Identifier
Mp00104: Binary words reverseBinary words
Mp00096: Binary words Foata bijectionBinary words
Mp00261: Binary words Burrows-WheelerBinary words
Images
0 => 0 => 0 => 0
1 => 1 => 1 => 1
00 => 00 => 00 => 00
01 => 10 => 10 => 10
10 => 01 => 01 => 10
11 => 11 => 11 => 11
000 => 000 => 000 => 000
001 => 100 => 010 => 100
010 => 010 => 100 => 100
011 => 110 => 110 => 110
100 => 001 => 001 => 100
101 => 101 => 101 => 110
110 => 011 => 011 => 110
111 => 111 => 111 => 111
0000 => 0000 => 0000 => 0000
0001 => 1000 => 0010 => 1000
0010 => 0100 => 0100 => 1000
0011 => 1100 => 0110 => 1010
0100 => 0010 => 1000 => 1000
0101 => 1010 => 1100 => 1010
0110 => 0110 => 1010 => 1100
0111 => 1110 => 1110 => 1110
1000 => 0001 => 0001 => 1000
1001 => 1001 => 0101 => 1100
1010 => 0101 => 1001 => 1010
1011 => 1101 => 1101 => 1110
1100 => 0011 => 0011 => 1010
1101 => 1011 => 1011 => 1110
1110 => 0111 => 0111 => 1110
1111 => 1111 => 1111 => 1111
00000 => 00000 => 00000 => 00000
00001 => 10000 => 00010 => 10000
00010 => 01000 => 00100 => 10000
00011 => 11000 => 00110 => 10010
00100 => 00100 => 01000 => 10000
00101 => 10100 => 01100 => 10010
00110 => 01100 => 01010 => 11000
00111 => 11100 => 01110 => 10110
01000 => 00010 => 10000 => 10000
01001 => 10010 => 10100 => 11000
01010 => 01010 => 11000 => 10010
01011 => 11010 => 11100 => 10110
01100 => 00110 => 10010 => 11000
01101 => 10110 => 11010 => 11100
01110 => 01110 => 10110 => 11100
01111 => 11110 => 11110 => 11110
10000 => 00001 => 00001 => 10000
10001 => 10001 => 00101 => 11000
10010 => 01001 => 01001 => 11000
10011 => 11001 => 01101 => 11100
10100 => 00101 => 10001 => 10010
10101 => 10101 => 11001 => 10110
10110 => 01101 => 10101 => 11100
10111 => 11101 => 11101 => 11110
11000 => 00011 => 00011 => 10010
11001 => 10011 => 01011 => 11100
11010 => 01011 => 10011 => 10110
11011 => 11011 => 11011 => 11110
11100 => 00111 => 00111 => 10110
11101 => 10111 => 10111 => 11110
11110 => 01111 => 01111 => 11110
11111 => 11111 => 11111 => 11111
000000 => 000000 => 000000 => 000000
000001 => 100000 => 000010 => 100000
000010 => 010000 => 000100 => 100000
000011 => 110000 => 000110 => 100010
000100 => 001000 => 001000 => 100000
000101 => 101000 => 001100 => 100010
000110 => 011000 => 001010 => 101000
000111 => 111000 => 001110 => 100110
001000 => 000100 => 010000 => 100000
001001 => 100100 => 010100 => 101000
001010 => 010100 => 011000 => 100010
001011 => 110100 => 011100 => 100110
001100 => 001100 => 010010 => 110000
001101 => 101100 => 011010 => 110010
001110 => 011100 => 010110 => 101100
001111 => 111100 => 011110 => 101110
010000 => 000010 => 100000 => 100000
010001 => 100010 => 100100 => 110000
010010 => 010010 => 101000 => 101000
010011 => 110010 => 101100 => 101100
010100 => 001010 => 110000 => 100010
010101 => 101010 => 111000 => 100110
010110 => 011010 => 110100 => 110010
010111 => 111010 => 111100 => 101110
011000 => 000110 => 100010 => 101000
011001 => 100110 => 101010 => 111000
011010 => 010110 => 110010 => 101100
011011 => 110110 => 111010 => 111010
011100 => 001110 => 100110 => 110010
011101 => 101110 => 110110 => 111100
011110 => 011110 => 101110 => 111010
011111 => 111110 => 111110 => 111110
100000 => 000001 => 000001 => 100000
100001 => 100001 => 000101 => 101000
100010 => 010001 => 001001 => 110000
100011 => 110001 => 001101 => 110010
100100 => 001001 => 010001 => 101000
100101 => 101001 => 011001 => 101100
100110 => 011001 => 010101 => 111000
>>> Load all 1542 entries. <<<
100111 => 111001 => 011101 => 111010
101000 => 000101 => 100001 => 100010
101001 => 100101 => 101001 => 110010
101010 => 010101 => 110001 => 100110
101011 => 110101 => 111001 => 101110
101100 => 001101 => 100101 => 101100
101101 => 101101 => 110101 => 111010
101110 => 011101 => 101101 => 111100
101111 => 111101 => 111101 => 111110
110000 => 000011 => 000011 => 100010
110001 => 100011 => 001011 => 101100
110010 => 010011 => 010011 => 110010
110011 => 110011 => 011011 => 111100
110100 => 001011 => 100011 => 100110
110101 => 101011 => 110011 => 101110
110110 => 011011 => 101011 => 111010
110111 => 111011 => 111011 => 111110
111000 => 000111 => 000111 => 100110
111001 => 100111 => 010111 => 111010
111010 => 010111 => 100111 => 101110
111011 => 110111 => 110111 => 111110
111100 => 001111 => 001111 => 101110
111101 => 101111 => 101111 => 111110
111110 => 011111 => 011111 => 111110
111111 => 111111 => 111111 => 111111
0000000 => 0000000 => 0000000 => 0000000
0000001 => 1000000 => 0000010 => 1000000
0000010 => 0100000 => 0000100 => 1000000
0000011 => 1100000 => 0000110 => 1000010
0000100 => 0010000 => 0001000 => 1000000
0000101 => 1010000 => 0001100 => 1000010
0000110 => 0110000 => 0001010 => 1001000
0000111 => 1110000 => 0001110 => 1000110
0001000 => 0001000 => 0010000 => 1000000
0001001 => 1001000 => 0010100 => 1001000
0001010 => 0101000 => 0011000 => 1000010
0001011 => 1101000 => 0011100 => 1000110
0001100 => 0011000 => 0010010 => 1100000
0001101 => 1011000 => 0011010 => 1010010
0001110 => 0111000 => 0010110 => 1001100
0001111 => 1111000 => 0011110 => 1001110
0010000 => 0000100 => 0100000 => 1000000
0010001 => 1000100 => 0100100 => 1100000
0010010 => 0100100 => 0101000 => 1001000
0010011 => 1100100 => 0101100 => 1001100
0010100 => 0010100 => 0110000 => 1000010
0010101 => 1010100 => 0111000 => 1000110
0010110 => 0110100 => 0110100 => 1010010
0010111 => 1110100 => 0111100 => 1001110
0011000 => 0001100 => 0100010 => 1100000
0011001 => 1001100 => 0101010 => 1110000
0011010 => 0101100 => 0110010 => 1100100
0011011 => 1101100 => 0111010 => 1100110
0011100 => 0011100 => 0100110 => 1100100
0011101 => 1011100 => 0110110 => 1101100
0011110 => 0111100 => 0101110 => 1011010
0011111 => 1111100 => 0111110 => 1011110
0100000 => 0000010 => 1000000 => 1000000
0100001 => 1000010 => 1000100 => 1100000
0100010 => 0100010 => 1001000 => 1100000
0100011 => 1100010 => 1001100 => 1100100
0100100 => 0010010 => 1010000 => 1001000
0100101 => 1010010 => 1011000 => 1001100
0100110 => 0110010 => 1010100 => 1110000
0100111 => 1110010 => 1011100 => 1011010
0101000 => 0001010 => 1100000 => 1000010
0101001 => 1001010 => 1101000 => 1010010
0101010 => 0101010 => 1110000 => 1000110
0101011 => 1101010 => 1111000 => 1001110
0101100 => 0011010 => 1100100 => 1100100
0101101 => 1011010 => 1110100 => 1100110
0101110 => 0111010 => 1101100 => 1101100
0101111 => 1111010 => 1111100 => 1011110
0110000 => 0000110 => 1000010 => 1001000
0110001 => 1000110 => 1001010 => 1110000
0110010 => 0100110 => 1010010 => 1110000
0110011 => 1100110 => 1011010 => 1111000
0110100 => 0010110 => 1100010 => 1001100
0110101 => 1010110 => 1110010 => 1011010
0110110 => 0110110 => 1101010 => 1111000
0110111 => 1110110 => 1111010 => 1110110
0111000 => 0001110 => 1000110 => 1010010
0111001 => 1001110 => 1010110 => 1111000
0111010 => 0101110 => 1100110 => 1101100
0111011 => 1101110 => 1110110 => 1111100
0111100 => 0011110 => 1001110 => 1100110
0111101 => 1011110 => 1101110 => 1111100
0111110 => 0111110 => 1011110 => 1110110
0111111 => 1111110 => 1111110 => 1111110
1000000 => 0000001 => 0000001 => 1000000
1000001 => 1000001 => 0000101 => 1001000
1000010 => 0100001 => 0001001 => 1100000
1000011 => 1100001 => 0001101 => 1010010
1000100 => 0010001 => 0010001 => 1100000
1000101 => 1010001 => 0011001 => 1100100
1000110 => 0110001 => 0010101 => 1110000
1000111 => 1110001 => 0011101 => 1100110
1001000 => 0001001 => 0100001 => 1001000
1001001 => 1001001 => 0101001 => 1110000
1001010 => 0101001 => 0110001 => 1001100
1001011 => 1101001 => 0111001 => 1011010
1001100 => 0011001 => 0100101 => 1110000
1001101 => 1011001 => 0110101 => 1111000
1001110 => 0111001 => 0101101 => 1111000
1001111 => 1111001 => 0111101 => 1110110
1010000 => 0000101 => 1000001 => 1000010
1010001 => 1000101 => 1001001 => 1100100
1010010 => 0100101 => 1010001 => 1010010
1010011 => 1100101 => 1011001 => 1101100
1010100 => 0010101 => 1100001 => 1000110
1010101 => 1010101 => 1110001 => 1001110
1010110 => 0110101 => 1101001 => 1100110
1010111 => 1110101 => 1111001 => 1011110
1011000 => 0001101 => 1000101 => 1001100
1011001 => 1001101 => 1010101 => 1111000
1011010 => 0101101 => 1100101 => 1011010
1011011 => 1101101 => 1110101 => 1110110
1011100 => 0011101 => 1001101 => 1101100
1011101 => 1011101 => 1101101 => 1111100
1011110 => 0111101 => 1011101 => 1111100
1011111 => 1111101 => 1111101 => 1111110
1100000 => 0000011 => 0000011 => 1000010
1100001 => 1000011 => 0001011 => 1001100
1100010 => 0100011 => 0010011 => 1100100
1100011 => 1100011 => 0011011 => 1101100
1100100 => 0010011 => 0100011 => 1010010
1100101 => 1010011 => 0110011 => 1101100
1100110 => 0110011 => 0101011 => 1111000
1100111 => 1110011 => 0111011 => 1111100
1101000 => 0001011 => 1000011 => 1000110
1101001 => 1001011 => 1010011 => 1100110
1101010 => 0101011 => 1100011 => 1001110
1101011 => 1101011 => 1110011 => 1011110
1101100 => 0011011 => 1001011 => 1011010
1101101 => 1011011 => 1101011 => 1110110
1101110 => 0111011 => 1011011 => 1111100
1101111 => 1111011 => 1111011 => 1111110
1110000 => 0000111 => 0000111 => 1000110
1110001 => 1000111 => 0010111 => 1011010
1110010 => 0100111 => 0100111 => 1100110
1110011 => 1100111 => 0110111 => 1111100
1110100 => 0010111 => 1000111 => 1001110
1110101 => 1010111 => 1100111 => 1011110
1110110 => 0110111 => 1010111 => 1110110
1110111 => 1110111 => 1110111 => 1111110
1111000 => 0001111 => 0001111 => 1001110
1111001 => 1001111 => 0101111 => 1110110
1111010 => 0101111 => 1001111 => 1011110
1111011 => 1101111 => 1101111 => 1111110
1111100 => 0011111 => 0011111 => 1011110
1111101 => 1011111 => 1011111 => 1111110
1111110 => 0111111 => 0111111 => 1111110
1111111 => 1111111 => 1111111 => 1111111
00000000 => 00000000 => 00000000 => 00000000
00000001 => 10000000 => 00000010 => 10000000
00000010 => 01000000 => 00000100 => 10000000
00000011 => 11000000 => 00000110 => 10000010
00000100 => 00100000 => 00001000 => 10000000
00000101 => 10100000 => 00001100 => 10000010
00000110 => 01100000 => 00001010 => 10001000
00000111 => 11100000 => 00001110 => 10000110
00001000 => 00010000 => 00010000 => 10000000
00001001 => 10010000 => 00010100 => 10001000
00001010 => 01010000 => 00011000 => 10000010
00001011 => 11010000 => 00011100 => 10000110
00001100 => 00110000 => 00010010 => 10100000
00001101 => 10110000 => 00011010 => 10010010
00001110 => 01110000 => 00010110 => 10001100
00001111 => 11110000 => 00011110 => 10001110
00010000 => 00001000 => 00100000 => 10000000
00010001 => 10001000 => 00100100 => 10100000
00010010 => 01001000 => 00101000 => 10001000
00010011 => 11001000 => 00101100 => 10001100
00010100 => 00101000 => 00110000 => 10000010
00010101 => 10101000 => 00111000 => 10000110
00010110 => 01101000 => 00110100 => 10010010
00010111 => 11101000 => 00111100 => 10001110
00011000 => 00011000 => 00100010 => 11000000
00011001 => 10011000 => 00101010 => 10110000
00011010 => 01011000 => 00110010 => 11000010
00011011 => 11011000 => 00111010 => 10100110
00011100 => 00111000 => 00100110 => 10100100
00011101 => 10111000 => 00110110 => 10101100
00011110 => 01111000 => 00101110 => 10011010
00011111 => 11111000 => 00111110 => 10011110
00100000 => 00000100 => 01000000 => 10000000
00100001 => 10000100 => 01000100 => 11000000
00100010 => 01000100 => 01001000 => 10100000
00100011 => 11000100 => 01001100 => 10100100
00100100 => 00100100 => 01010000 => 10001000
00100101 => 10100100 => 01011000 => 10001100
00100110 => 01100100 => 01010100 => 10110000
00100111 => 11100100 => 01011100 => 10011010
00101000 => 00010100 => 01100000 => 10000010
00101001 => 10010100 => 01101000 => 10010010
00101010 => 01010100 => 01110000 => 10000110
00101011 => 11010100 => 01111000 => 10001110
00101100 => 00110100 => 01100100 => 11000010
00101101 => 10110100 => 01110100 => 10100110
00101110 => 01110100 => 01101100 => 10101100
00101111 => 11110100 => 01111100 => 10011110
00110000 => 00001100 => 01000010 => 10100000
00110001 => 10001100 => 01001010 => 11100000
00110010 => 01001100 => 01010010 => 11100000
00110011 => 11001100 => 01011010 => 11010100
00110100 => 00101100 => 01100010 => 10100100
00110101 => 10101100 => 01110010 => 11001010
00110110 => 01101100 => 01101010 => 11100010
00110111 => 11101100 => 01111010 => 11001110
00111000 => 00011100 => 01000110 => 11000010
00111001 => 10011100 => 01010110 => 10111000
00111010 => 01011100 => 01100110 => 11001100
00111011 => 11011100 => 01110110 => 11011010
00111100 => 00111100 => 01001110 => 11001010
00111101 => 10111100 => 01101110 => 10111100
00111110 => 01111100 => 01011110 => 10110110
00111111 => 11111100 => 01111110 => 10111110
01000000 => 00000010 => 10000000 => 10000000
01000001 => 10000010 => 10000100 => 10100000
01000010 => 01000010 => 10001000 => 11000000
01000011 => 11000010 => 10001100 => 11000010
01000100 => 00100010 => 10010000 => 10100000
01000101 => 10100010 => 10011000 => 10100100
01000110 => 01100010 => 10010100 => 11100000
01000111 => 11100010 => 10011100 => 11001010
01001000 => 00010010 => 10100000 => 10001000
01001001 => 10010010 => 10101000 => 10110000
01001010 => 01010010 => 10110000 => 10001100
01001011 => 11010010 => 10111000 => 10011010
01001100 => 00110010 => 10100100 => 11100000
01001101 => 10110010 => 10110100 => 11010100
01001110 => 01110010 => 10101100 => 10111000
01001111 => 11110010 => 10111100 => 10110110
01010000 => 00001010 => 11000000 => 10000010
01010001 => 10001010 => 11001000 => 11000010
01010010 => 01001010 => 11010000 => 10010010
01010011 => 11001010 => 11011000 => 10101100
01010100 => 00101010 => 11100000 => 10000110
01010101 => 10101010 => 11110000 => 10001110
01010110 => 01101010 => 11101000 => 10100110
01010111 => 11101010 => 11111000 => 10011110
01011000 => 00011010 => 11000100 => 10100100
01011001 => 10011010 => 11010100 => 11100010
01011010 => 01011010 => 11100100 => 11001010
01011011 => 11011010 => 11110100 => 11001110
01011100 => 00111010 => 11001100 => 11001100
01011101 => 10111010 => 11101100 => 11011010
01011110 => 01111010 => 11011100 => 10111100
01011111 => 11111010 => 11111100 => 10111110
01100000 => 00000110 => 10000010 => 10001000
01100001 => 10000110 => 10001010 => 10110000
01100010 => 01000110 => 10010010 => 11100000
01100011 => 11000110 => 10011010 => 11100010
01100100 => 00100110 => 10100010 => 10110000
01100101 => 10100110 => 10110010 => 10111000
01100110 => 01100110 => 10101010 => 11110000
01100111 => 11100110 => 10111010 => 11110010
01101000 => 00010110 => 11000010 => 10001100
01101001 => 10010110 => 11010010 => 11010100
01101010 => 01010110 => 11100010 => 10011010
01101011 => 11010110 => 11110010 => 10110110
01101100 => 00110110 => 11001010 => 10111000
01101101 => 10110110 => 11101010 => 11110010
01101110 => 01110110 => 11011010 => 11111000
01101111 => 11110110 => 11111010 => 11101110
01110000 => 00001110 => 10000110 => 10010010
01110001 => 10001110 => 10010110 => 11010100
01110010 => 01001110 => 10100110 => 11100010
01110011 => 11001110 => 10110110 => 11111000
01110100 => 00101110 => 11000110 => 10101100
01110101 => 10101110 => 11100110 => 10111100
01110110 => 01101110 => 11010110 => 11111000
01110111 => 11101110 => 11110110 => 11111010
01111000 => 00011110 => 10001110 => 10100110
01111001 => 10011110 => 10101110 => 11110010
01111010 => 01011110 => 11001110 => 11011010
01111011 => 11011110 => 11101110 => 11111100
01111100 => 00111110 => 10011110 => 11001110
01111101 => 10111110 => 11011110 => 11111010
01111110 => 01111110 => 10111110 => 11101110
01111111 => 11111110 => 11111110 => 11111110
10000000 => 00000001 => 00000001 => 10000000
10000001 => 10000001 => 00000101 => 10001000
10000010 => 01000001 => 00001001 => 10100000
10000011 => 11000001 => 00001101 => 10010010
10000100 => 00100001 => 00010001 => 11000000
10000101 => 10100001 => 00011001 => 11000010
10000110 => 01100001 => 00010101 => 10110000
10000111 => 11100001 => 00011101 => 10100110
10001000 => 00010001 => 00100001 => 10100000
10001001 => 10010001 => 00101001 => 11100000
10001010 => 01010001 => 00110001 => 10100100
10001011 => 11010001 => 00111001 => 11001010
10001100 => 00110001 => 00100101 => 11100000
10001101 => 10110001 => 00110101 => 11100010
10001110 => 01110001 => 00101101 => 11010100
10001111 => 11110001 => 00111101 => 11001110
10010000 => 00001001 => 01000001 => 10001000
10010001 => 10001001 => 01001001 => 11100000
10010010 => 01001001 => 01010001 => 10110000
10010011 => 11001001 => 01011001 => 10111000
10010100 => 00101001 => 01100001 => 10001100
10010101 => 10101001 => 01110001 => 10011010
10010110 => 01101001 => 01101001 => 11010100
10010111 => 11101001 => 01111001 => 10110110
10011000 => 00011001 => 01000101 => 10110000
10011001 => 10011001 => 01010101 => 11110000
10011010 => 01011001 => 01100101 => 10111000
10011011 => 11011001 => 01110101 => 11110010
10011100 => 00111001 => 01001101 => 11100010
10011101 => 10111001 => 01101101 => 11111000
10011110 => 01111001 => 01011101 => 11110010
10011111 => 11111001 => 01111101 => 11101110
10100000 => 00000101 => 10000001 => 10000010
10100001 => 10000101 => 10001001 => 10100100
10100010 => 01000101 => 10010001 => 11000010
10100011 => 11000101 => 10011001 => 11001100
10100100 => 00100101 => 10100001 => 10010010
10100101 => 10100101 => 10110001 => 10101100
10100110 => 01100101 => 10101001 => 11100010
10100111 => 11100101 => 10111001 => 10111100
10101000 => 00010101 => 11000001 => 10000110
10101001 => 10010101 => 11010001 => 10100110
10101010 => 01010101 => 11100001 => 10001110
10101011 => 11010101 => 11110001 => 10011110
10101100 => 00110101 => 11001001 => 11001010
10101101 => 10110101 => 11101001 => 11001110
10101110 => 01110101 => 11011001 => 11011010
10101111 => 11110101 => 11111001 => 10111110
10110000 => 00001101 => 10000101 => 10001100
10110001 => 10001101 => 10010101 => 10111000
10110010 => 01001101 => 10100101 => 11010100
10110011 => 11001101 => 10110101 => 11111000
10110100 => 00101101 => 11000101 => 10011010
10110101 => 10101101 => 11100101 => 10110110
10110110 => 01101101 => 11010101 => 11110010
10110111 => 11101101 => 11110101 => 11101110
10111000 => 00011101 => 10001101 => 10101100
10111001 => 10011101 => 10101101 => 11111000
10111010 => 01011101 => 11001101 => 10111100
10111011 => 11011101 => 11101101 => 11111010
10111100 => 00111101 => 10011101 => 11011010
10111101 => 10111101 => 11011101 => 11111100
10111110 => 01111101 => 10111101 => 11111010
10111111 => 11111101 => 11111101 => 11111110
11000000 => 00000011 => 00000011 => 10000010
11000001 => 10000011 => 00001011 => 10001100
11000010 => 01000011 => 00010011 => 10100100
11000011 => 11000011 => 00011011 => 10101100
11000100 => 00100011 => 00100011 => 11000010
11000101 => 10100011 => 00110011 => 11001100
11000110 => 01100011 => 00101011 => 10111000
11000111 => 11100011 => 00111011 => 11011010
11001000 => 00010011 => 01000011 => 10010010
11001001 => 10010011 => 01010011 => 11100010
11001010 => 01010011 => 01100011 => 10101100
11001011 => 11010011 => 01110011 => 10111100
11001100 => 00110011 => 01001011 => 11010100
11001101 => 10110011 => 01101011 => 11111000
11001110 => 01110011 => 01011011 => 11111000
11001111 => 11110011 => 01111011 => 11111010
11010000 => 00001011 => 10000011 => 10000110
11010001 => 10001011 => 10010011 => 11001010
11010010 => 01001011 => 10100011 => 10100110
11010011 => 11001011 => 10110011 => 11011010
11010100 => 00101011 => 11000011 => 10001110
11010101 => 10101011 => 11100011 => 10011110
11010110 => 01101011 => 11010011 => 11001110
11010111 => 11101011 => 11110011 => 10111110
11011000 => 00011011 => 10001011 => 10011010
11011001 => 10011011 => 10101011 => 11110010
11011010 => 01011011 => 11001011 => 10110110
11011011 => 11011011 => 11101011 => 11101110
11011100 => 00111011 => 10011011 => 10111100
11011101 => 10111011 => 11011011 => 11111010
11011110 => 01111011 => 10111011 => 11111100
11011111 => 11111011 => 11111011 => 11111110
11100000 => 00000111 => 00000111 => 10000110
11100001 => 10000111 => 00010111 => 10011010
11100010 => 01000111 => 00100111 => 11001010
11100011 => 11000111 => 00110111 => 10111100
11100100 => 00100111 => 01000111 => 10100110
11100101 => 10100111 => 01100111 => 11011010
11100110 => 01100111 => 01010111 => 11110010
11100111 => 11100111 => 01110111 => 11111100
11101000 => 00010111 => 10000111 => 10001110
11101001 => 10010111 => 10100111 => 11001110
11101010 => 01010111 => 11000111 => 10011110
11101011 => 11010111 => 11100111 => 10111110
11101100 => 00110111 => 10010111 => 10110110
11101101 => 10110111 => 11010111 => 11101110
11101110 => 01110111 => 10110111 => 11111010
11101111 => 11110111 => 11110111 => 11111110
11110000 => 00001111 => 00001111 => 10001110
11110001 => 10001111 => 00101111 => 10110110
11110010 => 01001111 => 01001111 => 11001110
11110011 => 11001111 => 01101111 => 11111010
11110100 => 00101111 => 10001111 => 10011110
11110101 => 10101111 => 11001111 => 10111110
11110110 => 01101111 => 10101111 => 11101110
11110111 => 11101111 => 11101111 => 11111110
11111000 => 00011111 => 00011111 => 10011110
11111001 => 10011111 => 01011111 => 11101110
11111010 => 01011111 => 10011111 => 10111110
11111011 => 11011111 => 11011111 => 11111110
11111100 => 00111111 => 00111111 => 10111110
11111101 => 10111111 => 10111111 => 11111110
11111110 => 01111111 => 01111111 => 11111110
11111111 => 11111111 => 11111111 => 11111111
000000000 => 000000000 => 000000000 => 000000000
000000001 => 100000000 => 000000010 => 100000000
000000010 => 010000000 => 000000100 => 100000000
000000011 => 110000000 => 000000110 => 100000010
000000100 => 001000000 => 000001000 => 100000000
000000101 => 101000000 => 000001100 => 100000010
000000110 => 011000000 => 000001010 => 100001000
000000111 => 111000000 => 000001110 => 100000110
000001000 => 000100000 => 000010000 => 100000000
000001001 => 100100000 => 000010100 => 100001000
000001010 => 010100000 => 000011000 => 100000010
000001011 => 110100000 => 000011100 => 100000110
000001100 => 001100000 => 000010010 => 100100000
000001101 => 101100000 => 000011010 => 100010010
000001110 => 011100000 => 000010110 => 100001100
000001111 => 111100000 => 000011110 => 100001110
000010000 => 000010000 => 000100000 => 100000000
000010001 => 100010000 => 000100100 => 100100000
000010010 => 010010000 => 000101000 => 100001000
000010011 => 110010000 => 000101100 => 100001100
000010100 => 001010000 => 000110000 => 100000010
000010101 => 101010000 => 000111000 => 100000110
000010110 => 011010000 => 000110100 => 100010010
000010111 => 111010000 => 000111100 => 100001110
000011000 => 000110000 => 000100010 => 110000000
000011001 => 100110000 => 000101010 => 100110000
000011010 => 010110000 => 000110010 => 101000010
000011011 => 110110000 => 000111010 => 100100110
000011100 => 001110000 => 000100110 => 100100100
000011101 => 101110000 => 000110110 => 100101100
000011110 => 011110000 => 000101110 => 100011010
000011111 => 111110000 => 000111110 => 100011110
000100000 => 000001000 => 001000000 => 100000000
000100001 => 100001000 => 001000100 => 110000000
000100010 => 010001000 => 001001000 => 100100000
000100011 => 110001000 => 001001100 => 100100100
000100100 => 001001000 => 001010000 => 100001000
000100101 => 101001000 => 001011000 => 100001100
000100110 => 011001000 => 001010100 => 100110000
000100111 => 111001000 => 001011100 => 100011010
000101000 => 000101000 => 001100000 => 100000010
000101001 => 100101000 => 001101000 => 100010010
000101010 => 010101000 => 001110000 => 100000110
000101011 => 110101000 => 001111000 => 100001110
000101100 => 001101000 => 001100100 => 101000010
000101101 => 101101000 => 001110100 => 100100110
000101110 => 011101000 => 001101100 => 100101100
000101111 => 111101000 => 001111100 => 100011110
000110000 => 000011000 => 001000010 => 110000000
000110001 => 100011000 => 001001010 => 101100000
000110010 => 010011000 => 001010010 => 110010000
000110011 => 110011000 => 001011010 => 101010100
000110100 => 001011000 => 001100010 => 110000100
000110101 => 101011000 => 001110010 => 110000110
000110110 => 011011000 => 001101010 => 101100010
000110111 => 111011000 => 001111010 => 101001110
000111000 => 000111000 => 001000110 => 110000100
000111001 => 100111000 => 001010110 => 100111000
000111010 => 010111000 => 001100110 => 110001100
000111011 => 110111000 => 001110110 => 101011010
000111100 => 001111000 => 001001110 => 101001010
000111101 => 101111000 => 001101110 => 100111100
000111110 => 011111000 => 001011110 => 100110110
000111111 => 111111000 => 001111110 => 100111110
001000000 => 000000100 => 010000000 => 100000000
001000001 => 100000100 => 010000100 => 110000000
001000010 => 010000100 => 010001000 => 110000000
001000011 => 110000100 => 010001100 => 110000100
001000100 => 001000100 => 010010000 => 100100000
001000101 => 101000100 => 010011000 => 100100100
001000110 => 011000100 => 010010100 => 101100000
001000111 => 111000100 => 010011100 => 101001010
001001000 => 000100100 => 010100000 => 100001000
001001001 => 100100100 => 010101000 => 100110000
001001010 => 010100100 => 010110000 => 100001100
001001011 => 110100100 => 010111000 => 100011010
001001100 => 001100100 => 010100100 => 110010000
001001101 => 101100100 => 010110100 => 101010100
001001110 => 011100100 => 010101100 => 100111000
001001111 => 111100100 => 010111100 => 100110110
001010000 => 000010100 => 011000000 => 100000010
001010001 => 100010100 => 011001000 => 101000010
001010010 => 010010100 => 011010000 => 100010010
001010011 => 110010100 => 011011000 => 100101100
001010100 => 001010100 => 011100000 => 100000110
001010101 => 101010100 => 011110000 => 100001110
001010110 => 011010100 => 011101000 => 100100110
001010111 => 111010100 => 011111000 => 100011110
001011000 => 000110100 => 011000100 => 110000100
001011001 => 100110100 => 011010100 => 101100010
001011010 => 010110100 => 011100100 => 110000110
001011011 => 110110100 => 011110100 => 101001110
001011100 => 001110100 => 011001100 => 110001100
001011101 => 101110100 => 011101100 => 101011010
001011110 => 011110100 => 011011100 => 100111100
001011111 => 111110100 => 011111100 => 100111110
001100000 => 000001100 => 010000010 => 100100000
001100001 => 100001100 => 010001010 => 110010000
001100010 => 010001100 => 010010010 => 111000000
001100011 => 110001100 => 010011010 => 111000010
001100100 => 001001100 => 010100010 => 101100000
001100101 => 101001100 => 010110010 => 110011000
001100110 => 011001100 => 010101010 => 111100000
001100111 => 111001100 => 010111010 => 110101010
001101000 => 000101100 => 011000010 => 100100100
001101001 => 100101100 => 011010010 => 111000010
001101010 => 010101100 => 011100010 => 101001010
001101011 => 110101100 => 011110010 => 110010110
001101100 => 001101100 => 011001010 => 111001000
001101101 => 101101100 => 011101010 => 111000110
001101110 => 011101100 => 011011010 => 111001100
001101111 => 111101100 => 011111010 => 110011110
001110000 => 000011100 => 010000110 => 101000010
001110001 => 100011100 => 010010110 => 110011000
001110010 => 010011100 => 010100110 => 111001000
001110011 => 110011100 => 010110110 => 101111000
001110100 => 001011100 => 011000110 => 110001100
001110101 => 101011100 => 011100110 => 110011100
001110110 => 011011100 => 011010110 => 111011000
001110111 => 111011100 => 011110110 => 110110110
001111000 => 000111100 => 010001110 => 110000110
001111001 => 100111100 => 010101110 => 101110010
001111010 => 010111100 => 011001110 => 110011100
001111011 => 110111100 => 011101110 => 110111100
001111100 => 001111100 => 010011110 => 110010110
001111101 => 101111100 => 011011110 => 101111010
001111110 => 011111100 => 010111110 => 101101110
001111111 => 111111100 => 011111110 => 101111110
010000000 => 000000010 => 100000000 => 100000000
010000001 => 100000010 => 100000100 => 100100000
010000010 => 010000010 => 100001000 => 110000000
010000011 => 110000010 => 100001100 => 101000010
010000100 => 001000010 => 100010000 => 110000000
010000101 => 101000010 => 100011000 => 110000100
010000110 => 011000010 => 100010100 => 110010000
010000111 => 111000010 => 100011100 => 110000110
010001000 => 000100010 => 100100000 => 100100000
010001001 => 100100010 => 100101000 => 101100000
010001010 => 010100010 => 100110000 => 100100100
010001011 => 110100010 => 100111000 => 101001010
010001100 => 001100010 => 100100100 => 111000000
010001101 => 101100010 => 100110100 => 111000010
010001110 => 011100010 => 100101100 => 110011000
010001111 => 111100010 => 100111100 => 110010110
010010000 => 000010010 => 101000000 => 100001000
010010001 => 100010010 => 101001000 => 110010000
010010010 => 010010010 => 101010000 => 100110000
010010011 => 110010010 => 101011000 => 100111000
010010100 => 001010010 => 101100000 => 100001100
010010101 => 101010010 => 101110000 => 100011010
010010110 => 011010010 => 101101000 => 101010100
010010111 => 111010010 => 101111000 => 100110110
010011000 => 000110010 => 101000100 => 101100000
010011001 => 100110010 => 101010100 => 111100000
010011010 => 010110010 => 101100100 => 110011000
010011011 => 110110010 => 101110100 => 110101010
010011100 => 001110010 => 101001100 => 111001000
010011101 => 101110010 => 101101100 => 101111000
010011110 => 011110010 => 101011100 => 101110010
010011111 => 111110010 => 101111100 => 101101110
010100000 => 000001010 => 110000000 => 100000010
010100001 => 100001010 => 110001000 => 110000100
010100010 => 010001010 => 110010000 => 101000010
010100011 => 110001010 => 110011000 => 110001100
010100100 => 001001010 => 110100000 => 100010010
010100101 => 101001010 => 110110000 => 100101100
010100110 => 011001010 => 110101000 => 101100010
010100111 => 111001010 => 110111000 => 100111100
010101000 => 000101010 => 111000000 => 100000110
010101001 => 100101010 => 111010000 => 100100110
010101010 => 010101010 => 111100000 => 100001110
010101011 => 110101010 => 111110000 => 100011110
010101100 => 001101010 => 111001000 => 110000110
010101101 => 101101010 => 111101000 => 101001110
010101110 => 011101010 => 111011000 => 101011010
010101111 => 111101010 => 111111000 => 100111110
010110000 => 000011010 => 110000100 => 100100100
010110001 => 100011010 => 110010100 => 111001000
010110010 => 010011010 => 110100100 => 111000010
010110011 => 110011010 => 110110100 => 111001100
010110100 => 001011010 => 111000100 => 101001010
010110101 => 101011010 => 111100100 => 110010110
010110110 => 011011010 => 111010100 => 111000110
010110111 => 111011010 => 111110100 => 110011110
010111000 => 000111010 => 110001100 => 110001100
010111001 => 100111010 => 110101100 => 111011000
010111010 => 010111010 => 111001100 => 110011100
010111011 => 110111010 => 111101100 => 110110110
010111100 => 001111010 => 110011100 => 110011100
010111101 => 101111010 => 111011100 => 110111100
010111110 => 011111010 => 110111100 => 101111010
010111111 => 111111010 => 111111100 => 101111110
011000000 => 000000110 => 100000010 => 100001000
011000001 => 100000110 => 100001010 => 100110000
011000010 => 010000110 => 100010010 => 101100000
011000011 => 110000110 => 100011010 => 101100010
011000100 => 001000110 => 100100010 => 110010000
011000101 => 101000110 => 100110010 => 111001000
011000110 => 011000110 => 100101010 => 111100000
011000111 => 111000110 => 100111010 => 111000110
011001000 => 000100110 => 101000010 => 100110000
011001001 => 100100110 => 101010010 => 111100000
011001010 => 010100110 => 101100010 => 100111000
011001011 => 110100110 => 101110010 => 101110010
011001100 => 001100110 => 101001010 => 111100000
011001101 => 101100110 => 101101010 => 111110000
011001110 => 011100110 => 101011010 => 111110000
011001111 => 111100110 => 101111010 => 111100110
011010000 => 000010110 => 110000010 => 100001100
011010001 => 100010110 => 110010010 => 110011000
011010010 => 010010110 => 110100010 => 101010100
011010011 => 110010110 => 110110010 => 101111000
011010100 => 001010110 => 111000010 => 100011010
011010101 => 101010110 => 111100010 => 100110110
011010110 => 011010110 => 111010010 => 110101010
011010111 => 111010110 => 111110010 => 101101110
011011000 => 000110110 => 110001010 => 100111000
011011001 => 100110110 => 110101010 => 111110000
011011010 => 010110110 => 111001010 => 101110010
011011011 => 110110110 => 111101010 => 111100110
011011100 => 001110110 => 110011010 => 111011000
011011101 => 101110110 => 111011010 => 111110010
011011110 => 011110110 => 110111010 => 111101100
011011111 => 111110110 => 111111010 => 111011110
011100000 => 000001110 => 100000110 => 100010010
011100001 => 100001110 => 100010110 => 101010100
011100010 => 010001110 => 100100110 => 111000010
011100011 => 110001110 => 100110110 => 111001100
011100100 => 001001110 => 101000110 => 101100010
011100101 => 101001110 => 101100110 => 111011000
011100110 => 011001110 => 101010110 => 111110000
011100111 => 111001110 => 101110110 => 111110010
011101000 => 000101110 => 110000110 => 100101100
011101001 => 100101110 => 110100110 => 111001100
011101010 => 010101110 => 111000110 => 100111100
011101011 => 110101110 => 111100110 => 101111010
011101100 => 001101110 => 110010110 => 101111000
011101101 => 101101110 => 111010110 => 111101100
011101110 => 011101110 => 110110110 => 111111000
011101111 => 111101110 => 111110110 => 111110110
011110000 => 000011110 => 100001110 => 100100110
011110001 => 100011110 => 100101110 => 110101010
011110010 => 010011110 => 101001110 => 111000110
011110011 => 110011110 => 101101110 => 111101100
011110100 => 001011110 => 110001110 => 101011010
011110101 => 101011110 => 111001110 => 110111100
011110110 => 011011110 => 110101110 => 111110010
011110111 => 111011110 => 111101110 => 111111100
011111000 => 000111110 => 100011110 => 101001110
011111001 => 100111110 => 101011110 => 111100110
011111010 => 010111110 => 110011110 => 110110110
011111011 => 110111110 => 111011110 => 111111100
011111100 => 001111110 => 100111110 => 110011110
011111101 => 101111110 => 110111110 => 111110110
011111110 => 011111110 => 101111110 => 111011110
011111111 => 111111110 => 111111110 => 111111110
100000000 => 000000001 => 000000001 => 100000000
100000001 => 100000001 => 000000101 => 100001000
100000010 => 010000001 => 000001001 => 100100000
100000011 => 110000001 => 000001101 => 100010010
100000100 => 001000001 => 000010001 => 110000000
100000101 => 101000001 => 000011001 => 101000010
100000110 => 011000001 => 000010101 => 100110000
100000111 => 111000001 => 000011101 => 100100110
100001000 => 000100001 => 000100001 => 110000000
100001001 => 100100001 => 000101001 => 110010000
100001010 => 010100001 => 000110001 => 110000100
100001011 => 110100001 => 000111001 => 110000110
100001100 => 001100001 => 000100101 => 101100000
100001101 => 101100001 => 000110101 => 101100010
100001110 => 011100001 => 000101101 => 101010100
100001111 => 111100001 => 000111101 => 101001110
100010000 => 000010001 => 001000001 => 100100000
100010001 => 100010001 => 001001001 => 111000000
100010010 => 010010001 => 001010001 => 101100000
100010011 => 110010001 => 001011001 => 110011000
100010100 => 001010001 => 001100001 => 100100100
100010101 => 101010001 => 001110001 => 101001010
100010110 => 011010001 => 001101001 => 111000010
100010111 => 111010001 => 001111001 => 110010110
100011000 => 000110001 => 001000101 => 110010000
100011001 => 100110001 => 001010101 => 111100000
100011010 => 010110001 => 001100101 => 111001000
100011011 => 110110001 => 001110101 => 111000110
100011100 => 001110001 => 001001101 => 111000010
100011101 => 101110001 => 001101101 => 111001100
100011110 => 011110001 => 001011101 => 110101010
100011111 => 111110001 => 001111101 => 110011110
100100000 => 000001001 => 010000001 => 100001000
100100001 => 100001001 => 010001001 => 101100000
100100010 => 010001001 => 010010001 => 110010000
100100011 => 110001001 => 010011001 => 111001000
100100100 => 001001001 => 010100001 => 100110000
100100101 => 101001001 => 010110001 => 100111000
100100110 => 011001001 => 010101001 => 111100000
100100111 => 111001001 => 010111001 => 101110010
100101000 => 000101001 => 011000001 => 100001100
100101001 => 100101001 => 011010001 => 101010100
100101010 => 010101001 => 011100001 => 100011010
100101011 => 110101001 => 011110001 => 100110110
100101100 => 001101001 => 011001001 => 110011000
100101101 => 101101001 => 011101001 => 110101010
100101110 => 011101001 => 011011001 => 101111000
100101111 => 111101001 => 011111001 => 101101110
100110000 => 000011001 => 010000101 => 100110000
100110001 => 100011001 => 010010101 => 111100000
100110010 => 010011001 => 010100101 => 111100000
100110011 => 110011001 => 010110101 => 111110000
100110100 => 001011001 => 011000101 => 100111000
100110101 => 101011001 => 011100101 => 101110010
100110110 => 011011001 => 011010101 => 111110000
100110111 => 111011001 => 011110101 => 111100110
100111000 => 000111001 => 010001101 => 101100010
100111001 => 100111001 => 010101101 => 111110000
100111010 => 010111001 => 011001101 => 111011000
100111011 => 110111001 => 011101101 => 111110010
100111100 => 001111001 => 010011101 => 111000110
100111101 => 101111001 => 011011101 => 111101100
100111110 => 011111001 => 010111101 => 111100110
100111111 => 111111001 => 011111101 => 111011110
101000000 => 000000101 => 100000001 => 100000010
101000001 => 100000101 => 100001001 => 100100100
101000010 => 010000101 => 100010001 => 110000100
101000011 => 110000101 => 100011001 => 110001100
101000100 => 001000101 => 100100001 => 101000010
101000101 => 101000101 => 100110001 => 110001100
101000110 => 011000101 => 100101001 => 111001000
101000111 => 111000101 => 100111001 => 110011100
101001000 => 000100101 => 101000001 => 100010010
101001001 => 100100101 => 101010001 => 101100010
101001010 => 010100101 => 101100001 => 100101100
101001011 => 110100101 => 101110001 => 100111100
101001100 => 001100101 => 101001001 => 111000010
101001101 => 101100101 => 101101001 => 111001100
101001110 => 011100101 => 101011001 => 111011000
101001111 => 111100101 => 101111001 => 101111010
101010000 => 000010101 => 110000001 => 100000110
101010001 => 100010101 => 110010001 => 110000110
101010010 => 010010101 => 110100001 => 100100110
101010011 => 110010101 => 110110001 => 101011010
101010100 => 001010101 => 111000001 => 100001110
101010101 => 101010101 => 111100001 => 100011110
101010110 => 011010101 => 111010001 => 101001110
101010111 => 111010101 => 111110001 => 100111110
101011000 => 000110101 => 110001001 => 101001010
101011001 => 100110101 => 110101001 => 111000110
101011010 => 010110101 => 111001001 => 110010110
101011011 => 110110101 => 111101001 => 110011110
101011100 => 001110101 => 110011001 => 110011100
101011101 => 101110101 => 111011001 => 110110110
101011110 => 011110101 => 110111001 => 110111100
101011111 => 111110101 => 111111001 => 101111110
101100000 => 000001101 => 100000101 => 100001100
101100001 => 100001101 => 100010101 => 100111000
101100010 => 010001101 => 100100101 => 110011000
101100011 => 110001101 => 100110101 => 111011000
101100100 => 001001101 => 101000101 => 101010100
101100101 => 101001101 => 101100101 => 101111000
101100110 => 011001101 => 101010101 => 111110000
101100111 => 111001101 => 101110101 => 111101100
101101000 => 000101101 => 110000101 => 100011010
101101001 => 100101101 => 110100101 => 110101010
101101010 => 010101101 => 111000101 => 100110110
101101011 => 110101101 => 111100101 => 101101110
101101100 => 001101101 => 110010101 => 101110010
101101101 => 101101101 => 111010101 => 111100110
101101110 => 011101101 => 110110101 => 111110010
101101111 => 111101101 => 111110101 => 111011110
101110000 => 000011101 => 100001101 => 100101100
101110001 => 100011101 => 100101101 => 101111000
101110010 => 010011101 => 101001101 => 111001100
101110011 => 110011101 => 101101101 => 111111000
101110100 => 001011101 => 110001101 => 100111100
101110101 => 101011101 => 111001101 => 101111010
101110110 => 011011101 => 110101101 => 111101100
101110111 => 111011101 => 111101101 => 111110110
101111000 => 000111101 => 100011101 => 101011010
101111001 => 100111101 => 101011101 => 111110010
101111010 => 010111101 => 110011101 => 110111100
101111011 => 110111101 => 111011101 => 111111100
101111100 => 001111101 => 100111101 => 110110110
101111101 => 101111101 => 110111101 => 111111100
101111110 => 011111101 => 101111101 => 111110110
101111111 => 111111101 => 111111101 => 111111110
110000000 => 000000011 => 000000011 => 100000010
110000001 => 100000011 => 000001011 => 100001100
110000010 => 010000011 => 000010011 => 100100100
110000011 => 110000011 => 000011011 => 100101100
110000100 => 001000011 => 000100011 => 110000100
110000101 => 101000011 => 000110011 => 110001100
110000110 => 011000011 => 000101011 => 100111000
110000111 => 111000011 => 000111011 => 101011010
110001000 => 000100011 => 001000011 => 101000010
110001001 => 100100011 => 001010011 => 111001000
110001010 => 010100011 => 001100011 => 110001100
110001011 => 110100011 => 001110011 => 110011100
110001100 => 001100011 => 001001011 => 110011000
110001101 => 101100011 => 001101011 => 111011000
110001110 => 011100011 => 001011011 => 101111000
110001111 => 111100011 => 001111011 => 110110110
110010000 => 000010011 => 010000011 => 100010010
110010001 => 100010011 => 010010011 => 111000010
110010010 => 010010011 => 010100011 => 101100010
110010011 => 110010011 => 010110011 => 111011000
110010100 => 001010011 => 011000011 => 100101100
110010101 => 101010011 => 011100011 => 100111100
110010110 => 011010011 => 011010011 => 111001100
110010111 => 111010011 => 011110011 => 101111010
110011000 => 000110011 => 010001011 => 101010100
110011001 => 100110011 => 010101011 => 111110000
110011010 => 010110011 => 011001011 => 101111000
110011011 => 110110011 => 011101011 => 111101100
110011100 => 001110011 => 010011011 => 111001100
110011101 => 101110011 => 011011011 => 111111000
110011110 => 011110011 => 010111011 => 111110010
110011111 => 111110011 => 011111011 => 111110110
110100000 => 000001011 => 100000011 => 100000110
110100001 => 100001011 => 100010011 => 101001010
110100010 => 010001011 => 100100011 => 110000110
110100011 => 110001011 => 100110011 => 110011100
110100100 => 001001011 => 101000011 => 100100110
110100101 => 101001011 => 101100011 => 101011010
110100110 => 011001011 => 101010011 => 111000110
110100111 => 111001011 => 101110011 => 110111100
110101000 => 000101011 => 110000011 => 100001110
110101001 => 100101011 => 110100011 => 101001110
110101010 => 010101011 => 111000011 => 100011110
110101011 => 110101011 => 111100011 => 100111110
110101100 => 001101011 => 110010011 => 110010110
110101101 => 101101011 => 111010011 => 110011110
110101110 => 011101011 => 110110011 => 110110110
110101111 => 111101011 => 111110011 => 101111110
110110000 => 000011011 => 100001011 => 100011010
110110001 => 100011011 => 100101011 => 101110010
110110010 => 010011011 => 101001011 => 110101010
110110011 => 110011011 => 101101011 => 111110010
110110100 => 001011011 => 110001011 => 100110110
110110101 => 101011011 => 111001011 => 101101110
110110110 => 011011011 => 110101011 => 111100110
110110111 => 111011011 => 111101011 => 111011110
110111000 => 000111011 => 100011011 => 100111100
110111001 => 100111011 => 101011011 => 111101100
110111010 => 010111011 => 110011011 => 101111010
110111011 => 110111011 => 111011011 => 111110110
110111100 => 001111011 => 100111011 => 110111100
110111101 => 101111011 => 110111011 => 111111100
110111110 => 011111011 => 101111011 => 111111100
110111111 => 111111011 => 111111011 => 111111110
111000000 => 000000111 => 000000111 => 100000110
111000001 => 100000111 => 000010111 => 100011010
111000010 => 010000111 => 000100111 => 101001010
111000011 => 110000111 => 000110111 => 100111100
111000100 => 001000111 => 001000111 => 110000110
111000101 => 101000111 => 001100111 => 110011100
111000110 => 011000111 => 001010111 => 101110010
111000111 => 111000111 => 001110111 => 110111100
111001000 => 000100111 => 010000111 => 100100110
111001001 => 100100111 => 010100111 => 111000110
111001010 => 010100111 => 011000111 => 101011010
111001011 => 110100111 => 011100111 => 110111100
111001100 => 001100111 => 010010111 => 110101010
111001101 => 101100111 => 011010111 => 111110010
111001110 => 011100111 => 010110111 => 111101100
111001111 => 111100111 => 011110111 => 111111100
111010000 => 000010111 => 100000111 => 100001110
111010001 => 100010111 => 100100111 => 110010110
111010010 => 010010111 => 101000111 => 101001110
111010011 => 110010111 => 101100111 => 110110110
111010100 => 001010111 => 110000111 => 100011110
111010101 => 101010111 => 111000111 => 100111110
111010110 => 011010111 => 110100111 => 110011110
111010111 => 111010111 => 111100111 => 101111110
111011000 => 000110111 => 100010111 => 100110110
111011001 => 100110111 => 101010111 => 111100110
111011010 => 010110111 => 110010111 => 101101110
111011011 => 110110111 => 111010111 => 111011110
111011100 => 001110111 => 100110111 => 101111010
111011101 => 101110111 => 110110111 => 111110110
111011110 => 011110111 => 101110111 => 111111100
111011111 => 111110111 => 111110111 => 111111110
111100000 => 000001111 => 000001111 => 100001110
111100001 => 100001111 => 000101111 => 100110110
111100010 => 010001111 => 001001111 => 110010110
111100011 => 110001111 => 001101111 => 101111010
111100100 => 001001111 => 010001111 => 101001110
111100101 => 101001111 => 011001111 => 110110110
111100110 => 011001111 => 010101111 => 111100110
111100111 => 111001111 => 011101111 => 111111100
111101000 => 000101111 => 100001111 => 100011110
111101001 => 100101111 => 101001111 => 110011110
111101010 => 010101111 => 110001111 => 100111110
111101011 => 110101111 => 111001111 => 101111110
111101100 => 001101111 => 100101111 => 101101110
111101101 => 101101111 => 110101111 => 111011110
111101110 => 011101111 => 101101111 => 111110110
111101111 => 111101111 => 111101111 => 111111110
111110000 => 000011111 => 000011111 => 100011110
111110001 => 100011111 => 001011111 => 101101110
111110010 => 010011111 => 010011111 => 110011110
111110011 => 110011111 => 011011111 => 111110110
111110100 => 001011111 => 100011111 => 100111110
111110101 => 101011111 => 110011111 => 101111110
111110110 => 011011111 => 101011111 => 111011110
111110111 => 111011111 => 111011111 => 111111110
111111000 => 000111111 => 000111111 => 100111110
111111001 => 100111111 => 010111111 => 111011110
111111010 => 010111111 => 100111111 => 101111110
111111011 => 110111111 => 110111111 => 111111110
111111100 => 001111111 => 001111111 => 101111110
111111101 => 101111111 => 101111111 => 111111110
111111110 => 011111111 => 011111111 => 111111110
111111111 => 111111111 => 111111111 => 111111111
1100110010 => 0100110011 => 0101001011 => 1110100100
1100111000 => 0001110011 => 0100011011 => 1011001100
1101010010 => 0100101011 => 1101000011 => 1001001110
1101101000 => 0001011011 => 1100001011 => 1000110110
1110001010 => 0101000111 => 0011000111 => 1100011010
1110001100 => 0011000111 => 0010010111 => 1100110010
1110010010 => 0100100111 => 0101000111 => 1011000110
1110011000 => 0001100111 => 0100010111 => 1010101010
1111000010 => 0100001111 => 0001001111 => 1010010110
1111000100 => 0010001111 => 0010001111 => 1100001110
1111001000 => 0001001111 => 0100001111 => 1001001110
1111100000 => 0000011111 => 0000011111 => 1000011110
101010101010 => 010101010101 => 111110000001 => 100000111110
101010110010 => 010011010101 => 111010010001 => 110010001110
101010111000 => 000111010101 => 111000110001 => 110000111010
101011101000 => 000101110101 => 111000011001 => 100100111010
101100101010 => 010101001101 => 101110000101 => 100011101100
101100101100 => 001101001101 => 101100100101 => 110011101000
101100110010 => 010011001101 => 101010010101 => 111011001000
101100111000 => 000111001101 => 101000110101 => 101110011000
101101010010 => 010010101101 => 111010000101 => 100101010110
101101011000 => 000110101101 => 111000100101 => 101001100110
101110001010 => 010100011101 => 100110001101 => 110010111000
101110010100 => 001010011101 => 101100001101 => 100110111000
101110101000 => 000101011101 => 111000001101 => 100001111010
101111000010 => 010000111101 => 100010011101 => 101010101010
101111001000 => 000100111101 => 101000011101 => 100110011010
101111100000 => 000001111101 => 100000111101 => 100010110110
110011001100 => 001100110011 => 010100101011 => 111011001000
110011100010 => 010001110011 => 010010011011 => 111010001100
110011100100 => 001001110011 => 010100011011 => 101110001100
110011110000 => 000011110011 => 010000111011 => 100110011010
111000101100 => 001101000111 => 001100100111 => 111000110010
111000110010 => 010011000111 => 001010010111 => 111001100010
111000110100 => 001011000111 => 001100010111 => 101001110010
111000111000 => 000111000111 => 001000110111 => 110001011100
111001001100 => 001100100111 => 010100100111 => 111010000110
111001100010 => 010001100111 => 010010010111 => 111001001010
111001100100 => 001001100111 => 010100010111 => 101101001010
111001110000 => 000011100111 => 010000110111 => 100101011100
111010001010 => 010100010111 => 100110000111 => 101000110110
111010010100 => 001010010111 => 101100000111 => 100010110110
111010101000 => 000101010111 => 111000000111 => 100000111110
111011000010 => 010000110111 => 100010010111 => 101001100110
111011001000 => 000100110111 => 101000010111 => 100101010110
111011100000 => 000001110111 => 100000110111 => 100001111010
111100001010 => 010100001111 => 000110001111 => 110000111010
111100001100 => 001100001111 => 000100101111 => 101001100110
111100010010 => 010010001111 => 001010001111 => 110100010110
111100010100 => 001010001111 => 001100001111 => 101000110110
111100011000 => 000110001111 => 001000101111 => 110001010110
111100100010 => 010001001111 => 010010001111 => 110010001110
111100100100 => 001001001111 => 010100001111 => 100110001110
111100110000 => 000011001111 => 010000101111 => 100101010110
111110000010 => 010000011111 => 000010011111 => 100100101110
111110000100 => 001000011111 => 000100011111 => 110000101110
111110001000 => 000100011111 => 001000011111 => 101000011110
111110010000 => 000010011111 => 010000011111 => 100010011110
111110100000 => 000001011111 => 100000011111 => 100000111110
111111000000 => 000000111111 => 000000111111 => 100000111110
1111111111 => 1111111111 => 1111111111 => 1111111111
1111111110 => 0111111111 => 0111111111 => 1111111110
1111111010 => 0101111111 => 1001111111 => 1011111110
1111101110 => 0111011111 => 1011011111 => 1111101110
1111101101 => 1011011111 => 1101011111 => 1110111110
1111101011 => 1101011111 => 1110011111 => 1011111110
1111101000 => 0001011111 => 1000011111 => 1000111110
1111000001 => 1000001111 => 0000101111 => 1000110110
1110111110 => 0111110111 => 1011110111 => 1111111100
1110111011 => 1101110111 => 1110110111 => 1111101110
1110111000 => 0001110111 => 1000110111 => 1001111010
1110110110 => 0110110111 => 1101010111 => 1111001110
1110110010 => 0100110111 => 1010010111 => 1101010110
1110101111 => 1111010111 => 1111100111 => 1011111110
1110101010 => 0101010111 => 1110000111 => 1000111110
1110100101 => 1010010111 => 1011000111 => 1010110110
1110100011 => 1100010111 => 1001100111 => 1100111010
1110100000 => 0000010111 => 1000000111 => 1000001110
1110010001 => 1000100111 => 0100100111 => 1110000110
1110001001 => 1001000111 => 0010100111 => 1110010010
1110000110 => 0110000111 => 0001010111 => 1001110010
1110000101 => 1010000111 => 0001100111 => 1010011100
1110000011 => 1100000111 => 0000110111 => 1000111100
1101111101 => 1011111011 => 1101111011 => 1111111100
1101110110 => 0110111011 => 1101011011 => 1111011010
1101101111 => 1111011011 => 1111101011 => 1110111110
1101101100 => 0011011011 => 1100101011 => 1011100110
1101101001 => 1001011011 => 1101001011 => 1101010110
1101100110 => 0110011011 => 1010101011 => 1111100010
1101100001 => 1000011011 => 1000101011 => 1001110010
1101011001 => 1001101011 => 1101010011 => 1110001110
1100111111 => 1111110011 => 0111111011 => 1111101110
1100110001 => 1000110011 => 0100101011 => 1101101000
1100100110 => 0110010011 => 0101010011 => 1111000010
1100100011 => 1100010011 => 0100110011 => 1110001100
1100011010 => 0101100011 => 0011001011 => 1100111000
1100011001 => 1001100011 => 0010101011 => 1011110000
1100010110 => 0110100011 => 0011010011 => 1110001100
1100010011 => 1100100011 => 0010110011 => 1100111000
1100001110 => 0111000011 => 0001011011 => 1001111000
1100001101 => 1011000011 => 0001101011 => 1011011000
1100001011 => 1101000011 => 0001110011 => 1100011010
1100000111 => 1110000011 => 0000111011 => 1001011010
1011111110 => 0111111101 => 1011111101 => 1111101110
1011111011 => 1101111101 => 1110111101 => 1111111100
1011111000 => 0001111101 => 1000111101 => 1010110110
1011101111 => 1111011101 => 1111101101 => 1111101110
1011101010 => 0101011101 => 1110001101 => 1001111010
1011100101 => 1010011101 => 1011001101 => 1110111000
1011100011 => 1100011101 => 1001101101 => 1110111000
1011100000 => 0000011101 => 1000001101 => 1000101100
1011011001 => 1001101101 => 1101010101 => 1111100010
1011010110 => 0110101101 => 1110100101 => 1101010110
1011001110 => 0111001101 => 1010110101 => 1111110000
1011001011 => 1101001101 => 1011100101 => 1011101100
1010111111 => 1111110101 => 1111111001 => 1011111110
1010111010 => 0101110101 => 1110011001 => 1100111010
1010101110 => 0111010101 => 1110110001 => 1010110110
1010101011 => 1101010101 => 1111100001 => 1000111110
1010101000 => 0001010101 => 1110000001 => 1000001110
1010100110 => 0110010101 => 1101010001 => 1011000110
1010011101 => 1011100101 => 1011011001 => 1110111000
1010010111 => 1110100101 => 1011110001 => 1001111010
1010010100 => 0010100101 => 1011000001 => 1000101100
1010010001 => 1000100101 => 1010010001 => 1100100010
1010001111 => 1111000101 => 1001111001 => 1100111010
1010001010 => 0101000101 => 1001100001 => 1010001100
1010000101 => 1010000101 => 1000110001 => 1100001100
1010000000 => 0000000101 => 1000000001 => 1000000010
1001111111 => 1111111001 => 0111111101 => 1110111110
1001111000 => 0001111001 => 0100011101 => 1011000110
1001110010 => 0100111001 => 0101001101 => 1111000010
1001110001 => 1000111001 => 0100101101 => 1110100100
1001100110 => 0110011001 => 0101010101 => 1111100000
1001100011 => 1100011001 => 0100110101 => 1111000010
1001011111 => 1111101001 => 0111111001 => 1011011110
1001011011 => 1101101001 => 0111101001 => 1101010110
1001010111 => 1110101001 => 0111110001 => 1001101110
1001010110 => 0110101001 => 0111010001 => 1010101010
1001010101 => 1010101001 => 0111100001 => 1000110110
1001010010 => 0100101001 => 0110100001 => 1001010100
1001000000 => 0000001001 => 0100000001 => 1000001000
1000111100 => 0011110001 => 0010011101 => 1110000110
1000111010 => 0101110001 => 0011001101 => 1110001100
1000111001 => 1001110001 => 0010101101 => 1101101000
1000110110 => 0110110001 => 0011010101 => 1111000010
1000110011 => 1100110001 => 0010110101 => 1110100100
1000100000 => 0000010001 => 0010000001 => 1000100000
1000011110 => 0111100001 => 0001011101 => 1010101010
1000011101 => 1011100001 => 0001101101 => 1011001100
1000011011 => 1101100001 => 0001110101 => 1011000110
1000001111 => 1111000001 => 0000111101 => 1001001110
1000000000 => 0000000001 => 0000000001 => 1000000000
10000000000 => 00000000001 => 00000000001 => 10000000000
11111111110 => 01111111111 => 01111111111 => 11111111110
100000111110 => 011111000001 => 000010111101 => 100101010110
101111111110 => 011111111101 => 101111111101 => 111110111110
100001101110 => 011101100001 => 000110110101 => 101110001100
111011111110 => 011111110111 => 101111110111 => 111111111010
100001110110 => 011011100001 => 000110101101 => 101110011000
101010111110 => 011111010101 => 111011110001 => 101011111100
100011001110 => 011100110001 => 001010110101 => 111011001000
100001111010 => 010111100001 => 000110011101 => 101100011010
111110111110 => 011111011111 => 101111011111 => 111111111010
10010000000 => 00000001001 => 01000000001 => 10000001000
110000011110 => 011110000011 => 000010111011 => 100011110010
101000101110 => 011101000101 => 100110110001 => 101100111000
10010101010 => 01010101001 => 01111000001 => 10000110110
100001111100 => 001111100001 => 000100111101 => 101100001110
101101011110 => 011110101101 => 111011100101 => 101111011010
101011101110 => 011101110101 => 111011011001 => 111011100110
110000101110 => 011101000011 => 000110110011 => 110010111000
100110001110 => 011100011001 => 010010110101 => 111101000100
100011100110 => 011001110001 => 001010101101 => 110111010000
111111101110 => 011101111111 => 101101111111 => 111110111110
0111111111 => 1111111110 => 1111111110 => 1111111110
0111111101 => 1011111110 => 1101111110 => 1111101110
0111111001 => 1001111110 => 1010111110 => 1111001110
0111110001 => 1000111110 => 1001011110 => 1101010110
0111100001 => 1000011110 => 1000101110 => 1010101010
0111000001 => 1000001110 => 1000010110 => 1001010100
0110000001 => 1000000110 => 1000001010 => 1000110000
0100000001 => 1000000010 => 1000000100 => 1000100000
01111111111 => 11111111110 => 11111111110 => 11111111110
0101010101 => 1010101010 => 1111100000 => 1000011110
0101010011 => 1100101010 => 1110110000 => 1001011010
0101001101 => 1011001010 => 1101101000 => 1011001100
0101001011 => 1101001010 => 1101110000 => 1000111100
0101000111 => 1110001010 => 1100111000 => 1010011100
0100110101 => 1010110010 => 1011100100 => 1100110010
0100110011 => 1100110010 => 1010110100 => 1101101000
0100101101 => 1011010010 => 1011101000 => 1010101010
0100101011 => 1101010010 => 1011110000 => 1000110110
0100100111 => 1110010010 => 1010111000 => 1001110010
010101010101 => 101010101010 => 111111000000 => 100000111110
010101010011 => 110010101010 => 111101100000 => 100010110110
010101001101 => 101100101010 => 111011010000 => 100110011010
010101001011 => 110100101010 => 111011100000 => 100010111100
010101000111 => 111000101010 => 111001110000 => 101000111100
010100110101 => 101011001010 => 110111001000 => 110001011100
010100101101 => 101101001010 => 110111010000 => 100101011100
010100101011 => 110101001010 => 110111100000 => 100001111010
010100100111 => 111001001010 => 110101110000 => 100101110100
010100011101 => 101110001010 => 110011011000 => 101100111000
010100011011 => 110110001010 => 110011101000 => 101100011010
010100010111 => 111010001010 => 110011110000 => 100100111010
010011010101 => 101010110010 => 101111000100 => 101001100110
010011010011 => 110010110010 => 101101100100 => 110011101000
010011001101 => 101100110010 => 101011010100 => 111011001000
010011001011 => 110100110010 => 101011100100 => 110011100010
010010110101 => 101011010010 => 101111001000 => 110001010110
010010110011 => 110011010010 => 101101101000 => 101011011000
010010101101 => 101101010010 => 101111010000 => 100101010110
010010101011 => 110101010010 => 101111100000 => 100001101110
010010100111 => 111001010010 => 101101110000 => 100011101100
010010011101 => 101110010010 => 101011011000 => 100111101000
010010011011 => 110110010010 => 101011101000 => 101011010010
010010010111 => 111010010010 => 101011110000 => 100011100110
111111111111 => 111111111111 => 111111111111 => 111111111111
111110000001 => 100000011111 => 000001011111 => 100001101110
111110100101 => 101001011111 => 101100011111 => 101011011110
111001100001 => 100001100111 => 010001010111 => 101011010010
111000011001 => 100110000111 => 000101010111 => 100111100010
111000000111 => 111000000111 => 000001110111 => 100010111100
111000001101 => 101100000111 => 000011010111 => 100101110100
111000110001 => 100011000111 => 001001010111 => 110011100010
111000100101 => 101001000111 => 001011000111 => 110010110010
111011100101 => 101001110111 => 101100110111 => 110111101010
111010010111 => 111010010111 => 101111000111 => 101011111100
111010010001 => 100010010111 => 101001000111 => 110010001110
111010011101 => 101110010111 => 101101100111 => 111011100110
111010000101 => 101000010111 => 100011000111 => 110000111010
100111100001 => 100001111001 => 010001011101 => 101101001010
100110011001 => 100110011001 => 010101010101 => 111111000000
100110000111 => 111000011001 => 010001110101 => 101110000110
100110001101 => 101100011001 => 010011010101 => 111110000010
100001111001 => 100111100001 => 000101011101 => 101011010010
100001100111 => 111001100001 => 000101110101 => 101101001010
100001101101 => 101101100001 => 000111010101 => 101110000110
100000011111 => 111110000001 => 000001111101 => 100010011110
100000110111 => 111011000001 => 000011110101 => 100110001110
100000111101 => 101111000001 => 000011011101 => 100101011100
100011011001 => 100110110001 => 001101010101 => 111110000010
100011000111 => 111000110001 => 001001110101 => 111010000110
100011001101 => 101100110001 => 001011010101 => 111101000100
100011110001 => 100011110001 => 001001011101 => 111001001010
100011100101 => 101001110001 => 001011001101 => 111010011000
101100100101 => 101001001101 => 101011000101 => 101011110000
101111100101 => 101001111101 => 101100111101 => 111011100110
101110010111 => 111010011101 => 101111001101 => 101111110010
101110010001 => 100010011101 => 101001001101 => 111010001100
101110011101 => 101110011101 => 101101101101 => 111111110000
101110000101 => 101000011101 => 100011001101 => 101100111000
101001011111 => 111110100101 => 101111110001 => 100111101110
101001000111 => 111000100101 => 101001110001 => 101100101100
101001000001 => 100000100101 => 101000010001 => 101001000010
101001001101 => 101100100101 => 101011010001 => 101110011000
101001110111 => 111011100101 => 101111011001 => 110111101010
101001110001 => 100011100101 => 101001011001 => 111010011000
101001111101 => 101111100101 => 101101111001 => 101111110010
101000010111 => 111010000101 => 100011110001 => 110000111010
101000010001 => 100010000101 => 100010010001 => 111000001000
101000011101 => 101110000101 => 100011011001 => 110010111000
101000000101 => 101000000101 => 100000110001 => 101000001100
0110000000 => 0000000110 => 1000000010 => 1000001000
0111100000 => 0000011110 => 1000001110 => 1000100110
0111111000 => 0001111110 => 1000111110 => 1010011110
0111111110 => 0111111110 => 1011111110 => 1110111110
011001100110 => 011001100110 => 101010101010 => 111111000000
011001001110 => 011100100110 => 101010110010 => 101111100000
011001011010 => 010110100110 => 101110010010 => 110011100010
010010011110 => 011110010010 => 101010111000 => 100111100010
010011100110 => 011001110010 => 101010101100 => 101111100000
010011001110 => 011100110010 => 101010110100 => 110111010000
010011011010 => 010110110010 => 101110010100 => 111001100010
010110100110 => 011001011010 => 111010100100 => 111010000110
010110111000 => 000111011010 => 111000110100 => 101100101100
010110110010 => 010011011010 => 111010010100 => 111100001010
010110001110 => 011100011010 => 110010110100 => 111001101000
010110011010 => 010110011010 => 110110010100 => 111010100100
010111001010 => 010100111010 => 110110001100 => 101100111000
010100101110 => 011101001010 => 110110110000 => 100110111000
010100111010 => 010111001010 => 110110011000 => 110010111000
010101101010 => 010101101010 => 111110001000 => 110000101110
01111111110 => 01111111110 => 10111111110 => 11101111110
0100000000 => 0000000010 => 1000000000 => 1000000000
01000000000 => 00000000010 => 10000000000 => 10000000000
0101010110 => 0110101010 => 1111010000 => 1001001110
0101011001 => 1001101010 => 1110101000 => 1011000110
0101011010 => 0101101010 => 1111001000 => 1100001110
0101011100 => 0011101010 => 1110011000 => 1100011010
0101100101 => 1010011010 => 1101100100 => 1101010100
0101100110 => 0110011010 => 1101010100 => 1111000010
0101101001 => 1001011010 => 1110100100 => 1110000110
0101101010 => 0101011010 => 1111000100 => 1010010110
0101101100 => 0011011010 => 1110010100 => 1110010010
0101110001 => 1000111010 => 1100101100 => 1100111000
0101110010 => 0100111010 => 1101001100 => 1110001100
0101110100 => 0010111010 => 1110001100 => 1010011100
0110010101 => 1010100110 => 1011100010 => 1001110010
0110010110 => 0110100110 => 1011010010 => 1101101000
0110011001 => 1001100110 => 1010101010 => 1111100000
0110011010 => 0101100110 => 1011001010 => 1011110000
0110100101 => 1010010110 => 1101100010 => 1001111000
0110100110 => 0110010110 => 1101010010 => 1110100100
0110101001 => 1001010110 => 1110100010 => 1010101010
0110101010 => 0101010110 => 1111000010 => 1000110110
0110101100 => 0011010110 => 1110010010 => 1100110010
0110110001 => 1000110110 => 1100101010 => 1011110000
0110110010 => 0100110110 => 1101001010 => 1101101000
0110110100 => 0010110110 => 1110001010 => 1001110010
0111110000 => 0000111110 => 1000011110 => 1001001110
010101010110 => 011010101010 => 111110100000 => 100010011110
010101011001 => 100110101010 => 111101010000 => 100110001110
010101011010 => 010110101010 => 111110010000 => 101000011110
010101011100 => 001110101010 => 111100110000 => 101000110110
010101100101 => 101001101010 => 111011001000 => 110010011010
010101101001 => 100101101010 => 111101001000 => 110010001110
010101101100 => 001101101010 => 111100101000 => 110100010110
010101110001 => 100011101010 => 111001011000 => 110010110010
010101110010 => 010011101010 => 111010011000 => 110100101010
010101110100 => 001011101010 => 111100011000 => 110000111010
010101111000 => 000111101010 => 111000111000 => 110000111100
010110010101 => 101010011010 => 110111000100 => 101001101100
010110010110 => 011010011010 => 110110100100 => 111010001100
010110011001 => 100110011010 => 110101010100 => 111110000010
010110011100 => 001110011010 => 110100110100 => 111100001100
010110100101 => 101001011010 => 111011000100 => 101010101010
010110101001 => 100101011010 => 111101000100 => 101100001110
010110101010 => 010101011010 => 111110000100 => 100100101110
010110101100 => 001101011010 => 111100100100 => 111000100110
010110110001 => 100011011010 => 111001010100 => 111100100010
010110110100 => 001011011010 => 111100010100 => 101100100110
010111000101 => 101000111010 => 110011001100 => 111000111000
010111001001 => 100100111010 => 110101001100 => 111100010100
010111001100 => 001100111010 => 110100101100 => 111010011000
010111010001 => 100010111010 => 111001001100 => 111000101100
010111010010 => 010010111010 => 111010001100 => 101100011010
010111010100 => 001010111010 => 111100001100 => 100100111010
010111011000 => 000110111010 => 111000101100 => 101010110100
011001010101 => 101010100110 => 101111000010 => 100011100110
011001010110 => 011010100110 => 101110100010 => 101011010010
011001011001 => 100110100110 => 101101010010 => 111011001000
011001011100 => 001110100110 => 101100110010 => 110101110000
011001100101 => 101001100110 => 101011001010 => 101111100000
011001101001 => 100101100110 => 101101001010 => 110111010000
011001101100 => 001101100110 => 101100101010 => 101111100000
011010010101 => 101010010110 => 110111000010 => 100011101100
011010010110 => 011010010110 => 110110100010 => 101011011000
011010011001 => 100110010110 => 110101010010 => 111101000100
011010011010 => 010110010110 => 110110010010 => 110011101000
011010011100 => 001110010110 => 110100110010 => 111001101000
011010100101 => 101001010110 => 111011000010 => 100011110010
011010100110 => 011001010110 => 111010100010 => 101101001010
011010101001 => 100101010110 => 111101000010 => 100101010110
011010101010 => 010101010110 => 111110000010 => 100001101110
011010101100 => 001101010110 => 111100100010 => 110001010110
011010110001 => 100011010110 => 111001010010 => 111001100010
011010110010 => 010011010110 => 111010010010 => 111001001010
011010110100 => 001011010110 => 111100010010 => 101001100110
011010111000 => 000111010110 => 111000110010 => 110001110100
011011000101 => 101000110110 => 110011001010 => 110101110000
011011000110 => 011000110110 => 110010101010 => 101111100000
011011001001 => 100100110110 => 110101001010 => 111011001000
011011001010 => 010100110110 => 110110001010 => 100111101000
011011001100 => 001100110110 => 110100101010 => 110111010000
011011010001 => 100010110110 => 111001001010 => 110011100010
011011010010 => 010010110110 => 111010001010 => 101011010010
011011010100 => 001010110110 => 111100001010 => 100011100110
011011011000 => 000110110110 => 111000101010 => 100111100010
0100111010 => 0101110010 => 1011001100 => 1100111000
100111001100 => 001100111001 => 010100101101 => 111101000100
100011011100 => 001110110001 => 001100110101 => 111100010100
010011011100 => 001110110010 => 101100110100 => 111010011000
100111100100 => 001001111001 => 010100011101 => 101110000110
010011101010 => 010101110010 => 101110001100 => 110001110100
100011101100 => 001101110001 => 001100101101 => 111001101000
010011101100 => 001101110010 => 101100101100 => 110011110000
101001110100 => 001011100101 => 101100011001 => 101100111000
100111110000 => 000011111001 => 010000111101 => 100110001110
100011110100 => 001011110001 => 001100011101 => 110100101010
110001111000 => 000111100011 => 001000111011 => 110010011010
100011111000 => 000111110001 => 001000111101 => 110010001110
100111000101 => 101000111001 => 010011001101 => 111100010100
100111001001 => 100100111001 => 010101001101 => 111110000010
101001010101 => 101010100101 => 101111000001 => 100001111010
101010100101 => 101001010101 => 111011000001 => 100010110110
110001011001 => 100110100011 => 001101010011 => 111100010100
110001100101 => 101001100011 => 001011001011 => 110011110000
110001101001 => 100101100011 => 001101001011 => 111010011000
110001110001 => 100011100011 => 001001011011 => 110011101000
110010011001 => 100110010011 => 010101010011 => 111110000010
110011000101 => 101000110011 => 010011001011 => 111001101000
110011001001 => 100100110011 => 010101001011 => 111101000100
110011100001 => 100001110011 => 010001011011 => 101011011000
111000010101 => 101010000111 => 000111000111 => 110000111100
111000101001 => 100101000111 => 001101000111 => 110100011100
111001000101 => 101000100111 => 010011000111 => 110100101010
111001001001 => 100100100111 => 010101000111 => 101110000110
111100000101 => 101000001111 => 000011001111 => 100100111010
111100001001 => 100100001111 => 000101001111 => 101100100110
111100010001 => 100010001111 => 001001001111 => 111000100110
111100100001 => 100001001111 => 010001001111 => 101100001110
110011000011 => 110000110011 => 010001101011 => 101110011000
110000111100 => 001111000011 => 000100111011 => 101010101010
110000001111 => 111100000011 => 000001111011 => 100010110110
111001000011 => 110000100111 => 010001100111 => 101100011010
111010000011 => 110000010111 => 100001100111 => 100100111010
111000011100 => 001110000111 => 000100110111 => 101001101100
111100000011 => 110000001111 => 000001101111 => 100001111010
0110010011 => 1100100110 => 1010110010 => 1011110000
101100100011 => 110001001101 => 101001100101 => 111001101000
101001011010 => 010110100101 => 101110010001 => 110001011100
101000111010 => 010111000101 => 100110011001 => 111000111000
100011101001 => 100101110001 => 001101001101 => 111100001100
100001110101 => 101011100001 => 000111001101 => 110100011100
100011100011 => 110001110001 => 001001101101 => 111010001100
101001010011 => 110010100101 => 101101100001 => 100110111000
100001110011 => 110011100001 => 000101101101 => 101011011000
101000101011 => 110101000101 => 100111100001 => 100100111010
100000111011 => 110111000001 => 000011101101 => 100110011010
101000001111 => 111100000101 => 100001111001 => 101000110110
110000111001 => 100111000011 => 000101011011 => 100111101000
110000110101 => 101011000011 => 000111001011 => 110010110010
110010001101 => 101100010011 => 010011010011 => 111100001100
110000101101 => 101101000011 => 000111010011 => 110100101010
110000011101 => 101110000011 => 000011011011 => 100110111000
011010010011 => 110010010110 => 110101100010 => 101011110000
010110001011 => 110100011010 => 110011100100 => 111000101100
011010001011 => 110100010110 => 110011100010 => 101010110100
101110000011 => 110000011101 => 100001101101 => 100110111000
111000100011 => 110001000111 => 001001100111 => 111000101100
111000010011 => 110010000111 => 000101100111 => 101010110100
110000110011 => 110011000011 => 000101101011 => 101011110000
101100001011 => 110100001101 => 100011100101 => 110010110010
111000001011 => 110100000111 => 000011100111 => 101000111100
110000011011 => 110110000011 => 000011101011 => 100110110010
110010000111 => 111000010011 => 010001110011 => 110100011100
110000100111 => 111001000011 => 000101110011 => 101001110010
110000010111 => 111010000011 => 000011110011 => 101000110110
0100110110 => 0110110010 => 1011010100 => 1110100100
0101001110 => 0111001010 => 1101011000 => 1011011000
0100101110 => 0111010010 => 1011011000 => 1001111000
010010111010 => 010111010010 => 101110011000 => 101001110010
010011010110 => 011010110010 => 101110100100 => 111001001010
010100110110 => 011011001010 => 110110101000 => 101110001100
010010110110 => 011011010010 => 101110101000 => 101101001010
011010001110 => 011100010110 => 110010110010 => 110011110000
010101001110 => 011100101010 => 111010110000 => 100110110010
010010101110 => 011101010010 => 101110110000 => 100011110010
010100011110 => 011110001010 => 110010111000 => 110001110100
0111000000 => 0000001110 => 1000000110 => 1000010010
01110000000 => 00000001110 => 10000000110 => 10000010010
01111000000 => 00000011110 => 10000001110 => 10000100110
01111100000 => 00000111110 => 10000011110 => 10001001110
01111110000 => 00001111110 => 10000111110 => 10010011110
01111111000 => 00011111110 => 10001111110 => 10100111110
010100111100 => 001111001010 => 110100111000 => 101100101100
010010111100 => 001111010010 => 101100111000 => 101010110100
10010101000 => 00010101001 => 01110000001 => 10000011010
111000001110 => 011100000111 => 000010110111 => 100011101100
111000100110 => 011001000111 => 001010100111 => 111100100010
110010001110 => 011100010011 => 010010110011 => 111010011000
100110011100 => 001110011001 => 010100110101 => 111110000010
111000010110 => 011010000111 => 000110100111 => 101100101100
110000110110 => 011011000011 => 000110101011 => 101110110000
111000011010 => 010110000111 => 000110010111 => 110001110100
110010011100 => 001110010011 => 010100110011 => 111100010100
110001001101 => 101100100011 => 001011010011 => 111001101000
101000000000 => 000000000101 => 100000000001 => 100000000010
101000001010 => 010100000101 => 100001100001 => 110000001100
101000101000 => 000101000101 => 100110000001 => 100010001100
101010100000 => 000001010101 => 111000000001 => 100000001110
111011101010 => 010101110111 => 111000110111 => 100111101110
111011010110 => 011010110111 => 111010010111 => 110101011110
111010101110 => 011101010111 => 111011000111 => 101011011110
10011111111 => 11111111001 => 01111111101 => 11101111110
101011111111 => 111111110101 => 111111111001 => 101111111110
111010111111 => 111111010111 => 111111100111 => 101111111110
101110111111 => 111111011101 => 111111101101 => 111110111110
111110101111 => 111101011111 => 111110011111 => 101111111110
101010101111 => 111101010101 => 111111100001 => 100011111110
111011101111 => 111101110111 => 111110110111 => 111110111110
101111101111 => 111101111101 => 111110111101 => 111111111010
111111101011 => 110101111111 => 111001111111 => 101111111110
101011101011 => 110101110101 => 111110011001 => 110011101110
111010101011 => 110101010111 => 111110000111 => 100011111110
101110101011 => 110101011101 => 111110001101 => 100111101110
111110111011 => 110111011111 => 111011011111 => 111110111110
101010111011 => 110111010101 => 111110110001 => 101011011110
111011111011 => 110111110111 => 111011110111 => 111111111010
101111111011 => 110111111101 => 111011111101 => 111111111010
101101011011 => 110110101101 => 111110100101 => 110101011110
111111111010 => 010111111111 => 100111111111 => 101111111110
101011111010 => 010111110101 => 111001111001 => 110011111100
111010111010 => 010111010111 => 111001100111 => 110011101110
101110111010 => 010111011101 => 111001101101 => 101111110010
111110101010 => 010101011111 => 111000011111 => 100011111110
101111101010 => 010101111101 => 111000111101 => 101011111100
101110101110 => 011101011101 => 111011001101 => 110111101010
101111010110 => 011010111101 => 111010011101 => 110101111100
110011000110 => 011000110011 => 010010101011 => 110111010000
110001001110 => 011100100011 => 001010110011 => 110101110000
110001101100 => 001101100011 => 001100101011 => 110101110000
110001100110 => 011001100011 => 001010101011 => 101111100000
110001110010 => 010011100011 => 001010011011 => 111010100100
111001000110 => 011000100111 => 010010100111 => 111100001010
100111000011 => 110000111001 => 010001101101 => 101110001100
110001000111 => 111000100011 => 001001110011 => 111000110010
111100000110 => 011000001111 => 000010101111 => 100011100110
10010101011 => 11010101001 => 01111100001 => 10001101110
010110100011 => 110001011010 => 111001100100 => 111000110010
011001001011 => 110100100110 => 101011100010 => 100111100010
110001100011 => 110001100011 => 001001101011 => 110110101000
101001000100 => 001000100101 => 101001000001 => 100100100010
101000010100 => 001010000101 => 100011000001 => 101000001100
101001010000 => 000010100101 => 101100000001 => 100000101100
101001011100 => 001110100101 => 101100110001 => 110010111000
100111000110 => 011000111001 => 010010101101 => 111011001000
101100010110 => 011010001101 => 100110100101 => 111010011000
Map
reverse
Description
Return the reversal of a binary word.
Map
Foata bijection
Description
The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]).
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
For instance, to compute $\phi(4154223)$, the sequence of words is
  • 4,
  • |4|1 -- > 41,
  • |4|1|5 -- > 415,
  • |415|4 -- > 5414,
  • |5|4|14|2 -- > 54412,
  • |5441|2|2 -- > 154422,
  • |1|5442|2|3 -- > 1254423.
So $\phi(4154223) = 1254423$.
Map
Burrows-Wheeler
Description
The Burrows-Wheeler transform of a binary word.
The Burrows-Wheeler transform of a finite word $w$ is obtained from $w$ by first listing the conjugates of $w$ in lexicographic order and then concatenating the final letters of the conjugates in this order.