Identifier
Mp00278: Binary words rowmotionBinary words
Mp00104: Binary words reverseBinary words
Mp00096: Binary words Foata bijectionBinary words
Images
0 => 0 => 0 => 0
1 => 1 => 1 => 1
00 => 00 => 00 => 00
01 => 10 => 01 => 01
10 => 01 => 10 => 10
11 => 11 => 11 => 11
000 => 000 => 000 => 000
001 => 010 => 010 => 100
010 => 100 => 001 => 001
011 => 101 => 101 => 101
100 => 001 => 100 => 010
101 => 110 => 011 => 011
110 => 011 => 110 => 110
111 => 111 => 111 => 111
0000 => 0000 => 0000 => 0000
0001 => 0010 => 0100 => 0100
0010 => 0100 => 0010 => 1000
0011 => 0101 => 1010 => 1100
0100 => 1000 => 0001 => 0001
0101 => 1010 => 0101 => 1001
0110 => 1001 => 1001 => 0101
0111 => 1011 => 1101 => 1101
1000 => 0001 => 1000 => 0010
1001 => 0110 => 0110 => 1010
1010 => 1100 => 0011 => 0011
1011 => 1101 => 1011 => 1011
1100 => 0011 => 1100 => 0110
1101 => 1110 => 0111 => 0111
1110 => 0111 => 1110 => 1110
1111 => 1111 => 1111 => 1111
00000 => 00000 => 00000 => 00000
00001 => 00010 => 01000 => 00100
00010 => 00100 => 00100 => 01000
00011 => 00101 => 10100 => 01100
00100 => 01000 => 00010 => 10000
00101 => 01010 => 01010 => 11000
00110 => 01001 => 10010 => 10100
00111 => 01011 => 11010 => 11100
01000 => 10000 => 00001 => 00001
01001 => 10010 => 01001 => 01001
01010 => 10100 => 00101 => 10001
01011 => 10101 => 10101 => 11001
01100 => 10001 => 10001 => 00101
01101 => 10110 => 01101 => 10101
01110 => 10011 => 11001 => 01101
01111 => 10111 => 11101 => 11101
10000 => 00001 => 10000 => 00010
10001 => 00110 => 01100 => 01010
10010 => 01100 => 00110 => 10010
10011 => 01101 => 10110 => 11010
10100 => 11000 => 00011 => 00011
10101 => 11010 => 01011 => 10011
10110 => 11001 => 10011 => 01011
10111 => 11011 => 11011 => 11011
11000 => 00011 => 11000 => 00110
11001 => 01110 => 01110 => 10110
11010 => 11100 => 00111 => 00111
11011 => 11101 => 10111 => 10111
11100 => 00111 => 11100 => 01110
11101 => 11110 => 01111 => 01111
11110 => 01111 => 11110 => 11110
11111 => 11111 => 11111 => 11111
000000 => 000000 => 000000 => 000000
000001 => 000010 => 010000 => 000100
000010 => 000100 => 001000 => 001000
000011 => 000101 => 101000 => 001100
000100 => 001000 => 000100 => 010000
000101 => 001010 => 010100 => 011000
000110 => 001001 => 100100 => 010100
000111 => 001011 => 110100 => 011100
001000 => 010000 => 000010 => 100000
001001 => 010010 => 010010 => 101000
001010 => 010100 => 001010 => 110000
001011 => 010101 => 101010 => 111000
001100 => 010001 => 100010 => 100100
001101 => 010110 => 011010 => 110100
001110 => 010011 => 110010 => 101100
001111 => 010111 => 111010 => 111100
010000 => 100000 => 000001 => 000001
010001 => 100010 => 010001 => 001001
010010 => 100100 => 001001 => 010001
010011 => 100101 => 101001 => 011001
010100 => 101000 => 000101 => 100001
010101 => 101010 => 010101 => 110001
010110 => 101001 => 100101 => 101001
010111 => 101011 => 110101 => 111001
011000 => 100001 => 100001 => 000101
011001 => 100110 => 011001 => 010101
011010 => 101100 => 001101 => 100101
011011 => 101101 => 101101 => 110101
011100 => 100011 => 110001 => 001101
011101 => 101110 => 011101 => 101101
011110 => 100111 => 111001 => 011101
011111 => 101111 => 111101 => 111101
100000 => 000001 => 100000 => 000010
100001 => 000110 => 011000 => 001010
100010 => 001100 => 001100 => 010010
100011 => 001101 => 101100 => 011010
100100 => 011000 => 000110 => 100010
100101 => 011010 => 010110 => 110010
100110 => 011001 => 100110 => 101010
>>> Load all 2314 entries. <<<
100111 => 011011 => 110110 => 111010
101000 => 110000 => 000011 => 000011
101001 => 110010 => 010011 => 010011
101010 => 110100 => 001011 => 100011
101011 => 110101 => 101011 => 110011
101100 => 110001 => 100011 => 001011
101101 => 110110 => 011011 => 101011
101110 => 110011 => 110011 => 011011
101111 => 110111 => 111011 => 111011
110000 => 000011 => 110000 => 000110
110001 => 001110 => 011100 => 010110
110010 => 011100 => 001110 => 100110
110011 => 011101 => 101110 => 110110
110100 => 111000 => 000111 => 000111
110101 => 111010 => 010111 => 100111
110110 => 111001 => 100111 => 010111
110111 => 111011 => 110111 => 110111
111000 => 000111 => 111000 => 001110
111001 => 011110 => 011110 => 101110
111010 => 111100 => 001111 => 001111
111011 => 111101 => 101111 => 101111
111100 => 001111 => 111100 => 011110
111101 => 111110 => 011111 => 011111
111110 => 011111 => 111110 => 111110
111111 => 111111 => 111111 => 111111
0000000 => 0000000 => 0000000 => 0000000
0000001 => 0000010 => 0100000 => 0000100
0000010 => 0000100 => 0010000 => 0001000
0000011 => 0000101 => 1010000 => 0001100
0000100 => 0001000 => 0001000 => 0010000
0000101 => 0001010 => 0101000 => 0011000
0000110 => 0001001 => 1001000 => 0010100
0000111 => 0001011 => 1101000 => 0011100
0001000 => 0010000 => 0000100 => 0100000
0001001 => 0010010 => 0100100 => 0101000
0001010 => 0010100 => 0010100 => 0110000
0001011 => 0010101 => 1010100 => 0111000
0001100 => 0010001 => 1000100 => 0100100
0001101 => 0010110 => 0110100 => 0110100
0001110 => 0010011 => 1100100 => 0101100
0001111 => 0010111 => 1110100 => 0111100
0010000 => 0100000 => 0000010 => 1000000
0010001 => 0100010 => 0100010 => 1001000
0010010 => 0100100 => 0010010 => 1010000
0010011 => 0100101 => 1010010 => 1011000
0010100 => 0101000 => 0001010 => 1100000
0010101 => 0101010 => 0101010 => 1110000
0010110 => 0101001 => 1001010 => 1101000
0010111 => 0101011 => 1101010 => 1111000
0011000 => 0100001 => 1000010 => 1000100
0011001 => 0100110 => 0110010 => 1010100
0011010 => 0101100 => 0011010 => 1100100
0011011 => 0101101 => 1011010 => 1110100
0011100 => 0100011 => 1100010 => 1001100
0011101 => 0101110 => 0111010 => 1101100
0011110 => 0100111 => 1110010 => 1011100
0011111 => 0101111 => 1111010 => 1111100
0100000 => 1000000 => 0000001 => 0000001
0100001 => 1000010 => 0100001 => 0001001
0100010 => 1000100 => 0010001 => 0010001
0100011 => 1000101 => 1010001 => 0011001
0100100 => 1001000 => 0001001 => 0100001
0100101 => 1001010 => 0101001 => 0110001
0100110 => 1001001 => 1001001 => 0101001
0100111 => 1001011 => 1101001 => 0111001
0101000 => 1010000 => 0000101 => 1000001
0101001 => 1010010 => 0100101 => 1010001
0101010 => 1010100 => 0010101 => 1100001
0101011 => 1010101 => 1010101 => 1110001
0101100 => 1010001 => 1000101 => 1001001
0101101 => 1010110 => 0110101 => 1101001
0101110 => 1010011 => 1100101 => 1011001
0101111 => 1010111 => 1110101 => 1111001
0110000 => 1000001 => 1000001 => 0000101
0110001 => 1000110 => 0110001 => 0010101
0110010 => 1001100 => 0011001 => 0100101
0110011 => 1001101 => 1011001 => 0110101
0110100 => 1011000 => 0001101 => 1000101
0110101 => 1011010 => 0101101 => 1100101
0110110 => 1011001 => 1001101 => 1010101
0110111 => 1011011 => 1101101 => 1110101
0111000 => 1000011 => 1100001 => 0001101
0111001 => 1001110 => 0111001 => 0101101
0111010 => 1011100 => 0011101 => 1001101
0111011 => 1011101 => 1011101 => 1101101
0111100 => 1000111 => 1110001 => 0011101
0111101 => 1011110 => 0111101 => 1011101
0111110 => 1001111 => 1111001 => 0111101
0111111 => 1011111 => 1111101 => 1111101
1000000 => 0000001 => 1000000 => 0000010
1000001 => 0000110 => 0110000 => 0001010
1000010 => 0001100 => 0011000 => 0010010
1000011 => 0001101 => 1011000 => 0011010
1000100 => 0011000 => 0001100 => 0100010
1000101 => 0011010 => 0101100 => 0110010
1000110 => 0011001 => 1001100 => 0101010
1000111 => 0011011 => 1101100 => 0111010
1001000 => 0110000 => 0000110 => 1000010
1001001 => 0110010 => 0100110 => 1010010
1001010 => 0110100 => 0010110 => 1100010
1001011 => 0110101 => 1010110 => 1110010
1001100 => 0110001 => 1000110 => 1001010
1001101 => 0110110 => 0110110 => 1101010
1001110 => 0110011 => 1100110 => 1011010
1001111 => 0110111 => 1110110 => 1111010
1010000 => 1100000 => 0000011 => 0000011
1010001 => 1100010 => 0100011 => 0010011
1010010 => 1100100 => 0010011 => 0100011
1010011 => 1100101 => 1010011 => 0110011
1010100 => 1101000 => 0001011 => 1000011
1010101 => 1101010 => 0101011 => 1100011
1010110 => 1101001 => 1001011 => 1010011
1010111 => 1101011 => 1101011 => 1110011
1011000 => 1100001 => 1000011 => 0001011
1011001 => 1100110 => 0110011 => 0101011
1011010 => 1101100 => 0011011 => 1001011
1011011 => 1101101 => 1011011 => 1101011
1011100 => 1100011 => 1100011 => 0011011
1011101 => 1101110 => 0111011 => 1011011
1011110 => 1100111 => 1110011 => 0111011
1011111 => 1101111 => 1111011 => 1111011
1100000 => 0000011 => 1100000 => 0000110
1100001 => 0001110 => 0111000 => 0010110
1100010 => 0011100 => 0011100 => 0100110
1100011 => 0011101 => 1011100 => 0110110
1100100 => 0111000 => 0001110 => 1000110
1100101 => 0111010 => 0101110 => 1100110
1100110 => 0111001 => 1001110 => 1010110
1100111 => 0111011 => 1101110 => 1110110
1101000 => 1110000 => 0000111 => 0000111
1101001 => 1110010 => 0100111 => 0100111
1101010 => 1110100 => 0010111 => 1000111
1101011 => 1110101 => 1010111 => 1100111
1101100 => 1110001 => 1000111 => 0010111
1101101 => 1110110 => 0110111 => 1010111
1101110 => 1110011 => 1100111 => 0110111
1101111 => 1110111 => 1110111 => 1110111
1110000 => 0000111 => 1110000 => 0001110
1110001 => 0011110 => 0111100 => 0101110
1110010 => 0111100 => 0011110 => 1001110
1110011 => 0111101 => 1011110 => 1101110
1110100 => 1111000 => 0001111 => 0001111
1110101 => 1111010 => 0101111 => 1001111
1110110 => 1111001 => 1001111 => 0101111
1110111 => 1111011 => 1101111 => 1101111
1111000 => 0001111 => 1111000 => 0011110
1111001 => 0111110 => 0111110 => 1011110
1111010 => 1111100 => 0011111 => 0011111
1111011 => 1111101 => 1011111 => 1011111
1111100 => 0011111 => 1111100 => 0111110
1111101 => 1111110 => 0111111 => 0111111
1111110 => 0111111 => 1111110 => 1111110
1111111 => 1111111 => 1111111 => 1111111
00000000 => 00000000 => 00000000 => 00000000
00000001 => 00000010 => 01000000 => 00000100
00000010 => 00000100 => 00100000 => 00001000
00000011 => 00000101 => 10100000 => 00001100
00000100 => 00001000 => 00010000 => 00010000
00000101 => 00001010 => 01010000 => 00011000
00000110 => 00001001 => 10010000 => 00010100
00000111 => 00001011 => 11010000 => 00011100
00001000 => 00010000 => 00001000 => 00100000
00001001 => 00010010 => 01001000 => 00101000
00001010 => 00010100 => 00101000 => 00110000
00001011 => 00010101 => 10101000 => 00111000
00001100 => 00010001 => 10001000 => 00100100
00001101 => 00010110 => 01101000 => 00110100
00001110 => 00010011 => 11001000 => 00101100
00001111 => 00010111 => 11101000 => 00111100
00010000 => 00100000 => 00000100 => 01000000
00010001 => 00100010 => 01000100 => 01001000
00010010 => 00100100 => 00100100 => 01010000
00010011 => 00100101 => 10100100 => 01011000
00010100 => 00101000 => 00010100 => 01100000
00010101 => 00101010 => 01010100 => 01110000
00010110 => 00101001 => 10010100 => 01101000
00010111 => 00101011 => 11010100 => 01111000
00011000 => 00100001 => 10000100 => 01000100
00011001 => 00100110 => 01100100 => 01010100
00011010 => 00101100 => 00110100 => 01100100
00011011 => 00101101 => 10110100 => 01110100
00011100 => 00100011 => 11000100 => 01001100
00011101 => 00101110 => 01110100 => 01101100
00011110 => 00100111 => 11100100 => 01011100
00011111 => 00101111 => 11110100 => 01111100
00100000 => 01000000 => 00000010 => 10000000
00100001 => 01000010 => 01000010 => 10001000
00100010 => 01000100 => 00100010 => 10010000
00100011 => 01000101 => 10100010 => 10011000
00100100 => 01001000 => 00010010 => 10100000
00100101 => 01001010 => 01010010 => 10110000
00100110 => 01001001 => 10010010 => 10101000
00100111 => 01001011 => 11010010 => 10111000
00101000 => 01010000 => 00001010 => 11000000
00101001 => 01010010 => 01001010 => 11010000
00101010 => 01010100 => 00101010 => 11100000
00101011 => 01010101 => 10101010 => 11110000
00101100 => 01010001 => 10001010 => 11001000
00101101 => 01010110 => 01101010 => 11101000
00101110 => 01010011 => 11001010 => 11011000
00101111 => 01010111 => 11101010 => 11111000
00110000 => 01000001 => 10000010 => 10000100
00110001 => 01000110 => 01100010 => 10010100
00110010 => 01001100 => 00110010 => 10100100
00110011 => 01001101 => 10110010 => 10110100
00110100 => 01011000 => 00011010 => 11000100
00110101 => 01011010 => 01011010 => 11100100
00110110 => 01011001 => 10011010 => 11010100
00110111 => 01011011 => 11011010 => 11110100
00111000 => 01000011 => 11000010 => 10001100
00111001 => 01001110 => 01110010 => 10101100
00111010 => 01011100 => 00111010 => 11001100
00111011 => 01011101 => 10111010 => 11101100
00111100 => 01000111 => 11100010 => 10011100
00111101 => 01011110 => 01111010 => 11011100
00111110 => 01001111 => 11110010 => 10111100
00111111 => 01011111 => 11111010 => 11111100
01000000 => 10000000 => 00000001 => 00000001
01000001 => 10000010 => 01000001 => 00001001
01000010 => 10000100 => 00100001 => 00010001
01000011 => 10000101 => 10100001 => 00011001
01000100 => 10001000 => 00010001 => 00100001
01000101 => 10001010 => 01010001 => 00110001
01000110 => 10001001 => 10010001 => 00101001
01000111 => 10001011 => 11010001 => 00111001
01001000 => 10010000 => 00001001 => 01000001
01001001 => 10010010 => 01001001 => 01010001
01001010 => 10010100 => 00101001 => 01100001
01001011 => 10010101 => 10101001 => 01110001
01001100 => 10010001 => 10001001 => 01001001
01001101 => 10010110 => 01101001 => 01101001
01001110 => 10010011 => 11001001 => 01011001
01001111 => 10010111 => 11101001 => 01111001
01010000 => 10100000 => 00000101 => 10000001
01010001 => 10100010 => 01000101 => 10010001
01010010 => 10100100 => 00100101 => 10100001
01010011 => 10100101 => 10100101 => 10110001
01010100 => 10101000 => 00010101 => 11000001
01010101 => 10101010 => 01010101 => 11100001
01010110 => 10101001 => 10010101 => 11010001
01010111 => 10101011 => 11010101 => 11110001
01011000 => 10100001 => 10000101 => 10001001
01011001 => 10100110 => 01100101 => 10101001
01011010 => 10101100 => 00110101 => 11001001
01011011 => 10101101 => 10110101 => 11101001
01011100 => 10100011 => 11000101 => 10011001
01011101 => 10101110 => 01110101 => 11011001
01011110 => 10100111 => 11100101 => 10111001
01011111 => 10101111 => 11110101 => 11111001
01100000 => 10000001 => 10000001 => 00000101
01100001 => 10000110 => 01100001 => 00010101
01100010 => 10001100 => 00110001 => 00100101
01100011 => 10001101 => 10110001 => 00110101
01100100 => 10011000 => 00011001 => 01000101
01100101 => 10011010 => 01011001 => 01100101
01100110 => 10011001 => 10011001 => 01010101
01100111 => 10011011 => 11011001 => 01110101
01101000 => 10110000 => 00001101 => 10000101
01101001 => 10110010 => 01001101 => 10100101
01101010 => 10110100 => 00101101 => 11000101
01101011 => 10110101 => 10101101 => 11100101
01101100 => 10110001 => 10001101 => 10010101
01101101 => 10110110 => 01101101 => 11010101
01101110 => 10110011 => 11001101 => 10110101
01101111 => 10110111 => 11101101 => 11110101
01110000 => 10000011 => 11000001 => 00001101
01110001 => 10001110 => 01110001 => 00101101
01110010 => 10011100 => 00111001 => 01001101
01110011 => 10011101 => 10111001 => 01101101
01110100 => 10111000 => 00011101 => 10001101
01110101 => 10111010 => 01011101 => 11001101
01110110 => 10111001 => 10011101 => 10101101
01110111 => 10111011 => 11011101 => 11101101
01111000 => 10000111 => 11100001 => 00011101
01111001 => 10011110 => 01111001 => 01011101
01111010 => 10111100 => 00111101 => 10011101
01111011 => 10111101 => 10111101 => 11011101
01111100 => 10001111 => 11110001 => 00111101
01111101 => 10111110 => 01111101 => 10111101
01111110 => 10011111 => 11111001 => 01111101
01111111 => 10111111 => 11111101 => 11111101
10000000 => 00000001 => 10000000 => 00000010
10000001 => 00000110 => 01100000 => 00001010
10000010 => 00001100 => 00110000 => 00010010
10000011 => 00001101 => 10110000 => 00011010
10000100 => 00011000 => 00011000 => 00100010
10000101 => 00011010 => 01011000 => 00110010
10000110 => 00011001 => 10011000 => 00101010
10000111 => 00011011 => 11011000 => 00111010
10001000 => 00110000 => 00001100 => 01000010
10001001 => 00110010 => 01001100 => 01010010
10001010 => 00110100 => 00101100 => 01100010
10001011 => 00110101 => 10101100 => 01110010
10001100 => 00110001 => 10001100 => 01001010
10001101 => 00110110 => 01101100 => 01101010
10001110 => 00110011 => 11001100 => 01011010
10001111 => 00110111 => 11101100 => 01111010
10010000 => 01100000 => 00000110 => 10000010
10010001 => 01100010 => 01000110 => 10010010
10010010 => 01100100 => 00100110 => 10100010
10010011 => 01100101 => 10100110 => 10110010
10010100 => 01101000 => 00010110 => 11000010
10010101 => 01101010 => 01010110 => 11100010
10010110 => 01101001 => 10010110 => 11010010
10010111 => 01101011 => 11010110 => 11110010
10011000 => 01100001 => 10000110 => 10001010
10011001 => 01100110 => 01100110 => 10101010
10011010 => 01101100 => 00110110 => 11001010
10011011 => 01101101 => 10110110 => 11101010
10011100 => 01100011 => 11000110 => 10011010
10011101 => 01101110 => 01110110 => 11011010
10011110 => 01100111 => 11100110 => 10111010
10011111 => 01101111 => 11110110 => 11111010
10100000 => 11000000 => 00000011 => 00000011
10100001 => 11000010 => 01000011 => 00010011
10100010 => 11000100 => 00100011 => 00100011
10100011 => 11000101 => 10100011 => 00110011
10100100 => 11001000 => 00010011 => 01000011
10100101 => 11001010 => 01010011 => 01100011
10100110 => 11001001 => 10010011 => 01010011
10100111 => 11001011 => 11010011 => 01110011
10101000 => 11010000 => 00001011 => 10000011
10101001 => 11010010 => 01001011 => 10100011
10101010 => 11010100 => 00101011 => 11000011
10101011 => 11010101 => 10101011 => 11100011
10101100 => 11010001 => 10001011 => 10010011
10101101 => 11010110 => 01101011 => 11010011
10101110 => 11010011 => 11001011 => 10110011
10101111 => 11010111 => 11101011 => 11110011
10110000 => 11000001 => 10000011 => 00001011
10110001 => 11000110 => 01100011 => 00101011
10110010 => 11001100 => 00110011 => 01001011
10110011 => 11001101 => 10110011 => 01101011
10110100 => 11011000 => 00011011 => 10001011
10110101 => 11011010 => 01011011 => 11001011
10110110 => 11011001 => 10011011 => 10101011
10110111 => 11011011 => 11011011 => 11101011
10111000 => 11000011 => 11000011 => 00011011
10111001 => 11001110 => 01110011 => 01011011
10111010 => 11011100 => 00111011 => 10011011
10111011 => 11011101 => 10111011 => 11011011
10111100 => 11000111 => 11100011 => 00111011
10111101 => 11011110 => 01111011 => 10111011
10111110 => 11001111 => 11110011 => 01111011
10111111 => 11011111 => 11111011 => 11111011
11000000 => 00000011 => 11000000 => 00000110
11000001 => 00001110 => 01110000 => 00010110
11000010 => 00011100 => 00111000 => 00100110
11000011 => 00011101 => 10111000 => 00110110
11000100 => 00111000 => 00011100 => 01000110
11000101 => 00111010 => 01011100 => 01100110
11000110 => 00111001 => 10011100 => 01010110
11000111 => 00111011 => 11011100 => 01110110
11001000 => 01110000 => 00001110 => 10000110
11001001 => 01110010 => 01001110 => 10100110
11001010 => 01110100 => 00101110 => 11000110
11001011 => 01110101 => 10101110 => 11100110
11001100 => 01110001 => 10001110 => 10010110
11001101 => 01110110 => 01101110 => 11010110
11001110 => 01110011 => 11001110 => 10110110
11001111 => 01110111 => 11101110 => 11110110
11010000 => 11100000 => 00000111 => 00000111
11010001 => 11100010 => 01000111 => 00100111
11010010 => 11100100 => 00100111 => 01000111
11010011 => 11100101 => 10100111 => 01100111
11010100 => 11101000 => 00010111 => 10000111
11010101 => 11101010 => 01010111 => 11000111
11010110 => 11101001 => 10010111 => 10100111
11010111 => 11101011 => 11010111 => 11100111
11011000 => 11100001 => 10000111 => 00010111
11011001 => 11100110 => 01100111 => 01010111
11011010 => 11101100 => 00110111 => 10010111
11011011 => 11101101 => 10110111 => 11010111
11011100 => 11100011 => 11000111 => 00110111
11011101 => 11101110 => 01110111 => 10110111
11011110 => 11100111 => 11100111 => 01110111
11011111 => 11101111 => 11110111 => 11110111
11100000 => 00000111 => 11100000 => 00001110
11100001 => 00011110 => 01111000 => 00101110
11100010 => 00111100 => 00111100 => 01001110
11100011 => 00111101 => 10111100 => 01101110
11100100 => 01111000 => 00011110 => 10001110
11100101 => 01111010 => 01011110 => 11001110
11100110 => 01111001 => 10011110 => 10101110
11100111 => 01111011 => 11011110 => 11101110
11101000 => 11110000 => 00001111 => 00001111
11101001 => 11110010 => 01001111 => 01001111
11101010 => 11110100 => 00101111 => 10001111
11101011 => 11110101 => 10101111 => 11001111
11101100 => 11110001 => 10001111 => 00101111
11101101 => 11110110 => 01101111 => 10101111
11101110 => 11110011 => 11001111 => 01101111
11101111 => 11110111 => 11101111 => 11101111
11110000 => 00001111 => 11110000 => 00011110
11110001 => 00111110 => 01111100 => 01011110
11110010 => 01111100 => 00111110 => 10011110
11110011 => 01111101 => 10111110 => 11011110
11110100 => 11111000 => 00011111 => 00011111
11110101 => 11111010 => 01011111 => 10011111
11110110 => 11111001 => 10011111 => 01011111
11110111 => 11111011 => 11011111 => 11011111
11111000 => 00011111 => 11111000 => 00111110
11111001 => 01111110 => 01111110 => 10111110
11111010 => 11111100 => 00111111 => 00111111
11111011 => 11111101 => 10111111 => 10111111
11111100 => 00111111 => 11111100 => 01111110
11111101 => 11111110 => 01111111 => 01111111
11111110 => 01111111 => 11111110 => 11111110
11111111 => 11111111 => 11111111 => 11111111
000000000 => 000000000 => 000000000 => 000000000
000000001 => 000000010 => 010000000 => 000000100
000000010 => 000000100 => 001000000 => 000001000
000000011 => 000000101 => 101000000 => 000001100
000000100 => 000001000 => 000100000 => 000010000
000000101 => 000001010 => 010100000 => 000011000
000000110 => 000001001 => 100100000 => 000010100
000000111 => 000001011 => 110100000 => 000011100
000001000 => 000010000 => 000010000 => 000100000
000001001 => 000010010 => 010010000 => 000101000
000001010 => 000010100 => 001010000 => 000110000
000001011 => 000010101 => 101010000 => 000111000
000001100 => 000010001 => 100010000 => 000100100
000001101 => 000010110 => 011010000 => 000110100
000001110 => 000010011 => 110010000 => 000101100
000001111 => 000010111 => 111010000 => 000111100
000010000 => 000100000 => 000001000 => 001000000
000010001 => 000100010 => 010001000 => 001001000
000010010 => 000100100 => 001001000 => 001010000
000010011 => 000100101 => 101001000 => 001011000
000010100 => 000101000 => 000101000 => 001100000
000010101 => 000101010 => 010101000 => 001110000
000010110 => 000101001 => 100101000 => 001101000
000010111 => 000101011 => 110101000 => 001111000
000011000 => 000100001 => 100001000 => 001000100
000011001 => 000100110 => 011001000 => 001010100
000011010 => 000101100 => 001101000 => 001100100
000011011 => 000101101 => 101101000 => 001110100
000011100 => 000100011 => 110001000 => 001001100
000011101 => 000101110 => 011101000 => 001101100
000011110 => 000100111 => 111001000 => 001011100
000011111 => 000101111 => 111101000 => 001111100
000100000 => 001000000 => 000000100 => 010000000
000100001 => 001000010 => 010000100 => 010001000
000100010 => 001000100 => 001000100 => 010010000
000100011 => 001000101 => 101000100 => 010011000
000100100 => 001001000 => 000100100 => 010100000
000100101 => 001001010 => 010100100 => 010110000
000100110 => 001001001 => 100100100 => 010101000
000100111 => 001001011 => 110100100 => 010111000
000101000 => 001010000 => 000010100 => 011000000
000101001 => 001010010 => 010010100 => 011010000
000101010 => 001010100 => 001010100 => 011100000
000101011 => 001010101 => 101010100 => 011110000
000101100 => 001010001 => 100010100 => 011001000
000101101 => 001010110 => 011010100 => 011101000
000101110 => 001010011 => 110010100 => 011011000
000101111 => 001010111 => 111010100 => 011111000
000110000 => 001000001 => 100000100 => 010000100
000110001 => 001000110 => 011000100 => 010010100
000110010 => 001001100 => 001100100 => 010100100
000110011 => 001001101 => 101100100 => 010110100
000110100 => 001011000 => 000110100 => 011000100
000110101 => 001011010 => 010110100 => 011100100
000110110 => 001011001 => 100110100 => 011010100
000110111 => 001011011 => 110110100 => 011110100
000111000 => 001000011 => 110000100 => 010001100
000111001 => 001001110 => 011100100 => 010101100
000111010 => 001011100 => 001110100 => 011001100
000111011 => 001011101 => 101110100 => 011101100
000111100 => 001000111 => 111000100 => 010011100
000111101 => 001011110 => 011110100 => 011011100
000111110 => 001001111 => 111100100 => 010111100
000111111 => 001011111 => 111110100 => 011111100
001000000 => 010000000 => 000000010 => 100000000
001000001 => 010000010 => 010000010 => 100001000
001000010 => 010000100 => 001000010 => 100010000
001000011 => 010000101 => 101000010 => 100011000
001000100 => 010001000 => 000100010 => 100100000
001000101 => 010001010 => 010100010 => 100110000
001000110 => 010001001 => 100100010 => 100101000
001000111 => 010001011 => 110100010 => 100111000
001001000 => 010010000 => 000010010 => 101000000
001001001 => 010010010 => 010010010 => 101010000
001001010 => 010010100 => 001010010 => 101100000
001001011 => 010010101 => 101010010 => 101110000
001001100 => 010010001 => 100010010 => 101001000
001001101 => 010010110 => 011010010 => 101101000
001001110 => 010010011 => 110010010 => 101011000
001001111 => 010010111 => 111010010 => 101111000
001010000 => 010100000 => 000001010 => 110000000
001010001 => 010100010 => 010001010 => 110010000
001010010 => 010100100 => 001001010 => 110100000
001010011 => 010100101 => 101001010 => 110110000
001010100 => 010101000 => 000101010 => 111000000
001010101 => 010101010 => 010101010 => 111100000
001010110 => 010101001 => 100101010 => 111010000
001010111 => 010101011 => 110101010 => 111110000
001011000 => 010100001 => 100001010 => 110001000
001011001 => 010100110 => 011001010 => 110101000
001011010 => 010101100 => 001101010 => 111001000
001011011 => 010101101 => 101101010 => 111101000
001011100 => 010100011 => 110001010 => 110011000
001011101 => 010101110 => 011101010 => 111011000
001011110 => 010100111 => 111001010 => 110111000
001011111 => 010101111 => 111101010 => 111111000
001100000 => 010000001 => 100000010 => 100000100
001100001 => 010000110 => 011000010 => 100010100
001100010 => 010001100 => 001100010 => 100100100
001100011 => 010001101 => 101100010 => 100110100
001100100 => 010011000 => 000110010 => 101000100
001100101 => 010011010 => 010110010 => 101100100
001100110 => 010011001 => 100110010 => 101010100
001100111 => 010011011 => 110110010 => 101110100
001101000 => 010110000 => 000011010 => 110000100
001101001 => 010110010 => 010011010 => 110100100
001101010 => 010110100 => 001011010 => 111000100
001101011 => 010110101 => 101011010 => 111100100
001101100 => 010110001 => 100011010 => 110010100
001101101 => 010110110 => 011011010 => 111010100
001101110 => 010110011 => 110011010 => 110110100
001101111 => 010110111 => 111011010 => 111110100
001110000 => 010000011 => 110000010 => 100001100
001110001 => 010001110 => 011100010 => 100101100
001110010 => 010011100 => 001110010 => 101001100
001110011 => 010011101 => 101110010 => 101101100
001110100 => 010111000 => 000111010 => 110001100
001110101 => 010111010 => 010111010 => 111001100
001110110 => 010111001 => 100111010 => 110101100
001110111 => 010111011 => 110111010 => 111101100
001111000 => 010000111 => 111000010 => 100011100
001111001 => 010011110 => 011110010 => 101011100
001111010 => 010111100 => 001111010 => 110011100
001111011 => 010111101 => 101111010 => 111011100
001111100 => 010001111 => 111100010 => 100111100
001111101 => 010111110 => 011111010 => 110111100
001111110 => 010011111 => 111110010 => 101111100
001111111 => 010111111 => 111111010 => 111111100
010000000 => 100000000 => 000000001 => 000000001
010000001 => 100000010 => 010000001 => 000001001
010000010 => 100000100 => 001000001 => 000010001
010000011 => 100000101 => 101000001 => 000011001
010000100 => 100001000 => 000100001 => 000100001
010000101 => 100001010 => 010100001 => 000110001
010000110 => 100001001 => 100100001 => 000101001
010000111 => 100001011 => 110100001 => 000111001
010001000 => 100010000 => 000010001 => 001000001
010001001 => 100010010 => 010010001 => 001010001
010001010 => 100010100 => 001010001 => 001100001
010001011 => 100010101 => 101010001 => 001110001
010001100 => 100010001 => 100010001 => 001001001
010001101 => 100010110 => 011010001 => 001101001
010001110 => 100010011 => 110010001 => 001011001
010001111 => 100010111 => 111010001 => 001111001
010010000 => 100100000 => 000001001 => 010000001
010010001 => 100100010 => 010001001 => 010010001
010010010 => 100100100 => 001001001 => 010100001
010010011 => 100100101 => 101001001 => 010110001
010010100 => 100101000 => 000101001 => 011000001
010010101 => 100101010 => 010101001 => 011100001
010010110 => 100101001 => 100101001 => 011010001
010010111 => 100101011 => 110101001 => 011110001
010011000 => 100100001 => 100001001 => 010001001
010011001 => 100100110 => 011001001 => 010101001
010011010 => 100101100 => 001101001 => 011001001
010011011 => 100101101 => 101101001 => 011101001
010011100 => 100100011 => 110001001 => 010011001
010011101 => 100101110 => 011101001 => 011011001
010011110 => 100100111 => 111001001 => 010111001
010011111 => 100101111 => 111101001 => 011111001
010100000 => 101000000 => 000000101 => 100000001
010100001 => 101000010 => 010000101 => 100010001
010100010 => 101000100 => 001000101 => 100100001
010100011 => 101000101 => 101000101 => 100110001
010100100 => 101001000 => 000100101 => 101000001
010100101 => 101001010 => 010100101 => 101100001
010100110 => 101001001 => 100100101 => 101010001
010100111 => 101001011 => 110100101 => 101110001
010101000 => 101010000 => 000010101 => 110000001
010101001 => 101010010 => 010010101 => 110100001
010101010 => 101010100 => 001010101 => 111000001
010101011 => 101010101 => 101010101 => 111100001
010101100 => 101010001 => 100010101 => 110010001
010101101 => 101010110 => 011010101 => 111010001
010101110 => 101010011 => 110010101 => 110110001
010101111 => 101010111 => 111010101 => 111110001
010110000 => 101000001 => 100000101 => 100001001
010110001 => 101000110 => 011000101 => 100101001
010110010 => 101001100 => 001100101 => 101001001
010110011 => 101001101 => 101100101 => 101101001
010110100 => 101011000 => 000110101 => 110001001
010110101 => 101011010 => 010110101 => 111001001
010110110 => 101011001 => 100110101 => 110101001
010110111 => 101011011 => 110110101 => 111101001
010111000 => 101000011 => 110000101 => 100011001
010111001 => 101001110 => 011100101 => 101011001
010111010 => 101011100 => 001110101 => 110011001
010111011 => 101011101 => 101110101 => 111011001
010111100 => 101000111 => 111000101 => 100111001
010111101 => 101011110 => 011110101 => 110111001
010111110 => 101001111 => 111100101 => 101111001
010111111 => 101011111 => 111110101 => 111111001
011000000 => 100000001 => 100000001 => 000000101
011000001 => 100000110 => 011000001 => 000010101
011000010 => 100001100 => 001100001 => 000100101
011000011 => 100001101 => 101100001 => 000110101
011000100 => 100011000 => 000110001 => 001000101
011000101 => 100011010 => 010110001 => 001100101
011000110 => 100011001 => 100110001 => 001010101
011000111 => 100011011 => 110110001 => 001110101
011001000 => 100110000 => 000011001 => 010000101
011001001 => 100110010 => 010011001 => 010100101
011001010 => 100110100 => 001011001 => 011000101
011001011 => 100110101 => 101011001 => 011100101
011001100 => 100110001 => 100011001 => 010010101
011001101 => 100110110 => 011011001 => 011010101
011001110 => 100110011 => 110011001 => 010110101
011001111 => 100110111 => 111011001 => 011110101
011010000 => 101100000 => 000001101 => 100000101
011010001 => 101100010 => 010001101 => 100100101
011010010 => 101100100 => 001001101 => 101000101
011010011 => 101100101 => 101001101 => 101100101
011010100 => 101101000 => 000101101 => 110000101
011010101 => 101101010 => 010101101 => 111000101
011010110 => 101101001 => 100101101 => 110100101
011010111 => 101101011 => 110101101 => 111100101
011011000 => 101100001 => 100001101 => 100010101
011011001 => 101100110 => 011001101 => 101010101
011011010 => 101101100 => 001101101 => 110010101
011011011 => 101101101 => 101101101 => 111010101
011011100 => 101100011 => 110001101 => 100110101
011011101 => 101101110 => 011101101 => 110110101
011011110 => 101100111 => 111001101 => 101110101
011011111 => 101101111 => 111101101 => 111110101
011100000 => 100000011 => 110000001 => 000001101
011100001 => 100001110 => 011100001 => 000101101
011100010 => 100011100 => 001110001 => 001001101
011100011 => 100011101 => 101110001 => 001101101
011100100 => 100111000 => 000111001 => 010001101
011100101 => 100111010 => 010111001 => 011001101
011100110 => 100111001 => 100111001 => 010101101
011100111 => 100111011 => 110111001 => 011101101
011101000 => 101110000 => 000011101 => 100001101
011101001 => 101110010 => 010011101 => 101001101
011101010 => 101110100 => 001011101 => 110001101
011101011 => 101110101 => 101011101 => 111001101
011101100 => 101110001 => 100011101 => 100101101
011101101 => 101110110 => 011011101 => 110101101
011101110 => 101110011 => 110011101 => 101101101
011101111 => 101110111 => 111011101 => 111101101
011110000 => 100000111 => 111000001 => 000011101
011110001 => 100011110 => 011110001 => 001011101
011110010 => 100111100 => 001111001 => 010011101
011110011 => 100111101 => 101111001 => 011011101
011110100 => 101111000 => 000111101 => 100011101
011110101 => 101111010 => 010111101 => 110011101
011110110 => 101111001 => 100111101 => 101011101
011110111 => 101111011 => 110111101 => 111011101
011111000 => 100001111 => 111100001 => 000111101
011111001 => 100111110 => 011111001 => 010111101
011111010 => 101111100 => 001111101 => 100111101
011111011 => 101111101 => 101111101 => 110111101
011111100 => 100011111 => 111110001 => 001111101
011111101 => 101111110 => 011111101 => 101111101
011111110 => 100111111 => 111111001 => 011111101
011111111 => 101111111 => 111111101 => 111111101
100000000 => 000000001 => 100000000 => 000000010
100000001 => 000000110 => 011000000 => 000001010
100000010 => 000001100 => 001100000 => 000010010
100000011 => 000001101 => 101100000 => 000011010
100000100 => 000011000 => 000110000 => 000100010
100000101 => 000011010 => 010110000 => 000110010
100000110 => 000011001 => 100110000 => 000101010
100000111 => 000011011 => 110110000 => 000111010
100001000 => 000110000 => 000011000 => 001000010
100001001 => 000110010 => 010011000 => 001010010
100001010 => 000110100 => 001011000 => 001100010
100001011 => 000110101 => 101011000 => 001110010
100001100 => 000110001 => 100011000 => 001001010
100001101 => 000110110 => 011011000 => 001101010
100001110 => 000110011 => 110011000 => 001011010
100001111 => 000110111 => 111011000 => 001111010
100010000 => 001100000 => 000001100 => 010000010
100010001 => 001100010 => 010001100 => 010010010
100010010 => 001100100 => 001001100 => 010100010
100010011 => 001100101 => 101001100 => 010110010
100010100 => 001101000 => 000101100 => 011000010
100010101 => 001101010 => 010101100 => 011100010
100010110 => 001101001 => 100101100 => 011010010
100010111 => 001101011 => 110101100 => 011110010
100011000 => 001100001 => 100001100 => 010001010
100011001 => 001100110 => 011001100 => 010101010
100011010 => 001101100 => 001101100 => 011001010
100011011 => 001101101 => 101101100 => 011101010
100011100 => 001100011 => 110001100 => 010011010
100011101 => 001101110 => 011101100 => 011011010
100011110 => 001100111 => 111001100 => 010111010
100011111 => 001101111 => 111101100 => 011111010
100100000 => 011000000 => 000000110 => 100000010
100100001 => 011000010 => 010000110 => 100010010
100100010 => 011000100 => 001000110 => 100100010
100100011 => 011000101 => 101000110 => 100110010
100100100 => 011001000 => 000100110 => 101000010
100100101 => 011001010 => 010100110 => 101100010
100100110 => 011001001 => 100100110 => 101010010
100100111 => 011001011 => 110100110 => 101110010
100101000 => 011010000 => 000010110 => 110000010
100101001 => 011010010 => 010010110 => 110100010
100101010 => 011010100 => 001010110 => 111000010
100101011 => 011010101 => 101010110 => 111100010
100101100 => 011010001 => 100010110 => 110010010
100101101 => 011010110 => 011010110 => 111010010
100101110 => 011010011 => 110010110 => 110110010
100101111 => 011010111 => 111010110 => 111110010
100110000 => 011000001 => 100000110 => 100001010
100110001 => 011000110 => 011000110 => 100101010
100110010 => 011001100 => 001100110 => 101001010
100110011 => 011001101 => 101100110 => 101101010
100110100 => 011011000 => 000110110 => 110001010
100110101 => 011011010 => 010110110 => 111001010
100110110 => 011011001 => 100110110 => 110101010
100110111 => 011011011 => 110110110 => 111101010
100111000 => 011000011 => 110000110 => 100011010
100111001 => 011001110 => 011100110 => 101011010
100111010 => 011011100 => 001110110 => 110011010
100111011 => 011011101 => 101110110 => 111011010
100111100 => 011000111 => 111000110 => 100111010
100111101 => 011011110 => 011110110 => 110111010
100111110 => 011001111 => 111100110 => 101111010
100111111 => 011011111 => 111110110 => 111111010
101000000 => 110000000 => 000000011 => 000000011
101000001 => 110000010 => 010000011 => 000010011
101000010 => 110000100 => 001000011 => 000100011
101000011 => 110000101 => 101000011 => 000110011
101000100 => 110001000 => 000100011 => 001000011
101000101 => 110001010 => 010100011 => 001100011
101000110 => 110001001 => 100100011 => 001010011
101000111 => 110001011 => 110100011 => 001110011
101001000 => 110010000 => 000010011 => 010000011
101001001 => 110010010 => 010010011 => 010100011
101001010 => 110010100 => 001010011 => 011000011
101001011 => 110010101 => 101010011 => 011100011
101001100 => 110010001 => 100010011 => 010010011
101001101 => 110010110 => 011010011 => 011010011
101001110 => 110010011 => 110010011 => 010110011
101001111 => 110010111 => 111010011 => 011110011
101010000 => 110100000 => 000001011 => 100000011
101010001 => 110100010 => 010001011 => 100100011
101010010 => 110100100 => 001001011 => 101000011
101010011 => 110100101 => 101001011 => 101100011
101010100 => 110101000 => 000101011 => 110000011
101010101 => 110101010 => 010101011 => 111000011
101010110 => 110101001 => 100101011 => 110100011
101010111 => 110101011 => 110101011 => 111100011
101011000 => 110100001 => 100001011 => 100010011
101011001 => 110100110 => 011001011 => 101010011
101011010 => 110101100 => 001101011 => 110010011
101011011 => 110101101 => 101101011 => 111010011
101011100 => 110100011 => 110001011 => 100110011
101011101 => 110101110 => 011101011 => 110110011
101011110 => 110100111 => 111001011 => 101110011
101011111 => 110101111 => 111101011 => 111110011
101100000 => 110000001 => 100000011 => 000001011
101100001 => 110000110 => 011000011 => 000101011
101100010 => 110001100 => 001100011 => 001001011
101100011 => 110001101 => 101100011 => 001101011
101100100 => 110011000 => 000110011 => 010001011
101100101 => 110011010 => 010110011 => 011001011
101100110 => 110011001 => 100110011 => 010101011
101100111 => 110011011 => 110110011 => 011101011
101101000 => 110110000 => 000011011 => 100001011
101101001 => 110110010 => 010011011 => 101001011
101101010 => 110110100 => 001011011 => 110001011
101101011 => 110110101 => 101011011 => 111001011
101101100 => 110110001 => 100011011 => 100101011
101101101 => 110110110 => 011011011 => 110101011
101101110 => 110110011 => 110011011 => 101101011
101101111 => 110110111 => 111011011 => 111101011
101110000 => 110000011 => 110000011 => 000011011
101110001 => 110001110 => 011100011 => 001011011
101110010 => 110011100 => 001110011 => 010011011
101110011 => 110011101 => 101110011 => 011011011
101110100 => 110111000 => 000111011 => 100011011
101110101 => 110111010 => 010111011 => 110011011
101110110 => 110111001 => 100111011 => 101011011
101110111 => 110111011 => 110111011 => 111011011
101111000 => 110000111 => 111000011 => 000111011
101111001 => 110011110 => 011110011 => 010111011
101111010 => 110111100 => 001111011 => 100111011
101111011 => 110111101 => 101111011 => 110111011
101111100 => 110001111 => 111100011 => 001111011
101111101 => 110111110 => 011111011 => 101111011
101111110 => 110011111 => 111110011 => 011111011
101111111 => 110111111 => 111111011 => 111111011
110000000 => 000000011 => 110000000 => 000000110
110000001 => 000001110 => 011100000 => 000010110
110000010 => 000011100 => 001110000 => 000100110
110000011 => 000011101 => 101110000 => 000110110
110000100 => 000111000 => 000111000 => 001000110
110000101 => 000111010 => 010111000 => 001100110
110000110 => 000111001 => 100111000 => 001010110
110000111 => 000111011 => 110111000 => 001110110
110001000 => 001110000 => 000011100 => 010000110
110001001 => 001110010 => 010011100 => 010100110
110001010 => 001110100 => 001011100 => 011000110
110001011 => 001110101 => 101011100 => 011100110
110001100 => 001110001 => 100011100 => 010010110
110001101 => 001110110 => 011011100 => 011010110
110001110 => 001110011 => 110011100 => 010110110
110001111 => 001110111 => 111011100 => 011110110
110010000 => 011100000 => 000001110 => 100000110
110010001 => 011100010 => 010001110 => 100100110
110010010 => 011100100 => 001001110 => 101000110
110010011 => 011100101 => 101001110 => 101100110
110010100 => 011101000 => 000101110 => 110000110
110010101 => 011101010 => 010101110 => 111000110
110010110 => 011101001 => 100101110 => 110100110
110010111 => 011101011 => 110101110 => 111100110
110011000 => 011100001 => 100001110 => 100010110
110011001 => 011100110 => 011001110 => 101010110
110011010 => 011101100 => 001101110 => 110010110
110011011 => 011101101 => 101101110 => 111010110
110011100 => 011100011 => 110001110 => 100110110
110011101 => 011101110 => 011101110 => 110110110
110011110 => 011100111 => 111001110 => 101110110
110011111 => 011101111 => 111101110 => 111110110
110100000 => 111000000 => 000000111 => 000000111
110100001 => 111000010 => 010000111 => 000100111
110100010 => 111000100 => 001000111 => 001000111
110100011 => 111000101 => 101000111 => 001100111
110100100 => 111001000 => 000100111 => 010000111
110100101 => 111001010 => 010100111 => 011000111
110100110 => 111001001 => 100100111 => 010100111
110100111 => 111001011 => 110100111 => 011100111
110101000 => 111010000 => 000010111 => 100000111
110101001 => 111010010 => 010010111 => 101000111
110101010 => 111010100 => 001010111 => 110000111
110101011 => 111010101 => 101010111 => 111000111
110101100 => 111010001 => 100010111 => 100100111
110101101 => 111010110 => 011010111 => 110100111
110101110 => 111010011 => 110010111 => 101100111
110101111 => 111010111 => 111010111 => 111100111
110110000 => 111000001 => 100000111 => 000010111
110110001 => 111000110 => 011000111 => 001010111
110110010 => 111001100 => 001100111 => 010010111
110110011 => 111001101 => 101100111 => 011010111
110110100 => 111011000 => 000110111 => 100010111
110110101 => 111011010 => 010110111 => 110010111
110110110 => 111011001 => 100110111 => 101010111
110110111 => 111011011 => 110110111 => 111010111
110111000 => 111000011 => 110000111 => 000110111
110111001 => 111001110 => 011100111 => 010110111
110111010 => 111011100 => 001110111 => 100110111
110111011 => 111011101 => 101110111 => 110110111
110111100 => 111000111 => 111000111 => 001110111
110111101 => 111011110 => 011110111 => 101110111
110111110 => 111001111 => 111100111 => 011110111
110111111 => 111011111 => 111110111 => 111110111
111000000 => 000000111 => 111000000 => 000001110
111000001 => 000011110 => 011110000 => 000101110
111000010 => 000111100 => 001111000 => 001001110
111000011 => 000111101 => 101111000 => 001101110
111000100 => 001111000 => 000111100 => 010001110
111000101 => 001111010 => 010111100 => 011001110
111000110 => 001111001 => 100111100 => 010101110
111000111 => 001111011 => 110111100 => 011101110
111001000 => 011110000 => 000011110 => 100001110
111001001 => 011110010 => 010011110 => 101001110
111001010 => 011110100 => 001011110 => 110001110
111001011 => 011110101 => 101011110 => 111001110
111001100 => 011110001 => 100011110 => 100101110
111001101 => 011110110 => 011011110 => 110101110
111001110 => 011110011 => 110011110 => 101101110
111001111 => 011110111 => 111011110 => 111101110
111010000 => 111100000 => 000001111 => 000001111
111010001 => 111100010 => 010001111 => 001001111
111010010 => 111100100 => 001001111 => 010001111
111010011 => 111100101 => 101001111 => 011001111
111010100 => 111101000 => 000101111 => 100001111
111010101 => 111101010 => 010101111 => 110001111
111010110 => 111101001 => 100101111 => 101001111
111010111 => 111101011 => 110101111 => 111001111
111011000 => 111100001 => 100001111 => 000101111
111011001 => 111100110 => 011001111 => 010101111
111011010 => 111101100 => 001101111 => 100101111
111011011 => 111101101 => 101101111 => 110101111
111011100 => 111100011 => 110001111 => 001101111
111011101 => 111101110 => 011101111 => 101101111
111011110 => 111100111 => 111001111 => 011101111
111011111 => 111101111 => 111101111 => 111101111
111100000 => 000001111 => 111100000 => 000011110
111100001 => 000111110 => 011111000 => 001011110
111100010 => 001111100 => 001111100 => 010011110
111100011 => 001111101 => 101111100 => 011011110
111100100 => 011111000 => 000111110 => 100011110
111100101 => 011111010 => 010111110 => 110011110
111100110 => 011111001 => 100111110 => 101011110
111100111 => 011111011 => 110111110 => 111011110
111101000 => 111110000 => 000011111 => 000011111
111101001 => 111110010 => 010011111 => 010011111
111101010 => 111110100 => 001011111 => 100011111
111101011 => 111110101 => 101011111 => 110011111
111101100 => 111110001 => 100011111 => 001011111
111101101 => 111110110 => 011011111 => 101011111
111101110 => 111110011 => 110011111 => 011011111
111101111 => 111110111 => 111011111 => 111011111
111110000 => 000011111 => 111110000 => 000111110
111110001 => 001111110 => 011111100 => 010111110
111110010 => 011111100 => 001111110 => 100111110
111110011 => 011111101 => 101111110 => 110111110
111110100 => 111111000 => 000111111 => 000111111
111110101 => 111111010 => 010111111 => 100111111
111110110 => 111111001 => 100111111 => 010111111
111110111 => 111111011 => 110111111 => 110111111
111111000 => 000111111 => 111111000 => 001111110
111111001 => 011111110 => 011111110 => 101111110
111111010 => 111111100 => 001111111 => 001111111
111111011 => 111111101 => 101111111 => 101111111
111111100 => 001111111 => 111111100 => 011111110
111111101 => 111111110 => 011111111 => 011111111
111111110 => 011111111 => 111111110 => 111111110
111111111 => 111111111 => 111111111 => 111111111
1010101010 => 1101010100 => 0010101011 => 1110000011
1010101100 => 1101010001 => 1000101011 => 1100100011
1010110010 => 1101001100 => 0011001011 => 1010010011
1010110100 => 1101011000 => 0001101011 => 1100010011
1010111000 => 1101000011 => 1100001011 => 1000110011
1011001010 => 1100110100 => 0010110011 => 0110001011
1011001100 => 1100110001 => 1000110011 => 0100101011
1011010010 => 1101100100 => 0010011011 => 1010001011
1011010100 => 1101101000 => 0001011011 => 1100001011
1011011000 => 1101100001 => 1000011011 => 1000101011
1011100100 => 1100111000 => 0001110011 => 0100011011
1011101000 => 1101110000 => 0000111011 => 1000011011
1011110000 => 1100000111 => 1110000011 => 0000111011
1100101010 => 0111010100 => 0010101110 => 1110000110
1100101100 => 0111010001 => 1000101110 => 1100100110
1100110010 => 0111001100 => 0011001110 => 1010010110
1100110100 => 0111011000 => 0001101110 => 1100010110
1100111000 => 0111000011 => 1100001110 => 1000110110
1101001010 => 1110010100 => 0010100111 => 0110000111
1101001100 => 1110010001 => 1000100111 => 0100100111
1101010010 => 1110100100 => 0010010111 => 1010000111
1101010100 => 1110101000 => 0001010111 => 1100000111
1101011000 => 1110100001 => 1000010111 => 1000100111
1101100010 => 1110001100 => 0011000111 => 0010010111
1101100100 => 1110011000 => 0001100111 => 0100010111
1101101000 => 1110110000 => 0000110111 => 1000010111
1101110000 => 1110000011 => 1100000111 => 0000110111
1110001010 => 0011110100 => 0010111100 => 0110001110
1110001100 => 0011110001 => 1000111100 => 0100101110
1110010010 => 0111100100 => 0010011110 => 1010001110
1110010100 => 0111101000 => 0001011110 => 1100001110
1110011000 => 0111100001 => 1000011110 => 1000101110
1110100010 => 1111000100 => 0010001111 => 0010001111
1110100100 => 1111001000 => 0001001111 => 0100001111
1110101000 => 1111010000 => 0000101111 => 1000001111
1110110000 => 1111000001 => 1000001111 => 0000101111
1111000010 => 0001111100 => 0011111000 => 0010011110
1111000100 => 0011111000 => 0001111100 => 0100011110
1111001000 => 0111110000 => 0000111110 => 1000011110
1111010000 => 1111100000 => 0000011111 => 0000011111
1111100000 => 0000011111 => 1111100000 => 0000111110
101010101010 => 110101010100 => 001010101011 => 111100000011
101010101100 => 110101010001 => 100010101011 => 111001000011
101010110010 => 110101001100 => 001100101011 => 110100100011
101010110100 => 110101011000 => 000110101011 => 111000100011
101010111000 => 110101000011 => 110000101011 => 110001100011
101011001010 => 110100110100 => 001011001011 => 101100010011
101011001100 => 110100110001 => 100011001011 => 101001010011
101011010010 => 110101100100 => 001001101011 => 110100010011
101011010100 => 110101101000 => 000101101011 => 111000010011
101011011000 => 110101100001 => 100001101011 => 110001010011
101011100100 => 110100111000 => 000111001011 => 101000110011
101011101000 => 110101110000 => 000011101011 => 110000110011
101011110000 => 110100000111 => 111000001011 => 100001110011
101100101010 => 110011010100 => 001010110011 => 011100001011
101100101100 => 110011010001 => 100010110011 => 011001001011
101100110010 => 110011001100 => 001100110011 => 010100101011
101100110100 => 110011011000 => 000110110011 => 011000101011
101100111000 => 110011000011 => 110000110011 => 010001101011
101101001010 => 110110010100 => 001010011011 => 101100001011
101101001100 => 110110010001 => 100010011011 => 101001001011
101101010010 => 110110100100 => 001001011011 => 110100001011
101101010100 => 110110101000 => 000101011011 => 111000001011
101101011000 => 110110100001 => 100001011011 => 110001001011
101101100010 => 110110001100 => 001100011011 => 100100101011
101101100100 => 110110011000 => 000110011011 => 101000101011
101101101000 => 110110110000 => 000011011011 => 110000101011
101101110000 => 110110000011 => 110000011011 => 100001101011
101110001100 => 110001110001 => 100011100011 => 001001011011
101110010010 => 110011100100 => 001001110011 => 010100011011
101110010100 => 110011101000 => 000101110011 => 011000011011
101110011000 => 110011100001 => 100001110011 => 010001011011
101110100010 => 110111000100 => 001000111011 => 100100011011
101110100100 => 110111001000 => 000100111011 => 101000011011
101110101000 => 110111010000 => 000010111011 => 110000011011
101110110000 => 110111000001 => 100000111011 => 100001011011
101111000010 => 110000111100 => 001111000011 => 000100111011
101111000100 => 110001111000 => 000111100011 => 001000111011
101111001000 => 110011110000 => 000011110011 => 010000111011
101111010000 => 110111100000 => 000001111011 => 100000111011
101111100000 => 110000001111 => 111100000011 => 000001111011
110010101010 => 011101010100 => 001010101110 => 111100000110
110010101100 => 011101010001 => 100010101110 => 111001000110
110010110010 => 011101001100 => 001100101110 => 110100100110
110010110100 => 011101011000 => 000110101110 => 111000100110
110011001010 => 011100110100 => 001011001110 => 101100010110
110011001100 => 011100110001 => 100011001110 => 101001010110
110011010010 => 011101100100 => 001001101110 => 110100010110
110011010100 => 011101101000 => 000101101110 => 111000010110
110011011000 => 011101100001 => 100001101110 => 110001010110
110011100010 => 011100011100 => 001110001110 => 100100110110
110011100100 => 011100111000 => 000111001110 => 101000110110
110011101000 => 011101110000 => 000011101110 => 110000110110
110011110000 => 011100000111 => 111000001110 => 100001110110
110100101010 => 111001010100 => 001010100111 => 011100000111
110100101100 => 111001010001 => 100010100111 => 011001000111
110100110010 => 111001001100 => 001100100111 => 010100100111
110100110100 => 111001011000 => 000110100111 => 011000100111
110100111000 => 111001000011 => 110000100111 => 010001100111
110101001010 => 111010010100 => 001010010111 => 101100000111
110101001100 => 111010010001 => 100010010111 => 101001000111
110101010010 => 111010100100 => 001001010111 => 110100000111
110101010100 => 111010101000 => 000101010111 => 111000000111
110101011000 => 111010100001 => 100001010111 => 110001000111
110101100010 => 111010001100 => 001100010111 => 100100100111
110101100100 => 111010011000 => 000110010111 => 101000100111
110101101000 => 111010110000 => 000011010111 => 110000100111
110101110000 => 111010000011 => 110000010111 => 100001100111
110110001010 => 111000110100 => 001011000111 => 001100010111
110110001100 => 111000110001 => 100011000111 => 001001010111
110110010010 => 111001100100 => 001001100111 => 010100010111
110110010100 => 111001101000 => 000101100111 => 011000010111
110110011000 => 111001100001 => 100001100111 => 010001010111
110110100010 => 111011000100 => 001000110111 => 100100010111
110110100100 => 111011001000 => 000100110111 => 101000010111
110110101000 => 111011010000 => 000010110111 => 110000010111
110110110000 => 111011000001 => 100000110111 => 100001010111
110111000010 => 111000011100 => 001110000111 => 000100110111
110111000100 => 111000111000 => 000111000111 => 001000110111
110111001000 => 111001110000 => 000011100111 => 010000110111
110111010000 => 111011100000 => 000001110111 => 100000110111
110111100000 => 111000000111 => 111000000111 => 000001110111
111000101010 => 001111010100 => 001010111100 => 011100001110
111000110010 => 001111001100 => 001100111100 => 010100101110
111000110100 => 001111011000 => 000110111100 => 011000101110
111000111000 => 001111000011 => 110000111100 => 010001101110
111001001010 => 011110010100 => 001010011110 => 101100001110
111001001100 => 011110010001 => 100010011110 => 101001001110
111001010010 => 011110100100 => 001001011110 => 110100001110
111001010100 => 011110101000 => 000101011110 => 111000001110
111001011000 => 011110100001 => 100001011110 => 110001001110
111001100010 => 011110001100 => 001100011110 => 100100101110
111001100100 => 011110011000 => 000110011110 => 101000101110
111001101000 => 011110110000 => 000011011110 => 110000101110
111001110000 => 011110000011 => 110000011110 => 100001101110
111010001010 => 111100010100 => 001010001111 => 001100001111
111010001100 => 111100010001 => 100010001111 => 001001001111
111010010010 => 111100100100 => 001001001111 => 010100001111
111010010100 => 111100101000 => 000101001111 => 011000001111
111010011000 => 111100100001 => 100001001111 => 010001001111
111010100010 => 111101000100 => 001000101111 => 100100001111
111010100100 => 111101001000 => 000100101111 => 101000001111
111010101000 => 111101010000 => 000010101111 => 110000001111
111010110000 => 111101000001 => 100000101111 => 100001001111
111011000010 => 111100001100 => 001100001111 => 000100101111
111011000100 => 111100011000 => 000110001111 => 001000101111
111011001000 => 111100110000 => 000011001111 => 010000101111
111011010000 => 111101100000 => 000001101111 => 100000101111
111011100000 => 111100000011 => 110000001111 => 000001101111
111100001010 => 000111110100 => 001011111000 => 001100011110
111100001100 => 000111110001 => 100011111000 => 001001011110
111100010010 => 001111100100 => 001001111100 => 010100011110
111100010100 => 001111101000 => 000101111100 => 011000011110
111100011000 => 001111100001 => 100001111100 => 010001011110
111100100010 => 011111000100 => 001000111110 => 100100011110
111100100100 => 011111001000 => 000100111110 => 101000011110
111100101000 => 011111010000 => 000010111110 => 110000011110
111100110000 => 011111000001 => 100000111110 => 100001011110
111101000010 => 111110000100 => 001000011111 => 000100011111
111101000100 => 111110001000 => 000100011111 => 001000011111
111101001000 => 111110010000 => 000010011111 => 010000011111
111101010000 => 111110100000 => 000001011111 => 100000011111
111101100000 => 111110000001 => 100000011111 => 000001011111
111110000010 => 000011111100 => 001111110000 => 000100111110
111110000100 => 000111111000 => 000111111000 => 001000111110
111110001000 => 001111110000 => 000011111100 => 010000111110
111110010000 => 011111100000 => 000001111110 => 100000111110
111110100000 => 111111000000 => 000000111111 => 000000111111
111111000000 => 000000111111 => 111111000000 => 000001111110
10101010101010 => 11010101010100 => 00101010101011 => 11111000000011
10101010110100 => 11010101011000 => 00011010101011 => 11110001000011
10101011010100 => 11010101101000 => 00010110101011 => 11110000100011
10101011101000 => 11010101110000 => 00001110101011 => 11100001100011
10101101010100 => 11010110101000 => 00010101101011 => 11110000010011
10101110100100 => 11010111001000 => 00010011101011 => 11010000110011
10101110101000 => 11010111010000 => 00001011101011 => 11100000110011
10101111010000 => 11010111100000 => 00000111101011 => 11000001110011
10110101010100 => 11011010101000 => 00010101011011 => 11110000001011
10111010010100 => 11011100101000 => 00010100111011 => 10110000011011
10111010100100 => 11011101001000 => 00010010111011 => 11010000011011
10111011000100 => 11011100011000 => 00011000111011 => 10010001011011
10111011010000 => 11011101100000 => 00000110111011 => 11000001011011
10111101000100 => 11011110001000 => 00010001111011 => 10010000111011
10111101001000 => 11011110010000 => 00001001111011 => 10100000111011
10111101010000 => 11011110100000 => 00000101111011 => 11000000111011
10111110010000 => 11001111100000 => 00000111110011 => 01000001111011
10111110100000 => 11011111000000 => 00000011111011 => 10000001111011
11010101010100 => 11101010101000 => 00010101010111 => 11110000000111
11010101100100 => 11101010011000 => 00011001010111 => 11010001000111
11010101101000 => 11101010110000 => 00001101010111 => 11100001000111
11010110010100 => 11101001101000 => 00010110010111 => 10110000100111
11010110100100 => 11101011001000 => 00010011010111 => 11010000100111
11010110101000 => 11101011010000 => 00001011010111 => 11100000100111
11010111001000 => 11101001110000 => 00001110010111 => 10100001100111
11010111010000 => 11101011100000 => 00000111010111 => 11000001100111
11011001010100 => 11100110101000 => 00010101100111 => 01110000010111
11011001100100 => 11100110011000 => 00011001100111 => 01010001010111
11011001101000 => 11100110110000 => 00001101100111 => 01100001010111
11011010010100 => 11101100101000 => 00010100110111 => 10110000010111
11011010100100 => 11101101001000 => 00010010110111 => 11010000010111
11011010101000 => 11101101010000 => 00001010110111 => 11100000010111
11011011000100 => 11101100011000 => 00011000110111 => 10010001010111
11011011001000 => 11101100110000 => 00001100110111 => 10100001010111
11011011010000 => 11101101100000 => 00000110110111 => 11000001010111
11011100100100 => 11100111001000 => 00010011100111 => 01010000110111
11011100101000 => 11100111010000 => 00001011100111 => 01100000110111
11011101000100 => 11101110001000 => 00010001110111 => 10010000110111
11011101001000 => 11101110010000 => 00001001110111 => 10100000110111
11011101010000 => 11101110100000 => 00000101110111 => 11000000110111
11011110010000 => 11100111100000 => 00000111100111 => 01000001110111
11011110100000 => 11101111000000 => 00000011110111 => 10000001110111
11101001010100 => 11110010101000 => 00010101001111 => 01110000001111
11101001100100 => 11110010011000 => 00011001001111 => 01010001001111
11101001101000 => 11110010110000 => 00001101001111 => 01100001001111
11101010010100 => 11110100101000 => 00010100101111 => 10110000001111
11101010100100 => 11110101001000 => 00010010101111 => 11010000001111
11101010101000 => 11110101010000 => 00001010101111 => 11100000001111
11101011000100 => 11110100011000 => 00011000101111 => 10010001001111
11101011001000 => 11110100110000 => 00001100101111 => 10100001001111
11101011010000 => 11110101100000 => 00000110101111 => 11000001001111
11101100010100 => 11110001101000 => 00010110001111 => 00110000101111
11101100100100 => 11110011001000 => 00010011001111 => 01010000101111
11101100101000 => 11110011010000 => 00001011001111 => 01100000101111
11101101000010 => 11110110000100 => 00100001101111 => 10001000101111
11101101000100 => 11110110001000 => 00010001101111 => 10010000101111
11101101001000 => 11110110010000 => 00001001101111 => 10100000101111
11101101010000 => 11110110100000 => 00000101101111 => 11000000101111
11101110001000 => 11110001110000 => 00001110001111 => 00100001101111
11101110010000 => 11110011100000 => 00000111001111 => 01000001101111
11101110100000 => 11110111000000 => 00000011101111 => 10000001101111
11110100010100 => 11111000101000 => 00010100011111 => 00110000011111
11110100100010 => 11111001000100 => 00100010011111 => 01001000011111
11110100100100 => 11111001001000 => 00010010011111 => 01010000011111
11110100101000 => 11111001010000 => 00001010011111 => 01100000011111
11110101000010 => 11111010000100 => 00100001011111 => 10001000011111
11110101000100 => 11111010001000 => 00010001011111 => 10010000011111
11110101001000 => 11111010010000 => 00001001011111 => 10100000011111
11110101010000 => 11111010100000 => 00000101011111 => 11000000011111
11110110000010 => 11111000001100 => 00110000011111 => 00001001011111
11110110000100 => 11111000011000 => 00011000011111 => 00010001011111
11110110001000 => 11111000110000 => 00001100011111 => 00100001011111
11110110010000 => 11111001100000 => 00000110011111 => 01000001011111
11110110100000 => 11111011000000 => 00000011011111 => 10000001011111
11111010000010 => 11111100000100 => 00100000111111 => 00001000111111
11111010000100 => 11111100001000 => 00010000111111 => 00010000111111
11111010001000 => 11111100010000 => 00001000111111 => 00100000111111
11111010010000 => 11111100100000 => 00000100111111 => 01000000111111
11111010100000 => 11111101000000 => 00000010111111 => 10000000111111
11111101000000 => 11111110000000 => 00000001111111 => 00000001111111
11111110000000 => 00000001111111 => 11111110000000 => 00000011111110
1010101010101010 => 1101010101010100 => 0010101010101011 => 1111110000000011
1010101010110100 => 1101010101011000 => 0001101010101011 => 1111100010000011
1010101011010100 => 1101010101101000 => 0001011010101011 => 1111100001000011
1010101011101000 => 1101010101110000 => 0000111010101011 => 1111000011000011
1111111111 => 1111111111 => 1111111111 => 1111111111
1111111110 => 0111111111 => 1111111110 => 1111111110
1111111101 => 1111111110 => 0111111111 => 0111111111
1111111001 => 0111111110 => 0111111110 => 1011111110
1111101101 => 1111110110 => 0110111111 => 1010111111
1111101011 => 1111110101 => 1010111111 => 1100111111
1111100111 => 0111111011 => 1101111110 => 1110111110
1111100001 => 0001111110 => 0111111000 => 0010111110
1111000001 => 0000111110 => 0111110000 => 0001011110
1110111110 => 1111001111 => 1111001111 => 0111101111
1110111101 => 1111011110 => 0111101111 => 1011101111
1110110111 => 1111011011 => 1101101111 => 1110101111
1110110001 => 1111000110 => 0110001111 => 0010101111
1110101011 => 1111010101 => 1010101111 => 1110001111
1110100101 => 1111001010 => 0101001111 => 0110001111
1110100001 => 1111000010 => 0100001111 => 0001001111
1110011111 => 0111101111 => 1111011110 => 1111101110
1110011110 => 0111100111 => 1110011110 => 1011101110
1110011001 => 0111100110 => 0110011110 => 1010101110
1110010001 => 0111100010 => 0100011110 => 1001001110
1110001001 => 0011110010 => 0100111100 => 0101001110
1110000111 => 0001111011 => 1101111000 => 0011101110
1110000101 => 0001111010 => 0101111000 => 0011001110
1110000001 => 0000011110 => 0111100000 => 0000101110
1101111110 => 1110011111 => 1111100111 => 0111110111
1101111011 => 1110111101 => 1011110111 => 1101110111
1101101011 => 1110110101 => 1010110111 => 1110010111
1101100001 => 1110000110 => 0110000111 => 0001010111
1101011111 => 1110101111 => 1111010111 => 1111100111
1101011011 => 1110101101 => 1011010111 => 1110100111
1101010111 => 1110101011 => 1101010111 => 1111000111
1101010101 => 1110101010 => 0101010111 => 1110000111
1101010011 => 1110100101 => 1010010111 => 1011000111
1101010001 => 1110100010 => 0100010111 => 1001000111
1101001110 => 1110010011 => 1100100111 => 0101100111
1101001011 => 1110010101 => 1010100111 => 0111000111
1101001001 => 1110010010 => 0100100111 => 0101000111
1101000101 => 1110001010 => 0101000111 => 0011000111
1101000011 => 1110000101 => 1010000111 => 0001100111
1100110001 => 0111000110 => 0110001110 => 1001010110
1100101001 => 0111010010 => 0100101110 => 1101000110
1100100110 => 0111001001 => 1001001110 => 1010100110
1100100101 => 0111001010 => 0101001110 => 1011000110
1100011001 => 0011100110 => 0110011100 => 0101010110
1100010101 => 0011101010 => 0101011100 => 0111000110
1100010010 => 0011100100 => 0010011100 => 0101000110
1100001011 => 0001110101 => 1010111000 => 0011100110
1011111110 => 1100111111 => 1111110011 => 0111111011
1011111101 => 1101111110 => 0111111011 => 1011111011
1011110111 => 1101111011 => 1101111011 => 1110111011
1011110001 => 1100011110 => 0111100011 => 0010111011
1011100101 => 1100111010 => 0101110011 => 0110011011
1011100001 => 1100001110 => 0111000011 => 0001011011
1011011111 => 1101101111 => 1111011011 => 1111101011
1011011001 => 1101100110 => 0110011011 => 1010101011
1011010001 => 1101100010 => 0100011011 => 1001001011
1011001101 => 1100110110 => 0110110011 => 0110101011
1011001001 => 1100110010 => 0100110011 => 0101001011
1011000111 => 1100011011 => 1101100011 => 0011101011
1011000101 => 1100011010 => 0101100011 => 0011001011
1011000001 => 1100000110 => 0110000011 => 0000101011
1010111110 => 1101001111 => 1111001011 => 1011110011
1010110101 => 1101011010 => 0101101011 => 1110010011
1010110001 => 1101000110 => 0110001011 => 1001010011
1010101011 => 1101010101 => 1010101011 => 1111000011
1010101001 => 1101010010 => 0100101011 => 1101000011
1010100110 => 1101001001 => 1001001011 => 1010100011
1010100101 => 1101001010 => 0101001011 => 1011000011
1010011101 => 1100101110 => 0111010011 => 0110110011
1010011010 => 1100101100 => 0011010011 => 0110010011
1010011001 => 1100100110 => 0110010011 => 0101010011
1010010111 => 1100101011 => 1101010011 => 0111100011
1010010110 => 1100101001 => 1001010011 => 0110100011
1010010101 => 1100101010 => 0101010011 => 0111000011
1010010001 => 1100100010 => 0100010011 => 0100100011
1010001110 => 1100010011 => 1100100011 => 0010110011
1010000101 => 1100001010 => 0101000011 => 0001100011
1001111111 => 0110111111 => 1111110110 => 1111111010
1001111001 => 0110011110 => 0111100110 => 1010111010
1001111000 => 0110000111 => 1110000110 => 1000111010
1001110100 => 0110111000 => 0001110110 => 1100011010
1001110001 => 0110001110 => 0111000110 => 1001011010
1001101100 => 0110110001 => 1000110110 => 1100101010
1001101010 => 0110110100 => 0010110110 => 1110001010
1001101001 => 0110110010 => 0100110110 => 1101001010
1001100111 => 0110011011 => 1101100110 => 1011101010
1001100110 => 0110011001 => 1001100110 => 1010101010
1001100101 => 0110011010 => 0101100110 => 1011001010
1001100001 => 0110000110 => 0110000110 => 1000101010
1001011110 => 0110100111 => 1110010110 => 1101110010
1001011010 => 0110101100 => 0011010110 => 1110010010
1001011001 => 0110100110 => 0110010110 => 1101010010
1001010110 => 0110101001 => 1001010110 => 1110100010
1001010101 => 0110101010 => 0101010110 => 1111000010
1001001110 => 0110010011 => 1100100110 => 1010110010
1000111110 => 0011001111 => 1111001100 => 0101111010
1000111100 => 0011000111 => 1110001100 => 0100111010
1000111010 => 0011011100 => 0011101100 => 0110011010
1000110111 => 0011011011 => 1101101100 => 0111101010
1000110110 => 0011011001 => 1001101100 => 0110101010
1000110001 => 0011000110 => 0110001100 => 0100101010
1000101110 => 0011010011 => 1100101100 => 0110110010
1000101011 => 0011010101 => 1010101100 => 0111100010
1000100101 => 0011001010 => 0101001100 => 0101100010
1000011111 => 0001101111 => 1111011000 => 0011111010
1000011110 => 0001100111 => 1110011000 => 0010111010
1000011001 => 0001100110 => 0110011000 => 0010101010
1000010110 => 0001101001 => 1001011000 => 0011010010
1000001110 => 0000110011 => 1100110000 => 0001011010
1000001101 => 0000110110 => 0110110000 => 0001101010
1000000111 => 0000011011 => 1101100000 => 0000111010
1000000100 => 0000011000 => 0001100000 => 0000100010
1000000010 => 0000001100 => 0011000000 => 0000010010
1000000001 => 0000000110 => 0110000000 => 0000001010
1000000000 => 0000000001 => 1000000000 => 0000000010
10000000000 => 00000000001 => 10000000000 => 00000000010
11111111110 => 01111111111 => 11111111110 => 11111111110
100001111100 => 000110001111 => 111100011000 => 001001111010
10100101010 => 11001010100 => 00101010011 => 01110000011
=> => =>
0111111111 => 1011111111 => 1111111101 => 1111111101
0111111101 => 1011111110 => 0111111101 => 1011111101
0111111001 => 1001111110 => 0111111001 => 0101111101
0111110001 => 1000111110 => 0111110001 => 0010111101
0111100001 => 1000011110 => 0111100001 => 0001011101
0111000001 => 1000001110 => 0111000001 => 0000101101
0110000001 => 1000000110 => 0110000001 => 0000010101
0100000001 => 1000000010 => 0100000001 => 0000001001
0000000001 => 0000000010 => 0100000000 => 0000000100
01111111111 => 10111111111 => 11111111101 => 11111111101
01111111101 => 10111111110 => 01111111101 => 10111111101
0111111011 => 1011111101 => 1011111101 => 1101111101
01111111001 => 10011111110 => 01111111001 => 01011111101
0111110101 => 1011111010 => 0101111101 => 1100111101
01111110001 => 10001111110 => 01111110001 => 00101111101
01111100001 => 10000111110 => 01111100001 => 00010111101
0111010001 => 1011100010 => 0100011101 => 1001001101
01111000001 => 10000011110 => 01111000001 => 00001011101
01110000001 => 10000001110 => 01110000001 => 00000101101
0101000001 => 1010000010 => 0100000101 => 1000010001
01100000001 => 10000000110 => 01100000001 => 00000010101
0010000001 => 0100000010 => 0100000010 => 1000001000
01000000001 => 10000000010 => 01000000001 => 00000001001
00000000001 => 00000000010 => 01000000000 => 00000000100
0101010101 => 1010101010 => 0101010101 => 1111000001
0101010011 => 1010100101 => 1010010101 => 1101100001
0101001101 => 1010010110 => 0110100101 => 1011010001
0101001011 => 1010010101 => 1010100101 => 1011100001
0101000111 => 1010001011 => 1101000101 => 1001110001
0100110101 => 1001011010 => 0101101001 => 0111001001
0100110011 => 1001001101 => 1011001001 => 0101101001
0100101101 => 1001010110 => 0110101001 => 0111010001
0100101011 => 1001010101 => 1010101001 => 0111100001
0100100111 => 1001001011 => 1101001001 => 0101110001
0100011101 => 1000101110 => 0111010001 => 0011011001
0100011011 => 1000101101 => 1011010001 => 0011101001
0100010111 => 1000101011 => 1101010001 => 0011110001
0100001111 => 1000010111 => 1110100001 => 0001111001
0011010101 => 0101101010 => 0101011010 => 1111000100
0011010011 => 0101100101 => 1010011010 => 1101100100
0011001101 => 0100110110 => 0110110010 => 1011010100
0011001011 => 0100110101 => 1010110010 => 1011100100
0011000111 => 0100011011 => 1101100010 => 1001110100
0010110101 => 0101011010 => 0101101010 => 1111001000
0010110011 => 0101001101 => 1011001010 => 1101101000
0010101101 => 0101010110 => 0110101010 => 1111010000
0010101011 => 0101010101 => 1010101010 => 1111100000
0010100111 => 0101001011 => 1101001010 => 1101110000
0010011101 => 0100101110 => 0111010010 => 1011011000
0010011011 => 0100101101 => 1011010010 => 1011101000
0010010111 => 0100101011 => 1101010010 => 1011110000
0010001111 => 0100010111 => 1110100010 => 1001111000
0001110101 => 0010111010 => 0101110100 => 0111001100
0001110011 => 0010011101 => 1011100100 => 0101101100
0001101101 => 0010110110 => 0110110100 => 0111010100
0001101011 => 0010110101 => 1010110100 => 0111100100
0001100111 => 0010011011 => 1101100100 => 0101110100
0001011101 => 0010101110 => 0111010100 => 0111011000
0001011011 => 0010101101 => 1011010100 => 0111101000
0001010111 => 0010101011 => 1101010100 => 0111110000
0001001111 => 0010010111 => 1110100100 => 0101111000
0000111101 => 0001011110 => 0111101000 => 0011011100
0000111011 => 0001011101 => 1011101000 => 0011101100
0000110111 => 0001011011 => 1101101000 => 0011110100
0000101111 => 0001010111 => 1110101000 => 0011111000
0000011111 => 0000101111 => 1111010000 => 0001111100
010101010101 => 101010101010 => 010101010101 => 111110000001
010101010011 => 101010100101 => 101001010101 => 111011000001
010101001101 => 101010010110 => 011010010101 => 110110100001
010101001011 => 101010010101 => 101010010101 => 110111000001
010101000111 => 101010001011 => 110100010101 => 110011100001
010100110101 => 101001011010 => 010110100101 => 101110010001
010100110011 => 101001001101 => 101100100101 => 101011010001
010100101101 => 101001010110 => 011010100101 => 101110100001
010100101011 => 101001010101 => 101010100101 => 101111000001
010100100111 => 101001001011 => 110100100101 => 101011100001
010100011101 => 101000101110 => 011101000101 => 100110110001
010100011011 => 101000101101 => 101101000101 => 100111010001
010100010111 => 101000101011 => 110101000101 => 100111100001
010100001111 => 101000010111 => 111010000101 => 100011110001
010011010101 => 100101101010 => 010101101001 => 011110001001
010011010011 => 100101100101 => 101001101001 => 011011001001
010011001101 => 100100110110 => 011011001001 => 010110101001
010011001011 => 100100110101 => 101011001001 => 010111001001
010011000111 => 100100011011 => 110110001001 => 010011101001
010010110101 => 100101011010 => 010110101001 => 011110010001
010010110011 => 100101001101 => 101100101001 => 011011010001
010010101101 => 100101010110 => 011010101001 => 011110100001
010010101011 => 100101010101 => 101010101001 => 011111000001
010010100111 => 100101001011 => 110100101001 => 011011100001
010010011101 => 100100101110 => 011101001001 => 010110110001
010010011011 => 100100101101 => 101101001001 => 010111010001
010010010111 => 100100101011 => 110101001001 => 010111100001
010010001111 => 100100010111 => 111010001001 => 010011110001
010001110101 => 100010111010 => 010111010001 => 001110011001
010001110011 => 100010011101 => 101110010001 => 001011011001
010001101101 => 100010110110 => 011011010001 => 001110101001
010001101011 => 100010110101 => 101011010001 => 001111001001
010001100111 => 100010011011 => 110110010001 => 001011101001
010001011101 => 100010101110 => 011101010001 => 001110110001
010001011011 => 100010101101 => 101101010001 => 001111010001
010001010111 => 100010101011 => 110101010001 => 001111100001
010001001111 => 100010010111 => 111010010001 => 001011110001
010000111101 => 100001011110 => 011110100001 => 000110111001
010000111011 => 100001011101 => 101110100001 => 000111011001
010000110111 => 100001011011 => 110110100001 => 000111101001
010000101111 => 100001010111 => 111010100001 => 000111110001
010000011111 => 100000101111 => 111101000001 => 000011111001
001101010101 => 010110101010 => 010101011010 => 111110000100
001101010011 => 010110100101 => 101001011010 => 111011000100
001101001101 => 010110010110 => 011010011010 => 110110100100
001101001011 => 010110010101 => 101010011010 => 110111000100
001101000111 => 010110001011 => 110100011010 => 110011100100
001100110101 => 010011011010 => 010110110010 => 101110010100
001100110011 => 010011001101 => 101100110010 => 101011010100
001100101101 => 010011010110 => 011010110010 => 101110100100
001100101011 => 010011010101 => 101010110010 => 101111000100
001100100111 => 010011001011 => 110100110010 => 101011100100
001100011101 => 010001101110 => 011101100010 => 100110110100
001100011011 => 010001101101 => 101101100010 => 100111010100
001100010111 => 010001101011 => 110101100010 => 100111100100
001100001111 => 010000110111 => 111011000010 => 100011110100
001011010101 => 010101101010 => 010101101010 => 111110001000
001011010011 => 010101100101 => 101001101010 => 111011001000
001011001101 => 010100110110 => 011011001010 => 110110101000
001011001011 => 010100110101 => 101011001010 => 110111001000
001011000111 => 010100011011 => 110110001010 => 110011101000
001010110101 => 010101011010 => 010110101010 => 111110010000
001010110011 => 010101001101 => 101100101010 => 111011010000
001010101101 => 010101010110 => 011010101010 => 111110100000
001010101011 => 010101010101 => 101010101010 => 111111000000
001010100111 => 010101001011 => 110100101010 => 111011100000
001010011101 => 010100101110 => 011101001010 => 110110110000
001010011011 => 010100101101 => 101101001010 => 110111010000
001010010111 => 010100101011 => 110101001010 => 110111100000
001010001111 => 010100010111 => 111010001010 => 110011110000
001001110101 => 010010111010 => 010111010010 => 101110011000
001001110011 => 010010011101 => 101110010010 => 101011011000
001001101101 => 010010110110 => 011011010010 => 101110101000
001001101011 => 010010110101 => 101011010010 => 101111001000
001001100111 => 010010011011 => 110110010010 => 101011101000
001001011101 => 010010101110 => 011101010010 => 101110110000
001001011011 => 010010101101 => 101101010010 => 101111010000
001001010111 => 010010101011 => 110101010010 => 101111100000
001001001111 => 010010010111 => 111010010010 => 101011110000
001000111101 => 010001011110 => 011110100010 => 100110111000
001000111011 => 010001011101 => 101110100010 => 100111011000
001000110111 => 010001011011 => 110110100010 => 100111101000
001000101111 => 010001010111 => 111010100010 => 100111110000
001000011111 => 010000101111 => 111101000010 => 100011111000
000111010101 => 001011101010 => 010101110100 => 011110001100
000111010011 => 001011100101 => 101001110100 => 011011001100
000111001101 => 001001110110 => 011011100100 => 010110101100
000111001011 => 001001110101 => 101011100100 => 010111001100
000111000111 => 001000111011 => 110111000100 => 010011101100
000110110101 => 001011011010 => 010110110100 => 011110010100
000110110011 => 001011001101 => 101100110100 => 011011010100
000110101101 => 001011010110 => 011010110100 => 011110100100
000110101011 => 001011010101 => 101010110100 => 011111000100
000110100111 => 001011001011 => 110100110100 => 011011100100
000110011101 => 001001101110 => 011101100100 => 010110110100
000110011011 => 001001101101 => 101101100100 => 010111010100
000110010111 => 001001101011 => 110101100100 => 010111100100
000110001111 => 001000110111 => 111011000100 => 010011110100
000101110101 => 001010111010 => 010111010100 => 011110011000
000101110011 => 001010011101 => 101110010100 => 011011011000
000101101101 => 001010110110 => 011011010100 => 011110101000
000101101011 => 001010110101 => 101011010100 => 011111001000
000101100111 => 001010011011 => 110110010100 => 011011101000
000101011101 => 001010101110 => 011101010100 => 011110110000
000101011011 => 001010101101 => 101101010100 => 011111010000
000101010111 => 001010101011 => 110101010100 => 011111100000
000101001111 => 001010010111 => 111010010100 => 011011110000
000100111101 => 001001011110 => 011110100100 => 010110111000
000100111011 => 001001011101 => 101110100100 => 010111011000
000100110111 => 001001011011 => 110110100100 => 010111101000
000100101111 => 001001010111 => 111010100100 => 010111110000
000100011111 => 001000101111 => 111101000100 => 010011111000
000011110101 => 000101111010 => 010111101000 => 001110011100
000011110011 => 000100111101 => 101111001000 => 001011011100
000011101101 => 000101110110 => 011011101000 => 001110101100
000011101011 => 000101110101 => 101011101000 => 001111001100
000011100111 => 000100111011 => 110111001000 => 001011101100
000011011101 => 000101101110 => 011101101000 => 001110110100
000011011011 => 000101101101 => 101101101000 => 001111010100
000011010111 => 000101101011 => 110101101000 => 001111100100
000011001111 => 000100110111 => 111011001000 => 001011110100
000010111101 => 000101011110 => 011110101000 => 001110111000
000010111011 => 000101011101 => 101110101000 => 001111011000
000010110111 => 000101011011 => 110110101000 => 001111101000
000010101111 => 000101010111 => 111010101000 => 001111110000
000010011111 => 000100101111 => 111101001000 => 001011111000
000001111101 => 000010111110 => 011111010000 => 000110111100
000001111011 => 000010111101 => 101111010000 => 000111011100
000001110111 => 000010111011 => 110111010000 => 000111101100
000001101111 => 000010110111 => 111011010000 => 000111110100
000001011111 => 000010101111 => 111101010000 => 000111111000
000000111111 => 000001011111 => 111110100000 => 000011111100
11010101010 => 11101010100 => 00101010111 => 11100000111
10101010100 => 11010101000 => 00010101011 => 11100000011
111111111111 => 111111111111 => 111111111111 => 111111111111
111111111001 => 011111111110 => 011111111110 => 101111111110
111111100111 => 011111111011 => 110111111110 => 111011111110
111111100001 => 000111111110 => 011111111000 => 001011111110
111111101101 => 111111110110 => 011011111111 => 101011111111
111110011111 => 011111101111 => 111101111110 => 111110111110
111110011001 => 011111100110 => 011001111110 => 101010111110
111110000111 => 000111111011 => 110111111000 => 001110111110
111110000001 => 000001111110 => 011111100000 => 000010111110
111110110111 => 111111011011 => 110110111111 => 111010111111
111110110001 => 111111000110 => 011000111111 => 001010111111
111110111101 => 111111011110 => 011110111111 => 101110111111
111001111111 => 011110111111 => 111111011110 => 111111101110
111001111001 => 011110011110 => 011110011110 => 101011101110
111001100111 => 011110011011 => 110110011110 => 101110101110
111001100001 => 011110000110 => 011000011110 => 100010101110
111000011111 => 000111101111 => 111101111000 => 001111101110
111000011001 => 000111100110 => 011001111000 => 001010101110
111000000111 => 000001111011 => 110111100000 => 000011101110
111000000001 => 000000011110 => 011110000000 => 000000101110
111000001101 => 000011110110 => 011011110000 => 000110101110
111000110111 => 001111011011 => 110110111100 => 011110101110
111000110001 => 001111000110 => 011000111100 => 010010101110
111000111101 => 001111011110 => 011110111100 => 011011101110
111000100101 => 001111001010 => 010100111100 => 010110001110
111011011111 => 111101101111 => 111101101111 => 111110101111
111011011001 => 111101100110 => 011001101111 => 101010101111
111011000111 => 111100011011 => 110110001111 => 001110101111
111011000001 => 111100000110 => 011000001111 => 000010101111
111011001101 => 111100110110 => 011011001111 => 011010101111
111011110111 => 111101111011 => 110111101111 => 111011101111
111011110001 => 111100011110 => 011110001111 => 001011101111
111011111101 => 111101111110 => 011111101111 => 101111101111
111010010001 => 111100100010 => 010001001111 => 010010001111
111010000101 => 111100001010 => 010100001111 => 000110001111
111010110101 => 111101011010 => 010110101111 => 111001001111
100111111111 => 011011111111 => 111111110110 => 111111111010
100111111001 => 011001111110 => 011111100110 => 101011111010
100111100111 => 011001111011 => 110111100110 => 101110111010
100111100001 => 011000011110 => 011110000110 => 100010111010
100110011111 => 011001101111 => 111101100110 => 101111101010
100110011001 => 011001100110 => 011001100110 => 101010101010
100110000111 => 011000011011 => 110110000110 => 100011101010
100110000001 => 011000000110 => 011000000110 => 100000101010
100110001101 => 011000110110 => 011011000110 => 100110101010
100110110111 => 011011011011 => 110110110110 => 111110101010
100110110001 => 011011000110 => 011000110110 => 110010101010
100110100101 => 011011001010 => 010100110110 => 110110001010
100001111111 => 000110111111 => 111111011000 => 001111111010
100001111001 => 000110011110 => 011110011000 => 001010111010
100001100111 => 000110011011 => 110110011000 => 001011101010
100001100001 => 000110000110 => 011000011000 => 001000101010
100001101101 => 000110110110 => 011011011000 => 001110101010
100000011111 => 000001101111 => 111101100000 => 000011111010
100000011001 => 000001100110 => 011001100000 => 000010101010
100000000111 => 000000011011 => 110110000000 => 000000111010
100000000001 => 000000000110 => 011000000000 => 000000001010
100000001101 => 000000110110 => 011011000000 => 000001101010
100000110111 => 000011011011 => 110110110000 => 000111101010
100000110001 => 000011000110 => 011000110000 => 000100101010
100000111101 => 000011011110 => 011110110000 => 000110111010
100011011111 => 001101101111 => 111101101100 => 011111101010
100011011001 => 001101100110 => 011001101100 => 011010101010
100011000111 => 001100011011 => 110110001100 => 010011101010
100011000001 => 001100000110 => 011000001100 => 010000101010
100011001101 => 001100110110 => 011011001100 => 010110101010
100011110111 => 001101111011 => 110111101100 => 011110111010
100011110001 => 001100011110 => 011110001100 => 010010111010
100011100101 => 001100111010 => 010111001100 => 010110011010
100010010111 => 001100101011 => 110101001100 => 010111100010
100010011101 => 001100101110 => 011101001100 => 010110110010
100010110101 => 001101011010 => 010110101100 => 011110010010
101101111111 => 110110111111 => 111111011011 => 111111101011
101101111001 => 110110011110 => 011110011011 => 101011101011
101101100111 => 110110011011 => 110110011011 => 101110101011
101101100001 => 110110000110 => 011000011011 => 100010101011
101101101101 => 110110110110 => 011011011011 => 111010101011
101100011111 => 110001101111 => 111101100011 => 001111101011
101100011001 => 110001100110 => 011001100011 => 001010101011
101100000111 => 110000011011 => 110110000011 => 000011101011
101100000001 => 110000000110 => 011000000011 => 000000101011
101100001101 => 110000110110 => 011011000011 => 000110101011
101100110111 => 110011011011 => 110110110011 => 011110101011
101100110001 => 110011000110 => 011000110011 => 010010101011
101100111101 => 110011011110 => 011110110011 => 011011101011
101100100101 => 110011001010 => 010100110011 => 010110001011
101111011111 => 110111101111 => 111101111011 => 111110111011
101111011001 => 110111100110 => 011001111011 => 101010111011
101111000111 => 110001111011 => 110111100011 => 001110111011
101111000001 => 110000011110 => 011110000011 => 000010111011
101111001101 => 110011110110 => 011011110011 => 011010111011
101111110111 => 110111111011 => 110111111011 => 111011111011
101111110001 => 110001111110 => 011111100011 => 001011111011
101111111101 => 110111111110 => 011111111011 => 101111111011
101110010001 => 110011100010 => 010001110011 => 010010011011
101110110101 => 110111011010 => 010110111011 => 111001011011
101001011001 => 110010100110 => 011001010011 => 011010100011
101001000111 => 110010001011 => 110100010011 => 010011100011
101001001101 => 110010010110 => 011010010011 => 010110100011
101001110001 => 110010001110 => 011100010011 => 010010110011
101000010111 => 110000101011 => 110101000011 => 000111100011
101000011101 => 110000101110 => 011101000011 => 000110110011
101000110101 => 110001011010 => 010110100011 => 001110010011
101011010111 => 110101101011 => 110101101011 => 111110010011
101011010001 => 110101100010 => 010001101011 => 110010010011
101011011101 => 110101101110 => 011101101011 => 111011010011
101011000101 => 110100011010 => 010110001011 => 100110010011
101011110101 => 110101111010 => 010111101011 => 111001110011
101010010101 => 110100101010 => 010101001011 => 101110000011
0000000000 => 0000000000 => 0000000000 => 0000000000
0000000110 => 0000001001 => 1001000000 => 0000010100
0000011000 => 0000100001 => 1000010000 => 0001000100
0000011110 => 0000100111 => 1110010000 => 0001011100
0000010010 => 0000100100 => 0010010000 => 0001010000
0001100000 => 0010000001 => 1000000100 => 0100000100
0001100110 => 0010011001 => 1001100100 => 0101010100
0001111000 => 0010000111 => 1110000100 => 0100011100
0001111110 => 0010011111 => 1111100100 => 0101111100
0001110010 => 0010011100 => 0011100100 => 0101001100
0001001000 => 0010010000 => 0000100100 => 0101000000
0001001110 => 0010010011 => 1100100100 => 0101011000
0001000010 => 0010000100 => 0010000100 => 0100010000
0001011010 => 0010101100 => 0011010100 => 0111001000
0110000000 => 1000000001 => 1000000001 => 0000000101
0110000110 => 1000011001 => 1001100001 => 0001010101
0110011000 => 1001100001 => 1000011001 => 0100010101
0110011110 => 1001100111 => 1110011001 => 0101110101
0110010010 => 1001100100 => 0010011001 => 0101000101
0111100000 => 1000000111 => 1110000001 => 0000011101
0111100110 => 1001111001 => 1001111001 => 0101011101
0111111000 => 1000011111 => 1111100001 => 0001111101
0111111110 => 1001111111 => 1111111001 => 0111111101
0111110010 => 1001111100 => 0011111001 => 0100111101
0111001000 => 1001110000 => 0000111001 => 0100001101
0111001110 => 1001110011 => 1100111001 => 0101101101
0111000010 => 1000011100 => 0011100001 => 0001001101
0111011010 => 1011101100 => 0011011101 => 1100101101
0100100000 => 1001000000 => 0000001001 => 0100000001
0100111110 => 1001001111 => 1111001001 => 0101111001
0100110010 => 1001001100 => 0011001001 => 0101001001
0100001000 => 1000010000 => 0000100001 => 0001000001
0100001110 => 1000010011 => 1100100001 => 0001011001
0100000010 => 1000000100 => 0010000001 => 0000010001
0101101000 => 1010110000 => 0000110101 => 1100001001
0101101110 => 1010110011 => 1100110101 => 1101101001
0101111010 => 1010111100 => 0011110101 => 1100111001
0101001010 => 1010010100 => 0010100101 => 1011000001
000000000000 => 000000000000 => 000000000000 => 000000000000
000000000110 => 000000001001 => 100100000000 => 000000010100
000000011000 => 000000100001 => 100001000000 => 000001000100
000000011110 => 000000100111 => 111001000000 => 000001011100
000000010010 => 000000100100 => 001001000000 => 000001010000
000001100000 => 000010000001 => 100000010000 => 000100000100
000001100110 => 000010011001 => 100110010000 => 000101010100
000001111000 => 000010000111 => 111000010000 => 000100011100
000001111110 => 000010011111 => 111110010000 => 000101111100
000001110010 => 000010011100 => 001110010000 => 000101001100
000001001000 => 000010010000 => 000010010000 => 000101000000
000001001110 => 000010010011 => 110010010000 => 000101011000
000001000010 => 000010000100 => 001000010000 => 000100010000
000110000000 => 001000000001 => 100000000100 => 010000000100
000110000110 => 001000011001 => 100110000100 => 010001010100
000110011000 => 001001100001 => 100001100100 => 010100010100
000110011110 => 001001100111 => 111001100100 => 010101110100
000110010010 => 001001100100 => 001001100100 => 010101000100
000111100000 => 001000000111 => 111000000100 => 010000011100
000111100110 => 001001111001 => 100111100100 => 010101011100
000111111000 => 001000011111 => 111110000100 => 010001111100
000111111110 => 001001111111 => 111111100100 => 010111111100
000111110010 => 001001111100 => 001111100100 => 010100111100
000111001000 => 001001110000 => 000011100100 => 010100001100
000111001110 => 001001110011 => 110011100100 => 010101101100
000111000010 => 001000011100 => 001110000100 => 010001001100
000111011010 => 001011101100 => 001101110100 => 011100101100
000100100000 => 001001000000 => 000000100100 => 010100000000
000100100110 => 001001001001 => 100100100100 => 010101010000
000100111000 => 001001000011 => 110000100100 => 010100011000
000100111110 => 001001001111 => 111100100100 => 010101111000
000100110010 => 001001001100 => 001100100100 => 010101001000
000100001000 => 001000010000 => 000010000100 => 010001000000
000100001110 => 001000010011 => 110010000100 => 010001011000
000100000010 => 001000000100 => 001000000100 => 010000010000
000101101110 => 001010110011 => 110011010100 => 011101101000
000101111010 => 001010111100 => 001111010100 => 011100111000
000101001010 => 001010010100 => 001010010100 => 011011000000
011000000000 => 100000000001 => 100000000001 => 000000000101
011000000110 => 100000011001 => 100110000001 => 000001010101
011000011000 => 100001100001 => 100001100001 => 000100010101
011000011110 => 100001100111 => 111001100001 => 000101110101
011000010010 => 100001100100 => 001001100001 => 000101000101
011001100000 => 100110000001 => 100000011001 => 010000010101
011001100110 => 100110011001 => 100110011001 => 010101010101
011001111000 => 100110000111 => 111000011001 => 010001110101
011001111110 => 100110011111 => 111110011001 => 010111110101
011001110010 => 100110011100 => 001110011001 => 010100110101
011001001000 => 100110010000 => 000010011001 => 010100000101
011001001110 => 100110010011 => 110010011001 => 010101100101
011001000010 => 100110000100 => 001000011001 => 010001000101
011110000000 => 100000000111 => 111000000001 => 000000011101
011110000110 => 100001111001 => 100111100001 => 000101011101
011110011000 => 100111100001 => 100001111001 => 010001011101
011110011110 => 100111100111 => 111001111001 => 010111011101
011110010010 => 100111100100 => 001001111001 => 010100011101
011111100000 => 100000011111 => 111110000001 => 000001111101
011111100110 => 100111111001 => 100111111001 => 010101111101
011111111000 => 100001111111 => 111111100001 => 000111111101
011111111110 => 100111111111 => 111111111001 => 011111111101
011111110010 => 100111111100 => 001111111001 => 010011111101
011111001000 => 100111110000 => 000011111001 => 010000111101
011111000010 => 100001111100 => 001111100001 => 000100111101
011100100000 => 100111000000 => 000000111001 => 010000001101
011100100110 => 100111001001 => 100100111001 => 010101001101
011100111000 => 100111000011 => 110000111001 => 010001101101
011100111110 => 100111001111 => 111100111001 => 010111101101
011100110010 => 100111001100 => 001100111001 => 010100101101
011100001000 => 100001110000 => 000011100001 => 000100001101
011100001110 => 100001110011 => 110011100001 => 000101101101
011100000010 => 100000011100 => 001110000001 => 000001001101
011100011010 => 100011101100 => 001101110001 => 001100101101
011101101000 => 101110110000 => 000011011101 => 110000101101
011101100010 => 101110001100 => 001100011101 => 100100101101
011101001010 => 101110010100 => 001010011101 => 101100001101
010010000000 => 100100000000 => 000000001001 => 010000000001
010010011110 => 100100100111 => 111001001001 => 010101110001
010010010010 => 100100100100 => 001001001001 => 010101000001
010011100110 => 100100111001 => 100111001001 => 010101011001
010011111000 => 100100001111 => 111100001001 => 010001111001
010011111110 => 100100111111 => 111111001001 => 010111111001
010011110010 => 100100111100 => 001111001001 => 010100111001
010011001000 => 100100110000 => 000011001001 => 010100001001
010011001110 => 100100110011 => 110011001001 => 010101101001
010011000010 => 100100001100 => 001100001001 => 010001001001
010011011010 => 100101101100 => 001101101001 => 011100101001
010000100000 => 100001000000 => 000000100001 => 000100000001
010000100110 => 100001001001 => 100100100001 => 000101010001
010000111000 => 100001000011 => 110000100001 => 000100011001
010000111110 => 100001001111 => 111100100001 => 000101111001
010000110010 => 100001001100 => 001100100001 => 000101001001
010000001000 => 100000010000 => 000010000001 => 000001000001
010000000010 => 100000000100 => 001000000001 => 000000010001
010001101110 => 100010110011 => 110011010001 => 001101101001
010001001010 => 100010010100 => 001010010001 => 001011000001
010110100110 => 101011001001 => 100100110101 => 110101001001
010110111000 => 101011000011 => 110000110101 => 110001101001
010110110010 => 101011001100 => 001100110101 => 110100101001
010110001110 => 101000110011 => 110011000101 => 100101101001
010111101000 => 101011110000 => 000011110101 => 110000111001
010111111010 => 101011111100 => 001111110101 => 110011111001
010111001010 => 101001110100 => 001011100101 => 101100011001
010100101000 => 101001010000 => 000010100101 => 101100000001
010100101110 => 101001010011 => 110010100101 => 101101100001
010100100010 => 101001000100 => 001000100101 => 101001000001
010100111010 => 101001011100 => 001110100101 => 101100110001
010100001010 => 101000010100 => 001010000101 => 100011000001
010101101010 => 101010110100 => 001011010101 => 111100010001
0010101010 => 0101010100 => 0010101010 => 1111000000
0010101000 => 0101010000 => 0000101010 => 1110000000
0010101100 => 0101010001 => 1000101010 => 1110010000
0010100100 => 0101001000 => 0001001010 => 1101000000
0010110100 => 0101011000 => 0001101010 => 1110001000
0010010100 => 0100101000 => 0001010010 => 1011000000
0011010100 => 0101101000 => 0001011010 => 1110000100
0001010100 => 0010101000 => 0001010100 => 0111000000
0101010100 => 1010101000 => 0001010101 => 1110000001
00101010101 => 01010101010 => 01010101010 => 11111000000
00101010111 => 01010101011 => 11010101010 => 11111100000
0010101110 => 0101010011 => 1100101010 => 1110110000
00101010011 => 01010100101 => 10100101010 => 11101100000
0010100000 => 0101000000 => 0000001010 => 1100000000
00101011011 => 01010101101 => 10110101010 => 11111010000
0010111100 => 0101000111 => 1110001010 => 1100111000
00101001011 => 01010010101 => 10101001010 => 11011100000
0010000100 => 0100001000 => 0001000010 => 1000100000
00101101011 => 01010110101 => 10101101010 => 11111001000
0011110100 => 0101111000 => 0001111010 => 1100011100
00100101011 => 01001010101 => 10101010010 => 10111100000
0000010100 => 0000101000 => 0001010000 => 0001100000
00110101011 => 01011010101 => 10101011010 => 11111000100
0111010100 => 1011101000 => 0001011101 => 1100001101
00010101011 => 00101010101 => 10101010100 => 01111100000
01010101011 => 10101010101 => 10101010101 => 11111000001
0000000010 => 0000000100 => 0010000000 => 0000001000
0000111110 => 0001001111 => 1111001000 => 0010111100
0011111110 => 0100111111 => 1111110010 => 1011111100
00000000000 => 00000000000 => 00000000000 => 00000000000
00000000110 => 00000001001 => 10010000000 => 00000010100
0000001010 => 0000010100 => 0010100000 => 0000110000
0001011110 => 0010100111 => 1110010100 => 0110111000
0010111110 => 0101001111 => 1111001010 => 1101111000
00111111110 => 01001111111 => 11111110010 => 10111111100
01111111110 => 10011111111 => 11111111001 => 01111111101
0010110010 => 0101001100 => 0011001010 => 1101001000
0010111000 => 0101000011 => 1100001010 => 1100011000
0011001010 => 0100110100 => 0010110010 => 1011000100
0011001100 => 0100110001 => 1000110010 => 1010010100
0011010010 => 0101100100 => 0010011010 => 1101000100
0011100100 => 0100111000 => 0001110010 => 1010001100
0011101000 => 0101110000 => 0000111010 => 1100001100
0011110000 => 0100000111 => 1110000010 => 1000011100
0100110100 => 1001011000 => 0001101001 => 0110001001
0101001100 => 1010010001 => 1000100101 => 1010010001
0101010010 => 1010100100 => 0010010101 => 1101000001
0101011000 => 1010100001 => 1000010101 => 1100010001
0110001010 => 1000110100 => 0010110001 => 0011000101
0110001100 => 1000110001 => 1000110001 => 0010010101
0110100010 => 1011000100 => 0010001101 => 1001000101
0110101000 => 1011010000 => 0000101101 => 1100000101
0110110000 => 1011000001 => 1000001101 => 1000010101
0111010000 => 1011100000 => 0000011101 => 1000001101
001010101010 => 010101010100 => 001010101010 => 111110000000
001010110010 => 010101001100 => 001100101010 => 111010010000
001010110100 => 010101011000 => 000110101010 => 111100010000
001011001010 => 010100110100 => 001011001010 => 110110001000
001011010010 => 010101100100 => 001001101010 => 111010001000
001011010100 => 010101101000 => 000101101010 => 111100001000
001011100100 => 010100111000 => 000111001010 => 110100011000
001011101000 => 010101110000 => 000011101010 => 111000011000
001100101010 => 010011010100 => 001010110010 => 101110000100
001100110010 => 010011001100 => 001100110010 => 101010010100
001100110100 => 010011011000 => 000110110010 => 101100010100
001101001010 => 010110010100 => 001010011010 => 110110000100
001101010010 => 010110100100 => 001001011010 => 111010000100
001101010100 => 010110101000 => 000101011010 => 111100000100
001101100010 => 010110001100 => 001100011010 => 110010010100
001101100100 => 010110011000 => 000110011010 => 110100010100
001101101000 => 010110110000 => 000011011010 => 111000010100
001110010010 => 010011100100 => 001001110010 => 101010001100
001110010100 => 010011101000 => 000101110010 => 101100001100
001110100010 => 010111000100 => 001000111010 => 110010001100
001110100100 => 010111001000 => 000100111010 => 110100001100
001110101000 => 010111010000 => 000010111010 => 111000001100
001111001000 => 010011110000 => 000011110010 => 101000011100
001111010000 => 010111100000 => 000001111010 => 110000011100
010100110010 => 101001001100 => 001100100101 => 101010010001
010100110100 => 101001011000 => 000110100101 => 101100010001
010101001010 => 101010010100 => 001010010101 => 110110000001
010110001010 => 101000110100 => 001011000101 => 100110001001
010110010010 => 101001100100 => 001001100101 => 101010001001
010110100010 => 101011000100 => 001000110101 => 110010001001
010110101000 => 101011010000 => 000010110101 => 111000001001
010111000010 => 101000011100 => 001110000101 => 100010011001
010111001000 => 101001110000 => 000011100101 => 101000011001
011000110010 => 100011001100 => 001100110001 => 001010010101
011000110100 => 100011011000 => 000110110001 => 001100010101
011001010010 => 100110100100 => 001001011001 => 011010000101
011001100010 => 100110001100 => 001100011001 => 010010010101
011001100100 => 100110011000 => 000110011001 => 010100010101
011001101000 => 100110110000 => 000011011001 => 011000010101
011010010010 => 101100100100 => 001001001101 => 101010000101
011011000010 => 101100001100 => 001100001101 => 100010010101
011011000100 => 101100011000 => 000110001101 => 100100010101
011011001000 => 101100110000 => 000011001101 => 101000010101
011011010000 => 101101100000 => 000001101101 => 110000010101
011100010010 => 100011100100 => 001001110001 => 001010001101
011101000010 => 101110000100 => 001000011101 => 100010001101
011101001000 => 101110010000 => 000010011101 => 101000001101
011110000010 => 100000111100 => 001111000001 => 000010011101
011110000100 => 100001111000 => 000111100001 => 000100011101
011110001000 => 100011110000 => 000011110001 => 001000011101
011110010000 => 100111100000 => 000001111001 => 010000011101
011110100000 => 101111000000 => 000000111101 => 100000011101
10101010101 => 11010101010 => 01010101011 => 11110000011
10101010010 => 11010100100 => 00100101011 => 11010000011
10101001010 => 11010010100 => 00101001011 => 10110000011
10101000100 => 11010001000 => 00010001011 => 10010000011
10100010001 => 11000100010 => 01000100011 => 00100100011
01001010101 => 10010101010 => 01010101001 => 01111000001
01001010010 => 10010100100 => 00100101001 => 01101000001
01001001001 => 10010010010 => 01001001001 => 01010100001
01001001010 => 10010010100 => 00101001001 => 01011000001
01001000100 => 10010001000 => 00010001001 => 01001000001
01000100101 => 10001001010 => 01010010001 => 00101100001
01000100010 => 10001000100 => 00100010001 => 00100100001
01000101001 => 10001010010 => 01001010001 => 00110100001
01000101010 => 10001010100 => 00101010001 => 00111000001
01000100100 => 10001001000 => 00010010001 => 00101000001
01000010001 => 10000100010 => 01000100001 => 00010010001
01000010010 => 10000100100 => 00100100001 => 00010100001
01000010100 => 10000101000 => 00010100001 => 00011000001
01000001000 => 10000010000 => 00001000001 => 00001000001
01010010101 => 10100101010 => 01010100101 => 10111000001
01010010010 => 10100100100 => 00100100101 => 10101000001
01010001001 => 10100010010 => 01001000101 => 10010100001
01010001010 => 10100010100 => 00101000101 => 10011000001
01010000100 => 10100001000 => 00010000101 => 10001000001
01010100101 => 10101001010 => 01010010101 => 11011000001
01010100010 => 10101000100 => 00100010101 => 11001000001
01010101001 => 10101010010 => 01001010101 => 11101000001
01010101010 => 10101010100 => 00101010101 => 11110000001
01010100100 => 10101001000 => 00010010101 => 11010000001
01010010001 => 10100100010 => 01000100101 => 10100100001
01010010100 => 10100101000 => 00010100101 => 10110000001
01001000101 => 10010001010 => 01010001001 => 01001100001
01001000010 => 10010000100 => 00100001001 => 01000100001
01001010001 => 10010100010 => 01000101001 => 01100100001
01001010100 => 10010101000 => 00010101001 => 01110000001
01000100001 => 10001000010 => 01000010001 => 00100010001
00100010101 => 01000101010 => 01010100010 => 10011100000
00100010010 => 01000100100 => 00100100010 => 10010100000
00100001001 => 01000010010 => 01001000010 => 10001010000
00100001010 => 01000010100 => 00101000010 => 10001100000
00100000100 => 01000001000 => 00010000010 => 10000100000
00100100101 => 01001001010 => 01010010010 => 10101100000
00100100010 => 01001000100 => 00100010010 => 10100100000
00100101001 => 01001010010 => 01001010010 => 10110100000
00100101010 => 01001010100 => 00101010010 => 10111000000
00100100100 => 01001001000 => 00010010010 => 10101000000
00100010001 => 01000100010 => 01000100010 => 10010010000
00100010100 => 01000101000 => 00010100010 => 10011000000
00100001000 => 01000010000 => 00001000010 => 10001000000
00101000101 => 01010001010 => 01010001010 => 11001100000
00101000010 => 01010000100 => 00100001010 => 11000100000
00101001001 => 01010010010 => 01001001010 => 11010100000
00101001010 => 01010010100 => 00101001010 => 11011000000
00101000100 => 01010001000 => 00010001010 => 11001000000
00101010001 => 01010100010 => 01000101010 => 11100100000
00101010010 => 01010100100 => 00100101010 => 11101000000
00101010100 => 01010101000 => 00010101010 => 11110000000
00100100001 => 01001000010 => 01000010010 => 10100010000
00100010000 => 01000100000 => 00000100010 => 10010000000
00010000101 => 00100001010 => 01010000100 => 01000110000
00010000010 => 00100000100 => 00100000100 => 01000010000
00010001001 => 00100010010 => 01001000100 => 01001010000
00010001010 => 00100010100 => 00101000100 => 01001100000
00010000100 => 00100001000 => 00010000100 => 01000100000
00010010001 => 00100100010 => 01000100100 => 01010010000
00010010010 => 00100100100 => 00100100100 => 01010100000
00010010100 => 00100101000 => 00010100100 => 01011000000
00010001000 => 00100010000 => 00001000100 => 01001000000
00010100001 => 00101000010 => 01000010100 => 01100010000
00010100010 => 00101000100 => 00100010100 => 01100100000
00010100100 => 00101001000 => 00010010100 => 01101000000
00001000001 => 00010000010 => 01000001000 => 00100001000
00001000010 => 00010000100 => 00100001000 => 00100010000
00001000100 => 00010001000 => 00010001000 => 00100100000
00001001000 => 00010010000 => 00001001000 => 00101000000
101010101010101010 => 110101010101010100 => 001010101010101011 => 111111100000000011
101010101010110100 => 110101010101011000 => 000110101010101011 => 111111000100000011
10101010101010101010 => 11010101010101010100 => 00101010101010101011 => 11111111000000000011
0100000000 => 1000000000 => 0000000001 => 0000000001
0100000011 => 1000000101 => 1010000001 => 0000011001
0100000111 => 1000001011 => 1101000001 => 0000111001
0100011111 => 1000101111 => 1111010001 => 0011111001
0100111111 => 1001011111 => 1111101001 => 0111111001
0101111111 => 1010111111 => 1111110101 => 1111111001
01000000000 => 10000000000 => 00000000001 => 00000000001
0100000101 => 1000001010 => 0101000001 => 0000110001
0100101111 => 1001010111 => 1110101001 => 0111110001
0101011111 => 1010101111 => 1111010101 => 1111110001
0110111111 => 1011011111 => 1111101101 => 1111110101
0101010110 => 1010101001 => 1001010101 => 1110100001
0101011001 => 1010100110 => 0110010101 => 1101010001
0101011010 => 1010101100 => 0011010101 => 1110010001
0101011100 => 1010100011 => 1100010101 => 1100110001
0101100101 => 1010011010 => 0101100101 => 1011001001
0101100110 => 1010011001 => 1001100101 => 1010101001
0101101001 => 1010110010 => 0100110101 => 1101001001
0101101010 => 1010110100 => 0010110101 => 1110001001
0101101100 => 1010110001 => 1000110101 => 1100101001
0101110001 => 1010001110 => 0111000101 => 1001011001
0101110010 => 1010011100 => 0011100101 => 1010011001
0101110100 => 1010111000 => 0001110101 => 1100011001
0101111000 => 1010000111 => 1110000101 => 1000111001
0110010101 => 1001101010 => 0101011001 => 0111000101
0110010110 => 1001101001 => 1001011001 => 0110100101
0110011001 => 1001100110 => 0110011001 => 0101010101
0110011010 => 1001101100 => 0011011001 => 0110010101
0110011100 => 1001100011 => 1100011001 => 0100110101
0110100101 => 1011001010 => 0101001101 => 1011000101
0110100110 => 1011001001 => 1001001101 => 1010100101
0110101001 => 1011010010 => 0100101101 => 1101000101
0110101010 => 1011010100 => 0010101101 => 1110000101
0110101100 => 1011010001 => 1000101101 => 1100100101
0110110001 => 1011000110 => 0110001101 => 1001010101
0110110010 => 1011001100 => 0011001101 => 1010010101
0110110100 => 1011011000 => 0001101101 => 1100010101
0110111000 => 1011000011 => 1100001101 => 1000110101
0111000101 => 1000111010 => 0101110001 => 0011001101
0111000110 => 1000111001 => 1001110001 => 0010101101
0111001001 => 1001110010 => 0100111001 => 0101001101
0111001010 => 1001110100 => 0010111001 => 0110001101
0111001100 => 1001110001 => 1000111001 => 0100101101
0111010010 => 1011100100 => 0010011101 => 1010001101
0111011000 => 1011100001 => 1000011101 => 1000101101
0111100010 => 1000111100 => 0011110001 => 0010011101
0111100100 => 1001111000 => 0001111001 => 0100011101
0111101000 => 1011110000 => 0000111101 => 1000011101
0111110000 => 1000001111 => 1111000001 => 0000111101
010101010110 => 101010101001 => 100101010101 => 111101000001
010101011001 => 101010100110 => 011001010101 => 111010100001
010101011010 => 101010101100 => 001101010101 => 111100100001
010101100101 => 101010011010 => 010110010101 => 110110010001
010101101001 => 101010110010 => 010011010101 => 111010010001
010101101100 => 101010110001 => 100011010101 => 111001010001
010101110001 => 101010001110 => 011100010101 => 110010110001
010101110100 => 101010111000 => 000111010101 => 111000110001
010101111000 => 101010000111 => 111000010101 => 110001110001
010110010110 => 101001101001 => 100101100101 => 101101001001
010110011001 => 101001100110 => 011001100101 => 101010101001
010110011100 => 101001100011 => 110001100101 => 101001101001
010110100101 => 101011001010 => 010100110101 => 110110001001
010110101001 => 101011010010 => 010010110101 => 111010001001
010110101010 => 101011010100 => 001010110101 => 111100001001
010110101100 => 101011010001 => 100010110101 => 111001001001
010110110001 => 101011000110 => 011000110101 => 110010101001
010110110100 => 101011011000 => 000110110101 => 111000101001
010111000101 => 101000111010 => 010111000101 => 100110011001
010111000110 => 101000111001 => 100111000101 => 100101011001
010111001100 => 101001110001 => 100011100101 => 101001011001
010111010001 => 101011100010 => 010001110101 => 110010011001
010111010010 => 101011100100 => 001001110101 => 110100011001
010111010100 => 101011101000 => 000101110101 => 111000011001
010111011000 => 101011100001 => 100001110101 => 110001011001
010111100001 => 101000011110 => 011110000101 => 100010111001
010111100100 => 101001111000 => 000111100101 => 101000111001
010111110000 => 101000001111 => 111100000101 => 100001111001
011001010101 => 100110101010 => 010101011001 => 011110000101
011001010110 => 100110101001 => 100101011001 => 011101000101
011001011001 => 100110100110 => 011001011001 => 011010100101
011001011100 => 100110100011 => 110001011001 => 011001100101
011001100101 => 100110011010 => 010110011001 => 010110010101
011001101001 => 100110110010 => 010011011001 => 011010010101
011001101010 => 100110110100 => 001011011001 => 011100010101
011001101100 => 100110110001 => 100011011001 => 011001010101
011001110001 => 100110001110 => 011100011001 => 010010110101
011001110100 => 100110111000 => 000111011001 => 011000110101
011010010101 => 101100101010 => 010101001101 => 101110000101
011010011010 => 101100101100 => 001101001101 => 101100100101
011010011100 => 101100100011 => 110001001101 => 101001100101
011010100101 => 101101001010 => 010100101101 => 110110000101
011010100110 => 101101001001 => 100100101101 => 110101000101
011010101001 => 101101010010 => 010010101101 => 111010000101
011010101010 => 101101010100 => 001010101101 => 111100000101
011010101100 => 101101010001 => 100010101101 => 111001000101
011010110001 => 101101000110 => 011000101101 => 110010100101
011010110010 => 101101001100 => 001100101101 => 110100100101
011010110100 => 101101011000 => 000110101101 => 111000100101
011010111000 => 101101000011 => 110000101101 => 110001100101
011011000110 => 101100011001 => 100110001101 => 100101010101
011011001001 => 101100110010 => 010011001101 => 101010010101
011011001010 => 101100110100 => 001011001101 => 101100010101
011011001100 => 101100110001 => 100011001101 => 101001010101
011011010001 => 101101100010 => 010001101101 => 110010010101
011011010010 => 101101100100 => 001001101101 => 110100010101
011011010100 => 101101101000 => 000101101101 => 111000010101
011011011000 => 101101100001 => 100001101101 => 110001010101
011011100010 => 101100011100 => 001110001101 => 100100110101
011011100100 => 101100111000 => 000111001101 => 101000110101
011011101000 => 101101110000 => 000011101101 => 110000110101
011011110000 => 101100000111 => 111000001101 => 100001110101
011100010110 => 100011101001 => 100101110001 => 001101001101
011100011001 => 100011100110 => 011001110001 => 001010101101
011100011100 => 100011100011 => 110001110001 => 001001101101
011100101001 => 100111010010 => 010010111001 => 011010001101
011100101010 => 100111010100 => 001010111001 => 011100001101
011100101100 => 100111010001 => 100010111001 => 011001001101
011100110001 => 100111000110 => 011000111001 => 010010101101
011100110100 => 100111011000 => 000110111001 => 011000101101
011101000101 => 101110001010 => 010100011101 => 100110001101
011101000110 => 101110001001 => 100100011101 => 100101001101
011101001001 => 101110010010 => 010010011101 => 101010001101
011101001100 => 101110010001 => 100010011101 => 101001001101
011101010001 => 101110100010 => 010001011101 => 110010001101
011101010010 => 101110100100 => 001001011101 => 110100001101
011101010100 => 101110101000 => 000101011101 => 111000001101
011101011000 => 101110100001 => 100001011101 => 110001001101
011101100100 => 101110011000 => 000110011101 => 101000101101
011101110000 => 101110000011 => 110000011101 => 100001101101
011110000101 => 100001111010 => 010111100001 => 000110011101
011110001010 => 100011110100 => 001011110001 => 001100011101
011110001100 => 100011110001 => 100011110001 => 001001011101
011110010100 => 100111101000 => 000101111001 => 011000011101
011110100001 => 101111000010 => 010000111101 => 100010011101
011110100010 => 101111000100 => 001000111101 => 100100011101
011110100100 => 101111001000 => 000100111101 => 101000011101
011110101000 => 101111010000 => 000010111101 => 110000011101
011110110000 => 101111000001 => 100000111101 => 100001011101
011111000001 => 100000111110 => 011111000001 => 000010111101
011111000100 => 100011111000 => 000111110001 => 001000111101
011111010000 => 101111100000 => 000001111101 => 100000111101
0100000100 => 1000001000 => 0001000001 => 0000100001
0011101010 => 0101110100 => 0010111010 => 1110001100
0011101100 => 0101110001 => 1000111010 => 1100101100
0001101110 => 0010110011 => 1100110100 => 0110110100
0010110110 => 0101011001 => 1001101010 => 1110101000
0011110010 => 0100111100 => 0011110010 => 1010011100
0001110110 => 0010111001 => 1001110100 => 0110101100
0010111010 => 0101011100 => 0011101010 => 1110011000
0011111000 => 0100001111 => 1111000010 => 1000111100
0001111010 => 0010111100 => 0011110100 => 0110011100
0100111100 => 1001000111 => 1110001001 => 0100111001
0001111100 => 0010001111 => 1111000100 => 0100111100
001111001010 => 010011110100 => 001011110010 => 101100011100
100111001100 => 011001110001 => 100011100110 => 101001011010
001011010110 => 010101101001 => 100101101010 => 111101001000
001111010010 => 010111100100 => 001001111010 => 110100011100
100111010100 => 011011101000 => 000101110110 => 111000011010
001111010100 => 010111101000 => 000101111010 => 111000011100
000111010110 => 001011101001 => 100101110100 => 011101001100
001011011010 => 010101101100 => 001101101010 => 111100101000
100111011000 => 011011100001 => 100001110110 => 110001011010
001111011000 => 010111100001 => 100001111010 => 110001011100
010011011100 => 100101100011 => 110001101001 => 011001101001
000011011110 => 000101100111 => 111001101000 => 001101110100
001101100110 => 010110011001 => 100110011010 => 110101010100
001101101010 => 010110110100 => 001011011010 => 111100010100
100101101100 => 011010110001 => 100011010110 => 111001010010
001101101100 => 010110110001 => 100011011010 => 111001010100
001111100010 => 010001111100 => 001111100010 => 100100111100
100111100100 => 011001111000 => 000111100110 => 101000111010
001111100100 => 010011111000 => 000111110010 => 101000111100
010011101010 => 100101110100 => 001011101001 => 011100011001
001011101010 => 010101110100 => 001011101010 => 111100011000
100111101000 => 011011110000 => 000011110110 => 110000111010
001111101000 => 010111110000 => 000011111010 => 110000111100
000111101010 => 001011110100 => 001011110100 => 011100011100
100011101100 => 001101110001 => 100011101100 => 011001011010
010011101100 => 100101110001 => 100011101001 => 011001011001
001011101100 => 010101110001 => 100011101010 => 111001011000
000111101100 => 001011110001 => 100011110100 => 011001011100
101001110100 => 110010111000 => 000111010011 => 011000110011
001101110010 => 010110011100 => 001110011010 => 110100110100
100101110100 => 011010111000 => 000111010110 => 111000110010
001101110100 => 010110111000 => 000111011010 => 111000110100
000101110110 => 001010111001 => 100111010100 => 011101011000
001011110010 => 010100111100 => 001111001010 => 110100111000
100111110000 => 011000001111 => 111100000110 => 100001111010
001111110000 => 010000011111 => 111110000010 => 100001111100
100011110100 => 001101111000 => 000111101100 => 011000111010
010011110100 => 100101111000 => 000111101001 => 011000111001
001011110100 => 010101111000 => 000111101010 => 111000111000
000111110100 => 001011111000 => 000111110100 => 011000111100
000011110110 => 000101111001 => 100111101000 => 001101011100
110001111000 => 001110000111 => 111000011100 => 010001110110
101001111000 => 110010000111 => 111000010011 => 010001110011
001001111010 => 010010111100 => 001111010010 => 101100111000
100101111000 => 011010000111 => 111000010110 => 110001110010
001101111000 => 010110000111 => 111000011010 => 110001110100
100011111000 => 001100001111 => 111100001100 => 010001111010
001011111000 => 010100001111 => 111100001010 => 110001111000
000011111010 => 000101111100 => 001111101000 => 001100111100
010001111100 => 100010001111 => 111100010001 => 001001111001
001001111100 => 010010001111 => 111100010010 => 101001111000
000101111100 => 001010001111 => 111100010100 => 011001111000
000011111100 => 000100011111 => 111110001000 => 001001111100
0000000101 => 0000001010 => 0101000000 => 0000011000
0000001101 => 0000010110 => 0110100000 => 0000110100
0000011101 => 0000101110 => 0111010000 => 0001101100
0001111101 => 0010111110 => 0111110100 => 0110111100
0011111101 => 0101111110 => 0111111010 => 1101111100
0000001001 => 0000010010 => 0100100000 => 0000101000
0000010101 => 0000101010 => 0101010000 => 0001110000
00000011101 => 00000101110 => 01110100000 => 00001101100
0000101101 => 0001010110 => 0110101000 => 0011101000
00001111101 => 00010111110 => 01111101000 => 00110111100
0101111101 => 1010111110 => 0111110101 => 1101111001
11111111101 => 11111111110 => 01111111111 => 01111111111
100101010101 => 011010101010 => 010101010110 => 111110000010
100101011001 => 011010100110 => 011001010110 => 111010100010
100101100101 => 011010011010 => 010110010110 => 110110010010
100101101001 => 011010110010 => 010011010110 => 111010010010
100101110001 => 011010001110 => 011100010110 => 110010110010
100110101001 => 011011010010 => 010010110110 => 111010001010
100111000101 => 011000111010 => 010111000110 => 100110011010
100111001001 => 011001110010 => 010011100110 => 101010011010
100111010001 => 011011100010 => 010001110110 => 110010011010
101001010101 => 110010101010 => 010101010011 => 011110000011
101001101001 => 110010110010 => 010011010011 => 011010010011
101010011001 => 110100100110 => 011001001011 => 101010100011
101010100101 => 110101001010 => 010100101011 => 110110000011
101010101001 => 110101010010 => 010010101011 => 111010000011
101010110001 => 110101000110 => 011000101011 => 110010100011
101011001001 => 110100110010 => 010011001011 => 101010010011
101011100001 => 110100001110 => 011100001011 => 100010110011
101100101001 => 110011010010 => 010010110011 => 011010001011
101101000101 => 110110001010 => 010100011011 => 100110001011
101101001001 => 110110010010 => 010010011011 => 101010001011
101101010001 => 110110100010 => 010001011011 => 110010001011
101110001001 => 110001110010 => 010011100011 => 001010011011
101110100001 => 110111000010 => 010000111011 => 100010011011
110001010101 => 001110101010 => 010101011100 => 011110000110
110001011001 => 001110100110 => 011001011100 => 011010100110
110001100101 => 001110011010 => 010110011100 => 010110010110
110001101001 => 001110110010 => 010011011100 => 011010010110
110001110001 => 001110001110 => 011100011100 => 010010110110
110010010101 => 011100101010 => 010101001110 => 101110000110
110010011001 => 011100100110 => 011001001110 => 101010100110
110010100101 => 011101001010 => 010100101110 => 110110000110
110011000101 => 011100011010 => 010110001110 => 100110010110
110011001001 => 011100110010 => 010011001110 => 101010010110
110011010001 => 011101100010 => 010001101110 => 110010010110
110011100001 => 011100001110 => 011100001110 => 100010110110
110100010101 => 111000101010 => 010101000111 => 001110000111
110100011001 => 111000100110 => 011001000111 => 001010100111
110100100101 => 111001001010 => 010100100111 => 010110000111
110100101001 => 111001010010 => 010010100111 => 011010000111
110100110001 => 111001000110 => 011000100111 => 010010100111
110101000101 => 111010001010 => 010100010111 => 100110000111
110101001001 => 111010010010 => 010010010111 => 101010000111
110101010001 => 111010100010 => 010001010111 => 110010000111
110101100001 => 111010000110 => 011000010111 => 100010100111
110110000101 => 111000011010 => 010110000111 => 000110010111
110110001001 => 111000110010 => 010011000111 => 001010010111
110110010001 => 111001100010 => 010001100111 => 010010010111
110110100001 => 111011000010 => 010000110111 => 100010010111
110111000001 => 111000001110 => 011100000111 => 000010110111
111000010101 => 000111101010 => 010101111000 => 001110001110
111000101001 => 001111010010 => 010010111100 => 011010001110
111001000101 => 011110001010 => 010100011110 => 100110001110
111001001001 => 011110010010 => 010010011110 => 101010001110
111001010001 => 011110100010 => 010001011110 => 110010001110
111010001001 => 111100010010 => 010010001111 => 001010001111
111010100001 => 111101000010 => 010000101111 => 100010001111
111100000101 => 000011111010 => 010111110000 => 000110011110
111100001001 => 000111110010 => 010011111000 => 001010011110
111100010001 => 001111100010 => 010001111100 => 010010011110
111100100001 => 011111000010 => 010000111110 => 100010011110
111101000001 => 111110000010 => 010000011111 => 000010011111
Map
rowmotion
Description
Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
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 $\phi(4154223) = 1254423$.