=>

[1]=>[1]=>1=>1 [1,1]=>[1,1]=>11=>11 [2]=>[2]=>10=>00 [1,1,1]=>[1,1,1]=>111=>111 [1,2]=>[2,1]=>101=>100 [2,1]=>[1,2]=>110=>001 [3]=>[3]=>100=>010 [1,1,1,1]=>[1,1,1,1]=>1111=>1111 [1,1,2]=>[2,1,1]=>1011=>1100 [1,2,1]=>[1,2,1]=>1101=>1001 [1,3]=>[3,1]=>1001=>1010 [2,1,1]=>[1,1,2]=>1110=>0011 [2,2]=>[2,2]=>1010=>0000 [3,1]=>[1,3]=>1100=>0101 [4]=>[4]=>1000=>0110 [1,1,1,1,1]=>[1,1,1,1,1]=>11111=>11111 [1,1,1,2]=>[2,1,1,1]=>10111=>11100 [1,1,2,1]=>[1,2,1,1]=>11011=>11001 [1,1,3]=>[3,1,1]=>10011=>11010 [1,2,1,1]=>[1,1,2,1]=>11101=>10011 [1,2,2]=>[2,2,1]=>10101=>10000 [1,3,1]=>[1,3,1]=>11001=>10101 [1,4]=>[4,1]=>10001=>10110 [2,1,1,1]=>[1,1,1,2]=>11110=>00111 [2,1,2]=>[2,1,2]=>10110=>00100 [2,2,1]=>[1,2,2]=>11010=>00001 [2,3]=>[3,2]=>10010=>00010 [3,1,1]=>[1,1,3]=>11100=>01011 [3,2]=>[2,3]=>10100=>01000 [4,1]=>[1,4]=>11000=>01101 [5]=>[5]=>10000=>01110 [1,1,1,1,1,1]=>[1,1,1,1,1,1]=>111111=>111111 [1,1,1,1,2]=>[2,1,1,1,1]=>101111=>111100 [1,1,1,2,1]=>[1,2,1,1,1]=>110111=>111001 [1,1,1,3]=>[3,1,1,1]=>100111=>111010 [1,1,2,1,1]=>[1,1,2,1,1]=>111011=>110011 [1,1,2,2]=>[2,2,1,1]=>101011=>110000 [1,1,3,1]=>[1,3,1,1]=>110011=>110101 [1,1,4]=>[4,1,1]=>100011=>110110 [1,2,1,1,1]=>[1,1,1,2,1]=>111101=>100111 [1,2,1,2]=>[2,1,2,1]=>101101=>100100 [1,2,2,1]=>[1,2,2,1]=>110101=>100001 [1,2,3]=>[3,2,1]=>100101=>100010 [1,3,1,1]=>[1,1,3,1]=>111001=>101011 [1,3,2]=>[2,3,1]=>101001=>101000 [1,4,1]=>[1,4,1]=>110001=>101101 [1,5]=>[5,1]=>100001=>101110 [2,1,1,1,1]=>[1,1,1,1,2]=>111110=>001111 [2,1,1,2]=>[2,1,1,2]=>101110=>001100 [2,1,2,1]=>[1,2,1,2]=>110110=>001001 [2,1,3]=>[3,1,2]=>100110=>001010 [2,2,1,1]=>[1,1,2,2]=>111010=>000011 [2,2,2]=>[2,2,2]=>101010=>000000 [2,3,1]=>[1,3,2]=>110010=>000101 [2,4]=>[4,2]=>100010=>000110 [3,1,1,1]=>[1,1,1,3]=>111100=>010111 [3,1,2]=>[2,1,3]=>101100=>010100 [3,2,1]=>[1,2,3]=>110100=>010001 [3,3]=>[3,3]=>100100=>010010 [4,1,1]=>[1,1,4]=>111000=>011011 [4,2]=>[2,4]=>101000=>011000 [5,1]=>[1,5]=>110000=>011101 [6]=>[6]=>100000=>011110 [1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>1111111=>1111111 [1,1,1,1,1,2]=>[2,1,1,1,1,1]=>1011111=>1111100 [1,1,1,1,2,1]=>[1,2,1,1,1,1]=>1101111=>1111001 [1,1,1,1,3]=>[3,1,1,1,1]=>1001111=>1111010 [1,1,1,2,1,1]=>[1,1,2,1,1,1]=>1110111=>1110011 [1,1,1,2,2]=>[2,2,1,1,1]=>1010111=>1110000 [1,1,1,3,1]=>[1,3,1,1,1]=>1100111=>1110101 [1,1,1,4]=>[4,1,1,1]=>1000111=>1110110 [1,1,2,1,1,1]=>[1,1,1,2,1,1]=>1111011=>1100111 [1,1,2,1,2]=>[2,1,2,1,1]=>1011011=>1100100 [1,1,2,2,1]=>[1,2,2,1,1]=>1101011=>1100001 [1,1,2,3]=>[3,2,1,1]=>1001011=>1100010 [1,1,3,1,1]=>[1,1,3,1,1]=>1110011=>1101011 [1,1,3,2]=>[2,3,1,1]=>1010011=>1101000 [1,1,4,1]=>[1,4,1,1]=>1100011=>1101101 [1,1,5]=>[5,1,1]=>1000011=>1101110 [1,2,1,1,1,1]=>[1,1,1,1,2,1]=>1111101=>1001111 [1,2,1,1,2]=>[2,1,1,2,1]=>1011101=>1001100 [1,2,1,2,1]=>[1,2,1,2,1]=>1101101=>1001001 [1,2,1,3]=>[3,1,2,1]=>1001101=>1001010 [1,2,2,1,1]=>[1,1,2,2,1]=>1110101=>1000011 [1,2,2,2]=>[2,2,2,1]=>1010101=>1000000 [1,2,3,1]=>[1,3,2,1]=>1100101=>1000101 [1,2,4]=>[4,2,1]=>1000101=>1000110 [1,3,1,1,1]=>[1,1,1,3,1]=>1111001=>1010111 [1,3,1,2]=>[2,1,3,1]=>1011001=>1010100 [1,3,2,1]=>[1,2,3,1]=>1101001=>1010001 [1,3,3]=>[3,3,1]=>1001001=>1010010 [1,4,1,1]=>[1,1,4,1]=>1110001=>1011011 [1,4,2]=>[2,4,1]=>1010001=>1011000 [1,5,1]=>[1,5,1]=>1100001=>1011101 [1,6]=>[6,1]=>1000001=>1011110 [2,1,1,1,1,1]=>[1,1,1,1,1,2]=>1111110=>0011111 [2,1,1,1,2]=>[2,1,1,1,2]=>1011110=>0011100 [2,1,1,2,1]=>[1,2,1,1,2]=>1101110=>0011001 [2,1,1,3]=>[3,1,1,2]=>1001110=>0011010 [2,1,2,1,1]=>[1,1,2,1,2]=>1110110=>0010011 [2,1,2,2]=>[2,2,1,2]=>1010110=>0010000 [2,1,3,1]=>[1,3,1,2]=>1100110=>0010101 [2,1,4]=>[4,1,2]=>1000110=>0010110 [2,2,1,1,1]=>[1,1,1,2,2]=>1111010=>0000111 [2,2,1,2]=>[2,1,2,2]=>1011010=>0000100 [2,2,2,1]=>[1,2,2,2]=>1101010=>0000001 [2,2,3]=>[3,2,2]=>1001010=>0000010 [2,3,1,1]=>[1,1,3,2]=>1110010=>0001011 [2,3,2]=>[2,3,2]=>1010010=>0001000 [2,4,1]=>[1,4,2]=>1100010=>0001101 [2,5]=>[5,2]=>1000010=>0001110 [3,1,1,1,1]=>[1,1,1,1,3]=>1111100=>0101111 [3,1,1,2]=>[2,1,1,3]=>1011100=>0101100 [3,1,2,1]=>[1,2,1,3]=>1101100=>0101001 [3,1,3]=>[3,1,3]=>1001100=>0101010 [3,2,1,1]=>[1,1,2,3]=>1110100=>0100011 [3,2,2]=>[2,2,3]=>1010100=>0100000 [3,3,1]=>[1,3,3]=>1100100=>0100101 [3,4]=>[4,3]=>1000100=>0100110 [4,1,1,1]=>[1,1,1,4]=>1111000=>0110111 [4,1,2]=>[2,1,4]=>1011000=>0110100 [4,2,1]=>[1,2,4]=>1101000=>0110001 [4,3]=>[3,4]=>1001000=>0110010 [5,1,1]=>[1,1,5]=>1110000=>0111011 [5,2]=>[2,5]=>1010000=>0111000 [6,1]=>[1,6]=>1100000=>0111101 [7]=>[7]=>1000000=>0111110 [1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>11111111=>11111111 [1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]=>10111111=>11111100 [1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]=>11011111=>11111001 [1,1,1,1,1,3]=>[3,1,1,1,1,1]=>10011111=>11111010 [1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]=>11101111=>11110011 [1,1,1,1,2,2]=>[2,2,1,1,1,1]=>10101111=>11110000 [1,1,1,1,3,1]=>[1,3,1,1,1,1]=>11001111=>11110101 [1,1,1,1,4]=>[4,1,1,1,1]=>10001111=>11110110 [1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]=>11110111=>11100111 [1,1,1,2,1,2]=>[2,1,2,1,1,1]=>10110111=>11100100 [1,1,1,2,2,1]=>[1,2,2,1,1,1]=>11010111=>11100001 [1,1,1,2,3]=>[3,2,1,1,1]=>10010111=>11100010 [1,1,1,3,1,1]=>[1,1,3,1,1,1]=>11100111=>11101011 [1,1,1,3,2]=>[2,3,1,1,1]=>10100111=>11101000 [1,1,1,4,1]=>[1,4,1,1,1]=>11000111=>11101101 [1,1,1,5]=>[5,1,1,1]=>10000111=>11101110 [1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]=>11111011=>11001111 [1,1,2,1,1,2]=>[2,1,1,2,1,1]=>10111011=>11001100 [1,1,2,1,2,1]=>[1,2,1,2,1,1]=>11011011=>11001001 [1,1,2,1,3]=>[3,1,2,1,1]=>10011011=>11001010 [1,1,2,2,1,1]=>[1,1,2,2,1,1]=>11101011=>11000011 [1,1,2,2,2]=>[2,2,2,1,1]=>10101011=>11000000 [1,1,2,3,1]=>[1,3,2,1,1]=>11001011=>11000101 [1,1,2,4]=>[4,2,1,1]=>10001011=>11000110 [1,1,3,1,1,1]=>[1,1,1,3,1,1]=>11110011=>11010111 [1,1,3,1,2]=>[2,1,3,1,1]=>10110011=>11010100 [1,1,3,2,1]=>[1,2,3,1,1]=>11010011=>11010001 [1,1,3,3]=>[3,3,1,1]=>10010011=>11010010 [1,1,4,1,1]=>[1,1,4,1,1]=>11100011=>11011011 [1,1,4,2]=>[2,4,1,1]=>10100011=>11011000 [1,1,5,1]=>[1,5,1,1]=>11000011=>11011101 [1,1,6]=>[6,1,1]=>10000011=>11011110 [1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]=>11111101=>10011111 [1,2,1,1,1,2]=>[2,1,1,1,2,1]=>10111101=>10011100 [1,2,1,1,2,1]=>[1,2,1,1,2,1]=>11011101=>10011001 [1,2,1,1,3]=>[3,1,1,2,1]=>10011101=>10011010 [1,2,1,2,1,1]=>[1,1,2,1,2,1]=>11101101=>10010011 [1,2,1,2,2]=>[2,2,1,2,1]=>10101101=>10010000 [1,2,1,3,1]=>[1,3,1,2,1]=>11001101=>10010101 [1,2,1,4]=>[4,1,2,1]=>10001101=>10010110 [1,2,2,1,1,1]=>[1,1,1,2,2,1]=>11110101=>10000111 [1,2,2,1,2]=>[2,1,2,2,1]=>10110101=>10000100 [1,2,2,2,1]=>[1,2,2,2,1]=>11010101=>10000001 [1,2,2,3]=>[3,2,2,1]=>10010101=>10000010 [1,2,3,1,1]=>[1,1,3,2,1]=>11100101=>10001011 [1,2,3,2]=>[2,3,2,1]=>10100101=>10001000 [1,2,4,1]=>[1,4,2,1]=>11000101=>10001101 [1,2,5]=>[5,2,1]=>10000101=>10001110 [1,3,1,1,1,1]=>[1,1,1,1,3,1]=>11111001=>10101111 [1,3,1,1,2]=>[2,1,1,3,1]=>10111001=>10101100 [1,3,1,2,1]=>[1,2,1,3,1]=>11011001=>10101001 [1,3,1,3]=>[3,1,3,1]=>10011001=>10101010 [1,3,2,1,1]=>[1,1,2,3,1]=>11101001=>10100011 [1,3,2,2]=>[2,2,3,1]=>10101001=>10100000 [1,3,3,1]=>[1,3,3,1]=>11001001=>10100101 [1,3,4]=>[4,3,1]=>10001001=>10100110 [1,4,1,1,1]=>[1,1,1,4,1]=>11110001=>10110111 [1,4,1,2]=>[2,1,4,1]=>10110001=>10110100 [1,4,2,1]=>[1,2,4,1]=>11010001=>10110001 [1,4,3]=>[3,4,1]=>10010001=>10110010 [1,5,1,1]=>[1,1,5,1]=>11100001=>10111011 [1,5,2]=>[2,5,1]=>10100001=>10111000 [1,6,1]=>[1,6,1]=>11000001=>10111101 [1,7]=>[7,1]=>10000001=>10111110 [2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]=>11111110=>00111111 [2,1,1,1,1,2]=>[2,1,1,1,1,2]=>10111110=>00111100 [2,1,1,1,2,1]=>[1,2,1,1,1,2]=>11011110=>00111001 [2,1,1,1,3]=>[3,1,1,1,2]=>10011110=>00111010 [2,1,1,2,1,1]=>[1,1,2,1,1,2]=>11101110=>00110011 [2,1,1,2,2]=>[2,2,1,1,2]=>10101110=>00110000 [2,1,1,3,1]=>[1,3,1,1,2]=>11001110=>00110101 [2,1,1,4]=>[4,1,1,2]=>10001110=>00110110 [2,1,2,1,1,1]=>[1,1,1,2,1,2]=>11110110=>00100111 [2,1,2,1,2]=>[2,1,2,1,2]=>10110110=>00100100 [2,1,2,2,1]=>[1,2,2,1,2]=>11010110=>00100001 [2,1,2,3]=>[3,2,1,2]=>10010110=>00100010 [2,1,3,1,1]=>[1,1,3,1,2]=>11100110=>00101011 [2,1,3,2]=>[2,3,1,2]=>10100110=>00101000 [2,1,4,1]=>[1,4,1,2]=>11000110=>00101101 [2,1,5]=>[5,1,2]=>10000110=>00101110 [2,2,1,1,1,1]=>[1,1,1,1,2,2]=>11111010=>00001111 [2,2,1,1,2]=>[2,1,1,2,2]=>10111010=>00001100 [2,2,1,2,1]=>[1,2,1,2,2]=>11011010=>00001001 [2,2,1,3]=>[3,1,2,2]=>10011010=>00001010 [2,2,2,1,1]=>[1,1,2,2,2]=>11101010=>00000011 [2,2,2,2]=>[2,2,2,2]=>10101010=>00000000 [2,2,3,1]=>[1,3,2,2]=>11001010=>00000101 [2,2,4]=>[4,2,2]=>10001010=>00000110 [2,3,1,1,1]=>[1,1,1,3,2]=>11110010=>00010111 [2,3,1,2]=>[2,1,3,2]=>10110010=>00010100 [2,3,2,1]=>[1,2,3,2]=>11010010=>00010001 [2,3,3]=>[3,3,2]=>10010010=>00010010 [2,4,1,1]=>[1,1,4,2]=>11100010=>00011011 [2,4,2]=>[2,4,2]=>10100010=>00011000 [2,5,1]=>[1,5,2]=>11000010=>00011101 [2,6]=>[6,2]=>10000010=>00011110 [3,1,1,1,1,1]=>[1,1,1,1,1,3]=>11111100=>01011111 [3,1,1,1,2]=>[2,1,1,1,3]=>10111100=>01011100 [3,1,1,2,1]=>[1,2,1,1,3]=>11011100=>01011001 [3,1,1,3]=>[3,1,1,3]=>10011100=>01011010 [3,1,2,1,1]=>[1,1,2,1,3]=>11101100=>01010011 [3,1,2,2]=>[2,2,1,3]=>10101100=>01010000 [3,1,3,1]=>[1,3,1,3]=>11001100=>01010101 [3,1,4]=>[4,1,3]=>10001100=>01010110 [3,2,1,1,1]=>[1,1,1,2,3]=>11110100=>01000111 [3,2,1,2]=>[2,1,2,3]=>10110100=>01000100 [3,2,2,1]=>[1,2,2,3]=>11010100=>01000001 [3,2,3]=>[3,2,3]=>10010100=>01000010 [3,3,1,1]=>[1,1,3,3]=>11100100=>01001011 [3,3,2]=>[2,3,3]=>10100100=>01001000 [3,4,1]=>[1,4,3]=>11000100=>01001101 [3,5]=>[5,3]=>10000100=>01001110 [4,1,1,1,1]=>[1,1,1,1,4]=>11111000=>01101111 [4,1,1,2]=>[2,1,1,4]=>10111000=>01101100 [4,1,2,1]=>[1,2,1,4]=>11011000=>01101001 [4,1,3]=>[3,1,4]=>10011000=>01101010 [4,2,1,1]=>[1,1,2,4]=>11101000=>01100011 [4,2,2]=>[2,2,4]=>10101000=>01100000 [4,3,1]=>[1,3,4]=>11001000=>01100101 [4,4]=>[4,4]=>10001000=>01100110 [5,1,1,1]=>[1,1,1,5]=>11110000=>01110111 [5,1,2]=>[2,1,5]=>10110000=>01110100 [5,2,1]=>[1,2,5]=>11010000=>01110001 [5,3]=>[3,5]=>10010000=>01110010 [6,1,1]=>[1,1,6]=>11100000=>01111011 [6,2]=>[2,6]=>10100000=>01111000 [7,1]=>[1,7]=>11000000=>01111101 [8]=>[8]=>10000000=>01111110 [1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>111111111=>111111111 [1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]=>101111111=>111111100 [1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]=>110111111=>111111001 [1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]=>100111111=>111111010 [1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]=>111011111=>111110011 [1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]=>101011111=>111110000 [1,1,1,1,1,3,1]=>[1,3,1,1,1,1,1]=>110011111=>111110101 [1,1,1,1,1,4]=>[4,1,1,1,1,1]=>100011111=>111110110 [1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]=>111101111=>111100111 [1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]=>101101111=>111100100 [1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1]=>110101111=>111100001 [1,1,1,1,2,3]=>[3,2,1,1,1,1]=>100101111=>111100010 [1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]=>111001111=>111101011 [1,1,1,1,3,2]=>[2,3,1,1,1,1]=>101001111=>111101000 [1,1,1,1,4,1]=>[1,4,1,1,1,1]=>110001111=>111101101 [1,1,1,1,5]=>[5,1,1,1,1]=>100001111=>111101110 [1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]=>111110111=>111001111 [1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1]=>101110111=>111001100 [1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1]=>110110111=>111001001 [1,1,1,2,1,3]=>[3,1,2,1,1,1]=>100110111=>111001010 [1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1]=>111010111=>111000011 [1,1,1,2,2,2]=>[2,2,2,1,1,1]=>101010111=>111000000 [1,1,1,2,3,1]=>[1,3,2,1,1,1]=>110010111=>111000101 [1,1,1,2,4]=>[4,2,1,1,1]=>100010111=>111000110 [1,1,1,3,1,1,1]=>[1,1,1,3,1,1,1]=>111100111=>111010111 [1,1,1,3,1,2]=>[2,1,3,1,1,1]=>101100111=>111010100 [1,1,1,3,2,1]=>[1,2,3,1,1,1]=>110100111=>111010001 [1,1,1,3,3]=>[3,3,1,1,1]=>100100111=>111010010 [1,1,1,4,1,1]=>[1,1,4,1,1,1]=>111000111=>111011011 [1,1,1,4,2]=>[2,4,1,1,1]=>101000111=>111011000 [1,1,1,5,1]=>[1,5,1,1,1]=>110000111=>111011101 [1,1,1,6]=>[6,1,1,1]=>100000111=>111011110 [1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]=>111111011=>110011111 [1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]=>101111011=>110011100 [1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1]=>110111011=>110011001 [1,1,2,1,1,3]=>[3,1,1,2,1,1]=>100111011=>110011010 [1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]=>111011011=>110010011 [1,1,2,1,2,2]=>[2,2,1,2,1,1]=>101011011=>110010000 [1,1,2,1,3,1]=>[1,3,1,2,1,1]=>110011011=>110010101 [1,1,2,1,4]=>[4,1,2,1,1]=>100011011=>110010110 [1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1]=>111101011=>110000111 [1,1,2,2,1,2]=>[2,1,2,2,1,1]=>101101011=>110000100 [1,1,2,2,2,1]=>[1,2,2,2,1,1]=>110101011=>110000001 [1,1,2,2,3]=>[3,2,2,1,1]=>100101011=>110000010 [1,1,2,3,1,1]=>[1,1,3,2,1,1]=>111001011=>110001011 [1,1,2,3,2]=>[2,3,2,1,1]=>101001011=>110001000 [1,1,2,4,1]=>[1,4,2,1,1]=>110001011=>110001101 [1,1,2,5]=>[5,2,1,1]=>100001011=>110001110 [1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]=>111110011=>110101111 [1,1,3,1,1,2]=>[2,1,1,3,1,1]=>101110011=>110101100 [1,1,3,1,2,1]=>[1,2,1,3,1,1]=>110110011=>110101001 [1,1,3,1,3]=>[3,1,3,1,1]=>100110011=>110101010 [1,1,3,2,1,1]=>[1,1,2,3,1,1]=>111010011=>110100011 [1,1,3,2,2]=>[2,2,3,1,1]=>101010011=>110100000 [1,1,3,3,1]=>[1,3,3,1,1]=>110010011=>110100101 [1,1,3,4]=>[4,3,1,1]=>100010011=>110100110 [1,1,4,1,1,1]=>[1,1,1,4,1,1]=>111100011=>110110111 [1,1,4,1,2]=>[2,1,4,1,1]=>101100011=>110110100 [1,1,4,2,1]=>[1,2,4,1,1]=>110100011=>110110001 [1,1,4,3]=>[3,4,1,1]=>100100011=>110110010 [1,1,5,1,1]=>[1,1,5,1,1]=>111000011=>110111011 [1,1,5,2]=>[2,5,1,1]=>101000011=>110111000 [1,1,6,1]=>[1,6,1,1]=>110000011=>110111101 [1,1,7]=>[7,1,1]=>100000011=>110111110 [1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]=>111111101=>100111111 [1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1]=>101111101=>100111100 [1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1]=>110111101=>100111001 [1,2,1,1,1,3]=>[3,1,1,1,2,1]=>100111101=>100111010 [1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1]=>111011101=>100110011 [1,2,1,1,2,2]=>[2,2,1,1,2,1]=>101011101=>100110000 [1,2,1,1,3,1]=>[1,3,1,1,2,1]=>110011101=>100110101 [1,2,1,1,4]=>[4,1,1,2,1]=>100011101=>100110110 [1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1]=>111101101=>100100111 [1,2,1,2,1,2]=>[2,1,2,1,2,1]=>101101101=>100100100 [1,2,1,2,2,1]=>[1,2,2,1,2,1]=>110101101=>100100001 [1,2,1,2,3]=>[3,2,1,2,1]=>100101101=>100100010 [1,2,1,3,1,1]=>[1,1,3,1,2,1]=>111001101=>100101011 [1,2,1,3,2]=>[2,3,1,2,1]=>101001101=>100101000 [1,2,1,4,1]=>[1,4,1,2,1]=>110001101=>100101101 [1,2,1,5]=>[5,1,2,1]=>100001101=>100101110 [1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1]=>111110101=>100001111 [1,2,2,1,1,2]=>[2,1,1,2,2,1]=>101110101=>100001100 [1,2,2,1,2,1]=>[1,2,1,2,2,1]=>110110101=>100001001 [1,2,2,1,3]=>[3,1,2,2,1]=>100110101=>100001010 [1,2,2,2,1,1]=>[1,1,2,2,2,1]=>111010101=>100000011 [1,2,2,2,2]=>[2,2,2,2,1]=>101010101=>100000000 [1,2,2,3,1]=>[1,3,2,2,1]=>110010101=>100000101 [1,2,2,4]=>[4,2,2,1]=>100010101=>100000110 [1,2,3,1,1,1]=>[1,1,1,3,2,1]=>111100101=>100010111 [1,2,3,1,2]=>[2,1,3,2,1]=>101100101=>100010100 [1,2,3,2,1]=>[1,2,3,2,1]=>110100101=>100010001 [1,2,3,3]=>[3,3,2,1]=>100100101=>100010010 [1,2,4,1,1]=>[1,1,4,2,1]=>111000101=>100011011 [1,2,4,2]=>[2,4,2,1]=>101000101=>100011000 [1,2,5,1]=>[1,5,2,1]=>110000101=>100011101 [1,2,6]=>[6,2,1]=>100000101=>100011110 [1,3,1,1,1,1,1]=>[1,1,1,1,1,3,1]=>111111001=>101011111 [1,3,1,1,1,2]=>[2,1,1,1,3,1]=>101111001=>101011100 [1,3,1,1,2,1]=>[1,2,1,1,3,1]=>110111001=>101011001 [1,3,1,1,3]=>[3,1,1,3,1]=>100111001=>101011010 [1,3,1,2,1,1]=>[1,1,2,1,3,1]=>111011001=>101010011 [1,3,1,2,2]=>[2,2,1,3,1]=>101011001=>101010000 [1,3,1,3,1]=>[1,3,1,3,1]=>110011001=>101010101 [1,3,1,4]=>[4,1,3,1]=>100011001=>101010110 [1,3,2,1,1,1]=>[1,1,1,2,3,1]=>111101001=>101000111 [1,3,2,1,2]=>[2,1,2,3,1]=>101101001=>101000100 [1,3,2,2,1]=>[1,2,2,3,1]=>110101001=>101000001 [1,3,2,3]=>[3,2,3,1]=>100101001=>101000010 [1,3,3,1,1]=>[1,1,3,3,1]=>111001001=>101001011 [1,3,3,2]=>[2,3,3,1]=>101001001=>101001000 [1,3,4,1]=>[1,4,3,1]=>110001001=>101001101 [1,3,5]=>[5,3,1]=>100001001=>101001110 [1,4,1,1,1,1]=>[1,1,1,1,4,1]=>111110001=>101101111 [1,4,1,1,2]=>[2,1,1,4,1]=>101110001=>101101100 [1,4,1,2,1]=>[1,2,1,4,1]=>110110001=>101101001 [1,4,1,3]=>[3,1,4,1]=>100110001=>101101010 [1,4,2,1,1]=>[1,1,2,4,1]=>111010001=>101100011 [1,4,2,2]=>[2,2,4,1]=>101010001=>101100000 [1,4,3,1]=>[1,3,4,1]=>110010001=>101100101 [1,4,4]=>[4,4,1]=>100010001=>101100110 [1,5,1,1,1]=>[1,1,1,5,1]=>111100001=>101110111 [1,5,1,2]=>[2,1,5,1]=>101100001=>101110100 [1,5,2,1]=>[1,2,5,1]=>110100001=>101110001 [1,5,3]=>[3,5,1]=>100100001=>101110010 [1,6,1,1]=>[1,1,6,1]=>111000001=>101111011 [1,6,2]=>[2,6,1]=>101000001=>101111000 [1,7,1]=>[1,7,1]=>110000001=>101111101 [1,8]=>[8,1]=>100000001=>101111110 [2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]=>111111110=>001111111 [2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]=>101111110=>001111100 [2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]=>110111110=>001111001 [2,1,1,1,1,3]=>[3,1,1,1,1,2]=>100111110=>001111010 [2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]=>111011110=>001110011 [2,1,1,1,2,2]=>[2,2,1,1,1,2]=>101011110=>001110000 [2,1,1,1,3,1]=>[1,3,1,1,1,2]=>110011110=>001110101 [2,1,1,1,4]=>[4,1,1,1,2]=>100011110=>001110110 [2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]=>111101110=>001100111 [2,1,1,2,1,2]=>[2,1,2,1,1,2]=>101101110=>001100100 [2,1,1,2,2,1]=>[1,2,2,1,1,2]=>110101110=>001100001 [2,1,1,2,3]=>[3,2,1,1,2]=>100101110=>001100010 [2,1,1,3,1,1]=>[1,1,3,1,1,2]=>111001110=>001101011 [2,1,1,3,2]=>[2,3,1,1,2]=>101001110=>001101000 [2,1,1,4,1]=>[1,4,1,1,2]=>110001110=>001101101 [2,1,1,5]=>[5,1,1,2]=>100001110=>001101110 [2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]=>111110110=>001001111 [2,1,2,1,1,2]=>[2,1,1,2,1,2]=>101110110=>001001100 [2,1,2,1,2,1]=>[1,2,1,2,1,2]=>110110110=>001001001 [2,1,2,1,3]=>[3,1,2,1,2]=>100110110=>001001010 [2,1,2,2,1,1]=>[1,1,2,2,1,2]=>111010110=>001000011 [2,1,2,2,2]=>[2,2,2,1,2]=>101010110=>001000000 [2,1,2,3,1]=>[1,3,2,1,2]=>110010110=>001000101 [2,1,2,4]=>[4,2,1,2]=>100010110=>001000110 [2,1,3,1,1,1]=>[1,1,1,3,1,2]=>111100110=>001010111 [2,1,3,1,2]=>[2,1,3,1,2]=>101100110=>001010100 [2,1,3,2,1]=>[1,2,3,1,2]=>110100110=>001010001 [2,1,3,3]=>[3,3,1,2]=>100100110=>001010010 [2,1,4,1,1]=>[1,1,4,1,2]=>111000110=>001011011 [2,1,4,2]=>[2,4,1,2]=>101000110=>001011000 [2,1,5,1]=>[1,5,1,2]=>110000110=>001011101 [2,1,6]=>[6,1,2]=>100000110=>001011110 [2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2]=>111111010=>000011111 [2,2,1,1,1,2]=>[2,1,1,1,2,2]=>101111010=>000011100 [2,2,1,1,2,1]=>[1,2,1,1,2,2]=>110111010=>000011001 [2,2,1,1,3]=>[3,1,1,2,2]=>100111010=>000011010 [2,2,1,2,1,1]=>[1,1,2,1,2,2]=>111011010=>000010011 [2,2,1,2,2]=>[2,2,1,2,2]=>101011010=>000010000 [2,2,1,3,1]=>[1,3,1,2,2]=>110011010=>000010101 [2,2,1,4]=>[4,1,2,2]=>100011010=>000010110 [2,2,2,1,1,1]=>[1,1,1,2,2,2]=>111101010=>000000111 [2,2,2,1,2]=>[2,1,2,2,2]=>101101010=>000000100 [2,2,2,2,1]=>[1,2,2,2,2]=>110101010=>000000001 [2,2,2,3]=>[3,2,2,2]=>100101010=>000000010 [2,2,3,1,1]=>[1,1,3,2,2]=>111001010=>000001011 [2,2,3,2]=>[2,3,2,2]=>101001010=>000001000 [2,2,4,1]=>[1,4,2,2]=>110001010=>000001101 [2,2,5]=>[5,2,2]=>100001010=>000001110 [2,3,1,1,1,1]=>[1,1,1,1,3,2]=>111110010=>000101111 [2,3,1,1,2]=>[2,1,1,3,2]=>101110010=>000101100 [2,3,1,2,1]=>[1,2,1,3,2]=>110110010=>000101001 [2,3,1,3]=>[3,1,3,2]=>100110010=>000101010 [2,3,2,1,1]=>[1,1,2,3,2]=>111010010=>000100011 [2,3,2,2]=>[2,2,3,2]=>101010010=>000100000 [2,3,3,1]=>[1,3,3,2]=>110010010=>000100101 [2,3,4]=>[4,3,2]=>100010010=>000100110 [2,4,1,1,1]=>[1,1,1,4,2]=>111100010=>000110111 [2,4,1,2]=>[2,1,4,2]=>101100010=>000110100 [2,4,2,1]=>[1,2,4,2]=>110100010=>000110001 [2,4,3]=>[3,4,2]=>100100010=>000110010 [2,5,1,1]=>[1,1,5,2]=>111000010=>000111011 [2,5,2]=>[2,5,2]=>101000010=>000111000 [2,6,1]=>[1,6,2]=>110000010=>000111101 [2,7]=>[7,2]=>100000010=>000111110 [3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3]=>111111100=>010111111 [3,1,1,1,1,2]=>[2,1,1,1,1,3]=>101111100=>010111100 [3,1,1,1,2,1]=>[1,2,1,1,1,3]=>110111100=>010111001 [3,1,1,1,3]=>[3,1,1,1,3]=>100111100=>010111010 [3,1,1,2,1,1]=>[1,1,2,1,1,3]=>111011100=>010110011 [3,1,1,2,2]=>[2,2,1,1,3]=>101011100=>010110000 [3,1,1,3,1]=>[1,3,1,1,3]=>110011100=>010110101 [3,1,1,4]=>[4,1,1,3]=>100011100=>010110110 [3,1,2,1,1,1]=>[1,1,1,2,1,3]=>111101100=>010100111 [3,1,2,1,2]=>[2,1,2,1,3]=>101101100=>010100100 [3,1,2,2,1]=>[1,2,2,1,3]=>110101100=>010100001 [3,1,2,3]=>[3,2,1,3]=>100101100=>010100010 [3,1,3,1,1]=>[1,1,3,1,3]=>111001100=>010101011 [3,1,3,2]=>[2,3,1,3]=>101001100=>010101000 [3,1,4,1]=>[1,4,1,3]=>110001100=>010101101 [3,1,5]=>[5,1,3]=>100001100=>010101110 [3,2,1,1,1,1]=>[1,1,1,1,2,3]=>111110100=>010001111 [3,2,1,1,2]=>[2,1,1,2,3]=>101110100=>010001100 [3,2,1,2,1]=>[1,2,1,2,3]=>110110100=>010001001 [3,2,1,3]=>[3,1,2,3]=>100110100=>010001010 [3,2,2,1,1]=>[1,1,2,2,3]=>111010100=>010000011 [3,2,2,2]=>[2,2,2,3]=>101010100=>010000000 [3,2,3,1]=>[1,3,2,3]=>110010100=>010000101 [3,2,4]=>[4,2,3]=>100010100=>010000110 [3,3,1,1,1]=>[1,1,1,3,3]=>111100100=>010010111 [3,3,1,2]=>[2,1,3,3]=>101100100=>010010100 [3,3,2,1]=>[1,2,3,3]=>110100100=>010010001 [3,3,3]=>[3,3,3]=>100100100=>010010010 [3,4,1,1]=>[1,1,4,3]=>111000100=>010011011 [3,4,2]=>[2,4,3]=>101000100=>010011000 [3,5,1]=>[1,5,3]=>110000100=>010011101 [3,6]=>[6,3]=>100000100=>010011110 [4,1,1,1,1,1]=>[1,1,1,1,1,4]=>111111000=>011011111 [4,1,1,1,2]=>[2,1,1,1,4]=>101111000=>011011100 [4,1,1,2,1]=>[1,2,1,1,4]=>110111000=>011011001 [4,1,1,3]=>[3,1,1,4]=>100111000=>011011010 [4,1,2,1,1]=>[1,1,2,1,4]=>111011000=>011010011 [4,1,2,2]=>[2,2,1,4]=>101011000=>011010000 [4,1,3,1]=>[1,3,1,4]=>110011000=>011010101 [4,1,4]=>[4,1,4]=>100011000=>011010110 [4,2,1,1,1]=>[1,1,1,2,4]=>111101000=>011000111 [4,2,1,2]=>[2,1,2,4]=>101101000=>011000100 [4,2,2,1]=>[1,2,2,4]=>110101000=>011000001 [4,2,3]=>[3,2,4]=>100101000=>011000010 [4,3,1,1]=>[1,1,3,4]=>111001000=>011001011 [4,3,2]=>[2,3,4]=>101001000=>011001000 [4,4,1]=>[1,4,4]=>110001000=>011001101 [4,5]=>[5,4]=>100001000=>011001110 [5,1,1,1,1]=>[1,1,1,1,5]=>111110000=>011101111 [5,1,1,2]=>[2,1,1,5]=>101110000=>011101100 [5,1,2,1]=>[1,2,1,5]=>110110000=>011101001 [5,1,3]=>[3,1,5]=>100110000=>011101010 [5,2,1,1]=>[1,1,2,5]=>111010000=>011100011 [5,2,2]=>[2,2,5]=>101010000=>011100000 [5,3,1]=>[1,3,5]=>110010000=>011100101 [5,4]=>[4,5]=>100010000=>011100110 [6,1,1,1]=>[1,1,1,6]=>111100000=>011110111 [6,1,2]=>[2,1,6]=>101100000=>011110100 [6,2,1]=>[1,2,6]=>110100000=>011110001 [6,3]=>[3,6]=>100100000=>011110010 [7,1,1]=>[1,1,7]=>111000000=>011111011 [7,2]=>[2,7]=>101000000=>011111000 [8,1]=>[1,8]=>110000000=>011111101 [9]=>[9]=>100000000=>011111110 [1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]=>1111111111=>1111111111 [1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]=>1001111111=>1111111010 [1,1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1,1]=>1011011111=>1111100100 [1,1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1,1]=>1101011111=>1111100001 [1,1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1,1]=>1110011111=>1111101011 [1,1,1,1,1,5]=>[5,1,1,1,1,1]=>1000011111=>1111101110 [1,1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1,1]=>1011110111=>1110011100 [1,1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1,1]=>1110110111=>1110010011 [1,1,1,2,1,4]=>[4,1,2,1,1,1]=>1000110111=>1110010110 [1,1,1,2,2,2,1]=>[1,2,2,2,1,1,1]=>1101010111=>1110000001 [1,1,1,2,3,2]=>[2,3,2,1,1,1]=>1010010111=>1110001000 [1,1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1,1]=>1111100111=>1110101111 [1,1,1,3,1,3]=>[3,1,3,1,1,1]=>1001100111=>1110101010 [1,1,1,4,1,2]=>[2,1,4,1,1,1]=>1011000111=>1110110100 [1,1,1,5,1,1]=>[1,1,5,1,1,1]=>1110000111=>1110111011 [1,1,1,7]=>[7,1,1,1]=>1000000111=>1110111110 [1,1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1,1]=>1101111011=>1100111001 [1,1,2,1,2,2,1]=>[1,2,2,1,2,1,1]=>1101011011=>1100100001 [1,1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1,1]=>1111101011=>1100001111 [1,1,2,2,1,2,1]=>[1,2,1,2,2,1,1]=>1101101011=>1100001001 [1,1,2,2,2,1,1]=>[1,1,2,2,2,1,1]=>1110101011=>1100000011 [1,1,2,2,2,2]=>[2,2,2,2,1,1]=>1010101011=>1100000000 [1,1,2,2,3,1]=>[1,3,2,2,1,1]=>1100101011=>1100000101 [1,1,2,2,4]=>[4,2,2,1,1]=>1000101011=>1100000110 [1,1,2,3,2,1]=>[1,2,3,2,1,1]=>1101001011=>1100010001 [1,1,2,5,1]=>[1,5,2,1,1]=>1100001011=>1100011101 [1,1,3,2,2,1]=>[1,2,2,3,1,1]=>1101010011=>1101000001 [1,1,5,2,1]=>[1,2,5,1,1]=>1101000011=>1101110001 [1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1]=>1111111101=>1001111111 [1,2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2,1]=>1011111101=>1001111100 [1,2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2,1]=>1110111101=>1001110011 [1,2,1,1,1,4]=>[4,1,1,1,2,1]=>1000111101=>1001110110 [1,2,1,1,3,2]=>[2,3,1,1,2,1]=>1010011101=>1001101000 [1,2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2,1]=>1111101101=>1001001111 [1,2,1,2,1,3]=>[3,1,2,1,2,1]=>1001101101=>1001001010 [1,2,1,3,1,2]=>[2,1,3,1,2,1]=>1011001101=>1001010100 [1,2,1,4,1,1]=>[1,1,4,1,2,1]=>1110001101=>1001011011 [1,2,1,6]=>[6,1,2,1]=>1000001101=>1001011110 [1,2,2,1,2,2]=>[2,2,1,2,2,1]=>1010110101=>1000010000 [1,2,2,2,2,1]=>[1,2,2,2,2,1]=>1101010101=>1000000001 [1,2,2,2,3]=>[3,2,2,2,1]=>1001010101=>1000000010 [1,2,2,3,2]=>[2,3,2,2,1]=>1010010101=>1000001000 [1,2,2,4,1]=>[1,4,2,2,1]=>1100010101=>1000001101 [1,2,3,1,1,2]=>[2,1,1,3,2,1]=>1011100101=>1000101100 [1,2,3,1,3]=>[3,1,3,2,1]=>1001100101=>1000101010 [1,2,3,2,1,1]=>[1,1,2,3,2,1]=>1110100101=>1000100011 [1,2,3,2,2]=>[2,2,3,2,1]=>1010100101=>1000100000 [1,2,3,3,1]=>[1,3,3,2,1]=>1100100101=>1000100101 [1,2,3,4]=>[4,3,2,1]=>1000100101=>1000100110 [1,2,4,1,2]=>[2,1,4,2,1]=>1011000101=>1000110100 [1,2,4,2,1]=>[1,2,4,2,1]=>1101000101=>1000110001 [1,2,5,1,1]=>[1,1,5,2,1]=>1110000101=>1000111011 [1,2,5,2]=>[2,5,2,1]=>1010000101=>1000111000 [1,3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3,1]=>1111111001=>1010111111 [1,3,1,1,1,3]=>[3,1,1,1,3,1]=>1001111001=>1010111010 [1,3,1,2,1,2]=>[2,1,2,1,3,1]=>1011011001=>1010100100 [1,3,1,2,3]=>[3,2,1,3,1]=>1001011001=>1010100010 [1,3,1,3,1,1]=>[1,1,3,1,3,1]=>1110011001=>1010101011 [1,3,1,3,2]=>[2,3,1,3,1]=>1010011001=>1010101000 [1,3,1,4,1]=>[1,4,1,3,1]=>1100011001=>1010101101 [1,3,1,5]=>[5,1,3,1]=>1000011001=>1010101110 [1,3,2,1,3]=>[3,1,2,3,1]=>1001101001=>1010001010 [1,3,2,2,2]=>[2,2,2,3,1]=>1010101001=>1010000000 [1,3,2,3,1]=>[1,3,2,3,1]=>1100101001=>1010000101 [1,3,3,1,2]=>[2,1,3,3,1]=>1011001001=>1010010100 [1,3,3,2,1]=>[1,2,3,3,1]=>1101001001=>1010010001 [1,3,4,1,1]=>[1,1,4,3,1]=>1110001001=>1010011011 [1,4,1,1,1,2]=>[2,1,1,1,4,1]=>1011110001=>1011011100 [1,4,1,1,3]=>[3,1,1,4,1]=>1001110001=>1011011010 [1,4,1,2,1,1]=>[1,1,2,1,4,1]=>1110110001=>1011010011 [1,4,1,2,2]=>[2,2,1,4,1]=>1010110001=>1011010000 [1,4,1,3,1]=>[1,3,1,4,1]=>1100110001=>1011010101 [1,4,1,4]=>[4,1,4,1]=>1000110001=>1011010110 [1,4,2,1,2]=>[2,1,2,4,1]=>1011010001=>1011000100 [1,4,2,2,1]=>[1,2,2,4,1]=>1101010001=>1011000001 [1,4,3,1,1]=>[1,1,3,4,1]=>1110010001=>1011001011 [1,4,3,2]=>[2,3,4,1]=>1010010001=>1011001000 [1,5,1,1,1,1]=>[1,1,1,1,5,1]=>1111100001=>1011101111 [1,5,1,1,2]=>[2,1,1,5,1]=>1011100001=>1011101100 [1,5,1,2,1]=>[1,2,1,5,1]=>1101100001=>1011101001 [1,5,1,3]=>[3,1,5,1]=>1001100001=>1011101010 [1,5,2,1,1]=>[1,1,2,5,1]=>1110100001=>1011100011 [1,6,1,1,1]=>[1,1,1,6,1]=>1111000001=>1011110111 [1,6,1,2]=>[2,1,6,1]=>1011000001=>1011110100 [1,7,1,1]=>[1,1,7,1]=>1110000001=>1011111011 [1,9]=>[9,1]=>1000000001=>1011111110 [2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2]=>1111111110=>0011111111 [2,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,2]=>1011111110=>0011111100 [2,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,2]=>1101111110=>0011111001 [2,1,1,1,1,1,3]=>[3,1,1,1,1,1,2]=>1001111110=>0011111010 [2,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,2]=>1110111110=>0011110011 [2,1,1,1,1,2,2]=>[2,2,1,1,1,1,2]=>1010111110=>0011110000 [2,1,1,1,1,4]=>[4,1,1,1,1,2]=>1000111110=>0011110110 [2,1,1,1,2,3]=>[3,2,1,1,1,2]=>1001011110=>0011100010 [2,1,1,1,3,1,1]=>[1,1,3,1,1,1,2]=>1110011110=>0011101011 [2,1,1,1,5]=>[5,1,1,1,2]=>1000011110=>0011101110 [2,1,1,2,4]=>[4,2,1,1,2]=>1000101110=>0011000110 [2,1,1,3,2,1]=>[1,2,3,1,1,2]=>1101001110=>0011010001 [2,1,1,3,3]=>[3,3,1,1,2]=>1001001110=>0011010010 [2,1,1,4,2]=>[2,4,1,1,2]=>1010001110=>0011011000 [2,1,1,6]=>[6,1,1,2]=>1000001110=>0011011110 [2,1,2,1,4]=>[4,1,2,1,2]=>1000110110=>0010010110 [2,1,2,2,3]=>[3,2,2,1,2]=>1001010110=>0010000010 [2,1,2,3,2]=>[2,3,2,1,2]=>1010010110=>0010001000 [2,1,2,5]=>[5,2,1,2]=>1000010110=>0010001110 [2,1,3,1,3]=>[3,1,3,1,2]=>1001100110=>0010101010 [2,1,3,2,2]=>[2,2,3,1,2]=>1010100110=>0010100000 [2,1,3,3,1]=>[1,3,3,1,2]=>1100100110=>0010100101 [2,1,7]=>[7,1,2]=>1000000110=>0010111110 [2,2,1,1,4]=>[4,1,1,2,2]=>1000111010=>0000110110 [2,2,1,2,3]=>[3,2,1,2,2]=>1001011010=>0000100010 [2,2,1,3,2]=>[2,3,1,2,2]=>1010011010=>0000101000 [2,2,2,1,3]=>[3,1,2,2,2]=>1001101010=>0000001010 [2,2,2,2,2]=>[2,2,2,2,2]=>1010101010=>0000000000 [2,2,2,3,1]=>[1,3,2,2,2]=>1100101010=>0000000101 [2,2,3,1,2]=>[2,1,3,2,2]=>1011001010=>0000010100 [2,2,3,2,1]=>[1,2,3,2,2]=>1101001010=>0000010001 [2,2,4,1,1]=>[1,1,4,2,2]=>1110001010=>0000011011 [2,2,6]=>[6,2,2]=>1000001010=>0000011110 [2,3,1,2,2]=>[2,2,1,3,2]=>1010110010=>0001010000 [2,3,1,3,1]=>[1,3,1,3,2]=>1100110010=>0001010101 [2,3,2,1,2]=>[2,1,2,3,2]=>1011010010=>0001000100 [2,3,2,2,1]=>[1,2,2,3,2]=>1101010010=>0001000001 [2,3,3,1,1]=>[1,1,3,3,2]=>1110010010=>0001001011 [2,3,4,1]=>[1,4,3,2]=>1100010010=>0001001101 [2,4,1,1,2]=>[2,1,1,4,2]=>1011100010=>0001101100 [2,4,1,2,1]=>[1,2,1,4,2]=>1101100010=>0001101001 [2,4,2,1,1]=>[1,1,2,4,2]=>1110100010=>0001100011 [2,5,1,1,1]=>[1,1,1,5,2]=>1111000010=>0001110111 [2,8]=>[8,2]=>1000000010=>0001111110 [3,1,1,1,4]=>[4,1,1,1,3]=>1000111100=>0101110110 [3,1,2,1,3]=>[3,1,2,1,3]=>1001101100=>0101001010 [3,1,2,2,2]=>[2,2,2,1,3]=>1010101100=>0101000000 [3,1,2,3,1]=>[1,3,2,1,3]=>1100101100=>0101000101 [3,1,3,1,2]=>[2,1,3,1,3]=>1011001100=>0101010100 [3,1,3,2,1]=>[1,2,3,1,3]=>1101001100=>0101010001 [3,1,4,1,1]=>[1,1,4,1,3]=>1110001100=>0101011011 [3,2,1,1,3]=>[3,1,1,2,3]=>1001110100=>0100011010 [3,2,1,2,2]=>[2,2,1,2,3]=>1010110100=>0100010000 [3,2,1,3,1]=>[1,3,1,2,3]=>1100110100=>0100010101 [3,2,2,1,2]=>[2,1,2,2,3]=>1011010100=>0100000100 [3,2,2,2,1]=>[1,2,2,2,3]=>1101010100=>0100000001 [3,2,3,1,1]=>[1,1,3,2,3]=>1110010100=>0100001011 [3,3,1,1,2]=>[2,1,1,3,3]=>1011100100=>0100101100 [3,3,1,2,1]=>[1,2,1,3,3]=>1101100100=>0100101001 [3,3,2,1,1]=>[1,1,2,3,3]=>1110100100=>0100100011 [3,4,1,1,1]=>[1,1,1,4,3]=>1111000100=>0100110111 [3,7]=>[7,3]=>1000000100=>0100111110 [4,1,1,1,3]=>[3,1,1,1,4]=>1001111000=>0110111010 [4,1,1,2,2]=>[2,2,1,1,4]=>1010111000=>0110110000 [4,1,1,3,1]=>[1,3,1,1,4]=>1100111000=>0110110101 [4,1,2,1,2]=>[2,1,2,1,4]=>1011011000=>0110100100 [4,1,2,2,1]=>[1,2,2,1,4]=>1101011000=>0110100001 [4,1,3,1,1]=>[1,1,3,1,4]=>1110011000=>0110101011 [4,2,1,1,2]=>[2,1,1,2,4]=>1011101000=>0110001100 [4,2,1,2,1]=>[1,2,1,2,4]=>1101101000=>0110001001 [4,2,2,1,1]=>[1,1,2,2,4]=>1110101000=>0110000011 [4,3,1,1,1]=>[1,1,1,3,4]=>1111001000=>0110010111 [4,5,1]=>[1,5,4]=>1100001000=>0110011101 [5,1,1,1,2]=>[2,1,1,1,5]=>1011110000=>0111011100 [5,1,1,2,1]=>[1,2,1,1,5]=>1101110000=>0111011001 [5,1,2,1,1]=>[1,1,2,1,5]=>1110110000=>0111010011 [5,2,1,1,1]=>[1,1,1,2,5]=>1111010000=>0111000111 [6,1,1,1,1]=>[1,1,1,1,6]=>1111100000=>0111101111 [10]=>[10]=>1000000000=>0111111110