=>

0=>0=>[2] 1=>1=>[1,1] 00=>00=>[3] 01=>10=>[1,2] 10=>01=>[2,1] 11=>11=>[1,1,1] 000=>000=>[4] 001=>100=>[1,3] 010=>010=>[2,2] 011=>110=>[1,1,2] 100=>001=>[3,1] 101=>101=>[1,2,1] 110=>011=>[2,1,1] 111=>111=>[1,1,1,1] 0000=>0000=>[5] 0001=>1000=>[1,4] 0010=>0100=>[2,3] 0011=>1100=>[1,1,3] 0100=>0010=>[3,2] 0101=>1010=>[1,2,2] 0110=>0110=>[2,1,2] 0111=>1110=>[1,1,1,2] 1000=>0001=>[4,1] 1001=>1001=>[1,3,1] 1010=>0101=>[2,2,1] 1011=>1101=>[1,1,2,1] 1100=>0011=>[3,1,1] 1101=>1011=>[1,2,1,1] 1110=>0111=>[2,1,1,1] 1111=>1111=>[1,1,1,1,1] 00000=>00000=>[6] 00001=>10000=>[1,5] 00010=>01000=>[2,4] 00011=>11000=>[1,1,4] 00100=>00100=>[3,3] 00101=>10100=>[1,2,3] 00110=>01100=>[2,1,3] 00111=>11100=>[1,1,1,3] 01000=>00010=>[4,2] 01001=>10010=>[1,3,2] 01010=>01010=>[2,2,2] 01011=>11010=>[1,1,2,2] 01100=>00110=>[3,1,2] 01101=>10110=>[1,2,1,2] 01110=>01110=>[2,1,1,2] 01111=>11110=>[1,1,1,1,2] 10000=>00001=>[5,1] 10001=>10001=>[1,4,1] 10010=>01001=>[2,3,1] 10011=>11001=>[1,1,3,1] 10100=>00101=>[3,2,1] 10101=>10101=>[1,2,2,1] 10110=>01101=>[2,1,2,1] 10111=>11101=>[1,1,1,2,1] 11000=>00011=>[4,1,1] 11001=>10011=>[1,3,1,1] 11010=>01011=>[2,2,1,1] 11011=>11011=>[1,1,2,1,1] 11100=>00111=>[3,1,1,1] 11101=>10111=>[1,2,1,1,1] 11110=>01111=>[2,1,1,1,1] 11111=>11111=>[1,1,1,1,1,1] 000000=>000000=>[7] 000001=>100000=>[1,6] 000010=>010000=>[2,5] 000011=>110000=>[1,1,5] 000100=>001000=>[3,4] 000101=>101000=>[1,2,4] 000110=>011000=>[2,1,4] 000111=>111000=>[1,1,1,4] 001000=>000100=>[4,3] 001001=>100100=>[1,3,3] 001010=>010100=>[2,2,3] 001011=>110100=>[1,1,2,3] 001100=>001100=>[3,1,3] 001101=>101100=>[1,2,1,3] 001110=>011100=>[2,1,1,3] 001111=>111100=>[1,1,1,1,3] 010000=>000010=>[5,2] 010001=>100010=>[1,4,2] 010010=>010010=>[2,3,2] 010011=>110010=>[1,1,3,2] 010100=>001010=>[3,2,2] 010101=>101010=>[1,2,2,2] 010110=>011010=>[2,1,2,2] 010111=>111010=>[1,1,1,2,2] 011000=>000110=>[4,1,2] 011001=>100110=>[1,3,1,2] 011010=>010110=>[2,2,1,2] 011011=>110110=>[1,1,2,1,2] 011100=>001110=>[3,1,1,2] 011101=>101110=>[1,2,1,1,2] 011110=>011110=>[2,1,1,1,2] 011111=>111110=>[1,1,1,1,1,2] 100000=>000001=>[6,1] 100001=>100001=>[1,5,1] 100010=>010001=>[2,4,1] 100011=>110001=>[1,1,4,1] 100100=>001001=>[3,3,1] 100101=>101001=>[1,2,3,1] 100110=>011001=>[2,1,3,1] 100111=>111001=>[1,1,1,3,1] 101000=>000101=>[4,2,1] 101001=>100101=>[1,3,2,1] 101010=>010101=>[2,2,2,1] 101011=>110101=>[1,1,2,2,1] 101100=>001101=>[3,1,2,1] 101101=>101101=>[1,2,1,2,1] 101110=>011101=>[2,1,1,2,1] 101111=>111101=>[1,1,1,1,2,1] 110000=>000011=>[5,1,1] 110001=>100011=>[1,4,1,1] 110010=>010011=>[2,3,1,1] 110011=>110011=>[1,1,3,1,1] 110100=>001011=>[3,2,1,1] 110101=>101011=>[1,2,2,1,1] 110110=>011011=>[2,1,2,1,1] 110111=>111011=>[1,1,1,2,1,1] 111000=>000111=>[4,1,1,1] 111001=>100111=>[1,3,1,1,1] 111010=>010111=>[2,2,1,1,1] 111011=>110111=>[1,1,2,1,1,1] 111100=>001111=>[3,1,1,1,1] 111101=>101111=>[1,2,1,1,1,1] 111110=>011111=>[2,1,1,1,1,1] 111111=>111111=>[1,1,1,1,1,1,1] 0000000=>0000000=>[8] 0000001=>1000000=>[1,7] 0000010=>0100000=>[2,6] 0000011=>1100000=>[1,1,6] 0000100=>0010000=>[3,5] 0000101=>1010000=>[1,2,5] 0000110=>0110000=>[2,1,5] 0000111=>1110000=>[1,1,1,5] 0001000=>0001000=>[4,4] 0001001=>1001000=>[1,3,4] 0001010=>0101000=>[2,2,4] 0001011=>1101000=>[1,1,2,4] 0001100=>0011000=>[3,1,4] 0001101=>1011000=>[1,2,1,4] 0001110=>0111000=>[2,1,1,4] 0001111=>1111000=>[1,1,1,1,4] 0010000=>0000100=>[5,3] 0010001=>1000100=>[1,4,3] 0010010=>0100100=>[2,3,3] 0010011=>1100100=>[1,1,3,3] 0010100=>0010100=>[3,2,3] 0010101=>1010100=>[1,2,2,3] 0010110=>0110100=>[2,1,2,3] 0010111=>1110100=>[1,1,1,2,3] 0011000=>0001100=>[4,1,3] 0011001=>1001100=>[1,3,1,3] 0011010=>0101100=>[2,2,1,3] 0011011=>1101100=>[1,1,2,1,3] 0011100=>0011100=>[3,1,1,3] 0011101=>1011100=>[1,2,1,1,3] 0011110=>0111100=>[2,1,1,1,3] 0011111=>1111100=>[1,1,1,1,1,3] 0100000=>0000010=>[6,2] 0100001=>1000010=>[1,5,2] 0100010=>0100010=>[2,4,2] 0100011=>1100010=>[1,1,4,2] 0100100=>0010010=>[3,3,2] 0100101=>1010010=>[1,2,3,2] 0100110=>0110010=>[2,1,3,2] 0100111=>1110010=>[1,1,1,3,2] 0101000=>0001010=>[4,2,2] 0101001=>1001010=>[1,3,2,2] 0101010=>0101010=>[2,2,2,2] 0101011=>1101010=>[1,1,2,2,2] 0101100=>0011010=>[3,1,2,2] 0101101=>1011010=>[1,2,1,2,2] 0101110=>0111010=>[2,1,1,2,2] 0101111=>1111010=>[1,1,1,1,2,2] 0110000=>0000110=>[5,1,2] 0110001=>1000110=>[1,4,1,2] 0110010=>0100110=>[2,3,1,2] 0110011=>1100110=>[1,1,3,1,2] 0110100=>0010110=>[3,2,1,2] 0110101=>1010110=>[1,2,2,1,2] 0110110=>0110110=>[2,1,2,1,2] 0110111=>1110110=>[1,1,1,2,1,2] 0111000=>0001110=>[4,1,1,2] 0111001=>1001110=>[1,3,1,1,2] 0111010=>0101110=>[2,2,1,1,2] 0111011=>1101110=>[1,1,2,1,1,2] 0111100=>0011110=>[3,1,1,1,2] 0111101=>1011110=>[1,2,1,1,1,2] 0111110=>0111110=>[2,1,1,1,1,2] 0111111=>1111110=>[1,1,1,1,1,1,2] 1000000=>0000001=>[7,1] 1000001=>1000001=>[1,6,1] 1000010=>0100001=>[2,5,1] 1000011=>1100001=>[1,1,5,1] 1000100=>0010001=>[3,4,1] 1000101=>1010001=>[1,2,4,1] 1000110=>0110001=>[2,1,4,1] 1000111=>1110001=>[1,1,1,4,1] 1001000=>0001001=>[4,3,1] 1001001=>1001001=>[1,3,3,1] 1001010=>0101001=>[2,2,3,1] 1001011=>1101001=>[1,1,2,3,1] 1001100=>0011001=>[3,1,3,1] 1001101=>1011001=>[1,2,1,3,1] 1001110=>0111001=>[2,1,1,3,1] 1001111=>1111001=>[1,1,1,1,3,1] 1010000=>0000101=>[5,2,1] 1010001=>1000101=>[1,4,2,1] 1010010=>0100101=>[2,3,2,1] 1010011=>1100101=>[1,1,3,2,1] 1010100=>0010101=>[3,2,2,1] 1010101=>1010101=>[1,2,2,2,1] 1010110=>0110101=>[2,1,2,2,1] 1010111=>1110101=>[1,1,1,2,2,1] 1011000=>0001101=>[4,1,2,1] 1011001=>1001101=>[1,3,1,2,1] 1011010=>0101101=>[2,2,1,2,1] 1011011=>1101101=>[1,1,2,1,2,1] 1011100=>0011101=>[3,1,1,2,1] 1011101=>1011101=>[1,2,1,1,2,1] 1011110=>0111101=>[2,1,1,1,2,1] 1011111=>1111101=>[1,1,1,1,1,2,1] 1100000=>0000011=>[6,1,1] 1100001=>1000011=>[1,5,1,1] 1100010=>0100011=>[2,4,1,1] 1100011=>1100011=>[1,1,4,1,1] 1100100=>0010011=>[3,3,1,1] 1100101=>1010011=>[1,2,3,1,1] 1100110=>0110011=>[2,1,3,1,1] 1100111=>1110011=>[1,1,1,3,1,1] 1101000=>0001011=>[4,2,1,1] 1101001=>1001011=>[1,3,2,1,1] 1101010=>0101011=>[2,2,2,1,1] 1101011=>1101011=>[1,1,2,2,1,1] 1101100=>0011011=>[3,1,2,1,1] 1101101=>1011011=>[1,2,1,2,1,1] 1101110=>0111011=>[2,1,1,2,1,1] 1101111=>1111011=>[1,1,1,1,2,1,1] 1110000=>0000111=>[5,1,1,1] 1110001=>1000111=>[1,4,1,1,1] 1110010=>0100111=>[2,3,1,1,1] 1110011=>1100111=>[1,1,3,1,1,1] 1110100=>0010111=>[3,2,1,1,1] 1110101=>1010111=>[1,2,2,1,1,1] 1110110=>0110111=>[2,1,2,1,1,1] 1110111=>1110111=>[1,1,1,2,1,1,1] 1111000=>0001111=>[4,1,1,1,1] 1111001=>1001111=>[1,3,1,1,1,1] 1111010=>0101111=>[2,2,1,1,1,1] 1111011=>1101111=>[1,1,2,1,1,1,1] 1111100=>0011111=>[3,1,1,1,1,1] 1111101=>1011111=>[1,2,1,1,1,1,1] 1111110=>0111111=>[2,1,1,1,1,1,1] 1111111=>1111111=>[1,1,1,1,1,1,1,1] 00000000=>00000000=>[9] 00000001=>10000000=>[1,8] 00000010=>01000000=>[2,7] 00000011=>11000000=>[1,1,7] 00000100=>00100000=>[3,6] 00000101=>10100000=>[1,2,6] 00000110=>01100000=>[2,1,6] 00000111=>11100000=>[1,1,1,6] 00001000=>00010000=>[4,5] 00001001=>10010000=>[1,3,5] 00001010=>01010000=>[2,2,5] 00001011=>11010000=>[1,1,2,5] 00001100=>00110000=>[3,1,5] 00001101=>10110000=>[1,2,1,5] 00001110=>01110000=>[2,1,1,5] 00001111=>11110000=>[1,1,1,1,5] 00010000=>00001000=>[5,4] 00010001=>10001000=>[1,4,4] 00010010=>01001000=>[2,3,4] 00010011=>11001000=>[1,1,3,4] 00010100=>00101000=>[3,2,4] 00010101=>10101000=>[1,2,2,4] 00010110=>01101000=>[2,1,2,4] 00010111=>11101000=>[1,1,1,2,4] 00011000=>00011000=>[4,1,4] 00011001=>10011000=>[1,3,1,4] 00011010=>01011000=>[2,2,1,4] 00011011=>11011000=>[1,1,2,1,4] 00011100=>00111000=>[3,1,1,4] 00011101=>10111000=>[1,2,1,1,4] 00011110=>01111000=>[2,1,1,1,4] 00011111=>11111000=>[1,1,1,1,1,4] 00100000=>00000100=>[6,3] 00100001=>10000100=>[1,5,3] 00100010=>01000100=>[2,4,3] 00100011=>11000100=>[1,1,4,3] 00100100=>00100100=>[3,3,3] 00100101=>10100100=>[1,2,3,3] 00100110=>01100100=>[2,1,3,3] 00100111=>11100100=>[1,1,1,3,3] 00101000=>00010100=>[4,2,3] 00101001=>10010100=>[1,3,2,3] 00101010=>01010100=>[2,2,2,3] 00101011=>11010100=>[1,1,2,2,3] 00101100=>00110100=>[3,1,2,3] 00101101=>10110100=>[1,2,1,2,3] 00101110=>01110100=>[2,1,1,2,3] 00101111=>11110100=>[1,1,1,1,2,3] 00110000=>00001100=>[5,1,3] 00110001=>10001100=>[1,4,1,3] 00110010=>01001100=>[2,3,1,3] 00110011=>11001100=>[1,1,3,1,3] 00110100=>00101100=>[3,2,1,3] 00110101=>10101100=>[1,2,2,1,3] 00110110=>01101100=>[2,1,2,1,3] 00110111=>11101100=>[1,1,1,2,1,3] 00111000=>00011100=>[4,1,1,3] 00111001=>10011100=>[1,3,1,1,3] 00111010=>01011100=>[2,2,1,1,3] 00111011=>11011100=>[1,1,2,1,1,3] 00111100=>00111100=>[3,1,1,1,3] 00111101=>10111100=>[1,2,1,1,1,3] 00111110=>01111100=>[2,1,1,1,1,3] 00111111=>11111100=>[1,1,1,1,1,1,3] 01000000=>00000010=>[7,2] 01000001=>10000010=>[1,6,2] 01000010=>01000010=>[2,5,2] 01000011=>11000010=>[1,1,5,2] 01000100=>00100010=>[3,4,2] 01000101=>10100010=>[1,2,4,2] 01000110=>01100010=>[2,1,4,2] 01000111=>11100010=>[1,1,1,4,2] 01001000=>00010010=>[4,3,2] 01001001=>10010010=>[1,3,3,2] 01001010=>01010010=>[2,2,3,2] 01001011=>11010010=>[1,1,2,3,2] 01001100=>00110010=>[3,1,3,2] 01001101=>10110010=>[1,2,1,3,2] 01001110=>01110010=>[2,1,1,3,2] 01001111=>11110010=>[1,1,1,1,3,2] 01010000=>00001010=>[5,2,2] 01010001=>10001010=>[1,4,2,2] 01010010=>01001010=>[2,3,2,2] 01010011=>11001010=>[1,1,3,2,2] 01010100=>00101010=>[3,2,2,2] 01010101=>10101010=>[1,2,2,2,2] 01010110=>01101010=>[2,1,2,2,2] 01010111=>11101010=>[1,1,1,2,2,2] 01011000=>00011010=>[4,1,2,2] 01011001=>10011010=>[1,3,1,2,2] 01011010=>01011010=>[2,2,1,2,2] 01011011=>11011010=>[1,1,2,1,2,2] 01011100=>00111010=>[3,1,1,2,2] 01011101=>10111010=>[1,2,1,1,2,2] 01011110=>01111010=>[2,1,1,1,2,2] 01011111=>11111010=>[1,1,1,1,1,2,2] 01100000=>00000110=>[6,1,2] 01100001=>10000110=>[1,5,1,2] 01100010=>01000110=>[2,4,1,2] 01100011=>11000110=>[1,1,4,1,2] 01100100=>00100110=>[3,3,1,2] 01100101=>10100110=>[1,2,3,1,2] 01100110=>01100110=>[2,1,3,1,2] 01100111=>11100110=>[1,1,1,3,1,2] 01101000=>00010110=>[4,2,1,2] 01101001=>10010110=>[1,3,2,1,2] 01101010=>01010110=>[2,2,2,1,2] 01101011=>11010110=>[1,1,2,2,1,2] 01101100=>00110110=>[3,1,2,1,2] 01101101=>10110110=>[1,2,1,2,1,2] 01101110=>01110110=>[2,1,1,2,1,2] 01101111=>11110110=>[1,1,1,1,2,1,2] 01110000=>00001110=>[5,1,1,2] 01110001=>10001110=>[1,4,1,1,2] 01110010=>01001110=>[2,3,1,1,2] 01110011=>11001110=>[1,1,3,1,1,2] 01110100=>00101110=>[3,2,1,1,2] 01110101=>10101110=>[1,2,2,1,1,2] 01110110=>01101110=>[2,1,2,1,1,2] 01110111=>11101110=>[1,1,1,2,1,1,2] 01111000=>00011110=>[4,1,1,1,2] 01111001=>10011110=>[1,3,1,1,1,2] 01111010=>01011110=>[2,2,1,1,1,2] 01111011=>11011110=>[1,1,2,1,1,1,2] 01111100=>00111110=>[3,1,1,1,1,2] 01111101=>10111110=>[1,2,1,1,1,1,2] 01111110=>01111110=>[2,1,1,1,1,1,2] 01111111=>11111110=>[1,1,1,1,1,1,1,2] 10000000=>00000001=>[8,1] 10000001=>10000001=>[1,7,1] 10000010=>01000001=>[2,6,1] 10000011=>11000001=>[1,1,6,1] 10000100=>00100001=>[3,5,1] 10000101=>10100001=>[1,2,5,1] 10000110=>01100001=>[2,1,5,1] 10000111=>11100001=>[1,1,1,5,1] 10001000=>00010001=>[4,4,1] 10001001=>10010001=>[1,3,4,1] 10001010=>01010001=>[2,2,4,1] 10001011=>11010001=>[1,1,2,4,1] 10001100=>00110001=>[3,1,4,1] 10001101=>10110001=>[1,2,1,4,1] 10001110=>01110001=>[2,1,1,4,1] 10001111=>11110001=>[1,1,1,1,4,1] 10010000=>00001001=>[5,3,1] 10010001=>10001001=>[1,4,3,1] 10010010=>01001001=>[2,3,3,1] 10010011=>11001001=>[1,1,3,3,1] 10010100=>00101001=>[3,2,3,1] 10010101=>10101001=>[1,2,2,3,1] 10010110=>01101001=>[2,1,2,3,1] 10010111=>11101001=>[1,1,1,2,3,1] 10011000=>00011001=>[4,1,3,1] 10011001=>10011001=>[1,3,1,3,1] 10011010=>01011001=>[2,2,1,3,1] 10011011=>11011001=>[1,1,2,1,3,1] 10011100=>00111001=>[3,1,1,3,1] 10011101=>10111001=>[1,2,1,1,3,1] 10011110=>01111001=>[2,1,1,1,3,1] 10011111=>11111001=>[1,1,1,1,1,3,1] 10100000=>00000101=>[6,2,1] 10100001=>10000101=>[1,5,2,1] 10100010=>01000101=>[2,4,2,1] 10100011=>11000101=>[1,1,4,2,1] 10100100=>00100101=>[3,3,2,1] 10100101=>10100101=>[1,2,3,2,1] 10100110=>01100101=>[2,1,3,2,1] 10100111=>11100101=>[1,1,1,3,2,1] 10101000=>00010101=>[4,2,2,1] 10101001=>10010101=>[1,3,2,2,1] 10101010=>01010101=>[2,2,2,2,1] 10101011=>11010101=>[1,1,2,2,2,1] 10101100=>00110101=>[3,1,2,2,1] 10101101=>10110101=>[1,2,1,2,2,1] 10101110=>01110101=>[2,1,1,2,2,1] 10101111=>11110101=>[1,1,1,1,2,2,1] 10110000=>00001101=>[5,1,2,1] 10110001=>10001101=>[1,4,1,2,1] 10110010=>01001101=>[2,3,1,2,1] 10110011=>11001101=>[1,1,3,1,2,1] 10110100=>00101101=>[3,2,1,2,1] 10110101=>10101101=>[1,2,2,1,2,1] 10110110=>01101101=>[2,1,2,1,2,1] 10110111=>11101101=>[1,1,1,2,1,2,1] 10111000=>00011101=>[4,1,1,2,1] 10111001=>10011101=>[1,3,1,1,2,1] 10111010=>01011101=>[2,2,1,1,2,1] 10111011=>11011101=>[1,1,2,1,1,2,1] 10111100=>00111101=>[3,1,1,1,2,1] 10111101=>10111101=>[1,2,1,1,1,2,1] 10111110=>01111101=>[2,1,1,1,1,2,1] 10111111=>11111101=>[1,1,1,1,1,1,2,1] 11000000=>00000011=>[7,1,1] 11000001=>10000011=>[1,6,1,1] 11000010=>01000011=>[2,5,1,1] 11000011=>11000011=>[1,1,5,1,1] 11000100=>00100011=>[3,4,1,1] 11000101=>10100011=>[1,2,4,1,1] 11000110=>01100011=>[2,1,4,1,1] 11000111=>11100011=>[1,1,1,4,1,1] 11001000=>00010011=>[4,3,1,1] 11001001=>10010011=>[1,3,3,1,1] 11001010=>01010011=>[2,2,3,1,1] 11001011=>11010011=>[1,1,2,3,1,1] 11001100=>00110011=>[3,1,3,1,1] 11001101=>10110011=>[1,2,1,3,1,1] 11001110=>01110011=>[2,1,1,3,1,1] 11001111=>11110011=>[1,1,1,1,3,1,1] 11010000=>00001011=>[5,2,1,1] 11010001=>10001011=>[1,4,2,1,1] 11010010=>01001011=>[2,3,2,1,1] 11010011=>11001011=>[1,1,3,2,1,1] 11010100=>00101011=>[3,2,2,1,1] 11010101=>10101011=>[1,2,2,2,1,1] 11010110=>01101011=>[2,1,2,2,1,1] 11010111=>11101011=>[1,1,1,2,2,1,1] 11011000=>00011011=>[4,1,2,1,1] 11011001=>10011011=>[1,3,1,2,1,1] 11011010=>01011011=>[2,2,1,2,1,1] 11011011=>11011011=>[1,1,2,1,2,1,1] 11011100=>00111011=>[3,1,1,2,1,1] 11011101=>10111011=>[1,2,1,1,2,1,1] 11011110=>01111011=>[2,1,1,1,2,1,1] 11011111=>11111011=>[1,1,1,1,1,2,1,1] 11100000=>00000111=>[6,1,1,1] 11100001=>10000111=>[1,5,1,1,1] 11100010=>01000111=>[2,4,1,1,1] 11100011=>11000111=>[1,1,4,1,1,1] 11100100=>00100111=>[3,3,1,1,1] 11100101=>10100111=>[1,2,3,1,1,1] 11100110=>01100111=>[2,1,3,1,1,1] 11100111=>11100111=>[1,1,1,3,1,1,1] 11101000=>00010111=>[4,2,1,1,1] 11101001=>10010111=>[1,3,2,1,1,1] 11101010=>01010111=>[2,2,2,1,1,1] 11101011=>11010111=>[1,1,2,2,1,1,1] 11101100=>00110111=>[3,1,2,1,1,1] 11101101=>10110111=>[1,2,1,2,1,1,1] 11101110=>01110111=>[2,1,1,2,1,1,1] 11101111=>11110111=>[1,1,1,1,2,1,1,1] 11110000=>00001111=>[5,1,1,1,1] 11110001=>10001111=>[1,4,1,1,1,1] 11110010=>01001111=>[2,3,1,1,1,1] 11110011=>11001111=>[1,1,3,1,1,1,1] 11110100=>00101111=>[3,2,1,1,1,1] 11110101=>10101111=>[1,2,2,1,1,1,1] 11110110=>01101111=>[2,1,2,1,1,1,1] 11110111=>11101111=>[1,1,1,2,1,1,1,1] 11111000=>00011111=>[4,1,1,1,1,1] 11111001=>10011111=>[1,3,1,1,1,1,1] 11111010=>01011111=>[2,2,1,1,1,1,1] 11111011=>11011111=>[1,1,2,1,1,1,1,1] 11111100=>00111111=>[3,1,1,1,1,1,1] 11111101=>10111111=>[1,2,1,1,1,1,1,1] 11111110=>01111111=>[2,1,1,1,1,1,1,1] 11111111=>11111111=>[1,1,1,1,1,1,1,1,1] 000000000=>000000000=>[10] 000000001=>100000000=>[1,9] 000000010=>010000000=>[2,8] 000000011=>110000000=>[1,1,8] 000000100=>001000000=>[3,7] 000000101=>101000000=>[1,2,7] 000000110=>011000000=>[2,1,7] 000000111=>111000000=>[1,1,1,7] 000001000=>000100000=>[4,6] 000001001=>100100000=>[1,3,6] 000001010=>010100000=>[2,2,6] 000001011=>110100000=>[1,1,2,6] 000001100=>001100000=>[3,1,6] 000001101=>101100000=>[1,2,1,6] 000001110=>011100000=>[2,1,1,6] 000001111=>111100000=>[1,1,1,1,6] 000010000=>000010000=>[5,5] 000010001=>100010000=>[1,4,5] 000010010=>010010000=>[2,3,5] 000010011=>110010000=>[1,1,3,5] 000010100=>001010000=>[3,2,5] 000010101=>101010000=>[1,2,2,5] 000010110=>011010000=>[2,1,2,5] 000010111=>111010000=>[1,1,1,2,5] 000011000=>000110000=>[4,1,5] 000011001=>100110000=>[1,3,1,5] 000011010=>010110000=>[2,2,1,5] 000011011=>110110000=>[1,1,2,1,5] 000011100=>001110000=>[3,1,1,5] 000011101=>101110000=>[1,2,1,1,5] 000011110=>011110000=>[2,1,1,1,5] 000011111=>111110000=>[1,1,1,1,1,5] 000100000=>000001000=>[6,4] 000100001=>100001000=>[1,5,4] 000100010=>010001000=>[2,4,4] 000100011=>110001000=>[1,1,4,4] 000100100=>001001000=>[3,3,4] 000100101=>101001000=>[1,2,3,4] 000100110=>011001000=>[2,1,3,4] 000100111=>111001000=>[1,1,1,3,4] 000101000=>000101000=>[4,2,4] 000101001=>100101000=>[1,3,2,4] 000101010=>010101000=>[2,2,2,4] 000101011=>110101000=>[1,1,2,2,4] 000101100=>001101000=>[3,1,2,4] 000101101=>101101000=>[1,2,1,2,4] 000101110=>011101000=>[2,1,1,2,4] 000101111=>111101000=>[1,1,1,1,2,4] 000110000=>000011000=>[5,1,4] 000110001=>100011000=>[1,4,1,4] 000110010=>010011000=>[2,3,1,4] 000110011=>110011000=>[1,1,3,1,4] 000110100=>001011000=>[3,2,1,4] 000110101=>101011000=>[1,2,2,1,4] 000110110=>011011000=>[2,1,2,1,4] 000110111=>111011000=>[1,1,1,2,1,4] 000111000=>000111000=>[4,1,1,4] 000111001=>100111000=>[1,3,1,1,4] 000111010=>010111000=>[2,2,1,1,4] 000111011=>110111000=>[1,1,2,1,1,4] 000111100=>001111000=>[3,1,1,1,4] 000111101=>101111000=>[1,2,1,1,1,4] 000111110=>011111000=>[2,1,1,1,1,4] 000111111=>111111000=>[1,1,1,1,1,1,4] 001000000=>000000100=>[7,3] 001000001=>100000100=>[1,6,3] 001000010=>010000100=>[2,5,3] 001000011=>110000100=>[1,1,5,3] 001000100=>001000100=>[3,4,3] 001000101=>101000100=>[1,2,4,3] 001000110=>011000100=>[2,1,4,3] 001000111=>111000100=>[1,1,1,4,3] 001001000=>000100100=>[4,3,3] 001001001=>100100100=>[1,3,3,3] 001001010=>010100100=>[2,2,3,3] 001001011=>110100100=>[1,1,2,3,3] 001001100=>001100100=>[3,1,3,3] 001001101=>101100100=>[1,2,1,3,3] 001001110=>011100100=>[2,1,1,3,3] 001001111=>111100100=>[1,1,1,1,3,3] 001010000=>000010100=>[5,2,3] 001010001=>100010100=>[1,4,2,3] 001010010=>010010100=>[2,3,2,3] 001010011=>110010100=>[1,1,3,2,3] 001010100=>001010100=>[3,2,2,3] 001010101=>101010100=>[1,2,2,2,3] 001010110=>011010100=>[2,1,2,2,3] 001010111=>111010100=>[1,1,1,2,2,3] 001011000=>000110100=>[4,1,2,3] 001011001=>100110100=>[1,3,1,2,3] 001011010=>010110100=>[2,2,1,2,3] 001011011=>110110100=>[1,1,2,1,2,3] 001011100=>001110100=>[3,1,1,2,3] 001011101=>101110100=>[1,2,1,1,2,3] 001011110=>011110100=>[2,1,1,1,2,3] 001011111=>111110100=>[1,1,1,1,1,2,3] 001100000=>000001100=>[6,1,3] 001100001=>100001100=>[1,5,1,3] 001100010=>010001100=>[2,4,1,3] 001100011=>110001100=>[1,1,4,1,3] 001100100=>001001100=>[3,3,1,3] 001100101=>101001100=>[1,2,3,1,3] 001100110=>011001100=>[2,1,3,1,3] 001100111=>111001100=>[1,1,1,3,1,3] 001101000=>000101100=>[4,2,1,3] 001101001=>100101100=>[1,3,2,1,3] 001101010=>010101100=>[2,2,2,1,3] 001101011=>110101100=>[1,1,2,2,1,3] 001101100=>001101100=>[3,1,2,1,3] 001101101=>101101100=>[1,2,1,2,1,3] 001101110=>011101100=>[2,1,1,2,1,3] 001101111=>111101100=>[1,1,1,1,2,1,3] 001110000=>000011100=>[5,1,1,3] 001110001=>100011100=>[1,4,1,1,3] 001110010=>010011100=>[2,3,1,1,3] 001110011=>110011100=>[1,1,3,1,1,3] 001110100=>001011100=>[3,2,1,1,3] 001110101=>101011100=>[1,2,2,1,1,3] 001110110=>011011100=>[2,1,2,1,1,3] 001110111=>111011100=>[1,1,1,2,1,1,3] 001111000=>000111100=>[4,1,1,1,3] 001111001=>100111100=>[1,3,1,1,1,3] 001111010=>010111100=>[2,2,1,1,1,3] 001111011=>110111100=>[1,1,2,1,1,1,3] 001111100=>001111100=>[3,1,1,1,1,3] 001111101=>101111100=>[1,2,1,1,1,1,3] 001111110=>011111100=>[2,1,1,1,1,1,3] 001111111=>111111100=>[1,1,1,1,1,1,1,3] 010000000=>000000010=>[8,2] 010000001=>100000010=>[1,7,2] 010000010=>010000010=>[2,6,2] 010000011=>110000010=>[1,1,6,2] 010000100=>001000010=>[3,5,2] 010000101=>101000010=>[1,2,5,2] 010000110=>011000010=>[2,1,5,2] 010000111=>111000010=>[1,1,1,5,2] 010001000=>000100010=>[4,4,2] 010001001=>100100010=>[1,3,4,2] 010001010=>010100010=>[2,2,4,2] 010001011=>110100010=>[1,1,2,4,2] 010001100=>001100010=>[3,1,4,2] 010001101=>101100010=>[1,2,1,4,2] 010001110=>011100010=>[2,1,1,4,2] 010001111=>111100010=>[1,1,1,1,4,2] 010010000=>000010010=>[5,3,2] 010010001=>100010010=>[1,4,3,2] 010010010=>010010010=>[2,3,3,2] 010010011=>110010010=>[1,1,3,3,2] 010010100=>001010010=>[3,2,3,2] 010010101=>101010010=>[1,2,2,3,2] 010010110=>011010010=>[2,1,2,3,2] 010010111=>111010010=>[1,1,1,2,3,2] 010011000=>000110010=>[4,1,3,2] 010011001=>100110010=>[1,3,1,3,2] 010011010=>010110010=>[2,2,1,3,2] 010011011=>110110010=>[1,1,2,1,3,2] 010011100=>001110010=>[3,1,1,3,2] 010011101=>101110010=>[1,2,1,1,3,2] 010011110=>011110010=>[2,1,1,1,3,2] 010011111=>111110010=>[1,1,1,1,1,3,2] 010100000=>000001010=>[6,2,2] 010100001=>100001010=>[1,5,2,2] 010100010=>010001010=>[2,4,2,2] 010100011=>110001010=>[1,1,4,2,2] 010100100=>001001010=>[3,3,2,2] 010100101=>101001010=>[1,2,3,2,2] 010100110=>011001010=>[2,1,3,2,2] 010100111=>111001010=>[1,1,1,3,2,2] 010101000=>000101010=>[4,2,2,2] 010101001=>100101010=>[1,3,2,2,2] 010101010=>010101010=>[2,2,2,2,2] 010101011=>110101010=>[1,1,2,2,2,2] 010101100=>001101010=>[3,1,2,2,2] 010101101=>101101010=>[1,2,1,2,2,2] 010101110=>011101010=>[2,1,1,2,2,2] 010101111=>111101010=>[1,1,1,1,2,2,2] 010110000=>000011010=>[5,1,2,2] 010110001=>100011010=>[1,4,1,2,2] 010110010=>010011010=>[2,3,1,2,2] 010110011=>110011010=>[1,1,3,1,2,2] 010110100=>001011010=>[3,2,1,2,2] 010110101=>101011010=>[1,2,2,1,2,2] 010110110=>011011010=>[2,1,2,1,2,2] 010110111=>111011010=>[1,1,1,2,1,2,2] 010111000=>000111010=>[4,1,1,2,2] 010111001=>100111010=>[1,3,1,1,2,2] 010111010=>010111010=>[2,2,1,1,2,2] 010111011=>110111010=>[1,1,2,1,1,2,2] 010111100=>001111010=>[3,1,1,1,2,2] 010111101=>101111010=>[1,2,1,1,1,2,2] 010111110=>011111010=>[2,1,1,1,1,2,2] 010111111=>111111010=>[1,1,1,1,1,1,2,2] 011000000=>000000110=>[7,1,2] 011000001=>100000110=>[1,6,1,2] 011000010=>010000110=>[2,5,1,2] 011000011=>110000110=>[1,1,5,1,2] 011000100=>001000110=>[3,4,1,2] 011000101=>101000110=>[1,2,4,1,2] 011000110=>011000110=>[2,1,4,1,2] 011000111=>111000110=>[1,1,1,4,1,2] 011001000=>000100110=>[4,3,1,2] 011001001=>100100110=>[1,3,3,1,2] 011001010=>010100110=>[2,2,3,1,2] 011001011=>110100110=>[1,1,2,3,1,2] 011001100=>001100110=>[3,1,3,1,2] 011001101=>101100110=>[1,2,1,3,1,2] 011001110=>011100110=>[2,1,1,3,1,2] 011001111=>111100110=>[1,1,1,1,3,1,2] 011010000=>000010110=>[5,2,1,2] 011010001=>100010110=>[1,4,2,1,2] 011010010=>010010110=>[2,3,2,1,2] 011010011=>110010110=>[1,1,3,2,1,2] 011010100=>001010110=>[3,2,2,1,2] 011010101=>101010110=>[1,2,2,2,1,2] 011010110=>011010110=>[2,1,2,2,1,2] 011010111=>111010110=>[1,1,1,2,2,1,2] 011011000=>000110110=>[4,1,2,1,2] 011011001=>100110110=>[1,3,1,2,1,2] 011011010=>010110110=>[2,2,1,2,1,2] 011011011=>110110110=>[1,1,2,1,2,1,2] 011011100=>001110110=>[3,1,1,2,1,2] 011011101=>101110110=>[1,2,1,1,2,1,2] 011011110=>011110110=>[2,1,1,1,2,1,2] 011011111=>111110110=>[1,1,1,1,1,2,1,2] 011100000=>000001110=>[6,1,1,2] 011100001=>100001110=>[1,5,1,1,2] 011100010=>010001110=>[2,4,1,1,2] 011100011=>110001110=>[1,1,4,1,1,2] 011100100=>001001110=>[3,3,1,1,2] 011100101=>101001110=>[1,2,3,1,1,2] 011100110=>011001110=>[2,1,3,1,1,2] 011100111=>111001110=>[1,1,1,3,1,1,2] 011101000=>000101110=>[4,2,1,1,2] 011101001=>100101110=>[1,3,2,1,1,2] 011101010=>010101110=>[2,2,2,1,1,2] 011101011=>110101110=>[1,1,2,2,1,1,2] 011101100=>001101110=>[3,1,2,1,1,2] 011101101=>101101110=>[1,2,1,2,1,1,2] 011101110=>011101110=>[2,1,1,2,1,1,2] 011101111=>111101110=>[1,1,1,1,2,1,1,2] 011110000=>000011110=>[5,1,1,1,2] 011110001=>100011110=>[1,4,1,1,1,2] 011110010=>010011110=>[2,3,1,1,1,2] 011110011=>110011110=>[1,1,3,1,1,1,2] 011110100=>001011110=>[3,2,1,1,1,2] 011110101=>101011110=>[1,2,2,1,1,1,2] 011110110=>011011110=>[2,1,2,1,1,1,2] 011110111=>111011110=>[1,1,1,2,1,1,1,2] 011111000=>000111110=>[4,1,1,1,1,2] 011111001=>100111110=>[1,3,1,1,1,1,2] 011111010=>010111110=>[2,2,1,1,1,1,2] 011111011=>110111110=>[1,1,2,1,1,1,1,2] 011111100=>001111110=>[3,1,1,1,1,1,2] 011111101=>101111110=>[1,2,1,1,1,1,1,2] 011111110=>011111110=>[2,1,1,1,1,1,1,2] 011111111=>111111110=>[1,1,1,1,1,1,1,1,2] 100000000=>000000001=>[9,1] 100000001=>100000001=>[1,8,1] 100000010=>010000001=>[2,7,1] 100000011=>110000001=>[1,1,7,1] 100000100=>001000001=>[3,6,1] 100000101=>101000001=>[1,2,6,1] 100000110=>011000001=>[2,1,6,1] 100000111=>111000001=>[1,1,1,6,1] 100001000=>000100001=>[4,5,1] 100001001=>100100001=>[1,3,5,1] 100001010=>010100001=>[2,2,5,1] 100001011=>110100001=>[1,1,2,5,1] 100001100=>001100001=>[3,1,5,1] 100001101=>101100001=>[1,2,1,5,1] 100001110=>011100001=>[2,1,1,5,1] 100001111=>111100001=>[1,1,1,1,5,1] 100010000=>000010001=>[5,4,1] 100010001=>100010001=>[1,4,4,1] 100010010=>010010001=>[2,3,4,1] 100010011=>110010001=>[1,1,3,4,1] 100010100=>001010001=>[3,2,4,1] 100010101=>101010001=>[1,2,2,4,1] 100010110=>011010001=>[2,1,2,4,1] 100010111=>111010001=>[1,1,1,2,4,1] 100011000=>000110001=>[4,1,4,1] 100011001=>100110001=>[1,3,1,4,1] 100011010=>010110001=>[2,2,1,4,1] 100011011=>110110001=>[1,1,2,1,4,1] 100011100=>001110001=>[3,1,1,4,1] 100011101=>101110001=>[1,2,1,1,4,1] 100011110=>011110001=>[2,1,1,1,4,1] 100011111=>111110001=>[1,1,1,1,1,4,1] 100100000=>000001001=>[6,3,1] 100100001=>100001001=>[1,5,3,1] 100100010=>010001001=>[2,4,3,1] 100100011=>110001001=>[1,1,4,3,1] 100100100=>001001001=>[3,3,3,1] 100100101=>101001001=>[1,2,3,3,1] 100100110=>011001001=>[2,1,3,3,1] 100100111=>111001001=>[1,1,1,3,3,1] 100101000=>000101001=>[4,2,3,1] 100101001=>100101001=>[1,3,2,3,1] 100101010=>010101001=>[2,2,2,3,1] 100101011=>110101001=>[1,1,2,2,3,1] 100101100=>001101001=>[3,1,2,3,1] 100101101=>101101001=>[1,2,1,2,3,1] 100101110=>011101001=>[2,1,1,2,3,1] 100101111=>111101001=>[1,1,1,1,2,3,1] 100110000=>000011001=>[5,1,3,1] 100110001=>100011001=>[1,4,1,3,1] 100110010=>010011001=>[2,3,1,3,1] 100110011=>110011001=>[1,1,3,1,3,1] 100110100=>001011001=>[3,2,1,3,1] 100110101=>101011001=>[1,2,2,1,3,1] 100110110=>011011001=>[2,1,2,1,3,1] 100110111=>111011001=>[1,1,1,2,1,3,1] 100111000=>000111001=>[4,1,1,3,1] 100111001=>100111001=>[1,3,1,1,3,1] 100111010=>010111001=>[2,2,1,1,3,1] 100111011=>110111001=>[1,1,2,1,1,3,1] 100111100=>001111001=>[3,1,1,1,3,1] 100111101=>101111001=>[1,2,1,1,1,3,1] 100111110=>011111001=>[2,1,1,1,1,3,1] 100111111=>111111001=>[1,1,1,1,1,1,3,1] 101000000=>000000101=>[7,2,1] 101000001=>100000101=>[1,6,2,1] 101000010=>010000101=>[2,5,2,1] 101000011=>110000101=>[1,1,5,2,1] 101000100=>001000101=>[3,4,2,1] 101000101=>101000101=>[1,2,4,2,1] 101000110=>011000101=>[2,1,4,2,1] 101000111=>111000101=>[1,1,1,4,2,1] 101001000=>000100101=>[4,3,2,1] 101001001=>100100101=>[1,3,3,2,1] 101001010=>010100101=>[2,2,3,2,1] 101001011=>110100101=>[1,1,2,3,2,1] 101001100=>001100101=>[3,1,3,2,1] 101001101=>101100101=>[1,2,1,3,2,1] 101001110=>011100101=>[2,1,1,3,2,1] 101001111=>111100101=>[1,1,1,1,3,2,1] 101010000=>000010101=>[5,2,2,1] 101010001=>100010101=>[1,4,2,2,1] 101010010=>010010101=>[2,3,2,2,1] 101010011=>110010101=>[1,1,3,2,2,1] 101010100=>001010101=>[3,2,2,2,1] 101010101=>101010101=>[1,2,2,2,2,1] 101010110=>011010101=>[2,1,2,2,2,1] 101010111=>111010101=>[1,1,1,2,2,2,1] 101011000=>000110101=>[4,1,2,2,1] 101011001=>100110101=>[1,3,1,2,2,1] 101011010=>010110101=>[2,2,1,2,2,1] 101011011=>110110101=>[1,1,2,1,2,2,1] 101011100=>001110101=>[3,1,1,2,2,1] 101011101=>101110101=>[1,2,1,1,2,2,1] 101011110=>011110101=>[2,1,1,1,2,2,1] 101011111=>111110101=>[1,1,1,1,1,2,2,1] 101100000=>000001101=>[6,1,2,1] 101100001=>100001101=>[1,5,1,2,1] 101100010=>010001101=>[2,4,1,2,1] 101100011=>110001101=>[1,1,4,1,2,1] 101100100=>001001101=>[3,3,1,2,1] 101100101=>101001101=>[1,2,3,1,2,1] 101100110=>011001101=>[2,1,3,1,2,1] 101100111=>111001101=>[1,1,1,3,1,2,1] 101101000=>000101101=>[4,2,1,2,1] 101101001=>100101101=>[1,3,2,1,2,1] 101101010=>010101101=>[2,2,2,1,2,1] 101101011=>110101101=>[1,1,2,2,1,2,1] 101101100=>001101101=>[3,1,2,1,2,1] 101101101=>101101101=>[1,2,1,2,1,2,1] 101101110=>011101101=>[2,1,1,2,1,2,1] 101101111=>111101101=>[1,1,1,1,2,1,2,1] 101110000=>000011101=>[5,1,1,2,1] 101110001=>100011101=>[1,4,1,1,2,1] 101110010=>010011101=>[2,3,1,1,2,1] 101110011=>110011101=>[1,1,3,1,1,2,1] 101110100=>001011101=>[3,2,1,1,2,1] 101110101=>101011101=>[1,2,2,1,1,2,1] 101110110=>011011101=>[2,1,2,1,1,2,1] 101110111=>111011101=>[1,1,1,2,1,1,2,1] 101111000=>000111101=>[4,1,1,1,2,1] 101111001=>100111101=>[1,3,1,1,1,2,1] 101111010=>010111101=>[2,2,1,1,1,2,1] 101111011=>110111101=>[1,1,2,1,1,1,2,1] 101111100=>001111101=>[3,1,1,1,1,2,1] 101111101=>101111101=>[1,2,1,1,1,1,2,1] 101111110=>011111101=>[2,1,1,1,1,1,2,1] 101111111=>111111101=>[1,1,1,1,1,1,1,2,1] 110000000=>000000011=>[8,1,1] 110000001=>100000011=>[1,7,1,1] 110000010=>010000011=>[2,6,1,1] 110000011=>110000011=>[1,1,6,1,1] 110000100=>001000011=>[3,5,1,1] 110000101=>101000011=>[1,2,5,1,1] 110000110=>011000011=>[2,1,5,1,1] 110000111=>111000011=>[1,1,1,5,1,1] 110001000=>000100011=>[4,4,1,1] 110001001=>100100011=>[1,3,4,1,1] 110001010=>010100011=>[2,2,4,1,1] 110001011=>110100011=>[1,1,2,4,1,1] 110001100=>001100011=>[3,1,4,1,1] 110001101=>101100011=>[1,2,1,4,1,1] 110001110=>011100011=>[2,1,1,4,1,1] 110001111=>111100011=>[1,1,1,1,4,1,1] 110010000=>000010011=>[5,3,1,1] 110010001=>100010011=>[1,4,3,1,1] 110010010=>010010011=>[2,3,3,1,1] 110010011=>110010011=>[1,1,3,3,1,1] 110010100=>001010011=>[3,2,3,1,1] 110010101=>101010011=>[1,2,2,3,1,1] 110010110=>011010011=>[2,1,2,3,1,1] 110010111=>111010011=>[1,1,1,2,3,1,1] 110011000=>000110011=>[4,1,3,1,1] 110011001=>100110011=>[1,3,1,3,1,1] 110011010=>010110011=>[2,2,1,3,1,1] 110011011=>110110011=>[1,1,2,1,3,1,1] 110011100=>001110011=>[3,1,1,3,1,1] 110011101=>101110011=>[1,2,1,1,3,1,1] 110011110=>011110011=>[2,1,1,1,3,1,1] 110011111=>111110011=>[1,1,1,1,1,3,1,1] 110100000=>000001011=>[6,2,1,1] 110100001=>100001011=>[1,5,2,1,1] 110100010=>010001011=>[2,4,2,1,1] 110100011=>110001011=>[1,1,4,2,1,1] 110100100=>001001011=>[3,3,2,1,1] 110100101=>101001011=>[1,2,3,2,1,1] 110100110=>011001011=>[2,1,3,2,1,1] 110100111=>111001011=>[1,1,1,3,2,1,1] 110101000=>000101011=>[4,2,2,1,1] 110101001=>100101011=>[1,3,2,2,1,1] 110101010=>010101011=>[2,2,2,2,1,1] 110101011=>110101011=>[1,1,2,2,2,1,1] 110101100=>001101011=>[3,1,2,2,1,1] 110101101=>101101011=>[1,2,1,2,2,1,1] 110101110=>011101011=>[2,1,1,2,2,1,1] 110101111=>111101011=>[1,1,1,1,2,2,1,1] 110110000=>000011011=>[5,1,2,1,1] 110110001=>100011011=>[1,4,1,2,1,1] 110110010=>010011011=>[2,3,1,2,1,1] 110110011=>110011011=>[1,1,3,1,2,1,1] 110110100=>001011011=>[3,2,1,2,1,1] 110110101=>101011011=>[1,2,2,1,2,1,1] 110110110=>011011011=>[2,1,2,1,2,1,1] 110110111=>111011011=>[1,1,1,2,1,2,1,1] 110111000=>000111011=>[4,1,1,2,1,1] 110111001=>100111011=>[1,3,1,1,2,1,1] 110111010=>010111011=>[2,2,1,1,2,1,1] 110111011=>110111011=>[1,1,2,1,1,2,1,1] 110111100=>001111011=>[3,1,1,1,2,1,1] 110111101=>101111011=>[1,2,1,1,1,2,1,1] 110111110=>011111011=>[2,1,1,1,1,2,1,1] 110111111=>111111011=>[1,1,1,1,1,1,2,1,1] 111000000=>000000111=>[7,1,1,1] 111000001=>100000111=>[1,6,1,1,1] 111000010=>010000111=>[2,5,1,1,1] 111000011=>110000111=>[1,1,5,1,1,1] 111000100=>001000111=>[3,4,1,1,1] 111000101=>101000111=>[1,2,4,1,1,1] 111000110=>011000111=>[2,1,4,1,1,1] 111000111=>111000111=>[1,1,1,4,1,1,1] 111001000=>000100111=>[4,3,1,1,1] 111001001=>100100111=>[1,3,3,1,1,1] 111001010=>010100111=>[2,2,3,1,1,1] 111001011=>110100111=>[1,1,2,3,1,1,1] 111001100=>001100111=>[3,1,3,1,1,1] 111001101=>101100111=>[1,2,1,3,1,1,1] 111001110=>011100111=>[2,1,1,3,1,1,1] 111001111=>111100111=>[1,1,1,1,3,1,1,1] 111010000=>000010111=>[5,2,1,1,1] 111010001=>100010111=>[1,4,2,1,1,1] 111010010=>010010111=>[2,3,2,1,1,1] 111010011=>110010111=>[1,1,3,2,1,1,1] 111010100=>001010111=>[3,2,2,1,1,1] 111010101=>101010111=>[1,2,2,2,1,1,1] 111010110=>011010111=>[2,1,2,2,1,1,1] 111010111=>111010111=>[1,1,1,2,2,1,1,1] 111011000=>000110111=>[4,1,2,1,1,1] 111011001=>100110111=>[1,3,1,2,1,1,1] 111011010=>010110111=>[2,2,1,2,1,1,1] 111011011=>110110111=>[1,1,2,1,2,1,1,1] 111011100=>001110111=>[3,1,1,2,1,1,1] 111011101=>101110111=>[1,2,1,1,2,1,1,1] 111011110=>011110111=>[2,1,1,1,2,1,1,1] 111011111=>111110111=>[1,1,1,1,1,2,1,1,1] 111100000=>000001111=>[6,1,1,1,1] 111100001=>100001111=>[1,5,1,1,1,1] 111100010=>010001111=>[2,4,1,1,1,1] 111100011=>110001111=>[1,1,4,1,1,1,1] 111100100=>001001111=>[3,3,1,1,1,1] 111100101=>101001111=>[1,2,3,1,1,1,1] 111100110=>011001111=>[2,1,3,1,1,1,1] 111100111=>111001111=>[1,1,1,3,1,1,1,1] 111101000=>000101111=>[4,2,1,1,1,1] 111101001=>100101111=>[1,3,2,1,1,1,1] 111101010=>010101111=>[2,2,2,1,1,1,1] 111101011=>110101111=>[1,1,2,2,1,1,1,1] 111101100=>001101111=>[3,1,2,1,1,1,1] 111101101=>101101111=>[1,2,1,2,1,1,1,1] 111101110=>011101111=>[2,1,1,2,1,1,1,1] 111101111=>111101111=>[1,1,1,1,2,1,1,1,1] 111110000=>000011111=>[5,1,1,1,1,1] 111110001=>100011111=>[1,4,1,1,1,1,1] 111110010=>010011111=>[2,3,1,1,1,1,1] 111110011=>110011111=>[1,1,3,1,1,1,1,1] 111110100=>001011111=>[3,2,1,1,1,1,1] 111110101=>101011111=>[1,2,2,1,1,1,1,1] 111110110=>011011111=>[2,1,2,1,1,1,1,1] 111110111=>111011111=>[1,1,1,2,1,1,1,1,1] 111111000=>000111111=>[4,1,1,1,1,1,1] 111111001=>100111111=>[1,3,1,1,1,1,1,1] 111111010=>010111111=>[2,2,1,1,1,1,1,1] 111111011=>110111111=>[1,1,2,1,1,1,1,1,1] 111111100=>001111111=>[3,1,1,1,1,1,1,1] 111111101=>101111111=>[1,2,1,1,1,1,1,1,1] 111111110=>011111111=>[2,1,1,1,1,1,1,1,1] 111111111=>111111111=>[1,1,1,1,1,1,1,1,1,1] 1010101010=>0101010101=>[2,2,2,2,2,1] 1010101100=>0011010101=>[3,1,2,2,2,1] 1010110010=>0100110101=>[2,3,1,2,2,1] 1010110100=>0010110101=>[3,2,1,2,2,1] 1010111000=>0001110101=>[4,1,1,2,2,1] 1011001010=>0101001101=>[2,2,3,1,2,1] 1011001100=>0011001101=>[3,1,3,1,2,1] 1011010010=>0100101101=>[2,3,2,1,2,1] 1011010100=>0010101101=>[3,2,2,1,2,1] 1011011000=>0001101101=>[4,1,2,1,2,1] 1011100010=>0100011101=>[2,4,1,1,2,1] 1011100100=>0010011101=>[3,3,1,1,2,1] 1011101000=>0001011101=>[4,2,1,1,2,1] 1011110000=>0000111101=>[5,1,1,1,2,1] 1100101010=>0101010011=>[2,2,2,3,1,1] 1100101100=>0011010011=>[3,1,2,3,1,1] 1100110010=>0100110011=>[2,3,1,3,1,1] 1100110100=>0010110011=>[3,2,1,3,1,1] 1100111000=>0001110011=>[4,1,1,3,1,1] 1101001010=>0101001011=>[2,2,3,2,1,1] 1101001100=>0011001011=>[3,1,3,2,1,1] 1101010010=>0100101011=>[2,3,2,2,1,1] 1101010100=>0010101011=>[3,2,2,2,1,1] 1101011000=>0001101011=>[4,1,2,2,1,1] 1101100010=>0100011011=>[2,4,1,2,1,1] 1101100100=>0010011011=>[3,3,1,2,1,1] 1101101000=>0001011011=>[4,2,1,2,1,1] 1101110000=>0000111011=>[5,1,1,2,1,1] 1110001010=>0101000111=>[2,2,4,1,1,1] 1110001100=>0011000111=>[3,1,4,1,1,1] 1110010010=>0100100111=>[2,3,3,1,1,1] 1110010100=>0010100111=>[3,2,3,1,1,1] 1110011000=>0001100111=>[4,1,3,1,1,1] 1110100010=>0100010111=>[2,4,2,1,1,1] 1110100100=>0010010111=>[3,3,2,1,1,1] 1110101000=>0001010111=>[4,2,2,1,1,1] 1110110000=>0000110111=>[5,1,2,1,1,1] 1111000010=>0100001111=>[2,5,1,1,1,1] 1111000100=>0010001111=>[3,4,1,1,1,1] 1111001000=>0001001111=>[4,3,1,1,1,1] 1111010000=>0000101111=>[5,2,1,1,1,1] 1111100000=>0000011111=>[6,1,1,1,1,1] 101010101010=>010101010101=>[2,2,2,2,2,2,1] 101010101100=>001101010101=>[3,1,2,2,2,2,1] 101010110010=>010011010101=>[2,3,1,2,2,2,1] 101010110100=>001011010101=>[3,2,1,2,2,2,1] 101010111000=>000111010101=>[4,1,1,2,2,2,1] 101011001010=>010100110101=>[2,2,3,1,2,2,1] 101011001100=>001100110101=>[3,1,3,1,2,2,1] 101011010010=>010010110101=>[2,3,2,1,2,2,1] 101011010100=>001010110101=>[3,2,2,1,2,2,1] 101011011000=>000110110101=>[4,1,2,1,2,2,1] 101011100010=>010001110101=>[2,4,1,1,2,2,1] 101011100100=>001001110101=>[3,3,1,1,2,2,1] 101011101000=>000101110101=>[4,2,1,1,2,2,1] 101011110000=>000011110101=>[5,1,1,1,2,2,1] 101100101010=>010101001101=>[2,2,2,3,1,2,1] 101100101100=>001101001101=>[3,1,2,3,1,2,1] 101100110010=>010011001101=>[2,3,1,3,1,2,1] 101100110100=>001011001101=>[3,2,1,3,1,2,1] 101100111000=>000111001101=>[4,1,1,3,1,2,1] 101101001010=>010100101101=>[2,2,3,2,1,2,1] 101101001100=>001100101101=>[3,1,3,2,1,2,1] 101101010010=>010010101101=>[2,3,2,2,1,2,1] 101101010100=>001010101101=>[3,2,2,2,1,2,1] 101101011000=>000110101101=>[4,1,2,2,1,2,1] 101101100010=>010001101101=>[2,4,1,2,1,2,1] 101101100100=>001001101101=>[3,3,1,2,1,2,1] 101101101000=>000101101101=>[4,2,1,2,1,2,1] 101101110000=>000011101101=>[5,1,1,2,1,2,1] 101110001010=>010100011101=>[2,2,4,1,1,2,1] 101110001100=>001100011101=>[3,1,4,1,1,2,1] 101110010010=>010010011101=>[2,3,3,1,1,2,1] 101110010100=>001010011101=>[3,2,3,1,1,2,1] 101110011000=>000110011101=>[4,1,3,1,1,2,1] 101110100010=>010001011101=>[2,4,2,1,1,2,1] 101110100100=>001001011101=>[3,3,2,1,1,2,1] 101110101000=>000101011101=>[4,2,2,1,1,2,1] 101110110000=>000011011101=>[5,1,2,1,1,2,1] 101111000010=>010000111101=>[2,5,1,1,1,2,1] 101111000100=>001000111101=>[3,4,1,1,1,2,1] 101111001000=>000100111101=>[4,3,1,1,1,2,1] 101111010000=>000010111101=>[5,2,1,1,1,2,1] 101111100000=>000001111101=>[6,1,1,1,1,2,1] 110010101010=>010101010011=>[2,2,2,2,3,1,1] 110010101100=>001101010011=>[3,1,2,2,3,1,1] 110010110010=>010011010011=>[2,3,1,2,3,1,1] 110010110100=>001011010011=>[3,2,1,2,3,1,1] 110010111000=>000111010011=>[4,1,1,2,3,1,1] 110011001010=>010100110011=>[2,2,3,1,3,1,1] 110011001100=>001100110011=>[3,1,3,1,3,1,1] 110011010010=>010010110011=>[2,3,2,1,3,1,1] 110011010100=>001010110011=>[3,2,2,1,3,1,1] 110011011000=>000110110011=>[4,1,2,1,3,1,1] 110011100010=>010001110011=>[2,4,1,1,3,1,1] 110011100100=>001001110011=>[3,3,1,1,3,1,1] 110011101000=>000101110011=>[4,2,1,1,3,1,1] 110011110000=>000011110011=>[5,1,1,1,3,1,1] 110100101010=>010101001011=>[2,2,2,3,2,1,1] 110100101100=>001101001011=>[3,1,2,3,2,1,1] 110100110010=>010011001011=>[2,3,1,3,2,1,1] 110100110100=>001011001011=>[3,2,1,3,2,1,1] 110100111000=>000111001011=>[4,1,1,3,2,1,1] 110101001010=>010100101011=>[2,2,3,2,2,1,1] 110101001100=>001100101011=>[3,1,3,2,2,1,1] 110101010010=>010010101011=>[2,3,2,2,2,1,1] 110101010100=>001010101011=>[3,2,2,2,2,1,1] 110101011000=>000110101011=>[4,1,2,2,2,1,1] 110101100010=>010001101011=>[2,4,1,2,2,1,1] 110101100100=>001001101011=>[3,3,1,2,2,1,1] 110101101000=>000101101011=>[4,2,1,2,2,1,1] 110101110000=>000011101011=>[5,1,1,2,2,1,1] 110110001010=>010100011011=>[2,2,4,1,2,1,1] 110110001100=>001100011011=>[3,1,4,1,2,1,1] 110110010010=>010010011011=>[2,3,3,1,2,1,1] 110110010100=>001010011011=>[3,2,3,1,2,1,1] 110110011000=>000110011011=>[4,1,3,1,2,1,1] 110110100010=>010001011011=>[2,4,2,1,2,1,1] 110110100100=>001001011011=>[3,3,2,1,2,1,1] 110110101000=>000101011011=>[4,2,2,1,2,1,1] 110110110000=>000011011011=>[5,1,2,1,2,1,1] 110111000010=>010000111011=>[2,5,1,1,2,1,1] 110111000100=>001000111011=>[3,4,1,1,2,1,1] 110111001000=>000100111011=>[4,3,1,1,2,1,1] 110111010000=>000010111011=>[5,2,1,1,2,1,1] 110111100000=>000001111011=>[6,1,1,1,2,1,1] 111000101010=>010101000111=>[2,2,2,4,1,1,1] 111000101100=>001101000111=>[3,1,2,4,1,1,1] 111000110010=>010011000111=>[2,3,1,4,1,1,1] 111000110100=>001011000111=>[3,2,1,4,1,1,1] 111000111000=>000111000111=>[4,1,1,4,1,1,1] 111001001010=>010100100111=>[2,2,3,3,1,1,1] 111001001100=>001100100111=>[3,1,3,3,1,1,1] 111001010010=>010010100111=>[2,3,2,3,1,1,1] 111001010100=>001010100111=>[3,2,2,3,1,1,1] 111001011000=>000110100111=>[4,1,2,3,1,1,1] 111001100010=>010001100111=>[2,4,1,3,1,1,1] 111001100100=>001001100111=>[3,3,1,3,1,1,1] 111001101000=>000101100111=>[4,2,1,3,1,1,1] 111001110000=>000011100111=>[5,1,1,3,1,1,1] 111010001010=>010100010111=>[2,2,4,2,1,1,1] 111010001100=>001100010111=>[3,1,4,2,1,1,1] 111010010010=>010010010111=>[2,3,3,2,1,1,1] 111010010100=>001010010111=>[3,2,3,2,1,1,1] 111010011000=>000110010111=>[4,1,3,2,1,1,1] 111010100010=>010001010111=>[2,4,2,2,1,1,1] 111010100100=>001001010111=>[3,3,2,2,1,1,1] 111010101000=>000101010111=>[4,2,2,2,1,1,1] 111010110000=>000011010111=>[5,1,2,2,1,1,1] 111011000010=>010000110111=>[2,5,1,2,1,1,1] 111011000100=>001000110111=>[3,4,1,2,1,1,1] 111011001000=>000100110111=>[4,3,1,2,1,1,1] 111011010000=>000010110111=>[5,2,1,2,1,1,1] 111011100000=>000001110111=>[6,1,1,2,1,1,1] 111100001010=>010100001111=>[2,2,5,1,1,1,1] 111100001100=>001100001111=>[3,1,5,1,1,1,1] 111100010010=>010010001111=>[2,3,4,1,1,1,1] 111100010100=>001010001111=>[3,2,4,1,1,1,1] 111100011000=>000110001111=>[4,1,4,1,1,1,1] 111100100010=>010001001111=>[2,4,3,1,1,1,1] 111100100100=>001001001111=>[3,3,3,1,1,1,1] 111100101000=>000101001111=>[4,2,3,1,1,1,1] 111100110000=>000011001111=>[5,1,3,1,1,1,1] 111101000010=>010000101111=>[2,5,2,1,1,1,1] 111101000100=>001000101111=>[3,4,2,1,1,1,1] 111101001000=>000100101111=>[4,3,2,1,1,1,1] 111101010000=>000010101111=>[5,2,2,1,1,1,1] 111101100000=>000001101111=>[6,1,2,1,1,1,1] 111110000010=>010000011111=>[2,6,1,1,1,1,1] 111110000100=>001000011111=>[3,5,1,1,1,1,1] 111110001000=>000100011111=>[4,4,1,1,1,1,1] 111110010000=>000010011111=>[5,3,1,1,1,1,1] 111110100000=>000001011111=>[6,2,1,1,1,1,1] 111111000000=>000000111111=>[7,1,1,1,1,1,1] 1111111111=>1111111111=>[1,1,1,1,1,1,1,1,1,1,1] 1111111110=>0111111111=>[2,1,1,1,1,1,1,1,1,1] 1111111011=>1101111111=>[1,1,2,1,1,1,1,1,1,1] 1111111001=>1001111111=>[1,3,1,1,1,1,1,1,1] 1111110111=>1110111111=>[1,1,1,2,1,1,1,1,1,1] 1111110110=>0110111111=>[2,1,2,1,1,1,1,1,1] 1111110011=>1100111111=>[1,1,3,1,1,1,1,1,1] 1111110000=>0000111111=>[5,1,1,1,1,1,1] 1111101101=>1011011111=>[1,2,1,2,1,1,1,1,1] 1111101011=>1101011111=>[1,1,2,2,1,1,1,1,1] 1111100111=>1110011111=>[1,1,1,3,1,1,1,1,1] 1111100001=>1000011111=>[1,5,1,1,1,1,1] 1111011110=>0111101111=>[2,1,1,1,2,1,1,1,1] 1111011000=>0001101111=>[4,1,2,1,1,1,1] 1111010010=>0100101111=>[2,3,2,1,1,1,1] 1111001100=>0011001111=>[3,1,3,1,1,1,1] 1111001010=>0101001111=>[2,2,3,1,1,1,1] 1111000011=>1100001111=>[1,1,5,1,1,1,1] 1110111101=>1011110111=>[1,2,1,1,1,2,1,1,1] 1110111000=>0001110111=>[4,1,1,2,1,1,1] 1110110111=>1110110111=>[1,1,1,2,1,2,1,1,1] 1110110010=>0100110111=>[2,3,1,2,1,1,1] 1110110001=>1000110111=>[1,4,1,2,1,1,1] 1110101100=>0011010111=>[3,1,2,2,1,1,1] 1110100101=>1010010111=>[1,2,3,2,1,1,1] 1110011111=>1111100111=>[1,1,1,1,1,3,1,1,1] 1110011001=>1001100111=>[1,3,1,3,1,1,1] 1110001101=>1011000111=>[1,2,1,4,1,1,1] 1110000111=>1110000111=>[1,1,1,5,1,1,1] 1110000011=>1100000111=>[1,1,6,1,1,1] 1110000001=>1000000111=>[1,7,1,1,1] 1101111110=>0111111011=>[2,1,1,1,1,1,2,1,1] 1101100110=>0110011011=>[2,1,3,1,2,1,1] 1101100000=>0000011011=>[6,1,2,1,1] 1101010110=>0110101011=>[2,1,2,2,2,1,1] 1100111010=>0101110011=>[2,2,1,1,3,1,1] 1100110110=>0110110011=>[2,1,2,1,3,1,1] 1100110011=>1100110011=>[1,1,3,1,3,1,1] 1100101110=>0111010011=>[2,1,1,2,3,1,1] 1100101011=>1101010011=>[1,1,2,2,3,1,1] 1100100111=>1110010011=>[1,1,1,3,3,1,1] 1100100110=>0110010011=>[2,1,3,3,1,1] 1100100010=>0100010011=>[2,4,3,1,1] 1100011110=>0111100011=>[2,1,1,1,4,1,1] 1100011011=>1101100011=>[1,1,2,1,4,1,1] 1100011010=>0101100011=>[2,2,1,4,1,1] 1100011000=>0001100011=>[4,1,4,1,1] 1100010111=>1110100011=>[1,1,1,2,4,1,1] 1100010110=>0110100011=>[2,1,2,4,1,1] 1100010010=>0100100011=>[2,3,4,1,1] 1100001111=>1111000011=>[1,1,1,1,5,1,1] 1100001110=>0111000011=>[2,1,1,5,1,1] 1100001011=>1101000011=>[1,1,2,5,1,1] 1100001010=>0101000011=>[2,2,5,1,1] 1100000111=>1110000011=>[1,1,1,6,1,1] 1100000110=>0110000011=>[2,1,6,1,1] 1100000001=>1000000011=>[1,8,1,1] 1100000000=>0000000011=>[9,1,1] 1011111110=>0111111101=>[2,1,1,1,1,1,1,2,1] 1011111101=>1011111101=>[1,2,1,1,1,1,1,2,1] 1011110111=>1110111101=>[1,1,1,2,1,1,1,2,1] 1011110001=>1000111101=>[1,4,1,1,1,2,1] 1011100101=>1010011101=>[1,2,3,1,1,2,1] 1011011111=>1111101101=>[1,1,1,1,1,2,1,2,1] 1011011001=>1001101101=>[1,3,1,2,1,2,1] 1011001101=>1011001101=>[1,2,1,3,1,2,1] 1011001011=>1101001101=>[1,1,2,3,1,2,1] 1011000111=>1110001101=>[1,1,1,4,1,2,1] 1011000001=>1000001101=>[1,6,1,2,1] 1011000000=>0000001101=>[7,1,2,1] 1010111110=>0111110101=>[2,1,1,1,1,2,2,1] 1010110101=>1010110101=>[1,2,2,1,2,2,1] 1010110011=>1100110101=>[1,1,3,1,2,2,1] 1010110001=>1000110101=>[1,4,1,2,2,1] 1010110000=>0000110101=>[5,1,2,2,1] 1010101101=>1011010101=>[1,2,1,2,2,2,1] 1010101011=>1101010101=>[1,1,2,2,2,2,1] 1010101000=>0001010101=>[4,2,2,2,1] 1010100111=>1110010101=>[1,1,1,3,2,2,1] 1010100110=>0110010101=>[2,1,3,2,2,1] 1010100010=>0100010101=>[2,4,2,2,1] 1010011110=>0111100101=>[2,1,1,1,3,2,1] 1010011101=>1011100101=>[1,2,1,1,3,2,1] 1010011011=>1101100101=>[1,1,2,1,3,2,1] 1010010111=>1110100101=>[1,1,1,2,3,2,1] 1010010001=>1000100101=>[1,4,3,2,1] 1010001111=>1111000101=>[1,1,1,1,4,2,1] 1010001010=>0101000101=>[2,2,4,2,1] 1010000101=>1010000101=>[1,2,5,2,1] 1010000001=>1000000101=>[1,7,2,1] 1001111111=>1111111001=>[1,1,1,1,1,1,1,3,1] 1001111110=>0111111001=>[2,1,1,1,1,1,3,1] 1001111001=>1001111001=>[1,3,1,1,1,3,1] 1001110011=>1100111001=>[1,1,3,1,1,3,1] 1001110010=>0100111001=>[2,3,1,1,3,1] 1001101110=>0111011001=>[2,1,1,2,1,3,1] 1001101101=>1011011001=>[1,2,1,2,1,3,1] 1001101011=>1101011001=>[1,1,2,2,1,3,1] 1001100111=>1110011001=>[1,1,1,3,1,3,1] 1001100110=>0110011001=>[2,1,3,1,3,1] 1001100010=>0100011001=>[2,4,1,3,1] 1001100001=>1000011001=>[1,5,1,3,1] 1001100000=>0000011001=>[6,1,3,1] 1001011110=>0111101001=>[2,1,1,1,2,3,1] 1001011011=>1101101001=>[1,1,2,1,2,3,1] 1001011000=>0001101001=>[4,1,2,3,1] 1001010111=>1110101001=>[1,1,1,2,2,3,1] 1001010010=>0100101001=>[2,3,2,3,1] 1001001111=>1111001001=>[1,1,1,1,3,3,1] 1000111110=>0111110001=>[2,1,1,1,1,4,1] 1000111101=>1011110001=>[1,2,1,1,1,4,1] 1000111100=>0011110001=>[3,1,1,1,4,1] 1000111011=>1101110001=>[1,1,2,1,1,4,1] 1000111010=>0101110001=>[2,2,1,1,4,1] 1000110111=>1110110001=>[1,1,1,2,1,4,1] 1000110110=>0110110001=>[2,1,2,1,4,1] 1000110010=>0100110001=>[2,3,1,4,1] 1000110001=>1000110001=>[1,4,1,4,1] 1000101111=>1111010001=>[1,1,1,1,2,4,1] 1000101110=>0111010001=>[2,1,1,2,4,1] 1000101011=>1101010001=>[1,1,2,2,4,1] 1000101010=>0101010001=>[2,2,2,4,1] 1000100110=>0110010001=>[2,1,3,4,1] 1000100101=>1010010001=>[1,2,3,4,1] 1000100000=>0000010001=>[6,4,1] 1000011111=>1111100001=>[1,1,1,1,1,5,1] 1000011110=>0111100001=>[2,1,1,1,5,1] 1000011011=>1101100001=>[1,1,2,1,5,1] 1000011010=>0101100001=>[2,2,1,5,1] 1000011001=>1001100001=>[1,3,1,5,1] 1000010111=>1110100001=>[1,1,1,2,5,1] 1000010110=>0110100001=>[2,1,2,5,1] 1000010010=>0100100001=>[2,3,5,1] 1000001111=>1111000001=>[1,1,1,1,6,1] 1000001110=>0111000001=>[2,1,1,6,1] 1000001101=>1011000001=>[1,2,1,6,1] 1000001010=>0101000001=>[2,2,6,1] 1000001000=>0001000001=>[4,6,1] 1000000111=>1110000001=>[1,1,1,7,1] 1000000110=>0110000001=>[2,1,7,1] 1000000100=>0010000001=>[3,7,1] 1000000010=>0100000001=>[2,8,1] 1000000001=>1000000001=>[1,9,1] 1000000000=>0000000001=>[10,1] 10000000000=>00000000001=>[11,1] 10000000010=>01000000001=>[2,9,1] 10000000110=>01100000001=>[2,1,8,1] 10000001110=>01110000001=>[2,1,1,7,1] 10000011110=>01111000001=>[2,1,1,1,6,1] 10000111110=>01111100001=>[2,1,1,1,1,5,1] 10001111110=>01111110001=>[2,1,1,1,1,1,4,1] 10011111110=>01111111001=>[2,1,1,1,1,1,1,3,1] 10111111110=>01111111101=>[2,1,1,1,1,1,1,1,2,1] 11111111110=>01111111111=>[2,1,1,1,1,1,1,1,1,1,1] 100000000010=>010000000001=>[2,10,1] 100000111110=>011111000001=>[2,1,1,1,1,6,1] 10101111110=>01111110101=>[2,1,1,1,1,1,2,2,1] 100000010110=>011010000001=>[2,1,2,7,1] 100001011110=>011110100001=>[2,1,1,1,2,5,1] 100010011110=>011110010001=>[2,1,1,1,3,4,1] 100001101110=>011101100001=>[2,1,1,2,1,5,1] 100010101110=>011101010001=>[2,1,1,2,2,4,1] 100000100000=>000001000001=>[6,6,1] 100100101110=>011101001001=>[2,1,1,2,3,3,1] 100010110110=>011011010001=>[2,1,2,1,2,4,1] 100001010010=>010010100001=>[2,3,2,5,1] 110000011110=>011110000011=>[2,1,1,1,6,1,1] 100001111100=>001111100001=>[3,1,1,1,1,5,1] 10101010110=>01101010101=>[2,1,2,2,2,2,1] 110011011110=>011110110011=>[2,1,1,1,2,1,3,1,1] 110000101110=>011101000011=>[2,1,1,2,5,1,1] 101000110110=>011011000101=>[2,1,2,1,4,2,1] 100110001110=>011100011001=>[2,1,1,4,1,3,1] 100101010110=>011010101001=>[2,1,2,2,2,3,1] 100010111100=>001111010001=>[3,1,1,1,2,4,1] 110001101110=>011101100011=>[2,1,1,2,1,4,1,1] 100011111100=>001111110001=>[3,1,1,1,1,1,4,1] 0111111111=>1111111110=>[1,1,1,1,1,1,1,1,1,2] 0111111101=>1011111110=>[1,2,1,1,1,1,1,1,2] 0111111001=>1001111110=>[1,3,1,1,1,1,1,2] 0111110001=>1000111110=>[1,4,1,1,1,1,2] 0111100001=>1000011110=>[1,5,1,1,1,2] 0111000001=>1000001110=>[1,6,1,1,2] 0110000001=>1000000110=>[1,7,1,2] 0100000001=>1000000010=>[1,8,2] 0000000001=>1000000000=>[1,10] 01111111111=>11111111110=>[1,1,1,1,1,1,1,1,1,1,2] 01111111101=>10111111110=>[1,2,1,1,1,1,1,1,1,2] 0111111011=>1101111110=>[1,1,2,1,1,1,1,1,2] 0111110101=>1010111110=>[1,2,2,1,1,1,1,2] 0111101001=>1001011110=>[1,3,2,1,1,1,2] 0111010001=>1000101110=>[1,4,2,1,1,2] 0110100001=>1000010110=>[1,5,2,1,2] 0101000001=>1000001010=>[1,6,2,2] 01100000001=>10000000110=>[1,8,1,2] 0010000001=>1000000100=>[1,7,3] 01000000001=>10000000010=>[1,9,2] 00000000001=>10000000000=>[1,11] 0101010101=>1010101010=>[1,2,2,2,2,2] 0101010011=>1100101010=>[1,1,3,2,2,2] 0101001101=>1011001010=>[1,2,1,3,2,2] 0101001011=>1101001010=>[1,1,2,3,2,2] 0101000111=>1110001010=>[1,1,1,4,2,2] 0100110101=>1010110010=>[1,2,2,1,3,2] 0100110011=>1100110010=>[1,1,3,1,3,2] 0100101101=>1011010010=>[1,2,1,2,3,2] 0100101011=>1101010010=>[1,1,2,2,3,2] 0100100111=>1110010010=>[1,1,1,3,3,2] 0100011011=>1101100010=>[1,1,2,1,4,2] 0100010111=>1110100010=>[1,1,1,2,4,2] 0100001111=>1111000010=>[1,1,1,1,5,2] 0011010101=>1010101100=>[1,2,2,2,1,3] 0011010011=>1100101100=>[1,1,3,2,1,3] 0011000111=>1110001100=>[1,1,1,4,1,3] 0010110101=>1010110100=>[1,2,2,1,2,3] 0010110011=>1100110100=>[1,1,3,1,2,3] 0010101101=>1011010100=>[1,2,1,2,2,3] 0010101011=>1101010100=>[1,1,2,2,2,3] 0010011101=>1011100100=>[1,2,1,1,3,3] 0010011011=>1101100100=>[1,1,2,1,3,3] 0010010111=>1110100100=>[1,1,1,2,3,3] 0010001111=>1111000100=>[1,1,1,1,4,3] 0001110101=>1010111000=>[1,2,2,1,1,4] 0001110011=>1100111000=>[1,1,3,1,1,4] 0001101011=>1101011000=>[1,1,2,2,1,4] 0001100111=>1110011000=>[1,1,1,3,1,4] 0001011101=>1011101000=>[1,2,1,1,2,4] 0001011011=>1101101000=>[1,1,2,1,2,4] 0001010111=>1110101000=>[1,1,1,2,2,4] 0001001111=>1111001000=>[1,1,1,1,3,4] 0000110111=>1110110000=>[1,1,1,2,1,5] 0000101111=>1111010000=>[1,1,1,1,2,5] 0000011111=>1111100000=>[1,1,1,1,1,6] 010101010101=>101010101010=>[1,2,2,2,2,2,2] 010101001101=>101100101010=>[1,2,1,3,2,2,2] 010101001011=>110100101010=>[1,1,2,3,2,2,2] 010100110101=>101011001010=>[1,2,2,1,3,2,2] 010100101101=>101101001010=>[1,2,1,2,3,2,2] 010100101011=>110101001010=>[1,1,2,2,3,2,2] 010100100111=>111001001010=>[1,1,1,3,3,2,2] 010100011011=>110110001010=>[1,1,2,1,4,2,2] 010100010111=>111010001010=>[1,1,1,2,4,2,2] 010100001111=>111100001010=>[1,1,1,1,5,2,2] 010011010101=>101010110010=>[1,2,2,2,1,3,2] 010011010011=>110010110010=>[1,1,3,2,1,3,2] 010011001101=>101100110010=>[1,2,1,3,1,3,2] 010011001011=>110100110010=>[1,1,2,3,1,3,2] 010011000111=>111000110010=>[1,1,1,4,1,3,2] 010010110101=>101011010010=>[1,2,2,1,2,3,2] 010010101101=>101101010010=>[1,2,1,2,2,3,2] 010010101011=>110101010010=>[1,1,2,2,2,3,2] 010010011101=>101110010010=>[1,2,1,1,3,3,2] 010010011011=>110110010010=>[1,1,2,1,3,3,2] 010010010111=>111010010010=>[1,1,1,2,3,3,2] 010010001111=>111100010010=>[1,1,1,1,4,3,2] 010001101101=>101101100010=>[1,2,1,2,1,4,2] 010001101011=>110101100010=>[1,1,2,2,1,4,2] 010001011101=>101110100010=>[1,2,1,1,2,4,2] 010001011011=>110110100010=>[1,1,2,1,2,4,2] 010001010111=>111010100010=>[1,1,1,2,2,4,2] 010000111011=>110111000010=>[1,1,2,1,1,5,2] 010000110111=>111011000010=>[1,1,1,2,1,5,2] 010000101111=>111101000010=>[1,1,1,1,2,5,2] 010000011111=>111110000010=>[1,1,1,1,1,6,2] 001100101011=>110101001100=>[1,1,2,2,3,1,3] 001100100111=>111001001100=>[1,1,1,3,3,1,3] 001100011011=>110110001100=>[1,1,2,1,4,1,3] 001100010111=>111010001100=>[1,1,1,2,4,1,3] 001100001111=>111100001100=>[1,1,1,1,5,1,3] 001011010101=>101010110100=>[1,2,2,2,1,2,3] 001011001101=>101100110100=>[1,2,1,3,1,2,3] 001011001011=>110100110100=>[1,1,2,3,1,2,3] 001010110101=>101011010100=>[1,2,2,1,2,2,3] 001010101101=>101101010100=>[1,2,1,2,2,2,3] 001010101011=>110101010100=>[1,1,2,2,2,2,3] 001010011101=>101110010100=>[1,2,1,1,3,2,3] 001010011011=>110110010100=>[1,1,2,1,3,2,3] 001010010111=>111010010100=>[1,1,1,2,3,2,3] 001010001111=>111100010100=>[1,1,1,1,4,2,3] 001001110101=>101011100100=>[1,2,2,1,1,3,3] 001001101101=>101101100100=>[1,2,1,2,1,3,3] 001001101011=>110101100100=>[1,1,2,2,1,3,3] 001001011101=>101110100100=>[1,2,1,1,2,3,3] 001001011011=>110110100100=>[1,1,2,1,2,3,3] 001001010111=>111010100100=>[1,1,1,2,2,3,3] 001000111101=>101111000100=>[1,2,1,1,1,4,3] 001000111011=>110111000100=>[1,1,2,1,1,4,3] 001000110111=>111011000100=>[1,1,1,2,1,4,3] 001000101111=>111101000100=>[1,1,1,1,2,4,3] 001000011111=>111110000100=>[1,1,1,1,1,5,3] 000111010011=>110010111000=>[1,1,3,2,1,1,4] 000111000111=>111000111000=>[1,1,1,4,1,1,4] 000110110101=>101011011000=>[1,2,2,1,2,1,4] 000110101011=>110101011000=>[1,1,2,2,2,1,4] 000110011011=>110110011000=>[1,1,2,1,3,1,4] 000110010111=>111010011000=>[1,1,1,2,3,1,4] 000110001111=>111100011000=>[1,1,1,1,4,1,4] 000101110101=>101011101000=>[1,2,2,1,1,2,4] 000101101101=>101101101000=>[1,2,1,2,1,2,4] 000101101011=>110101101000=>[1,1,2,2,1,2,4] 000101011101=>101110101000=>[1,2,1,1,2,2,4] 000101011011=>110110101000=>[1,1,2,1,2,2,4] 000101010111=>111010101000=>[1,1,1,2,2,2,4] 000100111101=>101111001000=>[1,2,1,1,1,3,4] 000100111011=>110111001000=>[1,1,2,1,1,3,4] 000100110111=>111011001000=>[1,1,1,2,1,3,4] 000100101111=>111101001000=>[1,1,1,1,2,3,4] 000100011111=>111110001000=>[1,1,1,1,1,4,4] 000011011011=>110110110000=>[1,1,2,1,2,1,5] 000010111101=>101111010000=>[1,2,1,1,1,2,5] 000010111011=>110111010000=>[1,1,2,1,1,2,5] 000010110111=>111011010000=>[1,1,1,2,1,2,5] 000010101111=>111101010000=>[1,1,1,1,2,2,5] 000010011111=>111110010000=>[1,1,1,1,1,3,5] 000001111011=>110111100000=>[1,1,2,1,1,1,6] 000001110111=>111011100000=>[1,1,1,2,1,1,6] 000001101111=>111101100000=>[1,1,1,1,2,1,6] 000001011111=>111110100000=>[1,1,1,1,1,2,6] 000000111111=>111111000000=>[1,1,1,1,1,1,7] 111111111111=>111111111111=>[1,1,1,1,1,1,1,1,1,1,1,1,1] 111111111001=>100111111111=>[1,3,1,1,1,1,1,1,1,1,1] 111111100111=>111001111111=>[1,1,1,3,1,1,1,1,1,1,1] 111111100001=>100001111111=>[1,5,1,1,1,1,1,1,1] 111111101101=>101101111111=>[1,2,1,2,1,1,1,1,1,1,1] 111110011111=>111110011111=>[1,1,1,1,1,3,1,1,1,1,1] 111110011001=>100110011111=>[1,3,1,3,1,1,1,1,1] 111110000111=>111000011111=>[1,1,1,5,1,1,1,1,1] 111110000001=>100000011111=>[1,7,1,1,1,1,1] 111110001101=>101100011111=>[1,2,1,4,1,1,1,1,1] 111110110111=>111011011111=>[1,1,1,2,1,2,1,1,1,1,1] 111110110001=>100011011111=>[1,4,1,2,1,1,1,1,1] 111110111101=>101111011111=>[1,2,1,1,1,2,1,1,1,1,1] 111110100101=>101001011111=>[1,2,3,2,1,1,1,1,1] 111001111111=>111111100111=>[1,1,1,1,1,1,1,3,1,1,1] 111001111001=>100111100111=>[1,3,1,1,1,3,1,1,1] 111001100111=>111001100111=>[1,1,1,3,1,3,1,1,1] 111001100001=>100001100111=>[1,5,1,3,1,1,1] 111001101101=>101101100111=>[1,2,1,2,1,3,1,1,1] 111000011111=>111110000111=>[1,1,1,1,1,5,1,1,1] 111000011001=>100110000111=>[1,3,1,5,1,1,1] 111000000111=>111000000111=>[1,1,1,7,1,1,1] 111000000001=>100000000111=>[1,9,1,1,1] 111000001101=>101100000111=>[1,2,1,6,1,1,1] 111000110111=>111011000111=>[1,1,1,2,1,4,1,1,1] 111000110001=>100011000111=>[1,4,1,4,1,1,1] 111000111101=>101111000111=>[1,2,1,1,1,4,1,1,1] 111000100101=>101001000111=>[1,2,3,4,1,1,1] 111011011111=>111110110111=>[1,1,1,1,1,2,1,2,1,1,1] 111011011001=>100110110111=>[1,3,1,2,1,2,1,1,1] 111011000111=>111000110111=>[1,1,1,4,1,2,1,1,1] 111011000001=>100000110111=>[1,6,1,2,1,1,1] 111011001101=>101100110111=>[1,2,1,3,1,2,1,1,1] 111011110111=>111011110111=>[1,1,1,2,1,1,1,2,1,1,1] 111011110001=>100011110111=>[1,4,1,1,1,2,1,1,1] 111011111101=>101111110111=>[1,2,1,1,1,1,1,2,1,1,1] 111011100101=>101001110111=>[1,2,3,1,1,2,1,1,1] 111010010111=>111010010111=>[1,1,1,2,3,2,1,1,1] 111010010001=>100010010111=>[1,4,3,2,1,1,1] 111010011101=>101110010111=>[1,2,1,1,3,2,1,1,1] 111010000101=>101000010111=>[1,2,5,2,1,1,1] 111010110101=>101011010111=>[1,2,2,1,2,2,1,1,1] 100111111111=>111111111001=>[1,1,1,1,1,1,1,1,1,3,1] 100111111001=>100111111001=>[1,3,1,1,1,1,1,3,1] 100111100111=>111001111001=>[1,1,1,3,1,1,1,3,1] 100111100001=>100001111001=>[1,5,1,1,1,3,1] 100111101101=>101101111001=>[1,2,1,2,1,1,1,3,1] 100110011111=>111110011001=>[1,1,1,1,1,3,1,3,1] 100110011001=>100110011001=>[1,3,1,3,1,3,1] 100110000111=>111000011001=>[1,1,1,5,1,3,1] 100110000001=>100000011001=>[1,7,1,3,1] 100110001101=>101100011001=>[1,2,1,4,1,3,1] 100110110111=>111011011001=>[1,1,1,2,1,2,1,3,1] 100110110001=>100011011001=>[1,4,1,2,1,3,1] 100110111101=>101111011001=>[1,2,1,1,1,2,1,3,1] 100110100101=>101001011001=>[1,2,3,2,1,3,1] 100001111111=>111111100001=>[1,1,1,1,1,1,1,5,1] 100001111001=>100111100001=>[1,3,1,1,1,5,1] 100001100111=>111001100001=>[1,1,1,3,1,5,1] 100001100001=>100001100001=>[1,5,1,5,1] 100001101101=>101101100001=>[1,2,1,2,1,5,1] 100000011111=>111110000001=>[1,1,1,1,1,7,1] 100000011001=>100110000001=>[1,3,1,7,1] 100000000111=>111000000001=>[1,1,1,9,1] 100000000001=>100000000001=>[1,11,1] 100000001101=>101100000001=>[1,2,1,8,1] 100000110111=>111011000001=>[1,1,1,2,1,6,1] 100000110001=>100011000001=>[1,4,1,6,1] 100000111101=>101111000001=>[1,2,1,1,1,6,1] 100000100101=>101001000001=>[1,2,3,6,1] 100011011111=>111110110001=>[1,1,1,1,1,2,1,4,1] 100011011001=>100110110001=>[1,3,1,2,1,4,1] 100011000111=>111000110001=>[1,1,1,4,1,4,1] 100011000001=>100000110001=>[1,6,1,4,1] 100011001101=>101100110001=>[1,2,1,3,1,4,1] 100011110111=>111011110001=>[1,1,1,2,1,1,1,4,1] 100011110001=>100011110001=>[1,4,1,1,1,4,1] 100011111101=>101111110001=>[1,2,1,1,1,1,1,4,1] 100011100101=>101001110001=>[1,2,3,1,1,4,1] 100010010111=>111010010001=>[1,1,1,2,3,4,1] 100010010001=>100010010001=>[1,4,3,4,1] 100010011101=>101110010001=>[1,2,1,1,3,4,1] 100010000101=>101000010001=>[1,2,5,4,1] 100010110101=>101011010001=>[1,2,2,1,2,4,1] 101101111111=>111111101101=>[1,1,1,1,1,1,1,2,1,2,1] 101101111001=>100111101101=>[1,3,1,1,1,2,1,2,1] 101101100111=>111001101101=>[1,1,1,3,1,2,1,2,1] 101101100001=>100001101101=>[1,5,1,2,1,2,1] 101101101101=>101101101101=>[1,2,1,2,1,2,1,2,1] 101100011111=>111110001101=>[1,1,1,1,1,4,1,2,1] 101100011001=>100110001101=>[1,3,1,4,1,2,1] 101100000111=>111000001101=>[1,1,1,6,1,2,1] 101100000001=>100000001101=>[1,8,1,2,1] 101100001101=>101100001101=>[1,2,1,5,1,2,1] 101100110111=>111011001101=>[1,1,1,2,1,3,1,2,1] 101100110001=>100011001101=>[1,4,1,3,1,2,1] 101100111101=>101111001101=>[1,2,1,1,1,3,1,2,1] 101100100101=>101001001101=>[1,2,3,3,1,2,1] 101111011111=>111110111101=>[1,1,1,1,1,2,1,1,1,2,1] 101111011001=>100110111101=>[1,3,1,2,1,1,1,2,1] 101111000111=>111000111101=>[1,1,1,4,1,1,1,2,1] 101111000001=>100000111101=>[1,6,1,1,1,2,1] 101111001101=>101100111101=>[1,2,1,3,1,1,1,2,1] 101111110111=>111011111101=>[1,1,1,2,1,1,1,1,1,2,1] 101111110001=>100011111101=>[1,4,1,1,1,1,1,2,1] 101111111101=>101111111101=>[1,2,1,1,1,1,1,1,1,2,1] 101111100101=>101001111101=>[1,2,3,1,1,1,1,2,1] 101110010111=>111010011101=>[1,1,1,2,3,1,1,2,1] 101110010001=>100010011101=>[1,4,3,1,1,2,1] 101110011101=>101110011101=>[1,2,1,1,3,1,1,2,1] 101110000101=>101000011101=>[1,2,5,1,1,2,1] 101110110101=>101011011101=>[1,2,2,1,2,1,1,2,1] 101001011111=>111110100101=>[1,1,1,1,1,2,3,2,1] 101001011001=>100110100101=>[1,3,1,2,3,2,1] 101001000111=>111000100101=>[1,1,1,4,3,2,1] 101001000001=>100000100101=>[1,6,3,2,1] 101001001101=>101100100101=>[1,2,1,3,3,2,1] 101001110111=>111011100101=>[1,1,1,2,1,1,3,2,1] 101001110001=>100011100101=>[1,4,1,1,3,2,1] 101001111101=>101111100101=>[1,2,1,1,1,1,3,2,1] 101001100101=>101001100101=>[1,2,3,1,3,2,1] 101000010111=>111010000101=>[1,1,1,2,5,2,1] 101000010001=>100010000101=>[1,4,5,2,1] 101000011101=>101110000101=>[1,2,1,1,5,2,1] 101000000101=>101000000101=>[1,2,7,2,1] 101000110101=>101011000101=>[1,2,2,1,4,2,1] 101011010111=>111010110101=>[1,1,1,2,2,1,2,2,1] 101011010001=>100010110101=>[1,4,2,1,2,2,1] 101011011101=>101110110101=>[1,2,1,1,2,1,2,2,1] 101011000101=>101000110101=>[1,2,4,1,2,2,1] 101011110101=>101011110101=>[1,2,2,1,1,1,2,2,1] 101010010101=>101010010101=>[1,2,2,3,2,2,1] 0000000000=>0000000000=>[11] 0001100000=>0000011000=>[6,1,4] 0111100000=>0000011110=>[6,1,1,1,2] 0111111000=>0001111110=>[4,1,1,1,1,1,2] 0111111110=>0111111110=>[2,1,1,1,1,1,1,1,2] 0111110010=>0100111110=>[2,3,1,1,1,1,2] 000000000000=>000000000000=>[13] 000001111110=>011111100000=>[2,1,1,1,1,1,6] 000110011110=>011110011000=>[2,1,1,1,3,1,4] 000111111000=>000111111000=>[4,1,1,1,1,1,4] 000111001110=>011100111000=>[2,1,1,3,1,1,4] 000100111110=>011111001000=>[2,1,1,1,1,3,4] 000101101110=>011101101000=>[2,1,1,2,1,2,4] 0010101010=>0101010100=>[2,2,2,2,3] 0010101110=>0111010100=>[2,1,1,2,2,3] 0010100000=>0000010100=>[6,2,3] 0010111100=>0011110100=>[3,1,1,1,2,3] 0000111110=>0111110000=>[2,1,1,1,1,5] 0000001010=>0101000000=>[2,2,7] 0001011110=>0111101000=>[2,1,1,1,2,4] 01111111110=>01111111110=>[2,1,1,1,1,1,1,1,1,2] 0011010010=>0100101100=>[2,3,2,1,3] 0011011000=>0001101100=>[4,1,2,1,3] 0110001100=>0011000110=>[3,1,4,1,2] 0111000100=>0010001110=>[3,4,1,1,2] 001010101010=>010101010100=>[2,2,2,2,2,3] 001010101100=>001101010100=>[3,1,2,2,2,3] 001010110010=>010011010100=>[2,3,1,2,2,3] 001010110100=>001011010100=>[3,2,1,2,2,3] 001011001010=>010100110100=>[2,2,3,1,2,3] 001011001100=>001100110100=>[3,1,3,1,2,3] 001011010010=>010010110100=>[2,3,2,1,2,3] 001011010100=>001010110100=>[3,2,2,1,2,3] 001100101010=>010101001100=>[2,2,2,3,1,3] 001100101100=>001101001100=>[3,1,2,3,1,3] 001100110010=>010011001100=>[2,3,1,3,1,3] 001100110100=>001011001100=>[3,2,1,3,1,3] 001101001010=>010100101100=>[2,2,3,2,1,3] 001101001100=>001100101100=>[3,1,3,2,1,3] 001101010010=>010010101100=>[2,3,2,2,1,3] 001101010100=>001010101100=>[3,2,2,2,1,3] 010010101010=>010101010010=>[2,2,2,2,3,2] 010010101100=>001101010010=>[3,1,2,2,3,2] 010010110010=>010011010010=>[2,3,1,2,3,2] 010010110100=>001011010010=>[3,2,1,2,3,2] 010011001010=>010100110010=>[2,2,3,1,3,2] 010011001100=>001100110010=>[3,1,3,1,3,2] 010011010010=>010010110010=>[2,3,2,1,3,2] 010011010100=>001010110010=>[3,2,2,1,3,2] 010100101010=>010101001010=>[2,2,2,3,2,2] 010100101100=>001101001010=>[3,1,2,3,2,2] 010100110010=>010011001010=>[2,3,1,3,2,2] 010100110100=>001011001010=>[3,2,1,3,2,2] 010101001010=>010100101010=>[2,2,3,2,2,2] 010101001100=>001100101010=>[3,1,3,2,2,2] 010101010010=>010010101010=>[2,3,2,2,2,2] 010101010100=>001010101010=>[3,2,2,2,2,2] 10101010101=>10101010101=>[1,2,2,2,2,2,1] 0100000000=>0000000010=>[9,2] 01000000000=>00000000010=>[10,2] 0100101111=>1111010010=>[1,1,1,1,2,3,2] 0111101000=>0001011110=>[4,2,1,1,1,2] 0111110000=>0000111110=>[5,1,1,1,1,2] 0001101110=>0111011000=>[2,1,1,2,1,4] 0011111000=>0001111100=>[4,1,1,1,1,3] 0001111100=>0011111000=>[3,1,1,1,1,4] 000011011110=>011110110000=>[2,1,1,1,2,1,5] 001101101010=>010101101100=>[2,2,2,1,2,1,3] 000011101110=>011101110000=>[2,1,1,2,1,1,5] 001111110000=>000011111100=>[5,1,1,1,1,1,3] 100011111000=>000111110001=>[4,1,1,1,1,4,1] 001011111000=>000111110100=>[4,1,1,1,1,2,3] 001001111100=>001111100100=>[3,1,1,1,1,3,3] 000101111100=>001111101000=>[3,1,1,1,1,2,4] 000011111100=>001111110000=>[3,1,1,1,1,1,5] 0000101101=>1011010000=>[1,2,1,2,5] 110010011001=>100110010011=>[1,3,1,3,3,1,1] 110110000101=>101000011011=>[1,2,5,1,2,1,1] 110110001001=>100100011011=>[1,3,4,1,2,1,1] 111000010101=>101010000111=>[1,2,2,5,1,1,1] 111000101001=>100101000111=>[1,3,2,4,1,1,1] 111010001001=>100100010111=>[1,3,4,2,1,1,1] 0010110001=>1000110100=>[1,4,1,2,3] 0011000110=>0110001100=>[2,1,4,1,3] 0010010110=>0110100100=>[2,1,2,3,3] 0000110110=>0110110000=>[2,1,2,1,5] 001001110100=>001011100100=>[3,2,1,1,3,3] 000101110100=>001011101000=>[3,2,1,1,2,4] 010001101100=>001101100010=>[3,1,2,1,4,2] 001001101100=>001101100100=>[3,1,2,1,3,3] 000101101100=>001101101000=>[3,1,2,1,2,4] 010010011100=>001110010010=>[3,1,1,3,3,2] 001010011100=>001110010100=>[3,1,1,3,2,3] 010001011100=>001110100010=>[3,1,1,2,4,2] 001001011100=>001110100100=>[3,1,1,2,3,3] 000101011100=>001110101000=>[3,1,1,2,2,4] 001000111100=>001111000100=>[3,1,1,1,4,3] 000100111100=>001111001000=>[3,1,1,1,3,4] 000010111100=>001111010000=>[3,1,1,1,2,5] 001001011010=>010110100100=>[2,2,1,2,3,3] 001011000110=>011000110100=>[2,1,4,1,2,3] 010010100110=>011001010010=>[2,1,3,2,3,2] 001001100110=>011001100100=>[2,1,3,1,3,3] 001010010110=>011010010100=>[2,1,2,3,2,3] 001000110110=>011011000100=>[2,1,2,1,4,3] 0001101001=>1001011000=>[1,3,2,1,4] 10000000001=>10000000001=>[1,10,1] 11111111111=>11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1] 100101101010=>010101101001=>[2,2,2,1,2,3,1] 101010010110=>011010010101=>[2,1,2,3,2,2,1] 100001011101=>101110100001=>[1,2,1,1,2,5,1] 100010101011=>110101010001=>[1,1,2,2,2,4,1] 100010011011=>110110010001=>[1,1,2,1,3,4,1] 100001011011=>110110100001=>[1,1,2,1,2,5,1] 100000111011=>110111000001=>[1,1,2,1,1,6,1] 100001010111=>111010100001=>[1,1,1,2,2,5,1] 100010001111=>111100010001=>[1,1,1,1,4,4,1] 100000101111=>111101000001=>[1,1,1,1,2,6,1] 110111000101=>101000111011=>[1,2,4,1,1,2,1,1] 110111001001=>100100111011=>[1,3,3,1,1,2,1,1] 111001011001=>100110100111=>[1,3,1,2,3,1,1,1] 111011000101=>101000110111=>[1,2,4,1,2,1,1,1] 111011001001=>100100110111=>[1,3,3,1,2,1,1,1] 111100010101=>101010001111=>[1,2,2,4,1,1,1,1] 111100100101=>101001001111=>[1,2,3,3,1,1,1,1] 111100101001=>100101001111=>[1,3,2,3,1,1,1,1] 111101000101=>101000101111=>[1,2,4,2,1,1,1,1] 111101001001=>100100101111=>[1,3,3,2,1,1,1,1] 110000110101=>101011000011=>[1,2,2,1,5,1,1] 110010001101=>101100010011=>[1,2,1,4,3,1,1] 110000101101=>101101000011=>[1,2,1,2,5,1,1] 111100000011=>110000001111=>[1,1,7,1,1,1,1] 110000110011=>110011000011=>[1,1,3,1,5,1,1] 111000001011=>110100000111=>[1,1,2,6,1,1,1] 110000101011=>110101000011=>[1,1,2,2,5,1,1] 110000011011=>110110000011=>[1,1,2,1,6,1,1] 001110000111=>111000011100=>[1,1,1,5,1,1,3] 110000100111=>111001000011=>[1,1,1,3,5,1,1] 110000010111=>111010000011=>[1,1,1,2,6,1,1] 110000001111=>111100000011=>[1,1,1,1,7,1,1] 0011001110=>0111001100=>[2,1,1,3,1,3] 001101010110=>011010101100=>[2,1,2,2,2,1,3] 001010110110=>011011010100=>[2,1,2,1,2,2,3] 001110001110=>011100011100=>[2,1,1,4,1,1,3] 001100101110=>011101001100=>[2,1,1,2,3,1,3] 001010101110=>011101010100=>[2,1,1,2,2,2,3] 001001101110=>011101100100=>[2,1,1,2,1,3,3] 001100011110=>011110001100=>[2,1,1,1,4,1,3] 001001011110=>011110100100=>[2,1,1,1,2,3,3] 000101011110=>011110101000=>[2,1,1,1,2,2,4] 001000111110=>011111000100=>[2,1,1,1,1,4,3] 000010111110=>011111010000=>[2,1,1,1,1,2,5] 0010000000=>0000000100=>[8,3] 0110100000=>0000010110=>[6,2,1,2] 110001110101=>101011100011=>[1,2,2,1,1,4,1,1] 100011110101=>101011110001=>[1,2,2,1,1,1,4,1] 110011001101=>101100110011=>[1,2,1,3,1,3,1,1] 100111001101=>101100111001=>[1,2,1,3,1,1,3,1] 110001101101=>101101100011=>[1,2,1,2,1,4,1,1] 100011101101=>101101110001=>[1,2,1,2,1,1,4,1] 110010011101=>101110010011=>[1,2,1,1,3,3,1,1] 100110011101=>101110011001=>[1,2,1,1,3,1,3,1] 110001011101=>101110100011=>[1,2,1,1,2,4,1,1] 100011011101=>101110110001=>[1,2,1,1,2,1,4,1] 101100110011=>110011001101=>[1,1,3,1,3,1,2,1] 110010110011=>110011010011=>[1,1,3,1,2,3,1,1] 101010110011=>110011010101=>[1,1,3,1,2,2,2,1] 100110110011=>110011011001=>[1,1,3,1,2,1,3,1] 110001110011=>110011100011=>[1,1,3,1,1,4,1,1] 101001110011=>110011100101=>[1,1,3,1,1,3,2,1] 100101110011=>110011101001=>[1,1,3,1,1,2,3,1] 100011110011=>110011110001=>[1,1,3,1,1,1,4,1] 110011001011=>110100110011=>[1,1,2,3,1,3,1,1] 101011001011=>110100110101=>[1,1,2,3,1,2,2,1] 100111001011=>110100111001=>[1,1,2,3,1,1,3,1] 101100101011=>110101001101=>[1,1,2,2,3,1,2,1] 110010101011=>110101010011=>[1,1,2,2,2,3,1,1] 101010101011=>110101010101=>[1,1,2,2,2,2,2,1] 100110101011=>110101011001=>[1,1,2,2,2,1,3,1] 110001101011=>110101100011=>[1,1,2,2,1,4,1,1] 101001101011=>110101100101=>[1,1,2,2,1,3,2,1] 100101101011=>110101101001=>[1,1,2,2,1,2,3,1] 100011101011=>110101110001=>[1,1,2,2,1,1,4,1] 101100011011=>110110001101=>[1,1,2,1,4,1,2,1] 110010011011=>110110010011=>[1,1,2,1,3,3,1,1] 101010011011=>110110010101=>[1,1,2,1,3,2,2,1] 100110011011=>110110011001=>[1,1,2,1,3,1,3,1] 110001011011=>110110100011=>[1,1,2,1,2,4,1,1] 101001011011=>110110100101=>[1,1,2,1,2,3,2,1] 100101011011=>110110101001=>[1,1,2,1,2,2,3,1] 100011011011=>110110110001=>[1,1,2,1,2,1,4,1] 110000111011=>110111000011=>[1,1,2,1,1,5,1,1] 101000111011=>110111000101=>[1,1,2,1,1,4,2,1] 100100111011=>110111001001=>[1,1,2,1,1,3,3,1] 100010111011=>110111010001=>[1,1,2,1,1,2,4,1] 100001111011=>110111100001=>[1,1,2,1,1,1,5,1] 110011000111=>111000110011=>[1,1,1,4,1,3,1,1] 101011000111=>111000110101=>[1,1,1,4,1,2,2,1] 100111000111=>111000111001=>[1,1,1,4,1,1,3,1] 101100100111=>111001001101=>[1,1,1,3,3,1,2,1] 110010100111=>111001010011=>[1,1,1,3,2,3,1,1] 101010100111=>111001010101=>[1,1,1,3,2,2,2,1] 100110100111=>111001011001=>[1,1,1,3,2,1,3,1] 110001100111=>111001100011=>[1,1,1,3,1,4,1,1] 101001100111=>111001100101=>[1,1,1,3,1,3,2,1] 100101100111=>111001101001=>[1,1,1,3,1,2,3,1] 100011100111=>111001110001=>[1,1,1,3,1,1,4,1] 101100010111=>111010001101=>[1,1,1,2,4,1,2,1] 110010010111=>111010010011=>[1,1,1,2,3,3,1,1] 101010010111=>111010010101=>[1,1,1,2,3,2,2,1] 100110010111=>111010011001=>[1,1,1,2,3,1,3,1] 110001010111=>111010100011=>[1,1,1,2,2,4,1,1] 101001010111=>111010100101=>[1,1,1,2,2,3,2,1] 100101010111=>111010101001=>[1,1,1,2,2,2,3,1] 100011010111=>111010110001=>[1,1,1,2,2,1,4,1] 110000110111=>111011000011=>[1,1,1,2,1,5,1,1] 101000110111=>111011000101=>[1,1,1,2,1,4,2,1] 100100110111=>111011001001=>[1,1,1,2,1,3,3,1] 100010110111=>111011010001=>[1,1,1,2,1,2,4,1] 100001110111=>111011100001=>[1,1,1,2,1,1,5,1] 101100001111=>111100001101=>[1,1,1,1,5,1,2,1] 110010001111=>111100010011=>[1,1,1,1,4,3,1,1] 101010001111=>111100010101=>[1,1,1,1,4,2,2,1] 100110001111=>111100011001=>[1,1,1,1,4,1,3,1] 110001001111=>111100100011=>[1,1,1,1,3,4,1,1] 101001001111=>111100100101=>[1,1,1,1,3,3,2,1] 100101001111=>111100101001=>[1,1,1,1,3,2,3,1] 100011001111=>111100110001=>[1,1,1,1,3,1,4,1] 110000101111=>111101000011=>[1,1,1,1,2,5,1,1] 101000101111=>111101000101=>[1,1,1,1,2,4,2,1] 100100101111=>111101001001=>[1,1,1,1,2,3,3,1] 100010101111=>111101010001=>[1,1,1,1,2,2,4,1] 100001101111=>111101100001=>[1,1,1,1,2,1,5,1] 110000011111=>111110000011=>[1,1,1,1,1,6,1,1] 101000011111=>111110000101=>[1,1,1,1,1,5,2,1] 100100011111=>111110001001=>[1,1,1,1,1,4,3,1] 100010011111=>111110010001=>[1,1,1,1,1,3,4,1] 100001011111=>111110100001=>[1,1,1,1,1,2,5,1] 100000111111=>111111000001=>[1,1,1,1,1,1,6,1] 0000000011=>1100000000=>[1,1,9] 0000111111=>1111110000=>[1,1,1,1,1,1,5] 00000000011=>11000000000=>[1,1,10] 0011111100=>0011111100=>[3,1,1,1,1,1,3] 0011000000=>0000001100=>[7,1,3] 0011001111=>1111001100=>[1,1,1,1,3,1,3] 0010011001=>1001100100=>[1,3,1,3,3] 0010001101=>1011000100=>[1,2,1,4,3] 0010100101=>1010010100=>[1,2,3,2,3] 001111000011=>110000111100=>[1,1,5,1,1,1,3] 0111100011=>1100011110=>[1,1,4,1,1,1,2] 0001101111=>1111011000=>[1,1,1,1,2,1,4] 0100101001=>1001010010=>[1,3,2,3,2] 111010000110=>011000010111=>[2,1,5,2,1,1,1] 110010001110=>011100010011=>[2,1,1,4,3,1,1] 110100010110=>011010001011=>[2,1,2,4,2,1,1] 110000000110=>011000000011=>[2,1,8,1,1] 110000011000=>000110000011=>[4,1,6,1,1] 110000111100=>001111000011=>[3,1,1,1,5,1,1] 110000010010=>010010000011=>[2,3,6,1,1] 110001100000=>000001100011=>[6,1,4,1,1] 110001000010=>010000100011=>[2,5,4,1,1] 110110000000=>000000011011=>[8,1,2,1,1] 110110110110=>011011011011=>[2,1,2,1,2,1,2,1,1] 111100011110=>011110001111=>[2,1,1,1,4,1,1,1,1] 110101101110=>011101101011=>[2,1,1,2,1,2,2,1,1] 111101100110=>011001101111=>[2,1,3,1,2,1,1,1,1] 111101111000=>000111101111=>[4,1,1,1,2,1,1,1,1] 111101110010=>010011101111=>[2,3,1,1,2,1,1,1,1] 111101001110=>011100101111=>[2,1,1,3,2,1,1,1,1] 0100010101=>1010100010=>[1,2,2,4,2] 0010010101=>1010100100=>[1,2,2,3,3] 0101010111=>1110101010=>[1,1,1,2,2,2,2] 0001010101=>1010101000=>[1,2,2,2,4] 0000110101=>1010110000=>[1,2,2,1,5] 0011010111=>1110101100=>[1,1,1,2,2,1,3] 0001110111=>1110111000=>[1,1,1,2,1,1,4] 0110000011=>1100000110=>[1,1,6,1,2] 110110011001=>100110011011=>[1,3,1,3,1,2,1,1] 110110001101=>101100011011=>[1,2,1,4,1,2,1,1] 110011011001=>100110110011=>[1,3,1,2,1,3,1,1] 110011100011=>110001110011=>[1,1,4,1,1,3,1,1] 110011100101=>101001110011=>[1,2,3,1,1,3,1,1] 110011101001=>100101110011=>[1,3,2,1,1,3,1,1] 111001001101=>101100100111=>[1,2,1,3,3,1,1,1] 111001100101=>101001100111=>[1,2,3,1,3,1,1,1] 111001101001=>100101100111=>[1,3,2,1,3,1,1,1] 111000101011=>110101000111=>[1,1,2,2,4,1,1,1] 111000110011=>110011000111=>[1,1,3,1,4,1,1,1] 111000110101=>101011000111=>[1,2,2,1,4,1,1,1] 111010011001=>100110010111=>[1,3,1,3,2,1,1,1] 111010001101=>101100010111=>[1,2,1,4,2,1,1,1] 101011100011=>110001110101=>[1,1,4,1,1,2,2,1] 111110000011=>110000011111=>[1,1,6,1,1,1,1,1] 110001010110=>011010100011=>[2,1,2,2,4,1,1] 100110111000=>000111011001=>[4,1,1,2,1,3,1] 100110110010=>010011011001=>[2,3,1,2,1,3,1] 111000100110=>011001000111=>[2,1,3,4,1,1,1] 11110110000=>00001101111=>[5,1,2,1,1,1,1] 11110011000=>00011001111=>[4,1,3,1,1,1,1] 100001001001=>100100100001=>[1,3,3,5,1] 0100011001=>1001100010=>[1,3,1,4,2] 0100110001=>1000110010=>[1,4,1,3,2] 0101000011=>1100001010=>[1,1,5,2,2] 0100110111=>1110110010=>[1,1,1,2,1,3,2] 0101001111=>1111001010=>[1,1,1,1,3,2,2] 0111011100=>0011101110=>[3,1,1,2,1,1,2] 0101000101=>1010001010=>[1,2,4,2,2] 0101010001=>1000101010=>[1,4,2,2,2] 0111010011=>1100101110=>[1,1,3,2,1,1,2] 0011101110=>0111011100=>[2,1,1,2,1,1,3] 00111111100=>00111111100=>[3,1,1,1,1,1,1,3] 100110001001=>100100011001=>[1,3,4,1,3,1] 100111011001=>100110111001=>[1,3,1,2,1,1,3,1] 100001101001=>100101100001=>[1,3,2,1,5,1] 110111011101=>101110111011=>[1,2,1,1,2,1,1,2,1,1] 110111110101=>101011111011=>[1,2,2,1,1,1,1,2,1,1] 110010001001=>100100010011=>[1,3,4,3,1,1] 110010000101=>101000010011=>[1,2,5,3,1,1] 110001001001=>100100100011=>[1,3,3,4,1,1] 110001000101=>101000100011=>[1,2,4,4,1,1] 110000101001=>100101000011=>[1,3,2,5,1,1] 110000100101=>101001000011=>[1,2,3,5,1,1] 110000010101=>101010000011=>[1,2,2,6,1,1] 111101011101=>101110101111=>[1,2,1,1,2,2,1,1,1,1] 111101110101=>101011101111=>[1,2,2,1,1,2,1,1,1,1] 111111010101=>101010111111=>[1,2,2,2,1,1,1,1,1,1] 0000100010=>0100010000=>[2,4,5] 000000100010=>010001000000=>[2,4,7] 000000110110=>011011000000=>[2,1,2,1,7] 000010100000=>000001010000=>[6,2,5] 000011011000=>000110110000=>[4,1,2,1,5] 000011000110=>011000110000=>[2,1,4,1,5] 001010001010=>010100010100=>[2,2,4,2,3] 001010101000=>000101010100=>[4,2,2,2,3] 001000100000=>000001000100=>[6,4,3] 001000000010=>010000000100=>[2,8,3] 001000010110=>011010000100=>[2,1,2,5,3] 001001011000=>000110100100=>[4,1,2,3,3] 001001010010=>010010100100=>[2,3,2,3,3] 001001000110=>011000100100=>[2,1,4,3,3] 001101100000=>000001101100=>[6,1,2,1,3] 001101000010=>010000101100=>[2,5,2,1,3] 001100011000=>000110001100=>[4,1,4,1,3] 001100010010=>010010001100=>[2,3,4,1,3] 001100000110=>011000001100=>[2,1,6,1,3] 001111011110=>011110111100=>[2,1,1,1,2,1,1,1,3] 101000101000=>000101000101=>[4,2,4,2,1] 101010001000=>000100010101=>[4,4,2,2,1] 100010101000=>000101010001=>[4,2,2,4,1] 100001011000=>000110100001=>[4,1,2,5,1] 100101001000=>000100101001=>[4,3,2,3,1] 100100011000=>000110001001=>[4,1,4,3,1] 110010100110=>011001010011=>[2,1,3,2,3,1,1] 110011001110=>011100110011=>[2,1,1,3,1,3,1,1] 111000101110=>011101000111=>[2,1,1,2,4,1,1,1] 0010110000=>0000110100=>[5,1,2,3] 11000000000=>00000000011=>[10,1,1] 111000010111=>111010000111=>[1,1,1,2,5,1,1,1] 111100000111=>111000001111=>[1,1,1,6,1,1,1,1] 0001001101=>1011001000=>[1,2,1,3,4] 111000001111=>111100000111=>[1,1,1,1,6,1,1,1] 0001100101=>1010011000=>[1,2,3,1,4] 100110111100=>001111011001=>[3,1,1,1,2,1,3,1] 101100111100=>001111001101=>[3,1,1,1,3,1,2,1] 101001111100=>001111100101=>[3,1,1,1,1,3,2,1] 111111100000=>000001111111=>[6,1,1,1,1,1,1,1] 101111110000=>000011111101=>[5,1,1,1,1,1,2,1]