Identifier
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Images
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0=>0=>[1] 1=>1=>[1] 00=>01=>[1,1] 01=>00=>[2] 10=>11=>[2] 11=>10=>[1,1] 000=>010=>[1,1,1] 001=>011=>[1,2] 010=>000=>[3] 011=>001=>[2,1] 100=>110=>[2,1] 101=>111=>[3] 110=>100=>[1,2] 111=>101=>[1,1,1] 0000=>0101=>[1,1,1,1] 0001=>0100=>[1,1,2] 0010=>0111=>[1,3] 0011=>0110=>[1,2,1] 0100=>0001=>[3,1] 0101=>0000=>[4] 0110=>0011=>[2,2] 0111=>0010=>[2,1,1] 1000=>1101=>[2,1,1] 1001=>1100=>[2,2] 1010=>1111=>[4] 1011=>1110=>[3,1] 1100=>1001=>[1,2,1] 1101=>1000=>[1,3] 1110=>1011=>[1,1,2] 1111=>1010=>[1,1,1,1] 00000=>01010=>[1,1,1,1,1] 00001=>01011=>[1,1,1,2] 00010=>01000=>[1,1,3] 00011=>01001=>[1,1,2,1] 00100=>01110=>[1,3,1] 00101=>01111=>[1,4] 00110=>01100=>[1,2,2] 00111=>01101=>[1,2,1,1] 01000=>00010=>[3,1,1] 01001=>00011=>[3,2] 01010=>00000=>[5] 01011=>00001=>[4,1] 01100=>00110=>[2,2,1] 01101=>00111=>[2,3] 01110=>00100=>[2,1,2] 01111=>00101=>[2,1,1,1] 10000=>11010=>[2,1,1,1] 10001=>11011=>[2,1,2] 10010=>11000=>[2,3] 10011=>11001=>[2,2,1] 10100=>11110=>[4,1] 10101=>11111=>[5] 10110=>11100=>[3,2] 10111=>11101=>[3,1,1] 11000=>10010=>[1,2,1,1] 11001=>10011=>[1,2,2] 11010=>10000=>[1,4] 11011=>10001=>[1,3,1] 11100=>10110=>[1,1,2,1] 11101=>10111=>[1,1,3] 11110=>10100=>[1,1,1,2] 11111=>10101=>[1,1,1,1,1] 000000=>010101=>[1,1,1,1,1,1] 000001=>010100=>[1,1,1,1,2] 000010=>010111=>[1,1,1,3] 000011=>010110=>[1,1,1,2,1] 000100=>010001=>[1,1,3,1] 000101=>010000=>[1,1,4] 000110=>010011=>[1,1,2,2] 000111=>010010=>[1,1,2,1,1] 001000=>011101=>[1,3,1,1] 001001=>011100=>[1,3,2] 001010=>011111=>[1,5] 001011=>011110=>[1,4,1] 001100=>011001=>[1,2,2,1] 001101=>011000=>[1,2,3] 001110=>011011=>[1,2,1,2] 001111=>011010=>[1,2,1,1,1] 010000=>000101=>[3,1,1,1] 010001=>000100=>[3,1,2] 010010=>000111=>[3,3] 010011=>000110=>[3,2,1] 010100=>000001=>[5,1] 010101=>000000=>[6] 010110=>000011=>[4,2] 010111=>000010=>[4,1,1] 011000=>001101=>[2,2,1,1] 011001=>001100=>[2,2,2] 011010=>001111=>[2,4] 011011=>001110=>[2,3,1] 011100=>001001=>[2,1,2,1] 011101=>001000=>[2,1,3] 011110=>001011=>[2,1,1,2] 011111=>001010=>[2,1,1,1,1] 100000=>110101=>[2,1,1,1,1] 100001=>110100=>[2,1,1,2] 100010=>110111=>[2,1,3] 100011=>110110=>[2,1,2,1] 100100=>110001=>[2,3,1] 100101=>110000=>[2,4] 100110=>110011=>[2,2,2] 100111=>110010=>[2,2,1,1] 101000=>111101=>[4,1,1] 101001=>111100=>[4,2] 101010=>111111=>[6] 101011=>111110=>[5,1] 101100=>111001=>[3,2,1] 101101=>111000=>[3,3] 101110=>111011=>[3,1,2] 101111=>111010=>[3,1,1,1] 110000=>100101=>[1,2,1,1,1] 110001=>100100=>[1,2,1,2] 110010=>100111=>[1,2,3] 110011=>100110=>[1,2,2,1] 110100=>100001=>[1,4,1] 110101=>100000=>[1,5] 110110=>100011=>[1,3,2] 110111=>100010=>[1,3,1,1] 111000=>101101=>[1,1,2,1,1] 111001=>101100=>[1,1,2,2] 111010=>101111=>[1,1,4] 111011=>101110=>[1,1,3,1] 111100=>101001=>[1,1,1,2,1] 111101=>101000=>[1,1,1,3] 111110=>101011=>[1,1,1,1,2] 111111=>101010=>[1,1,1,1,1,1] 0000000=>0101010=>[1,1,1,1,1,1,1] 0000001=>0101011=>[1,1,1,1,1,2] 0000010=>0101000=>[1,1,1,1,3] 0000011=>0101001=>[1,1,1,1,2,1] 0000100=>0101110=>[1,1,1,3,1] 0000101=>0101111=>[1,1,1,4] 0000110=>0101100=>[1,1,1,2,2] 0000111=>0101101=>[1,1,1,2,1,1] 0001000=>0100010=>[1,1,3,1,1] 0001001=>0100011=>[1,1,3,2] 0001010=>0100000=>[1,1,5] 0001011=>0100001=>[1,1,4,1] 0001100=>0100110=>[1,1,2,2,1] 0001101=>0100111=>[1,1,2,3] 0001110=>0100100=>[1,1,2,1,2] 0001111=>0100101=>[1,1,2,1,1,1] 0010000=>0111010=>[1,3,1,1,1] 0010001=>0111011=>[1,3,1,2] 0010010=>0111000=>[1,3,3] 0010011=>0111001=>[1,3,2,1] 0010100=>0111110=>[1,5,1] 0010101=>0111111=>[1,6] 0010110=>0111100=>[1,4,2] 0010111=>0111101=>[1,4,1,1] 0011000=>0110010=>[1,2,2,1,1] 0011001=>0110011=>[1,2,2,2] 0011010=>0110000=>[1,2,4] 0011011=>0110001=>[1,2,3,1] 0011100=>0110110=>[1,2,1,2,1] 0011101=>0110111=>[1,2,1,3] 0011110=>0110100=>[1,2,1,1,2] 0011111=>0110101=>[1,2,1,1,1,1] 0100000=>0001010=>[3,1,1,1,1] 0100001=>0001011=>[3,1,1,2] 0100010=>0001000=>[3,1,3] 0100011=>0001001=>[3,1,2,1] 0100100=>0001110=>[3,3,1] 0100101=>0001111=>[3,4] 0100110=>0001100=>[3,2,2] 0100111=>0001101=>[3,2,1,1] 0101000=>0000010=>[5,1,1] 0101001=>0000011=>[5,2] 0101010=>0000000=>[7] 0101011=>0000001=>[6,1] 0101100=>0000110=>[4,2,1] 0101101=>0000111=>[4,3] 0101110=>0000100=>[4,1,2] 0101111=>0000101=>[4,1,1,1] 0110000=>0011010=>[2,2,1,1,1] 0110001=>0011011=>[2,2,1,2] 0110010=>0011000=>[2,2,3] 0110011=>0011001=>[2,2,2,1] 0110100=>0011110=>[2,4,1] 0110101=>0011111=>[2,5] 0110110=>0011100=>[2,3,2] 0110111=>0011101=>[2,3,1,1] 0111000=>0010010=>[2,1,2,1,1] 0111001=>0010011=>[2,1,2,2] 0111010=>0010000=>[2,1,4] 0111011=>0010001=>[2,1,3,1] 0111100=>0010110=>[2,1,1,2,1] 0111101=>0010111=>[2,1,1,3] 0111110=>0010100=>[2,1,1,1,2] 0111111=>0010101=>[2,1,1,1,1,1] 1000000=>1101010=>[2,1,1,1,1,1] 1000001=>1101011=>[2,1,1,1,2] 1000010=>1101000=>[2,1,1,3] 1000011=>1101001=>[2,1,1,2,1] 1000100=>1101110=>[2,1,3,1] 1000101=>1101111=>[2,1,4] 1000110=>1101100=>[2,1,2,2] 1000111=>1101101=>[2,1,2,1,1] 1001000=>1100010=>[2,3,1,1] 1001001=>1100011=>[2,3,2] 1001010=>1100000=>[2,5] 1001011=>1100001=>[2,4,1] 1001100=>1100110=>[2,2,2,1] 1001101=>1100111=>[2,2,3] 1001110=>1100100=>[2,2,1,2] 1001111=>1100101=>[2,2,1,1,1] 1010000=>1111010=>[4,1,1,1] 1010001=>1111011=>[4,1,2] 1010010=>1111000=>[4,3] 1010011=>1111001=>[4,2,1] 1010100=>1111110=>[6,1] 1010101=>1111111=>[7] 1010110=>1111100=>[5,2] 1010111=>1111101=>[5,1,1] 1011000=>1110010=>[3,2,1,1] 1011001=>1110011=>[3,2,2] 1011010=>1110000=>[3,4] 1011011=>1110001=>[3,3,1] 1011100=>1110110=>[3,1,2,1] 1011101=>1110111=>[3,1,3] 1011110=>1110100=>[3,1,1,2] 1011111=>1110101=>[3,1,1,1,1] 1100000=>1001010=>[1,2,1,1,1,1] 1100001=>1001011=>[1,2,1,1,2] 1100010=>1001000=>[1,2,1,3] 1100011=>1001001=>[1,2,1,2,1] 1100100=>1001110=>[1,2,3,1] 1100101=>1001111=>[1,2,4] 1100110=>1001100=>[1,2,2,2] 1100111=>1001101=>[1,2,2,1,1] 1101000=>1000010=>[1,4,1,1] 1101001=>1000011=>[1,4,2] 1101010=>1000000=>[1,6] 1101011=>1000001=>[1,5,1] 1101100=>1000110=>[1,3,2,1] 1101101=>1000111=>[1,3,3] 1101110=>1000100=>[1,3,1,2] 1101111=>1000101=>[1,3,1,1,1] 1110000=>1011010=>[1,1,2,1,1,1] 1110001=>1011011=>[1,1,2,1,2] 1110010=>1011000=>[1,1,2,3] 1110011=>1011001=>[1,1,2,2,1] 1110100=>1011110=>[1,1,4,1] 1110101=>1011111=>[1,1,5] 1110110=>1011100=>[1,1,3,2] 1110111=>1011101=>[1,1,3,1,1] 1111000=>1010010=>[1,1,1,2,1,1] 1111001=>1010011=>[1,1,1,2,2] 1111010=>1010000=>[1,1,1,4] 1111011=>1010001=>[1,1,1,3,1] 1111100=>1010110=>[1,1,1,1,2,1] 1111101=>1010111=>[1,1,1,1,3] 1111110=>1010100=>[1,1,1,1,1,2] 1111111=>1010101=>[1,1,1,1,1,1,1] 00000000=>01010101=>[1,1,1,1,1,1,1,1] 00000001=>01010100=>[1,1,1,1,1,1,2] 00000010=>01010111=>[1,1,1,1,1,3] 00000011=>01010110=>[1,1,1,1,1,2,1] 00000100=>01010001=>[1,1,1,1,3,1] 00000101=>01010000=>[1,1,1,1,4] 00000110=>01010011=>[1,1,1,1,2,2] 00000111=>01010010=>[1,1,1,1,2,1,1] 00001000=>01011101=>[1,1,1,3,1,1] 00001001=>01011100=>[1,1,1,3,2] 00001010=>01011111=>[1,1,1,5] 00001011=>01011110=>[1,1,1,4,1] 00001100=>01011001=>[1,1,1,2,2,1] 00001101=>01011000=>[1,1,1,2,3] 00001110=>01011011=>[1,1,1,2,1,2] 00001111=>01011010=>[1,1,1,2,1,1,1] 00010000=>01000101=>[1,1,3,1,1,1] 00010001=>01000100=>[1,1,3,1,2] 00010010=>01000111=>[1,1,3,3] 00010011=>01000110=>[1,1,3,2,1] 00010100=>01000001=>[1,1,5,1] 00010101=>01000000=>[1,1,6] 00010110=>01000011=>[1,1,4,2] 00010111=>01000010=>[1,1,4,1,1] 00011000=>01001101=>[1,1,2,2,1,1] 00011001=>01001100=>[1,1,2,2,2] 00011010=>01001111=>[1,1,2,4] 00011011=>01001110=>[1,1,2,3,1] 00011100=>01001001=>[1,1,2,1,2,1] 00011101=>01001000=>[1,1,2,1,3] 00011110=>01001011=>[1,1,2,1,1,2] 00011111=>01001010=>[1,1,2,1,1,1,1] 00100000=>01110101=>[1,3,1,1,1,1] 00100001=>01110100=>[1,3,1,1,2] 00100010=>01110111=>[1,3,1,3] 00100011=>01110110=>[1,3,1,2,1] 00100100=>01110001=>[1,3,3,1] 00100101=>01110000=>[1,3,4] 00100110=>01110011=>[1,3,2,2] 00100111=>01110010=>[1,3,2,1,1] 00101000=>01111101=>[1,5,1,1] 00101001=>01111100=>[1,5,2] 00101010=>01111111=>[1,7] 00101011=>01111110=>[1,6,1] 00101100=>01111001=>[1,4,2,1] 00101101=>01111000=>[1,4,3] 00101110=>01111011=>[1,4,1,2] 00101111=>01111010=>[1,4,1,1,1] 00110000=>01100101=>[1,2,2,1,1,1] 00110001=>01100100=>[1,2,2,1,2] 00110010=>01100111=>[1,2,2,3] 00110011=>01100110=>[1,2,2,2,1] 00110100=>01100001=>[1,2,4,1] 00110101=>01100000=>[1,2,5] 00110110=>01100011=>[1,2,3,2] 00110111=>01100010=>[1,2,3,1,1] 00111000=>01101101=>[1,2,1,2,1,1] 00111001=>01101100=>[1,2,1,2,2] 00111010=>01101111=>[1,2,1,4] 00111011=>01101110=>[1,2,1,3,1] 00111100=>01101001=>[1,2,1,1,2,1] 00111101=>01101000=>[1,2,1,1,3] 00111110=>01101011=>[1,2,1,1,1,2] 00111111=>01101010=>[1,2,1,1,1,1,1] 01000000=>00010101=>[3,1,1,1,1,1] 01000001=>00010100=>[3,1,1,1,2] 01000010=>00010111=>[3,1,1,3] 01000011=>00010110=>[3,1,1,2,1] 01000100=>00010001=>[3,1,3,1] 01000101=>00010000=>[3,1,4] 01000110=>00010011=>[3,1,2,2] 01000111=>00010010=>[3,1,2,1,1] 01001000=>00011101=>[3,3,1,1] 01001001=>00011100=>[3,3,2] 01001010=>00011111=>[3,5] 01001011=>00011110=>[3,4,1] 01001100=>00011001=>[3,2,2,1] 01001101=>00011000=>[3,2,3] 01001110=>00011011=>[3,2,1,2] 01001111=>00011010=>[3,2,1,1,1] 01010000=>00000101=>[5,1,1,1] 01010001=>00000100=>[5,1,2] 01010010=>00000111=>[5,3] 01010011=>00000110=>[5,2,1] 01010100=>00000001=>[7,1] 01010101=>00000000=>[8] 01010110=>00000011=>[6,2] 01010111=>00000010=>[6,1,1] 01011000=>00001101=>[4,2,1,1] 01011001=>00001100=>[4,2,2] 01011010=>00001111=>[4,4] 01011011=>00001110=>[4,3,1] 01011100=>00001001=>[4,1,2,1] 01011101=>00001000=>[4,1,3] 01011110=>00001011=>[4,1,1,2] 01011111=>00001010=>[4,1,1,1,1] 01100000=>00110101=>[2,2,1,1,1,1] 01100001=>00110100=>[2,2,1,1,2] 01100010=>00110111=>[2,2,1,3] 01100011=>00110110=>[2,2,1,2,1] 01100100=>00110001=>[2,2,3,1] 01100101=>00110000=>[2,2,4] 01100110=>00110011=>[2,2,2,2] 01100111=>00110010=>[2,2,2,1,1] 01101000=>00111101=>[2,4,1,1] 01101001=>00111100=>[2,4,2] 01101010=>00111111=>[2,6] 01101011=>00111110=>[2,5,1] 01101100=>00111001=>[2,3,2,1] 01101101=>00111000=>[2,3,3] 01101110=>00111011=>[2,3,1,2] 01101111=>00111010=>[2,3,1,1,1] 01110000=>00100101=>[2,1,2,1,1,1] 01110001=>00100100=>[2,1,2,1,2] 01110010=>00100111=>[2,1,2,3] 01110011=>00100110=>[2,1,2,2,1] 01110100=>00100001=>[2,1,4,1] 01110101=>00100000=>[2,1,5] 01110110=>00100011=>[2,1,3,2] 01110111=>00100010=>[2,1,3,1,1] 01111000=>00101101=>[2,1,1,2,1,1] 01111001=>00101100=>[2,1,1,2,2] 01111010=>00101111=>[2,1,1,4] 01111011=>00101110=>[2,1,1,3,1] 01111100=>00101001=>[2,1,1,1,2,1] 01111101=>00101000=>[2,1,1,1,3] 01111110=>00101011=>[2,1,1,1,1,2] 01111111=>00101010=>[2,1,1,1,1,1,1] 10000000=>11010101=>[2,1,1,1,1,1,1] 10000001=>11010100=>[2,1,1,1,1,2] 10000010=>11010111=>[2,1,1,1,3] 10000011=>11010110=>[2,1,1,1,2,1] 10000100=>11010001=>[2,1,1,3,1] 10000101=>11010000=>[2,1,1,4] 10000110=>11010011=>[2,1,1,2,2] 10000111=>11010010=>[2,1,1,2,1,1] 10001000=>11011101=>[2,1,3,1,1] 10001001=>11011100=>[2,1,3,2] 10001010=>11011111=>[2,1,5] 10001011=>11011110=>[2,1,4,1] 10001100=>11011001=>[2,1,2,2,1] 10001101=>11011000=>[2,1,2,3] 10001110=>11011011=>[2,1,2,1,2] 10001111=>11011010=>[2,1,2,1,1,1] 10010000=>11000101=>[2,3,1,1,1] 10010001=>11000100=>[2,3,1,2] 10010010=>11000111=>[2,3,3] 10010011=>11000110=>[2,3,2,1] 10010100=>11000001=>[2,5,1] 10010101=>11000000=>[2,6] 10010110=>11000011=>[2,4,2] 10010111=>11000010=>[2,4,1,1] 10011000=>11001101=>[2,2,2,1,1] 10011001=>11001100=>[2,2,2,2] 10011010=>11001111=>[2,2,4] 10011011=>11001110=>[2,2,3,1] 10011100=>11001001=>[2,2,1,2,1] 10011101=>11001000=>[2,2,1,3] 10011110=>11001011=>[2,2,1,1,2] 10011111=>11001010=>[2,2,1,1,1,1] 10100000=>11110101=>[4,1,1,1,1] 10100001=>11110100=>[4,1,1,2] 10100010=>11110111=>[4,1,3] 10100011=>11110110=>[4,1,2,1] 10100100=>11110001=>[4,3,1] 10100101=>11110000=>[4,4] 10100110=>11110011=>[4,2,2] 10100111=>11110010=>[4,2,1,1] 10101000=>11111101=>[6,1,1] 10101001=>11111100=>[6,2] 10101010=>11111111=>[8] 10101011=>11111110=>[7,1] 10101100=>11111001=>[5,2,1] 10101101=>11111000=>[5,3] 10101110=>11111011=>[5,1,2] 10101111=>11111010=>[5,1,1,1] 10110000=>11100101=>[3,2,1,1,1] 10110001=>11100100=>[3,2,1,2] 10110010=>11100111=>[3,2,3] 10110011=>11100110=>[3,2,2,1] 10110100=>11100001=>[3,4,1] 10110101=>11100000=>[3,5] 10110110=>11100011=>[3,3,2] 10110111=>11100010=>[3,3,1,1] 10111000=>11101101=>[3,1,2,1,1] 10111001=>11101100=>[3,1,2,2] 10111010=>11101111=>[3,1,4] 10111011=>11101110=>[3,1,3,1] 10111100=>11101001=>[3,1,1,2,1] 10111101=>11101000=>[3,1,1,3] 10111110=>11101011=>[3,1,1,1,2] 10111111=>11101010=>[3,1,1,1,1,1] 11000000=>10010101=>[1,2,1,1,1,1,1] 11000001=>10010100=>[1,2,1,1,1,2] 11000010=>10010111=>[1,2,1,1,3] 11000011=>10010110=>[1,2,1,1,2,1] 11000100=>10010001=>[1,2,1,3,1] 11000101=>10010000=>[1,2,1,4] 11000110=>10010011=>[1,2,1,2,2] 11000111=>10010010=>[1,2,1,2,1,1] 11001000=>10011101=>[1,2,3,1,1] 11001001=>10011100=>[1,2,3,2] 11001010=>10011111=>[1,2,5] 11001011=>10011110=>[1,2,4,1] 11001100=>10011001=>[1,2,2,2,1] 11001101=>10011000=>[1,2,2,3] 11001110=>10011011=>[1,2,2,1,2] 11001111=>10011010=>[1,2,2,1,1,1] 11010000=>10000101=>[1,4,1,1,1] 11010001=>10000100=>[1,4,1,2] 11010010=>10000111=>[1,4,3] 11010011=>10000110=>[1,4,2,1] 11010100=>10000001=>[1,6,1] 11010101=>10000000=>[1,7] 11010110=>10000011=>[1,5,2] 11010111=>10000010=>[1,5,1,1] 11011000=>10001101=>[1,3,2,1,1] 11011001=>10001100=>[1,3,2,2] 11011010=>10001111=>[1,3,4] 11011011=>10001110=>[1,3,3,1] 11011100=>10001001=>[1,3,1,2,1] 11011101=>10001000=>[1,3,1,3] 11011110=>10001011=>[1,3,1,1,2] 11011111=>10001010=>[1,3,1,1,1,1] 11100000=>10110101=>[1,1,2,1,1,1,1] 11100001=>10110100=>[1,1,2,1,1,2] 11100010=>10110111=>[1,1,2,1,3] 11100011=>10110110=>[1,1,2,1,2,1] 11100100=>10110001=>[1,1,2,3,1] 11100101=>10110000=>[1,1,2,4] 11100110=>10110011=>[1,1,2,2,2] 11100111=>10110010=>[1,1,2,2,1,1] 11101000=>10111101=>[1,1,4,1,1] 11101001=>10111100=>[1,1,4,2] 11101010=>10111111=>[1,1,6] 11101011=>10111110=>[1,1,5,1] 11101100=>10111001=>[1,1,3,2,1] 11101101=>10111000=>[1,1,3,3] 11101110=>10111011=>[1,1,3,1,2] 11101111=>10111010=>[1,1,3,1,1,1] 11110000=>10100101=>[1,1,1,2,1,1,1] 11110001=>10100100=>[1,1,1,2,1,2] 11110010=>10100111=>[1,1,1,2,3] 11110011=>10100110=>[1,1,1,2,2,1] 11110100=>10100001=>[1,1,1,4,1] 11110101=>10100000=>[1,1,1,5] 11110110=>10100011=>[1,1,1,3,2] 11110111=>10100010=>[1,1,1,3,1,1] 11111000=>10101101=>[1,1,1,1,2,1,1] 11111001=>10101100=>[1,1,1,1,2,2] 11111010=>10101111=>[1,1,1,1,4] 11111011=>10101110=>[1,1,1,1,3,1] 11111100=>10101001=>[1,1,1,1,1,2,1] 11111101=>10101000=>[1,1,1,1,1,3] 11111110=>10101011=>[1,1,1,1,1,1,2] 11111111=>10101010=>[1,1,1,1,1,1,1,1] 000000000=>010101010=>[1,1,1,1,1,1,1,1,1] 000000001=>010101011=>[1,1,1,1,1,1,1,2] 000000010=>010101000=>[1,1,1,1,1,1,3] 000000011=>010101001=>[1,1,1,1,1,1,2,1] 000000100=>010101110=>[1,1,1,1,1,3,1] 000000101=>010101111=>[1,1,1,1,1,4] 000000110=>010101100=>[1,1,1,1,1,2,2] 000000111=>010101101=>[1,1,1,1,1,2,1,1] 000001000=>010100010=>[1,1,1,1,3,1,1] 000001001=>010100011=>[1,1,1,1,3,2] 000001010=>010100000=>[1,1,1,1,5] 000001011=>010100001=>[1,1,1,1,4,1] 000001100=>010100110=>[1,1,1,1,2,2,1] 000001101=>010100111=>[1,1,1,1,2,3] 000001110=>010100100=>[1,1,1,1,2,1,2] 000001111=>010100101=>[1,1,1,1,2,1,1,1] 000010000=>010111010=>[1,1,1,3,1,1,1] 000010001=>010111011=>[1,1,1,3,1,2] 000010010=>010111000=>[1,1,1,3,3] 000010011=>010111001=>[1,1,1,3,2,1] 000010100=>010111110=>[1,1,1,5,1] 000010101=>010111111=>[1,1,1,6] 000010110=>010111100=>[1,1,1,4,2] 000010111=>010111101=>[1,1,1,4,1,1] 000011000=>010110010=>[1,1,1,2,2,1,1] 000011001=>010110011=>[1,1,1,2,2,2] 000011010=>010110000=>[1,1,1,2,4] 000011011=>010110001=>[1,1,1,2,3,1] 000011100=>010110110=>[1,1,1,2,1,2,1] 000011101=>010110111=>[1,1,1,2,1,3] 000011110=>010110100=>[1,1,1,2,1,1,2] 000011111=>010110101=>[1,1,1,2,1,1,1,1] 000100000=>010001010=>[1,1,3,1,1,1,1] 000100001=>010001011=>[1,1,3,1,1,2] 000100010=>010001000=>[1,1,3,1,3] 000100011=>010001001=>[1,1,3,1,2,1] 000100100=>010001110=>[1,1,3,3,1] 000100101=>010001111=>[1,1,3,4] 000100110=>010001100=>[1,1,3,2,2] 000100111=>010001101=>[1,1,3,2,1,1] 000101000=>010000010=>[1,1,5,1,1] 000101001=>010000011=>[1,1,5,2] 000101010=>010000000=>[1,1,7] 000101011=>010000001=>[1,1,6,1] 000101100=>010000110=>[1,1,4,2,1] 000101101=>010000111=>[1,1,4,3] 000101110=>010000100=>[1,1,4,1,2] 000101111=>010000101=>[1,1,4,1,1,1] 000110000=>010011010=>[1,1,2,2,1,1,1] 000110001=>010011011=>[1,1,2,2,1,2] 000110010=>010011000=>[1,1,2,2,3] 000110011=>010011001=>[1,1,2,2,2,1] 000110100=>010011110=>[1,1,2,4,1] 000110101=>010011111=>[1,1,2,5] 000110110=>010011100=>[1,1,2,3,2] 000110111=>010011101=>[1,1,2,3,1,1] 000111000=>010010010=>[1,1,2,1,2,1,1] 000111001=>010010011=>[1,1,2,1,2,2] 000111010=>010010000=>[1,1,2,1,4] 000111011=>010010001=>[1,1,2,1,3,1] 000111100=>010010110=>[1,1,2,1,1,2,1] 000111101=>010010111=>[1,1,2,1,1,3] 000111110=>010010100=>[1,1,2,1,1,1,2] 000111111=>010010101=>[1,1,2,1,1,1,1,1] 001000000=>011101010=>[1,3,1,1,1,1,1] 001000001=>011101011=>[1,3,1,1,1,2] 001000010=>011101000=>[1,3,1,1,3] 001000011=>011101001=>[1,3,1,1,2,1] 001000100=>011101110=>[1,3,1,3,1] 001000101=>011101111=>[1,3,1,4] 001000110=>011101100=>[1,3,1,2,2] 001000111=>011101101=>[1,3,1,2,1,1] 001001000=>011100010=>[1,3,3,1,1] 001001001=>011100011=>[1,3,3,2] 001001010=>011100000=>[1,3,5] 001001011=>011100001=>[1,3,4,1] 001001100=>011100110=>[1,3,2,2,1] 001001101=>011100111=>[1,3,2,3] 001001110=>011100100=>[1,3,2,1,2] 001001111=>011100101=>[1,3,2,1,1,1] 001010000=>011111010=>[1,5,1,1,1] 001010001=>011111011=>[1,5,1,2] 001010010=>011111000=>[1,5,3] 001010011=>011111001=>[1,5,2,1] 001010100=>011111110=>[1,7,1] 001010101=>011111111=>[1,8] 001010110=>011111100=>[1,6,2] 001010111=>011111101=>[1,6,1,1] 001011000=>011110010=>[1,4,2,1,1] 001011001=>011110011=>[1,4,2,2] 001011010=>011110000=>[1,4,4] 001011011=>011110001=>[1,4,3,1] 001011100=>011110110=>[1,4,1,2,1] 001011101=>011110111=>[1,4,1,3] 001011110=>011110100=>[1,4,1,1,2] 001011111=>011110101=>[1,4,1,1,1,1] 001100000=>011001010=>[1,2,2,1,1,1,1] 001100001=>011001011=>[1,2,2,1,1,2] 001100010=>011001000=>[1,2,2,1,3] 001100011=>011001001=>[1,2,2,1,2,1] 001100100=>011001110=>[1,2,2,3,1] 001100101=>011001111=>[1,2,2,4] 001100110=>011001100=>[1,2,2,2,2] 001100111=>011001101=>[1,2,2,2,1,1] 001101000=>011000010=>[1,2,4,1,1] 001101001=>011000011=>[1,2,4,2] 001101010=>011000000=>[1,2,6] 001101011=>011000001=>[1,2,5,1] 001101100=>011000110=>[1,2,3,2,1] 001101101=>011000111=>[1,2,3,3] 001101110=>011000100=>[1,2,3,1,2] 001101111=>011000101=>[1,2,3,1,1,1] 001110000=>011011010=>[1,2,1,2,1,1,1] 001110001=>011011011=>[1,2,1,2,1,2] 001110010=>011011000=>[1,2,1,2,3] 001110011=>011011001=>[1,2,1,2,2,1] 001110100=>011011110=>[1,2,1,4,1] 001110101=>011011111=>[1,2,1,5] 001110110=>011011100=>[1,2,1,3,2] 001110111=>011011101=>[1,2,1,3,1,1] 001111000=>011010010=>[1,2,1,1,2,1,1] 001111001=>011010011=>[1,2,1,1,2,2] 001111010=>011010000=>[1,2,1,1,4] 001111011=>011010001=>[1,2,1,1,3,1] 001111100=>011010110=>[1,2,1,1,1,2,1] 001111101=>011010111=>[1,2,1,1,1,3] 001111110=>011010100=>[1,2,1,1,1,1,2] 001111111=>011010101=>[1,2,1,1,1,1,1,1] 010000000=>000101010=>[3,1,1,1,1,1,1] 010000001=>000101011=>[3,1,1,1,1,2] 010000010=>000101000=>[3,1,1,1,3] 010000011=>000101001=>[3,1,1,1,2,1] 010000100=>000101110=>[3,1,1,3,1] 010000101=>000101111=>[3,1,1,4] 010000110=>000101100=>[3,1,1,2,2] 010000111=>000101101=>[3,1,1,2,1,1] 010001000=>000100010=>[3,1,3,1,1] 010001001=>000100011=>[3,1,3,2] 010001010=>000100000=>[3,1,5] 010001011=>000100001=>[3,1,4,1] 010001100=>000100110=>[3,1,2,2,1] 010001101=>000100111=>[3,1,2,3] 010001110=>000100100=>[3,1,2,1,2] 010001111=>000100101=>[3,1,2,1,1,1] 010010000=>000111010=>[3,3,1,1,1] 010010001=>000111011=>[3,3,1,2] 010010010=>000111000=>[3,3,3] 010010011=>000111001=>[3,3,2,1] 010010100=>000111110=>[3,5,1] 010010101=>000111111=>[3,6] 010010110=>000111100=>[3,4,2] 010010111=>000111101=>[3,4,1,1] 010011000=>000110010=>[3,2,2,1,1] 010011001=>000110011=>[3,2,2,2] 010011010=>000110000=>[3,2,4] 010011011=>000110001=>[3,2,3,1] 010011100=>000110110=>[3,2,1,2,1] 010011101=>000110111=>[3,2,1,3] 010011110=>000110100=>[3,2,1,1,2] 010011111=>000110101=>[3,2,1,1,1,1] 010100000=>000001010=>[5,1,1,1,1] 010100001=>000001011=>[5,1,1,2] 010100010=>000001000=>[5,1,3] 010100011=>000001001=>[5,1,2,1] 010100100=>000001110=>[5,3,1] 010100101=>000001111=>[5,4] 010100110=>000001100=>[5,2,2] 010100111=>000001101=>[5,2,1,1] 010101000=>000000010=>[7,1,1] 010101001=>000000011=>[7,2] 010101010=>000000000=>[9] 010101011=>000000001=>[8,1] 010101100=>000000110=>[6,2,1] 010101101=>000000111=>[6,3] 010101110=>000000100=>[6,1,2] 010101111=>000000101=>[6,1,1,1] 010110000=>000011010=>[4,2,1,1,1] 010110001=>000011011=>[4,2,1,2] 010110010=>000011000=>[4,2,3] 010110011=>000011001=>[4,2,2,1] 010110100=>000011110=>[4,4,1] 010110101=>000011111=>[4,5] 010110110=>000011100=>[4,3,2] 010110111=>000011101=>[4,3,1,1] 010111000=>000010010=>[4,1,2,1,1] 010111001=>000010011=>[4,1,2,2] 010111010=>000010000=>[4,1,4] 010111011=>000010001=>[4,1,3,1] 010111100=>000010110=>[4,1,1,2,1] 010111101=>000010111=>[4,1,1,3] 010111110=>000010100=>[4,1,1,1,2] 010111111=>000010101=>[4,1,1,1,1,1] 011000000=>001101010=>[2,2,1,1,1,1,1] 011000001=>001101011=>[2,2,1,1,1,2] 011000010=>001101000=>[2,2,1,1,3] 011000011=>001101001=>[2,2,1,1,2,1] 011000100=>001101110=>[2,2,1,3,1] 011000101=>001101111=>[2,2,1,4] 011000110=>001101100=>[2,2,1,2,2] 011000111=>001101101=>[2,2,1,2,1,1] 011001000=>001100010=>[2,2,3,1,1] 011001001=>001100011=>[2,2,3,2] 011001010=>001100000=>[2,2,5] 011001011=>001100001=>[2,2,4,1] 011001100=>001100110=>[2,2,2,2,1] 011001101=>001100111=>[2,2,2,3] 011001110=>001100100=>[2,2,2,1,2] 011001111=>001100101=>[2,2,2,1,1,1] 011010000=>001111010=>[2,4,1,1,1] 011010001=>001111011=>[2,4,1,2] 011010010=>001111000=>[2,4,3] 011010011=>001111001=>[2,4,2,1] 011010100=>001111110=>[2,6,1] 011010101=>001111111=>[2,7] 011010110=>001111100=>[2,5,2] 011010111=>001111101=>[2,5,1,1] 011011000=>001110010=>[2,3,2,1,1] 011011001=>001110011=>[2,3,2,2] 011011010=>001110000=>[2,3,4] 011011011=>001110001=>[2,3,3,1] 011011100=>001110110=>[2,3,1,2,1] 011011101=>001110111=>[2,3,1,3] 011011110=>001110100=>[2,3,1,1,2] 011011111=>001110101=>[2,3,1,1,1,1] 011100000=>001001010=>[2,1,2,1,1,1,1] 011100001=>001001011=>[2,1,2,1,1,2] 011100010=>001001000=>[2,1,2,1,3] 011100011=>001001001=>[2,1,2,1,2,1] 011100100=>001001110=>[2,1,2,3,1] 011100101=>001001111=>[2,1,2,4] 011100110=>001001100=>[2,1,2,2,2] 011100111=>001001101=>[2,1,2,2,1,1] 011101000=>001000010=>[2,1,4,1,1] 011101001=>001000011=>[2,1,4,2] 011101010=>001000000=>[2,1,6] 011101011=>001000001=>[2,1,5,1] 011101100=>001000110=>[2,1,3,2,1] 011101101=>001000111=>[2,1,3,3] 011101110=>001000100=>[2,1,3,1,2] 011101111=>001000101=>[2,1,3,1,1,1] 011110000=>001011010=>[2,1,1,2,1,1,1] 011110001=>001011011=>[2,1,1,2,1,2] 011110010=>001011000=>[2,1,1,2,3] 011110011=>001011001=>[2,1,1,2,2,1] 011110100=>001011110=>[2,1,1,4,1] 011110101=>001011111=>[2,1,1,5] 011110110=>001011100=>[2,1,1,3,2] 011110111=>001011101=>[2,1,1,3,1,1] 011111000=>001010010=>[2,1,1,1,2,1,1] 011111001=>001010011=>[2,1,1,1,2,2] 011111010=>001010000=>[2,1,1,1,4] 011111011=>001010001=>[2,1,1,1,3,1] 011111100=>001010110=>[2,1,1,1,1,2,1] 011111101=>001010111=>[2,1,1,1,1,3] 011111110=>001010100=>[2,1,1,1,1,1,2] 011111111=>001010101=>[2,1,1,1,1,1,1,1] 100000000=>110101010=>[2,1,1,1,1,1,1,1] 100000001=>110101011=>[2,1,1,1,1,1,2] 100000010=>110101000=>[2,1,1,1,1,3] 100000011=>110101001=>[2,1,1,1,1,2,1] 100000100=>110101110=>[2,1,1,1,3,1] 100000101=>110101111=>[2,1,1,1,4] 100000110=>110101100=>[2,1,1,1,2,2] 100000111=>110101101=>[2,1,1,1,2,1,1] 100001000=>110100010=>[2,1,1,3,1,1] 100001001=>110100011=>[2,1,1,3,2] 100001010=>110100000=>[2,1,1,5] 100001011=>110100001=>[2,1,1,4,1] 100001100=>110100110=>[2,1,1,2,2,1] 100001101=>110100111=>[2,1,1,2,3] 100001110=>110100100=>[2,1,1,2,1,2] 100001111=>110100101=>[2,1,1,2,1,1,1] 100010000=>110111010=>[2,1,3,1,1,1] 100010001=>110111011=>[2,1,3,1,2] 100010010=>110111000=>[2,1,3,3] 100010011=>110111001=>[2,1,3,2,1] 100010100=>110111110=>[2,1,5,1] 100010101=>110111111=>[2,1,6] 100010110=>110111100=>[2,1,4,2] 100010111=>110111101=>[2,1,4,1,1] 100011000=>110110010=>[2,1,2,2,1,1] 100011001=>110110011=>[2,1,2,2,2] 100011010=>110110000=>[2,1,2,4] 100011011=>110110001=>[2,1,2,3,1] 100011100=>110110110=>[2,1,2,1,2,1] 100011101=>110110111=>[2,1,2,1,3] 100011110=>110110100=>[2,1,2,1,1,2] 100011111=>110110101=>[2,1,2,1,1,1,1] 100100000=>110001010=>[2,3,1,1,1,1] 100100001=>110001011=>[2,3,1,1,2] 100100010=>110001000=>[2,3,1,3] 100100011=>110001001=>[2,3,1,2,1] 100100100=>110001110=>[2,3,3,1] 100100101=>110001111=>[2,3,4] 100100110=>110001100=>[2,3,2,2] 100100111=>110001101=>[2,3,2,1,1] 100101000=>110000010=>[2,5,1,1] 100101001=>110000011=>[2,5,2] 100101010=>110000000=>[2,7] 100101011=>110000001=>[2,6,1] 100101100=>110000110=>[2,4,2,1] 100101101=>110000111=>[2,4,3] 100101110=>110000100=>[2,4,1,2] 100101111=>110000101=>[2,4,1,1,1] 100110000=>110011010=>[2,2,2,1,1,1] 100110001=>110011011=>[2,2,2,1,2] 100110010=>110011000=>[2,2,2,3] 100110011=>110011001=>[2,2,2,2,1] 100110100=>110011110=>[2,2,4,1] 100110101=>110011111=>[2,2,5] 100110110=>110011100=>[2,2,3,2] 100110111=>110011101=>[2,2,3,1,1] 100111000=>110010010=>[2,2,1,2,1,1] 100111001=>110010011=>[2,2,1,2,2] 100111010=>110010000=>[2,2,1,4] 100111011=>110010001=>[2,2,1,3,1] 100111100=>110010110=>[2,2,1,1,2,1] 100111101=>110010111=>[2,2,1,1,3] 100111110=>110010100=>[2,2,1,1,1,2] 100111111=>110010101=>[2,2,1,1,1,1,1] 101000000=>111101010=>[4,1,1,1,1,1] 101000001=>111101011=>[4,1,1,1,2] 101000010=>111101000=>[4,1,1,3] 101000011=>111101001=>[4,1,1,2,1] 101000100=>111101110=>[4,1,3,1] 101000101=>111101111=>[4,1,4] 101000110=>111101100=>[4,1,2,2] 101000111=>111101101=>[4,1,2,1,1] 101001000=>111100010=>[4,3,1,1] 101001001=>111100011=>[4,3,2] 101001010=>111100000=>[4,5] 101001011=>111100001=>[4,4,1] 101001100=>111100110=>[4,2,2,1] 101001101=>111100111=>[4,2,3] 101001110=>111100100=>[4,2,1,2] 101001111=>111100101=>[4,2,1,1,1] 101010000=>111111010=>[6,1,1,1] 101010001=>111111011=>[6,1,2] 101010010=>111111000=>[6,3] 101010011=>111111001=>[6,2,1] 101010100=>111111110=>[8,1] 101010101=>111111111=>[9] 101010110=>111111100=>[7,2] 101010111=>111111101=>[7,1,1] 101011000=>111110010=>[5,2,1,1] 101011001=>111110011=>[5,2,2] 101011010=>111110000=>[5,4] 101011011=>111110001=>[5,3,1] 101011100=>111110110=>[5,1,2,1] 101011101=>111110111=>[5,1,3] 101011110=>111110100=>[5,1,1,2] 101011111=>111110101=>[5,1,1,1,1] 101100000=>111001010=>[3,2,1,1,1,1] 101100001=>111001011=>[3,2,1,1,2] 101100010=>111001000=>[3,2,1,3] 101100011=>111001001=>[3,2,1,2,1] 101100100=>111001110=>[3,2,3,1] 101100101=>111001111=>[3,2,4] 101100110=>111001100=>[3,2,2,2] 101100111=>111001101=>[3,2,2,1,1] 101101000=>111000010=>[3,4,1,1] 101101001=>111000011=>[3,4,2] 101101010=>111000000=>[3,6] 101101011=>111000001=>[3,5,1] 101101100=>111000110=>[3,3,2,1] 101101101=>111000111=>[3,3,3] 101101110=>111000100=>[3,3,1,2] 101101111=>111000101=>[3,3,1,1,1] 101110000=>111011010=>[3,1,2,1,1,1] 101110001=>111011011=>[3,1,2,1,2] 101110010=>111011000=>[3,1,2,3] 101110011=>111011001=>[3,1,2,2,1] 101110100=>111011110=>[3,1,4,1] 101110101=>111011111=>[3,1,5] 101110110=>111011100=>[3,1,3,2] 101110111=>111011101=>[3,1,3,1,1] 101111000=>111010010=>[3,1,1,2,1,1] 101111001=>111010011=>[3,1,1,2,2] 101111010=>111010000=>[3,1,1,4] 101111011=>111010001=>[3,1,1,3,1] 101111100=>111010110=>[3,1,1,1,2,1] 101111101=>111010111=>[3,1,1,1,3] 101111110=>111010100=>[3,1,1,1,1,2] 101111111=>111010101=>[3,1,1,1,1,1,1] 110000000=>100101010=>[1,2,1,1,1,1,1,1] 110000001=>100101011=>[1,2,1,1,1,1,2] 110000010=>100101000=>[1,2,1,1,1,3] 110000011=>100101001=>[1,2,1,1,1,2,1] 110000100=>100101110=>[1,2,1,1,3,1] 110000101=>100101111=>[1,2,1,1,4] 110000110=>100101100=>[1,2,1,1,2,2] 110000111=>100101101=>[1,2,1,1,2,1,1] 110001000=>100100010=>[1,2,1,3,1,1] 110001001=>100100011=>[1,2,1,3,2] 110001010=>100100000=>[1,2,1,5] 110001011=>100100001=>[1,2,1,4,1] 110001100=>100100110=>[1,2,1,2,2,1] 110001101=>100100111=>[1,2,1,2,3] 110001110=>100100100=>[1,2,1,2,1,2] 110001111=>100100101=>[1,2,1,2,1,1,1] 110010000=>100111010=>[1,2,3,1,1,1] 110010001=>100111011=>[1,2,3,1,2] 110010010=>100111000=>[1,2,3,3] 110010011=>100111001=>[1,2,3,2,1] 110010100=>100111110=>[1,2,5,1] 110010101=>100111111=>[1,2,6] 110010110=>100111100=>[1,2,4,2] 110010111=>100111101=>[1,2,4,1,1] 110011000=>100110010=>[1,2,2,2,1,1] 110011001=>100110011=>[1,2,2,2,2] 110011010=>100110000=>[1,2,2,4] 110011011=>100110001=>[1,2,2,3,1] 110011100=>100110110=>[1,2,2,1,2,1] 110011101=>100110111=>[1,2,2,1,3] 110011110=>100110100=>[1,2,2,1,1,2] 110011111=>100110101=>[1,2,2,1,1,1,1] 110100000=>100001010=>[1,4,1,1,1,1] 110100001=>100001011=>[1,4,1,1,2] 110100010=>100001000=>[1,4,1,3] 110100011=>100001001=>[1,4,1,2,1] 110100100=>100001110=>[1,4,3,1] 110100101=>100001111=>[1,4,4] 110100110=>100001100=>[1,4,2,2] 110100111=>100001101=>[1,4,2,1,1] 110101000=>100000010=>[1,6,1,1] 110101001=>100000011=>[1,6,2] 110101010=>100000000=>[1,8] 110101011=>100000001=>[1,7,1] 110101100=>100000110=>[1,5,2,1] 110101101=>100000111=>[1,5,3] 110101110=>100000100=>[1,5,1,2] 110101111=>100000101=>[1,5,1,1,1] 110110000=>100011010=>[1,3,2,1,1,1] 110110001=>100011011=>[1,3,2,1,2] 110110010=>100011000=>[1,3,2,3] 110110011=>100011001=>[1,3,2,2,1] 110110100=>100011110=>[1,3,4,1] 110110101=>100011111=>[1,3,5] 110110110=>100011100=>[1,3,3,2] 110110111=>100011101=>[1,3,3,1,1] 110111000=>100010010=>[1,3,1,2,1,1] 110111001=>100010011=>[1,3,1,2,2] 110111010=>100010000=>[1,3,1,4] 110111011=>100010001=>[1,3,1,3,1] 110111100=>100010110=>[1,3,1,1,2,1] 110111101=>100010111=>[1,3,1,1,3] 110111110=>100010100=>[1,3,1,1,1,2] 110111111=>100010101=>[1,3,1,1,1,1,1] 111000000=>101101010=>[1,1,2,1,1,1,1,1] 111000001=>101101011=>[1,1,2,1,1,1,2] 111000010=>101101000=>[1,1,2,1,1,3] 111000011=>101101001=>[1,1,2,1,1,2,1] 111000100=>101101110=>[1,1,2,1,3,1] 111000101=>101101111=>[1,1,2,1,4] 111000110=>101101100=>[1,1,2,1,2,2] 111000111=>101101101=>[1,1,2,1,2,1,1] 111001000=>101100010=>[1,1,2,3,1,1] 111001001=>101100011=>[1,1,2,3,2] 111001010=>101100000=>[1,1,2,5] 111001011=>101100001=>[1,1,2,4,1] 111001100=>101100110=>[1,1,2,2,2,1] 111001101=>101100111=>[1,1,2,2,3] 111001110=>101100100=>[1,1,2,2,1,2] 111001111=>101100101=>[1,1,2,2,1,1,1] 111010000=>101111010=>[1,1,4,1,1,1] 111010001=>101111011=>[1,1,4,1,2] 111010010=>101111000=>[1,1,4,3] 111010011=>101111001=>[1,1,4,2,1] 111010100=>101111110=>[1,1,6,1] 111010101=>101111111=>[1,1,7] 111010110=>101111100=>[1,1,5,2] 111010111=>101111101=>[1,1,5,1,1] 111011000=>101110010=>[1,1,3,2,1,1] 111011001=>101110011=>[1,1,3,2,2] 111011010=>101110000=>[1,1,3,4] 111011011=>101110001=>[1,1,3,3,1] 111011100=>101110110=>[1,1,3,1,2,1] 111011101=>101110111=>[1,1,3,1,3] 111011110=>101110100=>[1,1,3,1,1,2] 111011111=>101110101=>[1,1,3,1,1,1,1] 111100000=>101001010=>[1,1,1,2,1,1,1,1] 111100001=>101001011=>[1,1,1,2,1,1,2] 111100010=>101001000=>[1,1,1,2,1,3] 111100011=>101001001=>[1,1,1,2,1,2,1] 111100100=>101001110=>[1,1,1,2,3,1] 111100101=>101001111=>[1,1,1,2,4] 111100110=>101001100=>[1,1,1,2,2,2] 111100111=>101001101=>[1,1,1,2,2,1,1] 111101000=>101000010=>[1,1,1,4,1,1] 111101001=>101000011=>[1,1,1,4,2] 111101010=>101000000=>[1,1,1,6] 111101011=>101000001=>[1,1,1,5,1] 111101100=>101000110=>[1,1,1,3,2,1] 111101101=>101000111=>[1,1,1,3,3] 111101110=>101000100=>[1,1,1,3,1,2] 111101111=>101000101=>[1,1,1,3,1,1,1] 111110000=>101011010=>[1,1,1,1,2,1,1,1] 111110001=>101011011=>[1,1,1,1,2,1,2] 111110010=>101011000=>[1,1,1,1,2,3] 111110011=>101011001=>[1,1,1,1,2,2,1] 111110100=>101011110=>[1,1,1,1,4,1] 111110101=>101011111=>[1,1,1,1,5] 111110110=>101011100=>[1,1,1,1,3,2] 111110111=>101011101=>[1,1,1,1,3,1,1] 111111000=>101010010=>[1,1,1,1,1,2,1,1] 111111001=>101010011=>[1,1,1,1,1,2,2] 111111010=>101010000=>[1,1,1,1,1,4] 111111011=>101010001=>[1,1,1,1,1,3,1] 111111100=>101010110=>[1,1,1,1,1,1,2,1] 111111101=>101010111=>[1,1,1,1,1,1,3] 111111110=>101010100=>[1,1,1,1,1,1,1,2] 111111111=>101010101=>[1,1,1,1,1,1,1,1,1] 1010101010=>1111111111=>[10] 1010101100=>1111111001=>[7,2,1] 1010110100=>1111100001=>[5,4,1] 1011001010=>1110011111=>[3,2,5] 1011001100=>1110011001=>[3,2,2,2,1] 1011010010=>1110000111=>[3,4,3] 1011010100=>1110000001=>[3,6,1] 1011011000=>1110001101=>[3,3,2,1,1] 1011100100=>1110110001=>[3,1,2,3,1] 1011101000=>1110111101=>[3,1,4,1,1] 1011110000=>1110100101=>[3,1,1,2,1,1,1] 1100110010=>1001100111=>[1,2,2,2,3] 1100111000=>1001101101=>[1,2,2,1,2,1,1] 1101001010=>1000011111=>[1,4,5] 1101010100=>1000000001=>[1,8,1] 1101011000=>1000001101=>[1,5,2,1,1] 1101100010=>1000110111=>[1,3,2,1,3] 1101100100=>1000110001=>[1,3,2,3,1] 1101101000=>1000111101=>[1,3,4,1,1] 1110001100=>1011011001=>[1,1,2,1,2,2,1] 1110010010=>1011000111=>[1,1,2,3,3] 1110011000=>1011001101=>[1,1,2,2,2,1,1] 1110100010=>1011110111=>[1,1,4,1,3] 1110100100=>1011110001=>[1,1,4,3,1] 1110101000=>1011111101=>[1,1,6,1,1] 1111000010=>1010010111=>[1,1,1,2,1,1,3] 1111000100=>1010010001=>[1,1,1,2,1,3,1] 1111001000=>1010011101=>[1,1,1,2,3,1,1] 1111100000=>1010110101=>[1,1,1,1,2,1,1,1,1] 101010101010=>111111111111=>[12] 101011010100=>111110000001=>[5,6,1] 101100110100=>111001100001=>[3,2,2,4,1] 101101001100=>111000011001=>[3,4,2,2,1] 101101010010=>111000000111=>[3,6,3] 101101011000=>111000001101=>[3,5,2,1,1] 101101100100=>111000110001=>[3,3,2,3,1] 101101110000=>111000100101=>[3,3,1,2,1,1,1] 101110010100=>111011000001=>[3,1,2,5,1] 101111000100=>111010010001=>[3,1,1,2,1,3,1] 101111010000=>111010000101=>[3,1,1,4,1,1,1] 110010110100=>100111100001=>[1,2,4,4,1] 110011001100=>100110011001=>[1,2,2,2,2,2,1] 110011010010=>100110000111=>[1,2,2,4,3] 110011011000=>100110001101=>[1,2,2,3,2,1,1] 110011100010=>100110110111=>[1,2,2,1,2,1,3] 110011100100=>100110110001=>[1,2,2,1,2,3,1] 110011110000=>100110100101=>[1,2,2,1,1,2,1,1,1] 110100101100=>100001111001=>[1,4,4,2,1] 110100110010=>100001100111=>[1,4,2,2,3] 110100111000=>100001101101=>[1,4,2,1,2,1,1] 110101001010=>100000011111=>[1,6,5] 110101100010=>100000110111=>[1,5,2,1,3] 110101100100=>100000110001=>[1,5,2,3,1] 110101101000=>100000111101=>[1,5,4,1,1] 110110001100=>100011011001=>[1,3,2,1,2,2,1] 110110010010=>100011000111=>[1,3,2,3,3] 110110011000=>100011001101=>[1,3,2,2,2,1,1] 110110100100=>100011110001=>[1,3,4,3,1] 110110110000=>100011100101=>[1,3,3,2,1,1,1] 110111000010=>100010010111=>[1,3,1,2,1,1,3] 110111000100=>100010010001=>[1,3,1,2,1,3,1] 110111001000=>100010011101=>[1,3,1,2,3,1,1] 110111100000=>100010110101=>[1,3,1,1,2,1,1,1,1] 111000101100=>101101111001=>[1,1,2,1,4,2,1] 111000110010=>101101100111=>[1,1,2,1,2,2,3] 111000110100=>101101100001=>[1,1,2,1,2,4,1] 111000111000=>101101101101=>[1,1,2,1,2,1,2,1,1] 111001001010=>101100011111=>[1,1,2,3,5] 111001001100=>101100011001=>[1,1,2,3,2,2,1] 111001010010=>101100000111=>[1,1,2,5,3] 111001011000=>101100001101=>[1,1,2,4,2,1,1] 111001100010=>101100110111=>[1,1,2,2,2,1,3] 111001100100=>101100110001=>[1,1,2,2,2,3,1] 111001101000=>101100111101=>[1,1,2,2,4,1,1] 111001110000=>101100100101=>[1,1,2,2,1,2,1,1,1] 111010001100=>101111011001=>[1,1,4,1,2,2,1] 111010010010=>101111000111=>[1,1,4,3,3] 111010010100=>101111000001=>[1,1,4,5,1] 111010011000=>101111001101=>[1,1,4,2,2,1,1] 111010100100=>101111110001=>[1,1,6,3,1] 111011000010=>101110010111=>[1,1,3,2,1,1,3] 111011000100=>101110010001=>[1,1,3,2,1,3,1] 111011010000=>101110000101=>[1,1,3,4,1,1,1] 111100001010=>101001011111=>[1,1,1,2,1,1,5] 111100001100=>101001011001=>[1,1,1,2,1,1,2,2,1] 111100010010=>101001000111=>[1,1,1,2,1,3,3] 111100010100=>101001000001=>[1,1,1,2,1,5,1] 111100011000=>101001001101=>[1,1,1,2,1,2,2,1,1] 111100100010=>101001110111=>[1,1,1,2,3,1,3] 111100100100=>101001110001=>[1,1,1,2,3,3,1] 111100110000=>101001100101=>[1,1,1,2,2,2,1,1,1] 111101000010=>101000010111=>[1,1,1,4,1,1,3] 111101000100=>101000010001=>[1,1,1,4,1,3,1] 111101001000=>101000011101=>[1,1,1,4,3,1,1] 111101100000=>101000110101=>[1,1,1,3,2,1,1,1,1] 111110000100=>101011010001=>[1,1,1,1,2,1,1,3,1] 111110010000=>101011000101=>[1,1,1,1,2,3,1,1,1] 111111000000=>101010010101=>[1,1,1,1,1,2,1,1,1,1,1] 1111111111=>1010101010=>[1,1,1,1,1,1,1,1,1,1] 1111111110=>1010101011=>[1,1,1,1,1,1,1,1,2] 1111111101=>1010101000=>[1,1,1,1,1,1,1,3] 1111111100=>1010101001=>[1,1,1,1,1,1,1,2,1] 1111111010=>1010101111=>[1,1,1,1,1,1,4] 1111111000=>1010101101=>[1,1,1,1,1,1,2,1,1] 1111110111=>1010100010=>[1,1,1,1,1,3,1,1] 1111110110=>1010100011=>[1,1,1,1,1,3,2] 1111110101=>1010100000=>[1,1,1,1,1,5] 1111110011=>1010100110=>[1,1,1,1,1,2,2,1] 1111110010=>1010100111=>[1,1,1,1,1,2,3] 1111110001=>1010100100=>[1,1,1,1,1,2,1,2] 1111110000=>1010100101=>[1,1,1,1,1,2,1,1,1] 1111101011=>1010111110=>[1,1,1,1,5,1] 1111101010=>1010111111=>[1,1,1,1,6] 1111100111=>1010110010=>[1,1,1,1,2,2,1,1] 1111100110=>1010110011=>[1,1,1,1,2,2,2] 1111100100=>1010110001=>[1,1,1,1,2,3,1] 1111100010=>1010110111=>[1,1,1,1,2,1,3] 1111100001=>1010110100=>[1,1,1,1,2,1,1,2] 1111011111=>1010001010=>[1,1,1,3,1,1,1,1] 1111011110=>1010001011=>[1,1,1,3,1,1,2] 1111011011=>1010001110=>[1,1,1,3,3,1] 1111011010=>1010001111=>[1,1,1,3,4] 1111011001=>1010001100=>[1,1,1,3,2,2] 1111011000=>1010001101=>[1,1,1,3,2,1,1] 1111010111=>1010000010=>[1,1,1,5,1,1] 1111010101=>1010000000=>[1,1,1,7] 1111010100=>1010000001=>[1,1,1,6,1] 1111010010=>1010000111=>[1,1,1,4,3] 1111001111=>1010011010=>[1,1,1,2,2,1,1,1] 1111001110=>1010011011=>[1,1,1,2,2,1,2] 1111001100=>1010011001=>[1,1,1,2,2,2,1] 1111000111=>1010010010=>[1,1,1,2,1,2,1,1] 1111000110=>1010010011=>[1,1,1,2,1,2,2] 1111000011=>1010010110=>[1,1,1,2,1,1,2,1] 1111000001=>1010010100=>[1,1,1,2,1,1,1,2] 1111000000=>1010010101=>[1,1,1,2,1,1,1,1,1] 1110111101=>1011101000=>[1,1,3,1,1,3] 1110110110=>1011100011=>[1,1,3,3,2] 1110110101=>1011100000=>[1,1,3,5] 1110110100=>1011100001=>[1,1,3,4,1] 1110110001=>1011100100=>[1,1,3,2,1,2] 1110101111=>1011111010=>[1,1,5,1,1,1] 1110101101=>1011111000=>[1,1,5,3] 1110101011=>1011111110=>[1,1,7,1] 1110101010=>1011111111=>[1,1,8] 1110101001=>1011111100=>[1,1,6,2] 1110100101=>1011110000=>[1,1,4,4] 1110100001=>1011110100=>[1,1,4,1,1,2] 1110011111=>1011001010=>[1,1,2,2,1,1,1,1] 1110011110=>1011001011=>[1,1,2,2,1,1,2] 1110011100=>1011001001=>[1,1,2,2,1,2,1] 1110011001=>1011001100=>[1,1,2,2,2,2] 1110010111=>1011000010=>[1,1,2,4,1,1] 1110010110=>1011000011=>[1,1,2,4,2] 1110010101=>1011000000=>[1,1,2,6] 1110010001=>1011000100=>[1,1,2,3,1,2] 1110010000=>1011000101=>[1,1,2,3,1,1,1] 1110001101=>1011011000=>[1,1,2,1,2,3] 1110000111=>1011010010=>[1,1,2,1,1,2,1,1] 1110000110=>1011010011=>[1,1,2,1,1,2,2] 1110000101=>1011010000=>[1,1,2,1,1,4] 1110000100=>1011010001=>[1,1,2,1,1,3,1] 1110000010=>1011010111=>[1,1,2,1,1,1,3] 1110000001=>1011010100=>[1,1,2,1,1,1,1,2] 1110000000=>1011010101=>[1,1,2,1,1,1,1,1,1] 1101111111=>1000101010=>[1,3,1,1,1,1,1,1] 1101111110=>1000101011=>[1,3,1,1,1,1,2] 1101111011=>1000101110=>[1,3,1,1,3,1] 1101111010=>1000101111=>[1,3,1,1,4] 1101111001=>1000101100=>[1,3,1,1,2,2] 1101111000=>1000101101=>[1,3,1,1,2,1,1] 1101110010=>1000100111=>[1,3,1,2,3] 1101101111=>1000111010=>[1,3,3,1,1,1] 1101101110=>1000111011=>[1,3,3,1,2] 1101101100=>1000111001=>[1,3,3,2,1] 1101101011=>1000111110=>[1,3,5,1] 1101101001=>1000111100=>[1,3,4,2] 1101100110=>1000110011=>[1,3,2,2,2] 1101100011=>1000110110=>[1,3,2,1,2,1] 1101100001=>1000110100=>[1,3,2,1,1,2] 1101100000=>1000110101=>[1,3,2,1,1,1,1] 1101011111=>1000001010=>[1,5,1,1,1,1] 1101011110=>1000001011=>[1,5,1,1,2] 1101011011=>1000001110=>[1,5,3,1] 1101011010=>1000001111=>[1,5,4] 1101010111=>1000000010=>[1,7,1,1] 1101010110=>1000000011=>[1,7,2] 1101010101=>1000000000=>[1,9] 1101010011=>1000000110=>[1,6,2,1] 1101010001=>1000000100=>[1,6,1,2] 1101010000=>1000000101=>[1,6,1,1,1] 1101001110=>1000011011=>[1,4,2,1,2] 1101001011=>1000011110=>[1,4,4,1] 1101001000=>1000011101=>[1,4,3,1,1] 1101000011=>1000010110=>[1,4,1,1,2,1] 1101000010=>1000010111=>[1,4,1,1,3] 1101000000=>1000010101=>[1,4,1,1,1,1,1] 1100111111=>1001101010=>[1,2,2,1,1,1,1,1] 1100111110=>1001101011=>[1,2,2,1,1,1,2] 1100111101=>1001101000=>[1,2,2,1,1,3] 1100111100=>1001101001=>[1,2,2,1,1,2,1] 1100111001=>1001101100=>[1,2,2,1,2,2] 1100110111=>1001100010=>[1,2,2,3,1,1] 1100110110=>1001100011=>[1,2,2,3,2] 1100110011=>1001100110=>[1,2,2,2,2,1] 1100110001=>1001100100=>[1,2,2,2,1,2] 1100110000=>1001100101=>[1,2,2,2,1,1,1] 1100101101=>1001111000=>[1,2,4,3] 1100101011=>1001111110=>[1,2,6,1] 1100100110=>1001110011=>[1,2,3,2,2] 1100100101=>1001110000=>[1,2,3,4] 1100100100=>1001110001=>[1,2,3,3,1] 1100100001=>1001110100=>[1,2,3,1,1,2] 1100100000=>1001110101=>[1,2,3,1,1,1,1] 1100011111=>1001001010=>[1,2,1,2,1,1,1,1] 1100011110=>1001001011=>[1,2,1,2,1,1,2] 1100011011=>1001001110=>[1,2,1,2,3,1] 1100011010=>1001001111=>[1,2,1,2,4] 1100011001=>1001001100=>[1,2,1,2,2,2] 1100011000=>1001001101=>[1,2,1,2,2,1,1] 1100010101=>1001000000=>[1,2,1,6] 1100010010=>1001000111=>[1,2,1,3,3] 1100001111=>1001011010=>[1,2,1,1,2,1,1,1] 1100001110=>1001011011=>[1,2,1,1,2,1,2] 1100001101=>1001011000=>[1,2,1,1,2,3] 1100001100=>1001011001=>[1,2,1,1,2,2,1] 1100001011=>1001011110=>[1,2,1,1,4,1] 1100001010=>1001011111=>[1,2,1,1,5] 1100001000=>1001011101=>[1,2,1,1,3,1,1] 1100000111=>1001010010=>[1,2,1,1,1,2,1,1] 1100000110=>1001010011=>[1,2,1,1,1,2,2] 1100000011=>1001010110=>[1,2,1,1,1,1,2,1] 1100000010=>1001010111=>[1,2,1,1,1,1,3] 1100000001=>1001010100=>[1,2,1,1,1,1,1,2] 1100000000=>1001010101=>[1,2,1,1,1,1,1,1,1] 1011111111=>1110101010=>[3,1,1,1,1,1,1,1] 1011111110=>1110101011=>[3,1,1,1,1,1,2] 1011111101=>1110101000=>[3,1,1,1,1,3] 1011111100=>1110101001=>[3,1,1,1,1,2,1] 1011111010=>1110101111=>[3,1,1,1,4] 1011111001=>1110101100=>[3,1,1,1,2,2] 1011111000=>1110101101=>[3,1,1,1,2,1,1] 1011110111=>1110100010=>[3,1,1,3,1,1] 1011110110=>1110100011=>[3,1,1,3,2] 1011110100=>1110100001=>[3,1,1,4,1] 1011110001=>1110100100=>[3,1,1,2,1,2] 1011101110=>1110111011=>[3,1,3,1,2] 1011101010=>1110111111=>[3,1,6] 1011100101=>1110110000=>[3,1,2,4] 1011100001=>1110110100=>[3,1,2,1,1,2] 1011100000=>1110110101=>[3,1,2,1,1,1,1] 1011011111=>1110001010=>[3,3,1,1,1,1] 1011011100=>1110001001=>[3,3,1,2,1] 1011011001=>1110001100=>[3,3,2,2] 1011010111=>1110000010=>[3,5,1,1] 1011010110=>1110000011=>[3,5,2] 1011010000=>1110000101=>[3,4,1,1,1] 1011001101=>1110011000=>[3,2,2,3] 1011001011=>1110011110=>[3,2,4,1] 1011000111=>1110010010=>[3,2,1,2,1,1] 1011000110=>1110010011=>[3,2,1,2,2] 1011000100=>1110010001=>[3,2,1,3,1] 1011000001=>1110010100=>[3,2,1,1,1,2] 1011000000=>1110010101=>[3,2,1,1,1,1,1] 1010111111=>1111101010=>[5,1,1,1,1,1] 1010111100=>1111101001=>[5,1,1,2,1] 1010110111=>1111100010=>[5,3,1,1] 1010110110=>1111100011=>[5,3,2] 1010110101=>1111100000=>[5,5] 1010110001=>1111100100=>[5,2,1,2] 1010101111=>1111111010=>[7,1,1,1] 1010101110=>1111111011=>[7,1,2] 1010101011=>1111111110=>[9,1] 1010101001=>1111111100=>[8,2] 1010101000=>1111111101=>[8,1,1] 1010100111=>1111110010=>[6,2,1,1] 1010100110=>1111110011=>[6,2,2] 1010100101=>1111110000=>[6,4] 1010100100=>1111110001=>[6,3,1] 1010100011=>1111110110=>[6,1,2,1] 1010100000=>1111110101=>[6,1,1,1,1] 1010011111=>1111001010=>[4,2,1,1,1,1] 1010011110=>1111001011=>[4,2,1,1,2] 1010011101=>1111001000=>[4,2,1,3] 1010011100=>1111001001=>[4,2,1,2,1] 1010011010=>1111001111=>[4,2,4] 1010011001=>1111001100=>[4,2,2,2] 1010010111=>1111000010=>[4,4,1,1] 1010010110=>1111000011=>[4,4,2] 1010010101=>1111000000=>[4,6] 1010010100=>1111000001=>[4,5,1] 1010010011=>1111000110=>[4,3,2,1] 1010010010=>1111000111=>[4,3,3] 1010010001=>1111000100=>[4,3,1,2] 1010010000=>1111000101=>[4,3,1,1,1] 1010001110=>1111011011=>[4,1,2,1,2] 1010001101=>1111011000=>[4,1,2,3] 1010001011=>1111011110=>[4,1,4,1] 1010001000=>1111011101=>[4,1,3,1,1] 1010000111=>1111010010=>[4,1,1,2,1,1] 1010000110=>1111010011=>[4,1,1,2,2] 1010000101=>1111010000=>[4,1,1,4] 1010000100=>1111010001=>[4,1,1,3,1] 1010000010=>1111010111=>[4,1,1,1,3] 1010000001=>1111010100=>[4,1,1,1,1,2] 1010000000=>1111010101=>[4,1,1,1,1,1,1] 1001111111=>1100101010=>[2,2,1,1,1,1,1,1] 1001111110=>1100101011=>[2,2,1,1,1,1,2] 1001111100=>1100101001=>[2,2,1,1,1,2,1] 1001111011=>1100101110=>[2,2,1,1,3,1] 1001111000=>1100101101=>[2,2,1,1,2,1,1] 1001110110=>1100100011=>[2,2,1,3,2] 1001110011=>1100100110=>[2,2,1,2,2,1] 1001110010=>1100100111=>[2,2,1,2,3] 1001110000=>1100100101=>[2,2,1,2,1,1,1] 1001101100=>1100111001=>[2,2,3,2,1] 1001101010=>1100111111=>[2,2,6] 1001101001=>1100111100=>[2,2,4,2] 1001100111=>1100110010=>[2,2,2,2,1,1] 1001100110=>1100110011=>[2,2,2,2,2] 1001100101=>1100110000=>[2,2,2,4] 1001100100=>1100110001=>[2,2,2,3,1] 1001100011=>1100110110=>[2,2,2,1,2,1] 1001100000=>1100110101=>[2,2,2,1,1,1,1] 1001011111=>1100001010=>[2,4,1,1,1,1] 1001011110=>1100001011=>[2,4,1,1,2] 1001011101=>1100001000=>[2,4,1,3] 1001011010=>1100001111=>[2,4,4] 1001011001=>1100001100=>[2,4,2,2] 1001011000=>1100001101=>[2,4,2,1,1] 1001010111=>1100000010=>[2,6,1,1] 1001010110=>1100000011=>[2,6,2] 1001010101=>1100000000=>[2,8] 1001010100=>1100000001=>[2,7,1] 1001010011=>1100000110=>[2,5,2,1] 1001010010=>1100000111=>[2,5,3] 1001001110=>1100011011=>[2,3,2,1,2] 1001001101=>1100011000=>[2,3,2,3] 1001001100=>1100011001=>[2,3,2,2,1] 1001001011=>1100011110=>[2,3,4,1] 1001001001=>1100011100=>[2,3,3,2] 1001001000=>1100011101=>[2,3,3,1,1] 1001000111=>1100010010=>[2,3,1,2,1,1] 1001000110=>1100010011=>[2,3,1,2,2] 1001000010=>1100010111=>[2,3,1,1,3] 1001000000=>1100010101=>[2,3,1,1,1,1,1] 1000111101=>1101101000=>[2,1,2,1,1,3] 1000111100=>1101101001=>[2,1,2,1,1,2,1] 1000111010=>1101101111=>[2,1,2,1,4] 1000111001=>1101101100=>[2,1,2,1,2,2] 1000110111=>1101100010=>[2,1,2,3,1,1] 1000110110=>1101100011=>[2,1,2,3,2] 1000110101=>1101100000=>[2,1,2,5] 1000110100=>1101100001=>[2,1,2,4,1] 1000110011=>1101100110=>[2,1,2,2,2,1] 1000110001=>1101100100=>[2,1,2,2,1,2] 1000110000=>1101100101=>[2,1,2,2,1,1,1] 1000101110=>1101111011=>[2,1,4,1,2] 1000101101=>1101111000=>[2,1,4,3] 1000101100=>1101111001=>[2,1,4,2,1] 1000101011=>1101111110=>[2,1,6,1] 1000101010=>1101111111=>[2,1,7] 1000101000=>1101111101=>[2,1,5,1,1] 1000100111=>1101110010=>[2,1,3,2,1,1] 1000100101=>1101110000=>[2,1,3,4] 1000100100=>1101110001=>[2,1,3,3,1] 1000100010=>1101110111=>[2,1,3,1,3] 1000011111=>1101001010=>[2,1,1,2,1,1,1,1] 1000011110=>1101001011=>[2,1,1,2,1,1,2] 1000011101=>1101001000=>[2,1,1,2,1,3] 1000011100=>1101001001=>[2,1,1,2,1,2,1] 1000011011=>1101001110=>[2,1,1,2,3,1] 1000011010=>1101001111=>[2,1,1,2,4] 1000011000=>1101001101=>[2,1,1,2,2,1,1] 1000010111=>1101000010=>[2,1,1,4,1,1] 1000010110=>1101000011=>[2,1,1,4,2] 1000010100=>1101000001=>[2,1,1,5,1] 1000010010=>1101000111=>[2,1,1,3,3] 1000010000=>1101000101=>[2,1,1,3,1,1,1] 1000001111=>1101011010=>[2,1,1,1,2,1,1,1] 1000001101=>1101011000=>[2,1,1,1,2,3] 1000001100=>1101011001=>[2,1,1,1,2,2,1] 1000001010=>1101011111=>[2,1,1,1,5] 1000000111=>1101010010=>[2,1,1,1,1,2,1,1] 1000000110=>1101010011=>[2,1,1,1,1,2,2] 1000000100=>1101010001=>[2,1,1,1,1,3,1] 1000000010=>1101010111=>[2,1,1,1,1,1,3] 1000000001=>1101010100=>[2,1,1,1,1,1,1,2] 1000000000=>1101010101=>[2,1,1,1,1,1,1,1,1] 100000000000=>110101010101=>[2,1,1,1,1,1,1,1,1,1,1] 100000000010=>110101010111=>[2,1,1,1,1,1,1,1,3] 100000011110=>110101001011=>[2,1,1,1,1,2,1,1,2] 100000111110=>110101101011=>[2,1,1,1,2,1,1,1,2] 100001111110=>110100101011=>[2,1,1,2,1,1,1,1,2] 11011111110=>10001010100=>[1,3,1,1,1,1,1,2] 111111111110=>101010101011=>[1,1,1,1,1,1,1,1,1,1,2] 100000000100=>110101010001=>[2,1,1,1,1,1,1,3,1] 100000010110=>110101000011=>[2,1,1,1,1,4,2] 100001011110=>110100001011=>[2,1,1,4,1,1,2] 100101111110=>110000101011=>[2,4,1,1,1,1,2] 110111111110=>100010101011=>[1,3,1,1,1,1,1,1,2] 100000001000=>110101011101=>[2,1,1,1,1,1,3,1,1] 100001001110=>110100011011=>[2,1,1,3,2,1,2] 100000110110=>110101100011=>[2,1,1,1,2,3,2] 100010011110=>110111001011=>[2,1,3,2,1,1,2] 100001101110=>110100111011=>[2,1,1,2,3,1,2] 100100111110=>110001101011=>[2,3,2,1,1,1,2] 11000111110=>10010010100=>[1,2,1,2,1,1,1,2] 110011111110=>100110101011=>[1,2,2,1,1,1,1,1,2] 11110111110=>10100010100=>[1,1,1,3,1,1,1,2] 100001000110=>110100010011=>[2,1,1,3,1,2,2] 100000101010=>110101111111=>[2,1,1,1,7] 100100011110=>110001001011=>[2,3,1,2,1,1,2] 100010101110=>110111111011=>[2,1,6,1,2] 100001110110=>110100100011=>[2,1,1,2,1,3,2] 110001111110=>100100101011=>[1,2,1,2,1,1,1,1,2] 100111011110=>110010001011=>[2,2,1,3,1,1,2] 111101111110=>101000101011=>[1,1,1,3,1,1,1,1,2] 100000100000=>110101110101=>[2,1,1,1,3,1,1,1,1] 100001000010=>110100010111=>[2,1,1,3,1,1,3] 100010010110=>110111000011=>[2,1,3,4,2] 100001100110=>110100110011=>[2,1,1,2,2,2,2] 100001011010=>110100001111=>[2,1,1,4,4] 100000111100=>110101101001=>[2,1,1,1,2,1,1,2,1] 11000001110=>10010100100=>[1,2,1,1,1,2,1,2] 101000011110=>111101001011=>[4,1,1,2,1,1,2] 100100101110=>110001111011=>[2,3,4,1,2] 100011001110=>110110011011=>[2,1,2,2,2,1,2] 100010110110=>110111100011=>[2,1,4,3,2] 100001111010=>110100101111=>[2,1,1,2,1,1,4] 11000101110=>10010000100=>[1,2,1,4,1,2] 110000111110=>100101101011=>[1,2,1,1,2,1,1,1,2] 100110011110=>110011001011=>[2,2,2,2,1,1,2] 100101101110=>110000111011=>[2,4,3,1,2] 11011101110=>10001000100=>[1,3,1,3,1,2] 11111101110=>10101000100=>[1,1,1,1,1,3,1,2] 100001000000=>110100010101=>[2,1,1,3,1,1,1,1,1] 100010001010=>110111011111=>[2,1,3,1,5] 100001010010=>110100000111=>[2,1,1,5,3] 100001001100=>110100011001=>[2,1,1,3,2,2,1] 10001010100=>11011111110=>[2,1,7,1] 110000011110=>100101001011=>[1,2,1,1,1,2,1,1,2] 101000101110=>111101111011=>[4,1,4,1,2] 10010101010=>11000000000=>[2,9] 100101001110=>110000011011=>[2,5,2,1,2] 100100110110=>110001100011=>[2,3,2,3,2] 100011010110=>110110000011=>[2,1,2,5,2] 100010111010=>110111101111=>[2,1,4,1,4] 100001111100=>110100101001=>[2,1,1,2,1,1,1,2,1] 11010101110=>10000000100=>[1,7,1,2] 110100111110=>100001101011=>[1,4,2,1,1,1,2] 110011011110=>100110001011=>[1,2,2,3,1,1,2] 101101011110=>111000001011=>[3,5,1,1,2] 111111011110=>101010001011=>[1,1,1,1,1,3,1,1,2] 100010000000=>110111010101=>[2,1,3,1,1,1,1,1,1] 100010000100=>110111010001=>[2,1,3,1,1,3,1] 100001001000=>110100011101=>[2,1,1,3,3,1,1] 110000001110=>100101011011=>[1,2,1,1,1,1,2,1,2] 100011000110=>110110010011=>[2,1,2,2,1,2,2] 100010011100=>110111001001=>[2,1,3,2,1,2,1] 100001110010=>110100100111=>[2,1,1,2,1,2,3] 100001101100=>110100111001=>[2,1,1,2,3,2,1] 110000101110=>100101111011=>[1,2,1,1,4,1,2] 101001001110=>111100011011=>[4,3,2,1,2] 101000110110=>111101100011=>[4,1,2,3,2] 100110001110=>110011011011=>[2,2,2,1,2,1,2] 100101010110=>110000000011=>[2,8,2] 100100111010=>110001101111=>[2,3,2,1,4] 100011100110=>110110110011=>[2,1,2,1,2,2,2] 100011011010=>110110001111=>[2,1,2,3,4] 110010011110=>100111001011=>[1,2,3,2,1,1,2] 110001101110=>100100111011=>[1,2,1,2,3,1,2] 100111001110=>110010011011=>[2,2,1,2,2,1,2] 100011111100=>110110101001=>[2,1,2,1,1,1,1,2,1] 110011101110=>100110111011=>[1,2,2,1,3,1,2] =>=>[] 0111111111=>0010101010=>[2,1,1,1,1,1,1,1,1] 0111111001=>0010101100=>[2,1,1,1,1,2,2] 0111100001=>0010110100=>[2,1,1,2,1,1,2] 0110000001=>0011010100=>[2,2,1,1,1,1,2] 0000000001=>0101010100=>[1,1,1,1,1,1,1,1,2] 0111111011=>0010101110=>[2,1,1,1,1,3,1] 0111101001=>0010111100=>[2,1,1,4,2] 0110100001=>0011110100=>[2,4,1,1,2] 0101000001=>0000010100=>[5,1,1,1,2] 0010000001=>0111010100=>[1,3,1,1,1,1,2] 0101010101=>0000000000=>[10] 0101010011=>0000000110=>[7,2,1] 0101001101=>0000011000=>[5,2,3] 0101001011=>0000011110=>[5,4,1] 0100101011=>0001111110=>[3,6,1] 0011001101=>0110011000=>[1,2,2,2,3] 0011000111=>0110010010=>[1,2,2,1,2,1,1] 0010110101=>0111100000=>[1,4,5] 0010101011=>0111111110=>[1,8,1] 0010011101=>0111001000=>[1,3,2,1,3] 0010010111=>0111000010=>[1,3,4,1,1] 0001101101=>0100111000=>[1,1,2,3,3] 0001101011=>0100111110=>[1,1,2,5,1] 0001100111=>0100110010=>[1,1,2,2,2,1,1] 0001010111=>0100000010=>[1,1,6,1,1] 0000111101=>0101101000=>[1,1,1,2,1,1,3] 0000110111=>0101100010=>[1,1,1,2,3,1,1] 0000011111=>0101001010=>[1,1,1,1,2,1,1,1,1] 010101010101=>000000000000=>[12] 010100101011=>000001111110=>[5,6,1] 010011001011=>000110011110=>[3,2,2,4,1] 010010110011=>000111100110=>[3,4,2,2,1] 010010101101=>000111111000=>[3,6,3] 010010100111=>000111110010=>[3,5,2,1,1] 010010011011=>000111001110=>[3,3,2,3,1] 010010001111=>000111011010=>[3,3,1,2,1,1,1] 010001101011=>000100111110=>[3,1,2,5,1] 010000111011=>000101101110=>[3,1,1,2,1,3,1] 010000101111=>000101111010=>[3,1,1,4,1,1,1] 001101001011=>011000011110=>[1,2,4,4,1] 001100110011=>011001100110=>[1,2,2,2,2,2,1] 001100101101=>011001111000=>[1,2,2,4,3] 001100100111=>011001110010=>[1,2,2,3,2,1,1] 001100011011=>011001001110=>[1,2,2,1,2,3,1] 001100001111=>011001011010=>[1,2,2,1,1,2,1,1,1] 001011010011=>011110000110=>[1,4,4,2,1] 001011001101=>011110011000=>[1,4,2,2,3] 001011000111=>011110010010=>[1,4,2,1,2,1,1] 001010110101=>011111100000=>[1,6,5] 001010011101=>011111001000=>[1,5,2,1,3] 001010010111=>011111000010=>[1,5,4,1,1] 001001110011=>011100100110=>[1,3,2,1,2,2,1] 001001101101=>011100111000=>[1,3,2,3,3] 001001100111=>011100110010=>[1,3,2,2,2,1,1] 001001001111=>011100011010=>[1,3,3,2,1,1,1] 001000111101=>011101101000=>[1,3,1,2,1,1,3] 001000110111=>011101100010=>[1,3,1,2,3,1,1] 001000011111=>011101001010=>[1,3,1,1,2,1,1,1,1] 000111001011=>010010011110=>[1,1,2,1,2,4,1] 000110110011=>010011100110=>[1,1,2,3,2,2,1] 000110101101=>010011111000=>[1,1,2,5,3] 000110100111=>010011110010=>[1,1,2,4,2,1,1] 000110011011=>010011001110=>[1,1,2,2,2,3,1] 000110001111=>010011011010=>[1,1,2,2,1,2,1,1,1] 000101101011=>010000111110=>[1,1,4,5,1] 000100111011=>010001101110=>[1,1,3,2,1,3,1] 000100101111=>010001111010=>[1,1,3,4,1,1,1] 000011110011=>010110100110=>[1,1,1,2,1,1,2,2,1] 000011101101=>010110111000=>[1,1,1,2,1,3,3] 000011100111=>010110110010=>[1,1,1,2,1,2,2,1,1] 000011011011=>010110001110=>[1,1,1,2,3,3,1] 000011001111=>010110011010=>[1,1,1,2,2,2,1,1,1] 000010111101=>010111101000=>[1,1,1,4,1,1,3] 000010110111=>010111100010=>[1,1,1,4,3,1,1] 000010011111=>010111001010=>[1,1,1,3,2,1,1,1,1] 000001111011=>010100101110=>[1,1,1,1,2,1,1,3,1] 000001101111=>010100111010=>[1,1,1,1,2,3,1,1,1] 000000111111=>010101101010=>[1,1,1,1,1,2,1,1,1,1,1] 11010101010=>10000000000=>[1,10] 11010101000=>10000000010=>[1,8,1,1] 11010101100=>10000000110=>[1,7,2,1] 11010100100=>10000001110=>[1,6,3,1] 11010110100=>10000011110=>[1,5,4,1] 11010010100=>10000111110=>[1,4,5,1] 11011010100=>10001111110=>[1,3,6,1] 11001010100=>10011111110=>[1,2,7,1] 11101010100=>10111111110=>[1,1,8,1] 10101010100=>11111111110=>[10,1] 111111111111=>101010101010=>[1,1,1,1,1,1,1,1,1,1,1,1] 111110000001=>101011010100=>[1,1,1,1,2,1,1,1,1,2] 111110100101=>101011110000=>[1,1,1,1,4,4] 111001100001=>101100110100=>[1,1,2,2,2,1,1,2] 111001101101=>101100111000=>[1,1,2,2,3,3] 111000011001=>101101001100=>[1,1,2,1,1,2,2,2] 111000000111=>101101010010=>[1,1,2,1,1,1,1,2,1,1] 111000001101=>101101011000=>[1,1,2,1,1,1,2,3] 111000110001=>101101100100=>[1,1,2,1,2,2,1,2] 111000100101=>101101110000=>[1,1,2,1,3,4] 111011011001=>101110001100=>[1,1,3,3,2,2] 111011000001=>101110010100=>[1,1,3,2,1,1,1,2] 111011001101=>101110011000=>[1,1,3,2,2,3] 111011100101=>101110110000=>[1,1,3,1,2,4] 111010010001=>101111000100=>[1,1,4,3,1,2] 111010011101=>101111001000=>[1,1,4,2,1,3] 111010000101=>101111010000=>[1,1,4,1,1,4] 100111100001=>110010110100=>[2,2,1,1,2,1,1,2] 100111101101=>110010111000=>[2,2,1,1,3,3] 100110011001=>110011001100=>[2,2,2,2,2,2] 100110000111=>110011010010=>[2,2,2,1,1,2,1,1] 100110001101=>110011011000=>[2,2,2,1,2,3] 100110110111=>110011100010=>[2,2,3,3,1,1] 100110110001=>110011100100=>[2,2,3,2,1,2] 100110100101=>110011110000=>[2,2,4,4] 100001111001=>110100101100=>[2,1,1,2,1,1,2,2] 100001100111=>110100110010=>[2,1,1,2,2,2,1,1] 100001101101=>110100111000=>[2,1,1,2,3,3] 100000011111=>110101001010=>[2,1,1,1,1,2,1,1,1,1] 100000110111=>110101100010=>[2,1,1,1,2,3,1,1] 100000110001=>110101100100=>[2,1,1,1,2,2,1,2] 100000111101=>110101101000=>[2,1,1,1,2,1,1,3] 100000100101=>110101110000=>[2,1,1,1,3,4] 100011011001=>110110001100=>[2,1,2,3,2,2] 100011000111=>110110010010=>[2,1,2,2,1,2,1,1] 100011001101=>110110011000=>[2,1,2,2,2,3] 100011110001=>110110100100=>[2,1,2,1,1,2,1,2] 100011100101=>110110110000=>[2,1,2,1,2,4] 100010010111=>110111000010=>[2,1,3,4,1,1] 100010010001=>110111000100=>[2,1,3,3,1,2] 100010011101=>110111001000=>[2,1,3,2,1,3] 100010000101=>110111010000=>[2,1,3,1,1,4] 100010110101=>110111100000=>[2,1,4,5] 101101111001=>111000101100=>[3,3,1,1,2,2] 101101100111=>111000110010=>[3,3,2,2,1,1] 101101100001=>111000110100=>[3,3,2,1,1,2] 101101101101=>111000111000=>[3,3,3,3] 101100011111=>111001001010=>[3,2,1,2,1,1,1,1] 101100011001=>111001001100=>[3,2,1,2,2,2] 101100000111=>111001010010=>[3,2,1,1,1,2,1,1] 101100001101=>111001011000=>[3,2,1,1,2,3] 101100110111=>111001100010=>[3,2,2,3,1,1] 101100110001=>111001100100=>[3,2,2,2,1,2] 101100111101=>111001101000=>[3,2,2,1,1,3] 101100100101=>111001110000=>[3,2,3,4] 101111011001=>111010001100=>[3,1,1,3,2,2] 101111000111=>111010010010=>[3,1,1,2,1,2,1,1] 101111000001=>111010010100=>[3,1,1,2,1,1,1,2] 101111001101=>111010011000=>[3,1,1,2,2,3] 101111110001=>111010100100=>[3,1,1,1,1,2,1,2] 101110010111=>111011000010=>[3,1,2,4,1,1] 101110010001=>111011000100=>[3,1,2,3,1,2] 101110000101=>111011010000=>[3,1,2,1,1,4] 101001011111=>111100001010=>[4,4,1,1,1,1] 101001011001=>111100001100=>[4,4,2,2] 101001000111=>111100010010=>[4,3,1,2,1,1] 101001000001=>111100010100=>[4,3,1,1,1,2] 101001001101=>111100011000=>[4,3,2,3] 101001110111=>111100100010=>[4,2,1,3,1,1] 101001110001=>111100100100=>[4,2,1,2,1,2] 101001100101=>111100110000=>[4,2,2,4] 101000010111=>111101000010=>[4,1,1,4,1,1] 101000010001=>111101000100=>[4,1,1,3,1,2] 101000011101=>111101001000=>[4,1,1,2,1,3] 101000110101=>111101100000=>[4,1,2,5] 101011010001=>111110000100=>[5,4,1,2] 101011000101=>111110010000=>[5,2,1,4] 101010010101=>111111000000=>[6,6] 0000000000=>0101010101=>[1,1,1,1,1,1,1,1,1,1] 0000011110=>0101001011=>[1,1,1,1,2,1,1,2] 0000010010=>0101000111=>[1,1,1,1,3,3] 0001100110=>0100110011=>[1,1,2,2,2,2] 0001110010=>0100100111=>[1,1,2,1,2,3] 0001001110=>0100011011=>[1,1,3,2,1,2] 0001000010=>0100010111=>[1,1,3,1,1,3] 0001011010=>0100001111=>[1,1,4,4] 0110010010=>0011000111=>[2,2,3,3] 0111111110=>0010101011=>[2,1,1,1,1,1,1,2] 0111000010=>0010010111=>[2,1,2,1,1,3] 0100100110=>0001110011=>[3,3,2,2] 0100111110=>0001101011=>[3,2,1,1,1,2] 0100110010=>0001100111=>[3,2,2,3] 0100001000=>0001011101=>[3,1,1,3,1,1] 0100000010=>0001010111=>[3,1,1,1,1,3] 0100011010=>0001001111=>[3,1,2,4] 0101101000=>0000111101=>[4,4,1,1] 0101100010=>0000110111=>[4,2,1,3] 0101111010=>0000101111=>[4,1,1,4] 0101001010=>0000011111=>[5,5] 000000000000=>010101010101=>[1,1,1,1,1,1,1,1,1,1,1,1] 000001111110=>010100101011=>[1,1,1,1,2,1,1,1,1,2] 000110011110=>010011001011=>[1,1,2,2,2,1,1,2] 000111100110=>010010110011=>[1,1,2,1,1,2,2,2] 000111001110=>010010011011=>[1,1,2,1,2,2,1,2] 000111011010=>010010001111=>[1,1,2,1,3,4] 000100100000=>010001110101=>[1,1,3,3,1,1,1,1] 000100111110=>010001101011=>[1,1,3,2,1,1,1,2] 000101101110=>010000111011=>[1,1,4,3,1,2] 000101111010=>010000101111=>[1,1,4,1,1,4] 011000011110=>001101001011=>[2,2,1,1,2,1,1,2] 011001100110=>001100110011=>[2,2,2,2,2,2] 011001110010=>001100100111=>[2,2,2,1,2,3] 011001001110=>001100011011=>[2,2,3,2,1,2] 011001011010=>001100001111=>[2,2,4,4] 011110011000=>001011001101=>[2,1,1,2,2,2,1,1] 011110010010=>001011000111=>[2,1,1,2,3,3] 011111000010=>001010010111=>[2,1,1,1,2,1,1,3] 011101100010=>001000110111=>[2,1,3,2,1,3] 011101001010=>001000011111=>[2,1,4,5] 010010000110=>000111010011=>[3,3,1,1,2,2] 010010011110=>000111001011=>[3,3,2,1,1,2] 010011100110=>000110110011=>[3,2,1,2,2,2] 010011001110=>000110011011=>[3,2,2,2,1,2] 010011011010=>000110001111=>[3,2,3,4] 010000100000=>000101110101=>[3,1,1,3,1,1,1,1] 010000111110=>000101101011=>[3,1,1,2,1,1,1,2] 010001101110=>000100111011=>[3,1,2,3,1,2] 010001111010=>000100101111=>[3,1,2,1,1,4] 010110100000=>000011110101=>[4,4,1,1,1,1] 010110100110=>000011110011=>[4,4,2,2] 010110001000=>000011011101=>[4,2,1,3,1,1] 010110001110=>000011011011=>[4,2,1,2,1,2] 010110011010=>000011001111=>[4,2,2,4] 010111100010=>000010110111=>[4,1,1,2,1,3] 010111001010=>000010011111=>[4,1,2,5] 010100101000=>000001111101=>[5,5,1,1] 010100101110=>000001111011=>[5,4,1,2] 010100111010=>000001101111=>[5,2,1,4] 010101101010=>000000111111=>[6,6] 0010101010=>0111111111=>[1,9] 0010101000=>0111111101=>[1,7,1,1] 0010101100=>0111111001=>[1,6,2,1] 0010100100=>0111110001=>[1,5,3,1] 0010110100=>0111100001=>[1,4,4,1] 0001010100=>0100000001=>[1,1,7,1] 0101010100=>0000000001=>[9,1] 00101010101=>01111111111=>[1,10] 00101010111=>01111111101=>[1,8,1,1] 0010101110=>0111111011=>[1,6,1,2] 0010100000=>0111110101=>[1,5,1,1,1,1] 0010111100=>0111101001=>[1,4,1,1,2,1] 0010000100=>0111010001=>[1,3,1,1,3,1] 0011110100=>0110100001=>[1,2,1,1,4,1] 0000010100=>0101000001=>[1,1,1,1,5,1] 00010101011=>01000000001=>[1,1,8,1] 01010101011=>00000000001=>[10,1] 0000000010=>0101010111=>[1,1,1,1,1,1,1,3] 0000001110=>0101011011=>[1,1,1,1,1,2,1,2] 0000111110=>0101101011=>[1,1,1,2,1,1,1,2] 0011111110=>0110101011=>[1,2,1,1,1,1,1,2] 00000000000=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1] 0000000100=>0101010001=>[1,1,1,1,1,1,3,1] 0000001010=>0101011111=>[1,1,1,1,1,5] 00000001110=>01010100100=>[1,1,1,1,1,1,2,1,2] 0000010110=>0101000011=>[1,1,1,1,4,2] 0000101110=>0101111011=>[1,1,1,4,1,2] 00000111110=>01010010100=>[1,1,1,1,2,1,1,1,2] 0001011110=>0100001011=>[1,1,4,1,1,2] 00011111110=>01001010100=>[1,1,2,1,1,1,1,1,2] 00111111110=>01101010100=>[1,2,1,1,1,1,1,1,2] 01111111110=>00101010100=>[2,1,1,1,1,1,1,1,2] 0011001010=>0110011111=>[1,2,2,5] 0011001100=>0110011001=>[1,2,2,2,2,1] 0011010010=>0110000111=>[1,2,4,3] 0011100010=>0110110111=>[1,2,1,2,1,3] 0011100100=>0110110001=>[1,2,1,2,3,1] 0011110000=>0110100101=>[1,2,1,1,2,1,1,1] 0100101010=>0001111111=>[3,7] 0101001100=>0000011001=>[5,2,2,1] 0101010010=>0000000111=>[7,3] 0101011000=>0000001101=>[6,2,1,1] 0101100100=>0000110001=>[4,2,3,1] 0110001010=>0011011111=>[2,2,1,5] 0110001100=>0011011001=>[2,2,1,2,2,1] 0110100100=>0011110001=>[2,4,3,1] 0110101000=>0011111101=>[2,6,1,1] 001010110100=>011111100001=>[1,6,4,1] 001011001100=>011110011001=>[1,4,2,2,2,1] 001011010010=>011110000111=>[1,4,4,3] 001011011000=>011110001101=>[1,4,3,2,1,1] 001011100100=>011110110001=>[1,4,1,2,3,1] 001011110000=>011110100101=>[1,4,1,1,2,1,1,1] 010010101100=>000111111001=>[3,6,2,1] 010100101010=>000001111111=>[5,7] 010110101000=>000011111101=>[4,6,1,1] 011010001100=>001111011001=>[2,4,1,2,2,1] 011010010010=>001111000111=>[2,4,3,3] 011010011000=>001111001101=>[2,4,2,2,1,1] 011010100100=>001111110001=>[2,6,3,1] 011010110000=>001111100101=>[2,5,2,1,1,1] 10101010101=>11111111111=>[11] 10101001010=>11111100000=>[6,5] 01001010101=>00011111111=>[3,8] 01000100010=>00010001000=>[3,1,3,1,3] 01000001000=>00010100010=>[3,1,1,1,3,1,1] 01010010101=>00000111111=>[5,6] 01010001010=>00000100000=>[5,1,5] 01010100101=>00000001111=>[7,4] 01010101001=>00000000011=>[9,2] 01010101010=>00000000000=>[11] 01010100100=>00000001110=>[7,3,1] 01010010100=>00000111110=>[5,5,1] 01001010100=>00011111110=>[3,7,1] 01000101000=>00010000010=>[3,1,5,1,1] 00101000010=>01111101000=>[1,5,1,1,3] 00101001010=>01111100000=>[1,5,5] 00101010100=>01111111110=>[1,9,1] 00101001000=>01111100010=>[1,5,3,1,1] 00010000010=>01000101000=>[1,1,3,1,1,1,3] 00010001000=>01000100010=>[1,1,3,1,3,1,1] 00010100010=>01000001000=>[1,1,5,1,3] 00000100000=>01010001010=>[1,1,1,1,3,1,1,1,1] 0100000000=>0001010101=>[3,1,1,1,1,1,1,1] 0100000101=>0001010000=>[3,1,1,1,4] 0100001011=>0001011110=>[3,1,1,4,1] 0100101111=>0001111010=>[3,4,1,1,1] 0101011111=>0000001010=>[6,1,1,1,1] 0110111111=>0011101010=>[2,3,1,1,1,1,1] 0101010110=>0000000011=>[8,2] 0101011001=>0000001100=>[6,2,2] 0101011010=>0000001111=>[6,4] 0101011100=>0000001001=>[6,1,2,1] 0101100110=>0000110011=>[4,2,2,2] 0101101010=>0000111111=>[4,6] 0101111000=>0000101101=>[4,1,1,2,1,1] 0110010110=>0011000011=>[2,2,4,2] 0110011001=>0011001100=>[2,2,2,2,2] 0110011010=>0011001111=>[2,2,2,4] 0110100101=>0011110000=>[2,4,4] 0110100110=>0011110011=>[2,4,2,2] 0110101001=>0011111100=>[2,6,2] 0110101010=>0011111111=>[2,8] 0110101100=>0011111001=>[2,5,2,1] 0110110001=>0011100100=>[2,3,2,1,2] 0111100100=>0010110001=>[2,1,1,2,3,1] 0111101000=>0010111101=>[2,1,1,4,1,1] 010101010110=>000000000011=>[10,2] 010101011010=>000000001111=>[8,4] 010101100110=>000000110011=>[6,2,2,2] 010110010110=>000011000011=>[4,2,4,2] 010110101001=>000011111100=>[4,6,2] 010110101010=>000011111111=>[4,8] 010111100100=>000010110001=>[4,1,1,2,3,1] 011001010110=>001100000011=>[2,2,6,2] 011001101010=>001100111111=>[2,2,2,6] 011010010110=>001111000011=>[2,4,4,2] 011010011001=>001111001100=>[2,4,2,2,2] 011010011010=>001111001111=>[2,4,2,4] 011010011100=>001111001001=>[2,4,2,1,2,1] 011010100101=>001111110000=>[2,6,4] 011010100110=>001111110011=>[2,6,2,2] 011010101010=>001111111111=>[2,10] 011010110001=>001111100100=>[2,5,2,1,2] 011010110100=>001111100001=>[2,5,4,1] 011011010010=>001110000111=>[2,3,4,3] 011100101001=>001001111100=>[2,1,2,5,2] 011101100100=>001000110001=>[2,1,3,2,3,1] 011110001001=>001011011100=>[2,1,1,2,1,3,2] 011110001100=>001011011001=>[2,1,1,2,1,2,2,1] 011110100001=>001011110100=>[2,1,1,4,1,1,2] 011110100100=>001011110001=>[2,1,1,4,3,1] 011111000100=>001010010001=>[2,1,1,1,2,1,3,1] 0011100110=>0110110011=>[1,2,1,2,2,2] 0011101010=>0110111111=>[1,2,1,6] 0011101100=>0110111001=>[1,2,1,3,2,1] 0001101110=>0100111011=>[1,1,2,3,1,2] 0010110110=>0111100011=>[1,4,3,2] 0011110010=>0110100111=>[1,2,1,1,2,3] 0001110110=>0100100011=>[1,1,2,1,3,2] 0100111010=>0001101111=>[3,2,1,4] 0010111010=>0111101111=>[1,4,1,4] 0001111010=>0100101111=>[1,1,2,1,1,4] 0100111100=>0001101001=>[3,2,1,1,2,1] 0001111100=>0100101001=>[1,1,2,1,1,1,2,1] 001111000110=>011010010011=>[1,2,1,1,2,1,2,2] 100111001100=>110010011001=>[2,2,1,2,2,2,1] 001111001100=>011010011001=>[1,2,1,1,2,2,2,1] 001011010110=>011110000011=>[1,4,5,2] 001111010010=>011010000111=>[1,2,1,1,4,3] 001111010100=>011010000001=>[1,2,1,1,6,1] 000111010110=>010010000011=>[1,1,2,1,5,2] 001011011010=>011110001111=>[1,4,3,4] 100111011000=>110010001101=>[2,2,1,3,2,1,1] 100011011100=>110110001001=>[2,1,2,3,1,2,1] 010011011100=>000110001001=>[3,2,3,1,2,1] 001011011100=>011110001001=>[1,4,3,1,2,1] 000111011100=>010010001001=>[1,1,2,1,3,1,2,1] 000011011110=>010110001011=>[1,1,1,2,3,1,1,2] 001101100110=>011000110011=>[1,2,3,2,2,2] 001101101010=>011000111111=>[1,2,3,6] 100101101100=>110000111001=>[2,4,3,2,1] 001011100110=>011110110011=>[1,4,1,2,2,2] 001111100010=>011010110111=>[1,2,1,1,1,2,1,3] 100111100100=>110010110001=>[2,2,1,1,2,3,1] 001111100100=>011010110001=>[1,2,1,1,1,2,3,1] 010011101010=>000110111111=>[3,2,1,6] 001011101010=>011110111111=>[1,4,1,6] 000111101010=>010010111111=>[1,1,2,1,1,6] 001011101100=>011110111001=>[1,4,1,3,2,1] 000011101110=>010110111011=>[1,1,1,2,1,3,1,2] 101001110100=>111100100001=>[4,2,1,4,1] 001001110110=>011100100011=>[1,3,2,1,3,2] 001101110010=>011000100111=>[1,2,3,1,2,3] 001101110100=>011000100001=>[1,2,3,1,4,1] 000101110110=>010000100011=>[1,1,4,1,3,2] 001011110010=>011110100111=>[1,4,1,1,2,3] 100111110000=>110010100101=>[2,2,1,1,1,2,1,1,1] 001111110000=>011010100101=>[1,2,1,1,1,1,2,1,1,1] 100011110100=>110110100001=>[2,1,2,1,1,4,1] 010011110100=>000110100001=>[3,2,1,1,4,1] 001011110100=>011110100001=>[1,4,1,1,4,1] 000111110100=>010010100001=>[1,1,2,1,1,1,4,1] 000011110110=>010110100011=>[1,1,1,2,1,1,3,2] 110001111000=>100100101101=>[1,2,1,2,1,1,2,1,1] 101001111000=>111100101101=>[4,2,1,1,2,1,1] 001001111010=>011100101111=>[1,3,2,1,1,4] 100101111000=>110000101101=>[2,4,1,1,2,1,1] 000011111010=>010110101111=>[1,1,1,2,1,1,1,4] 010001111100=>000100101001=>[3,1,2,1,1,1,2,1] 001001111100=>011100101001=>[1,3,2,1,1,1,2,1] 000101111100=>010000101001=>[1,1,4,1,1,1,2,1] 000011111100=>010110101001=>[1,1,1,2,1,1,1,1,2,1] 0000001101=>0101011000=>[1,1,1,1,1,2,3] 0011111101=>0110101000=>[1,2,1,1,1,1,3] 0000001001=>0101011100=>[1,1,1,1,1,3,2] 0000010101=>0101000000=>[1,1,1,1,6] 0000101101=>0101111000=>[1,1,1,4,3] 0010111101=>0111101000=>[1,4,1,1,3] 100101010101=>110000000000=>[2,10] 100101011001=>110000001100=>[2,6,2,2] 100101100101=>110000110000=>[2,4,2,4] 100101101001=>110000111100=>[2,4,4,2] 100110010101=>110011000000=>[2,2,2,6] 100110101001=>110011111100=>[2,2,6,2] 101001010101=>111100000000=>[4,8] 101001101001=>111100111100=>[4,2,4,2] 101010011001=>111111001100=>[6,2,2,2] 101010100101=>111111110000=>[8,4] 101010101001=>111111111100=>[10,2] 101101001001=>111000011100=>[3,4,3,2] 110010011001=>100111001100=>[1,2,3,2,2,2] 110010100101=>100111110000=>[1,2,5,4] 110010110001=>100111100100=>[1,2,4,2,1,2] 110100101001=>100001111100=>[1,4,5,2] 110110001001=>100011011100=>[1,3,2,1,3,2] 110110100001=>100011110100=>[1,3,4,1,1,2] 111100100001=>101001110100=>[1,1,1,2,3,1,1,2] 0011110001=>0110100100=>[1,2,1,1,2,1,2] 110011000011=>100110010110=>[1,2,2,2,1,1,2,1] 110110000011=>100011010110=>[1,3,2,1,1,1,2,1] 110001110100=>100100100001=>[1,2,1,2,1,4,1] 110000111100=>100101101001=>[1,2,1,1,2,1,1,2,1] 110000001111=>100101011010=>[1,2,1,1,1,1,2,1,1,1] 111000011100=>101101001001=>[1,1,2,1,1,2,1,2,1] 001111010001=>011010000100=>[1,2,1,1,4,1,2] 001111000011=>011010010110=>[1,2,1,1,2,1,1,2,1] 011110000011=>001011010110=>[2,1,1,2,1,1,1,2,1] 111100000011=>101001010110=>[1,1,1,2,1,1,1,1,2,1] 000111110001=>010010100100=>[1,1,2,1,1,1,2,1,2] 001111100001=>011010110100=>[1,2,1,1,1,2,1,1,2] 01111111011=>00101010001=>[2,1,1,1,1,1,3,1] 0011110111=>0110100010=>[1,2,1,1,3,1,1] 0011101101=>0110111000=>[1,2,1,3,3] 0011011001=>0110001100=>[1,2,3,2,2] 0010110001=>0111100100=>[1,4,2,1,2] 0001100001=>0100110100=>[1,1,2,2,1,1,2] 0011110011=>0110100110=>[1,2,1,1,2,2,1] 0111100011=>0010110110=>[2,1,1,2,1,2,1] 0011111001=>0110101100=>[1,2,1,1,1,2,2] 0000111111=>0101101010=>[1,1,1,2,1,1,1,1,1] 001111001101=>011010011000=>[1,2,1,1,2,2,3] 001111011001=>011010001100=>[1,2,1,1,3,2,2] 001111000111=>011010010010=>[1,2,1,1,2,1,2,1,1] 011110100101=>001011110000=>[2,1,1,4,4] 011110001101=>001011011000=>[2,1,1,2,1,2,3] 011110011001=>001011001100=>[2,1,1,2,2,2,2] 011110110001=>001011100100=>[2,1,1,3,2,1,2] 011110000111=>001011010010=>[2,1,1,2,1,1,2,1,1] 001111100101=>011010110000=>[1,2,1,1,1,2,4] 000011111101=>010110101000=>[1,1,1,2,1,1,1,1,3] 000111111001=>010010101100=>[1,1,2,1,1,1,1,2,2] 001111110001=>011010100100=>[1,2,1,1,1,1,2,1,2] 011111100001=>001010110100=>[2,1,1,1,1,2,1,1,2] 000001111111=>010100101010=>[1,1,1,1,2,1,1,1,1,1,1] 0001110100=>0100100001=>[1,1,2,1,4,1] 0001101100=>0100111001=>[1,1,2,3,2,1] 0010011100=>0111001001=>[1,3,2,1,2,1] 0000111100=>0101101001=>[1,1,1,2,1,1,2,1] 0001101010=>0100111111=>[1,1,2,6] 0000111010=>0101101111=>[1,1,1,2,1,4] 0011000110=>0110010011=>[1,2,2,1,2,2] 0010010110=>0111000011=>[1,3,4,2] 0001010110=>0100000011=>[1,1,6,2] 0000110110=>0101100011=>[1,1,1,2,3,2] 001001101100=>011100111001=>[1,3,2,3,2,1] 001010011100=>011111001001=>[1,5,2,1,2,1] 001000111100=>011101101001=>[1,3,1,2,1,1,2,1] 001001011010=>011100001111=>[1,3,4,4] 001011000110=>011110010011=>[1,4,2,1,2,2] 010010100110=>000111110011=>[3,5,2,2] 001001100110=>011100110011=>[1,3,2,2,2,2] 001010010110=>011111000011=>[1,5,4,2] 001000110110=>011101100011=>[1,3,1,2,3,2] 0110111001=>0011101100=>[2,3,1,2,2] 0001101001=>0100111100=>[1,1,2,4,2] 0000110001=>0101100100=>[1,1,1,2,2,1,2] 11111111111=>10101010101=>[1,1,1,1,1,1,1,1,1,1,1] 0100111001=>0001101100=>[3,2,1,2,2] 0100010001=>0001000100=>[3,1,3,1,2] 0101100001=>0000110100=>[4,2,1,1,2] 0110011011=>0011001110=>[2,2,2,3,1] 0110111011=>0011101110=>[2,3,1,3,1] 0100111011=>0001101110=>[3,2,1,3,1] 0101111011=>0000101110=>[4,1,1,3,1] 0110010011=>0011000110=>[2,2,3,2,1] 0110110011=>0011100110=>[2,3,2,2,1] 0110100011=>0011110110=>[2,4,1,2,1] 0100100011=>0001110110=>[3,3,1,2,1] 0101000011=>0000010110=>[5,1,1,2,1] 0110110111=>0011100010=>[2,3,3,1,1] 0110100111=>0011110010=>[2,4,2,1,1] 0110101111=>0011111010=>[2,5,1,1,1] 100100111001=>110001101100=>[2,3,2,1,2,2] 101000111001=>111101101100=>[4,1,2,1,2,2] 100100100001=>110001110100=>[2,3,3,1,1,2] 100100011011=>110001001110=>[2,3,1,2,3,1] 101000011011=>111101001110=>[4,1,1,2,3,1] 100110010011=>110011000110=>[2,2,2,3,2,1] 100100110011=>110001100110=>[2,3,2,2,2,1] 101000110011=>111101100110=>[4,1,2,2,2,1] 100110100011=>110011110110=>[2,2,4,1,2,1] 100101100011=>110000110110=>[2,4,2,1,2,1] 101001100011=>111100110110=>[4,2,2,1,2,1] 100100010111=>110001000010=>[2,3,1,4,1,1] 100100100111=>110001110010=>[2,3,3,2,1,1] 101000100111=>111101110010=>[4,1,3,2,1,1] 100101000111=>110000010010=>[2,5,1,2,1,1] 101010000111=>111111010010=>[6,1,1,2,1,1] 100110101010=>110011111111=>[2,2,8] 101001101010=>111100111111=>[4,2,6] 100101101010=>110000111111=>[2,4,6] 100011101010=>110110111111=>[2,1,2,1,6] 101010011010=>111111001111=>[6,2,4] 100110011010=>110011001111=>[2,2,2,2,4] 101001011010=>111100001111=>[4,4,4] 100101011010=>110000001111=>[2,6,4] 101000111010=>111101101111=>[4,1,2,1,4] 101010100110=>111111110011=>[8,2,2] 100110100110=>110011110011=>[2,2,4,2,2] 101001100110=>111100110011=>[4,2,2,2,2] 100101100110=>110000110011=>[2,4,2,2,2] 101010010110=>111111000011=>[6,4,2] 100110010110=>110011000011=>[2,2,2,4,2] 101001010110=>111100000011=>[4,6,2] 101010001110=>111111011011=>[6,1,2,1,2] 100011101001=>110110111100=>[2,1,2,1,4,2] 100010111001=>110111101100=>[2,1,4,1,2,2] 100011010101=>110110000000=>[2,1,2,7] 100100110101=>110001100000=>[2,3,2,5] 100001110101=>110100100000=>[2,1,1,2,1,5] 101010001101=>111111011000=>[6,1,2,3] 100101001101=>110000011000=>[2,5,2,3] 101000101101=>111101111000=>[4,1,4,3] 100100101101=>110001111000=>[2,3,4,3] 100010101101=>110111111000=>[2,1,6,3] 100100011101=>110001001000=>[2,3,1,2,1,3] 100001011101=>110100001000=>[2,1,1,4,1,3] 101010100011=>111111110110=>[8,1,2,1] 100011100011=>110110110110=>[2,1,2,1,2,1,2,1] 101010010011=>111111000110=>[6,3,2,1] 101001010011=>111100000110=>[4,5,2,1] 100101010011=>110000000110=>[2,7,2,1] 100011010011=>110110000110=>[2,1,2,4,2,1] 100010110011=>110111100110=>[2,1,4,2,2,1] 100001110011=>110100100110=>[2,1,1,2,1,2,2,1] 101010001011=>111111011110=>[6,1,4,1] 100110001011=>110011011110=>[2,2,2,1,4,1] 101001001011=>111100011110=>[4,3,4,1] 100101001011=>110000011110=>[2,5,4,1] 100011001011=>110110011110=>[2,1,2,2,4,1] 101000101011=>111101111110=>[4,1,6,1] 100100101011=>110001111110=>[2,3,6,1] 100010101011=>110111111110=>[2,1,8,1] 100001101011=>110100111110=>[2,1,1,2,5,1] 100010011011=>110111001110=>[2,1,3,2,3,1] 100001011011=>110100001110=>[2,1,1,4,3,1] 100000111011=>110101101110=>[2,1,1,1,2,1,3,1] 100010100111=>110111110010=>[2,1,5,2,1,1] 100001010111=>110100000010=>[2,1,1,6,1,1] 101000001111=>111101011010=>[4,1,1,1,2,1,1,1] 100100001111=>110001011010=>[2,3,1,1,2,1,1,1] 100010001111=>110111011010=>[2,1,3,1,2,1,1,1] 100001001111=>110100011010=>[2,1,1,3,2,1,1,1] 100000101111=>110101111010=>[2,1,1,1,4,1,1,1] 01010101101=>00000000111=>[8,3] 01010110101=>00000011111=>[6,5] 01011010101=>00001111111=>[4,7] 01011101110=>00001000100=>[4,1,3,1,2] 01011101011=>00001000001=>[4,1,5,1] 01011110111=>00001011101=>[4,1,1,3,1,1] 01101011010=>00111110000=>[2,5,4] 01101010110=>00111111100=>[2,7,2] 01101010101=>00111111111=>[2,9] 01110111010=>00100010000=>[2,1,3,1,4] 01110111011=>00100010001=>[2,1,3,1,3,1] 01110101110=>00100000100=>[2,1,5,1,2] 01111010111=>00101111101=>[2,1,1,5,1,1] 01111101111=>00101000101=>[2,1,1,1,3,1,1,1] 10101011011=>11111110001=>[7,3,1] 10101101011=>11111000001=>[5,5,1] 10110101011=>11100000001=>[3,7,1] 11011110101=>10001011111=>[1,3,1,1,5] 11011111011=>10001010001=>[1,3,1,1,1,3,1] 11010111010=>10000010000=>[1,5,1,4] 11010111101=>10000010111=>[1,5,1,1,3] 11010101011=>10000000001=>[1,9,1] 11011101111=>10001000101=>[1,3,1,3,1,1,1] 11101010111=>10111111101=>[1,1,7,1,1] 11110111011=>10100010001=>[1,1,1,3,1,3,1] 0000001100=>0101011001=>[1,1,1,1,1,2,2,1] 0000011001=>0101001100=>[1,1,1,1,2,2,2] 0000110011=>0101100110=>[1,1,1,2,2,2,1] 0011001111=>0110011010=>[1,2,2,2,1,1,1] 0110011111=>0011001010=>[2,2,2,1,1,1,1] 0000110100=>0101100001=>[1,1,1,2,4,1] 0000000011=>0101010110=>[1,1,1,1,1,1,1,2,1] 0000011011=>0101001110=>[1,1,1,1,2,3,1] 0001101111=>0100111010=>[1,1,2,3,1,1,1] 0011011111=>0110001010=>[1,2,3,1,1,1,1] 00000000011=>01010101001=>[1,1,1,1,1,1,1,1,2,1] 11011111111=>10001010101=>[1,3,1,1,1,1,1,1,1] 10001010101=>11011111111=>[2,1,8] 0111001011=>0010011110=>[2,1,2,4,1] 0111100111=>0010110010=>[2,1,1,2,2,1,1] 11000000000=>10010101010=>[1,2,1,1,1,1,1,1,1,1] 0110001011=>0011011110=>[2,2,1,4,1] 0110000111=>0011010010=>[2,2,1,1,2,1,1] 110000111001=>100101101100=>[1,2,1,1,2,1,2,2] 110010001101=>100111011000=>[1,2,3,1,2,3] 110000101101=>100101111000=>[1,2,1,1,4,3] 011100100011=>001001110110=>[2,1,2,3,1,2,1] 011010010011=>001111000110=>[2,4,3,2,1] 011000110011=>001101100110=>[2,2,1,2,2,2,1] 010110001011=>000011011110=>[4,2,1,4,1] 011100001011=>001001011110=>[2,1,2,1,1,4,1] 011000011011=>001101001110=>[2,2,1,1,2,3,1] 110100100011=>100001110110=>[1,4,3,1,2,1] 110000110011=>100101100110=>[1,2,1,1,2,2,2,1] 110100001011=>100001011110=>[1,4,1,1,4,1] 110000011011=>100101001110=>[1,2,1,1,1,2,3,1] 001110000111=>011011010010=>[1,2,1,2,1,1,2,1,1] 011010000111=>001111010010=>[2,4,1,1,2,1,1] 011000100111=>001101110010=>[2,2,1,3,2,1,1] 011000001111=>001101011010=>[2,2,1,1,1,2,1,1,1] 0011011010=>0110001111=>[1,2,3,4] 0011010110=>0110000011=>[1,2,5,2] 0100110110=>0001100011=>[3,2,3,2] 0110001110=>0011011011=>[2,2,1,2,1,2] 0101001110=>0000011011=>[5,2,1,2] 0011001110=>0110011011=>[1,2,2,2,1,2] 0100101110=>0001111011=>[3,4,1,2] 0100011110=>0001001011=>[3,1,2,1,1,2] 0010011110=>0111001011=>[1,3,2,1,1,2] 001110101010=>011011111111=>[1,2,1,8] 001110011010=>011011001111=>[1,2,1,2,2,4] 001101011010=>011000001111=>[1,2,5,4] 011000111010=>001101101111=>[2,2,1,2,1,4] 001100111010=>011001101111=>[1,2,2,2,1,4] 010010111010=>000111101111=>[3,4,1,4] 001010111010=>011111101111=>[1,6,1,4] 000110111010=>010011101111=>[1,1,2,3,1,4] 001110100110=>011011110011=>[1,2,1,4,2,2] 001110010110=>011011000011=>[1,2,1,2,4,2] 001101010110=>011000000011=>[1,2,7,2] 010011010110=>000110000011=>[3,2,5,2] 011000110110=>001101100011=>[2,2,1,2,3,2] 010100110110=>000001100011=>[5,2,3,2] 001100110110=>011001100011=>[1,2,2,2,3,2] 010010110110=>000111100011=>[3,4,3,2] 001010110110=>011111100011=>[1,6,3,2] 000110110110=>010011100011=>[1,1,2,3,3,2] 010001110110=>000100100011=>[3,1,2,1,3,2] 011010001110=>001111011011=>[2,4,1,2,1,2] 001110001110=>011011011011=>[1,2,1,2,1,2,1,2] 010101001110=>000000011011=>[7,2,1,2] 001101001110=>011000011011=>[1,2,4,2,1,2] 001011001110=>011110011011=>[1,4,2,2,1,2] 011000101110=>001101111011=>[2,2,1,4,1,2] 001100101110=>011001111011=>[1,2,2,4,1,2] 010010101110=>000111111011=>[3,6,1,2] 001010101110=>011111111011=>[1,8,1,2] 000110101110=>010011111011=>[1,1,2,5,1,2] 001001101110=>011100111011=>[1,3,2,3,1,2] 010100011110=>000001001011=>[5,1,2,1,1,2] 001100011110=>011001001011=>[1,2,2,1,2,1,1,2] 001010011110=>011111001011=>[1,5,2,1,1,2] 010001011110=>000100001011=>[3,1,4,1,1,2] 001001011110=>011100001011=>[1,3,4,1,1,2] 000101011110=>010000001011=>[1,1,6,1,1,2] 001000111110=>011101101011=>[1,3,1,2,1,1,1,2] 000010111110=>010111101011=>[1,1,1,4,1,1,1,2] 0101000000=>0000010101=>[5,1,1,1,1,1] 0001010000=>0100000101=>[1,1,5,1,1,1] 0001000100=>0100010001=>[1,1,3,1,3,1] 0001010101=>0100000000=>[1,1,8] 0101010001=>0000000100=>[7,1,2] 0100101001=>0001111100=>[3,5,2] 0101011011=>0000001110=>[6,3,1] 0001001011=>0100011110=>[1,1,3,4,1] 0110101011=>0011111110=>[2,7,1] 0001100011=>0100110110=>[1,1,2,2,1,2,1] 0110000011=>0011010110=>[2,2,1,1,1,2,1] 0111101111=>0010111010=>[2,1,1,3,1,1,1] 010100000000=>000001010101=>[5,1,1,1,1,1,1,1] 000101000000=>010000010101=>[1,1,5,1,1,1,1,1] 010001000000=>000100010101=>[3,1,3,1,1,1,1,1] 000001010000=>010100000101=>[1,1,1,1,5,1,1,1] 010101010000=>000000000101=>[9,1,1,1] 000100010000=>010001000101=>[1,1,3,1,3,1,1,1] 010000010000=>000101000101=>[3,1,1,1,3,1,1,1] 000000010100=>010101000001=>[1,1,1,1,1,1,5,1] 010100010100=>000001000001=>[5,1,5,1] 000101010100=>010000000001=>[1,1,9,1] 010001010100=>000100000001=>[3,1,7,1] 000001000100=>010100010001=>[1,1,1,1,3,1,3,1] 010101000100=>000000010001=>[7,1,3,1] 000100000100=>010001010001=>[1,1,3,1,1,1,3,1] 010000000100=>000101010001=>[3,1,1,1,1,1,3,1] 011010000100=>001111010001=>[2,4,1,1,3,1] 010010100100=>000111110001=>[3,5,3,1] 000110001100=>010011011001=>[1,1,2,2,1,2,2,1] 010010001100=>000111011001=>[3,3,1,2,2,1] 000000000101=>010101010000=>[1,1,1,1,1,1,1,1,4] 010100000101=>000001010000=>[5,1,1,1,4] 000101000101=>010000010000=>[1,1,5,1,4] 010001000101=>000100010000=>[3,1,3,1,4] 000001010101=>010100000000=>[1,1,1,1,8] 000100010101=>010001000000=>[1,1,3,1,6] 010000010101=>000101000000=>[3,1,1,1,6] 000000010001=>010101000100=>[1,1,1,1,1,1,3,1,2] 010100010001=>000001000100=>[5,1,3,1,2] 000101010001=>010000000100=>[1,1,7,1,2] 010001010001=>000100000100=>[3,1,5,1,2] 000001000001=>010100010100=>[1,1,1,1,3,1,1,1,2] 010101000001=>000000010100=>[7,1,1,1,2] 000100000001=>010001010100=>[1,1,3,1,1,1,1,1,2] 010000000001=>000101010100=>[3,1,1,1,1,1,1,1,2] 011010000001=>001111010100=>[2,4,1,1,1,1,2] 000110100001=>010011110100=>[1,1,2,4,1,1,2] 010010100001=>000111110100=>[3,5,1,1,2] 011000100001=>001101110100=>[2,2,1,3,1,1,2] 000100101001=>010001111100=>[1,1,3,5,2] 010000101001=>000101111100=>[3,1,1,5,2] 000110001001=>010011011100=>[1,1,2,2,1,3,2] 010010001001=>000111011100=>[3,3,1,3,2] 000111011001=>010010001100=>[1,1,2,1,3,2,2] 010011011001=>000110001100=>[3,2,3,2,2] 011110111001=>001011101100=>[2,1,1,3,1,2,2] 000000011011=>010101001110=>[1,1,1,1,1,1,2,3,1] 011011011011=>001110001110=>[2,3,3,3,1] 000001001011=>010100011110=>[1,1,1,1,3,4,1] 000100001011=>010001011110=>[1,1,3,1,1,4,1] 010000001011=>000101011110=>[3,1,1,1,1,4,1] 011101101011=>001000111110=>[2,1,3,5,1] 000001100011=>010100110110=>[1,1,1,1,2,2,1,2,1] 000100100011=>010001110110=>[1,1,3,3,1,2,1] 010000100011=>000101110110=>[3,1,1,3,1,2,1] 000110000011=>010011010110=>[1,1,2,2,1,1,1,2,1] 010010000011=>000111010110=>[3,3,1,1,1,2,1] 011000000011=>001101010110=>[2,2,1,1,1,1,1,2,1] 011110110011=>001011100110=>[2,1,1,3,2,2,1] 011010110111=>001111100010=>[2,5,3,1,1] 011110100111=>001011110010=>[2,1,1,4,2,1,1] 000111101111=>010010111010=>[1,1,2,1,1,3,1,1,1] 010011101111=>000110111010=>[3,2,1,3,1,1,1] 011001101111=>001100111010=>[2,2,2,3,1,1,1] 011100101111=>001001111010=>[2,1,2,4,1,1,1] 011110001111=>001011011010=>[2,1,1,2,1,2,1,1,1] 0111000000=>0010010101=>[2,1,2,1,1,1,1,1] 0010000000=>0111010101=>[1,3,1,1,1,1,1,1] 01110000000=>00100101010=>[2,1,2,1,1,1,1,1,1] 0110100000=>0011110101=>[2,4,1,1,1,1] 01111100000=>00101001010=>[2,1,1,1,2,1,1,1,1] 01111111000=>00101010010=>[2,1,1,1,1,1,2,1,1] 0000000111=>0101010010=>[1,1,1,1,1,1,2,1,1] 0000001111=>0101011010=>[1,1,1,1,1,2,1,1,1] 0001111111=>0100101010=>[1,1,2,1,1,1,1,1,1] 0011111111=>0110101010=>[1,2,1,1,1,1,1,1,1] 00000001111=>01010100101=>[1,1,1,1,1,1,2,1,1,1] 00000111111=>01010010101=>[1,1,1,1,2,1,1,1,1,1] 00011111111=>01001010101=>[1,1,2,1,1,1,1,1,1,1] 00111111111=>01101010101=>[1,2,1,1,1,1,1,1,1,1] 0011011110=>0110001011=>[1,2,3,1,1,2] 0011101110=>0110111011=>[1,2,1,3,1,2] 0011110110=>0110100011=>[1,2,1,1,3,2] 0011111010=>0110101111=>[1,2,1,1,1,4] 0011111100=>0110101001=>[1,2,1,1,1,1,2,1] 00111111100=>01101010110=>[1,2,1,1,1,1,1,2,1] 0011011100=>0110001001=>[1,2,3,1,2,1] 0001111001=>0100101100=>[1,1,2,1,1,2,2] 010100111100=>000001101001=>[5,2,1,1,2,1] 001100111001=>011001101100=>[1,2,2,2,1,2,2] 001100111100=>011001101001=>[1,2,2,2,1,1,2,1] 000110111001=>010011101100=>[1,1,2,3,1,2,2] 001110110001=>011011100100=>[1,2,1,3,2,1,2] 001110110100=>011011100001=>[1,2,1,3,4,1] 001001111001=>011100101100=>[1,3,2,1,1,2,2] 000101111001=>010000101100=>[1,1,4,1,1,2,2] 001101110001=>011000100100=>[1,2,3,1,2,1,2] 001011100101=>011110110000=>[1,4,1,2,4] 001011101001=>011110111100=>[1,4,1,4,2] 000011111001=>010110101100=>[1,1,1,2,1,1,1,2,2] 001011110001=>011110100100=>[1,4,1,1,2,1,2] 000111100011=>010010110110=>[1,1,2,1,1,2,1,2,1] 000111100101=>010010110000=>[1,1,2,1,1,2,4] 0000011010=>0101001111=>[1,1,1,1,2,4] 0000101010=>0101111111=>[1,1,1,7] 11111111011=>10101010001=>[1,1,1,1,1,1,1,3,1] 11000000011=>10010101001=>[1,2,1,1,1,1,1,2,1] 0000100101=>0101110000=>[1,1,1,3,4] 0011100101=>0110110000=>[1,2,1,2,4] 000111100001=>010010110100=>[1,1,2,1,1,2,1,1,2] 000110011001=>010011001100=>[1,1,2,2,2,2,2] 000110110001=>010011100100=>[1,1,2,3,2,1,2] 000110100101=>010011110000=>[1,1,2,4,4] 001101100001=>011000110100=>[1,2,3,2,1,1,2] 001100011001=>011001001100=>[1,2,2,1,2,2,2] 001100110001=>011001100100=>[1,2,2,2,2,1,2] 001100100101=>011001110000=>[1,2,2,3,4] 001111000001=>011010010100=>[1,2,1,1,2,1,1,1,2] 001110010001=>011011000100=>[1,2,1,2,3,1,2] 001110000101=>011011010000=>[1,2,1,2,1,1,4] 001001011001=>011100001100=>[1,3,4,2,2] 001001110001=>011100100100=>[1,3,2,1,2,1,2] 001001100101=>011100110000=>[1,3,2,2,4] 001011010001=>011110000100=>[1,4,4,1,2] 001011000101=>011110010000=>[1,4,2,1,4] 001010010101=>011111000000=>[1,5,6] 11010001000=>10000100010=>[1,4,1,3,1,1] 11000100010=>10010001000=>[1,2,1,3,1,3] 10101001000=>11111100010=>[6,3,1,1] 10100101000=>11110000010=>[4,5,1,1] 00010010101=>01000111111=>[1,1,3,6] 00010100101=>01000001111=>[1,1,5,4] 10010101000=>11000000010=>[2,7,1,1] 00010101001=>01000000011=>[1,1,7,2] 00010101010=>01000000000=>[1,1,9] 00000100010=>01010001000=>[1,1,1,1,3,1,3] 001011011001=>011110001100=>[1,4,3,2,2] 001101011001=>011000001100=>[1,2,5,2,2] 001101011100=>011000001001=>[1,2,5,1,2,1] 001101100011=>011000110110=>[1,2,3,2,1,2,1] 001101100101=>011000110000=>[1,2,3,2,4] 001110001101=>011011011000=>[1,2,1,2,1,2,3] 001110010011=>011011000110=>[1,2,1,2,3,2,1] 001110010101=>011011000000=>[1,2,1,2,6] 001110011001=>011011001100=>[1,2,1,2,2,2,2] 001110011100=>011011001001=>[1,2,1,2,2,1,2,1] 001110100101=>011011110000=>[1,2,1,4,4] 001111000101=>011010010000=>[1,2,1,1,2,1,4] 001111001001=>011010011100=>[1,2,1,1,2,3,2] 010010111001=>000111101100=>[3,4,1,2,2] 010011100101=>000110110000=>[3,2,1,2,4] 010011110001=>000110100100=>[3,2,1,1,2,1,2] 010001111001=>000100101100=>[3,1,2,1,1,2,2] 11011100000=>10001001010=>[1,3,1,2,1,1,1,1] 11010100001=>10000001011=>[1,6,1,1,2] 10101010000=>11111111010=>[8,1,1,1] 01101010000=>00111111010=>[2,6,1,1,1] 11010100000=>10000001010=>[1,6,1,1,1,1] 01110100000=>00100001010=>[2,1,4,1,1,1,1] 11000100000=>10010001010=>[1,2,1,3,1,1,1,1] 01000100000=>00010001010=>[3,1,3,1,1,1,1] 00111000000=>01101101010=>[1,2,1,2,1,1,1,1,1] 101001110010=>111100100111=>[4,2,1,2,3] 101001101100=>111100111001=>[4,2,3,2,1] 101000111100=>111101101001=>[4,1,2,1,1,2,1] 110000111010=>100101101111=>[1,2,1,1,2,1,4] 111000100110=>101101110011=>[1,1,2,1,3,2,2] 100110011100=>110011001001=>[2,2,2,2,1,2,1] 100110110100=>110011100001=>[2,2,3,4,1] 00001010101=>01011111111=>[1,1,1,8] 000010010011=>010111000110=>[1,1,1,3,3,2,1] 0010010011=>0111000110=>[1,3,3,2,1] 00010001011=>01000100001=>[1,1,3,1,4,1] 0000101011=>0101111110=>[1,1,1,6,1] 0000100111=>0101110010=>[1,1,1,3,2,1,1] 0010010010=>0111000111=>[1,3,3,3] 0001001010=>0100011111=>[1,1,3,5] 0001000101=>0100010000=>[1,1,3,1,4] 0000100100=>0101110001=>[1,1,1,3,3,1] 0000100010=>0101110111=>[1,1,1,3,1,3] 1111101000000101=>1010111101010000=>[1,1,1,1,4,1,1,1,1,4] 0011000000=>0110010101=>[1,2,2,1,1,1,1,1] 11111110011=>10101011001=>[1,1,1,1,1,1,2,2,1] 0010110000=>0111100101=>[1,4,2,1,1,1] 00110000000=>01100101010=>[1,2,2,1,1,1,1,1,1] 0101010111=>0000000010=>[8,1,1] 111000010110=>101101000011=>[1,1,2,1,1,4,2] 100100111100=>110001101001=>[2,3,2,1,1,2,1] 110000110110=>100101100011=>[1,2,1,1,2,3,2] 110100011010=>100001001111=>[1,4,1,2,4] 111000011010=>101101001111=>[1,1,2,1,1,2,4] 101010011100=>111111001001=>[6,2,1,2,1] 101100011100=>111001001001=>[3,2,1,2,1,2,1] 110010011100=>100111001001=>[1,2,3,2,1,2,1] 111000101110=>101101111011=>[1,1,2,1,4,1,2] 110011001110=>100110011011=>[1,2,2,2,2,1,2] 111100001110=>101001011011=>[1,1,1,2,1,1,2,1,2] 101100111100=>111001101001=>[3,2,2,1,1,2,1] 100110111100=>110011101001=>[2,2,3,1,1,2,1] 111000011110=>101101001011=>[1,1,2,1,1,2,1,1,2] 110011111000=>100110101101=>[1,2,2,1,1,1,2,1,1] 101001111100=>111100101001=>[4,2,1,1,1,2,1] 101111110000=>111010100101=>[3,1,1,1,1,2,1,1,1] 100111111000=>110010101101=>[2,2,1,1,1,1,2,1,1] 111111100000=>101010110101=>[1,1,1,1,1,1,2,1,1,1,1] 01101010100=>00111111110=>[2,8,1] 11111100000=>10101001010=>[1,1,1,1,1,2,1,1,1,1] 00111110000=>01101011010=>[1,2,1,1,1,2,1,1,1] 01111100010=>00101001000=>[2,1,1,1,2,1,3] 01111101000=>00101000010=>[2,1,1,1,4,1,1] 100011001100=>110110011001=>[2,1,2,2,2,2,1] 100011110000=>110110100101=>[2,1,2,1,1,2,1,1,1] 110000101100=>100101111001=>[1,2,1,1,4,2,1] 110000110010=>100101100111=>[1,2,1,1,2,2,3] 110000100110=>100101110011=>[1,2,1,1,3,2,2] 110000111000=>100101101101=>[1,2,1,1,2,1,2,1,1] 100001111000=>110100101101=>[2,1,1,2,1,1,2,1,1] 111000001010=>101101011111=>[1,1,2,1,1,1,5] 110000011010=>100101001111=>[1,2,1,1,1,2,4] 110000010110=>100101000011=>[1,2,1,1,1,4,2] 111100000010=>101001010111=>[1,1,1,2,1,1,1,1,3] 111000000110=>101101010011=>[1,1,2,1,1,1,1,2,2] 111110000000=>101011010101=>[1,1,1,1,2,1,1,1,1,1,1] 10101001011=>11111100001=>[6,4,1] 00111010101=>01101111111=>[1,2,1,7] 01001110101=>00011011111=>[3,2,1,5] 01000101111=>00010000101=>[3,1,4,1,1,1] 10011010101=>11001111111=>[2,2,7] 0000001000=>0101011101=>[1,1,1,1,1,3,1,1] 0000101100=>0101111001=>[1,1,1,4,2,1] 00101111111=>01111010101=>[1,4,1,1,1,1,1,1] 0011100001=>0110110100=>[1,2,1,2,1,1,2] 01010101000=>00000000010=>[9,1,1] 01000000010=>00010101000=>[3,1,1,1,1,1,3] 00010000000=>01000101010=>[1,1,3,1,1,1,1,1,1] 00000001000=>01010100010=>[1,1,1,1,1,1,3,1,1] 100001001001=>110100011100=>[2,1,1,3,3,2] 111100101101=>101001111000=>[1,1,1,2,4,3] 0000101000=>0101111101=>[1,1,1,5,1,1] 000000001010=>010101011111=>[1,1,1,1,1,1,1,5] 000000101000=>010101111101=>[1,1,1,1,1,5,1,1] 000000100010=>010101110111=>[1,1,1,1,1,3,1,3] 000000110110=>010101100011=>[1,1,1,1,1,2,3,2] 000010100000=>010111110101=>[1,1,1,5,1,1,1,1] 000010101010=>010111111111=>[1,1,1,9] 000010001000=>010111011101=>[1,1,1,3,1,3,1,1] 000010000010=>010111010111=>[1,1,1,3,1,1,1,3] 000011010010=>010110000111=>[1,1,1,2,4,3] 001010000000=>011111010101=>[1,5,1,1,1,1,1,1] 001010001010=>011111011111=>[1,5,1,5] 001010101000=>011111111101=>[1,9,1,1] 001010100010=>011111110111=>[1,7,1,3] 001000100000=>011101110101=>[1,3,1,3,1,1,1,1] 001000101010=>011101111111=>[1,3,1,7] 001000001000=>011101011101=>[1,3,1,1,1,3,1,1] 001000000010=>011101010111=>[1,3,1,1,1,1,1,3] 001000010110=>011101000011=>[1,3,1,1,4,2] 001001010010=>011100000111=>[1,3,5,3] 001001000110=>011100010011=>[1,3,3,1,2,2] 001101100000=>011000110101=>[1,2,3,2,1,1,1,1] 001101000010=>011000010111=>[1,2,4,1,1,3] 001100010010=>011001000111=>[1,2,2,1,3,3] 001100000110=>011001010011=>[1,2,2,1,1,1,2,2] 001111011110=>011010001011=>[1,2,1,1,3,1,1,2] 101000000000=>111101010101=>[4,1,1,1,1,1,1,1,1] 101000001010=>111101011111=>[4,1,1,1,5] 101000101000=>111101111101=>[4,1,5,1,1] 101000100010=>111101110111=>[4,1,3,1,3] 101010100000=>111111110101=>[8,1,1,1,1] 101010001000=>111111011101=>[6,1,3,1,1] 101010000010=>111111010111=>[6,1,1,1,3] 100010101000=>110111111101=>[2,1,7,1,1] 100010100010=>110111110111=>[2,1,5,1,3] 100001011000=>110100001101=>[2,1,1,4,2,1,1] 100101100000=>110000110101=>[2,4,2,1,1,1,1] 100101001000=>110000011101=>[2,5,3,1,1] 100101000010=>110000010111=>[2,5,1,1,3] 110110000000=>100011010101=>[1,3,2,1,1,1,1,1,1] 110110110110=>100011100011=>[1,3,3,3,2] 110100100000=>100001110101=>[1,4,3,1,1,1,1] 110100001000=>100001011101=>[1,4,1,1,3,1,1] 110100000010=>100001010111=>[1,4,1,1,1,1,3] 110101101110=>100000111011=>[1,5,3,1,2] 110001100000=>100100110101=>[1,2,1,2,2,1,1,1,1] 110001001000=>100100011101=>[1,2,1,3,3,1,1] 110001000010=>100100010111=>[1,2,1,3,1,1,3] 110000011000=>100101001101=>[1,2,1,1,1,2,2,1,1] 110000010010=>100101000111=>[1,2,1,1,1,3,3] 110000000110=>100101010011=>[1,2,1,1,1,1,1,2,2] 111011010110=>101110000011=>[1,1,3,5,2] 111001011110=>101100001011=>[1,1,2,4,1,1,2] 111101111000=>101000101101=>[1,1,1,3,1,1,2,1,1] 111101110010=>101000100111=>[1,1,1,3,1,2,3] 111101100110=>101000110011=>[1,1,1,3,2,2,2] 111101001110=>101000011011=>[1,1,1,4,2,1,2] 111100011110=>101001001011=>[1,1,1,2,1,2,1,1,2] 10000000011=>11010101001=>[2,1,1,1,1,1,1,2,1] 111011001100=>101110011001=>[1,1,3,2,2,2,1] 111011100010=>101110110111=>[1,1,3,1,2,1,3] 111011100100=>101110110001=>[1,1,3,1,2,3,1] 111100101100=>101001111001=>[1,1,1,2,4,2,1] 111100110010=>101001100111=>[1,1,1,2,2,2,3] 111100110100=>101001100001=>[1,1,1,2,2,4,1] 111100111000=>101001101101=>[1,1,1,2,2,1,2,1,1] 111101001010=>101000011111=>[1,1,1,4,5] 111101001100=>101000011001=>[1,1,1,4,2,2,1] 111101100010=>101000110111=>[1,1,1,3,2,1,3] 111101100100=>101000110001=>[1,1,1,3,2,3,1] 111101101000=>101000111101=>[1,1,1,3,4,1,1] 111110001010=>101011011111=>[1,1,1,1,2,1,5] 111110010010=>101011000111=>[1,1,1,1,2,3,3] 111110010100=>101011000001=>[1,1,1,1,2,5,1] 111110011000=>101011001101=>[1,1,1,1,2,2,2,1,1] 111110100010=>101011110111=>[1,1,1,1,4,1,3] 111110100100=>101011110001=>[1,1,1,1,4,3,1] 111111000010=>101010010111=>[1,1,1,1,1,2,1,1,3] 111111001000=>101010011101=>[1,1,1,1,1,2,3,1,1] 100010110100=>110111100001=>[2,1,4,4,1] 100011010010=>110110000111=>[2,1,2,4,3] 100011011000=>110110001101=>[2,1,2,3,2,1,1] 100011100100=>110110110001=>[2,1,2,1,2,3,1] 100100101100=>110001111001=>[2,3,4,2,1] 100100110010=>110001100111=>[2,3,2,2,3] 100100111000=>110001101101=>[2,3,2,1,2,1,1] 100101001010=>110000011111=>[2,5,5] 100101100010=>110000110111=>[2,4,2,1,3] 100101101000=>110000111101=>[2,4,4,1,1] 100110001100=>110011011001=>[2,2,2,1,2,2,1] 100110010010=>110011000111=>[2,2,2,3,3] 100110011000=>110011001101=>[2,2,2,2,2,1,1] 100110100100=>110011110001=>[2,2,4,3,1] 100110110000=>110011100101=>[2,2,3,2,1,1,1] 100111000010=>110010010111=>[2,2,1,2,1,1,3] 100111001000=>110010011101=>[2,2,1,2,3,1,1] 100111100000=>110010110101=>[2,2,1,1,2,1,1,1,1] 101000110100=>111101100001=>[4,1,2,4,1] 101001001100=>111100011001=>[4,3,2,2,1] 101001010010=>111100000111=>[4,5,3] 101001011000=>111100001101=>[4,4,2,1,1] 101001100100=>111100110001=>[4,2,2,3,1] 101001110000=>111100100101=>[4,2,1,2,1,1,1] 101010010100=>111111000001=>[6,5,1] 101011000100=>111110010001=>[5,2,1,3,1] 101011010000=>111110000101=>[5,4,1,1,1] 101100001100=>111001011001=>[3,2,1,1,2,2,1] 101100010010=>111001000111=>[3,2,1,3,3] 101100011000=>111001001101=>[3,2,1,2,2,1,1] 101100100100=>111001110001=>[3,2,3,3,1] 101100110000=>111001100101=>[3,2,2,2,1,1,1] 101101001000=>111000011101=>[3,4,3,1,1] 101101100000=>111000110101=>[3,3,2,1,1,1,1] 101110000100=>111011010001=>[3,1,2,1,1,3,1] 101110010000=>111011000101=>[3,1,2,3,1,1,1] 101111000000=>111010010101=>[3,1,1,2,1,1,1,1,1] 011010000110=>001111010011=>[2,4,1,1,2,2] 011010111100=>001111101001=>[2,5,1,1,2,1] 011010001000=>001111011101=>[2,4,1,3,1,1] 011010100000=>001111110101=>[2,6,1,1,1,1] 010010100000=>000111110101=>[3,5,1,1,1,1] 010101100000=>000000110101=>[6,2,1,1,1,1] 00100000000=>01110101010=>[1,3,1,1,1,1,1,1,1] 111110010110=>101011000011=>[1,1,1,1,2,4,2] 101111010110=>111010000011=>[3,1,1,5,2] 111001110110=>101100100011=>[1,1,2,2,1,3,2] 101101110110=>111000100011=>[3,3,1,3,2] 111111100100=>101010110001=>[1,1,1,1,1,1,2,3,1] 100100100100=>110001110001=>[2,3,3,3,1] 111110110100=>101011100001=>[1,1,1,1,3,4,1] 111011110100=>101110100001=>[1,1,3,1,1,4,1] 101111110100=>111010100001=>[3,1,1,1,1,4,1] 100010010100=>110111000001=>[2,1,3,5,1] 111110011100=>101011001001=>[1,1,1,1,2,2,1,2,1] 111011011100=>101110001001=>[1,1,3,3,1,2,1] 101111011100=>111010001001=>[3,1,1,3,1,2,1] 111001111100=>101100101001=>[1,1,2,2,1,1,1,2,1] 101101111100=>111000101001=>[3,3,1,1,1,2,1] 100111111100=>110010101001=>[2,2,1,1,1,1,1,2,1] 111000010000=>101101000101=>[1,1,2,1,1,3,1,1,1] 101100010000=>111001000101=>[3,2,1,3,1,1,1] 100110010000=>110011000101=>[2,2,2,3,1,1,1] 100011010000=>110110000101=>[2,1,2,4,1,1,1] 100001110000=>110100100101=>[2,1,1,2,1,2,1,1,1] 0011000100=>0110010001=>[1,2,2,1,3,1] 0011000010=>0110010111=>[1,2,2,1,1,3] 0001001100=>0100011001=>[1,1,3,2,2,1] 0001000110=>0100010011=>[1,1,3,1,2,2] 0001100100=>0100110001=>[1,1,2,2,3,1] 0001100010=>0100110111=>[1,1,2,2,1,3] 0000100110=>0101110011=>[1,1,1,3,2,2] 0000110010=>0101100111=>[1,1,1,2,2,3] 110011000100=>100110010001=>[1,2,2,2,1,3,1] 110011000110=>100110010011=>[1,2,2,2,1,2,2] 110011000010=>100110010111=>[1,2,2,2,1,1,3] 110011101100=>100110111001=>[1,2,2,1,3,2,1] 110011100110=>100110110011=>[1,2,2,1,2,2,2] 110011110100=>100110100001=>[1,2,2,1,1,4,1] 110011110110=>100110100011=>[1,2,2,1,1,3,2] 110011110010=>100110100111=>[1,2,2,1,1,2,3] 110011111010=>100110101111=>[1,2,2,1,1,1,4] 110001001100=>100100011001=>[1,2,1,3,2,2,1] 110001001110=>100100011011=>[1,2,1,3,2,1,2] 110001000100=>100100010001=>[1,2,1,3,1,3,1] 110001000110=>100100010011=>[1,2,1,3,1,2,2] 110001101100=>100100111001=>[1,2,1,2,3,2,1] 110001100100=>100100110001=>[1,2,1,2,2,3,1] 110001100110=>100100110011=>[1,2,1,2,2,2,2] 110001100010=>100100110111=>[1,2,1,2,2,1,3] 110001110110=>100100100011=>[1,2,1,2,1,3,2] 110001110010=>100100100111=>[1,2,1,2,1,2,3] 110001111010=>100100101111=>[1,2,1,2,1,1,4] 110000100100=>100101110001=>[1,2,1,1,3,3,1] 110000100010=>100101110111=>[1,2,1,1,3,1,3] 110000110100=>100101100001=>[1,2,1,1,2,4,1] 110000010100=>100101000001=>[1,2,1,1,1,5,1] 110000001010=>100101011111=>[1,2,1,1,1,1,5] 111011001110=>101110011011=>[1,1,3,2,2,1,2] 111011000110=>101110010011=>[1,1,3,2,1,2,2] 111011101100=>101110111001=>[1,1,3,1,3,2,1] 111011101110=>101110111011=>[1,1,3,1,3,1,2] 111011100110=>101110110011=>[1,1,3,1,2,2,2] 111011110110=>101110100011=>[1,1,3,1,1,3,2] 111011110010=>101110100111=>[1,1,3,1,1,2,3] 111011111010=>101110101111=>[1,1,3,1,1,1,4] 111001001110=>101100011011=>[1,1,2,3,2,1,2] 111001000100=>101100010001=>[1,1,2,3,1,3,1] 111001000110=>101100010011=>[1,1,2,3,1,2,2] 111001000010=>101100010111=>[1,1,2,3,1,1,3] 111001101100=>101100111001=>[1,1,2,2,3,2,1] 111001101110=>101100111011=>[1,1,2,2,3,1,2] 111001100110=>101100110011=>[1,1,2,2,2,2,2] 111001110100=>101100100001=>[1,1,2,2,1,4,1] 111001110010=>101100100111=>[1,1,2,2,1,2,3] 111001111010=>101100101111=>[1,1,2,2,1,1,4] 111000100100=>101101110001=>[1,1,2,1,3,3,1] 111000100010=>101101110111=>[1,1,2,1,3,1,3] 111000110110=>101101100011=>[1,1,2,1,2,3,2] 111000111010=>101101101111=>[1,1,2,1,2,1,4] 111000010100=>101101000001=>[1,1,2,1,1,5,1] 111000010010=>101101000111=>[1,1,2,1,1,3,3] 111101000110=>101000010011=>[1,1,1,4,1,2,2] 111101101100=>101000111001=>[1,1,1,3,3,2,1] 111101101110=>101000111011=>[1,1,1,3,3,1,2] 111101110100=>101000100001=>[1,1,1,3,1,4,1] 111101110110=>101000100011=>[1,1,1,3,1,3,2] 111101111010=>101000101111=>[1,1,1,3,1,1,4] 111100101110=>101001111011=>[1,1,1,2,4,1,2] 111100100110=>101001110011=>[1,1,1,2,3,2,2] 111100110110=>101001100011=>[1,1,1,2,2,3,2] 111100111010=>101001101111=>[1,1,1,2,2,1,4] 111100010110=>101001000011=>[1,1,1,2,1,4,2] 111100011010=>101001001111=>[1,1,1,2,1,2,4] 111110101100=>101011111001=>[1,1,1,1,5,2,1] 111110101110=>101011111011=>[1,1,1,1,5,1,2] 111110100110=>101011110011=>[1,1,1,1,4,2,2] 111110110110=>101011100011=>[1,1,1,1,3,3,2] 111110110010=>101011100111=>[1,1,1,1,3,2,3] 111110111010=>101011101111=>[1,1,1,1,3,1,4] 111110011010=>101011001111=>[1,1,1,1,2,2,4] 111111010100=>101010000001=>[1,1,1,1,1,6,1] 111111010110=>101010000011=>[1,1,1,1,1,5,2] 111111010010=>101010000111=>[1,1,1,1,1,4,3] 111111011010=>101010001111=>[1,1,1,1,1,3,4] 111111001010=>101010011111=>[1,1,1,1,1,2,5] 111111101010=>101010111111=>[1,1,1,1,1,1,6] 110001001011=>100100011110=>[1,2,1,3,4,1] 110110000110=>100011010011=>[1,3,2,1,1,2,2] 111100000110=>101001010011=>[1,1,1,2,1,1,1,2,2] 110100001110=>100001011011=>[1,4,1,1,2,1,2] 10101010011=>11111111001=>[8,2,1] 10100101011=>11110000001=>[4,6,1] 10010101011=>11000000001=>[2,8,1] 01100110101=>00110011111=>[2,2,2,5] 01011001101=>00001100111=>[4,2,2,3] 01010110011=>00000011001=>[6,2,2,1] 01010100111=>00000001101=>[7,2,1,1] 01010011101=>00000110111=>[5,2,1,3] 01010010111=>00000111101=>[5,4,1,1] 01001010111=>00011111101=>[3,6,1,1] 01000111011=>00010010001=>[3,1,2,1,3,1] 00010111011=>01000010001=>[1,1,4,1,3,1] 110010001000=>100111011101=>[1,2,3,1,3,1,1] 110010010000=>100111000101=>[1,2,3,3,1,1,1] 0101001000=>0000011101=>[5,3,1,1] 0101010000=>0000000101=>[7,1,1,1] 0010010000=>0111000101=>[1,3,3,1,1,1] 0100101000=>0001111101=>[3,5,1,1] 01010101111=>00000000101=>[8,1,1,1] 10101010111=>11111111101=>[9,1,1] 010011100011=>000110110110=>[3,2,1,2,1,2,1] 010110100011=>000011110110=>[4,4,1,2,1] 011001001011=>001100011110=>[2,2,3,4,1] 011001100011=>001100110110=>[2,2,2,2,1,2,1] 011011000011=>001110010110=>[2,3,2,1,1,2,1] 110001100011=>100100110110=>[1,2,1,2,2,1,2,1] 0111101010=>0010111111=>[2,1,1,6] 0001000000=>0100010101=>[1,1,3,1,1,1,1,1] 0010011001=>0111001100=>[1,3,2,2,2] 0010100101=>0111110000=>[1,5,4] 0011001001=>0110011100=>[1,2,2,3,2] 0010110111=>0111100010=>[1,4,3,1,1] 0010011111=>0111001010=>[1,3,2,1,1,1,1] 0000111001=>0101101100=>[1,1,1,2,1,2,2] 0010001101=>0111011000=>[1,3,1,2,3] 11000001000=>10010100010=>[1,2,1,1,1,3,1,1] 11111111000=>10101010010=>[1,1,1,1,1,1,1,2,1,1] 0110101101=>0011111000=>[2,5,3] 0110001111=>0011011010=>[2,2,1,2,1,1,1] 0101101011=>0000111110=>[4,5,1] 0011000011=>0110010110=>[1,2,2,1,1,2,1] 0011011011=>0110001110=>[1,2,3,3,1] 0001111011=>0100101110=>[1,1,2,1,1,3,1] 111111110011=>101010100110=>[1,1,1,1,1,1,1,2,2,1] 111111001111=>101010011010=>[1,1,1,1,1,2,2,1,1,1] 111111000011=>101010010110=>[1,1,1,1,1,2,1,1,2,1] 111111011011=>101010001110=>[1,1,1,1,1,3,3,1] 111100111111=>101001101010=>[1,1,1,2,2,1,1,1,1,1] 111100110011=>101001100110=>[1,1,1,2,2,2,2,1] 111100001111=>101001011010=>[1,1,1,2,1,1,2,1,1,1] 111100011011=>101001001110=>[1,1,1,2,1,2,3,1] 111101101111=>101000111010=>[1,1,1,3,3,1,1,1] 111101100011=>101000110110=>[1,1,1,3,2,1,2,1] 111101111011=>101000101110=>[1,1,1,3,1,1,3,1] 111101001011=>101000011110=>[1,1,1,4,4,1] 110011111111=>100110101010=>[1,2,2,1,1,1,1,1,1,1] 110011110011=>100110100110=>[1,2,2,1,1,2,2,1] 110011001111=>100110011010=>[1,2,2,2,2,1,1,1] 110011011011=>100110001110=>[1,2,2,3,3,1] 110000111111=>100101101010=>[1,2,1,1,2,1,1,1,1,1] 110000000011=>100101010110=>[1,2,1,1,1,1,1,1,2,1] 110001101111=>100100111010=>[1,2,1,2,3,1,1,1] 110001111011=>100100101110=>[1,2,1,2,1,1,3,1] 110110111111=>100011101010=>[1,3,3,1,1,1,1,1] 110110110011=>100011100110=>[1,3,3,2,2,1] 110110001111=>100011011010=>[1,3,2,1,2,1,1,1] 110110011011=>100011001110=>[1,3,2,2,3,1] 110111101111=>100010111010=>[1,3,1,1,3,1,1,1] 110111100011=>100010110110=>[1,3,1,1,2,1,2,1] 110111111011=>100010101110=>[1,3,1,1,1,1,3,1] 110111001011=>100010011110=>[1,3,1,2,4,1] 110100101111=>100001111010=>[1,4,4,1,1,1] 110100111011=>100001101110=>[1,4,2,1,3,1] 110101101011=>100000111110=>[1,5,5,1] 001111111111=>011010101010=>[1,2,1,1,1,1,1,1,1,1,1] 001111110011=>011010100110=>[1,2,1,1,1,1,2,2,1] 001111001111=>011010011010=>[1,2,1,1,2,2,1,1,1] 001111011011=>011010001110=>[1,2,1,1,3,3,1] 001100111111=>011001101010=>[1,2,2,2,1,1,1,1,1] 001100000011=>011001010110=>[1,2,2,1,1,1,1,2,1] 001101101111=>011000111010=>[1,2,3,3,1,1,1] 001101111011=>011000101110=>[1,2,3,1,1,3,1] 000011111111=>010110101010=>[1,1,1,2,1,1,1,1,1,1,1] 000011000011=>010110010110=>[1,1,1,2,2,1,1,2,1] 000000110011=>010101100110=>[1,1,1,1,1,2,2,2,1] 000000001111=>010101011010=>[1,1,1,1,1,1,1,2,1,1,1] 000000000011=>010101010110=>[1,1,1,1,1,1,1,1,1,2,1] 000110111111=>010011101010=>[1,1,2,3,1,1,1,1,1] 000111111011=>010010101110=>[1,1,2,1,1,1,1,3,1] 011011111111=>001110101010=>[2,3,1,1,1,1,1,1,1] 011011110011=>001110100110=>[2,3,1,1,2,2,1] 011011001111=>001110011010=>[2,3,2,2,1,1,1] 011000111111=>001101101010=>[2,2,1,2,1,1,1,1,1] 011001111011=>001100101110=>[2,2,2,1,1,3,1] 011110111111=>001011101010=>[2,1,1,3,1,1,1,1,1] 011110011011=>001011001110=>[2,1,1,2,2,3,1] 011111101111=>001010111010=>[2,1,1,1,1,3,1,1,1] 011111100011=>001010110110=>[2,1,1,1,1,2,1,2,1] 011111111011=>001010101110=>[2,1,1,1,1,1,1,3,1] 011111001011=>001010011110=>[2,1,1,1,2,4,1] 011100111011=>001001101110=>[2,1,2,2,1,3,1] 010010111111=>000111101010=>[3,4,1,1,1,1,1] 010011111011=>000110101110=>[3,2,1,1,1,3,1] 010110101111=>000011111010=>[4,5,1,1,1] 010110111011=>000011101110=>[4,3,1,3,1] 010111101011=>000010111110=>[4,1,1,5,1] 11110000000=>10100101010=>[1,1,1,2,1,1,1,1,1,1] 11011100010=>10001001000=>[1,3,1,2,1,3] 11011101000=>10001000010=>[1,3,1,4,1,1] 11100101010=>10110000000=>[1,1,2,7] 11101001010=>10111100000=>[1,1,4,5] 11101010010=>10111111000=>[1,1,6,3] 11110100010=>10100001000=>[1,1,1,4,1,3] 111111111100=>101010101001=>[1,1,1,1,1,1,1,1,1,2,1] 111111110000=>101010100101=>[1,1,1,1,1,1,1,2,1,1,1] 111111110110=>101010100011=>[1,1,1,1,1,1,1,3,2] 111111001100=>101010011001=>[1,1,1,1,1,2,2,2,1] 111111000110=>101010010011=>[1,1,1,1,1,2,1,2,2] 111111011000=>101010001101=>[1,1,1,1,1,3,2,1,1] 111100111100=>101001101001=>[1,1,1,2,2,1,1,2,1] 111100000000=>101001010101=>[1,1,1,2,1,1,1,1,1,1,1] 111101011010=>101000001111=>[1,1,1,5,4] 110011111100=>100110101001=>[1,2,2,1,1,1,1,2,1] 110011000000=>100110010101=>[1,2,2,2,1,1,1,1,1] 110000110000=>100101100101=>[1,2,1,1,2,2,1,1,1] 110000001100=>100101011001=>[1,2,1,1,1,1,2,2,1] 110000000000=>100101010101=>[1,2,1,1,1,1,1,1,1,1,1] 110001011010=>100100001111=>[1,2,1,4,4] 110110111100=>100011101001=>[1,3,3,1,1,2,1] 110110011110=>100011001011=>[1,3,2,2,1,1,2] 110111101100=>100010111001=>[1,3,1,1,3,2,1] 110111100110=>100010110011=>[1,3,1,1,2,2,2] 110111111000=>100010101101=>[1,3,1,1,1,1,2,1,1] 110111110010=>100010100111=>[1,3,1,1,1,2,3] 110111001110=>100010011011=>[1,3,1,2,2,1,2] 110111011010=>100010001111=>[1,3,1,3,4] 110100100110=>100001110011=>[1,4,3,2,2] 110101111010=>100000101111=>[1,5,1,1,4] 0010011000=>0111001101=>[1,3,2,2,1,1] 0000100000=>0101110101=>[1,1,1,3,1,1,1,1] 010101001000=>000000011101=>[7,3,1,1] 010010101000=>000111111101=>[3,7,1,1] 101000010000=>111101000101=>[4,1,1,3,1,1,1] 001000110000=>011101100101=>[1,3,1,2,2,1,1,1] 100010010000=>110111000101=>[2,1,3,3,1,1,1] 001010010000=>011111000101=>[1,5,3,1,1,1] 0010000111=>0111010010=>[1,3,1,1,2,1,1] 0011100111=>0110110010=>[1,2,1,2,2,1,1] 11110101010=>10100000000=>[1,1,1,8] 001010010001=>011111000100=>[1,5,3,1,2] 000010110001=>010111100100=>[1,1,1,4,2,1,2] 001000110001=>011101100100=>[1,3,1,2,2,1,2] 110000000010=>100101010111=>[1,2,1,1,1,1,1,1,3] 01000001011=>00010100001=>[3,1,1,1,4,1] 01000010111=>00010111101=>[3,1,1,4,1,1] 01010111111=>00000010101=>[6,1,1,1,1,1] 110001101000=>100100111101=>[1,2,1,2,4,1,1] 110010011000=>100111001101=>[1,2,3,2,2,1,1] 110011001000=>100110011101=>[1,2,2,2,3,1,1] 110011100000=>100110110101=>[1,2,2,1,2,1,1,1,1] 110100101000=>100001111101=>[1,4,5,1,1] 110110001000=>100011011101=>[1,3,2,1,3,1,1] 110110100000=>100011110101=>[1,3,4,1,1,1,1] 111000011000=>101101001101=>[1,1,2,1,1,2,2,1,1] 111001001000=>101100011101=>[1,1,2,3,3,1,1] 111001100000=>101100110101=>[1,1,2,2,2,1,1,1,1] 111100001000=>101001011101=>[1,1,1,2,1,1,3,1,1] 111100100000=>101001110101=>[1,1,1,2,3,1,1,1,1] 0010001100=>0111011001=>[1,3,1,2,2,1] 11010000010=>10000101000=>[1,4,1,1,1,3] 0010000110=>0111010011=>[1,3,1,1,2,2] 11101010101=>10111111111=>[1,1,9] 01110111111=>00100010101=>[2,1,3,1,1,1,1,1] 11111010101=>10101111111=>[1,1,1,1,7] 11010111111=>10000010101=>[1,5,1,1,1,1,1] 110100100010=>100001110111=>[1,4,3,1,3] 110010010010=>100111000111=>[1,2,3,3,3] 110010000100=>100111010001=>[1,2,3,1,1,3,1] 110001001010=>100100011111=>[1,2,1,3,5] 110000100001=>100101110100=>[1,2,1,1,3,1,1,2] 110000101000=>100101111101=>[1,2,1,1,5,1,1] 101001000100=>111100010001=>[4,3,1,3,1] 101000010100=>111101000001=>[4,1,1,5,1] 100100001000=>110001011101=>[2,3,1,1,3,1,1] 01000100011=>00010001001=>[3,1,3,1,2,1] 11010101111=>10000000101=>[1,7,1,1,1]
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
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 $w$.