>01110100=>10001011=>[1,4,2,1,1] 00101111=>11110100=>00001011=>[5,2,1,1] 00110000=>00001100=>11110011=>[1,1,1,1,3,1,1] 00110001=>10001100=>01110011=>[2,1,1,3,1,1] 00110010=>01001100=>10110011=>[1,2,1,3,1,1] 00110011=>11001100=>00110011=>[3,1,3,1,1] 00110100=>00101100=>11010011=>[1,1,2,3,1,1] 00110101=>10101100=>01010011=>[2,2,3,1,1] 00110110=>01101100=>10010011=>[1,3,3,1,1] 00110111=>11101100=>00010011=>[4,3,1,1] 00111000=>00011100=>11100011=>[1,1,1,4,1,1] 00111001=>10011100=>01100011=>[2,1,4,1,1] 00111010=>01011100=>10100011=>[1,2,4,1,1] 00111011=>11011100=>00100011=>[3,4,1,1] 00111100=>00111100=>11000011=>[1,1,5,1,1] 00111101=>10111100=>01000011=>[2,5,1,1] 00111110=>01111100=>10000011=>[1,6,1,1] 00111111=>11111100=>00000011=>[7,1,1] 01000000=>00000010=>11111101=>[1,1,1,1,1,1,2,1] 01000001=>10000010=>01111101=>[2,1,1,1,1,2,1] 01000010=>01000010=>10111101=>[1,2,1,1,1,2,1] 01000011=>11000010=>00111101=>[3,1,1,1,2,1] 01000100=>00100010=>11011101=>[1,1,2,1,1,2,1] 01000101=>10100010=>01011101=>[2,2,1,1,2,1] 01000110=>01100010=>10011101=>[1,3,1,1,2,1] 01000111=>11100010=>00011101=>[4,1,1,2,1] 01001000=>00010010=>11101101=>[1,1,1,2,1,2,1] 01001001=>10010010=>01101101=>[2,1,2,1,2,1] 01001010=>01010010=>10101101=>[1,2,2,1,2,1] 01001011=>11010010=>00101101=>[3,2,1,2,1] 01001100=>00110010=>11001101=>[1,1,3,1,2,1] 01001101=>10110010=>01001101=>[2,3,1,2,1] 01001110=>01110010=>10001101=>[1,4,1,2,1] 01001111=>11110010=>00001101=>[5,1,2,1] 01010000=>00001010=>11110101=>[1,1,1,1,2,2,1] 01010001=>10001010=>01110101=>[2,1,1,2,2,1] 01010010=>01001010=>10110101=>[1,2,1,2,2,1] 01010011=>11001010=>00110101=>[3,1,2,2,1] 01010100=>00101010=>11010101=>[1,1,2,2,2,1] 01010101=>10101010=>01010101=>[2,2,2,2,1] 01010110=>01101010=>10010101=>[1,3,2,2,1] 01010111=>11101010=>00010101=>[4,2,2,1] 01011000=>00011010=>11100101=>[1,1,1,3,2,1] 01011001=>10011010=>01100101=>[2,1,3,2,1] 01011010=>01011010=>10100101=>[1,2,3,2,1] 01011011=>11011010=>00100101=>[3,3,2,1] 01011100=>00111010=>11000101=>[1,1,4,2,1] 01011101=>10111010=>01000101=>[2,4,2,1] 01011110=>01111010=>10000101=>[1,5,2,1] 01011111=>11111010=>00000101=>[6,2,1] 01100000=>00000110=>11111001=>[1,1,1,1,1,3,1] 01100001=>10000110=>01111001=>[2,1,1,1,3,1] 01100010=>01000110=>10111001=>[1,2,1,1,3,1] 01100011=>11000110=>00111001=>[3,1,1,3,1] 01100100=>00100110=>11011001=>[1,1,2,1,3,1] 01100101=>10100110=>01011001=>[2,2,1,3,1] 01100110=>01100110=>10011001=>[1,3,1,3,1] 01100111=>11100110=>00011001=>[4,1,3,1] 01101000=>00010110=>11101001=>[1,1,1,2,3,1] 01101001=>10010110=>01101001=>[2,1,2,3,1] 01101010=>01010110=>10101001=>[1,2,2,3,1] 01101011=>11010110=>00101001=>[3,2,3,1] 01101100=>00110110=>11001001=>[1,1,3,3,1] 01101101=>10110110=>01001001=>[2,3,3,1] 01101110=>01110110=>10001001=>[1,4,3,1] 01101111=>11110110=>00001001=>[5,3,1] 01110000=>00001110=>11110001=>[1,1,1,1,4,1] 01110001=>10001110=>01110001=>[2,1,1,4,1] 01110010=>01001110=>10110001=>[1,2,1,4,1] 01110011=>11001110=>00110001=>[3,1,4,1] 01110100=>00101110=>11010001=>[1,1,2,4,1] 01110101=>10101110=>01010001=>[2,2,4,1] 01110110=>01101110=>10010001=>[1,3,4,1] 01110111=>11101110=>00010001=>[4,4,1] 01111000=>00011110=>11100001=>[1,1,1,5,1] 01111001=>10011110=>01100001=>[2,1,5,1] 01111010=>01011110=>10100001=>[1,2,5,1] 01111011=>11011110=>00100001=>[3,5,1] 01111100=>00111110=>11000001=>[1,1,6,1] 01111101=>10111110=>01000001=>[2,6,1] 01111110=>01111110=>10000001=>[1,7,1] 01111111=>11111110=>00000001=>[8,1] 10000000=>00000001=>11111110=>[1,1,1,1,1,1,1,2] 10000001=>10000001=>01111110=>[2,1,1,1,1,1,2] 10000010=>01000001=>10111110=>[1,2,1,1,1,1,2] 10000011=>11000001=>00111110=>[3,1,1,1,1,2] 10000100=>00100001=>11011110=>[1,1,2,1,1,1,2] 10000101=>10100001=>01011110=>[2,2,1,1,1,2] 10000110=>01100001=>10011110=>[1,3,1,1,1,2] 10000111=>11100001=>00011110=>[4,1,1,1,2] 10001000=>00010001=>11101110=>[1,1,1,2,1,1,2] 10001001=>10010001=>01101110=>[2,1,2,1,1,2] 10001010=>01010001=>10101110=>[1,2,2,1,1,2] 10001011=>11010001=>00101110=>[3,2,1,1,2] 10001100=>00110001=>11001110=>[1,1,3,1,1,2] 10001101=>10110001=>01001110=>[2,3,1,1,2] 10001110=>01110001=>10001110=>[1,4,1,1,2] 10001111=>11110001=>00001110=>[5,1,1,2] 10010000=>00001001=>11110110=>[1,1,1,1,2,1,2] 10010001=>10001001=>01110110=>[2,1,1,2,1,2] 10010010=>01001001=>10110110=>[1,2,1,2,1,2] 10010011=>11001001=>00110110=>[3,1,2,1,2] 10010100=>00101001=>11010110=>[1,1,2,2,1,2] 10010101=>10101001=>01010110=>[2,2,2,1,2] 10010110=>01101001=>10010110=>[1,3,2,1,2] 10010111=>11101001=>00010110=>[4,2,1,2] 10011000=>00011001=>11100110=>[1,1,1,3,1,2] 10011001=>10011001=>01100110=>[2,1,3,1,2] 10011010=>01011001=>10100110=>[1,2,3,1,2] 10011011=>11011001=>00100110=>[3,3,1,2] 10011100=>00111001=>11000110=>[1,1,4,1,2] 10011101=>10111001=>01000110=>[2,4,1,2] 10011110=>01111001=>10000110=>[1,5,1,2] 10011111=>11111001=>00000110=>[6,1,2] 10100000=>00000101=>11111010=>[1,1,1,1,1,2,2] 10100001=>10000101=>01111010=>[2,1,1,1,2,2] 10100010=>01000101=>10111010=>[1,2,1,1,2,2] 10100011=>11000101=>00111010=>[3,1,1,2,2] 10100100=>00100101=>11011010=>[1,1,2,1,2,2] 10100101=>10100101=>01011010=>[2,2,1,2,2] 10100110=>01100101=>10011010=>[1,3,1,2,2] 10100111=>11100101=>00011010=>[4,1,2,2] 10101000=>00010101=>11101010=>[1,1,1,2,2,2] 10101001=>10010101=>01101010=>[2,1,2,2,2] 10101010=>01010101=>10101010=>[1,2,2,2,2] 10101011=>11010101=>00101010=>[3,2,2,2] 10101100=>00110101=>11001010=>[1,1,3,2,2] 10101101=>10110101=>01001010=>[2,3,2,2] 10101110=>01110101=>10001010=>[1,4,2,2] 10101111=>11110101=>00001010=>[5,2,2] 10110000=>00001101=>11110010=>[1,1,1,1,3,2] 10110001=>10001101=>01110010=>[2,1,1,3,2] 10110010=>01001101=>10110010=>[1,2,1,3,2] 10110011=>11001101=>00110010=>[3,1,3,2] 10110100=>00101101=>11010010=>[1,1,2,3,2] 10110101=>10101101=>01010010=>[2,2,3,2] 10110110=>01101101=>10010010=>[1,3,3,2] 10110111=>11101101=>00010010=>[4,3,2] 10111000=>00011101=>11100010=>[1,1,1,4,2] 10111001=>10011101=>01100010=>[2,1,4,2] 10111010=>01011101=>10100010=>[1,2,4,2] 10111011=>11011101=>00100010=>[3,4,2] 10111100=>00111101=>11000010=>[1,1,5,2] 10111101=>10111101=>01000010=>[2,5,2] 10111110=>01111101=>10000010=>[1,6,2] 10111111=>11111101=>00000010=>[7,2] 11000000=>00000011=>11111100=>[1,1,1,1,1,1,3] 11000001=>10000011=>01111100=>[2,1,1,1,1,3] 11000010=>01000011=>10111100=>[1,2,1,1,1,3] 11000011=>11000011=>00111100=>[3,1,1,1,3] 11000100=>00100011=>11011100=>[1,1,2,1,1,3] 11000101=>10100011=>01011100=>[2,2,1,1,3] 11000110=>01100011=>10011100=>[1,3,1,1,3] 11000111=>11100011=>00011100=>[4,1,1,3] 11001000=>00010011=>11101100=>[1,1,1,2,1,3] 11001001=>10010011=>01101100=>[2,1,2,1,3] 11001010=>01010011=>10101100=>[1,2,2,1,3] 11001011=>11010011=>00101100=>[3,2,1,3] 11001100=>00110011=>11001100=>[1,1,3,1,3] 11001101=>10110011=>01001100=>[2,3,1,3] 11001110=>01110011=>10001100=>[1,4,1,3] 11001111=>11110011=>00001100=>[5,1,3] 11010000=>00001011=>11110100=>[1,1,1,1,2,3] 11010001=>10001011=>01110100=>[2,1,1,2,3] 11010010=>01001011=>10110100=>[1,2,1,2,3] 11010011=>11001011=>00110100=>[3,1,2,3] 11010100=>00101011=>11010100=>[1,1,2,2,3] 11010101=>10101011=>01010100=>[2,2,2,3] 11010110=>01101011=>10010100=>[1,3,2,3] 11010111=>11101011=>00010100=>[4,2,3] 11011000=>00011011=>11100100=>[1,1,1,3,3] 11011001=>10011011=>01100100=>[2,1,3,3] 11011010=>01011011=>10100100=>[1,2,3,3] 11011011=>11011011=>00100100=>[3,3,3] 11011100=>00111011=>11000100=>[1,1,4,3] 11011101=>10111011=>01000100=>[2,4,3] 11011110=>01111011=>10000100=>[1,5,3] 11011111=>11111011=>00000100=>[6,3] 11100000=>00000111=>11111000=>[1,1,1,1,1,4] 11100001=>10000111=>01111000=>[2,1,1,1,4] 11100010=>01000111=>10111000=>[1,2,1,1,4] 11100011=>11000111=>00111000=>[3,1,1,4] 11100100=>00100111=>11011000=>[1,1,2,1,4] 11100101=>10100111=>01011000=>[2,2,1,4] 11100110=>01100111=>10011000=>[1,3,1,4] 11100111=>11100111=>00011000=>[4,1,4] 11101000=>00010111=>11101000=>[1,1,1,2,4] 11101001=>10010111=>01101000=>[2,1,2,4] 11101010=>01010111=>10101000=>[1,2,2,4] 11101011=>11010111=>00101000=>[3,2,4] 11101100=>00110111=>11001000=>[1,1,3,4] 11101101=>10110111=>01001000=>[2,3,4] 11101110=>01110111=>10001000=>[1,4,4] 11101111=>11110111=>00001000=>[5,4] 11110000=>00001111=>11110000=>[1,1,1,1,5] 11110001=>10001111=>01110000=>[2,1,1,5] 11110010=>01001111=>10110000=>[1,2,1,5] 11110011=>11001111=>00110000=>[3,1,5] 11110100=>00101111=>11010000=>[1,1,2,5] 11110101=>10101111=>01010000=>[2,2,5] 11110110=>01101111=>10010000=>[1,3,5] 11110111=>11101111=>00010000=>[4,5] 11111000=>00011111=>11100000=>[1,1,1,6] 11111001=>10011111=>01100000=>[2,1,6] 11111010=>01011111=>10100000=>[1,2,6] 11111011=>11011111=>00100000=>[3,6] 11111100=>00111111=>11000000=>[1,1,7] 11111101=>10111111=>01000000=>[2,7] 11111110=>01111111=>10000000=>[1,8] 11111111=>11111111=>00000000=>[9] 000000000=>000000000=>111111111=>[1,1,1,1,1,1,1,1,1,1] 000000001=>100000000=>011111111=>[2,1,1,1,1,1,1,1,1] 000000010=>010000000=>101111111=>[1,2,1,1,1,1,1,1,1] 000000011=>110000000=>001111111=>[3,1,1,1,1,1,1,1] 000000100=>001000000=>110111111=>[1,1,2,1,1,1,1,1,1] 000000101=>101000000=>010111111=>[2,2,1,1,1,1,1,1] 000000110=>011000000=>100111111=>[1,3,1,1,1,1,1,1] 000000111=>111000000=>000111111=>[4,1,1,1,1,1,1] 000001000=>000100000=>111011111=>[1,1,1,2,1,1,1,1,1] 000001001=>100100000=>011011111=>[2,1,2,1,1,1,1,1] 000001010=>010100000=>101011111=>[1,2,2,1,1,1,1,1] 000001011=>110100000=>001011111=>[3,2,1,1,1,1,1] 000001100=>001100000=>110011111=>[1,1,3,1,1,1,1,1] 000001101=>101100000=>010011111=>[2,3,1,1,1,1,1] 000001110=>011100000=>100011111=>[1,4,1,1,1,1,1] 000001111=>111100000=>000011111=>[5,1,1,1,1,1] 000010000=>000010000=>111101111=>[1,1,1,1,2,1,1,1,1] 000010001=>100010000=>011101111=>[2,1,1,2,1,1,1,1] 000010010=>010010000=>101101111=>[1,2,1,2,1,1,1,1] 000010011=>110010000=>001101111=>[3,1,2,1,1,1,1] 000010100=>001010000=>110101111=>[1,1,2,2,1,1,1,1] 000010101=>101010000=>010101111=>[2,2,2,1,1,1,1] 000010110=>011010000=>100101111=>[1,3,2,1,1,1,1] 000010111=>111010000=>000101111=>[4,2,1,1,1,1] 000011000=>000110000=>111001111=>[1,1,1,3,1,1,1,1] 000011001=>100110000=>011001111=>[2,1,3,1,1,1,1] 000011010=>010110000=>101001111=>[1,2,3,1,1,1,1] 000011011=>110110000=>001001111=>[3,3,1,1,1,1] 000011100=>001110000=>110001111=>[1,1,4,1,1,1,1] 000011101=>101110000=>010001111=>[2,4,1,1,1,1] 000011110=>011110000=>100001111=>[1,5,1,1,1,1] 000011111=>111110000=>000001111=>[6,1,1,1,1] 000100000=>000001000=>111110111=>[1,1,1,1,1,2,1,1,1] 000100001=>100001000=>011110111=>[2,1,1,1,2,1,1,1] 000100010=>010001000=>101110111=>[1,2,1,1,2,1,1,1] 000100011=>110001000=>001110111=>[3,1,1,2,1,1,1] 000100100=>001001000=>110110111=>[1,1,2,1,2,1,1,1] 000100101=>101001000=>010110111=>[2,2,1,2,1,1,1] 000100110=>011001000=>100110111=>[1,3,1,2,1,1,1] 000100111=>111001000=>000110111=>[4,1,2,1,1,1] 000101000=>000101000=>111010111=>[1,1,1,2,2,1,1,1] 000101001=>100101000=>011010111=>[2,1,2,2,1,1,1] 000101010=>010101000=>101010111=>[1,2,2,2,1,1,1] 000101011=>110101000=>001010111=>[3,2,2,1,1,1] 000101100=>001101000=>110010111=>[1,1,3,2,1,1,1] 000101101=>101101000=>010010111=>[2,3,2,1,1,1] 000101110=>011101000=>100010111=>[1,4,2,1,1,1] 000101111=>111101000=>000010111=>[5,2,1,1,1] 000110000=>000011000=>111100111=>[1,1,1,1,3,1,1,1] 000110001=>100011000=>011100111=>[2,1,1,3,1,1,1] 000110010=>010011000=>101100111=>[1,2,1,3,1,1,1] 000110011=>110011000=>001100111=>[3,1,3,1,1,1] 000110100=>001011000=>110100111=>[1,1,2,3,1,1,1] 000110101=>101011000=>010100111=>[2,2,3,1,1,1] 000110110=>011011000=>100100111=>[1,3,3,1,1,1] 000110111=>111011000=>000100111=>[4,3,1,1,1] 000111000=>000111000=>111000111=>[1,1,1,4,1,1,1] 000111001=>100111000=>011000111=>[2,1,4,1,1,1] 000111010=>010111000=>101000111=>[1,2,4,1,1,1] 000111011=>110111000=>001000111=>[3,4,1,1,1] 000111100=>001111000=>110000111=>[1,1,5,1,1,1] 000111101=>101111000=>010000111=>[2,5,1,1,1] 000111110=>011111000=>100000111=>[1,6,1,1,1] 000111111=>111111000=>000000111=>[7,1,1,1] 001000000=>000000100=>111111011=>[1,1,1,1,1,1,2,1,1] 001000001=>100000100=>011111011=>[2,1,1,1,1,2,1,1] 001000010=>010000100=>101111011=>[1,2,1,1,1,2,1,1] 001000011=>110000100=>001111011=>[3,1,1,1,2,1,1] 001000100=>001000100=>110111011=>[1,1,2,1,1,2,1,1] 001000101=>101000100=>010111011=>[2,2,1,1,2,1,1] 001000110=>011000100=>100111011=>[1,3,1,1,2,1,1] 001000111=>111000100=>000111011=>[4,1,1,2,1,1] 001001000=>000100100=>111011011=>[1,1,1,2,1,2,1,1] 001001001=>100100100=>011011011=>[2,1,2,1,2,1,1] 001001010=>010100100=>101011011=>[1,2,2,1,2,1,1] 001001011=>110100100=>001011011=>[3,2,1,2,1,1] 001001100=>001100100=>110011011=>[1,1,3,1,2,1,1] 001001101=>101100100=>010011011=>[2,3,1,2,1,1] 001001110=>011100100=>100011011=>[1,4,1,2,1,1] 001001111=>111100100=>000011011=>[5,1,2,1,1] 001010000=>000010100=>111101011=>[1,1,1,1,2,2,1,1] 001010001=>100010100=>011101011=>[2,1,1,2,2,1,1] 001010010=>010010100=>101101011=>[1,2,1,2,2,1,1] 001010011=>110010100=>001101011=>[3,1,2,2,1,1] 001010100=>001010100=>110101011=>[1,1,2,2,2,1,1] 001010101=>101010100=>010101011=>[2,2,2,2,1,1] 001010110=>011010100=>100101011=>[1,3,2,2,1,1] 001010111=>111010100=>000101011=>[4,2,2,1,1] 001011000=>000110100=>111001011=>[1,1,1,3,2,1,1] 001011001=>100110100=>011001011=>[2,1,3,2,1,1] 001011010=>010110100=>101001011=>[1,2,3,2,1,1] 001011011=>110110100=>001001011=>[3,3,2,1,1] 001011100=>001110100=>110001011=>[1,1,4,2,1,1] 001011101=>101110100=>010001011=>[2,4,2,1,1] 001011110=>011110100=>100001011=>[1,5,2,1,1] 001011111=>111110100=>000001011=>[6,2,1,1] 001100000=>000001100=>111110011=>[1,1,1,1,1,3,1,1] 001100001=>100001100=>011110011=>[2,1,1,1,3,1,1] 001100010=>010001100=>101110011=>[1,2,1,1,3,1,1] 001100011=>110001100=>001110011=>[3,1,1,3,1,1] 001100100=>001001100=>110110011=>[1,1,2,1,3,1,1] 001100101=>101001100=>010110011=>[2,2,1,3,1,1] 001100110=>011001100=>100110011=>[1,3,1,3,1,1] 001100111=>111001100=>000110011=>[4,1,3,1,1] 001101000=>000101100=>111010011=>[1,1,1,2,3,1,1] 001101001=>100101100=>011010011=>[2,1,2,3,1,1] 001101010=>010101100=>101010011=>[1,2,2,3,1,1] 001101011=>110101100=>001010011=>[3,2,3,1,1] 001101100=>001101100=>110010011=>[1,1,3,3,1,1] 001101101=>101101100=>010010011=>[2,3,3,1,1] 001101110=>011101100=>100010011=>[1,4,3,1,1] 001101111=>111101100=>000010011=>[5,3,1,1] 001110000=>000011100=>111100011=>[1,1,1,1,4,1,1] 001110001=>100011100=>011100011=>[2,1,1,4,1,1] 001110010=>010011100=>101100011=>[1,2,1,4,1,1] 001110011=>110011100=>001100011=>[3,1,4,1,1] 001110100=>001011100=>110100011=>[1,1,2,4,1,1] 001110101=>101011100=>010100011=>[2,2,4,1,1] 001110110=>011011100=>100100011=>[1,3,4,1,1] 001110111=>111011100=>000100011=>[4,4,1,1] 001111000=>000111100=>111000011=>[1,1,1,5,1,1] 001111001=>100111100=>011000011=>[2,1,5,1,1] 001111010=>010111100=>101000011=>[1,2,5,1,1] 001111011=>110111100=>001000011=>[3,5,1,1] 001111100=>001111100=>110000011=>[1,1,6,1,1] 001111101=>101111100=>010000011=>[2,6,1,1] 001111110=>011111100=>100000011=>[1,7,1,1] 001111111=>111111100=>000000011=>[8,1,1] 010000000=>000000010=>111111101=>[1,1,1,1,1,1,1,2,1] 010000001=>100000010=>011111101=>[2,1,1,1,1,1,2,1] 010000010=>010000010=>101111101=>[1,2,1,1,1,1,2,1] 010000011=>110000010=>001111101=>[3,1,1,1,1,2,1] 010000100=>001000010=>110111101=>[1,1,2,1,1,1,2,1] 010000101=>101000010=>010111101=>[2,2,1,1,1,2,1] 010000110=>011000010=>100111101=>[1,3,1,1,1,2,1] 010000111=>111000010=>000111101=>[4,1,1,1,2,1] 010001000=>000100010=>111011101=>[1,1,1,2,1,1,2,1] 010001001=>100100010=>011011101=>[2,1,2,1,1,2,1] 010001010=>010100010=>101011101=>[1,2,2,1,1,2,1] 010001011=>110100010=>001011101=>[3,2,1,1,2,1] 010001100=>001100010=>110011101=>[1,1,3,1,1,2,1] 010001101=>101100010=>010011101=>[2,3,1,1,2,1] 010001110=>011100010=>100011101=>[1,4,1,1,2,1] 010001111=>111100010=>000011101=>[5,1,1,2,1] 010010000=>000010010=>111101101=>[1,1,1,1,2,1,2,1] 010010001=>100010010=>011101101=>[2,1,1,2,1,2,1] 010010010=>010010010=>101101101=>[1,2,1,2,1,2,1] 010010011=>110010010=>001101101=>[3,1,2,1,2,1] 010010100=>001010010=>110101101=>[1,1,2,2,1,2,1] 010010101=>101010010=>010101101=>[2,2,2,1,2,1] 010010110=>011010010=>100101101=>[1,3,2,1,2,1] 010010111=>111010010=>000101101=>[4,2,1,2,1] 010011000=>000110010=>111001101=>[1,1,1,3,1,2,1] 010011001=>100110010=>011001101=>[2,1,3,1,2,1] 010011010=>010110010=>101001101=>[1,2,3,1,2,1] 010011011=>110110010=>001001101=>[3,3,1,2,1] 010011100=>001110010=>110001101=>[1,1,4,1,2,1] 010011101=>101110010=>010001101=>[2,4,1,2,1] 010011110=>011110010=>100001101=>[1,5,1,2,1] 010011111=>111110010=>000001101=>[6,1,2,1] 010100000=>000001010=>111110101=>[1,1,1,1,1,2,2,1] 010100001=>100001010=>011110101=>[2,1,1,1,2,2,1] 010100010=>010001010=>101110101=>[1,2,1,1,2,2,1] 010100011=>110001010=>001110101=>[3,1,1,2,2,1] 010100100=>001001010=>110110101=>[1,1,2,1,2,2,1] 010100101=>101001010=>010110101=>[2,2,1,2,2,1] 010100110=>011001010=>100110101=>[1,3,1,2,2,1] 010100111=>111001010=>000110101=>[4,1,2,2,1] 010101000=>000101010=>111010101=>[1,1,1,2,2,2,1] 010101001=>100101010=>011010101=>[2,1,2,2,2,1] 010101010=>010101010=>101010101=>[1,2,2,2,2,1] 010101011=>110101010=>001010101=>[3,2,2,2,1] 010101100=>001101010=>110010101=>[1,1,3,2,2,1] 010101101=>101101010=>010010101=>[2,3,2,2,1] 010101110=>011101010=>100010101=>[1,4,2,2,1] 010101111=>111101010=>000010101=>[5,2,2,1] 010110000=>000011010=>111100101=>[1,1,1,1,3,2,1] 010110001=>100011010=>011100101=>[2,1,1,3,2,1] 010110010=>010011010=>101100101=>[1,2,1,3,2,1] 010110011=>110011010=>001100101=>[3,1,3,2,1] 010110100=>001011010=>110100101=>[1,1,2,3,2,1] 010110101=>101011010=>010100101=>[2,2,3,2,1] 010110110=>011011010=>100100101=>[1,3,3,2,1] 010110111=>111011010=>000100101=>[4,3,2,1] 010111000=>000111010=>111000101=>[1,1,1,4,2,1] 010111001=>100111010=>011000101=>[2,1,4,2,1] 010111010=>010111010=>101000101=>[1,2,4,2,1] 010111011=>110111010=>001000101=>[3,4,2,1] 010111100=>001111010=>110000101=>[1,1,5,2,1] 010111101=>101111010=>010000101=>[2,5,2,1] 010111110=>011111010=>100000101=>[1,6,2,1] 010111111=>111111010=>000000101=>[7,2,1] 011000000=>000000110=>111111001=>[1,1,1,1,1,1,3,1] 011000001=>100000110=>011111001=>[2,1,1,1,1,3,1] 011000010=>010000110=>101111001=>[1,2,1,1,1,3,1] 011000011=>110000110=>001111001=>[3,1,1,1,3,1] 011000100=>001000110=>110111001=>[1,1,2,1,1,3,1] 011000101=>101000110=>010111001=>[2,2,1,1,3,1] 011000110=>011000110=>100111001=>[1,3,1,1,3,1] 011000111=>111000110=>000111001=>[4,1,1,3,1] 011001000=>000100110=>111011001=>[1,1,1,2,1,3,1] 011001001=>100100110=>011011001=>[2,1,2,1,3,1] 011001010=>010100110=>101011001=>[1,2,2,1,3,1] 011001011=>110100110=>001011001=>[3,2,1,3,1] 011001100=>001100110=>110011001=>[1,1,3,1,3,1] 011001101=>101100110=>010011001=>[2,3,1,3,1] 011001110=>011100110=>100011001=>[1,4,1,3,1] 011001111=>111100110=>000011001=>[5,1,3,1] 011010000=>000010110=>111101001=>[1,1,1,1,2,3,1] 011010001=>100010110=>011101001=>[2,1,1,2,3,1] 011010010=>010010110=>101101001=>[1,2,1,2,3,1] 011010011=>110010110=>001101001=>[3,1,2,3,1] 011010100=>001010110=>110101001=>[1,1,2,2,3,1] 011010101=>101010110=>010101001=>[2,2,2,3,1] 011010110=>011010110=>100101001=>[1,3,2,3,1] 011010111=>111010110=>000101001=>[4,2,3,1] 011011000=>000110110=>111001001=>[1,1,1,3,3,1] 011011001=>100110110=>011001001=>[2,1,3,3,1] 011011010=>010110110=>101001001=>[1,2,3,3,1] 011011011=>110110110=>001001001=>[3,3,3,1] 011011100=>001110110=>110001001=>[1,1,4,3,1] 011011101=>101110110=>010001001=>[2,4,3,1] 011011110=>011110110=>100001001=>[1,5,3,1] 011011111=>111110110=>000001001=>[6,3,1] 011100000=>000001110=>111110001=>[1,1,1,1,1,4,1] 011100001=>100001110=>011110001=>[2,1,1,1,4,1] 011100010=>010001110=>101110001=>[1,2,1,1,4,1] 011100011=>110001110=>001110001=>[3,1,1,4,1] 011100100=>001001110=>110110001=>[1,1,2,1,4,1] 011100101=>101001110=>010110001=>[2,2,1,4,1] 011100110=>011001110=>100110001=>[1,3,1,4,1] 011100111=>111001110=>000110001=>[4,1,4,1] 011101000=>000101110=>111010001=>[1,1,1,2,4,1] 011101001=>100101110=>011010001=>[2,1,2,4,1] 011101010=>010101110=>101010001=>[1,2,2,4,1] 011101011=>110101110=>001010001=>[3,2,4,1] 011101100=>001101110=>110010001=>[1,1,3,4,1] 011101101=>101101110=>010010001=>[2,3,4,1] 011101110=>011101110=>100010001=>[1,4,4,1] 011101111=>111101110=>000010001=>[5,4,1] 011110000=>000011110=>111100001=>[1,1,1,1,5,1] 011110001=>100011110=>011100001=>[2,1,1,5,1] 011110010=>010011110=>101100001=>[1,2,1,5,1] 011110011=>110011110=>001100001=>[3,1,5,1] 011110100=>001011110=>110100001=>[1,1,2,5,1] 011110101=>101011110=>010100001=>[2,2,5,1] 011110110=>011011110=>100100001=>[1,3,5,1] 011110111=>111011110=>000100001=>[4,5,1] 011111000=>000111110=>111000001=>[1,1,1,6,1] 011111001=>100111110=>011000001=>[2,1,6,1] 011111010=>010111110=>101000001=>[1,2,6,1] 011111011=>110111110=>001000001=>[3,6,1] 011111100=>001111110=>110000001=>[1,1,7,1] 011111101=>101111110=>010000001=>[2,7,1] 011111110=>011111110=>100000001=>[1,8,1] 011111111=>111111110=>000000001=>[9,1] 100000000=>000000001=>111111110=>[1,1,1,1,1,1,1,1,2] 100000001=>100000001=>011111110=>[2,1,1,1,1,1,1,2] 100000010=>010000001=>101111110=>[1,2,1,1,1,1,1,2] 100000011=>110000001=>001111110=>[3,1,1,1,1,1,2] 100000100=>001000001=>110111110=>[1,1,2,1,1,1,1,2] 100000101=>101000001=>010111110=>[2,2,1,1,1,1,2] 100000110=>011000001=>100111110=>[1,3,1,1,1,1,2] 100000111=>111000001=>000111110=>[4,1,1,1,1,2] 100001000=>000100001=>111011110=>[1,1,1,2,1,1,1,2] 100001001=>100100001=>011011110=>[2,1,2,1,1,1,2] 100001010=>010100001=>101011110=>[1,2,2,1,1,1,2] 100001011=>110100001=>001011110=>[3,2,1,1,1,2] 100001100=>001100001=>110011110=>[1,1,3,1,1,1,2] 100001101=>101100001=>010011110=>[2,3,1,1,1,2] 100001110=>011100001=>100011110=>[1,4,1,1,1,2] 100001111=>111100001=>000011110=>[5,1,1,1,2] 100010000=>000010001=>111101110=>[1,1,1,1,2,1,1,2] 100010001=>100010001=>011101110=>[2,1,1,2,1,1,2] 100010010=>010010001=>101101110=>[1,2,1,2,1,1,2] 100010011=>110010001=>001101110=>[3,1,2,1,1,2] 100010100=>001010001=>110101110=>[1,1,2,2,1,1,2] 100010101=>101010001=>010101110=>[2,2,2,1,1,2] 100010110=>011010001=>100101110=>[1,3,2,1,1,2] 100010111=>111010001=>000101110=>[4,2,1,1,2] 100011000=>000110001=>111001110=>[1,1,1,3,1,1,2] 100011001=>100110001=>011001110=>[2,1,3,1,1,2] 100011010=>010110001=>101001110=>[1,2,3,1,1,2] 100011011=>110110001=>001001110=>[3,3,1,1,2] 100011100=>001110001=>110001110=>[1,1,4,1,1,2] 100011101=>101110001=>010001110=>[2,4,1,1,2] 100011110=>011110001=>100001110=>[1,5,1,1,2] 100011111=>111110001=>000001110=>[6,1,1,2] 100100000=>000001001=>111110110=>[1,1,1,1,1,2,1,2] 100100001=>100001001=>011110110=>[2,1,1,1,2,1,2] 100100010=>010001001=>101110110=>[1,2,1,1,2,1,2] 100100011=>110001001=>001110110=>[3,1,1,2,1,2] 100100100=>001001001=>110110110=>[1,1,2,1,2,1,2] 100100101=>101001001=>010110110=>[2,2,1,2,1,2] 100100110=>011001001=>100110110=>[1,3,1,2,1,2] 100100111=>111001001=>000110110=>[4,1,2,1,2] 100101000=>000101001=>111010110=>[1,1,1,2,2,1,2] 100101001=>100101001=>011010110=>[2,1,2,2,1,2] 100101010=>010101001=>101010110=>[1,2,2,2,1,2] 100101011=>110101001=>001010110=>[3,2,2,1,2] 100101100=>001101001=>110010110=>[1,1,3,2,1,2] 100101101=>101101001=>010010110=>[2,3,2,1,2] 100101110=>011101001=>100010110=>[1,4,2,1,2] 100101111=>111101001=>000010110=>[5,2,1,2] 100110000=>000011001=>111100110=>[1,1,1,1,3,1,2] 100110001=>100011001=>011100110=>[2,1,1,3,1,2] 100110010=>010011001=>101100110=>[1,2,1,3,1,2] 100110011=>110011001=>001100110=>[3,1,3,1,2] 100110100=>001011001=>110100110=>[1,1,2,3,1,2] 100110101=>101011001=>010100110=>[2,2,3,1,2] 100110110=>011011001=>100100110=>[1,3,3,1,2] 100110111=>111011001=>000100110=>[4,3,1,2] 100111000=>000111001=>111000110=>[1,1,1,4,1,2] 100111001=>100111001=>011000110=>[2,1,4,1,2] 100111010=>010111001=>101000110=>[1,2,4,1,2] 100111011=>110111001=>001000110=>[3,4,1,2] 100111100=>001111001=>110000110=>[1,1,5,1,2] 100111101=>101111001=>010000110=>[2,5,1,2] 100111110=>011111001=>100000110=>[1,6,1,2] 100111111=>111111001=>000000110=>[7,1,2] 101000000=>000000101=>111111010=>[1,1,1,1,1,1,2,2] 101000001=>100000101=>011111010=>[2,1,1,1,1,2,2] 101000010=>010000101=>101111010=>[1,2,1,1,1,2,2] 101000011=>110000101=>001111010=>[3,1,1,1,2,2] 101000100=>001000101=>110111010=>[1,1,2,1,1,2,2] 101000101=>101000101=>010111010=>[2,2,1,1,2,2] 101000110=>011000101=>100111010=>[1,3,1,1,2,2] 101000111=>111000101=>000111010=>[4,1,1,2,2] 101001000=>000100101=>111011010=>[1,1,1,2,1,2,2] 101001001=>100100101=>011011010=>[2,1,2,1,2,2] 101001010=>010100101=>101011010=>[1,2,2,1,2,2] 101001011=>110100101=>001011010=>[3,2,1,2,2] 101001100=>001100101=>110011010=>[1,1,3,1,2,2] 101001101=>101100101=>010011010=>[2,3,1,2,2] 101001110=>011100101=>100011010=>[1,4,1,2,2] 101001111=>111100101=>000011010=>[5,1,2,2] 101010000=>000010101=>111101010=>[1,1,1,1,2,2,2] 101010001=>100010101=>011101010=>[2,1,1,2,2,2] 101010010=>010010101=>101101010=>[1,2,1,2,2,2] 101010011=>110010101=>001101010=>[3,1,2,2,2] 101010100=>001010101=>110101010=>[1,1,2,2,2,2] 101010101=>101010101=>010101010=>[2,2,2,2,2] 101010110=>011010101=>100101010=>[1,3,2,2,2] 101010111=>111010101=>000101010=>[4,2,2,2] 101011000=>000110101=>111001010=>[1,1,1,3,2,2] 101011001=>100110101=>011001010=>[2,1,3,2,2] 101011010=>010110101=>101001010=>[1,2,3,2,2] 101011011=>110110101=>001001010=>[3,3,2,2] 101011100=>001110101=>110001010=>[1,1,4,2,2] 101011101=>101110101=>010001010=>[2,4,2,2] 101011110=>011110101=>100001010=>[1,5,2,2] 101011111=>111110101=>000001010=>[6,2,2] 101100000=>000001101=>111110010=>[1,1,1,1,1,3,2] 101100001=>100001101=>011110010=>[2,1,1,1,3,2] 101100010=>010001101=>101110010=>[1,2,1,1,3,2] 101100011=>110001101=>001110010=>[3,1,1,3,2] 101100100=>001001101=>110110010=>[1,1,2,1,3,2] 101100101=>101001101=>010110010=>[2,2,1,3,2] 101100110=>011001101=>100110010=>[1,3,1,3,2] 101100111=>111001101=>000110010=>[4,1,3,2] 101101000=>000101101=>111010010=>[1,1,1,2,3,2] 101101001=>100101101=>011010010=>[2,1,2,3,2] 101101010=>010101101=>101010010=>[1,2,2,3,2] 101101011=>110101101=>001010010=>[3,2,3,2] 101101100=>001101101=>110010010=>[1,1,3,3,2] 101101101=>101101101=>010010010=>[2,3,3,2] 101101110=>011101101=>100010010=>[1,4,3,2] 101101111=>111101101=>000010010=>[5,3,2] 101110000=>000011101=>111100010=>[1,1,1,1,4,2] 101110001=>100011101=>011100010=>[2,1,1,4,2] 101110010=>010011101=>101100010=>[1,2,1,4,2] 101110011=>110011101=>001100010=>[3,1,4,2] 101110100=>001011101=>110100010=>[1,1,2,4,2] 101110101=>101011101=>010100010=>[2,2,4,2] 101110110=>011011101=>100100010=>[1,3,4,2] 101110111=>111011101=>000100010=>[4,4,2] 101111000=>000111101=>111000010=>[1,1,1,5,2] 101111001=>100111101=>011000010=>[2,1,5,2] 101111010=>010111101=>101000010=>[1,2,5,2] 101111011=>110111101=>001000010=>[3,5,2] 101111100=>001111101=>110000010=>[1,1,6,2] 101111101=>101111101=>010000010=>[2,6,2] 101111110=>011111101=>100000010=>[1,7,2] 101111111=>111111101=>000000010=>[8,2] 110000000=>000000011=>111111100=>[1,1,1,1,1,1,1,3] 110000001=>100000011=>011111100=>[2,1,1,1,1,1,3] 110000010=>010000011=>101111100=>[1,2,1,1,1,1,3] 110000011=>110000011=>001111100=>[3,1,1,1,1,3] 110000100=>001000011=>110111100=>[1,1,2,1,1,1,3] 110000101=>101000011=>010111100=>[2,2,1,1,1,3] 110000110=>011000011=>100111100=>[1,3,1,1,1,3] 110000111=>111000011=>000111100=>[4,1,1,1,3] 110001000=>000100011=>111011100=>[1,1,1,2,1,1,3] 110001001=>100100011=>011011100=>[2,1,2,1,1,3] 110001010=>010100011=>101011100=>[1,2,2,1,1,3] 110001011=>110100011=>001011100=>[3,2,1,1,3] 110001100=>001100011=>110011100=>[1,1,3,1,1,3] 110001101=>101100011=>010011100=>[2,3,1,1,3] 110001110=>011100011=>100011100=>[1,4,1,1,3] 110001111=>111100011=>000011100=>[5,1,1,3] 110010000=>000010011=>111101100=>[1,1,1,1,2,1,3] 110010001=>100010011=>011101100=>[2,1,1,2,1,3] 110010010=>010010011=>101101100=>[1,2,1,2,1,3] 110010011=>110010011=>001101100=>[3,1,2,1,3] 110010100=>001010011=>110101100=>[1,1,2,2,1,3] 110010101=>101010011=>010101100=>[2,2,2,1,3] 110010110=>011010011=>100101100=>[1,3,2,1,3] 110010111=>111010011=>000101100=>[4,2,1,3] 110011000=>000110011=>111001100=>[1,1,1,3,1,3] 110011001=>100110011=>011001100=>[2,1,3,1,3] 110011010=>010110011=>101001100=>[1,2,3,1,3] 110011011=>110110011=>001001100=>[3,3,1,3] 110011100=>001110011=>110001100=>[1,1,4,1,3] 110011101=>101110011=>010001100=>[2,4,1,3] 110011110=>011110011=>100001100=>[1,5,1,3] 110011111=>111110011=>000001100=>[6,1,3] 110100000=>000001011=>111110100=>[1,1,1,1,1,2,3] 110100001=>100001011=>011110100=>[2,1,1,1,2,3] 110100010=>010001011=>101110100=>[1,2,1,1,2,3] 110100011=>110001011=>001110100=>[3,1,1,2,3] 110100100=>001001011=>110110100=>[1,1,2,1,2,3] 110100101=>101001011=>010110100=>[2,2,1,2,3] 110100110=>011001011=>100110100=>[1,3,1,2,3] 110100111=>111001011=>000110100=>[4,1,2,3] 110101000=>000101011=>111010100=>[1,1,1,2,2,3] 110101001=>100101011=>011010100=>[2,1,2,2,3] 110101010=>010101011=>101010100=>[1,2,2,2,3] 110101011=>110101011=>001010100=>[3,2,2,3] 110101100=>001101011=>110010100=>[1,1,3,2,3] 110101101=>101101011=>010010100=>[2,3,2,3] 110101110=>011101011=>100010100=>[1,4,2,3] 110101111=>111101011=>000010100=>[5,2,3] 110110000=>000011011=>111100100=>[1,1,1,1,3,3] 110110001=>100011011=>011100100=>[2,1,1,3,3] 110110010=>010011011=>101100100=>[1,2,1,3,3] 110110011=>110011011=>001100100=>[3,1,3,3] 110110100=>001011011=>110100100=>[1,1,2,3,3] 110110101=>101011011=>010100100=>[2,2,3,3] 110110110=>011011011=>100100100=>[1,3,3,3] 110110111=>111011011=>000100100=>[4,3,3] 110111000=>000111011=>111000100=>[1,1,1,4,3] 110111001=>100111011=>011000100=>[2,1,4,3] 110111010=>010111011=>101000100=>[1,2,4,3] 110111011=>110111011=>001000100=>[3,4,3] 110111100=>001111011=>110000100=>[1,1,5,3] 110111101=>101111011=>010000100=>[2,5,3] 110111110=>011111011=>100000100=>[1,6,3] 110111111=>111111011=>000000100=>[7,3] 111000000=>000000111=>111111000=>[1,1,1,1,1,1,4] 111000001=>100000111=>011111000=>[2,1,1,1,1,4] 111000010=>010000111=>101111000=>[1,2,1,1,1,4] 111000011=>110000111=>001111000=>[3,1,1,1,4] 111000100=>001000111=>110111000=>[1,1,2,1,1,4] 111000101=>101000111=>010111000=>[2,2,1,1,4] 111000110=>011000111=>100111000=>[1,3,1,1,4] 111000111=>111000111=>000111000=>[4,1,1,4] 111001000=>000100111=>111011000=>[1,1,1,2,1,4] 111001001=>100100111=>011011000=>[2,1,2,1,4] 111001010=>010100111=>101011000=>[1,2,2,1,4] 111001011=>110100111=>001011000=>[3,2,1,4] 111001100=>001100111=>110011000=>[1,1,3,1,4] 111001101=>101100111=>010011000=>[2,3,1,4] 111001110=>011100111=>100011000=>[1,4,1,4] 111001111=>111100111=>000011000=>[5,1,4] 111010000=>000010111=>111101000=>[1,1,1,1,2,4] 111010001=>100010111=>011101000=>[2,1,1,2,4] 111010010=>010010111=>101101000=>[1,2,1,2,4] 111010011=>110010111=>001101000=>[3,1,2,4] 111010100=>001010111=>110101000=>[1,1,2,2,4] 111010101=>101010111=>010101000=>[2,2,2,4] 111010110=>011010111=>100101000=>[1,3,2,4] 111010111=>111010111=>000101000=>[4,2,4] 111011000=>000110111=>111001000=>[1,1,1,3,4] 111011001=>100110111=>011001000=>[2,1,3,4] 111011010=>010110111=>101001000=>[1,2,3,4] 111011011=>110110111=>001001000=>[3,3,4] 111011100=>001110111=>110001000=>[1,1,4,4] 111011101=>101110111=>010001000=>[2,4,4] 111011110=>011110111=>100001000=>[1,5,4] 111011111=>111110111=>000001000=>[6,4] 111100000=>000001111=>111110000=>[1,1,1,1,1,5] 111100001=>100001111=>011110000=>[2,1,1,1,5] 111100010=>010001111=>101110000=>[1,2,1,1,5] 111100011=>110001111=>001110000=>[3,1,1,5] 111100100=>001001111=>110110000=>[1,1,2,1,5] 111100101=>101001111=>010110000=>[2,2,1,5] 111100110=>011001111=>100110000=>[1,3,1,5] 111100111=>111001111=>000110000=>[4,1,5] 111101000=>000101111=>111010000=>[1,1,1,2,5] 111101001=>100101111=>011010000=>[2,1,2,5] 111101010=>010101111=>101010000=>[1,2,2,5] 111101011=>110101111=>001010000=>[3,2,5] 111101100=>001101111=>110010000=>[1,1,3,5] 111101101=>101101111=>010010000=>[2,3,5] 111101110=>011101111=>100010000=>[1,4,5] 111101111=>111101111=>000010000=>[5,5] 111110000=>000011111=>111100000=>[1,1,1,1,6] 111110001=>100011111=>011100000=>[2,1,1,6] 111110010=>010011111=>101100000=>[1,2,1,6] 111110011=>110011111=>001100000=>[3,1,6] 111110100=>001011111=>110100000=>[1,1,2,6] 111110101=>101011111=>010100000=>[2,2,6] 111110110=>011011111=>100100000=>[1,3,6] 111110111=>111011111=>000100000=>[4,6] 111111000=>000111111=>111000000=>[1,1,1,7] 111111001=>100111111=>011000000=>[2,1,7] 111111010=>010111111=>101000000=>[1,2,7] 111111011=>110111111=>001000000=>[3,7] 111111100=>001111111=>110000000=>[1,1,8] 111111101=>101111111=>010000000=>[2,8] 111111110=>011111111=>100000000=>[1,9] 111111111=>111111111=>000000000=>[10] 1010101010=>0101010101=>1010101010=>[1,2,2,2,2,2] 1010101100=>0011010101=>1100101010=>[1,1,3,2,2,2] 1010110010=>0100110101=>1011001010=>[1,2,1,3,2,2] 1010110100=>0010110101=>1101001010=>[1,1,2,3,2,2] 1010111000=>0001110101=>1110001010=>[1,1,1,4,2,2] 1011001010=>0101001101=>1010110010=>[1,2,2,1,3,2] 1011001100=>0011001101=>1100110010=>[1,1,3,1,3,2] 1011010010=>0100101101=>1011010010=>[1,2,1,2,3,2] 1011010100=>0010101101=>1101010010=>[1,1,2,2,3,2] 1011011000=>0001101101=>1110010010=>[1,1,1,3,3,2] 1011100010=>0100011101=>1011100010=>[1,2,1,1,4,2] 1011100100=>0010011101=>1101100010=>[1,1,2,1,4,2] 1011101000=>0001011101=>1110100010=>[1,1,1,2,4,2] 1011110000=>0000111101=>1111000010=>[1,1,1,1,5,2] 1100101010=>0101010011=>1010101100=>[1,2,2,2,1,3] 1100101100=>0011010011=>1100101100=>[1,1,3,2,1,3] 1100110010=>0100110011=>1011001100=>[1,2,1,3,1,3] 1100110100=>0010110011=>1101001100=>[1,1,2,3,1,3] 1100111000=>0001110011=>1110001100=>[1,1,1,4,1,3] 1101001010=>0101001011=>1010110100=>[1,2,2,1,2,3] 1101001100=>0011001011=>1100110100=>[1,1,3,1,2,3] 1101010010=>0100101011=>1011010100=>[1,2,1,2,2,3] 1101010100=>0010101011=>1101010100=>[1,1,2,2,2,3] 1101011000=>0001101011=>1110010100=>[1,1,1,3,2,3] 1101100010=>0100011011=>1011100100=>[1,2,1,1,3,3] 1101100100=>0010011011=>1101100100=>[1,1,2,1,3,3] 1101101000=>0001011011=>1110100100=>[1,1,1,2,3,3] 1101110000=>0000111011=>1111000100=>[1,1,1,1,4,3] 1110001010=>0101000111=>1010111000=>[1,2,2,1,1,4] 1110001100=>0011000111=>1100111000=>[1,1,3,1,1,4] 1110010010=>0100100111=>1011011000=>[1,2,1,2,1,4] 1110010100=>0010100111=>1101011000=>[1,1,2,2,1,4] 1110011000=>0001100111=>1110011000=>[1,1,1,3,1,4] 1110100010=>0100010111=>1011101000=>[1,2,1,1,2,4] 1110100100=>0010010111=>1101101000=>[1,1,2,1,2,4] 1110101000=>0001010111=>1110101000=>[1,1,1,2,2,4] 1110110000=>0000110111=>1111001000=>[1,1,1,1,3,4] 1111000010=>0100001111=>1011110000=>[1,2,1,1,1,5] 1111000100=>0010001111=>1101110000=>[1,1,2,1,1,5] 1111001000=>0001001111=>1110110000=>[1,1,1,2,1,5] 1111010000=>0000101111=>1111010000=>[1,1,1,1,2,5] 1111100000=>0000011111=>1111100000=>[1,1,1,1,1,6] 101010101010=>010101010101=>101010101010=>[1,2,2,2,2,2,2] 101010101100=>001101010101=>110010101010=>[1,1,3,2,2,2,2] 101010110010=>010011010101=>101100101010=>[1,2,1,3,2,2,2] 101010110100=>001011010101=>110100101010=>[1,1,2,3,2,2,2] 101010111000=>000111010101=>111000101010=>[1,1,1,4,2,2,2] 101011001010=>010100110101=>101011001010=>[1,2,2,1,3,2,2] 101011001100=>001100110101=>110011001010=>[1,1,3,1,3,2,2] 101011010010=>010010110101=>101101001010=>[1,2,1,2,3,2,2] 101011010100=>001010110101=>110101001010=>[1,1,2,2,3,2,2] 101011011000=>000110110101=>111001001010=>[1,1,1,3,3,2,2] 101011100010=>010001110101=>101110001010=>[1,2,1,1,4,2,2] 101011100100=>001001110101=>110110001010=>[1,1,2,1,4,2,2] 101011101000=>000101110101=>111010001010=>[1,1,1,2,4,2,2] 101011110000=>000011110101=>111100001010=>[1,1,1,1,5,2,2] 101100101010=>010101001101=>101010110010=>[1,2,2,2,1,3,2] 101100101100=>001101001101=>110010110010=>[1,1,3,2,1,3,2] 101100110010=>010011001101=>101100110010=>[1,2,1,3,1,3,2] 101100110100=>001011001101=>110100110010=>[1,1,2,3,1,3,2] 101100111000=>000111001101=>111000110010=>[1,1,1,4,1,3,2] 101101001010=>010100101101=>101011010010=>[1,2,2,1,2,3,2] 101101001100=>001100101101=>110011010010=>[1,1,3,1,2,3,2] 101101010010=>010010101101=>101101010010=>[1,2,1,2,2,3,2] 101101010100=>001010101101=>110101010010=>[1,1,2,2,2,3,2] 101101011000=>000110101101=>111001010010=>[1,1,1,3,2,3,2] 101101100010=>010001101101=>101110010010=>[1,2,1,1,3,3,2] 101101100100=>001001101101=>110110010010=>[1,1,2,1,3,3,2] 101101101000=>000101101101=>111010010010=>[1,1,1,2,3,3,2] 101101110000=>000011101101=>111100010010=>[1,1,1,1,4,3,2] 101110001010=>010100011101=>101011100010=>[1,2,2,1,1,4,2] 101110001100=>001100011101=>110011100010=>[1,1,3,1,1,4,2] 101110010010=>010010011101=>101101100010=>[1,2,1,2,1,4,2] 101110010100=>001010011101=>110101100010=>[1,1,2,2,1,4,2] 101110011000=>000110011101=>111001100010=>[1,1,1,3,1,4,2] 101110100010=>010001011101=>101110100010=>[1,2,1,1,2,4,2] 101110100100=>001001011101=>110110100010=>[1,1,2,1,2,4,2] 101110101000=>000101011101=>111010100010=>[1,1,1,2,2,4,2] 101110110000=>000011011101=>111100100010=>[1,1,1,1,3,4,2] 101111000010=>010000111101=>101111000010=>[1,2,1,1,1,5,2] 101111000100=>001000111101=>110111000010=>[1,1,2,1,1,5,2] 101111001000=>000100111101=>111011000010=>[1,1,1,2,1,5,2] 101111010000=>000010111101=>111101000010=>[1,1,1,1,2,5,2] 101111100000=>000001111101=>111110000010=>[1,1,1,1,1,6,2] 110010101010=>010101010011=>101010101100=>[1,2,2,2,2,1,3] 110010101100=>001101010011=>110010101100=>[1,1,3,2,2,1,3] 110010110010=>010011010011=>101100101100=>[1,2,1,3,2,1,3] 110010110100=>001011010011=>110100101100=>[1,1,2,3,2,1,3] 110010111000=>000111010011=>111000101100=>[1,1,1,4,2,1,3] 110011001010=>010100110011=>101011001100=>[1,2,2,1,3,1,3] 110011001100=>001100110011=>110011001100=>[1,1,3,1,3,1,3] 110011010010=>010010110011=>101101001100=>[1,2,1,2,3,1,3] 110011010100=>001010110011=>110101001100=>[1,1,2,2,3,1,3] 110011011000=>000110110011=>111001001100=>[1,1,1,3,3,1,3] 110011100010=>010001110011=>101110001100=>[1,2,1,1,4,1,3] 110011100100=>001001110011=>110110001100=>[1,1,2,1,4,1,3] 110011101000=>000101110011=>111010001100=>[1,1,1,2,4,1,3] 110011110000=>000011110011=>111100001100=>[1,1,1,1,5,1,3] 110100101010=>010101001011=>101010110100=>[1,2,2,2,1,2,3] 110100101100=>001101001011=>110010110100=>[1,1,3,2,1,2,3] 110100110010=>010011001011=>101100110100=>[1,2,1,3,1,2,3] 110100110100=>001011001011=>110100110100=>[1,1,2,3,1,2,3] 110100111000=>000111001011=>111000110100=>[1,1,1,4,1,2,3] 110101001010=>010100101011=>101011010100=>[1,2,2,1,2,2,3] 110101001100=>001100101011=>110011010100=>[1,1,3,1,2,2,3] 110101010010=>010010101011=>101101010100=>[1,2,1,2,2,2,3] 110101010100=>001010101011=>110101010100=>[1,1,2,2,2,2,3] 110101011000=>000110101011=>111001010100=>[1,1,1,3,2,2,3] 110101100010=>010001101011=>101110010100=>[1,2,1,1,3,2,3] 110101100100=>001001101011=>110110010100=>[1,1,2,1,3,2,3] 110101101000=>000101101011=>111010010100=>[1,1,1,2,3,2,3] 110101110000=>000011101011=>111100010100=>[1,1,1,1,4,2,3] 110110001010=>010100011011=>101011100100=>[1,2,2,1,1,3,3] 110110001100=>001100011011=>110011100100=>[1,1,3,1,1,3,3] 110110010010=>010010011011=>101101100100=>[1,2,1,2,1,3,3] 110110010100=>001010011011=>110101100100=>[1,1,2,2,1,3,3] 110110011000=>000110011011=>111001100100=>[1,1,1,3,1,3,3] 110110100010=>010001011011=>101110100100=>[1,2,1,1,2,3,3] 110110100100=>001001011011=>110110100100=>[1,1,2,1,2,3,3] 110110101000=>000101011011=>111010100100=>[1,1,1,2,2,3,3] 110110110000=>000011011011=>111100100100=>[1,1,1,1,3,3,3] 110111000010=>010000111011=>101111000100=>[1,2,1,1,1,4,3] 110111000100=>001000111011=>110111000100=>[1,1,2,1,1,4,3] 110111001000=>000100111011=>111011000100=>[1,1,1,2,1,4,3] 110111010000=>000010111011=>111101000100=>[1,1,1,1,2,4,3] 110111100000=>000001111011=>111110000100=>[1,1,1,1,1,5,3] 111000101010=>010101000111=>101010111000=>[1,2,2,2,1,1,4] 111000101100=>001101000111=>110010111000=>[1,1,3,2,1,1,4] 111000110010=>010011000111=>101100111000=>[1,2,1,3,1,1,4] 111000110100=>001011000111=>110100111000=>[1,1,2,3,1,1,4] 111000111000=>000111000111=>111000111000=>[1,1,1,4,1,1,4] 111001001010=>010100100111=>101011011000=>[1,2,2,1,2,1,4] 111001001100=>001100100111=>110011011000=>[1,1,3,1,2,1,4] 111001010010=>010010100111=>101101011000=>[1,2,1,2,2,1,4] 111001010100=>001010100111=>110101011000=>[1,1,2,2,2,1,4] 111001011000=>000110100111=>111001011000=>[1,1,1,3,2,1,4] 111001100010=>010001100111=>101110011000=>[1,2,1,1,3,1,4] 111001100100=>001001100111=>110110011000=>[1,1,2,1,3,1,4] 111001101000=>000101100111=>111010011000=>[1,1,1,2,3,1,4] 111001110000=>000011100111=>111100011000=>[1,1,1,1,4,1,4] 111010001010=>010100010111=>101011101000=>[1,2,2,1,1,2,4] 111010001100=>001100010111=>110011101000=>[1,1,3,1,1,2,4] 111010010010=>010010010111=>101101101000=>[1,2,1,2,1,2,4] 111010010100=>001010010111=>110101101000=>[1,1,2,2,1,2,4] 111010011000=>000110010111=>111001101000=>[1,1,1,3,1,2,4] 111010100010=>010001010111=>101110101000=>[1,2,1,1,2,2,4] 111010100100=>001001010111=>110110101000=>[1,1,2,1,2,2,4] 111010101000=>000101010111=>111010101000=>[1,1,1,2,2,2,4] 111010110000=>000011010111=>111100101000=>[1,1,1,1,3,2,4] 111011000010=>010000110111=>101111001000=>[1,2,1,1,1,3,4] 111011000100=>001000110111=>110111001000=>[1,1,2,1,1,3,4] 111011001000=>000100110111=>111011001000=>[1,1,1,2,1,3,4] 111011010000=>000010110111=>111101001000=>[1,1,1,1,2,3,4] 111011100000=>000001110111=>111110001000=>[1,1,1,1,1,4,4] 111100001010=>010100001111=>101011110000=>[1,2,2,1,1,1,5] 111100001100=>001100001111=>110011110000=>[1,1,3,1,1,1,5] 111100010010=>010010001111=>101101110000=>[1,2,1,2,1,1,5] 111100010100=>001010001111=>110101110000=>[1,1,2,2,1,1,5] 111100011000=>000110001111=>111001110000=>[1,1,1,3,1,1,5] 111100100010=>010001001111=>101110110000=>[1,2,1,1,2,1,5] 111100100100=>001001001111=>110110110000=>[1,1,2,1,2,1,5] 111100101000=>000101001111=>111010110000=>[1,1,1,2,2,1,5] 111100110000=>000011001111=>111100110000=>[1,1,1,1,3,1,5] 111101000010=>010000101111=>101111010000=>[1,2,1,1,1,2,5] 111101000100=>001000101111=>110111010000=>[1,1,2,1,1,2,5] 111101001000=>000100101111=>111011010000=>[1,1,1,2,1,2,5] 111101010000=>000010101111=>111101010000=>[1,1,1,1,2,2,5] 111101100000=>000001101111=>111110010000=>[1,1,1,1,1,3,5] 111110000010=>010000011111=>101111100000=>[1,2,1,1,1,1,6] 111110000100=>001000011111=>110111100000=>[1,1,2,1,1,1,6] 111110001000=>000100011111=>111011100000=>[1,1,1,2,1,1,6] 111110010000=>000010011111=>111101100000=>[1,1,1,1,2,1,6] 111110100000=>000001011111=>111110100000=>[1,1,1,1,1,2,6] 111111000000=>000000111111=>111111000000=>[1,1,1,1,1,1,7] 1111111111=>1111111111=>0000000000=>[11] 1111111110=>0111111111=>1000000000=>[1,10] 1111100010=>0100011111=>1011100000=>[1,2,1,1,6] 1111010111=>1110101111=>0001010000=>[4,2,5] 1111010010=>0100101111=>1011010000=>[1,2,1,2,5] 1111001010=>0101001111=>1010110000=>[1,2,2,1,5] 1111001001=>1001001111=>0110110000=>[2,1,2,1,5] 1111000110=>0110001111=>1001110000=>[1,3,1,1,5] 1111000011=>1100001111=>0011110000=>[3,1,1,1,5] 1111000001=>1000001111=>0111110000=>[2,1,1,1,1,5] 1110110010=>0100110111=>1011001000=>[1,2,1,3,4] 1110101010=>0101010111=>1010101000=>[1,2,2,2,4] 1110100001=>1000010111=>0111101000=>[2,1,1,1,2,4] 1110100000=>0000010111=>1111101000=>[1,1,1,1,1,2,4] 1110000011=>1100000111=>0011111000=>[3,1,1,1,1,4] 1101111111=>1111111011=>0000000100=>[8,3] 1101111110=>0111111011=>1000000100=>[1,7,3] 1101101001=>1001011011=>0110100100=>[2,1,2,3,3] 1101100110=>0110011011=>1001100100=>[1,3,1,3,3] 1101100001=>1000011011=>0111100100=>[2,1,1,1,3,3] 1101100000=>0000011011=>1111100100=>[1,1,1,1,1,3,3] 1101011111=>1111101011=>0000010100=>[6,2,3] 1101010110=>0110101011=>1001010100=>[1,3,2,2,3] 1101010101=>1010101011=>0101010100=>[2,2,2,2,3] 1101010001=>1000101011=>0111010100=>[2,1,1,2,2,3] 1101010000=>0000101011=>1111010100=>[1,1,1,1,2,2,3] 1101001110=>0111001011=>1000110100=>[1,4,1,2,3] 1101000011=>1100001011=>0011110100=>[3,1,1,1,2,3] 1100111111=>1111110011=>0000001100=>[7,1,3] 1100111010=>0101110011=>1010001100=>[1,2,4,1,3] 1100111001=>1001110011=>0110001100=>[2,1,4,1,3] 1100110110=>0110110011=>1001001100=>[1,3,3,1,3] 1100101110=>0111010011=>1000101100=>[1,4,2,1,3] 1100101101=>1011010011=>0100101100=>[2,3,2,1,3] 1100101000=>0001010011=>1110101100=>[1,1,1,2,2,1,3] 1100100111=>1110010011=>0001101100=>[4,1,2,1,3] 1100000111=>1110000011=>0001111100=>[4,1,1,1,1,3] 1100000011=>1100000011=>0011111100=>[3,1,1,1,1,1,3] 1011111111=>1111111101=>0000000010=>[9,2] 1011111110=>0111111101=>1000000010=>[1,8,2] 1011110010=>0100111101=>1011000010=>[1,2,1,5,2] 1011100000=>0000011101=>1111100010=>[1,1,1,1,1,4,2] 1011010110=>0110101101=>1001010010=>[1,3,2,3,2] 1011010000=>0000101101=>1111010010=>[1,1,1,1,2,3,2] 1011001000=>0001001101=>1110110010=>[1,1,1,2,1,3,2] 1010111110=>0111110101=>1000001010=>[1,6,2,2] 1010110000=>0000110101=>1111001010=>[1,1,1,1,3,2,2] 1010101000=>0001010101=>1110101010=>[1,1,1,2,2,2,2] 1001111110=>0111111001=>1000000110=>[1,7,1,2] 1001110011=>1100111001=>0011000110=>[3,1,4,1,2] 1001011111=>1111101001=>0000010110=>[6,2,1,2] 1001011110=>0111101001=>1000010110=>[1,5,2,1,2] 1001000011=>1100001001=>0011110110=>[3,1,1,1,2,1,2] 1000111110=>0111110001=>1000001110=>[1,6,1,1,2] 1000111011=>1101110001=>0010001110=>[3,4,1,1,2] 1000101110=>0111010001=>1000101110=>[1,4,2,1,1,2] 1000101100=>0011010001=>1100101110=>[1,1,3,2,1,1,2] 1000011111=>1111100001=>0000011110=>[6,1,1,1,2] 1000011110=>0111100001=>1000011110=>[1,5,1,1,1,2] 1000010111=>1110100001=>0001011110=>[4,2,1,1,1,2] 1000010110=>0110100001=>1001011110=>[1,3,2,1,1,1,2] 1000001111=>1111000001=>0000111110=>[5,1,1,1,1,2] 1000001110=>0111000001=>1000111110=>[1,4,1,1,1,1,2] 1000001101=>1011000001=>0100111110=>[2,3,1,1,1,1,2] 1000001011=>1101000001=>0010111110=>[3,2,1,1,1,1,2] 1000001010=>0101000001=>1010111110=>[1,2,2,1,1,1,1,2] 1000001000=>0001000001=>1110111110=>[1,1,1,2,1,1,1,1,2] 1000000111=>1110000001=>0001111110=>[4,1,1,1,1,1,2] 1000000110=>0110000001=>1001111110=>[1,3,1,1,1,1,1,2] 1000000101=>1010000001=>0101111110=>[2,2,1,1,1,1,1,2] 1000000100=>0010000001=>1101111110=>[1,1,2,1,1,1,1,1,2] 1000000011=>1100000001=>0011111110=>[3,1,1,1,1,1,1,2] 1000000010=>0100000001=>1011111110=>[1,2,1,1,1,1,1,1,2] 1000000001=>1000000001=>0111111110=>[2,1,1,1,1,1,1,1,2] 1000000000=>0000000001=>1111111110=>[1,1,1,1,1,1,1,1,1,2] 10000000000=>00000000001=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2] 10000000010=>01000000001=>10111111110=>[1,2,1,1,1,1,1,1,1,2] 10000000110=>01100000001=>10011111110=>[1,3,1,1,1,1,1,1,2] 10000001110=>01110000001=>10001111110=>[1,4,1,1,1,1,1,2] 10000011110=>01111000001=>10000111110=>[1,5,1,1,1,1,2] 10000111110=>01111100001=>10000011110=>[1,6,1,1,1,2] 10001111110=>01111110001=>10000001110=>[1,7,1,1,2] 10011111110=>01111111001=>10000000110=>[1,8,1,2] 10111111110=>01111111101=>10000000010=>[1,9,2] 11111111110=>01111111111=>10000000000=>[1,11] 0111111111=>1111111110=>0000000001=>[10,1] 0111111101=>1011111110=>0100000001=>[2,8,1] 0111111001=>1001111110=>0110000001=>[2,1,7,1] 0111110001=>1000111110=>0111000001=>[2,1,1,6,1] 0111100001=>1000011110=>0111100001=>[2,1,1,1,5,1] 0111000001=>1000001110=>0111110001=>[2,1,1,1,1,4,1] 0110000001=>1000000110=>0111111001=>[2,1,1,1,1,1,3,1] 0100000001=>1000000010=>0111111101=>[2,1,1,1,1,1,1,2,1] 0000000001=>1000000000=>0111111111=>[2,1,1,1,1,1,1,1,1,1] 01111111111=>11111111110=>00000000001=>[11,1] 01111111101=>10111111110=>01000000001=>[2,9,1] 0111111011=>1101111110=>0010000001=>[3,7,1] 0111110101=>1010111110=>0101000001=>[2,2,6,1] 0111101001=>1001011110=>0110100001=>[2,1,2,5,1] 0111010001=>1000101110=>0111010001=>[2,1,1,2,4,1] 0110100001=>1000010110=>0111101001=>[2,1,1,1,2,3,1] 0101000001=>1000001010=>0111110101=>[2,1,1,1,1,2,2,1] 01100000001=>10000000110=>01111111001=>[2,1,1,1,1,1,1,3,1] 0010000001=>1000000100=>0111111011=>[2,1,1,1,1,1,2,1,1] 01000000001=>10000000010=>01111111101=>[2,1,1,1,1,1,1,1,2,1] 00000000001=>10000000000=>01111111111=>[2,1,1,1,1,1,1,1,1,1,1] 0101010101=>1010101010=>0101010101=>[2,2,2,2,2,1] 0101010011=>1100101010=>0011010101=>[3,1,2,2,2,1] 0101001101=>1011001010=>0100110101=>[2,3,1,2,2,1] 0101001011=>1101001010=>0010110101=>[3,2,1,2,2,1] 0101000111=>1110001010=>0001110101=>[4,1,1,2,2,1] 0100110101=>1010110010=>0101001101=>[2,2,3,1,2,1] 0100110011=>1100110010=>0011001101=>[3,1,3,1,2,1] 0100101101=>1011010010=>0100101101=>[2,3,2,1,2,1] 0100101011=>1101010010=>0010101101=>[3,2,2,1,2,1] 0100100111=>1110010010=>0001101101=>[4,1,2,1,2,1] 0100011011=>1101100010=>0010011101=>[3,3,1,1,2,1] 0100010111=>1110100010=>0001011101=>[4,2,1,1,2,1] 0100001111=>1111000010=>0000111101=>[5,1,1,1,2,1] 0011010101=>1010101100=>0101010011=>[2,2,2,3,1,1] 0011010011=>1100101100=>0011010011=>[3,1,2,3,1,1] 0011000111=>1110001100=>0001110011=>[4,1,1,3,1,1] 0010110101=>1010110100=>0101001011=>[2,2,3,2,1,1] 0010110011=>1100110100=>0011001011=>[3,1,3,2,1,1] 0010101101=>1011010100=>0100101011=>[2,3,2,2,1,1] 0010101011=>1101010100=>0010101011=>[3,2,2,2,1,1] 0010011101=>1011100100=>0100011011=>[2,4,1,2,1,1] 0010011011=>1101100100=>0010011011=>[3,3,1,2,1,1] 0010010111=>1110100100=>0001011011=>[4,2,1,2,1,1] 0010001111=>1111000100=>0000111011=>[5,1,1,2,1,1] 0001110101=>1010111000=>0101000111=>[2,2,4,1,1,1] 0001110011=>1100111000=>0011000111=>[3,1,4,1,1,1] 0001101011=>1101011000=>0010100111=>[3,2,3,1,1,1] 0001100111=>1110011000=>0001100111=>[4,1,3,1,1,1] 0001011101=>1011101000=>0100010111=>[2,4,2,1,1,1] 0001011011=>1101101000=>0010010111=>[3,3,2,1,1,1] 0001010111=>1110101000=>0001010111=>[4,2,2,1,1,1] 0001001111=>1111001000=>0000110111=>[5,1,2,1,1,1] 0000110111=>1110110000=>0001001111=>[4,3,1,1,1,1] 0000101111=>1111010000=>0000101111=>[5,2,1,1,1,1] 0000011111=>1111100000=>0000011111=>[6,1,1,1,1,1] 010101010101=>101010101010=>010101010101=>[2,2,2,2,2,2,1] 010101001101=>101100101010=>010011010101=>[2,3,1,2,2,2,1] 010101001011=>110100101010=>001011010101=>[3,2,1,2,2,2,1] 010100110101=>101011001010=>010100110101=>[2,2,3,1,2,2,1] 010100101101=>101101001010=>010010110101=>[2,3,2,1,2,2,1] 010100101011=>110101001010=>001010110101=>[3,2,2,1,2,2,1] 010100100111=>111001001010=>000110110101=>[4,1,2,1,2,2,1] 010100011011=>110110001010=>001001110101=>[3,3,1,1,2,2,1] 010100010111=>111010001010=>000101110101=>[4,2,1,1,2,2,1] 010100001111=>111100001010=>000011110101=>[5,1,1,1,2,2,1] 010011010101=>101010110010=>010101001101=>[2,2,2,3,1,2,1] 010011010011=>110010110010=>001101001101=>[3,1,2,3,1,2,1] 010011001101=>101100110010=>010011001101=>[2,3,1,3,1,2,1] 010011001011=>110100110010=>001011001101=>[3,2,1,3,1,2,1] 010011000111=>111000110010=>000111001101=>[4,1,1,3,1,2,1] 010010110101=>101011010010=>010100101101=>[2,2,3,2,1,2,1] 010010101101=>101101010010=>010010101101=>[2,3,2,2,1,2,1] 010010101011=>110101010010=>001010101101=>[3,2,2,2,1,2,1] 010010011101=>101110010010=>010001101101=>[2,4,1,2,1,2,1] 010010011011=>110110010010=>001001101101=>[3,3,1,2,1,2,1] 010010010111=>111010010010=>000101101101=>[4,2,1,2,1,2,1] 010010001111=>111100010010=>000011101101=>[5,1,1,2,1,2,1] 010001101101=>101101100010=>010010011101=>[2,3,3,1,1,2,1] 010001101011=>110101100010=>001010011101=>[3,2,3,1,1,2,1] 010001011101=>101110100010=>010001011101=>[2,4,2,1,1,2,1] 010001011011=>110110100010=>001001011101=>[3,3,2,1,1,2,1] 010001010111=>111010100010=>000101011101=>[4,2,2,1,1,2,1] 010000111011=>110111000010=>001000111101=>[3,4,1,1,1,2,1] 010000110111=>111011000010=>000100111101=>[4,3,1,1,1,2,1] 010000101111=>111101000010=>000010111101=>[5,2,1,1,1,2,1] 010000011111=>111110000010=>000001111101=>[6,1,1,1,1,2,1] 001100101011=>110101001100=>001010110011=>[3,2,2,1,3,1,1] 001100100111=>111001001100=>000110110011=>[4,1,2,1,3,1,1] 001100011011=>110110001100=>001001110011=>[3,3,1,1,3,1,1] 001100010111=>111010001100=>000101110011=>[4,2,1,1,3,1,1] 001100001111=>111100001100=>000011110011=>[5,1,1,1,3,1,1] 001011010101=>101010110100=>010101001011=>[2,2,2,3,2,1,1] 001011001101=>101100110100=>010011001011=>[2,3,1,3,2,1,1] 001011001011=>110100110100=>001011001011=>[3,2,1,3,2,1,1] 001010110101=>101011010100=>010100101011=>[2,2,3,2,2,1,1] 001010101101=>101101010100=>010010101011=>[2,3,2,2,2,1,1] 001010101011=>110101010100=>001010101011=>[3,2,2,2,2,1,1] 001010011101=>101110010100=>010001101011=>[2,4,1,2,2,1,1] 001010011011=>110110010100=>001001101011=>[3,3,1,2,2,1,1] 001010010111=>111010010100=>000101101011=>[4,2,1,2,2,1,1] 001010001111=>111100010100=>000011101011=>[5,1,1,2,2,1,1] 001001110101=>101011100100=>010100011011=>[2,2,4,1,2,1,1] 001001101101=>101101100100=>010010011011=>[2,3,3,1,2,1,1] 001001101011=>110101100100=>001010011011=>[3,2,3,1,2,1,1] 001001011101=>101110100100=>010001011011=>[2,4,2,1,2,1,1] 001001011011=>110110100100=>001001011011=>[3,3,2,1,2,1,1] 001001010111=>111010100100=>000101011011=>[4,2,2,1,2,1,1] 001000111101=>101111000100=>010000111011=>[2,5,1,1,2,1,1] 001000111011=>110111000100=>001000111011=>[3,4,1,1,2,1,1] 001000110111=>111011000100=>000100111011=>[4,3,1,1,2,1,1] 001000101111=>111101000100=>000010111011=>[5,2,1,1,2,1,1] 001000011111=>111110000100=>000001111011=>[6,1,1,1,2,1,1] 000111010011=>110010111000=>001101000111=>[3,1,2,4,1,1,1] 000111000111=>111000111000=>000111000111=>[4,1,1,4,1,1,1] 000110110101=>101011011000=>010100100111=>[2,2,3,3,1,1,1] 000110101011=>110101011000=>001010100111=>[3,2,2,3,1,1,1] 000110011011=>110110011000=>001001100111=>[3,3,1,3,1,1,1] 000110010111=>111010011000=>000101100111=>[4,2,1,3,1,1,1] 000110001111=>111100011000=>000011100111=>[5,1,1,3,1,1,1] 000101110101=>101011101000=>010100010111=>[2,2,4,2,1,1,1] 000101101101=>101101101000=>010010010111=>[2,3,3,2,1,1,1] 000101101011=>110101101000=>001010010111=>[3,2,3,2,1,1,1] 000101011101=>101110101000=>010001010111=>[2,4,2,2,1,1,1] 000101011011=>110110101000=>001001010111=>[3,3,2,2,1,1,1] 000101010111=>111010101000=>000101010111=>[4,2,2,2,1,1,1] 000100111101=>101111001000=>010000110111=>[2,5,1,2,1,1,1] 000100111011=>110111001000=>001000110111=>[3,4,1,2,1,1,1] 000100110111=>111011001000=>000100110111=>[4,3,1,2,1,1,1] 000100101111=>111101001000=>000010110111=>[5,2,1,2,1,1,1] 000100011111=>111110001000=>000001110111=>[6,1,1,2,1,1,1] 000011011011=>110110110000=>001001001111=>[3,3,3,1,1,1,1] 000010111101=>101111010000=>010000101111=>[2,5,2,1,1,1,1] 000010111011=>110111010000=>001000101111=>[3,4,2,1,1,1,1] 000010110111=>111011010000=>000100101111=>[4,3,2,1,1,1,1] 000010101111=>111101010000=>000010101111=>[5,2,2,1,1,1,1] 000010011111=>111110010000=>000001101111=>[6,1,2,1,1,1,1] 000001111011=>110111100000=>001000011111=>[3,5,1,1,1,1,1] 000001110111=>111011100000=>000100011111=>[4,4,1,1,1,1,1] 000001101111=>111101100000=>000010011111=>[5,3,1,1,1,1,1] 000001011111=>111110100000=>000001011111=>[6,2,1,1,1,1,1] 000000111111=>111111000000=>000000111111=>[7,1,1,1,1,1,1] 111111111111=>111111111111=>000000000000=>[13] 111110000001=>100000011111=>011111100000=>[2,1,1,1,1,1,6] 111000000111=>111000000111=>000111111000=>[4,1,1,1,1,1,4] 111011000001=>100000110111=>011111001000=>[2,1,1,1,1,3,4] 111010010001=>100010010111=>011101101000=>[2,1,1,2,1,2,4] 0000000000=>0000000000=>1111111111=>[1,1,1,1,1,1,1,1,1,1,1] 0000000110=>0110000000=>1001111111=>[1,3,1,1,1,1,1,1,1] 0000011000=>0001100000=>1110011111=>[1,1,1,3,1,1,1,1,1] 0000011110=>0111100000=>1000011111=>[1,5,1,1,1,1,1] 0000010010=>0100100000=>1011011111=>[1,2,1,2,1,1,1,1,1] 0001100000=>0000011000=>1111100111=>[1,1,1,1,1,3,1,1,1] 0001100110=>0110011000=>1001100111=>[1,3,1,3,1,1,1] 0001111000=>0001111000=>1110000111=>[1,1,1,5,1,1,1] 0001111110=>0111111000=>1000000111=>[1,7,1,1,1] 0001110010=>0100111000=>1011000111=>[1,2,1,4,1,1,1] 0001001110=>0111001000=>1000110111=>[1,4,1,2,1,1,1] 0001000010=>0100001000=>1011110111=>[1,2,1,1,1,2,1,1,1] 0001011010=>0101101000=>1010010111=>[1,2,3,2,1,1,1] 0110000000=>0000000110=>1111111001=>[1,1,1,1,1,1,1,3,1] 0110000110=>0110000110=>1001111001=>[1,3,1,1,1,3,1] 0110011000=>0001100110=>1110011001=>[1,1,1,3,1,3,1] 0110011110=>0111100110=>1000011001=>[1,5,1,3,1] 0110010010=>0100100110=>1011011001=>[1,2,1,2,1,3,1] 0111100000=>0000011110=>1111100001=>[1,1,1,1,1,5,1] 0111100110=>0110011110=>1001100001=>[1,3,1,5,1] 0111111000=>0001111110=>1110000001=>[1,1,1,7,1] 0111111110=>0111111110=>1000000001=>[1,9,1] 0111110010=>0100111110=>1011000001=>[1,2,1,6,1] 0111001000=>0001001110=>1110110001=>[1,1,1,2,1,4,1] 0111000010=>0100001110=>1011110001=>[1,2,1,1,1,4,1] 0100100000=>0000010010=>1111101101=>[1,1,1,1,1,2,1,2,1] 0100100110=>0110010010=>1001101101=>[1,3,1,2,1,2,1] 0100111000=>0001110010=>1110001101=>[1,1,1,4,1,2,1] 0100111110=>0111110010=>1000001101=>[1,6,1,2,1] 0100110010=>0100110010=>1011001101=>[1,2,1,3,1,2,1] 0100001000=>0001000010=>1110111101=>[1,1,1,2,1,1,1,2,1] 0100001110=>0111000010=>1000111101=>[1,4,1,1,1,2,1] 0100000010=>0100000010=>1011111101=>[1,2,1,1,1,1,1,2,1] 0100011010=>0101100010=>1010011101=>[1,2,3,1,1,2,1] 0101101000=>0001011010=>1110100101=>[1,1,1,2,3,2,1] 0101100010=>0100011010=>1011100101=>[1,2,1,1,3,2,1] 0101001010=>0101001010=>1010110101=>[1,2,2,1,2,2,1] 000000000000=>000000000000=>111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1] 000000000110=>011000000000=>100111111111=>[1,3,1,1,1,1,1,1,1,1,1] 000000011000=>000110000000=>111001111111=>[1,1,1,3,1,1,1,1,1,1,1] 000000011110=>011110000000=>100001111111=>[1,5,1,1,1,1,1,1,1] 000001100000=>000001100000=>111110011111=>[1,1,1,1,1,3,1,1,1,1,1] 000001100110=>011001100000=>100110011111=>[1,3,1,3,1,1,1,1,1] 000001111000=>000111100000=>111000011111=>[1,1,1,5,1,1,1,1,1] 000001111110=>011111100000=>100000011111=>[1,7,1,1,1,1,1] 000001001000=>000100100000=>111011011111=>[1,1,1,2,1,2,1,1,1,1,1] 000001000010=>010000100000=>101111011111=>[1,2,1,1,1,2,1,1,1,1,1] 000110000000=>000000011000=>111111100111=>[1,1,1,1,1,1,1,3,1,1,1] 000110000110=>011000011000=>100111100111=>[1,3,1,1,1,3,1,1,1] 000110011000=>000110011000=>111001100111=>[1,1,1,3,1,3,1,1,1] 000110011110=>011110011000=>100001100111=>[1,5,1,3,1,1,1] 000110010010=>010010011000=>101101100111=>[1,2,1,2,1,3,1,1,1] 000111100000=>000001111000=>111110000111=>[1,1,1,1,1,5,1,1,1] 000111100110=>011001111000=>100110000111=>[1,3,1,5,1,1,1] 000111111000=>000111111000=>111000000111=>[1,1,1,7,1,1,1] 000111111110=>011111111000=>100000000111=>[1,9,1,1,1] 000111110010=>010011111000=>101100000111=>[1,2,1,6,1,1,1] 000111001000=>000100111000=>111011000111=>[1,1,1,2,1,4,1,1,1] 000111001110=>011100111000=>100011000111=>[1,4,1,4,1,1,1] 000111011010=>010110111000=>101001000111=>[1,2,3,4,1,1,1] 000100100000=>000001001000=>111110110111=>[1,1,1,1,1,2,1,2,1,1,1] 000100111000=>000111001000=>111000110111=>[1,1,1,4,1,2,1,1,1] 000100111110=>011111001000=>100000110111=>[1,6,1,2,1,1,1] 000100110010=>010011001000=>101100110111=>[1,2,1,3,1,2,1,1,1] 000100011010=>010110001000=>101001110111=>[1,2,3,1,1,2,1,1,1] 000101101000=>000101101000=>111010010111=>[1,1,1,2,3,2,1,1,1] 000101101110=>011101101000=>100010010111=>[1,4,3,2,1,1,1] 000101100010=>010001101000=>101110010111=>[1,2,1,1,3,2,1,1,1] 000101111010=>010111101000=>101000010111=>[1,2,5,2,1,1,1] 000101001010=>010100101000=>101011010111=>[1,2,2,1,2,2,1,1,1] 011000000000=>000000000110=>111111111001=>[1,1,1,1,1,1,1,1,1,3,1] 011000000110=>011000000110=>100111111001=>[1,3,1,1,1,1,1,3,1] 011000011000=>000110000110=>111001111001=>[1,1,1,3,1,1,1,3,1] 011000011110=>011110000110=>100001111001=>[1,5,1,1,1,3,1] 011001100000=>000001100110=>111110011001=>[1,1,1,1,1,3,1,3,1] 011001100110=>011001100110=>100110011001=>[1,3,1,3,1,3,1] 011001111000=>000111100110=>111000011001=>[1,1,1,5,1,3,1] 011001111110=>011111100110=>100000011001=>[1,7,1,3,1] 011001110010=>010011100110=>101100011001=>[1,2,1,4,1,3,1] 011110000000=>000000011110=>111111100001=>[1,1,1,1,1,1,1,5,1] 011110000110=>011000011110=>100111100001=>[1,3,1,1,1,5,1] 011110011000=>000110011110=>111001100001=>[1,1,1,3,1,5,1] 011110011110=>011110011110=>100001100001=>[1,5,1,5,1] 011111100000=>000001111110=>111110000001=>[1,1,1,1,1,7,1] 011111100110=>011001111110=>100110000001=>[1,3,1,7,1] 011111111000=>000111111110=>111000000001=>[1,1,1,9,1] 011111111110=>011111111110=>100000000001=>[1,11,1] 011111001000=>000100111110=>111011000001=>[1,1,1,2,1,6,1] 011111000010=>010000111110=>101111000001=>[1,2,1,1,1,6,1] 011100111000=>000111001110=>111000110001=>[1,1,1,4,1,4,1] 011101101000=>000101101110=>111010010001=>[1,1,1,2,3,4,1] 011101100010=>010001101110=>101110010001=>[1,2,1,1,3,4,1] 011101001010=>010100101110=>101011010001=>[1,2,2,1,2,4,1] 010010011000=>000110010010=>111001101101=>[1,1,1,3,1,2,1,2,1] 010011100110=>011001110010=>100110001101=>[1,3,1,4,1,2,1] 010011111000=>000111110010=>111000001101=>[1,1,1,6,1,2,1] 010011110010=>010011110010=>101100001101=>[1,2,1,5,1,2,1] 010011001000=>000100110010=>111011001101=>[1,1,1,2,1,3,1,2,1] 010011011010=>010110110010=>101001001101=>[1,2,3,3,1,2,1] 010000100000=>000001000010=>111110111101=>[1,1,1,1,1,2,1,1,1,2,1] 010000111110=>011111000010=>100000111101=>[1,6,1,1,1,2,1] 010001101000=>000101100010=>111010011101=>[1,1,1,2,3,1,1,2,1] 010001101110=>011101100010=>100010011101=>[1,4,3,1,1,2,1] 010001111010=>010111100010=>101000011101=>[1,2,5,1,1,2,1] 010110111000=>000111011010=>111000100101=>[1,1,1,4,3,2,1] 010110110010=>010011011010=>101100100101=>[1,2,1,3,3,2,1] 010110001000=>000100011010=>111011100101=>[1,1,1,2,1,1,3,2,1] 010111101000=>000101111010=>111010000101=>[1,1,1,2,5,2,1] 010111100010=>010001111010=>101110000101=>[1,2,1,1,5,2,1] 010111001010=>010100111010=>101011000101=>[1,2,2,1,4,2,1] 010100101000=>000101001010=>111010110101=>[1,1,1,2,2,1,2,2,1] 010100101110=>011101001010=>100010110101=>[1,4,2,1,2,2,1] 010100111010=>010111001010=>101000110101=>[1,2,4,1,2,2,1] 010101101010=>010101101010=>101010010101=>[1,2,2,3,2,2,1] 0011010100=>0010101100=>1101010011=>[1,1,2,2,3,1,1] 0101010100=>0010101010=>1101010101=>[1,1,2,2,2,2,1] 0011110100=>0010111100=>1101000011=>[1,1,2,5,1,1] 0000010100=>0010100000=>1101011111=>[1,1,2,2,1,1,1,1,1] 0111010100=>0010101110=>1101010001=>[1,1,2,2,4,1] 0011111110=>0111111100=>1000000011=>[1,8,1,1] 00000000000=>00000000000=>11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1] 0000000100=>0010000000=>1101111111=>[1,1,2,1,1,1,1,1,1,1] 0101111110=>0111111010=>1000000101=>[1,7,2,1] 01111111110=>01111111110=>10000000001=>[1,10,1] 0011001100=>0011001100=>1100110011=>[1,1,3,1,3,1,1] 0011011000=>0001101100=>1110010011=>[1,1,1,3,3,1,1] 0011100100=>0010011100=>1101100011=>[1,1,2,1,4,1,1] 0011101000=>0001011100=>1110100011=>[1,1,1,2,4,1,1] 0011110000=>0000111100=>1111000011=>[1,1,1,1,5,1,1] 0100110100=>0010110010=>1101001101=>[1,1,2,3,1,2,1] 0101001100=>0011001010=>1100110101=>[1,1,3,1,2,2,1] 0101010010=>0100101010=>1011010101=>[1,2,1,2,2,2,1] 0101011000=>0001101010=>1110010101=>[1,1,1,3,2,2,1] 0101100100=>0010011010=>1101100101=>[1,1,2,1,3,2,1] 0101110000=>0000111010=>1111000101=>[1,1,1,1,4,2,1] 0110001100=>0011000110=>1100111001=>[1,1,3,1,1,3,1] 0110010100=>0010100110=>1101011001=>[1,1,2,2,1,3,1] 0110100100=>0010010110=>1101101001=>[1,1,2,1,2,3,1] 0110101000=>0001010110=>1110101001=>[1,1,1,2,2,3,1] 0110110000=>0000110110=>1111001001=>[1,1,1,1,3,3,1] 0111000100=>0010001110=>1101110001=>[1,1,2,1,1,4,1] 0111010000=>0000101110=>1111010001=>[1,1,1,1,2,4,1] 001100110010=>010011001100=>101100110011=>[1,2,1,3,1,3,1,1] 001100110100=>001011001100=>110100110011=>[1,1,2,3,1,3,1,1] 001100111000=>000111001100=>111000110011=>[1,1,1,4,1,3,1,1] 001101001100=>001100101100=>110011010011=>[1,1,3,1,2,3,1,1] 001101010100=>001010101100=>110101010011=>[1,1,2,2,2,3,1,1] 001101011000=>000110101100=>111001010011=>[1,1,1,3,2,3,1,1] 001101100010=>010001101100=>101110010011=>[1,2,1,1,3,3,1,1] 001101100100=>001001101100=>110110010011=>[1,1,2,1,3,3,1,1] 001101101000=>000101101100=>111010010011=>[1,1,1,2,3,3,1,1] 001101110000=>000011101100=>111100010011=>[1,1,1,1,4,3,1,1] 001110001010=>010100011100=>101011100011=>[1,2,2,1,1,4,1,1] 001110001100=>001100011100=>110011100011=>[1,1,3,1,1,4,1,1] 001110010010=>010010011100=>101101100011=>[1,2,1,2,1,4,1,1] 001110010100=>001010011100=>110101100011=>[1,1,2,2,1,4,1,1] 001110011000=>000110011100=>111001100011=>[1,1,1,3,1,4,1,1] 001110100010=>010001011100=>101110100011=>[1,2,1,1,2,4,1,1] 001110100100=>001001011100=>110110100011=>[1,1,2,1,2,4,1,1] 001110101000=>000101011100=>111010100011=>[1,1,1,2,2,4,1,1] 001110110000=>000011011100=>111100100011=>[1,1,1,1,3,4,1,1] 001111000100=>001000111100=>110111000011=>[1,1,2,1,1,5,1,1] 001111001000=>000100111100=>111011000011=>[1,1,1,2,1,5,1,1] 001111010000=>000010111100=>111101000011=>[1,1,1,1,2,5,1,1] 001111100000=>000001111100=>111110000011=>[1,1,1,1,1,6,1,1] 010011001100=>001100110010=>110011001101=>[1,1,3,1,3,1,2,1] 010011010100=>001010110010=>110101001101=>[1,1,2,2,3,1,2,1] 010011011000=>000110110010=>111001001101=>[1,1,1,3,3,1,2,1] 010011100100=>001001110010=>110110001101=>[1,1,2,1,4,1,2,1] 010011101000=>000101110010=>111010001101=>[1,1,1,2,4,1,2,1] 010011110000=>000011110010=>111100001101=>[1,1,1,1,5,1,2,1] 010100110100=>001011001010=>110100110101=>[1,1,2,3,1,2,2,1] 010100111000=>000111001010=>111000110101=>[1,1,1,4,1,2,2,1] 010101001100=>001100101010=>110011010101=>[1,1,3,1,2,2,2,1] 010101010100=>001010101010=>110101010101=>[1,1,2,2,2,2,2,1] 010101011000=>000110101010=>111001010101=>[1,1,1,3,2,2,2,1] 010101100100=>001001101010=>110110010101=>[1,1,2,1,3,2,2,1] 010101101000=>000101101010=>111010010101=>[1,1,1,2,3,2,2,1] 010101110000=>000011101010=>111100010101=>[1,1,1,1,4,2,2,1] 010110001100=>001100011010=>110011100101=>[1,1,3,1,1,3,2,1] 010110010100=>001010011010=>110101100101=>[1,1,2,2,1,3,2,1] 010110011000=>000110011010=>111001100101=>[1,1,1,3,1,3,2,1] 010110100100=>001001011010=>110110100101=>[1,1,2,1,2,3,2,1] 010110101000=>000101011010=>111010100101=>[1,1,1,2,2,3,2,1] 010110110000=>000011011010=>111100100101=>[1,1,1,1,3,3,2,1] 010111000100=>001000111010=>110111000101=>[1,1,2,1,1,4,2,1] 010111001000=>000100111010=>111011000101=>[1,1,1,2,1,4,2,1] 010111010000=>000010111010=>111101000101=>[1,1,1,1,2,4,2,1] 010111100000=>000001111010=>111110000101=>[1,1,1,1,1,5,2,1] 011000110010=>010011000110=>101100111001=>[1,2,1,3,1,1,3,1] 011000110100=>001011000110=>110100111001=>[1,1,2,3,1,1,3,1] 011000111000=>000111000110=>111000111001=>[1,1,1,4,1,1,3,1] 011001001100=>001100100110=>110011011001=>[1,1,3,1,2,1,3,1] 011001010100=>001010100110=>110101011001=>[1,1,2,2,2,1,3,1] 011001011000=>000110100110=>111001011001=>[1,1,1,3,2,1,3,1] 011001100010=>010001100110=>101110011001=>[1,2,1,1,3,1,3,1] 011001100100=>001001100110=>110110011001=>[1,1,2,1,3,1,3,1] 011001101000=>000101100110=>111010011001=>[1,1,1,2,3,1,3,1] 011001110000=>000011100110=>111100011001=>[1,1,1,1,4,1,3,1] 011010001100=>001100010110=>110011101001=>[1,1,3,1,1,2,3,1] 011010010100=>001010010110=>110101101001=>[1,1,2,2,1,2,3,1] 011010011000=>000110010110=>111001101001=>[1,1,1,3,1,2,3,1] 011010100100=>001001010110=>110110101001=>[1,1,2,1,2,2,3,1] 011010101000=>000101010110=>111010101001=>[1,1,1,2,2,2,3,1] 011010110000=>000011010110=>111100101001=>[1,1,1,1,3,2,3,1] 011011000100=>001000110110=>110111001001=>[1,1,2,1,1,3,3,1] 011011001000=>000100110110=>111011001001=>[1,1,1,2,1,3,3,1] 011011010000=>000010110110=>111101001001=>[1,1,1,1,2,3,3,1] 011011100000=>000001110110=>111110001001=>[1,1,1,1,1,4,3,1] 011100001010=>010100001110=>101011110001=>[1,2,2,1,1,1,4,1] 011100001100=>001100001110=>110011110001=>[1,1,3,1,1,1,4,1] 011100010010=>010010001110=>101101110001=>[1,2,1,2,1,1,4,1] 011100010100=>001010001110=>110101110001=>[1,1,2,2,1,1,4,1] 011100011000=>000110001110=>111001110001=>[1,1,1,3,1,1,4,1] 011100100010=>010001001110=>101110110001=>[1,2,1,1,2,1,4,1] 011100100100=>001001001110=>110110110001=>[1,1,2,1,2,1,4,1] 011100101000=>000101001110=>111010110001=>[1,1,1,2,2,1,4,1] 011100110000=>000011001110=>111100110001=>[1,1,1,1,3,1,4,1] 011101000100=>001000101110=>110111010001=>[1,1,2,1,1,2,4,1] 011101001000=>000100101110=>111011010001=>[1,1,1,2,1,2,4,1] 011101010000=>000010101110=>111101010001=>[1,1,1,1,2,2,4,1] 011101100000=>000001101110=>111110010001=>[1,1,1,1,1,3,4,1] 011110000100=>001000011110=>110111100001=>[1,1,2,1,1,1,5,1] 011110001000=>000100011110=>111011100001=>[1,1,1,2,1,1,5,1] 011110010000=>000010011110=>111101100001=>[1,1,1,1,2,1,5,1] 011110100000=>000001011110=>111110100001=>[1,1,1,1,1,2,5,1] 011111000000=>000000111110=>111111000001=>[1,1,1,1,1,1,6,1] 01010101010=>01010101010=>10101010101=>[1,2,2,2,2,2,1] 0101111111=>1111111010=>0000000101=>[8,2,1] 0101010110=>0110101010=>1001010101=>[1,3,2,2,2,1] 0101011001=>1001101010=>0110010101=>[2,1,3,2,2,1] 0110011001=>1001100110=>0110011001=>[2,1,3,1,3,1] 0111001100=>0011001110=>1100110001=>[1,1,3,1,4,1] 0111011000=>0001101110=>1110010001=>[1,1,1,3,4,1] 0111100100=>0010011110=>1101100001=>[1,1,2,1,5,1] 0111101000=>0001011110=>1110100001=>[1,1,1,2,5,1] 0111110000=>0000111110=>1111000001=>[1,1,1,1,6,1] 010101101001=>100101101010=>011010010101=>[2,1,2,3,2,2,1] 011001011001=>100110100110=>011001011001=>[2,1,3,2,1,3,1] 011010010101=>101010010110=>010101101001=>[2,2,2,1,2,3,1] 011010101001=>100101010110=>011010101001=>[2,1,2,2,2,3,1] 011011010001=>100010110110=>011101001001=>[2,1,1,2,3,3,1] 011100011100=>001110001110=>110001110001=>[1,1,4,1,1,4,1] 011101001001=>100100101110=>011011010001=>[2,1,2,1,2,4,1] 011101001100=>001100101110=>110011010001=>[1,1,3,1,2,4,1] 011101010001=>100010101110=>011101010001=>[2,1,1,2,2,4,1] 011101010100=>001010101110=>110101010001=>[1,1,2,2,2,4,1] 011101100001=>100001101110=>011110010001=>[2,1,1,1,3,4,1] 011101100100=>001001101110=>110110010001=>[1,1,2,1,3,4,1] 011101110000=>000011101110=>111100010001=>[1,1,1,1,4,4,1] 011110001100=>001100011110=>110011100001=>[1,1,3,1,1,5,1] 011110010001=>100010011110=>011101100001=>[2,1,1,2,1,5,1] 011110100001=>100001011110=>011110100001=>[2,1,1,1,2,5,1] 011110100100=>001001011110=>110110100001=>[1,1,2,1,2,5,1] 011110101000=>000101011110=>111010100001=>[1,1,1,2,2,5,1] 011110110000=>000011011110=>111100100001=>[1,1,1,1,3,5,1] 011111000001=>100000111110=>011111000001=>[2,1,1,1,1,6,1] 011111000100=>001000111110=>110111000001=>[1,1,2,1,1,6,1] 011111010000=>000010111110=>111101000001=>[1,1,1,1,2,6,1] 0011111000=>0001111100=>1110000011=>[1,1,1,6,1,1] 0001111100=>0011111000=>1100000111=>[1,1,6,1,1,1] 001111001010=>010100111100=>101011000011=>[1,2,2,1,5,1,1] 001111001100=>001100111100=>110011000011=>[1,1,3,1,5,1,1] 001111010010=>010010111100=>101101000011=>[1,2,1,2,5,1,1] 001111010100=>001010111100=>110101000011=>[1,1,2,2,5,1,1] 000111010110=>011010111000=>100101000111=>[1,3,2,4,1,1,1] 001111011000=>000110111100=>111001000011=>[1,1,1,3,5,1,1] 001101100110=>011001101100=>100110010011=>[1,3,1,3,3,1,1] 001111100100=>001001111100=>110110000011=>[1,1,2,1,6,1,1] 001111101000=>000101111100=>111010000011=>[1,1,1,2,6,1,1] 000111101010=>010101111000=>101010000111=>[1,2,2,5,1,1,1] 001001110110=>011011100100=>100100011011=>[1,3,4,1,2,1,1] 001101110010=>010011101100=>101100010011=>[1,2,1,4,3,1,1] 000101110110=>011011101000=>100100010111=>[1,3,4,2,1,1,1] 001111110000=>000011111100=>111100000011=>[1,1,1,1,7,1,1] 000111110100=>001011111000=>110100000111=>[1,1,2,6,1,1,1] 110001111000=>000111100011=>111000011100=>[1,1,1,5,1,1,3] 001001111010=>010111100100=>101000011011=>[1,2,5,1,2,1,1] 000011111100=>001111110000=>110000001111=>[1,1,7,1,1,1,1] 0000101101=>1011010000=>0100101111=>[2,3,2,1,1,1,1] 110010010101=>101010010011=>010101101100=>[2,2,2,1,2,1,3] 110101001001=>100100101011=>011011010100=>[2,1,2,1,2,2,3] 110101010001=>100010101011=>011101010100=>[2,1,1,2,2,2,3] 110110010001=>100010011011=>011101100100=>[2,1,1,2,1,3,3] 110110100001=>100001011011=>011110100100=>[2,1,1,1,2,3,3] 110111000001=>100000111011=>011111000100=>[2,1,1,1,1,4,3] 111010100001=>100001010111=>011110101000=>[2,1,1,1,2,2,4] 111100010001=>100010001111=>011101110000=>[2,1,1,2,1,1,5] 111101000001=>100000101111=>011111010000=>[2,1,1,1,1,2,5] 0011101101=>1011011100=>0100100011=>[2,3,4,1,1] 0011011001=>1001101100=>0110010011=>[2,1,3,3,1,1] 01010000001=>10000001010=>01111110101=>[2,1,1,1,1,1,2,2,1] 0001110100=>0010111000=>1101000111=>[1,1,2,4,1,1,1] 001001100110=>011001100100=>100110011011=>[1,3,1,3,1,2,1,1] 001000110110=>011011000100=>100100111011=>[1,3,3,1,1,2,1,1] 0110111001=>1001110110=>0110001001=>[2,1,4,3,1] 0001101001=>1001011000=>0110100111=>[2,1,2,3,1,1,1] 10000000001=>10000000001=>01111111110=>[2,1,1,1,1,1,1,1,1,2] 110101010101=>101010101011=>010101010100=>[2,2,2,2,2,3] 110101011001=>100110101011=>011001010100=>[2,1,3,2,2,3] 110101100101=>101001101011=>010110010100=>[2,2,1,3,2,3] 110101101001=>100101101011=>011010010100=>[2,1,2,3,2,3] 110101110001=>100011101011=>011100010100=>[2,1,1,4,2,3] 110110010101=>101010011011=>010101100100=>[2,2,2,1,3,3] 110110100101=>101001011011=>010110100100=>[2,2,1,2,3,3] 110110101001=>100101011011=>011010100100=>[2,1,2,2,3,3] 110110110001=>100011011011=>011100100100=>[2,1,1,3,3,3] 110111000101=>101000111011=>010111000100=>[2,2,1,1,4,3] 110111001001=>100100111011=>011011000100=>[2,1,2,1,4,3] 110111010001=>100010111011=>011101000100=>[2,1,1,2,4,3] 110111100001=>100001111011=>011110000100=>[2,1,1,1,5,3] 111001010101=>101010100111=>010101011000=>[2,2,2,2,1,4] 111001011001=>100110100111=>011001011000=>[2,1,3,2,1,4] 111010010101=>101010010111=>010101101000=>[2,2,2,1,2,4] 111010100101=>101001010111=>010110101000=>[2,2,1,2,2,4] 111010101001=>100101010111=>011010101000=>[2,1,2,2,2,4] 111010110001=>100011010111=>011100101000=>[2,1,1,3,2,4] 111011000101=>101000110111=>010111001000=>[2,2,1,1,3,4] 111011001001=>100100110111=>011011001000=>[2,1,2,1,3,4] 111011010001=>100010110111=>011101001000=>[2,1,1,2,3,4] 111011100001=>100001110111=>011110001000=>[2,1,1,1,4,4] 111100010101=>101010001111=>010101110000=>[2,2,2,1,1,5] 111100100101=>101001001111=>010110110000=>[2,2,1,2,1,5] 111100101001=>100101001111=>011010110000=>[2,1,2,2,1,5] 111101000101=>101000101111=>010111010000=>[2,2,1,1,2,5] 111101001001=>100100101111=>011011010000=>[2,1,2,1,2,5] 111101010001=>100010101111=>011101010000=>[2,1,1,2,2,5] 111101100001=>100001101111=>011110010000=>[2,1,1,1,3,5] 111110000101=>101000011111=>010111100000=>[2,2,1,1,1,6] 111110001001=>100100011111=>011011100000=>[2,1,2,1,1,6] 111110010001=>100010011111=>011101100000=>[2,1,1,2,1,6] 111110100001=>100001011111=>011110100000=>[2,1,1,1,2,6] 111111000001=>100000111111=>011111000000=>[2,1,1,1,1,7] 0111000011=>1100001110=>0011110001=>[3,1,1,1,4,1] 011110000011=>110000011110=>001111100001=>[3,1,1,1,1,5,1] 110110000011=>110000011011=>001111100100=>[3,1,1,1,1,3,3] 111010000011=>110000010111=>001111101000=>[3,1,1,1,1,2,4] 111100000011=>110000001111=>001111110000=>[3,1,1,1,1,1,5] 011100000111=>111000001110=>000111110001=>[4,1,1,1,1,4,1] 110100000111=>111000001011=>000111110100=>[4,1,1,1,1,2,3] 110000001111=>111100000011=>000011111100=>[5,1,1,1,1,1,3] 001100111010=>010111001100=>101000110011=>[1,2,4,1,3,1,1] 000110111010=>010111011000=>101000100111=>[1,2,4,3,1,1,1] 011000110110=>011011000110=>100100111001=>[1,3,3,1,1,3,1] 000110110110=>011011011000=>100100100111=>[1,3,3,3,1,1,1] 101101010101=>101010101101=>010101010010=>[2,2,2,2,3,2] 110011010101=>101010110011=>010101001100=>[2,2,2,3,1,3] 101011010101=>101010110101=>010101001010=>[2,2,2,3,2,2] 110100110101=>101011001011=>010100110100=>[2,2,3,1,2,3] 101100110101=>101011001101=>010100110010=>[2,2,3,1,3,2] 110010110101=>101011010011=>010100101100=>[2,2,3,2,1,3] 101010110101=>101011010101=>010100101010=>[2,2,3,2,2,2] 110101001101=>101100101011=>010011010100=>[2,3,1,2,2,3] 101101001101=>101100101101=>010011010010=>[2,3,1,2,3,2] 110011001101=>101100110011=>010011001100=>[2,3,1,3,1,3] 101011001101=>101100110101=>010011001010=>[2,3,1,3,2,2] 110100101101=>101101001011=>010010110100=>[2,3,2,1,2,3] 101100101101=>101101001101=>010010110010=>[2,3,2,1,3,2] 110010101101=>101101010011=>010010101100=>[2,3,2,2,1,3] 101010101101=>101101010101=>010010101010=>[2,3,2,2,2,2] 110101010011=>110010101011=>001101010100=>[3,1,2,2,2,3] 101101010011=>110010101101=>001101010010=>[3,1,2,2,3,2] 110011010011=>110010110011=>001101001100=>[3,1,2,3,1,3] 101011010011=>110010110101=>001101001010=>[3,1,2,3,2,2] 110100110011=>110011001011=>001100110100=>[3,1,3,1,2,3] 101100110011=>110011001101=>001100110010=>[3,1,3,1,3,2] 110010110011=>110011010011=>001100101100=>[3,1,3,2,1,3] 101010110011=>110011010101=>001100101010=>[3,1,3,2,2,2] 110101001011=>110100101011=>001011010100=>[3,2,1,2,2,3] 101101001011=>110100101101=>001011010010=>[3,2,1,2,3,2] 110011001011=>110100110011=>001011001100=>[3,2,1,3,1,3] 101011001011=>110100110101=>001011001010=>[3,2,1,3,2,2] 110100101011=>110101001011=>001010110100=>[3,2,2,1,2,3] 101100101011=>110101001101=>001010110010=>[3,2,2,1,3,2] 110010101011=>110101010011=>001010101100=>[3,2,2,2,1,3] 101010101011=>110101010101=>001010101010=>[3,2,2,2,2,2] 0000000011=>1100000000=>0011111111=>[3,1,1,1,1,1,1,1,1] 0011111111=>1111111100=>0000000011=>[9,1,1] 00000000011=>11000000000=>00111111111=>[3,1,1,1,1,1,1,1,1,1] 00111111111=>11111111100=>00000000011=>[10,1,1] 10111111111=>11111111101=>00000000010=>[10,2] 0011110001=>1000111100=>0111000011=>[2,1,1,5,1,1] 000101111001=>100111101000=>011000010111=>[2,1,5,2,1,1,1] 001101110001=>100011101100=>011100010011=>[2,1,1,4,3,1,1] 001011101001=>100101110100=>011010001011=>[2,1,2,4,2,1,1] 000111110001=>100011111000=>011100000111=>[2,1,1,6,1,1,1] 001111100001=>100001111100=>011110000011=>[2,1,1,1,6,1,1] 0011111001=>1001111100=>0110000011=>[2,1,6,1,1] 0011100111=>1110011100=>0001100011=>[4,1,4,1,1] 0011001111=>1111001100=>0000110011=>[5,1,3,1,1] 0010011001=>1001100100=>0110011011=>[2,1,3,1,2,1,1] 0010001101=>1011000100=>0100111011=>[2,3,1,1,2,1,1] 0000001100=>0011000000=>1100111111=>[1,1,3,1,1,1,1,1,1] 0000100111=>1110010000=>0001101111=>[4,1,2,1,1,1,1] 001111000011=>110000111100=>001111000011=>[3,1,1,1,5,1,1] 0110100111=>1110010110=>0001101001=>[4,1,2,3,1] 0110101101=>1011010110=>0100101001=>[2,3,2,3,1] 011010110111=>111011010110=>000100101001=>[4,3,2,3,1] 011110111001=>100111011110=>011000100001=>[2,1,4,5,1] 011000100001=>100001000110=>011110111001=>[2,1,1,1,2,1,1,3,1] 011110100111=>111001011110=>000110100001=>[4,1,2,5,1] 000110100001=>100001011000=>011110100111=>[2,1,1,1,2,3,1,1,1] 000100101001=>100101001000=>011010110111=>[2,1,2,2,1,2,1,1,1] 110011000011=>110000110011=>001111001100=>[3,1,1,1,3,1,3] 111000011100=>001110000111=>110001111000=>[1,1,4,1,1,1,4] 110101000011=>110000101011=>001111010100=>[3,1,1,1,2,2,3] 111001000011=>110000100111=>001111011000=>[3,1,1,1,2,1,4] 110001000111=>111000100011=>000111011100=>[4,1,1,2,1,1,3] 110000111100=>001111000011=>110000111100=>[1,1,5,1,1,1,3] 0010010101=>1010100100=>0101011011=>[2,2,2,1,2,1,1] 0101010111=>1110101010=>0001010101=>[4,2,2,2,1] 0000110101=>1010110000=>0101001111=>[2,2,3,1,1,1,1] 0111010101=>1010101110=>0101010001=>[2,2,2,4,1] 0011011101=>1011101100=>0100010011=>[2,4,3,1,1] 0101110101=>1010111010=>0101000101=>[2,2,4,2,1] 0011110101=>1010111100=>0101000011=>[2,2,5,1,1] 000100010101=>101010001000=>010101110111=>[2,2,2,1,1,2,1,1,1] 010101110111=>111011101010=>000100010101=>[4,4,2,2,1] 011101010111=>111010101110=>000101010001=>[4,2,2,4,1] 011101110101=>101011101110=>010100010001=>[2,2,4,4,1] 011111011111=>111110111110=>000001000001=>[6,6,1] 0110000011=>1100000110=>0011111001=>[3,1,1,1,1,3,1] 110101100011=>110001101011=>001110010100=>[3,1,1,3,2,3] 110100111001=>100111001011=>011000110100=>[2,1,4,1,2,3] 110110010011=>110010011011=>001101100100=>[3,1,2,1,3,3] 110110011001=>100110011011=>011001100100=>[2,1,3,1,3,3] 110110001101=>101100011011=>010011100100=>[2,3,1,1,3,3] 110110100011=>110001011011=>001110100100=>[3,1,1,2,3,3] 110010111001=>100111010011=>011000101100=>[2,1,4,2,1,3] 110111000011=>110000111011=>001111000100=>[3,1,1,1,4,3] 110011011001=>100110110011=>011001001100=>[2,1,3,3,1,3] 110011100011=>110001110011=>001110001100=>[3,1,1,4,1,3] 110011100101=>101001110011=>010110001100=>[2,2,1,4,1,3] 110011101001=>100101110011=>011010001100=>[2,1,2,4,1,3] 110011110001=>100011110011=>011100001100=>[2,1,1,5,1,3] 111001010011=>110010100111=>001101011000=>[3,1,2,2,1,4] 111001001101=>101100100111=>010011011000=>[2,3,1,2,1,4] 111001100101=>101001100111=>010110011000=>[2,2,1,3,1,4] 111001100011=>110001100111=>001110011000=>[3,1,1,3,1,4] 111001101001=>100101100111=>011010011000=>[2,1,2,3,1,4] 111000101011=>110101000111=>001010111000=>[3,2,2,1,1,4] 111001110001=>100011100111=>011100011000=>[2,1,1,4,1,4] 111000110011=>110011000111=>001100111000=>[3,1,3,1,1,4] 111000110101=>101011000111=>010100111000=>[2,2,3,1,1,4] 111000111001=>100111000111=>011000111000=>[2,1,4,1,1,4] 111010010011=>110010010111=>001101101000=>[3,1,2,1,2,4] 111010011001=>100110010111=>011001101000=>[2,1,3,1,2,4] 111010001011=>110100010111=>001011101000=>[3,2,1,1,2,4] 111010001101=>101100010111=>010011101000=>[2,3,1,1,2,4] 111010100011=>110001010111=>001110101000=>[3,1,1,2,2,4] 111011000011=>110000110111=>001111001000=>[3,1,1,1,3,4] 101011100011=>110001110101=>001110001010=>[3,1,1,4,2,2] 101011110001=>100011110101=>011100001010=>[2,1,1,5,2,2] 111100010011=>110010001111=>001101110000=>[3,1,2,1,1,5] 111100011001=>100110001111=>011001110000=>[2,1,3,1,1,5] 111100001101=>101100001111=>010011110000=>[2,3,1,1,1,5] 111100100011=>110001001111=>001110110000=>[3,1,1,2,1,5] 111100110001=>100011001111=>011100110000=>[2,1,1,3,1,5] 101100111001=>100111001101=>011000110010=>[2,1,4,1,3,2] 111101000011=>110000101111=>001111010000=>[3,1,1,1,2,5] 101101100011=>110001101101=>001110010010=>[3,1,1,3,3,2] 101101110001=>100011101101=>011100010010=>[2,1,1,4,3,2] 111110000011=>110000011111=>001111100000=>[3,1,1,1,1,6] 101110010011=>110010011101=>001101100010=>[3,1,2,1,4,2] 101110011001=>100110011101=>011001100010=>[2,1,3,1,4,2] 101110100011=>110001011101=>001110100010=>[3,1,1,2,4,2] 101110110001=>100011011101=>011100100010=>[2,1,1,3,4,2] 0000011001=>1001100000=>0110011111=>[2,1,3,1,1,1,1,1] 0011100101=>1010011100=>0101100011=>[2,2,1,4,1,1] 000011110001=>100011110000=>011100001111=>[2,1,1,5,1,1,1,1] 001100000111=>111000001100=>000111110011=>[4,1,1,1,1,3,1,1] 001100110001=>100011001100=>011100110011=>[2,1,1,3,1,3,1,1] 001101100001=>100001101100=>011110010011=>[2,1,1,1,3,3,1,1] 001110010001=>100010011100=>011101100011=>[2,1,1,2,1,4,1,1] 110001110100=>001011100011=>110100011100=>[1,1,2,4,1,1,3] 0110010001=>1000100110=>0111011001=>[2,1,1,2,1,3,1] 0111100101=>1010011110=>0101100001=>[2,2,1,5,1] 000111011001=>100110111000=>011001000111=>[2,1,3,4,1,1,1] 001111010001=>100010111100=>011101000011=>[2,1,1,2,5,1,1] 011001000111=>111000100110=>000111011001=>[4,1,1,2,1,3,1] 011101000011=>110000101110=>001111010001=>[3,1,1,1,2,4,1] 0111011001=>1001101110=>0110010001=>[2,1,3,4,1] 0101100001=>1000011010=>0111100101=>[2,1,1,1,3,2,1] 0100110001=>1000110010=>0111001101=>[2,1,1,3,1,2,1] 0101000011=>1100001010=>0011110101=>[3,1,1,1,2,2,1] 0101001111=>1111001010=>0000110101=>[5,1,2,2,1] 0101010001=>1000101010=>0111010101=>[2,1,1,2,2,2,1] 0110001001=>1001000110=>0110111001=>[2,1,2,1,1,3,1] 010100010001=>100010001010=>011101110101=>[2,1,1,2,1,1,2,2,1] 000101010001=>100010101000=>011101010111=>[2,1,1,2,2,2,1,1,1] 000001000001=>100000100000=>011111011111=>[2,1,1,1,1,2,1,1,1,1,1] 001000010110=>011010000100=>100101111011=>[1,3,2,1,1,1,2,1,1] 001100010010=>010010001100=>101101110011=>[1,2,1,2,1,1,3,1,1] 0000110100=>0010110000=>1101001111=>[1,1,2,3,1,1,1,1] 0001000111=>1110001000=>0001110111=>[4,1,1,2,1,1,1] 0001001101=>1011001000=>0100110111=>[2,3,1,2,1,1,1] 0010001001=>1001000100=>0110111011=>[2,1,2,1,1,2,1,1] 0001010011=>1100101000=>0011010111=>[3,1,2,2,1,1,1] 0001100101=>1010011000=>0101100111=>[2,2,1,3,1,1,1] 0001000101=>1010001000=>0101110111=>[2,2,1,1,2,1,1,1] 0110011101=>1011100110=>0100011001=>[2,4,1,3,1] 0111001101=>1011001110=>0100110001=>[2,3,1,4,1] 011110110110=>011011011110=>100100100001=>[1,3,3,5,1] 10000011111=>11111000001=>00000111110=>[6,1,1,1,1,2] 00001100111=>11100110000=>00011001111=>[4,1,3,1,1,1,1] 00011001111=>11110011000=>00001100111=>[5,1,3,1,1,1] 00010011111=>11111001000=>00000110111=>[6,1,2,1,1,1]