Identifier
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Images
=>
0=>0=>1=>[1] 1=>1=>0=>[1] 00=>01=>11=>[2] 01=>00=>10=>[1,1] 10=>11=>01=>[1,1] 11=>10=>00=>[2] 000=>010=>110=>[2,1] 001=>011=>111=>[3] 010=>000=>100=>[1,2] 011=>001=>101=>[1,1,1] 100=>110=>010=>[1,1,1] 101=>111=>011=>[1,2] 110=>100=>000=>[3] 111=>101=>001=>[2,1] 0000=>0101=>1101=>[2,1,1] 0001=>0100=>1100=>[2,2] 0010=>0111=>1111=>[4] 0011=>0110=>1110=>[3,1] 0100=>0001=>1001=>[1,2,1] 0101=>0000=>1000=>[1,3] 0110=>0011=>1011=>[1,1,2] 0111=>0010=>1010=>[1,1,1,1] 1000=>1101=>0101=>[1,1,1,1] 1001=>1100=>0100=>[1,1,2] 1010=>1111=>0111=>[1,3] 1011=>1110=>0110=>[1,2,1] 1100=>1001=>0001=>[3,1] 1101=>1000=>0000=>[4] 1110=>1011=>0011=>[2,2] 1111=>1010=>0010=>[2,1,1] 00000=>01010=>11010=>[2,1,1,1] 00001=>01011=>11011=>[2,1,2] 00010=>01000=>11000=>[2,3] 00011=>01001=>11001=>[2,2,1] 00100=>01110=>11110=>[4,1] 00101=>01111=>11111=>[5] 00110=>01100=>11100=>[3,2] 00111=>01101=>11101=>[3,1,1] 01000=>00010=>10010=>[1,2,1,1] 01001=>00011=>10011=>[1,2,2] 01010=>00000=>10000=>[1,4] 01011=>00001=>10001=>[1,3,1] 01100=>00110=>10110=>[1,1,2,1] 01101=>00111=>10111=>[1,1,3] 01110=>00100=>10100=>[1,1,1,2] 01111=>00101=>10101=>[1,1,1,1,1] 10000=>11010=>01010=>[1,1,1,1,1] 10001=>11011=>01011=>[1,1,1,2] 10010=>11000=>01000=>[1,1,3] 10011=>11001=>01001=>[1,1,2,1] 10100=>11110=>01110=>[1,3,1] 10101=>11111=>01111=>[1,4] 10110=>11100=>01100=>[1,2,2] 10111=>11101=>01101=>[1,2,1,1] 11000=>10010=>00010=>[3,1,1] 11001=>10011=>00011=>[3,2] 11010=>10000=>00000=>[5] 11011=>10001=>00001=>[4,1] 11100=>10110=>00110=>[2,2,1] 11101=>10111=>00111=>[2,3] 11110=>10100=>00100=>[2,1,2] 11111=>10101=>00101=>[2,1,1,1] 000000=>010101=>110101=>[2,1,1,1,1] 000001=>010100=>110100=>[2,1,1,2] 000010=>010111=>110111=>[2,1,3] 000011=>010110=>110110=>[2,1,2,1] 000100=>010001=>110001=>[2,3,1] 000101=>010000=>110000=>[2,4] 000110=>010011=>110011=>[2,2,2] 000111=>010010=>110010=>[2,2,1,1] 001000=>011101=>111101=>[4,1,1] 001001=>011100=>111100=>[4,2] 001010=>011111=>111111=>[6] 001011=>011110=>111110=>[5,1] 001100=>011001=>111001=>[3,2,1] 001101=>011000=>111000=>[3,3] 001110=>011011=>111011=>[3,1,2] 001111=>011010=>111010=>[3,1,1,1] 010000=>000101=>100101=>[1,2,1,1,1] 010001=>000100=>100100=>[1,2,1,2] 010010=>000111=>100111=>[1,2,3] 010011=>000110=>100110=>[1,2,2,1] 010100=>000001=>100001=>[1,4,1] 010101=>000000=>100000=>[1,5] 010110=>000011=>100011=>[1,3,2] 010111=>000010=>100010=>[1,3,1,1] 011000=>001101=>101101=>[1,1,2,1,1] 011001=>001100=>101100=>[1,1,2,2] 011010=>001111=>101111=>[1,1,4] 011011=>001110=>101110=>[1,1,3,1] 011100=>001001=>101001=>[1,1,1,2,1] 011101=>001000=>101000=>[1,1,1,3] 011110=>001011=>101011=>[1,1,1,1,2] 011111=>001010=>101010=>[1,1,1,1,1,1] 100000=>110101=>010101=>[1,1,1,1,1,1] 100001=>110100=>010100=>[1,1,1,1,2] 100010=>110111=>010111=>[1,1,1,3] 100011=>110110=>010110=>[1,1,1,2,1] 100100=>110001=>010001=>[1,1,3,1] 100101=>110000=>010000=>[1,1,4] 100110=>110011=>010011=>[1,1,2,2] 100111=>110010=>010010=>[1,1,2,1,1] 101000=>111101=>011101=>[1,3,1,1] 101001=>111100=>011100=>[1,3,2] 101010=>111111=>011111=>[1,5] 101011=>111110=>011110=>[1,4,1] 101100=>111001=>011001=>[1,2,2,1] 101101=>111000=>011000=>[1,2,3] 101110=>111011=>011011=>[1,2,1,2] 101111=>111010=>011010=>[1,2,1,1,1] 110000=>100101=>000101=>[3,1,1,1] 110001=>100100=>000100=>[3,1,2] 110010=>100111=>000111=>[3,3] 110011=>100110=>000110=>[3,2,1] 110100=>100001=>000001=>[5,1] 110101=>100000=>000000=>[6] 110110=>100011=>000011=>[4,2] 110111=>100010=>000010=>[4,1,1] 111000=>101101=>001101=>[2,2,1,1] 111001=>101100=>001100=>[2,2,2] 111010=>101111=>001111=>[2,4] 111011=>101110=>001110=>[2,3,1] 111100=>101001=>001001=>[2,1,2,1] 111101=>101000=>001000=>[2,1,3] 111110=>101011=>001011=>[2,1,1,2] 111111=>101010=>001010=>[2,1,1,1,1] 0000000=>0101010=>1101010=>[2,1,1,1,1,1] 0000001=>0101011=>1101011=>[2,1,1,1,2] 0000010=>0101000=>1101000=>[2,1,1,3] 0000011=>0101001=>1101001=>[2,1,1,2,1] 0000100=>0101110=>1101110=>[2,1,3,1] 0000101=>0101111=>1101111=>[2,1,4] 0000110=>0101100=>1101100=>[2,1,2,2] 0000111=>0101101=>1101101=>[2,1,2,1,1] 0001000=>0100010=>1100010=>[2,3,1,1] 0001001=>0100011=>1100011=>[2,3,2] 0001010=>0100000=>1100000=>[2,5] 0001011=>0100001=>1100001=>[2,4,1] 0001100=>0100110=>1100110=>[2,2,2,1] 0001101=>0100111=>1100111=>[2,2,3] 0001110=>0100100=>1100100=>[2,2,1,2] 0001111=>0100101=>1100101=>[2,2,1,1,1] 0010000=>0111010=>1111010=>[4,1,1,1] 0010001=>0111011=>1111011=>[4,1,2] 0010010=>0111000=>1111000=>[4,3] 0010011=>0111001=>1111001=>[4,2,1] 0010100=>0111110=>1111110=>[6,1] 0010101=>0111111=>1111111=>[7] 0010110=>0111100=>1111100=>[5,2] 0010111=>0111101=>1111101=>[5,1,1] 0011000=>0110010=>1110010=>[3,2,1,1] 0011001=>0110011=>1110011=>[3,2,2] 0011010=>0110000=>1110000=>[3,4] 0011011=>0110001=>1110001=>[3,3,1] 0011100=>0110110=>1110110=>[3,1,2,1] 0011101=>0110111=>1110111=>[3,1,3] 0011110=>0110100=>1110100=>[3,1,1,2] 0011111=>0110101=>1110101=>[3,1,1,1,1] 0100000=>0001010=>1001010=>[1,2,1,1,1,1] 0100001=>0001011=>1001011=>[1,2,1,1,2] 0100010=>0001000=>1001000=>[1,2,1,3] 0100011=>0001001=>1001001=>[1,2,1,2,1] 0100100=>0001110=>1001110=>[1,2,3,1] 0100101=>0001111=>1001111=>[1,2,4] 0100110=>0001100=>1001100=>[1,2,2,2] 0100111=>0001101=>1001101=>[1,2,2,1,1] 0101000=>0000010=>1000010=>[1,4,1,1] 0101001=>0000011=>1000011=>[1,4,2] 0101010=>0000000=>1000000=>[1,6] 0101011=>0000001=>1000001=>[1,5,1] 0101100=>0000110=>1000110=>[1,3,2,1] 0101101=>0000111=>1000111=>[1,3,3] 0101110=>0000100=>1000100=>[1,3,1,2] 0101111=>0000101=>1000101=>[1,3,1,1,1] 0110000=>0011010=>1011010=>[1,1,2,1,1,1] 0110001=>0011011=>1011011=>[1,1,2,1,2] 0110010=>0011000=>1011000=>[1,1,2,3] 0110011=>0011001=>1011001=>[1,1,2,2,1] 0110100=>0011110=>1011110=>[1,1,4,1] 0110101=>0011111=>1011111=>[1,1,5] 0110110=>0011100=>1011100=>[1,1,3,2] 0110111=>0011101=>1011101=>[1,1,3,1,1] 0111000=>0010010=>1010010=>[1,1,1,2,1,1] 0111001=>0010011=>1010011=>[1,1,1,2,2] 0111010=>0010000=>1010000=>[1,1,1,4] 0111011=>0010001=>1010001=>[1,1,1,3,1] 0111100=>0010110=>1010110=>[1,1,1,1,2,1] 0111101=>0010111=>1010111=>[1,1,1,1,3] 0111110=>0010100=>1010100=>[1,1,1,1,1,2] 0111111=>0010101=>1010101=>[1,1,1,1,1,1,1] 1000000=>1101010=>0101010=>[1,1,1,1,1,1,1] 1000001=>1101011=>0101011=>[1,1,1,1,1,2] 1000010=>1101000=>0101000=>[1,1,1,1,3] 1000011=>1101001=>0101001=>[1,1,1,1,2,1] 1000100=>1101110=>0101110=>[1,1,1,3,1] 1000101=>1101111=>0101111=>[1,1,1,4] 1000110=>1101100=>0101100=>[1,1,1,2,2] 1000111=>1101101=>0101101=>[1,1,1,2,1,1] 1001000=>1100010=>0100010=>[1,1,3,1,1] 1001001=>1100011=>0100011=>[1,1,3,2] 1001010=>1100000=>0100000=>[1,1,5] 1001011=>1100001=>0100001=>[1,1,4,1] 1001100=>1100110=>0100110=>[1,1,2,2,1] 1001101=>1100111=>0100111=>[1,1,2,3] 1001110=>1100100=>0100100=>[1,1,2,1,2] 1001111=>1100101=>0100101=>[1,1,2,1,1,1] 1010000=>1111010=>0111010=>[1,3,1,1,1] 1010001=>1111011=>0111011=>[1,3,1,2] 1010010=>1111000=>0111000=>[1,3,3] 1010011=>1111001=>0111001=>[1,3,2,1] 1010100=>1111110=>0111110=>[1,5,1] 1010101=>1111111=>0111111=>[1,6] 1010110=>1111100=>0111100=>[1,4,2] 1010111=>1111101=>0111101=>[1,4,1,1] 1011000=>1110010=>0110010=>[1,2,2,1,1] 1011001=>1110011=>0110011=>[1,2,2,2] 1011010=>1110000=>0110000=>[1,2,4] 1011011=>1110001=>0110001=>[1,2,3,1] 1011100=>1110110=>0110110=>[1,2,1,2,1] 1011101=>1110111=>0110111=>[1,2,1,3] 1011110=>1110100=>0110100=>[1,2,1,1,2] 1011111=>1110101=>0110101=>[1,2,1,1,1,1] 1100000=>1001010=>0001010=>[3,1,1,1,1] 1100001=>1001011=>0001011=>[3,1,1,2] 1100010=>1001000=>0001000=>[3,1,3] 1100011=>1001001=>0001001=>[3,1,2,1] 1100100=>1001110=>0001110=>[3,3,1] 1100101=>1001111=>0001111=>[3,4] 1100110=>1001100=>0001100=>[3,2,2] 1100111=>1001101=>0001101=>[3,2,1,1] 1101000=>1000010=>0000010=>[5,1,1] 1101001=>1000011=>0000011=>[5,2] 1101010=>1000000=>0000000=>[7] 1101011=>1000001=>0000001=>[6,1] 1101100=>1000110=>0000110=>[4,2,1] 1101101=>1000111=>0000111=>[4,3] 1101110=>1000100=>0000100=>[4,1,2] 1101111=>1000101=>0000101=>[4,1,1,1] 1110000=>1011010=>0011010=>[2,2,1,1,1] 1110001=>1011011=>0011011=>[2,2,1,2] 1110010=>1011000=>0011000=>[2,2,3] 1110011=>1011001=>0011001=>[2,2,2,1] 1110100=>1011110=>0011110=>[2,4,1] 1110101=>1011111=>0011111=>[2,5] 1110110=>1011100=>0011100=>[2,3,2] 1110111=>1011101=>0011101=>[2,3,1,1] 1111000=>1010010=>0010010=>[2,1,2,1,1] 1111001=>1010011=>0010011=>[2,1,2,2] 1111010=>1010000=>0010000=>[2,1,4] 1111011=>1010001=>0010001=>[2,1,3,1] 1111100=>1010110=>0010110=>[2,1,1,2,1] 1111101=>1010111=>0010111=>[2,1,1,3] 1111110=>1010100=>0010100=>[2,1,1,1,2] 1111111=>1010101=>0010101=>[2,1,1,1,1,1] 00000000=>01010101=>11010101=>[2,1,1,1,1,1,1] 00000001=>01010100=>11010100=>[2,1,1,1,1,2] 00000010=>01010111=>11010111=>[2,1,1,1,3] 00000011=>01010110=>11010110=>[2,1,1,1,2,1] 00000100=>01010001=>11010001=>[2,1,1,3,1] 00000101=>01010000=>11010000=>[2,1,1,4] 00000110=>01010011=>11010011=>[2,1,1,2,2] 00000111=>01010010=>11010010=>[2,1,1,2,1,1] 00001000=>01011101=>11011101=>[2,1,3,1,1] 00001001=>01011100=>11011100=>[2,1,3,2] 00001010=>01011111=>11011111=>[2,1,5] 00001011=>01011110=>11011110=>[2,1,4,1] 00001100=>01011001=>11011001=>[2,1,2,2,1] 00001101=>01011000=>11011000=>[2,1,2,3] 00001110=>01011011=>11011011=>[2,1,2,1,2] 00001111=>01011010=>11011010=>[2,1,2,1,1,1] 00010000=>01000101=>11000101=>[2,3,1,1,1] 00010001=>01000100=>11000100=>[2,3,1,2] 00010010=>01000111=>11000111=>[2,3,3] 00010011=>01000110=>11000110=>[2,3,2,1] 00010100=>01000001=>11000001=>[2,5,1] 00010101=>01000000=>11000000=>[2,6] 00010110=>01000011=>11000011=>[2,4,2] 00010111=>01000010=>11000010=>[2,4,1,1] 00011000=>01001101=>11001101=>[2,2,2,1,1] 00011001=>01001100=>11001100=>[2,2,2,2] 00011010=>01001111=>11001111=>[2,2,4] 00011011=>01001110=>11001110=>[2,2,3,1] 00011100=>01001001=>11001001=>[2,2,1,2,1] 00011101=>01001000=>11001000=>[2,2,1,3] 00011110=>01001011=>11001011=>[2,2,1,1,2] 00011111=>01001010=>11001010=>[2,2,1,1,1,1] 00100000=>01110101=>11110101=>[4,1,1,1,1] 00100001=>01110100=>11110100=>[4,1,1,2] 00100010=>01110111=>11110111=>[4,1,3] 00100011=>01110110=>11110110=>[4,1,2,1] 00100100=>01110001=>11110001=>[4,3,1] 00100101=>01110000=>11110000=>[4,4] 00100110=>01110011=>11110011=>[4,2,2] 00100111=>01110010=>11110010=>[4,2,1,1] 00101000=>01111101=>11111101=>[6,1,1] 00101001=>01111100=>11111100=>[6,2] 00101010=>01111111=>11111111=>[8] 00101011=>01111110=>11111110=>[7,1] 00101100=>01111001=>11111001=>[5,2,1] 00101101=>01111000=>11111000=>[5,3] 00101110=>01111011=>11111011=>[5,1,2] 00101111=>01111010=>11111010=>[5,1,1,1] 00110000=>01100101=>11100101=>[3,2,1,1,1] 00110001=>01100100=>11100100=>[3,2,1,2] 00110010=>01100111=>11100111=>[3,2,3] 00110011=>01100110=>11100110=>[3,2,2,1] 00110100=>01100001=>11100001=>[3,4,1] 00110101=>01100000=>11100000=>[3,5] 00110110=>01100011=>11100011=>[3,3,2] 00110111=>01100010=>11100010=>[3,3,1,1] 00111000=>01101101=>11101101=>[3,1,2,1,1] 00111001=>01101100=>11101100=>[3,1,2,2] 00111010=>01101111=>11101111=>[3,1,4] 00111011=>01101110=>11101110=>[3,1,3,1] 00111100=>01101001=>11101001=>[3,1,1,2,1] 00111101=>01101000=>11101000=>[3,1,1,3] 00111110=>01101011=>11101011=>[3,1,1,1,2] 00111111=>01101010=>11101010=>[3,1,1,1,1,1] 01000000=>00010101=>10010101=>[1,2,1,1,1,1,1] 01000001=>00010100=>10010100=>[1,2,1,1,1,2] 01000010=>00010111=>10010111=>[1,2,1,1,3] 01000011=>00010110=>10010110=>[1,2,1,1,2,1] 01000100=>00010001=>10010001=>[1,2,1,3,1] 01000101=>00010000=>10010000=>[1,2,1,4] 01000110=>00010011=>10010011=>[1,2,1,2,2] 01000111=>00010010=>10010010=>[1,2,1,2,1,1] 01001000=>00011101=>10011101=>[1,2,3,1,1] 01001001=>00011100=>10011100=>[1,2,3,2] 01001010=>00011111=>10011111=>[1,2,5] 01001011=>00011110=>10011110=>[1,2,4,1] 01001100=>00011001=>10011001=>[1,2,2,2,1] 01001101=>00011000=>10011000=>[1,2,2,3] 01001110=>00011011=>10011011=>[1,2,2,1,2] 01001111=>00011010=>10011010=>[1,2,2,1,1,1] 01010000=>00000101=>10000101=>[1,4,1,1,1] 01010001=>00000100=>10000100=>[1,4,1,2] 01010010=>00000111=>10000111=>[1,4,3] 01010011=>00000110=>10000110=>[1,4,2,1] 01010100=>00000001=>10000001=>[1,6,1] 01010101=>00000000=>10000000=>[1,7] 01010110=>00000011=>10000011=>[1,5,2] 01010111=>00000010=>10000010=>[1,5,1,1] 01011000=>00001101=>10001101=>[1,3,2,1,1] 01011001=>00001100=>10001100=>[1,3,2,2] 01011010=>00001111=>10001111=>[1,3,4] 01011011=>00001110=>10001110=>[1,3,3,1] 01011100=>00001001=>10001001=>[1,3,1,2,1] 01011101=>00001000=>10001000=>[1,3,1,3] 01011110=>00001011=>10001011=>[1,3,1,1,2] 01011111=>00001010=>10001010=>[1,3,1,1,1,1] 01100000=>00110101=>10110101=>[1,1,2,1,1,1,1] 01100001=>00110100=>10110100=>[1,1,2,1,1,2] 01100010=>00110111=>10110111=>[1,1,2,1,3] 01100011=>00110110=>10110110=>[1,1,2,1,2,1] 01100100=>00110001=>10110001=>[1,1,2,3,1] 01100101=>00110000=>10110000=>[1,1,2,4] 01100110=>00110011=>10110011=>[1,1,2,2,2] 01100111=>00110010=>10110010=>[1,1,2,2,1,1] 01101000=>00111101=>10111101=>[1,1,4,1,1] 01101001=>00111100=>10111100=>[1,1,4,2] 01101010=>00111111=>10111111=>[1,1,6] 01101011=>00111110=>10111110=>[1,1,5,1] 01101100=>00111001=>10111001=>[1,1,3,2,1] 01101101=>00111000=>10111000=>[1,1,3,3] 01101110=>00111011=>10111011=>[1,1,3,1,2] 01101111=>00111010=>10111010=>[1,1,3,1,1,1] 01110000=>00100101=>10100101=>[1,1,1,2,1,1,1] 01110001=>00100100=>10100100=>[1,1,1,2,1,2] 01110010=>00100111=>10100111=>[1,1,1,2,3] 01110011=>00100110=>10100110=>[1,1,1,2,2,1] 01110100=>00100001=>10100001=>[1,1,1,4,1] 01110101=>00100000=>10100000=>[1,1,1,5] 01110110=>00100011=>10100011=>[1,1,1,3,2] 01110111=>00100010=>10100010=>[1,1,1,3,1,1] 01111000=>00101101=>10101101=>[1,1,1,1,2,1,1] 01111001=>00101100=>10101100=>[1,1,1,1,2,2] 01111010=>00101111=>10101111=>[1,1,1,1,4] 01111011=>00101110=>10101110=>[1,1,1,1,3,1] 01111100=>00101001=>10101001=>[1,1,1,1,1,2,1] 01111101=>00101000=>10101000=>[1,1,1,1,1,3] 01111110=>00101011=>10101011=>[1,1,1,1,1,1,2] 01111111=>00101010=>10101010=>[1,1,1,1,1,1,1,1] 10000000=>11010101=>01010101=>[1,1,1,1,1,1,1,1] 10000001=>11010100=>01010100=>[1,1,1,1,1,1,2] 10000010=>11010111=>01010111=>[1,1,1,1,1,3] 10000011=>11010110=>01010110=>[1,1,1,1,1,2,1] 10000100=>11010001=>01010001=>[1,1,1,1,3,1] 10000101=>11010000=>01010000=>[1,1,1,1,4] 10000110=>11010011=>01010011=>[1,1,1,1,2,2] 10000111=>11010010=>01010010=>[1,1,1,1,2,1,1] 10001000=>11011101=>01011101=>[1,1,1,3,1,1] 10001001=>11011100=>01011100=>[1,1,1,3,2] 10001010=>11011111=>01011111=>[1,1,1,5] 10001011=>11011110=>01011110=>[1,1,1,4,1] 10001100=>11011001=>01011001=>[1,1,1,2,2,1] 10001101=>11011000=>01011000=>[1,1,1,2,3] 10001110=>11011011=>01011011=>[1,1,1,2,1,2] 10001111=>11011010=>01011010=>[1,1,1,2,1,1,1] 10010000=>11000101=>01000101=>[1,1,3,1,1,1] 10010001=>11000100=>01000100=>[1,1,3,1,2] 10010010=>11000111=>01000111=>[1,1,3,3] 10010011=>11000110=>01000110=>[1,1,3,2,1] 10010100=>11000001=>01000001=>[1,1,5,1] 10010101=>11000000=>01000000=>[1,1,6] 10010110=>11000011=>01000011=>[1,1,4,2] 10010111=>11000010=>01000010=>[1,1,4,1,1] 10011000=>11001101=>01001101=>[1,1,2,2,1,1] 10011001=>11001100=>01001100=>[1,1,2,2,2] 10011010=>11001111=>01001111=>[1,1,2,4] 10011011=>11001110=>01001110=>[1,1,2,3,1] 10011100=>11001001=>01001001=>[1,1,2,1,2,1] 10011101=>11001000=>01001000=>[1,1,2,1,3] 10011110=>11001011=>01001011=>[1,1,2,1,1,2] 10011111=>11001010=>01001010=>[1,1,2,1,1,1,1] 10100000=>11110101=>01110101=>[1,3,1,1,1,1] 10100001=>11110100=>01110100=>[1,3,1,1,2] 10100010=>11110111=>01110111=>[1,3,1,3] 10100011=>11110110=>01110110=>[1,3,1,2,1] 10100100=>11110001=>01110001=>[1,3,3,1] 10100101=>11110000=>01110000=>[1,3,4] 10100110=>11110011=>01110011=>[1,3,2,2] 10100111=>11110010=>01110010=>[1,3,2,1,1] 10101000=>11111101=>01111101=>[1,5,1,1] 10101001=>11111100=>01111100=>[1,5,2] 10101010=>11111111=>01111111=>[1,7] 10101011=>11111110=>01111110=>[1,6,1] 10101100=>11111001=>01111001=>[1,4,2,1] 10101101=>11111000=>01111000=>[1,4,3] 10101110=>11111011=>01111011=>[1,4,1,2] 10101111=>11111010=>01111010=>[1,4,1,1,1] 10110000=>11100101=>01100101=>[1,2,2,1,1,1] 10110001=>11100100=>01100100=>[1,2,2,1,2] 10110010=>11100111=>01100111=>[1,2,2,3] 10110011=>11100110=>01100110=>[1,2,2,2,1] 10110100=>11100001=>01100001=>[1,2,4,1] 10110101=>11100000=>01100000=>[1,2,5] 10110110=>11100011=>01100011=>[1,2,3,2] 10110111=>11100010=>01100010=>[1,2,3,1,1] 10111000=>11101101=>01101101=>[1,2,1,2,1,1] 10111001=>11101100=>01101100=>[1,2,1,2,2] 10111010=>11101111=>01101111=>[1,2,1,4] 10111011=>11101110=>01101110=>[1,2,1,3,1] 10111100=>11101001=>01101001=>[1,2,1,1,2,1] 10111101=>11101000=>01101000=>[1,2,1,1,3] 10111110=>11101011=>01101011=>[1,2,1,1,1,2] 10111111=>11101010=>01101010=>[1,2,1,1,1,1,1] 11000000=>10010101=>00010101=>[3,1,1,1,1,1] 11000001=>10010100=>00010100=>[3,1,1,1,2] 11000010=>10010111=>00010111=>[3,1,1,3] 11000011=>10010110=>00010110=>[3,1,1,2,1] 11000100=>10010001=>00010001=>[3,1,3,1] 11000101=>10010000=>00010000=>[3,1,4] 11000110=>10010011=>00010011=>[3,1,2,2] 11000111=>10010010=>00010010=>[3,1,2,1,1] 11001000=>10011101=>00011101=>[3,3,1,1] 11001001=>10011100=>00011100=>[3,3,2] 11001010=>10011111=>00011111=>[3,5] 11001011=>10011110=>00011110=>[3,4,1] 11001100=>10011001=>00011001=>[3,2,2,1] 11001101=>10011000=>00011000=>[3,2,3] 11001110=>10011011=>00011011=>[3,2,1,2] 11001111=>10011010=>00011010=>[3,2,1,1,1] 11010000=>10000101=>00000101=>[5,1,1,1] 11010001=>10000100=>00000100=>[5,1,2] 11010010=>10000111=>00000111=>[5,3] 11010011=>10000110=>00000110=>[5,2,1] 11010100=>10000001=>00000001=>[7,1] 11010101=>10000000=>00000000=>[8] 11010110=>10000011=>00000011=>[6,2] 11010111=>10000010=>00000010=>[6,1,1] 11011000=>10001101=>00001101=>[4,2,1,1] 11011001=>10001100=>00001100=>[4,2,2] 11011010=>10001111=>00001111=>[4,4] 11011011=>10001110=>00001110=>[4,3,1] 11011100=>10001001=>00001001=>[4,1,2,1] 11011101=>10001000=>00001000=>[4,1,3] 11011110=>10001011=>00001011=>[4,1,1,2] 11011111=>10001010=>00001010=>[4,1,1,1,1] 11100000=>10110101=>00110101=>[2,2,1,1,1,1] 11100001=>10110100=>00110100=>[2,2,1,1,2] 11100010=>10110111=>00110111=>[2,2,1,3] 11100011=>10110110=>00110110=>[2,2,1,2,1] 11100100=>10110001=>00110001=>[2,2,3,1] 11100101=>10110000=>00110000=>[2,2,4] 11100110=>10110011=>00110011=>[2,2,2,2] 11100111=>10110010=>00110010=>[2,2,2,1,1] 11101000=>10111101=>00111101=>[2,4,1,1] 11101001=>10111100=>00111100=>[2,4,2] 11101010=>10111111=>00111111=>[2,6] 11101011=>10111110=>00111110=>[2,5,1] 11101100=>10111001=>00111001=>[2,3,2,1] 11101101=>10111000=>00111000=>[2,3,3] 11101110=>10111011=>00111011=>[2,3,1,2] 11101111=>10111010=>00111010=>[2,3,1,1,1] 11110000=>10100101=>00100101=>[2,1,2,1,1,1] 11110001=>10100100=>00100100=>[2,1,2,1,2] 11110010=>10100111=>00100111=>[2,1,2,3] 11110011=>10100110=>00100110=>[2,1,2,2,1] 11110100=>10100001=>00100001=>[2,1,4,1] 11110101=>10100000=>00100000=>[2,1,5] 11110110=>10100011=>00100011=>[2,1,3,2] 11110111=>10100010=>00100010=>[2,1,3,1,1] 11111000=>10101101=>00101101=>[2,1,1,2,1,1] 11111001=>10101100=>00101100=>[2,1,1,2,2] 11111010=>10101111=>00101111=>[2,1,1,4] 11111011=>10101110=>00101110=>[2,1,1,3,1] 11111100=>10101001=>00101001=>[2,1,1,1,2,1] 11111101=>10101000=>00101000=>[2,1,1,1,3] 11111110=>10101011=>00101011=>[2,1,1,1,1,2] 11111111=>10101010=>00101010=>[2,1,1,1,1,1,1] 000000000=>010101010=>110101010=>[2,1,1,1,1,1,1,1] 000000001=>010101011=>110101011=>[2,1,1,1,1,1,2] 000000010=>010101000=>110101000=>[2,1,1,1,1,3] 000000011=>010101001=>110101001=>[2,1,1,1,1,2,1] 000000100=>010101110=>110101110=>[2,1,1,1,3,1] 000000101=>010101111=>110101111=>[2,1,1,1,4] 000000110=>010101100=>110101100=>[2,1,1,1,2,2] 000000111=>010101101=>110101101=>[2,1,1,1,2,1,1] 000001000=>010100010=>110100010=>[2,1,1,3,1,1] 000001001=>010100011=>110100011=>[2,1,1,3,2] 000001010=>010100000=>110100000=>[2,1,1,5] 000001011=>010100001=>110100001=>[2,1,1,4,1] 000001100=>010100110=>110100110=>[2,1,1,2,2,1] 000001101=>010100111=>110100111=>[2,1,1,2,3] 000001110=>010100100=>110100100=>[2,1,1,2,1,2] 000001111=>010100101=>110100101=>[2,1,1,2,1,1,1] 000010000=>010111010=>110111010=>[2,1,3,1,1,1] 000010001=>010111011=>110111011=>[2,1,3,1,2] 000010010=>010111000=>110111000=>[2,1,3,3] 000010011=>010111001=>110111001=>[2,1,3,2,1] 000010100=>010111110=>110111110=>[2,1,5,1] 000010101=>010111111=>110111111=>[2,1,6] 000010110=>010111100=>110111100=>[2,1,4,2] 000010111=>010111101=>110111101=>[2,1,4,1,1] 000011000=>010110010=>110110010=>[2,1,2,2,1,1] 000011001=>010110011=>110110011=>[2,1,2,2,2] 000011010=>010110000=>110110000=>[2,1,2,4] 000011011=>010110001=>110110001=>[2,1,2,3,1] 000011100=>010110110=>110110110=>[2,1,2,1,2,1] 000011101=>010110111=>110110111=>[2,1,2,1,3] 000011110=>010110100=>110110100=>[2,1,2,1,1,2] 000011111=>010110101=>110110101=>[2,1,2,1,1,1,1] 000100000=>010001010=>110001010=>[2,3,1,1,1,1] 000100001=>010001011=>110001011=>[2,3,1,1,2] 000100010=>010001000=>110001000=>[2,3,1,3] 000100011=>010001001=>110001001=>[2,3,1,2,1] 000100100=>010001110=>110001110=>[2,3,3,1] 000100101=>010001111=>110001111=>[2,3,4] 000100110=>010001100=>110001100=>[2,3,2,2] 000100111=>010001101=>110001101=>[2,3,2,1,1] 000101000=>010000010=>110000010=>[2,5,1,1] 000101001=>010000011=>110000011=>[2,5,2] 000101010=>010000000=>110000000=>[2,7] 000101011=>010000001=>110000001=>[2,6,1] 000101100=>010000110=>110000110=>[2,4,2,1] 000101101=>010000111=>110000111=>[2,4,3] 000101110=>010000100=>110000100=>[2,4,1,2] 000101111=>010000101=>110000101=>[2,4,1,1,1] 000110000=>010011010=>110011010=>[2,2,2,1,1,1] 000110001=>010011011=>110011011=>[2,2,2,1,2] 000110010=>010011000=>110011000=>[2,2,2,3] 000110011=>010011001=>110011001=>[2,2,2,2,1] 000110100=>010011110=>110011110=>[2,2,4,1] 000110101=>010011111=>110011111=>[2,2,5] 000110110=>010011100=>110011100=>[2,2,3,2] 000110111=>010011101=>110011101=>[2,2,3,1,1] 000111000=>010010010=>110010010=>[2,2,1,2,1,1] 000111001=>010010011=>110010011=>[2,2,1,2,2] 000111010=>010010000=>110010000=>[2,2,1,4] 000111011=>010010001=>110010001=>[2,2,1,3,1] 000111100=>010010110=>110010110=>[2,2,1,1,2,1] 000111101=>010010111=>110010111=>[2,2,1,1,3] 000111110=>010010100=>110010100=>[2,2,1,1,1,2] 000111111=>010010101=>110010101=>[2,2,1,1,1,1,1] 001000000=>011101010=>111101010=>[4,1,1,1,1,1] 001000001=>011101011=>111101011=>[4,1,1,1,2] 001000010=>011101000=>111101000=>[4,1,1,3] 001000011=>011101001=>111101001=>[4,1,1,2,1] 001000100=>011101110=>111101110=>[4,1,3,1] 001000101=>011101111=>111101111=>[4,1,4] 001000110=>011101100=>111101100=>[4,1,2,2] 001000111=>011101101=>111101101=>[4,1,2,1,1] 001001000=>011100010=>111100010=>[4,3,1,1] 001001001=>011100011=>111100011=>[4,3,2] 001001010=>011100000=>111100000=>[4,5] 001001011=>011100001=>111100001=>[4,4,1] 001001100=>011100110=>111100110=>[4,2,2,1] 001001101=>011100111=>111100111=>[4,2,3] 001001110=>011100100=>111100100=>[4,2,1,2] 001001111=>011100101=>111100101=>[4,2,1,1,1] 001010000=>011111010=>111111010=>[6,1,1,1] 001010001=>011111011=>111111011=>[6,1,2] 001010010=>011111000=>111111000=>[6,3] 001010011=>011111001=>111111001=>[6,2,1] 001010100=>011111110=>111111110=>[8,1] 001010101=>011111111=>111111111=>[9] 001010110=>011111100=>111111100=>[7,2] 001010111=>011111101=>111111101=>[7,1,1] 001011000=>011110010=>111110010=>[5,2,1,1] 001011001=>011110011=>111110011=>[5,2,2] 001011010=>011110000=>111110000=>[5,4] 001011011=>011110001=>111110001=>[5,3,1] 001011100=>011110110=>111110110=>[5,1,2,1] 001011101=>011110111=>111110111=>[5,1,3] 001011110=>011110100=>111110100=>[5,1,1,2] 001011111=>011110101=>111110101=>[5,1,1,1,1] 001100000=>011001010=>111001010=>[3,2,1,1,1,1] 001100001=>011001011=>111001011=>[3,2,1,1,2] 001100010=>011001000=>111001000=>[3,2,1,3] 001100011=>011001001=>111001001=>[3,2,1,2,1] 001100100=>011001110=>111001110=>[3,2,3,1] 001100101=>011001111=>111001111=>[3,2,4] 001100110=>011001100=>111001100=>[3,2,2,2] 001100111=>011001101=>111001101=>[3,2,2,1,1] 001101000=>011000010=>111000010=>[3,4,1,1] 001101001=>011000011=>111000011=>[3,4,2] 001101010=>011000000=>111000000=>[3,6] 001101011=>011000001=>111000001=>[3,5,1] 001101100=>011000110=>111000110=>[3,3,2,1] 001101101=>011000111=>111000111=>[3,3,3] 001101110=>011000100=>111000100=>[3,3,1,2] 001101111=>011000101=>111000101=>[3,3,1,1,1] 001110000=>011011010=>111011010=>[3,1,2,1,1,1] 001110001=>011011011=>111011011=>[3,1,2,1,2] 001110010=>011011000=>111011000=>[3,1,2,3] 001110011=>011011001=>111011001=>[3,1,2,2,1] 001110100=>011011110=>111011110=>[3,1,4,1] 001110101=>011011111=>111011111=>[3,1,5] 001110110=>011011100=>111011100=>[3,1,3,2] 001110111=>011011101=>111011101=>[3,1,3,1,1] 001111000=>011010010=>111010010=>[3,1,1,2,1,1] 001111001=>011010011=>111010011=>[3,1,1,2,2] 001111010=>011010000=>111010000=>[3,1,1,4] 001111011=>011010001=>111010001=>[3,1,1,3,1] 001111100=>011010110=>111010110=>[3,1,1,1,2,1] 001111101=>011010111=>111010111=>[3,1,1,1,3] 001111110=>011010100=>111010100=>[3,1,1,1,1,2] 001111111=>011010101=>111010101=>[3,1,1,1,1,1,1] 010000000=>000101010=>100101010=>[1,2,1,1,1,1,1,1] 010000001=>000101011=>100101011=>[1,2,1,1,1,1,2] 010000010=>000101000=>100101000=>[1,2,1,1,1,3] 010000011=>000101001=>100101001=>[1,2,1,1,1,2,1] 010000100=>000101110=>100101110=>[1,2,1,1,3,1] 010000101=>000101111=>100101111=>[1,2,1,1,4] 010000110=>000101100=>100101100=>[1,2,1,1,2,2] 010000111=>000101101=>100101101=>[1,2,1,1,2,1,1] 010001000=>000100010=>100100010=>[1,2,1,3,1,1] 010001001=>000100011=>100100011=>[1,2,1,3,2] 010001010=>000100000=>100100000=>[1,2,1,5] 010001011=>000100001=>100100001=>[1,2,1,4,1] 010001100=>000100110=>100100110=>[1,2,1,2,2,1] 010001101=>000100111=>100100111=>[1,2,1,2,3] 010001110=>000100100=>100100100=>[1,2,1,2,1,2] 010001111=>000100101=>100100101=>[1,2,1,2,1,1,1] 010010000=>000111010=>100111010=>[1,2,3,1,1,1] 010010001=>000111011=>100111011=>[1,2,3,1,2] 010010010=>000111000=>100111000=>[1,2,3,3] 010010011=>000111001=>100111001=>[1,2,3,2,1] 010010100=>000111110=>100111110=>[1,2,5,1] 010010101=>000111111=>100111111=>[1,2,6] 010010110=>000111100=>100111100=>[1,2,4,2] 010010111=>000111101=>100111101=>[1,2,4,1,1] 010011000=>000110010=>100110010=>[1,2,2,2,1,1] 010011001=>000110011=>100110011=>[1,2,2,2,2] 010011010=>000110000=>100110000=>[1,2,2,4] 010011011=>000110001=>100110001=>[1,2,2,3,1] 010011100=>000110110=>100110110=>[1,2,2,1,2,1] 010011101=>000110111=>100110111=>[1,2,2,1,3] 010011110=>000110100=>100110100=>[1,2,2,1,1,2] 010011111=>000110101=>100110101=>[1,2,2,1,1,1,1] 010100000=>000001010=>100001010=>[1,4,1,1,1,1] 010100001=>000001011=>100001011=>[1,4,1,1,2] 010100010=>000001000=>100001000=>[1,4,1,3] 010100011=>000001001=>100001001=>[1,4,1,2,1] 010100100=>000001110=>100001110=>[1,4,3,1] 010100101=>000001111=>100001111=>[1,4,4] 010100110=>000001100=>100001100=>[1,4,2,2] 010100111=>000001101=>100001101=>[1,4,2,1,1] 010101000=>000000010=>100000010=>[1,6,1,1] 010101001=>000000011=>100000011=>[1,6,2] 010101010=>000000000=>100000000=>[1,8] 010101011=>000000001=>100000001=>[1,7,1] 010101100=>000000110=>100000110=>[1,5,2,1] 010101101=>000000111=>100000111=>[1,5,3] 010101110=>000000100=>100000100=>[1,5,1,2] 010101111=>000000101=>100000101=>[1,5,1,1,1] 010110000=>000011010=>100011010=>[1,3,2,1,1,1] 010110001=>000011011=>100011011=>[1,3,2,1,2] 010110010=>000011000=>100011000=>[1,3,2,3] 010110011=>000011001=>100011001=>[1,3,2,2,1] 010110100=>000011110=>100011110=>[1,3,4,1] 010110101=>000011111=>100011111=>[1,3,5] 010110110=>000011100=>100011100=>[1,3,3,2] 010110111=>000011101=>100011101=>[1,3,3,1,1] 010111000=>000010010=>100010010=>[1,3,1,2,1,1] 010111001=>000010011=>100010011=>[1,3,1,2,2] 010111010=>000010000=>100010000=>[1,3,1,4] 010111011=>000010001=>100010001=>[1,3,1,3,1] 010111100=>000010110=>100010110=>[1,3,1,1,2,1] 010111101=>000010111=>100010111=>[1,3,1,1,3] 010111110=>000010100=>100010100=>[1,3,1,1,1,2] 010111111=>000010101=>100010101=>[1,3,1,1,1,1,1] 011000000=>001101010=>101101010=>[1,1,2,1,1,1,1,1] 011000001=>001101011=>101101011=>[1,1,2,1,1,1,2] 011000010=>001101000=>101101000=>[1,1,2,1,1,3] 011000011=>001101001=>101101001=>[1,1,2,1,1,2,1] 011000100=>001101110=>101101110=>[1,1,2,1,3,1] 011000101=>001101111=>101101111=>[1,1,2,1,4] 011000110=>001101100=>101101100=>[1,1,2,1,2,2] 011000111=>001101101=>101101101=>[1,1,2,1,2,1,1] 011001000=>001100010=>101100010=>[1,1,2,3,1,1] 011001001=>001100011=>101100011=>[1,1,2,3,2] 011001010=>001100000=>101100000=>[1,1,2,5] 011001011=>001100001=>101100001=>[1,1,2,4,1] 011001100=>001100110=>101100110=>[1,1,2,2,2,1] 011001101=>001100111=>101100111=>[1,1,2,2,3] 011001110=>001100100=>101100100=>[1,1,2,2,1,2] 011001111=>001100101=>101100101=>[1,1,2,2,1,1,1] 011010000=>001111010=>101111010=>[1,1,4,1,1,1] 011010001=>001111011=>101111011=>[1,1,4,1,2] 011010010=>001111000=>101111000=>[1,1,4,3] 011010011=>001111001=>101111001=>[1,1,4,2,1] 011010100=>001111110=>101111110=>[1,1,6,1] 011010101=>001111111=>101111111=>[1,1,7] 011010110=>001111100=>101111100=>[1,1,5,2] 011010111=>001111101=>101111101=>[1,1,5,1,1] 011011000=>001110010=>101110010=>[1,1,3,2,1,1] 011011001=>001110011=>101110011=>[1,1,3,2,2] 011011010=>001110000=>101110000=>[1,1,3,4] 011011011=>001110001=>101110001=>[1,1,3,3,1] 011011100=>001110110=>101110110=>[1,1,3,1,2,1] 011011101=>001110111=>101110111=>[1,1,3,1,3] 011011110=>001110100=>101110100=>[1,1,3,1,1,2] 011011111=>001110101=>101110101=>[1,1,3,1,1,1,1] 011100000=>001001010=>101001010=>[1,1,1,2,1,1,1,1] 011100001=>001001011=>101001011=>[1,1,1,2,1,1,2] 011100010=>001001000=>101001000=>[1,1,1,2,1,3] 011100011=>001001001=>101001001=>[1,1,1,2,1,2,1] 011100100=>001001110=>101001110=>[1,1,1,2,3,1] 011100101=>001001111=>101001111=>[1,1,1,2,4] 011100110=>001001100=>101001100=>[1,1,1,2,2,2] 011100111=>001001101=>101001101=>[1,1,1,2,2,1,1] 011101000=>001000010=>101000010=>[1,1,1,4,1,1] 011101001=>001000011=>101000011=>[1,1,1,4,2] 011101010=>001000000=>101000000=>[1,1,1,6] 011101011=>001000001=>101000001=>[1,1,1,5,1] 011101100=>001000110=>101000110=>[1,1,1,3,2,1] 011101101=>001000111=>101000111=>[1,1,1,3,3] 011101110=>001000100=>101000100=>[1,1,1,3,1,2] 011101111=>001000101=>101000101=>[1,1,1,3,1,1,1] 011110000=>001011010=>101011010=>[1,1,1,1,2,1,1,1] 011110001=>001011011=>101011011=>[1,1,1,1,2,1,2] 011110010=>001011000=>101011000=>[1,1,1,1,2,3] 011110011=>001011001=>101011001=>[1,1,1,1,2,2,1] 011110100=>001011110=>101011110=>[1,1,1,1,4,1] 011110101=>001011111=>101011111=>[1,1,1,1,5] 011110110=>001011100=>101011100=>[1,1,1,1,3,2] 011110111=>001011101=>101011101=>[1,1,1,1,3,1,1] 011111000=>001010010=>101010010=>[1,1,1,1,1,2,1,1] 011111001=>001010011=>101010011=>[1,1,1,1,1,2,2] 011111010=>001010000=>101010000=>[1,1,1,1,1,4] 011111011=>001010001=>101010001=>[1,1,1,1,1,3,1] 011111100=>001010110=>101010110=>[1,1,1,1,1,1,2,1] 011111101=>001010111=>101010111=>[1,1,1,1,1,1,3] 011111110=>001010100=>101010100=>[1,1,1,1,1,1,1,2] 011111111=>001010101=>101010101=>[1,1,1,1,1,1,1,1,1] 100000000=>110101010=>010101010=>[1,1,1,1,1,1,1,1,1] 100000001=>110101011=>010101011=>[1,1,1,1,1,1,1,2] 100000010=>110101000=>010101000=>[1,1,1,1,1,1,3] 100000011=>110101001=>010101001=>[1,1,1,1,1,1,2,1] 100000100=>110101110=>010101110=>[1,1,1,1,1,3,1] 100000101=>110101111=>010101111=>[1,1,1,1,1,4] 100000110=>110101100=>010101100=>[1,1,1,1,1,2,2] 100000111=>110101101=>010101101=>[1,1,1,1,1,2,1,1] 100001000=>110100010=>010100010=>[1,1,1,1,3,1,1] 100001001=>110100011=>010100011=>[1,1,1,1,3,2] 100001010=>110100000=>010100000=>[1,1,1,1,5] 100001011=>110100001=>010100001=>[1,1,1,1,4,1] 100001100=>110100110=>010100110=>[1,1,1,1,2,2,1] 100001101=>110100111=>010100111=>[1,1,1,1,2,3] 100001110=>110100100=>010100100=>[1,1,1,1,2,1,2] 100001111=>110100101=>010100101=>[1,1,1,1,2,1,1,1] 100010000=>110111010=>010111010=>[1,1,1,3,1,1,1] 100010001=>110111011=>010111011=>[1,1,1,3,1,2] 100010010=>110111000=>010111000=>[1,1,1,3,3] 100010011=>110111001=>010111001=>[1,1,1,3,2,1] 100010100=>110111110=>010111110=>[1,1,1,5,1] 100010101=>110111111=>010111111=>[1,1,1,6] 100010110=>110111100=>010111100=>[1,1,1,4,2] 100010111=>110111101=>010111101=>[1,1,1,4,1,1] 100011000=>110110010=>010110010=>[1,1,1,2,2,1,1] 100011001=>110110011=>010110011=>[1,1,1,2,2,2] 100011010=>110110000=>010110000=>[1,1,1,2,4] 100011011=>110110001=>010110001=>[1,1,1,2,3,1] 100011100=>110110110=>010110110=>[1,1,1,2,1,2,1] 100011101=>110110111=>010110111=>[1,1,1,2,1,3] 100011110=>110110100=>010110100=>[1,1,1,2,1,1,2] 100011111=>110110101=>010110101=>[1,1,1,2,1,1,1,1] 100100000=>110001010=>010001010=>[1,1,3,1,1,1,1] 100100001=>110001011=>010001011=>[1,1,3,1,1,2] 100100010=>110001000=>010001000=>[1,1,3,1,3] 100100011=>110001001=>010001001=>[1,1,3,1,2,1] 100100100=>110001110=>010001110=>[1,1,3,3,1] 100100101=>110001111=>010001111=>[1,1,3,4] 100100110=>110001100=>010001100=>[1,1,3,2,2] 100100111=>110001101=>010001101=>[1,1,3,2,1,1] 100101000=>110000010=>010000010=>[1,1,5,1,1] 100101001=>110000011=>010000011=>[1,1,5,2] 100101010=>110000000=>010000000=>[1,1,7] 100101011=>110000001=>010000001=>[1,1,6,1] 100101100=>110000110=>010000110=>[1,1,4,2,1] 100101101=>110000111=>010000111=>[1,1,4,3] 100101110=>110000100=>010000100=>[1,1,4,1,2] 100101111=>110000101=>010000101=>[1,1,4,1,1,1] 100110000=>110011010=>010011010=>[1,1,2,2,1,1,1] 100110001=>110011011=>010011011=>[1,1,2,2,1,2] 100110010=>110011000=>010011000=>[1,1,2,2,3] 100110011=>110011001=>010011001=>[1,1,2,2,2,1] 100110100=>110011110=>010011110=>[1,1,2,4,1] 100110101=>110011111=>010011111=>[1,1,2,5] 100110110=>110011100=>010011100=>[1,1,2,3,2] 100110111=>110011101=>010011101=>[1,1,2,3,1,1] 100111000=>110010010=>010010010=>[1,1,2,1,2,1,1] 100111001=>110010011=>010010011=>[1,1,2,1,2,2] 100111010=>110010000=>010010000=>[1,1,2,1,4] 100111011=>110010001=>010010001=>[1,1,2,1,3,1] 100111100=>110010110=>010010110=>[1,1,2,1,1,2,1] 100111101=>110010111=>010010111=>[1,1,2,1,1,3] 100111110=>110010100=>010010100=>[1,1,2,1,1,1,2] 100111111=>110010101=>010010101=>[1,1,2,1,1,1,1,1] 101000000=>111101010=>011101010=>[1,3,1,1,1,1,1] 101000001=>111101011=>011101011=>[1,3,1,1,1,2] 101000010=>111101000=>011101000=>[1,3,1,1,3] 101000011=>111101001=>011101001=>[1,3,1,1,2,1] 101000100=>111101110=>011101110=>[1,3,1,3,1] 101000101=>111101111=>011101111=>[1,3,1,4] 101000110=>111101100=>011101100=>[1,3,1,2,2] 101000111=>111101101=>011101101=>[1,3,1,2,1,1] 101001000=>111100010=>011100010=>[1,3,3,1,1] 101001001=>111100011=>011100011=>[1,3,3,2] 101001010=>111100000=>011100000=>[1,3,5] 101001011=>111100001=>011100001=>[1,3,4,1] 101001100=>111100110=>011100110=>[1,3,2,2,1] 101001101=>111100111=>011100111=>[1,3,2,3] 101001110=>111100100=>011100100=>[1,3,2,1,2] 101001111=>111100101=>011100101=>[1,3,2,1,1,1] 101010000=>111111010=>011111010=>[1,5,1,1,1] 101010001=>111111011=>011111011=>[1,5,1,2] 101010010=>111111000=>011111000=>[1,5,3] 101010011=>111111001=>011111001=>[1,5,2,1] 101010100=>111111110=>011111110=>[1,7,1] 101010101=>111111111=>011111111=>[1,8] 101010110=>111111100=>011111100=>[1,6,2] 101010111=>111111101=>011111101=>[1,6,1,1] 101011000=>111110010=>011110010=>[1,4,2,1,1] 101011001=>111110011=>011110011=>[1,4,2,2] 101011010=>111110000=>011110000=>[1,4,4] 101011011=>111110001=>011110001=>[1,4,3,1] 101011100=>111110110=>011110110=>[1,4,1,2,1] 101011101=>111110111=>011110111=>[1,4,1,3] 101011110=>111110100=>011110100=>[1,4,1,1,2] 101011111=>111110101=>011110101=>[1,4,1,1,1,1] 101100000=>111001010=>011001010=>[1,2,2,1,1,1,1] 101100001=>111001011=>011001011=>[1,2,2,1,1,2] 101100010=>111001000=>011001000=>[1,2,2,1,3] 101100011=>111001001=>011001001=>[1,2,2,1,2,1] 101100100=>111001110=>011001110=>[1,2,2,3,1] 101100101=>111001111=>011001111=>[1,2,2,4] 101100110=>111001100=>011001100=>[1,2,2,2,2] 101100111=>111001101=>011001101=>[1,2,2,2,1,1] 101101000=>111000010=>011000010=>[1,2,4,1,1] 101101001=>111000011=>011000011=>[1,2,4,2] 101101010=>111000000=>011000000=>[1,2,6] 101101011=>111000001=>011000001=>[1,2,5,1] 101101100=>111000110=>011000110=>[1,2,3,2,1] 101101101=>111000111=>011000111=>[1,2,3,3] 101101110=>111000100=>011000100=>[1,2,3,1,2] 101101111=>111000101=>011000101=>[1,2,3,1,1,1] 101110000=>111011010=>011011010=>[1,2,1,2,1,1,1] 101110001=>111011011=>011011011=>[1,2,1,2,1,2] 101110010=>111011000=>011011000=>[1,2,1,2,3] 101110011=>111011001=>011011001=>[1,2,1,2,2,1] 101110100=>111011110=>011011110=>[1,2,1,4,1] 101110101=>111011111=>011011111=>[1,2,1,5] 101110110=>111011100=>011011100=>[1,2,1,3,2] 101110111=>111011101=>011011101=>[1,2,1,3,1,1] 101111000=>111010010=>011010010=>[1,2,1,1,2,1,1] 101111001=>111010011=>011010011=>[1,2,1,1,2,2] 101111010=>111010000=>011010000=>[1,2,1,1,4] 101111011=>111010001=>011010001=>[1,2,1,1,3,1] 101111100=>111010110=>011010110=>[1,2,1,1,1,2,1] 101111101=>111010111=>011010111=>[1,2,1,1,1,3] 101111110=>111010100=>011010100=>[1,2,1,1,1,1,2] 101111111=>111010101=>011010101=>[1,2,1,1,1,1,1,1] 110000000=>100101010=>000101010=>[3,1,1,1,1,1,1] 110000001=>100101011=>000101011=>[3,1,1,1,1,2] 110000010=>100101000=>000101000=>[3,1,1,1,3] 110000011=>100101001=>000101001=>[3,1,1,1,2,1] 110000100=>100101110=>000101110=>[3,1,1,3,1] 110000101=>100101111=>000101111=>[3,1,1,4] 110000110=>100101100=>000101100=>[3,1,1,2,2] 110000111=>100101101=>000101101=>[3,1,1,2,1,1] 110001000=>100100010=>000100010=>[3,1,3,1,1] 110001001=>100100011=>000100011=>[3,1,3,2] 110001010=>100100000=>000100000=>[3,1,5] 110001011=>100100001=>000100001=>[3,1,4,1] 110001100=>100100110=>000100110=>[3,1,2,2,1] 110001101=>100100111=>000100111=>[3,1,2,3] 110001110=>100100100=>000100100=>[3,1,2,1,2] 110001111=>100100101=>000100101=>[3,1,2,1,1,1] 110010000=>100111010=>000111010=>[3,3,1,1,1] 110010001=>100111011=>000111011=>[3,3,1,2] 110010010=>100111000=>000111000=>[3,3,3] 110010011=>100111001=>000111001=>[3,3,2,1] 110010100=>100111110=>000111110=>[3,5,1] 110010101=>100111111=>000111111=>[3,6] 110010110=>100111100=>000111100=>[3,4,2] 110010111=>100111101=>000111101=>[3,4,1,1] 110011000=>100110010=>000110010=>[3,2,2,1,1] 110011001=>100110011=>000110011=>[3,2,2,2] 110011010=>100110000=>000110000=>[3,2,4] 110011011=>100110001=>000110001=>[3,2,3,1] 110011100=>100110110=>000110110=>[3,2,1,2,1] 110011101=>100110111=>000110111=>[3,2,1,3] 110011110=>100110100=>000110100=>[3,2,1,1,2] 110011111=>100110101=>000110101=>[3,2,1,1,1,1] 110100000=>100001010=>000001010=>[5,1,1,1,1] 110100001=>100001011=>000001011=>[5,1,1,2] 110100010=>100001000=>000001000=>[5,1,3] 110100011=>100001001=>000001001=>[5,1,2,1] 110100100=>100001110=>000001110=>[5,3,1] 110100101=>100001111=>000001111=>[5,4] 110100110=>100001100=>000001100=>[5,2,2] 110100111=>100001101=>000001101=>[5,2,1,1] 110101000=>100000010=>000000010=>[7,1,1] 110101001=>100000011=>000000011=>[7,2] 110101010=>100000000=>000000000=>[9] 110101011=>100000001=>000000001=>[8,1] 110101100=>100000110=>000000110=>[6,2,1] 110101101=>100000111=>000000111=>[6,3] 110101110=>100000100=>000000100=>[6,1,2] 110101111=>100000101=>000000101=>[6,1,1,1] 110110000=>100011010=>000011010=>[4,2,1,1,1] 110110001=>100011011=>000011011=>[4,2,1,2] 110110010=>100011000=>000011000=>[4,2,3] 110110011=>100011001=>000011001=>[4,2,2,1] 110110100=>100011110=>000011110=>[4,4,1] 110110101=>100011111=>000011111=>[4,5] 110110110=>100011100=>000011100=>[4,3,2] 110110111=>100011101=>000011101=>[4,3,1,1] 110111000=>100010010=>000010010=>[4,1,2,1,1] 110111001=>100010011=>000010011=>[4,1,2,2] 110111010=>100010000=>000010000=>[4,1,4] 110111011=>100010001=>000010001=>[4,1,3,1] 110111100=>100010110=>000010110=>[4,1,1,2,1] 110111101=>100010111=>000010111=>[4,1,1,3] 110111110=>100010100=>000010100=>[4,1,1,1,2] 110111111=>100010101=>000010101=>[4,1,1,1,1,1] 111000000=>101101010=>001101010=>[2,2,1,1,1,1,1] 111000001=>101101011=>001101011=>[2,2,1,1,1,2] 111000010=>101101000=>001101000=>[2,2,1,1,3] 111000011=>101101001=>001101001=>[2,2,1,1,2,1] 111000100=>101101110=>001101110=>[2,2,1,3,1] 111000101=>101101111=>001101111=>[2,2,1,4] 111000110=>101101100=>001101100=>[2,2,1,2,2] 111000111=>101101101=>001101101=>[2,2,1,2,1,1] 111001000=>101100010=>001100010=>[2,2,3,1,1] 111001001=>101100011=>001100011=>[2,2,3,2] 111001010=>101100000=>001100000=>[2,2,5] 111001011=>101100001=>001100001=>[2,2,4,1] 111001100=>101100110=>001100110=>[2,2,2,2,1] 111001101=>101100111=>001100111=>[2,2,2,3] 111001110=>101100100=>001100100=>[2,2,2,1,2] 111001111=>101100101=>001100101=>[2,2,2,1,1,1] 111010000=>101111010=>001111010=>[2,4,1,1,1] 111010001=>101111011=>001111011=>[2,4,1,2] 111010010=>101111000=>001111000=>[2,4,3] 111010011=>101111001=>001111001=>[2,4,2,1] 111010100=>101111110=>001111110=>[2,6,1] 111010101=>101111111=>001111111=>[2,7] 111010110=>101111100=>001111100=>[2,5,2] 111010111=>101111101=>001111101=>[2,5,1,1] 111011000=>101110010=>001110010=>[2,3,2,1,1] 111011001=>101110011=>001110011=>[2,3,2,2] 111011010=>101110000=>001110000=>[2,3,4] 111011011=>101110001=>001110001=>[2,3,3,1] 111011100=>101110110=>001110110=>[2,3,1,2,1] 111011101=>101110111=>001110111=>[2,3,1,3] 111011110=>101110100=>001110100=>[2,3,1,1,2] 111011111=>101110101=>001110101=>[2,3,1,1,1,1] 111100000=>101001010=>001001010=>[2,1,2,1,1,1,1] 111100001=>101001011=>001001011=>[2,1,2,1,1,2] 111100010=>101001000=>001001000=>[2,1,2,1,3] 111100011=>101001001=>001001001=>[2,1,2,1,2,1] 111100100=>101001110=>001001110=>[2,1,2,3,1] 111100101=>101001111=>001001111=>[2,1,2,4] 111100110=>101001100=>001001100=>[2,1,2,2,2] 111100111=>101001101=>001001101=>[2,1,2,2,1,1] 111101000=>101000010=>001000010=>[2,1,4,1,1] 111101001=>101000011=>001000011=>[2,1,4,2] 111101010=>101000000=>001000000=>[2,1,6] 111101011=>101000001=>001000001=>[2,1,5,1] 111101100=>101000110=>001000110=>[2,1,3,2,1] 111101101=>101000111=>001000111=>[2,1,3,3] 111101110=>101000100=>001000100=>[2,1,3,1,2] 111101111=>101000101=>001000101=>[2,1,3,1,1,1] 111110000=>101011010=>001011010=>[2,1,1,2,1,1,1] 111110001=>101011011=>001011011=>[2,1,1,2,1,2] 111110010=>101011000=>001011000=>[2,1,1,2,3] 111110011=>101011001=>001011001=>[2,1,1,2,2,1] 111110100=>101011110=>001011110=>[2,1,1,4,1] 111110101=>101011111=>001011111=>[2,1,1,5] 111110110=>101011100=>001011100=>[2,1,1,3,2] 111110111=>101011101=>001011101=>[2,1,1,3,1,1] 111111000=>101010010=>001010010=>[2,1,1,1,2,1,1] 111111001=>101010011=>001010011=>[2,1,1,1,2,2] 111111010=>101010000=>001010000=>[2,1,1,1,4] 111111011=>101010001=>001010001=>[2,1,1,1,3,1] 111111100=>101010110=>001010110=>[2,1,1,1,1,2,1] 111111101=>101010111=>001010111=>[2,1,1,1,1,3] 111111110=>101010100=>001010100=>[2,1,1,1,1,1,2] 111111111=>101010101=>001010101=>[2,1,1,1,1,1,1,1] 1010101010=>1111111111=>0111111111=>[1,9] 1010101100=>1111111001=>0111111001=>[1,6,2,1] 1010110100=>1111100001=>0111100001=>[1,4,4,1] 1011001010=>1110011111=>0110011111=>[1,2,2,5] 1011001100=>1110011001=>0110011001=>[1,2,2,2,2,1] 1011010010=>1110000111=>0110000111=>[1,2,4,3] 1011100010=>1110110111=>0110110111=>[1,2,1,2,1,3] 1011100100=>1110110001=>0110110001=>[1,2,1,2,3,1] 1011110000=>1110100101=>0110100101=>[1,2,1,1,2,1,1,1] 1100101010=>1001111111=>0001111111=>[3,7] 1100110010=>1001100111=>0001100111=>[3,2,2,3] 1101001010=>1000011111=>0000011111=>[5,5] 1101001100=>1000011001=>0000011001=>[5,2,2,1] 1101010010=>1000000111=>0000000111=>[7,3] 1101010100=>1000000001=>0000000001=>[9,1] 1101011000=>1000001101=>0000001101=>[6,2,1,1] 1101100010=>1000110111=>0000110111=>[4,2,1,3] 1101100100=>1000110001=>0000110001=>[4,2,3,1] 1101101000=>1000111101=>0000111101=>[4,4,1,1] 1110001010=>1011011111=>0011011111=>[2,2,1,5] 1110001100=>1011011001=>0011011001=>[2,2,1,2,2,1] 1110010010=>1011000111=>0011000111=>[2,2,3,3] 1110100100=>1011110001=>0011110001=>[2,4,3,1] 1110101000=>1011111101=>0011111101=>[2,6,1,1] 1111000010=>1010010111=>0010010111=>[2,1,2,1,1,3] 101010110100=>111111100001=>011111100001=>[1,6,4,1] 101011001100=>111110011001=>011110011001=>[1,4,2,2,2,1] 101011010010=>111110000111=>011110000111=>[1,4,4,3] 101011011000=>111110001101=>011110001101=>[1,4,3,2,1,1] 101011100100=>111110110001=>011110110001=>[1,4,1,2,3,1] 101011110000=>111110100101=>011110100101=>[1,4,1,1,2,1,1,1] 110010101100=>100111111001=>000111111001=>[3,6,2,1] 110100101010=>100001111111=>000001111111=>[5,7] 110110101000=>100011111101=>000011111101=>[4,6,1,1] 111010001100=>101111011001=>001111011001=>[2,4,1,2,2,1] 111010010010=>101111000111=>001111000111=>[2,4,3,3] 111010011000=>101111001101=>001111001101=>[2,4,2,2,1,1] 111010100100=>101111110001=>001111110001=>[2,6,3,1] 111010110000=>101111100101=>001111100101=>[2,5,2,1,1,1] 1111111111=>1010101010=>0010101010=>[2,1,1,1,1,1,1,1,1] 1111111110=>1010101011=>0010101011=>[2,1,1,1,1,1,1,2] 1111101011=>1010111110=>0010111110=>[2,1,1,5,1] 1111101010=>1010111111=>0010111111=>[2,1,1,6] 1111100111=>1010110010=>0010110010=>[2,1,1,2,2,1,1] 1111100100=>1010110001=>0010110001=>[2,1,1,2,3,1] 1111100001=>1010110100=>0010110100=>[2,1,1,2,1,1,2] 1111011011=>1010001110=>0010001110=>[2,1,3,3,1] 1111000000=>1010010101=>0010010101=>[2,1,2,1,1,1,1,1] 1110111101=>1011101000=>0011101000=>[2,3,1,1,3] 1110110001=>1011100100=>0011100100=>[2,3,2,1,2] 1110101111=>1011111010=>0011111010=>[2,5,1,1,1] 1110101101=>1011111000=>0011111000=>[2,5,3] 1110101011=>1011111110=>0011111110=>[2,7,1] 1110101010=>1011111111=>0011111111=>[2,8] 1110101001=>1011111100=>0011111100=>[2,6,2] 1110100101=>1011110000=>0011110000=>[2,4,4] 1110100001=>1011110100=>0011110100=>[2,4,1,1,2] 1110011111=>1011001010=>0011001010=>[2,2,2,1,1,1,1] 1110011001=>1011001100=>0011001100=>[2,2,2,2,2] 1110010110=>1011000011=>0011000011=>[2,2,4,2] 1110001101=>1011011000=>0011011000=>[2,2,1,2,3] 1110000111=>1011010010=>0011010010=>[2,2,1,1,2,1,1] 1110000110=>1011010011=>0011010011=>[2,2,1,1,2,2] 1110000010=>1011010111=>0011010111=>[2,2,1,1,1,3] 1110000001=>1011010100=>0011010100=>[2,2,1,1,1,1,2] 1101111011=>1000101110=>0000101110=>[4,1,1,3,1] 1101111010=>1000101111=>0000101111=>[4,1,1,4] 1101111000=>1000101101=>0000101101=>[4,1,1,2,1,1] 1101101011=>1000111110=>0000111110=>[4,5,1] 1101101010=>1000111111=>0000111111=>[4,6] 1101100110=>1000110011=>0000110011=>[4,2,2,2] 1101100001=>1000110100=>0000110100=>[4,2,1,1,2] 1101100000=>1000110101=>0000110101=>[4,2,1,1,1,1] 1101011111=>1000001010=>0000001010=>[6,1,1,1,1] 1101011110=>1000001011=>0000001011=>[6,1,1,2] 1101011011=>1000001110=>0000001110=>[6,3,1] 1101011010=>1000001111=>0000001111=>[6,4] 1101010111=>1000000010=>0000000010=>[8,1,1] 1101010110=>1000000011=>0000000011=>[8,2] 1101010101=>1000000000=>0000000000=>[10] 1101010011=>1000000110=>0000000110=>[7,2,1] 1101010001=>1000000100=>0000000100=>[7,1,2] 1101010000=>1000000101=>0000000101=>[7,1,1,1] 1101001110=>1000011011=>0000011011=>[5,2,1,2] 1101001101=>1000011000=>0000011000=>[5,2,3] 1101001011=>1000011110=>0000011110=>[5,4,1] 1101001000=>1000011101=>0000011101=>[5,3,1,1] 1101000011=>1000010110=>0000010110=>[5,1,1,2,1] 1101000010=>1000010111=>0000010111=>[5,1,1,3] 1101000000=>1000010101=>0000010101=>[5,1,1,1,1,1] 1100111100=>1001101001=>0001101001=>[3,2,1,1,2,1] 1100111001=>1001101100=>0001101100=>[3,2,1,2,2] 1100110110=>1001100011=>0001100011=>[3,2,3,2] 1100101110=>1001111011=>0001111011=>[3,4,1,2] 1100101011=>1001111110=>0001111110=>[3,6,1] 1100101001=>1001111100=>0001111100=>[3,5,2] 1100100110=>1001110011=>0001110011=>[3,3,2,2] 1100100011=>1001110110=>0001110110=>[3,3,1,2,1] 1100011110=>1001001011=>0001001011=>[3,1,2,1,1,2] 1100001011=>1001011110=>0001011110=>[3,1,1,4,1] 1100001010=>1001011111=>0001011111=>[3,1,1,5] 1100001000=>1001011101=>0001011101=>[3,1,1,3,1,1] 1100000010=>1001010111=>0001010111=>[3,1,1,1,1,3] 1100000000=>1001010101=>0001010101=>[3,1,1,1,1,1,1,1] 1011111111=>1110101010=>0110101010=>[1,2,1,1,1,1,1,1,1] 1011111110=>1110101011=>0110101011=>[1,2,1,1,1,1,1,2] 1011111101=>1110101000=>0110101000=>[1,2,1,1,1,1,3] 1011111100=>1110101001=>0110101001=>[1,2,1,1,1,1,2,1] 1011111010=>1110101111=>0110101111=>[1,2,1,1,1,4] 1011111001=>1110101100=>0110101100=>[1,2,1,1,1,2,2] 1011110111=>1110100010=>0110100010=>[1,2,1,1,3,1,1] 1011110110=>1110100011=>0110100011=>[1,2,1,1,3,2] 1011110100=>1110100001=>0110100001=>[1,2,1,1,4,1] 1011110001=>1110100100=>0110100100=>[1,2,1,1,2,1,2] 1011101110=>1110111011=>0110111011=>[1,2,1,3,1,2] 1011101010=>1110111111=>0110111111=>[1,2,1,6] 1011100101=>1110110000=>0110110000=>[1,2,1,2,4] 1011100001=>1110110100=>0110110100=>[1,2,1,2,1,1,2] 1011100000=>1110110101=>0110110101=>[1,2,1,2,1,1,1,1] 1011011111=>1110001010=>0110001010=>[1,2,3,1,1,1,1] 1011011110=>1110001011=>0110001011=>[1,2,3,1,1,2] 1011011100=>1110001001=>0110001001=>[1,2,3,1,2,1] 1011011001=>1110001100=>0110001100=>[1,2,3,2,2] 1011010110=>1110000011=>0110000011=>[1,2,5,2] 1011001101=>1110011000=>0110011000=>[1,2,2,2,3] 1011001001=>1110011100=>0110011100=>[1,2,2,3,2] 1011000111=>1110010010=>0110010010=>[1,2,2,1,2,1,1] 1011000110=>1110010011=>0110010011=>[1,2,2,1,2,2] 1011000100=>1110010001=>0110010001=>[1,2,2,1,3,1] 1011000011=>1110010110=>0110010110=>[1,2,2,1,1,2,1] 1011000001=>1110010100=>0110010100=>[1,2,2,1,1,1,2] 1011000000=>1110010101=>0110010101=>[1,2,2,1,1,1,1,1] 1010110111=>1111100010=>0111100010=>[1,4,3,1,1] 1010110110=>1111100011=>0111100011=>[1,4,3,2] 1010110101=>1111100000=>0111100000=>[1,4,5] 1010110001=>1111100100=>0111100100=>[1,4,2,1,2] 1010101011=>1111111110=>0111111110=>[1,8,1] 1010101000=>1111111101=>0111111101=>[1,7,1,1] 1010100101=>1111110000=>0111110000=>[1,5,4] 1010100000=>1111110101=>0111110101=>[1,5,1,1,1,1] 1010011111=>1111001010=>0111001010=>[1,3,2,1,1,1,1] 1010011110=>1111001011=>0111001011=>[1,3,2,1,1,2] 1010011101=>1111001000=>0111001000=>[1,3,2,1,3] 1010011100=>1111001001=>0111001001=>[1,3,2,1,2,1] 1010011001=>1111001100=>0111001100=>[1,3,2,2,2] 1010010111=>1111000010=>0111000010=>[1,3,4,1,1] 1010010110=>1111000011=>0111000011=>[1,3,4,2] 1010010011=>1111000110=>0111000110=>[1,3,3,2,1] 1010010010=>1111000111=>0111000111=>[1,3,3,3] 1010010001=>1111000100=>0111000100=>[1,3,3,1,2] 1010010000=>1111000101=>0111000101=>[1,3,3,1,1,1] 1010001101=>1111011000=>0111011000=>[1,3,1,2,3] 1010000111=>1111010010=>0111010010=>[1,3,1,1,2,1,1] 1010000110=>1111010011=>0111010011=>[1,3,1,1,2,2] 1010000101=>1111010000=>0111010000=>[1,3,1,1,4] 1010000100=>1111010001=>0111010001=>[1,3,1,1,3,1] 1010000001=>1111010100=>0111010100=>[1,3,1,1,1,1,2] 1010000000=>1111010101=>0111010101=>[1,3,1,1,1,1,1,1] 1001111111=>1100101010=>0100101010=>[1,1,2,1,1,1,1,1,1] 1001111100=>1100101001=>0100101001=>[1,1,2,1,1,1,2,1] 1001111011=>1100101110=>0100101110=>[1,1,2,1,1,3,1] 1001110110=>1100100011=>0100100011=>[1,1,2,1,3,2] 1001110100=>1100100001=>0100100001=>[1,1,2,1,4,1] 1001101100=>1100111001=>0100111001=>[1,1,2,3,2,1] 1001101010=>1100111111=>0100111111=>[1,1,2,6] 1001101001=>1100111100=>0100111100=>[1,1,2,4,2] 1001100111=>1100110010=>0100110010=>[1,1,2,2,2,1,1] 1001100110=>1100110011=>0100110011=>[1,1,2,2,2,2] 1001100100=>1100110001=>0100110001=>[1,1,2,2,3,1] 1001100011=>1100110110=>0100110110=>[1,1,2,2,1,2,1] 1001011110=>1100001011=>0100001011=>[1,1,4,1,1,2] 1001011010=>1100001111=>0100001111=>[1,1,4,4] 1001010111=>1100000010=>0100000010=>[1,1,6,1,1] 1001010110=>1100000011=>0100000011=>[1,1,6,2] 1001010101=>1100000000=>0100000000=>[1,1,8] 1001010010=>1100000111=>0100000111=>[1,1,5,3] 1001001110=>1100011011=>0100011011=>[1,1,3,2,1,2] 1001001100=>1100011001=>0100011001=>[1,1,3,2,2,1] 1001001011=>1100011110=>0100011110=>[1,1,3,4,1] 1001000110=>1100010011=>0100010011=>[1,1,3,1,2,2] 1001000000=>1100010101=>0100010101=>[1,1,3,1,1,1,1,1] 1000111110=>1101101011=>0101101011=>[1,1,1,2,1,1,1,2] 1000111101=>1101101000=>0101101000=>[1,1,1,2,1,1,3] 1000111100=>1101101001=>0101101001=>[1,1,1,2,1,1,2,1] 1000111010=>1101101111=>0101101111=>[1,1,1,2,1,4] 1000111001=>1101101100=>0101101100=>[1,1,1,2,1,2,2] 1000110111=>1101100010=>0101100010=>[1,1,1,2,3,1,1] 1000110110=>1101100011=>0101100011=>[1,1,1,2,3,2] 1000110100=>1101100001=>0101100001=>[1,1,1,2,4,1] 1000110011=>1101100110=>0101100110=>[1,1,1,2,2,2,1] 1000110001=>1101100100=>0101100100=>[1,1,1,2,2,1,2] 1000110000=>1101100101=>0101100101=>[1,1,1,2,2,1,1,1] 1000101110=>1101111011=>0101111011=>[1,1,1,4,1,2] 1000101101=>1101111000=>0101111000=>[1,1,1,4,3] 1000101100=>1101111001=>0101111001=>[1,1,1,4,2,1] 1000101011=>1101111110=>0101111110=>[1,1,1,6,1] 1000101010=>1101111111=>0101111111=>[1,1,1,7] 1000101000=>1101111101=>0101111101=>[1,1,1,5,1,1] 1000100111=>1101110010=>0101110010=>[1,1,1,3,2,1,1] 1000100101=>1101110000=>0101110000=>[1,1,1,3,4] 1000100100=>1101110001=>0101110001=>[1,1,1,3,3,1] 1000100010=>1101110111=>0101110111=>[1,1,1,3,1,3] 1000011111=>1101001010=>0101001010=>[1,1,1,1,2,1,1,1,1] 1000011110=>1101001011=>0101001011=>[1,1,1,1,2,1,1,2] 1000011011=>1101001110=>0101001110=>[1,1,1,1,2,3,1] 1000011010=>1101001111=>0101001111=>[1,1,1,1,2,4] 1000010110=>1101000011=>0101000011=>[1,1,1,1,4,2] 1000010010=>1101000111=>0101000111=>[1,1,1,1,3,3] 1000010000=>1101000101=>0101000101=>[1,1,1,1,3,1,1,1] 1000001111=>1101011010=>0101011010=>[1,1,1,1,1,2,1,1,1] 1000001110=>1101011011=>0101011011=>[1,1,1,1,1,2,1,2] 1000001101=>1101011000=>0101011000=>[1,1,1,1,1,2,3] 1000001100=>1101011001=>0101011001=>[1,1,1,1,1,2,2,1] 1000001010=>1101011111=>0101011111=>[1,1,1,1,1,5] 1000000111=>1101010010=>0101010010=>[1,1,1,1,1,1,2,1,1] 1000000100=>1101010001=>0101010001=>[1,1,1,1,1,1,3,1] 1000000010=>1101010111=>0101010111=>[1,1,1,1,1,1,1,3] 1000000001=>1101010100=>0101010100=>[1,1,1,1,1,1,1,1,2] 1000000000=>1101010101=>0101010101=>[1,1,1,1,1,1,1,1,1,1] 10000000000=>11010101010=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1] 10000001110=>11010100100=>01010100100=>[1,1,1,1,1,1,2,1,2] 10000111110=>11010010100=>01010010100=>[1,1,1,1,2,1,1,1,2] 10011111110=>11001010100=>01001010100=>[1,1,2,1,1,1,1,1,2] 10111111110=>11101010100=>01101010100=>[1,2,1,1,1,1,1,1,2] 11111111110=>10101010100=>00101010100=>[2,1,1,1,1,1,1,1,2] 100000000000=>110101010101=>010101010101=>[1,1,1,1,1,1,1,1,1,1,1,1] 100000011110=>110101001011=>010101001011=>[1,1,1,1,1,1,2,1,1,2] 10000101110=>11010000100=>01010000100=>[1,1,1,1,4,1,2] 100001111110=>110100101011=>010100101011=>[1,1,1,1,2,1,1,1,1,2] 10010111110=>11000010100=>01000010100=>[1,1,4,1,1,1,2] 111111111110=>101010101011=>001010101011=>[2,1,1,1,1,1,1,1,1,2] 10000100010=>11010001000=>01010001000=>[1,1,1,1,3,1,3] 100000110110=>110101100011=>010101100011=>[1,1,1,1,1,2,3,2] 100011011110=>110110001011=>010110001011=>[1,1,1,2,3,1,1,2] 11000111110=>10010010100=>00010010100=>[3,1,2,1,1,1,2] 11110111110=>10100010100=>00100010100=>[2,1,3,1,1,1,2] 100001011010=>110100001111=>010100001111=>[1,1,1,1,4,4] 100000111100=>110101101001=>010101101001=>[1,1,1,1,1,2,1,1,2,1] 11000001110=>10010100100=>00010100100=>[3,1,1,1,2,1,2] 11000101110=>10010000100=>00010000100=>[3,1,4,1,2] 101001011110=>111100001011=>011100001011=>[1,3,4,1,1,2] 100110011110=>110011001011=>010011001011=>[1,1,2,2,2,1,1,2] 11011101110=>10001000100=>00001000100=>[4,1,3,1,2] 11111101110=>10101000100=>00101000100=>[2,1,1,1,3,1,2] 10010101010=>11000000000=>01000000000=>[1,1,9] 100010000100=>110111010001=>010111010001=>[1,1,1,3,1,1,3,1] 10010001000=>11000100010=>01000100010=>[1,1,3,1,3,1,1] 10010100010=>11000001000=>01000001000=>[1,1,5,1,3] 100010011100=>110111001001=>010111001001=>[1,1,1,3,2,1,2,1] 101000110110=>111101100011=>011101100011=>[1,3,1,2,3,2] 110001101110=>100100111011=>000100111011=>[3,1,2,3,1,2] 101100011110=>111001001011=>011001001011=>[1,2,2,1,2,1,1,2] 100011111100=>110110101001=>010110101001=>[1,1,1,2,1,1,1,1,2,1] 0111111111=>0010101010=>1010101010=>[1,1,1,1,1,1,1,1,1,1] 0111111101=>0010101000=>1010101000=>[1,1,1,1,1,1,1,3] 0111111001=>0010101100=>1010101100=>[1,1,1,1,1,1,2,2] 0111110001=>0010100100=>1010100100=>[1,1,1,1,1,2,1,2] 0111100001=>0010110100=>1010110100=>[1,1,1,1,2,1,1,2] 0111000001=>0010010100=>1010010100=>[1,1,1,2,1,1,1,2] 0110000001=>0011010100=>1011010100=>[1,1,2,1,1,1,1,2] 0100000001=>0001010100=>1001010100=>[1,2,1,1,1,1,1,2] 0000000001=>0101010100=>1101010100=>[2,1,1,1,1,1,1,2] 01111111111=>00101010101=>10101010101=>[1,1,1,1,1,1,1,1,1,1,1] 0111110101=>0010100000=>1010100000=>[1,1,1,1,1,5] 0110100001=>0011110100=>1011110100=>[1,1,4,1,1,2] 0010000001=>0111010100=>1111010100=>[4,1,1,1,1,2] 0101010101=>0000000000=>1000000000=>[1,9] 0101010011=>0000000110=>1000000110=>[1,6,2,1] 0101001011=>0000011110=>1000011110=>[1,4,4,1] 0100110011=>0001100110=>1001100110=>[1,2,2,2,2,1] 0100101101=>0001111000=>1001111000=>[1,2,4,3] 0100101011=>0001111110=>1001111110=>[1,2,6,1] 0100011011=>0001001110=>1001001110=>[1,2,1,2,3,1] 0100001111=>0001011010=>1001011010=>[1,2,1,1,2,1,1,1] 0011001101=>0110011000=>1110011000=>[3,2,2,3] 0011001011=>0110011110=>1110011110=>[3,2,4,1] 0011000111=>0110010010=>1110010010=>[3,2,1,2,1,1] 0010110101=>0111100000=>1111100000=>[5,5] 0010101011=>0111111110=>1111111110=>[9,1] 0010100111=>0111110010=>1111110010=>[6,2,1,1] 0010011101=>0111001000=>1111001000=>[4,2,1,3] 0010010111=>0111000010=>1111000010=>[4,4,1,1] 0001110011=>0100100110=>1100100110=>[2,2,1,2,2,1] 0001101101=>0100111000=>1100111000=>[2,2,3,3] 0001100111=>0100110010=>1100110010=>[2,2,2,2,1,1] 0001011101=>0100001000=>1100001000=>[2,4,1,3] 0001010111=>0100000010=>1100000010=>[2,6,1,1] 0000111101=>0101101000=>1101101000=>[2,1,2,1,1,3] 0000110111=>0101100010=>1101100010=>[2,1,2,3,1,1] 0000011111=>0101001010=>1101001010=>[2,1,1,2,1,1,1,1] 11010101010=>10000000000=>00000000000=>[11] 11010101000=>10000000010=>00000000010=>[9,1,1] 11010101100=>10000000110=>00000000110=>[8,2,1] 11010100100=>10000001110=>00000001110=>[7,3,1] 11010110100=>10000011110=>00000011110=>[6,4,1] 11010010100=>10000111110=>00000111110=>[5,5,1] 11011010100=>10001111110=>00001111110=>[4,6,1] 11001010100=>10011111110=>00011111110=>[3,7,1] 11101010100=>10111111110=>00111111110=>[2,8,1] 10101010100=>11111111110=>01111111110=>[1,9,1] 111111111111=>101010101010=>001010101010=>[2,1,1,1,1,1,1,1,1,1,1] 111110000001=>101011010100=>001011010100=>[2,1,1,2,1,1,1,1,2] 111110100101=>101011110000=>001011110000=>[2,1,1,4,4] 111001100001=>101100110100=>001100110100=>[2,2,2,2,1,1,2] 111001101101=>101100111000=>001100111000=>[2,2,2,3,3] 111000011001=>101101001100=>001101001100=>[2,2,1,1,2,2,2] 111000000111=>101101010010=>001101010010=>[2,2,1,1,1,1,2,1,1] 111000001101=>101101011000=>001101011000=>[2,2,1,1,1,2,3] 111000110001=>101101100100=>001101100100=>[2,2,1,2,2,1,2] 111000100101=>101101110000=>001101110000=>[2,2,1,3,4] 111011011001=>101110001100=>001110001100=>[2,3,3,2,2] 111011000001=>101110010100=>001110010100=>[2,3,2,1,1,1,2] 111011001101=>101110011000=>001110011000=>[2,3,2,2,3] 111011100101=>101110110000=>001110110000=>[2,3,1,2,4] 111010010001=>101111000100=>001111000100=>[2,4,3,1,2] 111010011101=>101111001000=>001111001000=>[2,4,2,1,3] 111010000101=>101111010000=>001111010000=>[2,4,1,1,4] 100111100001=>110010110100=>010010110100=>[1,1,2,1,1,2,1,1,2] 100111101101=>110010111000=>010010111000=>[1,1,2,1,1,3,3] 100110011001=>110011001100=>010011001100=>[1,1,2,2,2,2,2] 100110000111=>110011010010=>010011010010=>[1,1,2,2,1,1,2,1,1] 100110001101=>110011011000=>010011011000=>[1,1,2,2,1,2,3] 100110110111=>110011100010=>010011100010=>[1,1,2,3,3,1,1] 100110110001=>110011100100=>010011100100=>[1,1,2,3,2,1,2] 100110100101=>110011110000=>010011110000=>[1,1,2,4,4] 100001111001=>110100101100=>010100101100=>[1,1,1,1,2,1,1,2,2] 100001100111=>110100110010=>010100110010=>[1,1,1,1,2,2,2,1,1] 100001101101=>110100111000=>010100111000=>[1,1,1,1,2,3,3] 100000011111=>110101001010=>010101001010=>[1,1,1,1,1,1,2,1,1,1,1] 100000110111=>110101100010=>010101100010=>[1,1,1,1,1,2,3,1,1] 100000110001=>110101100100=>010101100100=>[1,1,1,1,1,2,2,1,2] 100000111101=>110101101000=>010101101000=>[1,1,1,1,1,2,1,1,3] 100000100101=>110101110000=>010101110000=>[1,1,1,1,1,3,4] 100011011001=>110110001100=>010110001100=>[1,1,1,2,3,2,2] 100011000111=>110110010010=>010110010010=>[1,1,1,2,2,1,2,1,1] 100011001101=>110110011000=>010110011000=>[1,1,1,2,2,2,3] 100011110001=>110110100100=>010110100100=>[1,1,1,2,1,1,2,1,2] 100011100101=>110110110000=>010110110000=>[1,1,1,2,1,2,4] 100010010111=>110111000010=>010111000010=>[1,1,1,3,4,1,1] 100010010001=>110111000100=>010111000100=>[1,1,1,3,3,1,2] 100010011101=>110111001000=>010111001000=>[1,1,1,3,2,1,3] 100010000101=>110111010000=>010111010000=>[1,1,1,3,1,1,4] 100010110101=>110111100000=>010111100000=>[1,1,1,4,5] 101101111001=>111000101100=>011000101100=>[1,2,3,1,1,2,2] 101101100111=>111000110010=>011000110010=>[1,2,3,2,2,1,1] 101101100001=>111000110100=>011000110100=>[1,2,3,2,1,1,2] 101101101101=>111000111000=>011000111000=>[1,2,3,3,3] 101100011111=>111001001010=>011001001010=>[1,2,2,1,2,1,1,1,1] 101100011001=>111001001100=>011001001100=>[1,2,2,1,2,2,2] 101100000111=>111001010010=>011001010010=>[1,2,2,1,1,1,2,1,1] 101100001101=>111001011000=>011001011000=>[1,2,2,1,1,2,3] 101100110111=>111001100010=>011001100010=>[1,2,2,2,3,1,1] 101100110001=>111001100100=>011001100100=>[1,2,2,2,2,1,2] 101100111101=>111001101000=>011001101000=>[1,2,2,2,1,1,3] 101100100101=>111001110000=>011001110000=>[1,2,2,3,4] 101111011001=>111010001100=>011010001100=>[1,2,1,1,3,2,2] 101111000111=>111010010010=>011010010010=>[1,2,1,1,2,1,2,1,1] 101111000001=>111010010100=>011010010100=>[1,2,1,1,2,1,1,1,2] 101111001101=>111010011000=>011010011000=>[1,2,1,1,2,2,3] 101111110001=>111010100100=>011010100100=>[1,2,1,1,1,1,2,1,2] 101110010111=>111011000010=>011011000010=>[1,2,1,2,4,1,1] 101110010001=>111011000100=>011011000100=>[1,2,1,2,3,1,2] 101110000101=>111011010000=>011011010000=>[1,2,1,2,1,1,4] 101001011111=>111100001010=>011100001010=>[1,3,4,1,1,1,1] 101001011001=>111100001100=>011100001100=>[1,3,4,2,2] 101001000111=>111100010010=>011100010010=>[1,3,3,1,2,1,1] 101001000001=>111100010100=>011100010100=>[1,3,3,1,1,1,2] 101001001101=>111100011000=>011100011000=>[1,3,3,2,3] 101001110111=>111100100010=>011100100010=>[1,3,2,1,3,1,1] 101001110001=>111100100100=>011100100100=>[1,3,2,1,2,1,2] 101001100101=>111100110000=>011100110000=>[1,3,2,2,4] 101000010111=>111101000010=>011101000010=>[1,3,1,1,4,1,1] 101000010001=>111101000100=>011101000100=>[1,3,1,1,3,1,2] 101000011101=>111101001000=>011101001000=>[1,3,1,1,2,1,3] 101000110101=>111101100000=>011101100000=>[1,3,1,2,5] 101011010001=>111110000100=>011110000100=>[1,4,4,1,2] 101011000101=>111110010000=>011110010000=>[1,4,2,1,4] 101010010101=>111111000000=>011111000000=>[1,5,6] 0000000000=>0101010101=>1101010101=>[2,1,1,1,1,1,1,1,1] 0000000110=>0101010011=>1101010011=>[2,1,1,1,1,2,2] 0000011000=>0101001101=>1101001101=>[2,1,1,2,2,1,1] 0000011110=>0101001011=>1101001011=>[2,1,1,2,1,1,2] 0000010010=>0101000111=>1101000111=>[2,1,1,3,3] 0001100000=>0100110101=>1100110101=>[2,2,2,1,1,1,1] 0001100110=>0100110011=>1100110011=>[2,2,2,2,2] 0001111000=>0100101101=>1100101101=>[2,2,1,1,2,1,1] 0001111110=>0100101011=>1100101011=>[2,2,1,1,1,1,2] 0001110010=>0100100111=>1100100111=>[2,2,1,2,3] 0001001110=>0100011011=>1100011011=>[2,3,2,1,2] 0001000010=>0100010111=>1100010111=>[2,3,1,1,3] 0001011010=>0100001111=>1100001111=>[2,4,4] 0110000000=>0011010101=>1011010101=>[1,1,2,1,1,1,1,1,1] 0110011000=>0011001101=>1011001101=>[1,1,2,2,2,1,1] 0110010010=>0011000111=>1011000111=>[1,1,2,3,3] 0111100000=>0010110101=>1010110101=>[1,1,1,1,2,1,1,1,1] 0111111000=>0010101101=>1010101101=>[1,1,1,1,1,1,2,1,1] 0111111110=>0010101011=>1010101011=>[1,1,1,1,1,1,1,1,2] 0111110010=>0010100111=>1010100111=>[1,1,1,1,1,2,3] 0111001000=>0010011101=>1010011101=>[1,1,1,2,3,1,1] 0111000010=>0010010111=>1010010111=>[1,1,1,2,1,1,3] 0100100110=>0001110011=>1001110011=>[1,2,3,2,2] 0100111000=>0001101101=>1001101101=>[1,2,2,1,2,1,1] 0100111110=>0001101011=>1001101011=>[1,2,2,1,1,1,2] 0100110010=>0001100111=>1001100111=>[1,2,2,2,3] 0100001000=>0001011101=>1001011101=>[1,2,1,1,3,1,1] 0100001110=>0001011011=>1001011011=>[1,2,1,1,2,1,2] 0100000010=>0001010111=>1001010111=>[1,2,1,1,1,1,3] 0100011010=>0001001111=>1001001111=>[1,2,1,2,4] 0101101000=>0000111101=>1000111101=>[1,3,4,1,1] 0101100010=>0000110111=>1000110111=>[1,3,2,1,3] 0101111010=>0000101111=>1000101111=>[1,3,1,1,4] 0101001010=>0000011111=>1000011111=>[1,4,5] 000000000000=>010101010101=>110101010101=>[2,1,1,1,1,1,1,1,1,1,1] 000001111110=>010100101011=>110100101011=>[2,1,1,2,1,1,1,1,2] 000110011110=>010011001011=>110011001011=>[2,2,2,2,1,1,2] 000111100110=>010010110011=>110010110011=>[2,2,1,1,2,2,2] 000111111000=>010010101101=>110010101101=>[2,2,1,1,1,1,2,1,1] 000111110010=>010010100111=>110010100111=>[2,2,1,1,1,2,3] 000111001110=>010010011011=>110010011011=>[2,2,1,2,2,1,2] 000111011010=>010010001111=>110010001111=>[2,2,1,3,4] 000100100000=>010001110101=>110001110101=>[2,3,3,1,1,1,1] 000100111000=>010001101101=>110001101101=>[2,3,2,1,2,1,1] 000100111110=>010001101011=>110001101011=>[2,3,2,1,1,1,2] 000101101000=>010000111101=>110000111101=>[2,4,4,1,1] 000101101110=>010000111011=>110000111011=>[2,4,3,1,2] 000101111010=>010000101111=>110000101111=>[2,4,1,1,4] 011000011110=>001101001011=>101101001011=>[1,1,2,1,1,2,1,1,2] 011001100110=>001100110011=>101100110011=>[1,1,2,2,2,2,2] 011001111000=>001100101101=>101100101101=>[1,1,2,2,1,1,2,1,1] 011001110010=>001100100111=>101100100111=>[1,1,2,2,1,2,3] 011001001000=>001100011101=>101100011101=>[1,1,2,3,3,1,1] 011001001110=>001100011011=>101100011011=>[1,1,2,3,2,1,2] 011001011010=>001100001111=>101100001111=>[1,1,2,4,4] 011110000110=>001011010011=>101011010011=>[1,1,1,1,2,1,1,2,2] 011110011000=>001011001101=>101011001101=>[1,1,1,1,2,2,2,1,1] 011110010010=>001011000111=>101011000111=>[1,1,1,1,2,3,3] 011111100000=>001010110101=>101010110101=>[1,1,1,1,1,1,2,1,1,1,1] 011111001000=>001010011101=>101010011101=>[1,1,1,1,1,2,3,1,1] 011111000010=>001010010111=>101010010111=>[1,1,1,1,1,2,1,1,3] 011100100110=>001001110011=>101001110011=>[1,1,1,2,3,2,2] 011100111000=>001001101101=>101001101101=>[1,1,1,2,2,1,2,1,1] 011100110010=>001001100111=>101001100111=>[1,1,1,2,2,2,3] 011100011010=>001001001111=>101001001111=>[1,1,1,2,1,2,4] 011101101000=>001000111101=>101000111101=>[1,1,1,3,4,1,1] 011101100010=>001000110111=>101000110111=>[1,1,1,3,2,1,3] 011101001010=>001000011111=>101000011111=>[1,1,1,4,5] 010010000110=>000111010011=>100111010011=>[1,2,3,1,1,2,2] 010010011000=>000111001101=>100111001101=>[1,2,3,2,2,1,1] 010010011110=>000111001011=>100111001011=>[1,2,3,2,1,1,2] 010011100110=>000110110011=>100110110011=>[1,2,2,1,2,2,2] 010011111000=>000110101101=>100110101101=>[1,2,2,1,1,1,2,1,1] 010011110010=>000110100111=>100110100111=>[1,2,2,1,1,2,3] 010011001000=>000110011101=>100110011101=>[1,2,2,2,3,1,1] 010011001110=>000110011011=>100110011011=>[1,2,2,2,2,1,2] 010011011010=>000110001111=>100110001111=>[1,2,2,3,4] 010000100000=>000101110101=>100101110101=>[1,2,1,1,3,1,1,1,1] 010000111110=>000101101011=>100101101011=>[1,2,1,1,2,1,1,1,2] 010001101000=>000100111101=>100100111101=>[1,2,1,2,4,1,1] 010001101110=>000100111011=>100100111011=>[1,2,1,2,3,1,2] 010001111010=>000100101111=>100100101111=>[1,2,1,2,1,1,4] 010110100000=>000011110101=>100011110101=>[1,3,4,1,1,1,1] 010110100110=>000011110011=>100011110011=>[1,3,4,2,2] 010110111000=>000011101101=>100011101101=>[1,3,3,1,2,1,1] 010110111110=>000011101011=>100011101011=>[1,3,3,1,1,1,2] 010110110010=>000011100111=>100011100111=>[1,3,3,2,3] 010110001000=>000011011101=>100011011101=>[1,3,2,1,3,1,1] 010110001110=>000011011011=>100011011011=>[1,3,2,1,2,1,2] 010110011010=>000011001111=>100011001111=>[1,3,2,2,4] 010111101000=>000010111101=>100010111101=>[1,3,1,1,4,1,1] 010111101110=>000010111011=>100010111011=>[1,3,1,1,3,1,2] 010111100010=>000010110111=>100010110111=>[1,3,1,1,2,1,3] 010111001010=>000010011111=>100010011111=>[1,3,1,2,5] 010100101000=>000001111101=>100001111101=>[1,4,5,1,1] 010100101110=>000001111011=>100001111011=>[1,4,4,1,2] 010100111010=>000001101111=>100001101111=>[1,4,2,1,4] 010101101010=>000000111111=>100000111111=>[1,5,6] 0010101010=>0111111111=>1111111111=>[10] 0010101000=>0111111101=>1111111101=>[8,1,1] 0010101100=>0111111001=>1111111001=>[7,2,1] 0010100100=>0111110001=>1111110001=>[6,3,1] 0010110100=>0111100001=>1111100001=>[5,4,1] 0010010100=>0111000001=>1111000001=>[4,5,1] 0011010100=>0110000001=>1110000001=>[3,6,1] 0001010100=>0100000001=>1100000001=>[2,7,1] 0101010100=>0000000001=>1000000001=>[1,8,1] 00101010101=>01111111111=>11111111111=>[11] 00101010111=>01111111101=>11111111101=>[9,1,1] 0010101110=>0111111011=>1111111011=>[7,1,2] 00101010011=>01111111001=>11111111001=>[8,2,1] 0010100000=>0111110101=>1111110101=>[6,1,1,1,1] 00101011011=>01111110001=>11111110001=>[7,3,1] 0010111100=>0111101001=>1111101001=>[5,1,1,2,1] 00101001011=>01111100001=>11111100001=>[6,4,1] 0010000100=>0111010001=>1111010001=>[4,1,1,3,1] 00101101011=>01111000001=>11111000001=>[5,5,1] 0011110100=>0110100001=>1110100001=>[3,1,1,4,1] 00100101011=>01110000001=>11110000001=>[4,6,1] 0000010100=>0101000001=>1101000001=>[2,1,1,5,1] 00110101011=>01100000001=>11100000001=>[3,7,1] 0111010100=>0010000001=>1010000001=>[1,1,1,6,1] 00010101011=>01000000001=>11000000001=>[2,8,1] 01010101011=>00000000001=>10000000001=>[1,9,1] 0000000010=>0101010111=>1101010111=>[2,1,1,1,1,1,3] 0000001010=>0101011111=>1101011111=>[2,1,1,1,5] 0000010110=>0101000011=>1101000011=>[2,1,1,4,2] 0000101110=>0101111011=>1101111011=>[2,1,4,1,2] 0001011110=>0100001011=>1100001011=>[2,4,1,1,2] 0011001010=>0110011111=>1110011111=>[3,2,5] 0011001100=>0110011001=>1110011001=>[3,2,2,2,1] 0011010010=>0110000111=>1110000111=>[3,4,3] 0011100100=>0110110001=>1110110001=>[3,1,2,3,1] 0011110000=>0110100101=>1110100101=>[3,1,1,2,1,1,1] 0101011000=>0000001101=>1000001101=>[1,5,2,1,1] 0101100100=>0000110001=>1000110001=>[1,3,2,3,1] 0110001100=>0011011001=>1011011001=>[1,1,2,1,2,2,1] 0110100010=>0011110111=>1011110111=>[1,1,4,1,3] 0110100100=>0011110001=>1011110001=>[1,1,4,3,1] 0110101000=>0011111101=>1011111101=>[1,1,6,1,1] 011010001100=>001111011001=>101111011001=>[1,1,4,1,2,2,1] 011010010010=>001111000111=>101111000111=>[1,1,4,3,3] 011010011000=>001111001101=>101111001101=>[1,1,4,2,2,1,1] 011010100100=>001111110001=>101111110001=>[1,1,6,3,1] 10101010101=>11111111111=>01111111111=>[1,10] 10101001010=>11111100000=>01111100000=>[1,5,5] 10010010101=>11000111111=>01000111111=>[1,1,3,6] 10010100101=>11000001111=>01000001111=>[1,1,5,4] 10010101001=>11000000011=>01000000011=>[1,1,7,2] 01000100010=>00010001000=>10010001000=>[1,2,1,3,1,3] 01000010100=>00010111110=>10010111110=>[1,2,1,1,5,1] 01000001000=>00010100010=>10010100010=>[1,2,1,1,1,3,1,1] 01010000100=>00000101110=>10000101110=>[1,4,1,1,3,1] 01010101010=>00000000000=>10000000000=>[1,10] 01010100100=>00000001110=>10000001110=>[1,6,3,1] 01010010100=>00000111110=>10000111110=>[1,4,5,1] 01010001000=>00000100010=>10000100010=>[1,4,1,3,1,1] 01001010100=>00011111110=>10011111110=>[1,2,7,1] 00101001010=>01111100000=>11111100000=>[6,5] 00101010100=>01111111110=>11111111110=>[10,1] 00101001000=>01111100010=>11111100010=>[6,3,1,1] 00100101000=>01110000010=>11110000010=>[4,5,1,1] 00010101000=>01000000010=>11000000010=>[2,7,1,1] 0100000000=>0001010101=>1001010101=>[1,2,1,1,1,1,1,1,1] 0100000011=>0001010110=>1001010110=>[1,2,1,1,1,1,2,1] 0100000111=>0001010010=>1001010010=>[1,2,1,1,1,2,1,1] 0100011111=>0001001010=>1001001010=>[1,2,1,2,1,1,1,1] 0100111111=>0001101010=>1001101010=>[1,2,2,1,1,1,1,1] 0101111111=>0000101010=>1000101010=>[1,3,1,1,1,1,1,1] 01000000000=>00010101010=>10010101010=>[1,2,1,1,1,1,1,1,1,1] 01000000011=>00010101001=>10010101001=>[1,2,1,1,1,1,1,2,1] 0100001011=>0001011110=>1001011110=>[1,2,1,1,4,1] 01000001111=>00010100101=>10010100101=>[1,2,1,1,1,2,1,1,1] 01000111111=>00010010101=>10010010101=>[1,2,1,2,1,1,1,1,1] 0101011111=>0000001010=>1000001010=>[1,5,1,1,1,1] 01011111111=>00001010101=>10001010101=>[1,3,1,1,1,1,1,1,1] 0101010110=>0000000011=>1000000011=>[1,7,2] 0101011010=>0000001111=>1000001111=>[1,5,4] 0101011100=>0000001001=>1000001001=>[1,5,1,2,1] 0101100110=>0000110011=>1000110011=>[1,3,2,2,2] 0101101001=>0000111100=>1000111100=>[1,3,4,2] 0101101100=>0000111001=>1000111001=>[1,3,3,2,1] 0101110010=>0000100111=>1000100111=>[1,3,1,2,3] 0101111000=>0000101101=>1000101101=>[1,3,1,1,2,1,1] 0110010101=>0011000000=>1011000000=>[1,1,2,6] 0110010110=>0011000011=>1011000011=>[1,1,2,4,2] 0110011001=>0011001100=>1011001100=>[1,1,2,2,2,2] 0110011100=>0011001001=>1011001001=>[1,1,2,2,1,2,1] 0110100101=>0011110000=>1011110000=>[1,1,4,4] 0110101001=>0011111100=>1011111100=>[1,1,6,2] 0110101010=>0011111111=>1011111111=>[1,1,8] 0110110001=>0011100100=>1011100100=>[1,1,3,2,1,2] 0110110100=>0011100001=>1011100001=>[1,1,3,4,1] 0111000110=>0010010011=>1010010011=>[1,1,1,2,1,2,2] 0111001100=>0010011001=>1010011001=>[1,1,1,2,2,2,1] 0111010010=>0010000111=>1010000111=>[1,1,1,4,3] 0111011000=>0010001101=>1010001101=>[1,1,1,3,2,1,1] 0111100010=>0010110111=>1010110111=>[1,1,1,1,2,1,3] 0111100100=>0010110001=>1010110001=>[1,1,1,1,2,3,1] 0111110000=>0010100101=>1010100101=>[1,1,1,1,1,2,1,1,1] 011001101100=>001100111001=>101100111001=>[1,1,2,2,3,2,1] 011001110100=>001100100001=>101100100001=>[1,1,2,2,1,4,1] 011011000110=>001110010011=>101110010011=>[1,1,3,2,1,2,2] 011011001100=>001110011001=>101110011001=>[1,1,3,2,2,2,1] 011011100010=>001110110111=>101110110111=>[1,1,3,1,2,1,3] 011011100100=>001110110001=>101110110001=>[1,1,3,1,2,3,1] 011100010110=>001001000011=>101001000011=>[1,1,1,2,1,4,2] 011100101100=>001001111001=>101001111001=>[1,1,1,2,4,2,1] 011100110100=>001001100001=>101001100001=>[1,1,1,2,2,4,1] 011101000110=>001000010011=>101000010011=>[1,1,1,4,1,2,2] 011101001100=>001000011001=>101000011001=>[1,1,1,4,2,2,1] 011101100100=>001000110001=>101000110001=>[1,1,1,3,2,3,1] 011110001010=>001011011111=>101011011111=>[1,1,1,1,2,1,5] 011110010100=>001011000001=>101011000001=>[1,1,1,1,2,5,1] 011110100010=>001011110111=>101011110111=>[1,1,1,1,4,1,3] 011110100100=>001011110001=>101011110001=>[1,1,1,1,4,3,1] 0011101010=>0110111111=>1110111111=>[3,1,6] 0010110110=>0111100011=>1111100011=>[5,3,2] 0001110110=>0100100011=>1100100011=>[2,2,1,3,2] 0011111000=>0110101101=>1110101101=>[3,1,1,1,2,1,1] 0100111100=>0001101001=>1001101001=>[1,2,2,1,1,2,1] 0001111100=>0100101001=>1100101001=>[2,2,1,1,1,2,1] 001111000110=>011010010011=>111010010011=>[3,1,1,2,1,2,2] 001111001100=>011010011001=>111010011001=>[3,1,1,2,2,2,1] 001011010110=>011110000011=>111110000011=>[5,5,2] 001111010010=>011010000111=>111010000111=>[3,1,1,4,3] 001111011000=>011010001101=>111010001101=>[3,1,1,3,2,1,1] 001011011100=>011110001001=>111110001001=>[5,3,1,2,1] 001101100110=>011000110011=>111000110011=>[3,3,2,2,2] 001101101100=>011000111001=>111000111001=>[3,3,3,2,1] 001111100100=>011010110001=>111010110001=>[3,1,1,1,2,3,1] 010011101100=>000110111001=>100110111001=>[1,2,2,1,3,2,1] 001001110110=>011100100011=>111100100011=>[4,2,1,3,2] 001111110000=>011010100101=>111010100101=>[3,1,1,1,1,2,1,1,1] 010011110100=>000110100001=>100110100001=>[1,2,2,1,1,4,1] 001011110100=>011110100001=>111110100001=>[5,1,1,4,1] 000011110110=>010110100011=>110110100011=>[2,1,2,1,1,3,2] 001001111100=>011100101001=>111100101001=>[4,2,1,1,1,2,1] 000011111100=>010110101001=>110110101001=>[2,1,2,1,1,1,1,2,1] 0000001101=>0101011000=>1101011000=>[2,1,1,1,2,3] 0000011101=>0101001000=>1101001000=>[2,1,1,2,1,3] 0011111101=>0110101000=>1110101000=>[3,1,1,1,1,3] 0000101101=>0101111000=>1101111000=>[2,1,4,3] 0010111101=>0111101000=>1111101000=>[5,1,1,3] 0111000011=>0010010110=>1010010110=>[1,1,1,2,1,1,2,1] 01111111011=>00101010001=>10101010001=>[1,1,1,1,1,1,1,3,1] 0011101101=>0110111000=>1110111000=>[3,1,3,3] 0010110001=>0111100100=>1111100100=>[5,2,1,2] 0001100001=>0100110100=>1100110100=>[2,2,2,1,1,2] 0111010101=>0010000000=>1010000000=>[1,1,1,7] 0011111001=>0110101100=>1110101100=>[3,1,1,1,2,2] 011100110011=>001001100110=>101001100110=>[1,1,1,2,2,2,2,1] 011101100011=>001000110110=>101000110110=>[1,1,1,3,2,1,2,1] 011100001111=>001001011010=>101001011010=>[1,1,1,2,1,1,2,1,1,1] 001111001101=>011010011000=>111010011000=>[3,1,1,2,2,3] 001111011001=>011010001100=>111010001100=>[3,1,1,3,2,2] 001111000111=>011010010010=>111010010010=>[3,1,1,2,1,2,1,1] 011110100101=>001011110000=>101011110000=>[1,1,1,1,4,4] 011110001101=>001011011000=>101011011000=>[1,1,1,1,2,1,2,3] 011110011001=>001011001100=>101011001100=>[1,1,1,1,2,2,2,2] 011110110001=>001011100100=>101011100100=>[1,1,1,1,3,2,1,2] 011110000111=>001011010010=>101011010010=>[1,1,1,1,2,1,1,2,1,1] 001111100101=>011010110000=>111010110000=>[3,1,1,1,2,4] 011111000011=>001010010110=>101010010110=>[1,1,1,1,1,2,1,1,2,1] 000011111101=>010110101000=>110110101000=>[2,1,2,1,1,1,1,3] 000111111001=>010010101100=>110010101100=>[2,2,1,1,1,1,2,2] 001111110001=>011010100100=>111010100100=>[3,1,1,1,1,2,1,2] 011111100001=>001010110100=>101010110100=>[1,1,1,1,1,1,2,1,1,2] 000001111111=>010100101010=>110100101010=>[2,1,1,2,1,1,1,1,1,1] 0001101100=>0100111001=>1100111001=>[2,2,3,2,1] 0010011100=>0111001001=>1111001001=>[4,2,1,2,1] 0000111100=>0101101001=>1101101001=>[2,1,2,1,1,2,1] 0001101010=>0100111111=>1100111111=>[2,2,6] 0000111010=>0101101111=>1101101111=>[2,1,2,1,4] 0011000110=>0110010011=>1110010011=>[3,2,1,2,2] 0010010110=>0111000011=>1111000011=>[4,4,2] 0001010110=>0100000011=>1100000011=>[2,6,2] 0000110110=>0101100011=>1101100011=>[2,1,2,3,2] 001001101100=>011100111001=>111100111001=>[4,2,3,2,1] 001010011100=>011111001001=>111111001001=>[6,2,1,2,1] 001000111100=>011101101001=>111101101001=>[4,1,2,1,1,2,1] 001001011010=>011100001111=>111100001111=>[4,4,4] 001001100110=>011100110011=>111100110011=>[4,2,2,2,2] 001010010110=>011111000011=>111111000011=>[6,4,2] 001000110110=>011101100011=>111101100011=>[4,1,2,3,2] 0001101001=>0100111100=>1100111100=>[2,2,4,2] 0100111001=>0001101100=>1001101100=>[1,2,2,1,2,2] 0100100001=>0001110100=>1001110100=>[1,2,3,1,1,2] 0101100001=>0000110100=>1000110100=>[1,3,2,1,1,2] 0101111011=>0000101110=>1000101110=>[1,3,1,1,3,1] 0101100011=>0000110110=>1000110110=>[1,3,2,1,2,1] 0101000011=>0000010110=>1000010110=>[1,4,1,1,2,1] 0101101111=>0000111010=>1000111010=>[1,3,3,1,1,1] 101001011010=>111100001111=>011100001111=>[1,3,4,4] 101001100110=>111100110011=>011100110011=>[1,3,2,2,2,2] 101010010110=>111111000011=>011111000011=>[1,5,4,2] 01011101110=>00001000100=>10001000100=>[1,3,1,3,1,2] 01101011010=>00111110000=>10111110000=>[1,1,5,4] 01101010101=>00111111111=>10111111111=>[1,1,9] 01110111011=>00100010001=>10100010001=>[1,1,1,3,1,3,1] 11011010101=>10001111111=>00001111111=>[4,7] 11010110101=>10000011111=>00000011111=>[6,5] 11010101101=>10000000111=>00000000111=>[8,3] 11010101011=>10000000001=>00000000001=>[10,1] 11101010111=>10111111101=>00111111101=>[2,7,1,1] 11110111011=>10100010001=>00100010001=>[2,1,3,1,3,1] 0000001100=>0101011001=>1101011001=>[2,1,1,1,2,2,1] 0000011001=>0101001100=>1101001100=>[2,1,1,2,2,2] 0000110011=>0101100110=>1101100110=>[2,1,2,2,2,1] 0110011111=>0011001010=>1011001010=>[1,1,2,2,1,1,1,1] 0000110100=>0101100001=>1101100001=>[2,1,2,4,1] 0000011011=>0101001110=>1101001110=>[2,1,1,2,3,1] 00000000011=>01010101001=>11010101001=>[2,1,1,1,1,1,1,2,1] 10001010101=>11011111111=>01011111111=>[1,1,1,8] 0111100111=>0010110010=>1010110010=>[1,1,1,1,2,2,1,1] 0110000111=>0011010010=>1011010010=>[1,1,2,1,1,2,1,1] 0011010110=>0110000011=>1110000011=>[3,5,2] 0100110110=>0001100011=>1001100011=>[1,2,2,3,2] 0101001110=>0000011011=>1000011011=>[1,4,2,1,2] 0100011110=>0001001011=>1001001011=>[1,2,1,2,1,1,2] 0010011110=>0111001011=>1111001011=>[4,2,1,1,2] 001101011010=>011000001111=>111000001111=>[3,5,4] 011000111010=>001101101111=>101101101111=>[1,1,2,1,2,1,4] 001110010110=>011011000011=>111011000011=>[3,1,2,4,2] 011000110110=>001101100011=>101101100011=>[1,1,2,1,2,3,2] 001100110110=>011001100011=>111001100011=>[3,2,2,3,2] 000110110110=>010011100011=>110011100011=>[2,2,3,3,2] 010001110110=>000100100011=>100100100011=>[1,2,1,2,1,3,2] 011000101110=>001101111011=>101101111011=>[1,1,2,1,4,1,2] 0101000000=>0000010101=>1000010101=>[1,4,1,1,1,1,1] 0001010101=>0100000000=>1100000000=>[2,8] 0101010001=>0000000100=>1000000100=>[1,6,1,2] 0101011011=>0000001110=>1000001110=>[1,5,3,1] 0001001011=>0100011110=>1100011110=>[2,3,4,1] 0110101011=>0011111110=>1011111110=>[1,1,7,1] 0001100011=>0100110110=>1100110110=>[2,2,2,1,2,1] 011000100100=>001101110001=>101101110001=>[1,1,2,1,3,3,1] 010000101100=>000101111001=>100101111001=>[1,2,1,1,4,2,1] 0111000000=>0010010101=>1010010101=>[1,1,1,2,1,1,1,1,1] 0010000000=>0111010101=>1111010101=>[4,1,1,1,1,1,1] 01110000000=>00100101010=>10100101010=>[1,1,1,2,1,1,1,1,1,1] 01111100000=>00101001010=>10101001010=>[1,1,1,1,1,2,1,1,1,1] 01111111000=>00101010010=>10101010010=>[1,1,1,1,1,1,1,2,1,1] 0000000111=>0101010010=>1101010010=>[2,1,1,1,1,2,1,1] 0000001111=>0101011010=>1101011010=>[2,1,1,1,2,1,1,1] 0001111111=>0100101010=>1100101010=>[2,2,1,1,1,1,1,1] 0011111111=>0110101010=>1110101010=>[3,1,1,1,1,1,1,1] 0011101110=>0110111011=>1110111011=>[3,1,3,1,2] 0011110110=>0110100011=>1110100011=>[3,1,1,3,2] 0011111010=>0110101111=>1110101111=>[3,1,1,1,4] 0011111100=>0110101001=>1110101001=>[3,1,1,1,1,2,1] 0001111001=>0100101100=>1100101100=>[2,2,1,1,2,2] 001100111100=>011001101001=>111001101001=>[3,2,2,1,1,2,1] 001110110100=>011011100001=>111011100001=>[3,1,3,4,1] 0000011010=>0101001111=>1101001111=>[2,1,1,2,4] 0000101010=>0101111111=>1101111111=>[2,1,7] 11111111011=>10101010001=>00101010001=>[2,1,1,1,1,1,3,1] 000111100001=>010010110100=>110010110100=>[2,2,1,1,2,1,1,2] 000110011001=>010011001100=>110011001100=>[2,2,2,2,2,2] 000110110001=>010011100100=>110011100100=>[2,2,3,2,1,2] 000110100101=>010011110000=>110011110000=>[2,2,4,4] 001101100001=>011000110100=>111000110100=>[3,3,2,1,1,2] 001100011001=>011001001100=>111001001100=>[3,2,1,2,2,2] 001100110001=>011001100100=>111001100100=>[3,2,2,2,1,2] 001100100101=>011001110000=>111001110000=>[3,2,3,4] 001111000001=>011010010100=>111010010100=>[3,1,1,2,1,1,1,2] 001110010001=>011011000100=>111011000100=>[3,1,2,3,1,2] 001110000101=>011011010000=>111011010000=>[3,1,2,1,1,4] 001001011001=>011100001100=>111100001100=>[4,4,2,2] 001001110001=>011100100100=>111100100100=>[4,2,1,2,1,2] 001001100101=>011100110000=>111100110000=>[4,2,2,4] 001011010001=>011110000100=>111110000100=>[5,4,1,2] 001011000101=>011110010000=>111110010000=>[5,2,1,4] 001010010101=>011111000000=>111111000000=>[6,6] 11000100010=>10010001000=>00010001000=>[3,1,3,1,3] 10101001000=>11111100010=>01111100010=>[1,5,3,1,1] 00010101010=>01000000000=>11000000000=>[2,9] 001110011100=>011011001001=>111011001001=>[3,1,2,2,1,2,1] 11000100000=>10010001010=>00010001010=>[3,1,3,1,1,1,1] 01000100000=>00010001010=>10010001010=>[1,2,1,3,1,1,1,1] 101001101100=>111100111001=>011100111001=>[1,3,2,3,2,1] 101000111100=>111101101001=>011101101001=>[1,3,1,2,1,1,2,1] 0010010101=>0111000000=>1111000000=>[4,6] 00001010101=>01011111111=>11011111111=>[2,1,8] 0010010011=>0111000110=>1111000110=>[4,3,2,1] 0000101011=>0101111110=>1101111110=>[2,1,6,1] 0000100111=>0101110010=>1101110010=>[2,1,3,2,1,1] 0010010010=>0111000111=>1111000111=>[4,3,3] 0001001001=>0100011100=>1100011100=>[2,3,3,2] 0000100100=>0101110001=>1101110001=>[2,1,3,3,1] 0000100010=>0101110111=>1101110111=>[2,1,3,1,3] 0011000000=>0110010101=>1110010101=>[3,2,1,1,1,1,1] 0101010111=>0000000010=>1000000010=>[1,7,1,1] 11010101001=>10000000011=>00000000011=>[9,2] 101010011100=>111111001001=>011111001001=>[1,5,2,1,2,1] 111000101110=>101101111011=>001101111011=>[2,2,1,4,1,2] 110011001110=>100110011011=>000110011011=>[3,2,2,2,1,2] 101100111100=>111001101001=>011001101001=>[1,2,2,2,1,1,2,1] 111000011110=>101101001011=>001101001011=>[2,2,1,1,2,1,1,2] 101001111100=>111100101001=>011100101001=>[1,3,2,1,1,1,2,1] 101111110000=>111010100101=>011010100101=>[1,2,1,1,1,1,2,1,1,1] 11111100000=>10101001010=>00101001010=>[2,1,1,1,2,1,1,1,1] 100011001100=>110110011001=>010110011001=>[1,1,1,2,2,2,2,1] 100011110000=>110110100101=>010110100101=>[1,1,1,2,1,1,2,1,1,1] 111000001010=>101101011111=>001101011111=>[2,2,1,1,1,5] 111110000000=>101011010101=>001011010101=>[2,1,1,2,1,1,1,1,1,1] 11001010101=>10011111111=>00011111111=>[3,8] 10011010101=>11001111111=>01001111111=>[1,1,2,7] 0000101100=>0101111001=>1101111001=>[2,1,4,2,1] 0010101111=>0111111010=>1111111010=>[7,1,1,1] 0011100001=>0110110100=>1110110100=>[3,1,2,1,1,2] 01010101000=>00000000010=>10000000010=>[1,8,1,1] 0000101000=>0101111101=>1101111101=>[2,1,5,1,1] 000011010010=>010110000111=>110110000111=>[2,1,2,4,3] 001000010110=>011101000011=>111101000011=>[4,1,1,4,2] 001001010010=>011100000111=>111100000111=>[4,5,3] 001001000110=>011100010011=>111100010011=>[4,3,1,2,2] 101000000000=>111101010101=>011101010101=>[1,3,1,1,1,1,1,1,1,1] 10000000011=>11010101001=>01010101001=>[1,1,1,1,1,1,1,1,2,1] 111010110100=>101111100001=>001111100001=>[2,5,4,1] 111101100010=>101000110111=>001000110111=>[2,1,3,2,1,3] 111101100100=>101000110001=>001000110001=>[2,1,3,2,3,1] 111110001100=>101011011001=>001011011001=>[2,1,1,2,1,2,2,1] 111110010010=>101011000111=>001011000111=>[2,1,1,2,3,3] 111110011000=>101011001101=>001011001101=>[2,1,1,2,2,2,1,1] 111110100100=>101011110001=>001011110001=>[2,1,1,4,3,1] 100010110100=>110111100001=>010111100001=>[1,1,1,4,4,1] 100011010010=>110110000111=>010110000111=>[1,1,1,2,4,3] 100011100100=>110110110001=>010110110001=>[1,1,1,2,1,2,3,1] 100101001010=>110000011111=>010000011111=>[1,1,5,5] 100110001100=>110011011001=>010011011001=>[1,1,2,2,1,2,2,1] 100110010010=>110011000111=>010011000111=>[1,1,2,2,3,3] 100111100000=>110010110101=>010010110101=>[1,1,2,1,1,2,1,1,1,1] 101000110100=>111101100001=>011101100001=>[1,3,1,2,4,1] 101001001100=>111100011001=>011100011001=>[1,3,3,2,2,1] 101001010010=>111100000111=>011100000111=>[1,3,5,3] 101001100100=>111100110001=>011100110001=>[1,3,2,2,3,1] 101001110000=>111100100101=>011100100101=>[1,3,2,1,2,1,1,1] 101010010100=>111111000001=>011111000001=>[1,5,5,1] 101011000100=>111110010001=>011110010001=>[1,4,2,1,3,1] 101011010000=>111110000101=>011110000101=>[1,4,4,1,1,1] 101100001100=>111001011001=>011001011001=>[1,2,2,1,1,2,2,1] 101100010010=>111001000111=>011001000111=>[1,2,2,1,3,3] 101100100100=>111001110001=>011001110001=>[1,2,2,3,3,1] 101100110000=>111001100101=>011001100101=>[1,2,2,2,2,1,1,1] 101101100000=>111000110101=>011000110101=>[1,2,3,2,1,1,1,1] 101110000100=>111011010001=>011011010001=>[1,2,1,2,1,1,3,1] 101110010000=>111011000101=>011011000101=>[1,2,1,2,3,1,1,1] 101111000000=>111010010101=>011010010101=>[1,2,1,1,2,1,1,1,1,1] 010010100000=>000111110101=>100111110101=>[1,2,5,1,1,1,1] 0011000100=>0110010001=>1110010001=>[3,2,1,3,1] 0001001100=>0100011001=>1100011001=>[2,3,2,2,1] 0001000110=>0100010011=>1100010011=>[2,3,1,2,2] 0001100100=>0100110001=>1100110001=>[2,2,2,3,1] 110011000010=>100110010111=>000110010111=>[3,2,2,1,1,3] 110011100110=>100110110011=>000110110011=>[3,2,1,2,2,2] 110011110100=>100110100001=>000110100001=>[3,2,1,1,4,1] 110001100010=>100100110111=>000100110111=>[3,1,2,2,1,3] 110001110110=>100100100011=>000100100011=>[3,1,2,1,3,2] 110001111010=>100100101111=>000100101111=>[3,1,2,1,1,4] 111001001110=>101100011011=>001100011011=>[2,2,3,2,1,2] 111001000010=>101100010111=>001100010111=>[2,2,3,1,1,3] 111001100110=>101100110011=>001100110011=>[2,2,2,2,2,2] 111001110010=>101100100111=>001100100111=>[2,2,2,1,2,3] 111000100010=>101101110111=>001101110111=>[2,2,1,3,1,3] 111000110110=>101101100011=>001101100011=>[2,2,1,2,3,2] 111000111010=>101101101111=>001101101111=>[2,2,1,2,1,4] 111101111010=>101000101111=>001000101111=>[2,1,3,1,1,4] 111111011010=>101010001111=>001010001111=>[2,1,1,1,3,4] 01000111011=>00010010001=>10010010001=>[1,2,1,2,1,3,1] 0101001000=>0000011101=>1000011101=>[1,4,3,1,1] 0101010000=>0000000101=>1000000101=>[1,6,1,1,1] 0010010000=>0111000101=>1111000101=>[4,3,1,1,1] 01010101111=>00000000101=>10000000101=>[1,7,1,1,1] 10101010111=>11111111101=>01111111101=>[1,8,1,1] 0111101010=>0010111111=>1010111111=>[1,1,1,1,6] 0001000000=>0100010101=>1100010101=>[2,3,1,1,1,1,1] 0010011001=>0111001100=>1111001100=>[4,2,2,2] 0010100101=>0111110000=>1111110000=>[6,4] 0010101001=>0111111100=>1111111100=>[8,2] 000101101001=>010000111100=>110000111100=>[2,4,4,2] 0010110111=>0111100010=>1111100010=>[5,3,1,1] 0010011111=>0111001010=>1111001010=>[4,2,1,1,1,1] 0000111001=>0101101100=>1101101100=>[2,1,2,1,2,2] 0010001101=>0111011000=>1111011000=>[4,1,2,3] 11000001000=>10010100010=>00010100010=>[3,1,1,1,3,1,1] 11010010101=>10000111111=>00000111111=>[5,6] 11010100101=>10000001111=>00000001111=>[7,4] 11111111000=>10101010010=>00101010010=>[2,1,1,1,1,1,2,1,1] 0110101101=>0011111000=>1011111000=>[1,1,5,3] 0101101011=>0000111110=>1000111110=>[1,3,5,1] 0001111011=>0100101110=>1100101110=>[2,2,1,1,3,1] 11110000000=>10100101010=>00100101010=>[2,1,2,1,1,1,1,1,1] 11011100010=>10001001000=>00001001000=>[4,1,2,1,3] 11011101000=>10001000010=>00001000010=>[4,1,4,1,1] 11110100010=>10100001000=>00100001000=>[2,1,4,1,3] 101000010000=>111101000101=>011101000101=>[1,3,1,1,3,1,1,1] 100010010000=>110111000101=>010111000101=>[1,1,1,3,3,1,1,1] 0010000111=>0111010010=>1111010010=>[4,1,1,2,1,1] 0011100111=>0110110010=>1110110010=>[3,1,2,2,1,1] 0111001111=>0010011010=>1010011010=>[1,1,1,2,2,1,1,1] 01010111111=>00000010101=>10000010101=>[1,5,1,1,1,1,1] 111010000100=>101111010001=>001111010001=>[2,4,1,1,3,1] 0010000110=>0111010011=>1111010011=>[4,1,1,2,2] 11101010101=>10111111111=>00111111111=>[2,9] 11010111111=>10000010101=>00000010101=>[6,1,1,1,1,1] 01000100011=>00010001001=>10010001001=>[1,2,1,3,1,2,1] 11010101111=>10000000101=>00000000101=>[8,1,1,1]
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.
Map
twist
Description
Return the binary word with first letter inverted.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.