Identifier
Mp00105:
Binary words
—complement⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Images
0 => 1 => 1 => 1
1 => 0 => 0 => 0
00 => 11 => 11 => 11
01 => 10 => 10 => 01
10 => 01 => 01 => 10
11 => 00 => 00 => 00
000 => 111 => 111 => 111
001 => 110 => 110 => 101
010 => 101 => 101 => 011
011 => 100 => 010 => 100
100 => 011 => 011 => 110
101 => 010 => 100 => 001
110 => 001 => 001 => 010
111 => 000 => 000 => 000
0000 => 1111 => 1111 => 1111
0001 => 1110 => 1110 => 1101
0010 => 1101 => 1101 => 1011
0011 => 1100 => 0110 => 1100
0100 => 1011 => 1011 => 0111
0101 => 1010 => 1100 => 1001
0110 => 1001 => 0101 => 1010
0111 => 1000 => 0010 => 0100
1000 => 0111 => 0111 => 1110
1001 => 0110 => 1010 => 0101
1010 => 0101 => 1001 => 0011
1011 => 0100 => 0100 => 1000
1100 => 0011 => 0011 => 0110
1101 => 0010 => 1000 => 0001
1110 => 0001 => 0001 => 0010
1111 => 0000 => 0000 => 0000
00000 => 11111 => 11111 => 11111
00001 => 11110 => 11110 => 11101
00010 => 11101 => 11101 => 11011
00011 => 11100 => 01110 => 11100
00100 => 11011 => 11011 => 10111
00101 => 11010 => 11100 => 11001
00110 => 11001 => 01101 => 11010
00111 => 11000 => 00110 => 01100
01000 => 10111 => 10111 => 01111
01001 => 10110 => 11010 => 10101
01010 => 10101 => 11001 => 10011
01011 => 10100 => 01100 => 11000
01100 => 10011 => 01011 => 10110
01101 => 10010 => 10100 => 01001
01110 => 10001 => 00101 => 01010
01111 => 10000 => 00010 => 00100
10000 => 01111 => 01111 => 11110
10001 => 01110 => 10110 => 01101
10010 => 01101 => 10101 => 01011
10011 => 01100 => 01010 => 10100
10100 => 01011 => 10011 => 00111
10101 => 01010 => 11000 => 10001
10110 => 01001 => 01001 => 10010
10111 => 01000 => 00100 => 01000
11000 => 00111 => 00111 => 01110
11001 => 00110 => 10010 => 00101
11010 => 00101 => 10001 => 00011
11011 => 00100 => 01000 => 10000
11100 => 00011 => 00011 => 00110
11101 => 00010 => 10000 => 00001
11110 => 00001 => 00001 => 00010
11111 => 00000 => 00000 => 00000
000000 => 111111 => 111111 => 111111
000001 => 111110 => 111110 => 111101
000010 => 111101 => 111101 => 111011
000011 => 111100 => 011110 => 111100
000100 => 111011 => 111011 => 110111
000101 => 111010 => 111100 => 111001
000110 => 111001 => 011101 => 111010
000111 => 111000 => 001110 => 011100
001000 => 110111 => 110111 => 101111
001001 => 110110 => 111010 => 110101
001010 => 110101 => 111001 => 110011
001011 => 110100 => 011100 => 111000
001100 => 110011 => 011011 => 110110
001101 => 110010 => 101100 => 011001
001110 => 110001 => 001101 => 011010
001111 => 110000 => 000110 => 001100
010000 => 101111 => 101111 => 011111
010001 => 101110 => 110110 => 101101
010010 => 101101 => 110101 => 101011
010011 => 101100 => 011010 => 110100
010100 => 101011 => 110011 => 100111
010101 => 101010 => 111000 => 110001
010110 => 101001 => 011001 => 110010
010111 => 101000 => 001100 => 011000
011000 => 100111 => 010111 => 101110
011001 => 100110 => 101010 => 010101
011010 => 100101 => 101001 => 010011
011011 => 100100 => 010100 => 101000
011100 => 100011 => 001011 => 010110
011101 => 100010 => 100100 => 001001
011110 => 100001 => 000101 => 001010
011111 => 100000 => 000010 => 000100
100000 => 011111 => 011111 => 111110
100001 => 011110 => 101110 => 011101
100010 => 011101 => 101101 => 011011
100011 => 011100 => 010110 => 101100
100100 => 011011 => 101011 => 010111
100101 => 011010 => 110100 => 101001
100110 => 011001 => 010101 => 101010
>>> Load all 3037 entries. <<<
100111 => 011000 => 001010 => 010100
101000 => 010111 => 100111 => 001111
101001 => 010110 => 110010 => 100101
101010 => 010101 => 110001 => 100011
101011 => 010100 => 011000 => 110000
101100 => 010011 => 010011 => 100110
101101 => 010010 => 101000 => 010001
101110 => 010001 => 001001 => 010010
101111 => 010000 => 000100 => 001000
110000 => 001111 => 001111 => 011110
110001 => 001110 => 100110 => 001101
110010 => 001101 => 100101 => 001011
110011 => 001100 => 010010 => 100100
110100 => 001011 => 100011 => 000111
110101 => 001010 => 110000 => 100001
110110 => 001001 => 010001 => 100010
110111 => 001000 => 001000 => 010000
111000 => 000111 => 000111 => 001110
111001 => 000110 => 100010 => 000101
111010 => 000101 => 100001 => 000011
111011 => 000100 => 010000 => 100000
111100 => 000011 => 000011 => 000110
111101 => 000010 => 100000 => 000001
111110 => 000001 => 000001 => 000010
111111 => 000000 => 000000 => 000000
0000000 => 1111111 => 1111111 => 1111111
0000001 => 1111110 => 1111110 => 1111101
0000010 => 1111101 => 1111101 => 1111011
0000011 => 1111100 => 0111110 => 1111100
0000100 => 1111011 => 1111011 => 1110111
0000101 => 1111010 => 1111100 => 1111001
0000110 => 1111001 => 0111101 => 1111010
0000111 => 1111000 => 0011110 => 0111100
0001000 => 1110111 => 1110111 => 1101111
0001001 => 1110110 => 1111010 => 1110101
0001010 => 1110101 => 1111001 => 1110011
0001011 => 1110100 => 0111100 => 1111000
0001100 => 1110011 => 0111011 => 1110110
0001101 => 1110010 => 1011100 => 0111001
0001110 => 1110001 => 0011101 => 0111010
0001111 => 1110000 => 0001110 => 0011100
0010000 => 1101111 => 1101111 => 1011111
0010001 => 1101110 => 1110110 => 1101101
0010010 => 1101101 => 1110101 => 1101011
0010011 => 1101100 => 0111010 => 1110100
0010100 => 1101011 => 1110011 => 1100111
0010101 => 1101010 => 1111000 => 1110001
0010110 => 1101001 => 0111001 => 1110010
0010111 => 1101000 => 0011100 => 0111000
0011000 => 1100111 => 0110111 => 1101110
0011001 => 1100110 => 1011010 => 0110101
0011010 => 1100101 => 1011001 => 0110011
0011011 => 1100100 => 0101100 => 1011000
0011100 => 1100011 => 0011011 => 0110110
0011101 => 1100010 => 1001100 => 0011001
0011110 => 1100001 => 0001101 => 0011010
0011111 => 1100000 => 0000110 => 0001100
0100000 => 1011111 => 1011111 => 0111111
0100001 => 1011110 => 1101110 => 1011101
0100010 => 1011101 => 1101101 => 1011011
0100011 => 1011100 => 0110110 => 1101100
0100100 => 1011011 => 1101011 => 1010111
0100101 => 1011010 => 1110100 => 1101001
0100110 => 1011001 => 0110101 => 1101010
0100111 => 1011000 => 0011010 => 0110100
0101000 => 1010111 => 1100111 => 1001111
0101001 => 1010110 => 1110010 => 1100101
0101010 => 1010101 => 1110001 => 1100011
0101011 => 1010100 => 0111000 => 1110000
0101100 => 1010011 => 0110011 => 1100110
0101101 => 1010010 => 1011000 => 0110001
0101110 => 1010001 => 0011001 => 0110010
0101111 => 1010000 => 0001100 => 0011000
0110000 => 1001111 => 0101111 => 1011110
0110001 => 1001110 => 1010110 => 0101101
0110010 => 1001101 => 1010101 => 0101011
0110011 => 1001100 => 0101010 => 1010100
0110100 => 1001011 => 1010011 => 0100111
0110101 => 1001010 => 1101000 => 1010001
0110110 => 1001001 => 0101001 => 1010010
0110111 => 1001000 => 0010100 => 0101000
0111000 => 1000111 => 0010111 => 0101110
0111001 => 1000110 => 1001010 => 0010101
0111010 => 1000101 => 1001001 => 0010011
0111011 => 1000100 => 0100100 => 1001000
0111100 => 1000011 => 0001011 => 0010110
0111101 => 1000010 => 1000100 => 0001001
0111110 => 1000001 => 0000101 => 0001010
0111111 => 1000000 => 0000010 => 0000100
1000000 => 0111111 => 0111111 => 1111110
1000001 => 0111110 => 1011110 => 0111101
1000010 => 0111101 => 1011101 => 0111011
1000011 => 0111100 => 0101110 => 1011100
1000100 => 0111011 => 1011011 => 0110111
1000101 => 0111010 => 1101100 => 1011001
1000110 => 0111001 => 0101101 => 1011010
1000111 => 0111000 => 0010110 => 0101100
1001000 => 0110111 => 1010111 => 0101111
1001001 => 0110110 => 1101010 => 1010101
1001010 => 0110101 => 1101001 => 1010011
1001011 => 0110100 => 0110100 => 1101000
1001100 => 0110011 => 0101011 => 1010110
1001101 => 0110010 => 1010100 => 0101001
1001110 => 0110001 => 0010101 => 0101010
1001111 => 0110000 => 0001010 => 0010100
1010000 => 0101111 => 1001111 => 0011111
1010001 => 0101110 => 1100110 => 1001101
1010010 => 0101101 => 1100101 => 1001011
1010011 => 0101100 => 0110010 => 1100100
1010100 => 0101011 => 1100011 => 1000111
1010101 => 0101010 => 1110000 => 1100001
1010110 => 0101001 => 0110001 => 1100010
1010111 => 0101000 => 0011000 => 0110000
1011000 => 0100111 => 0100111 => 1001110
1011001 => 0100110 => 1010010 => 0100101
1011010 => 0100101 => 1010001 => 0100011
1011011 => 0100100 => 0101000 => 1010000
1011100 => 0100011 => 0010011 => 0100110
1011101 => 0100010 => 1001000 => 0010001
1011110 => 0100001 => 0001001 => 0010010
1011111 => 0100000 => 0000100 => 0001000
1100000 => 0011111 => 0011111 => 0111110
1100001 => 0011110 => 1001110 => 0011101
1100010 => 0011101 => 1001101 => 0011011
1100011 => 0011100 => 0100110 => 1001100
1100100 => 0011011 => 1001011 => 0010111
1100101 => 0011010 => 1100100 => 1001001
1100110 => 0011001 => 0100101 => 1001010
1100111 => 0011000 => 0010010 => 0100100
1101000 => 0010111 => 1000111 => 0001111
1101001 => 0010110 => 1100010 => 1000101
1101010 => 0010101 => 1100001 => 1000011
1101011 => 0010100 => 0110000 => 1100000
1101100 => 0010011 => 0100011 => 1000110
1101101 => 0010010 => 1010000 => 0100001
1101110 => 0010001 => 0010001 => 0100010
1101111 => 0010000 => 0001000 => 0010000
1110000 => 0001111 => 0001111 => 0011110
1110001 => 0001110 => 1000110 => 0001101
1110010 => 0001101 => 1000101 => 0001011
1110011 => 0001100 => 0100010 => 1000100
1110100 => 0001011 => 1000011 => 0000111
1110101 => 0001010 => 1100000 => 1000001
1110110 => 0001001 => 0100001 => 1000010
1110111 => 0001000 => 0010000 => 0100000
1111000 => 0000111 => 0000111 => 0001110
1111001 => 0000110 => 1000010 => 0000101
1111010 => 0000101 => 1000001 => 0000011
1111011 => 0000100 => 0100000 => 1000000
1111100 => 0000011 => 0000011 => 0000110
1111101 => 0000010 => 1000000 => 0000001
1111110 => 0000001 => 0000001 => 0000010
1111111 => 0000000 => 0000000 => 0000000
00000000 => 11111111 => 11111111 => 11111111
00000001 => 11111110 => 11111110 => 11111101
00000010 => 11111101 => 11111101 => 11111011
00000011 => 11111100 => 01111110 => 11111100
00000100 => 11111011 => 11111011 => 11110111
00000101 => 11111010 => 11111100 => 11111001
00000110 => 11111001 => 01111101 => 11111010
00000111 => 11111000 => 00111110 => 01111100
00001000 => 11110111 => 11110111 => 11101111
00001001 => 11110110 => 11111010 => 11110101
00001010 => 11110101 => 11111001 => 11110011
00001011 => 11110100 => 01111100 => 11111000
00001100 => 11110011 => 01111011 => 11110110
00001101 => 11110010 => 10111100 => 01111001
00001110 => 11110001 => 00111101 => 01111010
00001111 => 11110000 => 00011110 => 00111100
00010000 => 11101111 => 11101111 => 11011111
00010001 => 11101110 => 11110110 => 11101101
00010010 => 11101101 => 11110101 => 11101011
00010011 => 11101100 => 01111010 => 11110100
00010100 => 11101011 => 11110011 => 11100111
00010101 => 11101010 => 11111000 => 11110001
00010110 => 11101001 => 01111001 => 11110010
00010111 => 11101000 => 00111100 => 01111000
00011000 => 11100111 => 01110111 => 11101110
00011001 => 11100110 => 10111010 => 01110101
00011010 => 11100101 => 10111001 => 01110011
00011011 => 11100100 => 01011100 => 10111000
00011100 => 11100011 => 00111011 => 01110110
00011101 => 11100010 => 10011100 => 00111001
00011110 => 11100001 => 00011101 => 00111010
00011111 => 11100000 => 00001110 => 00011100
00100000 => 11011111 => 11011111 => 10111111
00100001 => 11011110 => 11101110 => 11011101
00100010 => 11011101 => 11101101 => 11011011
00100011 => 11011100 => 01110110 => 11101100
00100100 => 11011011 => 11101011 => 11010111
00100101 => 11011010 => 11110100 => 11101001
00100110 => 11011001 => 01110101 => 11101010
00100111 => 11011000 => 00111010 => 01110100
00101000 => 11010111 => 11100111 => 11001111
00101001 => 11010110 => 11110010 => 11100101
00101010 => 11010101 => 11110001 => 11100011
00101011 => 11010100 => 01111000 => 11110000
00101100 => 11010011 => 01110011 => 11100110
00101101 => 11010010 => 10111000 => 01110001
00101110 => 11010001 => 00111001 => 01110010
00101111 => 11010000 => 00011100 => 00111000
00110000 => 11001111 => 01101111 => 11011110
00110001 => 11001110 => 10110110 => 01101101
00110010 => 11001101 => 10110101 => 01101011
00110011 => 11001100 => 01011010 => 10110100
00110100 => 11001011 => 10110011 => 01100111
00110101 => 11001010 => 11011000 => 10110001
00110110 => 11001001 => 01011001 => 10110010
00110111 => 11001000 => 00101100 => 01011000
00111000 => 11000111 => 00110111 => 01101110
00111001 => 11000110 => 10011010 => 00110101
00111010 => 11000101 => 10011001 => 00110011
00111011 => 11000100 => 01001100 => 10011000
00111100 => 11000011 => 00011011 => 00110110
00111101 => 11000010 => 10001100 => 00011001
00111110 => 11000001 => 00001101 => 00011010
00111111 => 11000000 => 00000110 => 00001100
01000000 => 10111111 => 10111111 => 01111111
01000001 => 10111110 => 11011110 => 10111101
01000010 => 10111101 => 11011101 => 10111011
01000011 => 10111100 => 01101110 => 11011100
01000100 => 10111011 => 11011011 => 10110111
01000101 => 10111010 => 11101100 => 11011001
01000110 => 10111001 => 01101101 => 11011010
01000111 => 10111000 => 00110110 => 01101100
01001000 => 10110111 => 11010111 => 10101111
01001001 => 10110110 => 11101010 => 11010101
01001010 => 10110101 => 11101001 => 11010011
01001011 => 10110100 => 01110100 => 11101000
01001100 => 10110011 => 01101011 => 11010110
01001101 => 10110010 => 10110100 => 01101001
01001110 => 10110001 => 00110101 => 01101010
01001111 => 10110000 => 00011010 => 00110100
01010000 => 10101111 => 11001111 => 10011111
01010001 => 10101110 => 11100110 => 11001101
01010010 => 10101101 => 11100101 => 11001011
01010011 => 10101100 => 01110010 => 11100100
01010100 => 10101011 => 11100011 => 11000111
01010101 => 10101010 => 11110000 => 11100001
01010110 => 10101001 => 01110001 => 11100010
01010111 => 10101000 => 00111000 => 01110000
01011000 => 10100111 => 01100111 => 11001110
01011001 => 10100110 => 10110010 => 01100101
01011010 => 10100101 => 10110001 => 01100011
01011011 => 10100100 => 01011000 => 10110000
01011100 => 10100011 => 00110011 => 01100110
01011101 => 10100010 => 10011000 => 00110001
01011110 => 10100001 => 00011001 => 00110010
01011111 => 10100000 => 00001100 => 00011000
01100000 => 10011111 => 01011111 => 10111110
01100001 => 10011110 => 10101110 => 01011101
01100010 => 10011101 => 10101101 => 01011011
01100011 => 10011100 => 01010110 => 10101100
01100100 => 10011011 => 10101011 => 01010111
01100101 => 10011010 => 11010100 => 10101001
01100110 => 10011001 => 01010101 => 10101010
01100111 => 10011000 => 00101010 => 01010100
01101000 => 10010111 => 10100111 => 01001111
01101001 => 10010110 => 11010010 => 10100101
01101010 => 10010101 => 11010001 => 10100011
01101011 => 10010100 => 01101000 => 11010000
01101100 => 10010011 => 01010011 => 10100110
01101101 => 10010010 => 10101000 => 01010001
01101110 => 10010001 => 00101001 => 01010010
01101111 => 10010000 => 00010100 => 00101000
01110000 => 10001111 => 00101111 => 01011110
01110001 => 10001110 => 10010110 => 00101101
01110010 => 10001101 => 10010101 => 00101011
01110011 => 10001100 => 01001010 => 10010100
01110100 => 10001011 => 10010011 => 00100111
01110101 => 10001010 => 11001000 => 10010001
01110110 => 10001001 => 01001001 => 10010010
01110111 => 10001000 => 00100100 => 01001000
01111000 => 10000111 => 00010111 => 00101110
01111001 => 10000110 => 10001010 => 00010101
01111010 => 10000101 => 10001001 => 00010011
01111011 => 10000100 => 01000100 => 10001000
01111100 => 10000011 => 00001011 => 00010110
01111101 => 10000010 => 10000100 => 00001001
01111110 => 10000001 => 00000101 => 00001010
01111111 => 10000000 => 00000010 => 00000100
10000000 => 01111111 => 01111111 => 11111110
10000001 => 01111110 => 10111110 => 01111101
10000010 => 01111101 => 10111101 => 01111011
10000011 => 01111100 => 01011110 => 10111100
10000100 => 01111011 => 10111011 => 01110111
10000101 => 01111010 => 11011100 => 10111001
10000110 => 01111001 => 01011101 => 10111010
10000111 => 01111000 => 00101110 => 01011100
10001000 => 01110111 => 10110111 => 01101111
10001001 => 01110110 => 11011010 => 10110101
10001010 => 01110101 => 11011001 => 10110011
10001011 => 01110100 => 01101100 => 11011000
10001100 => 01110011 => 01011011 => 10110110
10001101 => 01110010 => 10101100 => 01011001
10001110 => 01110001 => 00101101 => 01011010
10001111 => 01110000 => 00010110 => 00101100
10010000 => 01101111 => 10101111 => 01011111
10010001 => 01101110 => 11010110 => 10101101
10010010 => 01101101 => 11010101 => 10101011
10010011 => 01101100 => 01101010 => 11010100
10010100 => 01101011 => 11010011 => 10100111
10010101 => 01101010 => 11101000 => 11010001
10010110 => 01101001 => 01101001 => 11010010
10010111 => 01101000 => 00110100 => 01101000
10011000 => 01100111 => 01010111 => 10101110
10011001 => 01100110 => 10101010 => 01010101
10011010 => 01100101 => 10101001 => 01010011
10011011 => 01100100 => 01010100 => 10101000
10011100 => 01100011 => 00101011 => 01010110
10011101 => 01100010 => 10010100 => 00101001
10011110 => 01100001 => 00010101 => 00101010
10011111 => 01100000 => 00001010 => 00010100
10100000 => 01011111 => 10011111 => 00111111
10100001 => 01011110 => 11001110 => 10011101
10100010 => 01011101 => 11001101 => 10011011
10100011 => 01011100 => 01100110 => 11001100
10100100 => 01011011 => 11001011 => 10010111
10100101 => 01011010 => 11100100 => 11001001
10100110 => 01011001 => 01100101 => 11001010
10100111 => 01011000 => 00110010 => 01100100
10101000 => 01010111 => 11000111 => 10001111
10101001 => 01010110 => 11100010 => 11000101
10101010 => 01010101 => 11100001 => 11000011
10101011 => 01010100 => 01110000 => 11100000
10101100 => 01010011 => 01100011 => 11000110
10101101 => 01010010 => 10110000 => 01100001
10101110 => 01010001 => 00110001 => 01100010
10101111 => 01010000 => 00011000 => 00110000
10110000 => 01001111 => 01001111 => 10011110
10110001 => 01001110 => 10100110 => 01001101
10110010 => 01001101 => 10100101 => 01001011
10110011 => 01001100 => 01010010 => 10100100
10110100 => 01001011 => 10100011 => 01000111
10110101 => 01001010 => 11010000 => 10100001
10110110 => 01001001 => 01010001 => 10100010
10110111 => 01001000 => 00101000 => 01010000
10111000 => 01000111 => 00100111 => 01001110
10111001 => 01000110 => 10010010 => 00100101
10111010 => 01000101 => 10010001 => 00100011
10111011 => 01000100 => 01001000 => 10010000
10111100 => 01000011 => 00010011 => 00100110
10111101 => 01000010 => 10001000 => 00010001
10111110 => 01000001 => 00001001 => 00010010
10111111 => 01000000 => 00000100 => 00001000
11000000 => 00111111 => 00111111 => 01111110
11000001 => 00111110 => 10011110 => 00111101
11000010 => 00111101 => 10011101 => 00111011
11000011 => 00111100 => 01001110 => 10011100
11000100 => 00111011 => 10011011 => 00110111
11000101 => 00111010 => 11001100 => 10011001
11000110 => 00111001 => 01001101 => 10011010
11000111 => 00111000 => 00100110 => 01001100
11001000 => 00110111 => 10010111 => 00101111
11001001 => 00110110 => 11001010 => 10010101
11001010 => 00110101 => 11001001 => 10010011
11001011 => 00110100 => 01100100 => 11001000
11001100 => 00110011 => 01001011 => 10010110
11001101 => 00110010 => 10100100 => 01001001
11001110 => 00110001 => 00100101 => 01001010
11001111 => 00110000 => 00010010 => 00100100
11010000 => 00101111 => 10001111 => 00011111
11010001 => 00101110 => 11000110 => 10001101
11010010 => 00101101 => 11000101 => 10001011
11010011 => 00101100 => 01100010 => 11000100
11010100 => 00101011 => 11000011 => 10000111
11010101 => 00101010 => 11100000 => 11000001
11010110 => 00101001 => 01100001 => 11000010
11010111 => 00101000 => 00110000 => 01100000
11011000 => 00100111 => 01000111 => 10001110
11011001 => 00100110 => 10100010 => 01000101
11011010 => 00100101 => 10100001 => 01000011
11011011 => 00100100 => 01010000 => 10100000
11011100 => 00100011 => 00100011 => 01000110
11011101 => 00100010 => 10010000 => 00100001
11011110 => 00100001 => 00010001 => 00100010
11011111 => 00100000 => 00001000 => 00010000
11100000 => 00011111 => 00011111 => 00111110
11100001 => 00011110 => 10001110 => 00011101
11100010 => 00011101 => 10001101 => 00011011
11100011 => 00011100 => 01000110 => 10001100
11100100 => 00011011 => 10001011 => 00010111
11100101 => 00011010 => 11000100 => 10001001
11100110 => 00011001 => 01000101 => 10001010
11100111 => 00011000 => 00100010 => 01000100
11101000 => 00010111 => 10000111 => 00001111
11101001 => 00010110 => 11000010 => 10000101
11101010 => 00010101 => 11000001 => 10000011
11101011 => 00010100 => 01100000 => 11000000
11101100 => 00010011 => 01000011 => 10000110
11101101 => 00010010 => 10100000 => 01000001
11101110 => 00010001 => 00100001 => 01000010
11101111 => 00010000 => 00010000 => 00100000
11110000 => 00001111 => 00001111 => 00011110
11110001 => 00001110 => 10000110 => 00001101
11110010 => 00001101 => 10000101 => 00001011
11110011 => 00001100 => 01000010 => 10000100
11110100 => 00001011 => 10000011 => 00000111
11110101 => 00001010 => 11000000 => 10000001
11110110 => 00001001 => 01000001 => 10000010
11110111 => 00001000 => 00100000 => 01000000
11111000 => 00000111 => 00000111 => 00001110
11111001 => 00000110 => 10000010 => 00000101
11111010 => 00000101 => 10000001 => 00000011
11111011 => 00000100 => 01000000 => 10000000
11111100 => 00000011 => 00000011 => 00000110
11111101 => 00000010 => 10000000 => 00000001
11111110 => 00000001 => 00000001 => 00000010
11111111 => 00000000 => 00000000 => 00000000
000000000 => 111111111 => 111111111 => 111111111
000000001 => 111111110 => 111111110 => 111111101
000000010 => 111111101 => 111111101 => 111111011
000000011 => 111111100 => 011111110 => 111111100
000000100 => 111111011 => 111111011 => 111110111
000000101 => 111111010 => 111111100 => 111111001
000000110 => 111111001 => 011111101 => 111111010
000000111 => 111111000 => 001111110 => 011111100
000001000 => 111110111 => 111110111 => 111101111
000001001 => 111110110 => 111111010 => 111110101
000001010 => 111110101 => 111111001 => 111110011
000001011 => 111110100 => 011111100 => 111111000
000001100 => 111110011 => 011111011 => 111110110
000001101 => 111110010 => 101111100 => 011111001
000001110 => 111110001 => 001111101 => 011111010
000001111 => 111110000 => 000111110 => 001111100
000010000 => 111101111 => 111101111 => 111011111
000010001 => 111101110 => 111110110 => 111101101
000010010 => 111101101 => 111110101 => 111101011
000010011 => 111101100 => 011111010 => 111110100
000010100 => 111101011 => 111110011 => 111100111
000010101 => 111101010 => 111111000 => 111110001
000010110 => 111101001 => 011111001 => 111110010
000010111 => 111101000 => 001111100 => 011111000
000011000 => 111100111 => 011110111 => 111101110
000011001 => 111100110 => 101111010 => 011110101
000011010 => 111100101 => 101111001 => 011110011
000011011 => 111100100 => 010111100 => 101111000
000011100 => 111100011 => 001111011 => 011110110
000011101 => 111100010 => 100111100 => 001111001
000011110 => 111100001 => 000111101 => 001111010
000011111 => 111100000 => 000011110 => 000111100
000100000 => 111011111 => 111011111 => 110111111
000100001 => 111011110 => 111101110 => 111011101
000100010 => 111011101 => 111101101 => 111011011
000100011 => 111011100 => 011110110 => 111101100
000100100 => 111011011 => 111101011 => 111010111
000100101 => 111011010 => 111110100 => 111101001
000100110 => 111011001 => 011110101 => 111101010
000100111 => 111011000 => 001111010 => 011110100
000101000 => 111010111 => 111100111 => 111001111
000101001 => 111010110 => 111110010 => 111100101
000101010 => 111010101 => 111110001 => 111100011
000101011 => 111010100 => 011111000 => 111110000
000101100 => 111010011 => 011110011 => 111100110
000101101 => 111010010 => 101111000 => 011110001
000101110 => 111010001 => 001111001 => 011110010
000101111 => 111010000 => 000111100 => 001111000
000110000 => 111001111 => 011101111 => 111011110
000110001 => 111001110 => 101110110 => 011101101
000110010 => 111001101 => 101110101 => 011101011
000110011 => 111001100 => 010111010 => 101110100
000110100 => 111001011 => 101110011 => 011100111
000110101 => 111001010 => 110111000 => 101110001
000110110 => 111001001 => 010111001 => 101110010
000110111 => 111001000 => 001011100 => 010111000
000111000 => 111000111 => 001110111 => 011101110
000111001 => 111000110 => 100111010 => 001110101
000111010 => 111000101 => 100111001 => 001110011
000111011 => 111000100 => 010011100 => 100111000
000111100 => 111000011 => 000111011 => 001110110
000111101 => 111000010 => 100011100 => 000111001
000111110 => 111000001 => 000011101 => 000111010
000111111 => 111000000 => 000001110 => 000011100
001000000 => 110111111 => 110111111 => 101111111
001000001 => 110111110 => 111011110 => 110111101
001000010 => 110111101 => 111011101 => 110111011
001000011 => 110111100 => 011101110 => 111011100
001000100 => 110111011 => 111011011 => 110110111
001000101 => 110111010 => 111101100 => 111011001
001000110 => 110111001 => 011101101 => 111011010
001000111 => 110111000 => 001110110 => 011101100
001001000 => 110110111 => 111010111 => 110101111
001001001 => 110110110 => 111101010 => 111010101
001001010 => 110110101 => 111101001 => 111010011
001001011 => 110110100 => 011110100 => 111101000
001001100 => 110110011 => 011101011 => 111010110
001001101 => 110110010 => 101110100 => 011101001
001001110 => 110110001 => 001110101 => 011101010
001001111 => 110110000 => 000111010 => 001110100
001010000 => 110101111 => 111001111 => 110011111
001010001 => 110101110 => 111100110 => 111001101
001010010 => 110101101 => 111100101 => 111001011
001010011 => 110101100 => 011110010 => 111100100
001010100 => 110101011 => 111100011 => 111000111
001010101 => 110101010 => 111110000 => 111100001
001010110 => 110101001 => 011110001 => 111100010
001010111 => 110101000 => 001111000 => 011110000
001011000 => 110100111 => 011100111 => 111001110
001011001 => 110100110 => 101110010 => 011100101
001011010 => 110100101 => 101110001 => 011100011
001011011 => 110100100 => 010111000 => 101110000
001011100 => 110100011 => 001110011 => 011100110
001011101 => 110100010 => 100111000 => 001110001
001011110 => 110100001 => 000111001 => 001110010
001011111 => 110100000 => 000011100 => 000111000
001100000 => 110011111 => 011011111 => 110111110
001100001 => 110011110 => 101101110 => 011011101
001100010 => 110011101 => 101101101 => 011011011
001100011 => 110011100 => 010110110 => 101101100
001100100 => 110011011 => 101101011 => 011010111
001100101 => 110011010 => 110110100 => 101101001
001100110 => 110011001 => 010110101 => 101101010
001100111 => 110011000 => 001011010 => 010110100
001101000 => 110010111 => 101100111 => 011001111
001101001 => 110010110 => 110110010 => 101100101
001101010 => 110010101 => 110110001 => 101100011
001101011 => 110010100 => 011011000 => 110110000
001101100 => 110010011 => 010110011 => 101100110
001101101 => 110010010 => 101011000 => 010110001
001101110 => 110010001 => 001011001 => 010110010
001101111 => 110010000 => 000101100 => 001011000
001110000 => 110001111 => 001101111 => 011011110
001110001 => 110001110 => 100110110 => 001101101
001110010 => 110001101 => 100110101 => 001101011
001110011 => 110001100 => 010011010 => 100110100
001110100 => 110001011 => 100110011 => 001100111
001110101 => 110001010 => 110011000 => 100110001
001110110 => 110001001 => 010011001 => 100110010
001110111 => 110001000 => 001001100 => 010011000
001111000 => 110000111 => 000110111 => 001101110
001111001 => 110000110 => 100011010 => 000110101
001111010 => 110000101 => 100011001 => 000110011
001111011 => 110000100 => 010001100 => 100011000
001111100 => 110000011 => 000011011 => 000110110
001111101 => 110000010 => 100001100 => 000011001
001111110 => 110000001 => 000001101 => 000011010
001111111 => 110000000 => 000000110 => 000001100
010000000 => 101111111 => 101111111 => 011111111
010000001 => 101111110 => 110111110 => 101111101
010000010 => 101111101 => 110111101 => 101111011
010000011 => 101111100 => 011011110 => 110111100
010000100 => 101111011 => 110111011 => 101110111
010000101 => 101111010 => 111011100 => 110111001
010000110 => 101111001 => 011011101 => 110111010
010000111 => 101111000 => 001101110 => 011011100
010001000 => 101110111 => 110110111 => 101101111
010001001 => 101110110 => 111011010 => 110110101
010001010 => 101110101 => 111011001 => 110110011
010001011 => 101110100 => 011101100 => 111011000
010001100 => 101110011 => 011011011 => 110110110
010001101 => 101110010 => 101101100 => 011011001
010001110 => 101110001 => 001101101 => 011011010
010001111 => 101110000 => 000110110 => 001101100
010010000 => 101101111 => 110101111 => 101011111
010010001 => 101101110 => 111010110 => 110101101
010010010 => 101101101 => 111010101 => 110101011
010010011 => 101101100 => 011101010 => 111010100
010010100 => 101101011 => 111010011 => 110100111
010010101 => 101101010 => 111101000 => 111010001
010010110 => 101101001 => 011101001 => 111010010
010010111 => 101101000 => 001110100 => 011101000
010011000 => 101100111 => 011010111 => 110101110
010011001 => 101100110 => 101101010 => 011010101
010011010 => 101100101 => 101101001 => 011010011
010011011 => 101100100 => 010110100 => 101101000
010011100 => 101100011 => 001101011 => 011010110
010011101 => 101100010 => 100110100 => 001101001
010011110 => 101100001 => 000110101 => 001101010
010011111 => 101100000 => 000011010 => 000110100
010100000 => 101011111 => 110011111 => 100111111
010100001 => 101011110 => 111001110 => 110011101
010100010 => 101011101 => 111001101 => 110011011
010100011 => 101011100 => 011100110 => 111001100
010100100 => 101011011 => 111001011 => 110010111
010100101 => 101011010 => 111100100 => 111001001
010100110 => 101011001 => 011100101 => 111001010
010100111 => 101011000 => 001110010 => 011100100
010101000 => 101010111 => 111000111 => 110001111
010101001 => 101010110 => 111100010 => 111000101
010101010 => 101010101 => 111100001 => 111000011
010101011 => 101010100 => 011110000 => 111100000
010101100 => 101010011 => 011100011 => 111000110
010101101 => 101010010 => 101110000 => 011100001
010101110 => 101010001 => 001110001 => 011100010
010101111 => 101010000 => 000111000 => 001110000
010110000 => 101001111 => 011001111 => 110011110
010110001 => 101001110 => 101100110 => 011001101
010110010 => 101001101 => 101100101 => 011001011
010110011 => 101001100 => 010110010 => 101100100
010110100 => 101001011 => 101100011 => 011000111
010110101 => 101001010 => 110110000 => 101100001
010110110 => 101001001 => 010110001 => 101100010
010110111 => 101001000 => 001011000 => 010110000
010111000 => 101000111 => 001100111 => 011001110
010111001 => 101000110 => 100110010 => 001100101
010111010 => 101000101 => 100110001 => 001100011
010111011 => 101000100 => 010011000 => 100110000
010111100 => 101000011 => 000110011 => 001100110
010111101 => 101000010 => 100011000 => 000110001
010111110 => 101000001 => 000011001 => 000110010
010111111 => 101000000 => 000001100 => 000011000
011000000 => 100111111 => 010111111 => 101111110
011000001 => 100111110 => 101011110 => 010111101
011000010 => 100111101 => 101011101 => 010111011
011000011 => 100111100 => 010101110 => 101011100
011000100 => 100111011 => 101011011 => 010110111
011000101 => 100111010 => 110101100 => 101011001
011000110 => 100111001 => 010101101 => 101011010
011000111 => 100111000 => 001010110 => 010101100
011001000 => 100110111 => 101010111 => 010101111
011001001 => 100110110 => 110101010 => 101010101
011001010 => 100110101 => 110101001 => 101010011
011001011 => 100110100 => 011010100 => 110101000
011001100 => 100110011 => 010101011 => 101010110
011001101 => 100110010 => 101010100 => 010101001
011001110 => 100110001 => 001010101 => 010101010
011001111 => 100110000 => 000101010 => 001010100
011010000 => 100101111 => 101001111 => 010011111
011010001 => 100101110 => 110100110 => 101001101
011010010 => 100101101 => 110100101 => 101001011
011010011 => 100101100 => 011010010 => 110100100
011010100 => 100101011 => 110100011 => 101000111
011010101 => 100101010 => 111010000 => 110100001
011010110 => 100101001 => 011010001 => 110100010
011010111 => 100101000 => 001101000 => 011010000
011011000 => 100100111 => 010100111 => 101001110
011011001 => 100100110 => 101010010 => 010100101
011011010 => 100100101 => 101010001 => 010100011
011011011 => 100100100 => 010101000 => 101010000
011011100 => 100100011 => 001010011 => 010100110
011011101 => 100100010 => 100101000 => 001010001
011011110 => 100100001 => 000101001 => 001010010
011011111 => 100100000 => 000010100 => 000101000
011100000 => 100011111 => 001011111 => 010111110
011100001 => 100011110 => 100101110 => 001011101
011100010 => 100011101 => 100101101 => 001011011
011100011 => 100011100 => 010010110 => 100101100
011100100 => 100011011 => 100101011 => 001010111
011100101 => 100011010 => 110010100 => 100101001
011100110 => 100011001 => 010010101 => 100101010
011100111 => 100011000 => 001001010 => 010010100
011101000 => 100010111 => 100100111 => 001001111
011101001 => 100010110 => 110010010 => 100100101
011101010 => 100010101 => 110010001 => 100100011
011101011 => 100010100 => 011001000 => 110010000
011101100 => 100010011 => 010010011 => 100100110
011101101 => 100010010 => 101001000 => 010010001
011101110 => 100010001 => 001001001 => 010010010
011101111 => 100010000 => 000100100 => 001001000
011110000 => 100001111 => 000101111 => 001011110
011110001 => 100001110 => 100010110 => 000101101
011110010 => 100001101 => 100010101 => 000101011
011110011 => 100001100 => 010001010 => 100010100
011110100 => 100001011 => 100010011 => 000100111
011110101 => 100001010 => 110001000 => 100010001
011110110 => 100001001 => 010001001 => 100010010
011110111 => 100001000 => 001000100 => 010001000
011111000 => 100000111 => 000010111 => 000101110
011111001 => 100000110 => 100001010 => 000010101
011111010 => 100000101 => 100001001 => 000010011
011111011 => 100000100 => 010000100 => 100001000
011111100 => 100000011 => 000001011 => 000010110
011111101 => 100000010 => 100000100 => 000001001
011111110 => 100000001 => 000000101 => 000001010
011111111 => 100000000 => 000000010 => 000000100
100000000 => 011111111 => 011111111 => 111111110
100000001 => 011111110 => 101111110 => 011111101
100000010 => 011111101 => 101111101 => 011111011
100000011 => 011111100 => 010111110 => 101111100
100000100 => 011111011 => 101111011 => 011110111
100000101 => 011111010 => 110111100 => 101111001
100000110 => 011111001 => 010111101 => 101111010
100000111 => 011111000 => 001011110 => 010111100
100001000 => 011110111 => 101110111 => 011101111
100001001 => 011110110 => 110111010 => 101110101
100001010 => 011110101 => 110111001 => 101110011
100001011 => 011110100 => 011011100 => 110111000
100001100 => 011110011 => 010111011 => 101110110
100001101 => 011110010 => 101011100 => 010111001
100001110 => 011110001 => 001011101 => 010111010
100001111 => 011110000 => 000101110 => 001011100
100010000 => 011101111 => 101101111 => 011011111
100010001 => 011101110 => 110110110 => 101101101
100010010 => 011101101 => 110110101 => 101101011
100010011 => 011101100 => 011011010 => 110110100
100010100 => 011101011 => 110110011 => 101100111
100010101 => 011101010 => 111011000 => 110110001
100010110 => 011101001 => 011011001 => 110110010
100010111 => 011101000 => 001101100 => 011011000
100011000 => 011100111 => 010110111 => 101101110
100011001 => 011100110 => 101011010 => 010110101
100011010 => 011100101 => 101011001 => 010110011
100011011 => 011100100 => 010101100 => 101011000
100011100 => 011100011 => 001011011 => 010110110
100011101 => 011100010 => 100101100 => 001011001
100011110 => 011100001 => 000101101 => 001011010
100011111 => 011100000 => 000010110 => 000101100
100100000 => 011011111 => 101011111 => 010111111
100100001 => 011011110 => 110101110 => 101011101
100100010 => 011011101 => 110101101 => 101011011
100100011 => 011011100 => 011010110 => 110101100
100100100 => 011011011 => 110101011 => 101010111
100100101 => 011011010 => 111010100 => 110101001
100100110 => 011011001 => 011010101 => 110101010
100100111 => 011011000 => 001101010 => 011010100
100101000 => 011010111 => 110100111 => 101001111
100101001 => 011010110 => 111010010 => 110100101
100101010 => 011010101 => 111010001 => 110100011
100101011 => 011010100 => 011101000 => 111010000
100101100 => 011010011 => 011010011 => 110100110
100101101 => 011010010 => 101101000 => 011010001
100101110 => 011010001 => 001101001 => 011010010
100101111 => 011010000 => 000110100 => 001101000
100110000 => 011001111 => 010101111 => 101011110
100110001 => 011001110 => 101010110 => 010101101
100110010 => 011001101 => 101010101 => 010101011
100110011 => 011001100 => 010101010 => 101010100
100110100 => 011001011 => 101010011 => 010100111
100110101 => 011001010 => 110101000 => 101010001
100110110 => 011001001 => 010101001 => 101010010
100110111 => 011001000 => 001010100 => 010101000
100111000 => 011000111 => 001010111 => 010101110
100111001 => 011000110 => 100101010 => 001010101
100111010 => 011000101 => 100101001 => 001010011
100111011 => 011000100 => 010010100 => 100101000
100111100 => 011000011 => 000101011 => 001010110
100111101 => 011000010 => 100010100 => 000101001
100111110 => 011000001 => 000010101 => 000101010
100111111 => 011000000 => 000001010 => 000010100
101000000 => 010111111 => 100111111 => 001111111
101000001 => 010111110 => 110011110 => 100111101
101000010 => 010111101 => 110011101 => 100111011
101000011 => 010111100 => 011001110 => 110011100
101000100 => 010111011 => 110011011 => 100110111
101000101 => 010111010 => 111001100 => 110011001
101000110 => 010111001 => 011001101 => 110011010
101000111 => 010111000 => 001100110 => 011001100
101001000 => 010110111 => 110010111 => 100101111
101001001 => 010110110 => 111001010 => 110010101
101001010 => 010110101 => 111001001 => 110010011
101001011 => 010110100 => 011100100 => 111001000
101001100 => 010110011 => 011001011 => 110010110
101001101 => 010110010 => 101100100 => 011001001
101001110 => 010110001 => 001100101 => 011001010
101001111 => 010110000 => 000110010 => 001100100
101010000 => 010101111 => 110001111 => 100011111
101010001 => 010101110 => 111000110 => 110001101
101010010 => 010101101 => 111000101 => 110001011
101010011 => 010101100 => 011100010 => 111000100
101010100 => 010101011 => 111000011 => 110000111
101010101 => 010101010 => 111100000 => 111000001
101010110 => 010101001 => 011100001 => 111000010
101010111 => 010101000 => 001110000 => 011100000
101011000 => 010100111 => 011000111 => 110001110
101011001 => 010100110 => 101100010 => 011000101
101011010 => 010100101 => 101100001 => 011000011
101011011 => 010100100 => 010110000 => 101100000
101011100 => 010100011 => 001100011 => 011000110
101011101 => 010100010 => 100110000 => 001100001
101011110 => 010100001 => 000110001 => 001100010
101011111 => 010100000 => 000011000 => 000110000
101100000 => 010011111 => 010011111 => 100111110
101100001 => 010011110 => 101001110 => 010011101
101100010 => 010011101 => 101001101 => 010011011
101100011 => 010011100 => 010100110 => 101001100
101100100 => 010011011 => 101001011 => 010010111
101100101 => 010011010 => 110100100 => 101001001
101100110 => 010011001 => 010100101 => 101001010
101100111 => 010011000 => 001010010 => 010100100
101101000 => 010010111 => 101000111 => 010001111
101101001 => 010010110 => 110100010 => 101000101
101101010 => 010010101 => 110100001 => 101000011
101101011 => 010010100 => 011010000 => 110100000
101101100 => 010010011 => 010100011 => 101000110
101101101 => 010010010 => 101010000 => 010100001
101101110 => 010010001 => 001010001 => 010100010
101101111 => 010010000 => 000101000 => 001010000
101110000 => 010001111 => 001001111 => 010011110
101110001 => 010001110 => 100100110 => 001001101
101110010 => 010001101 => 100100101 => 001001011
101110011 => 010001100 => 010010010 => 100100100
101110100 => 010001011 => 100100011 => 001000111
101110101 => 010001010 => 110010000 => 100100001
101110110 => 010001001 => 010010001 => 100100010
101110111 => 010001000 => 001001000 => 010010000
101111000 => 010000111 => 000100111 => 001001110
101111001 => 010000110 => 100010010 => 000100101
101111010 => 010000101 => 100010001 => 000100011
101111011 => 010000100 => 010001000 => 100010000
101111100 => 010000011 => 000010011 => 000100110
101111101 => 010000010 => 100001000 => 000010001
101111110 => 010000001 => 000001001 => 000010010
101111111 => 010000000 => 000000100 => 000001000
110000000 => 001111111 => 001111111 => 011111110
110000001 => 001111110 => 100111110 => 001111101
110000010 => 001111101 => 100111101 => 001111011
110000011 => 001111100 => 010011110 => 100111100
110000100 => 001111011 => 100111011 => 001110111
110000101 => 001111010 => 110011100 => 100111001
110000110 => 001111001 => 010011101 => 100111010
110000111 => 001111000 => 001001110 => 010011100
110001000 => 001110111 => 100110111 => 001101111
110001001 => 001110110 => 110011010 => 100110101
110001010 => 001110101 => 110011001 => 100110011
110001011 => 001110100 => 011001100 => 110011000
110001100 => 001110011 => 010011011 => 100110110
110001101 => 001110010 => 101001100 => 010011001
110001110 => 001110001 => 001001101 => 010011010
110001111 => 001110000 => 000100110 => 001001100
110010000 => 001101111 => 100101111 => 001011111
110010001 => 001101110 => 110010110 => 100101101
110010010 => 001101101 => 110010101 => 100101011
110010011 => 001101100 => 011001010 => 110010100
110010100 => 001101011 => 110010011 => 100100111
110010101 => 001101010 => 111001000 => 110010001
110010110 => 001101001 => 011001001 => 110010010
110010111 => 001101000 => 001100100 => 011001000
110011000 => 001100111 => 010010111 => 100101110
110011001 => 001100110 => 101001010 => 010010101
110011010 => 001100101 => 101001001 => 010010011
110011011 => 001100100 => 010100100 => 101001000
110011100 => 001100011 => 001001011 => 010010110
110011101 => 001100010 => 100100100 => 001001001
110011110 => 001100001 => 000100101 => 001001010
110011111 => 001100000 => 000010010 => 000100100
110100000 => 001011111 => 100011111 => 000111111
110100001 => 001011110 => 110001110 => 100011101
110100010 => 001011101 => 110001101 => 100011011
110100011 => 001011100 => 011000110 => 110001100
110100100 => 001011011 => 110001011 => 100010111
110100101 => 001011010 => 111000100 => 110001001
110100110 => 001011001 => 011000101 => 110001010
110100111 => 001011000 => 001100010 => 011000100
110101000 => 001010111 => 110000111 => 100001111
110101001 => 001010110 => 111000010 => 110000101
110101010 => 001010101 => 111000001 => 110000011
110101011 => 001010100 => 011100000 => 111000000
110101100 => 001010011 => 011000011 => 110000110
110101101 => 001010010 => 101100000 => 011000001
110101110 => 001010001 => 001100001 => 011000010
110101111 => 001010000 => 000110000 => 001100000
110110000 => 001001111 => 010001111 => 100011110
110110001 => 001001110 => 101000110 => 010001101
110110010 => 001001101 => 101000101 => 010001011
110110011 => 001001100 => 010100010 => 101000100
110110100 => 001001011 => 101000011 => 010000111
110110101 => 001001010 => 110100000 => 101000001
110110110 => 001001001 => 010100001 => 101000010
110110111 => 001001000 => 001010000 => 010100000
110111000 => 001000111 => 001000111 => 010001110
110111001 => 001000110 => 100100010 => 001000101
110111010 => 001000101 => 100100001 => 001000011
110111011 => 001000100 => 010010000 => 100100000
110111100 => 001000011 => 000100011 => 001000110
110111101 => 001000010 => 100010000 => 000100001
110111110 => 001000001 => 000010001 => 000100010
110111111 => 001000000 => 000001000 => 000010000
111000000 => 000111111 => 000111111 => 001111110
111000001 => 000111110 => 100011110 => 000111101
111000010 => 000111101 => 100011101 => 000111011
111000011 => 000111100 => 010001110 => 100011100
111000100 => 000111011 => 100011011 => 000110111
111000101 => 000111010 => 110001100 => 100011001
111000110 => 000111001 => 010001101 => 100011010
111000111 => 000111000 => 001000110 => 010001100
111001000 => 000110111 => 100010111 => 000101111
111001001 => 000110110 => 110001010 => 100010101
111001010 => 000110101 => 110001001 => 100010011
111001011 => 000110100 => 011000100 => 110001000
111001100 => 000110011 => 010001011 => 100010110
111001101 => 000110010 => 101000100 => 010001001
111001110 => 000110001 => 001000101 => 010001010
111001111 => 000110000 => 000100010 => 001000100
111010000 => 000101111 => 100001111 => 000011111
111010001 => 000101110 => 110000110 => 100001101
111010010 => 000101101 => 110000101 => 100001011
111010011 => 000101100 => 011000010 => 110000100
111010100 => 000101011 => 110000011 => 100000111
111010101 => 000101010 => 111000000 => 110000001
111010110 => 000101001 => 011000001 => 110000010
111010111 => 000101000 => 001100000 => 011000000
111011000 => 000100111 => 010000111 => 100001110
111011001 => 000100110 => 101000010 => 010000101
111011010 => 000100101 => 101000001 => 010000011
111011011 => 000100100 => 010100000 => 101000000
111011100 => 000100011 => 001000011 => 010000110
111011101 => 000100010 => 100100000 => 001000001
111011110 => 000100001 => 000100001 => 001000010
111011111 => 000100000 => 000010000 => 000100000
111100000 => 000011111 => 000011111 => 000111110
111100001 => 000011110 => 100001110 => 000011101
111100010 => 000011101 => 100001101 => 000011011
111100011 => 000011100 => 010000110 => 100001100
111100100 => 000011011 => 100001011 => 000010111
111100101 => 000011010 => 110000100 => 100001001
111100110 => 000011001 => 010000101 => 100001010
111100111 => 000011000 => 001000010 => 010000100
111101000 => 000010111 => 100000111 => 000001111
111101001 => 000010110 => 110000010 => 100000101
111101010 => 000010101 => 110000001 => 100000011
111101011 => 000010100 => 011000000 => 110000000
111101100 => 000010011 => 010000011 => 100000110
111101101 => 000010010 => 101000000 => 010000001
111101110 => 000010001 => 001000001 => 010000010
111101111 => 000010000 => 000100000 => 001000000
111110000 => 000001111 => 000001111 => 000011110
111110001 => 000001110 => 100000110 => 000001101
111110010 => 000001101 => 100000101 => 000001011
111110011 => 000001100 => 010000010 => 100000100
111110100 => 000001011 => 100000011 => 000000111
111110101 => 000001010 => 110000000 => 100000001
111110110 => 000001001 => 010000001 => 100000010
111110111 => 000001000 => 001000000 => 010000000
111111000 => 000000111 => 000000111 => 000001110
111111001 => 000000110 => 100000010 => 000000101
111111010 => 000000101 => 100000001 => 000000011
111111011 => 000000100 => 010000000 => 100000000
111111100 => 000000011 => 000000011 => 000000110
111111101 => 000000010 => 100000000 => 000000001
111111110 => 000000001 => 000000001 => 000000010
111111111 => 000000000 => 000000000 => 000000000
1010101010 => 0101010101 => 1111000001 => 1110000011
1010101100 => 0101010011 => 0111000011 => 1110000110
1010110010 => 0101001101 => 1011000101 => 0110001011
1010110100 => 0101001011 => 1011000011 => 0110000111
1010111000 => 0101000111 => 0011000111 => 0110001110
1011001010 => 0100110101 => 1101001001 => 1010010011
1011001100 => 0100110011 => 0101001011 => 1010010110
1011010010 => 0100101101 => 1101000101 => 1010001011
1011010100 => 0100101011 => 1101000011 => 1010000111
1011011000 => 0100100111 => 0101000111 => 1010001110
1011100010 => 0100011101 => 1001001101 => 0010011011
1011100100 => 0100011011 => 1001001011 => 0010010111
1011101000 => 0100010111 => 1001000111 => 0010001111
1011110000 => 0100001111 => 0001001111 => 0010011110
1100101010 => 0011010101 => 1110010001 => 1100100011
1100101100 => 0011010011 => 0110010011 => 1100100110
1100110010 => 0011001101 => 1010010101 => 0100101011
1100110100 => 0011001011 => 1010010011 => 0100100111
1100111000 => 0011000111 => 0010010111 => 0100101110
1101001010 => 0010110101 => 1110001001 => 1100010011
1101001100 => 0010110011 => 0110001011 => 1100010110
1101010010 => 0010101101 => 1110000101 => 1100001011
1101010100 => 0010101011 => 1110000011 => 1100000111
1101011000 => 0010100111 => 0110000111 => 1100001110
1101100010 => 0010011101 => 1010001101 => 0100011011
1101100100 => 0010011011 => 1010001011 => 0100010111
1101101000 => 0010010111 => 1010000111 => 0100001111
1101110000 => 0010001111 => 0010001111 => 0100011110
1110001010 => 0001110101 => 1100011001 => 1000110011
1110001100 => 0001110011 => 0100011011 => 1000110110
1110010010 => 0001101101 => 1100010101 => 1000101011
1110010100 => 0001101011 => 1100010011 => 1000100111
1110011000 => 0001100111 => 0100010111 => 1000101110
1110100010 => 0001011101 => 1100001101 => 1000011011
1110100100 => 0001011011 => 1100001011 => 1000010111
1110101000 => 0001010111 => 1100000111 => 1000001111
1110110000 => 0001001111 => 0100001111 => 1000011110
1111000010 => 0000111101 => 1000011101 => 0000111011
1111000100 => 0000111011 => 1000011011 => 0000110111
1111001000 => 0000110111 => 1000010111 => 0000101111
1111010000 => 0000101111 => 1000001111 => 0000011111
1111100000 => 0000011111 => 0000011111 => 0000111110
101010101010 => 010101010101 => 111110000001 => 111100000011
101010101100 => 010101010011 => 011110000011 => 111100000110
101010110010 => 010101001101 => 101110000101 => 011100001011
101010110100 => 010101001011 => 101110000011 => 011100000111
101010111000 => 010101000111 => 001110000111 => 011100001110
101011001010 => 010100110101 => 110110001001 => 101100010011
101011001100 => 010100110011 => 010110001011 => 101100010110
101011010010 => 010100101101 => 110110000101 => 101100001011
101011010100 => 010100101011 => 110110000011 => 101100000111
101011011000 => 010100100111 => 010110000111 => 101100001110
101011100010 => 010100011101 => 100110001101 => 001100011011
101011100100 => 010100011011 => 100110001011 => 001100010111
101011101000 => 010100010111 => 100110000111 => 001100001111
101011110000 => 010100001111 => 000110001111 => 001100011110
101100101010 => 010011010101 => 111010010001 => 110100100011
101100101100 => 010011010011 => 011010010011 => 110100100110
101100110010 => 010011001101 => 101010010101 => 010100101011
101100110100 => 010011001011 => 101010010011 => 010100100111
101100111000 => 010011000111 => 001010010111 => 010100101110
101101001010 => 010010110101 => 111010001001 => 110100010011
101101001100 => 010010110011 => 011010001011 => 110100010110
101101010010 => 010010101101 => 111010000101 => 110100001011
101101010100 => 010010101011 => 111010000011 => 110100000111
101101011000 => 010010100111 => 011010000111 => 110100001110
101101100010 => 010010011101 => 101010001101 => 010100011011
101101100100 => 010010011011 => 101010001011 => 010100010111
101101101000 => 010010010111 => 101010000111 => 010100001111
101101110000 => 010010001111 => 001010001111 => 010100011110
101110001010 => 010001110101 => 110010011001 => 100100110011
101110001100 => 010001110011 => 010010011011 => 100100110110
101110010010 => 010001101101 => 110010010101 => 100100101011
101110010100 => 010001101011 => 110010010011 => 100100100111
101110011000 => 010001100111 => 010010010111 => 100100101110
101110100010 => 010001011101 => 110010001101 => 100100011011
101110100100 => 010001011011 => 110010001011 => 100100010111
101110101000 => 010001010111 => 110010000111 => 100100001111
101110110000 => 010001001111 => 010010001111 => 100100011110
101111000010 => 010000111101 => 100010011101 => 000100111011
101111000100 => 010000111011 => 100010011011 => 000100110111
101111001000 => 010000110111 => 100010010111 => 000100101111
101111010000 => 010000101111 => 100010001111 => 000100011111
101111100000 => 010000011111 => 000010011111 => 000100111110
110010101010 => 001101010101 => 111100100001 => 111001000011
110010101100 => 001101010011 => 011100100011 => 111001000110
110010110010 => 001101001101 => 101100100101 => 011001001011
110010110100 => 001101001011 => 101100100011 => 011001000111
110010111000 => 001101000111 => 001100100111 => 011001001110
110011001010 => 001100110101 => 110100101001 => 101001010011
110011001100 => 001100110011 => 010100101011 => 101001010110
110011010010 => 001100101101 => 110100100101 => 101001001011
110011010100 => 001100101011 => 110100100011 => 101001000111
110011011000 => 001100100111 => 010100100111 => 101001001110
110011100010 => 001100011101 => 100100101101 => 001001011011
110011100100 => 001100011011 => 100100101011 => 001001010111
110011101000 => 001100010111 => 100100100111 => 001001001111
110011110000 => 001100001111 => 000100101111 => 001001011110
110100101010 => 001011010101 => 111100010001 => 111000100011
110100101100 => 001011010011 => 011100010011 => 111000100110
110100110010 => 001011001101 => 101100010101 => 011000101011
110100110100 => 001011001011 => 101100010011 => 011000100111
110100111000 => 001011000111 => 001100010111 => 011000101110
110101001010 => 001010110101 => 111100001001 => 111000010011
110101001100 => 001010110011 => 011100001011 => 111000010110
110101010010 => 001010101101 => 111100000101 => 111000001011
110101010100 => 001010101011 => 111100000011 => 111000000111
110101011000 => 001010100111 => 011100000111 => 111000001110
110101100010 => 001010011101 => 101100001101 => 011000011011
110101100100 => 001010011011 => 101100001011 => 011000010111
110101101000 => 001010010111 => 101100000111 => 011000001111
110101110000 => 001010001111 => 001100001111 => 011000011110
110110001010 => 001001110101 => 110100011001 => 101000110011
110110001100 => 001001110011 => 010100011011 => 101000110110
110110010010 => 001001101101 => 110100010101 => 101000101011
110110010100 => 001001101011 => 110100010011 => 101000100111
110110011000 => 001001100111 => 010100010111 => 101000101110
110110100010 => 001001011101 => 110100001101 => 101000011011
110110100100 => 001001011011 => 110100001011 => 101000010111
110110101000 => 001001010111 => 110100000111 => 101000001111
110110110000 => 001001001111 => 010100001111 => 101000011110
110111000010 => 001000111101 => 100100011101 => 001000111011
110111000100 => 001000111011 => 100100011011 => 001000110111
110111001000 => 001000110111 => 100100010111 => 001000101111
110111010000 => 001000101111 => 100100001111 => 001000011111
110111100000 => 001000011111 => 000100011111 => 001000111110
111000101010 => 000111010101 => 111000110001 => 110001100011
111000101100 => 000111010011 => 011000110011 => 110001100110
111000110010 => 000111001101 => 101000110101 => 010001101011
111000110100 => 000111001011 => 101000110011 => 010001100111
111000111000 => 000111000111 => 001000110111 => 010001101110
111001001010 => 000110110101 => 111000101001 => 110001010011
111001001100 => 000110110011 => 011000101011 => 110001010110
111001010010 => 000110101101 => 111000100101 => 110001001011
111001010100 => 000110101011 => 111000100011 => 110001000111
111001011000 => 000110100111 => 011000100111 => 110001001110
111001100010 => 000110011101 => 101000101101 => 010001011011
111001100100 => 000110011011 => 101000101011 => 010001010111
111001101000 => 000110010111 => 101000100111 => 010001001111
111001110000 => 000110001111 => 001000101111 => 010001011110
111010001010 => 000101110101 => 111000011001 => 110000110011
111010001100 => 000101110011 => 011000011011 => 110000110110
111010010010 => 000101101101 => 111000010101 => 110000101011
111010010100 => 000101101011 => 111000010011 => 110000100111
111010011000 => 000101100111 => 011000010111 => 110000101110
111010100010 => 000101011101 => 111000001101 => 110000011011
111010100100 => 000101011011 => 111000001011 => 110000010111
111010101000 => 000101010111 => 111000000111 => 110000001111
111010110000 => 000101001111 => 011000001111 => 110000011110
111011000010 => 000100111101 => 101000011101 => 010000111011
111011000100 => 000100111011 => 101000011011 => 010000110111
111011001000 => 000100110111 => 101000010111 => 010000101111
111011010000 => 000100101111 => 101000001111 => 010000011111
111011100000 => 000100011111 => 001000011111 => 010000111110
111100001010 => 000011110101 => 110000111001 => 100001110011
111100001100 => 000011110011 => 010000111011 => 100001110110
111100010010 => 000011101101 => 110000110101 => 100001101011
111100010100 => 000011101011 => 110000110011 => 100001100111
111100011000 => 000011100111 => 010000110111 => 100001101110
111100100010 => 000011011101 => 110000101101 => 100001011011
111100100100 => 000011011011 => 110000101011 => 100001010111
111100101000 => 000011010111 => 110000100111 => 100001001111
111100110000 => 000011001111 => 010000101111 => 100001011110
111101000010 => 000010111101 => 110000011101 => 100000111011
111101000100 => 000010111011 => 110000011011 => 100000110111
111101001000 => 000010110111 => 110000010111 => 100000101111
111101010000 => 000010101111 => 110000001111 => 100000011111
111101100000 => 000010011111 => 010000011111 => 100000111110
111110000010 => 000001111101 => 100000111101 => 000001111011
111110000100 => 000001111011 => 100000111011 => 000001110111
111110001000 => 000001110111 => 100000110111 => 000001101111
111110010000 => 000001101111 => 100000101111 => 000001011111
111110100000 => 000001011111 => 100000011111 => 000000111111
111111000000 => 000000111111 => 000000111111 => 000001111110
10110111100000 => 01001000011111 => 00010100011111 => 00101000111110
10111011100000 => 01000100011111 => 00100100011111 => 01001000111110
10111100110000 => 01000011001111 => 01000100101111 => 10001001011110
10111101100000 => 01000010011111 => 01000100011111 => 10001000111110
10111111000000 => 01000000111111 => 00000100111111 => 00001001111110
11001111100000 => 00110000011111 => 00001001011111 => 00010010111110
11010111100000 => 00101000011111 => 00011000011111 => 00110000111110
11011001110000 => 00100110001111 => 00101000101111 => 01010001011110
11011011100000 => 00100100011111 => 00101000011111 => 01010000111110
11011101100000 => 00100010011111 => 01001000011111 => 10010000111110
11011111000000 => 00100000111111 => 00001000111111 => 00010001111110
11100110011000 => 00011001100111 => 01010001010111 => 10100010101110
11100110110000 => 00011001001111 => 01010001001111 => 10100010011110
11100111100000 => 00011000011111 => 00010001011111 => 00100010111110
11101011100000 => 00010100011111 => 00110000011111 => 01100000111110
11101100110000 => 00010011001111 => 01010000101111 => 10100001011110
11101111000000 => 00010000111111 => 00010000111111 => 00100001111110
11110001110000 => 00001110001111 => 00100001101111 => 01000011011110
11110011100000 => 00001100011111 => 00100001011111 => 01000010111110
11110111000000 => 00001000111111 => 00100000111111 => 01000001111110
11111000001100 => 00000111110011 => 01000001111011 => 10000011110110
11111000011000 => 00000111100111 => 01000001110111 => 10000011101110
11111000110000 => 00000111001111 => 01000001101111 => 10000011011110
11111001100000 => 00000110011111 => 01000001011111 => 10000010111110
11111011000000 => 00000100111111 => 01000000111111 => 10000001111110
11111110000000 => 00000001111111 => 00000001111111 => 00000011111110
1010101010101010 => 0101010101010101 => 1111111000000001 => 1111110000000011
1011111011000000 => 0100000100111111 => 0100001000111111 => 1000010001111110
1111111111 => 0000000000 => 0000000000 => 0000000000
1111111110 => 0000000001 => 0000000001 => 0000000010
1111111101 => 0000000010 => 1000000000 => 0000000001
1111111100 => 0000000011 => 0000000011 => 0000000110
1111111011 => 0000000100 => 0100000000 => 1000000000
1111111010 => 0000000101 => 1000000001 => 0000000011
1111111001 => 0000000110 => 1000000010 => 0000000101
1111111000 => 0000000111 => 0000000111 => 0000001110
1111110110 => 0000001001 => 0100000001 => 1000000010
1111110101 => 0000001010 => 1100000000 => 1000000001
1111110100 => 0000001011 => 1000000011 => 0000000111
1111110011 => 0000001100 => 0100000010 => 1000000100
1111110010 => 0000001101 => 1000000101 => 0000001011
1111110001 => 0000001110 => 1000000110 => 0000001101
1111110000 => 0000001111 => 0000001111 => 0000011110
1111101110 => 0000010001 => 0010000001 => 0100000010
1111101011 => 0000010100 => 0110000000 => 1100000000
1111101010 => 0000010101 => 1100000001 => 1000000011
1111101001 => 0000010110 => 1100000010 => 1000000101
1111101000 => 0000010111 => 1000000111 => 0000001111
1111100100 => 0000011011 => 1000001011 => 0000010111
1111100010 => 0000011101 => 1000001101 => 0000011011
1111100001 => 0000011110 => 1000001110 => 0000011101
1111011110 => 0000100001 => 0001000001 => 0010000010
1111011011 => 0000100100 => 0101000000 => 1010000000
1111011010 => 0000100101 => 1010000001 => 0100000011
1111010111 => 0000101000 => 0011000000 => 0110000000
1111010100 => 0000101011 => 1100000011 => 1000000111
1111010001 => 0000101110 => 1100000110 => 1000001101
1111001110 => 0000110001 => 0010000101 => 0100001010
1111001100 => 0000110011 => 0100001011 => 1000010110
1111001001 => 0000110110 => 1100001010 => 1000010101
1111000101 => 0000111010 => 1100001100 => 1000011001
1111000011 => 0000111100 => 0100001110 => 1000011100
1111000001 => 0000111110 => 1000011110 => 0000111101
1111000000 => 0000111111 => 0000111111 => 0001111110
1110111110 => 0001000001 => 0000100001 => 0001000010
1110111011 => 0001000100 => 0100100000 => 1001000000
1110110111 => 0001001000 => 0010100000 => 0101000000
1110101111 => 0001010000 => 0001100000 => 0011000000
1110101110 => 0001010001 => 0011000001 => 0110000010
1110101011 => 0001010100 => 0111000000 => 1110000000
1110101010 => 0001010101 => 1110000001 => 1100000011
1110101001 => 0001010110 => 1110000010 => 1100000101
1110100101 => 0001011010 => 1110000100 => 1100001001
1110100011 => 0001011100 => 0110000110 => 1100001100
1110100000 => 0001011111 => 1000011111 => 0000111111
1110011001 => 0001100110 => 1010001010 => 0100010101
1110010110 => 0001101001 => 0110001001 => 1100010010
1110010011 => 0001101100 => 0110001010 => 1100010100
1110010000 => 0001101111 => 1000101111 => 0001011111
1110001101 => 0001110010 => 1010001100 => 0100011001
1110001011 => 0001110100 => 0110001100 => 1100011000
1110001000 => 0001110111 => 1000110111 => 0001101111
1110000111 => 0001111000 => 0010001110 => 0100011100
1110000110 => 0001111001 => 0100011101 => 1000111010
1110000101 => 0001111010 => 1100011100 => 1000111001
1110000100 => 0001111011 => 1000111011 => 0001110111
1110000011 => 0001111100 => 0100011110 => 1000111100
1110000010 => 0001111101 => 1000111101 => 0001111011
1110000001 => 0001111110 => 1000111110 => 0001111101
1110000000 => 0001111111 => 0001111111 => 0011111110
1101111110 => 0010000001 => 0000010001 => 0000100010
1101111101 => 0010000010 => 1000010000 => 0000100001
1101111011 => 0010000100 => 0100010000 => 1000100000
1101110001 => 0010001110 => 1001000110 => 0010001101
1101101111 => 0010010000 => 0001010000 => 0010100000
1101101100 => 0010010011 => 0101000011 => 1010000110
1101101011 => 0010010100 => 0110100000 => 1101000000
1101101010 => 0010010101 => 1101000001 => 1010000011
1101101001 => 0010010110 => 1101000010 => 1010000101
1101100110 => 0010011001 => 0101000101 => 1010001010
1101100011 => 0010011100 => 0101000110 => 1010001100
1101100001 => 0010011110 => 1010001110 => 0100011101
1101011111 => 0010100000 => 0000110000 => 0001100000
1101011010 => 0010100101 => 1011000001 => 0110000011
1101011001 => 0010100110 => 1011000010 => 0110000101
1101010101 => 0010101010 => 1111000000 => 1110000001
1101010011 => 0010101100 => 0111000010 => 1110000100
1101001101 => 0010110010 => 1011000100 => 0110001001
1101001011 => 0010110100 => 0111000100 => 1110001000
1101001001 => 0010110110 => 1110001010 => 1100010101
1101001000 => 0010110111 => 1100010111 => 1000101111
1101000111 => 0010111000 => 0011000110 => 0110001100
1101000110 => 0010111001 => 0110001101 => 1100011010
1101000101 => 0010111010 => 1110001100 => 1100011001
1101000011 => 0010111100 => 0110001110 => 1100011100
1101000010 => 0010111101 => 1100011101 => 1000111011
1101000001 => 0010111110 => 1100011110 => 1000111101
1101000000 => 0010111111 => 1000111111 => 0001111111
1100111111 => 0011000000 => 0000010010 => 0000100100
1100111110 => 0011000001 => 0000100101 => 0001001010
1100111100 => 0011000011 => 0001001011 => 0010010110
1100111001 => 0011000110 => 1001001010 => 0010010101
1100110011 => 0011001100 => 0101001010 => 1010010100
1100110001 => 0011001110 => 1010010110 => 0100101101
1100101101 => 0011010010 => 1011001000 => 0110010001
1100101011 => 0011010100 => 0111001000 => 1110010000
1100101001 => 0011010110 => 1110010010 => 1100100101
1100101000 => 0011010111 => 1100100111 => 1001001111
1100100111 => 0011011000 => 0011001010 => 0110010100
1100100110 => 0011011001 => 0110010101 => 1100101010
1100100101 => 0011011010 => 1110010100 => 1100101001
1100100100 => 0011011011 => 1100101011 => 1001010111
1100100011 => 0011011100 => 0110010110 => 1100101100
1100100010 => 0011011101 => 1100101101 => 1001011011
1100100001 => 0011011110 => 1100101110 => 1001011101
1100100000 => 0011011111 => 1001011111 => 0010111111
1100011101 => 0011100010 => 1001001100 => 0010011001
1100011011 => 0011100100 => 0101001100 => 1010011000
1100011010 => 0011100101 => 1010011001 => 0100110011
1100011001 => 0011100110 => 1010011010 => 0100110101
1100011000 => 0011100111 => 0100110111 => 1001101110
1100010111 => 0011101000 => 0011001100 => 0110011000
1100010101 => 0011101010 => 1110011000 => 1100110001
1100010011 => 0011101100 => 0110011010 => 1100110100
1100010010 => 0011101101 => 1100110101 => 1001101011
1100001111 => 0011110000 => 0001001110 => 0010011100
1100001110 => 0011110001 => 0010011101 => 0100111010
1100001100 => 0011110011 => 0100111011 => 1001110110
1100001010 => 0011110101 => 1100111001 => 1001110011
1100000111 => 0011111000 => 0010011110 => 0100111100
1100000101 => 0011111010 => 1100111100 => 1001111001
1100000011 => 0011111100 => 0100111110 => 1001111100
1100000001 => 0011111110 => 1001111110 => 0011111101
1100000000 => 0011111111 => 0011111111 => 0111111110
1011111111 => 0100000000 => 0000000100 => 0000001000
1011111110 => 0100000001 => 0000001001 => 0000010010
1011111011 => 0100000100 => 0100001000 => 1000010000
1011111000 => 0100000111 => 0000100111 => 0001001110
1011101111 => 0100010000 => 0001001000 => 0010010000
1011101110 => 0100010001 => 0010010001 => 0100100010
1011101100 => 0100010011 => 0100100011 => 1001000110
1011101010 => 0100010101 => 1100100001 => 1001000011
1011100101 => 0100011010 => 1100100100 => 1001001001
1011100011 => 0100011100 => 0100100110 => 1001001100
1011100001 => 0100011110 => 1001001110 => 0010011101
1011100000 => 0100011111 => 0010011111 => 0100111110
1011011111 => 0100100000 => 0000101000 => 0001010000
1011011110 => 0100100001 => 0001010001 => 0010100010
1011011001 => 0100100110 => 1010100010 => 0101000101
1011010110 => 0100101001 => 0110100001 => 1101000010
1011010011 => 0100101100 => 0110100010 => 1101000100
1011010000 => 0100101111 => 1010001111 => 0100011111
1011001110 => 0100110001 => 0010100101 => 0101001010
1011001101 => 0100110010 => 1010100100 => 0101001001
1011001011 => 0100110100 => 0110100100 => 1101001000
1011001001 => 0100110110 => 1101001010 => 1010010101
1011001000 => 0100110111 => 1010010111 => 0100101111
1011000111 => 0100111000 => 0010100110 => 0101001100
1011000110 => 0100111001 => 0101001101 => 1010011010
1011000101 => 0100111010 => 1101001100 => 1010011001
1011000100 => 0100111011 => 1010011011 => 0100110111
1011000011 => 0100111100 => 0101001110 => 1010011100
1010111111 => 0101000000 => 0000011000 => 0000110000
1010111110 => 0101000001 => 0000110001 => 0001100010
1010111100 => 0101000011 => 0001100011 => 0011000110
1010111010 => 0101000101 => 1001100001 => 0011000011
1010111001 => 0101000110 => 1001100010 => 0011000101
1010110011 => 0101001100 => 0101100010 => 1011000100
1010110000 => 0101001111 => 0110001111 => 1100011110
1010101110 => 0101010001 => 0011100001 => 0111000010
1010101101 => 0101010010 => 1011100000 => 0111000001
1010101011 => 0101010100 => 0111100000 => 1111000000
1010101001 => 0101010110 => 1111000010 => 1110000101
1010101000 => 0101010111 => 1110000111 => 1100001111
1010100111 => 0101011000 => 0011100010 => 0111000100
1010100110 => 0101011001 => 0111000101 => 1110001010
1010100101 => 0101011010 => 1111000100 => 1110001001
1010100100 => 0101011011 => 1110001011 => 1100010111
1010100010 => 0101011101 => 1110001101 => 1100011011
1010011101 => 0101100010 => 1001100100 => 0011001001
1010011100 => 0101100011 => 0011001011 => 0110010110
1010011011 => 0101100100 => 0101100100 => 1011001000
1010011010 => 0101100101 => 1011001001 => 0110010011
1010011000 => 0101100111 => 0110010111 => 1100101110
1010010111 => 0101101000 => 0011100100 => 0111001000
1010010110 => 0101101001 => 0111001001 => 1110010010
1010010101 => 0101101010 => 1111001000 => 1110010001
1010010100 => 0101101011 => 1110010011 => 1100100111
1010010001 => 0101101110 => 1110010110 => 1100101101
1010001111 => 0101110000 => 0001100110 => 0011001100
1010001110 => 0101110001 => 0011001101 => 0110011010
1010001101 => 0101110010 => 1011001100 => 0110011001
1010001100 => 0101110011 => 0110011011 => 1100110110
1010001011 => 0101110100 => 0111001100 => 1110011000
1010001010 => 0101110101 => 1110011001 => 1100110011
1010000111 => 0101111000 => 0011001110 => 0110011100
1010000000 => 0101111111 => 1001111111 => 0011111111
1001111111 => 0110000000 => 0000001010 => 0000010100
1001111110 => 0110000001 => 0000010101 => 0000101010
1001111100 => 0110000011 => 0000101011 => 0001010110
1001111000 => 0110000111 => 0001010111 => 0010101110
1001110110 => 0110001001 => 0100101001 => 1001010010
1001110011 => 0110001100 => 0100101010 => 1001010100
1001110010 => 0110001101 => 1001010101 => 0010101011
1001110001 => 0110001110 => 1001010110 => 0010101101
1001101101 => 0110010010 => 1010101000 => 0101010001
1001101100 => 0110010011 => 0101010011 => 1010100110
1001101011 => 0110010100 => 0110101000 => 1101010000
1001101010 => 0110010101 => 1101010001 => 1010100011
1001101001 => 0110010110 => 1101010010 => 1010100101
1001101000 => 0110010111 => 1010100111 => 0101001111
1001100111 => 0110011000 => 0010101010 => 0101010100
1001100110 => 0110011001 => 0101010101 => 1010101010
1001100101 => 0110011010 => 1101010100 => 1010101001
1001100100 => 0110011011 => 1010101011 => 0101010111
1001100011 => 0110011100 => 0101010110 => 1010101100
1001100000 => 0110011111 => 0101011111 => 1010111110
1001011111 => 0110100000 => 0000110100 => 0001101000
1001011110 => 0110100001 => 0001101001 => 0011010010
1001011101 => 0110100010 => 1001101000 => 0011010001
1001011100 => 0110100011 => 0011010011 => 0110100110
1001011011 => 0110100100 => 0101101000 => 1011010000
1001011010 => 0110100101 => 1011010001 => 0110100011
1001011001 => 0110100110 => 1011010010 => 0110100101
1001011000 => 0110100111 => 0110100111 => 1101001110
1001010111 => 0110101000 => 0011101000 => 0111010000
1001010110 => 0110101001 => 0111010001 => 1110100010
1001010101 => 0110101010 => 1111010000 => 1110100001
1001010100 => 0110101011 => 1110100011 => 1101000111
1001010010 => 0110101101 => 1110100101 => 1101001011
1001010000 => 0110101111 => 1101001111 => 1010011111
1001001111 => 0110110000 => 0001101010 => 0011010100
1001001110 => 0110110001 => 0011010101 => 0110101010
1001001101 => 0110110010 => 1011010100 => 0110101001
1001001100 => 0110110011 => 0110101011 => 1101010110
1001001011 => 0110110100 => 0111010100 => 1110101000
1001001010 => 0110110101 => 1110101001 => 1101010011
1001001000 => 0110110111 => 1101010111 => 1010101111
1001000111 => 0110111000 => 0011010110 => 0110101100
1001000110 => 0110111001 => 0110101101 => 1101011010
1001000100 => 0110111011 => 1101011011 => 1010110111
1001000000 => 0110111111 => 1010111111 => 0101111111
1000111111 => 0111000000 => 0000010110 => 0000101100
1000111110 => 0111000001 => 0000101101 => 0001011010
1000111101 => 0111000010 => 1000101100 => 0001011001
1000111100 => 0111000011 => 0001011011 => 0010110110
1000111011 => 0111000100 => 0100101100 => 1001011000
1000111010 => 0111000101 => 1001011001 => 0010110011
1000111001 => 0111000110 => 1001011010 => 0010110101
1000111000 => 0111000111 => 0010110111 => 0101101110
1000110111 => 0111001000 => 0010101100 => 0101011000
1000110110 => 0111001001 => 0101011001 => 1010110010
1000110101 => 0111001010 => 1101011000 => 1010110001
1000110100 => 0111001011 => 1010110011 => 0101100111
1000110011 => 0111001100 => 0101011010 => 1010110100
1000110010 => 0111001101 => 1010110101 => 0101101011
1000101111 => 0111010000 => 0001101100 => 0011011000
1000101110 => 0111010001 => 0011011001 => 0110110010
1000101101 => 0111010010 => 1011011000 => 0110110001
1000101100 => 0111010011 => 0110110011 => 1101100110
1000101011 => 0111010100 => 0111011000 => 1110110000
1000101010 => 0111010101 => 1110110001 => 1101100011
1000100111 => 0111011000 => 0011011010 => 0110110100
1000100110 => 0111011001 => 0110110101 => 1101101010
1000100101 => 0111011010 => 1110110100 => 1101101001
1000100000 => 0111011111 => 1011011111 => 0110111111
1000011111 => 0111100000 => 0000101110 => 0001011100
1000011110 => 0111100001 => 0001011101 => 0010111010
1000011011 => 0111100100 => 0101011100 => 1010111000
1000011010 => 0111100101 => 1010111001 => 0101110011
1000011000 => 0111100111 => 0101110111 => 1011101110
1000010110 => 0111101001 => 0110111001 => 1101110010
1000001111 => 0111110000 => 0001011110 => 0010111100
1000001110 => 0111110001 => 0010111101 => 0101111010
1000001010 => 0111110101 => 1101111001 => 1011110011
1000001000 => 0111110111 => 1011110111 => 0111101111
1000000111 => 0111111000 => 0010111110 => 0101111100
1000000110 => 0111111001 => 0101111101 => 1011111010
1000000100 => 0111111011 => 1011111011 => 0111110111
1000000011 => 0111111100 => 0101111110 => 1011111100
1000000010 => 0111111101 => 1011111101 => 0111111011
1000000001 => 0111111110 => 1011111110 => 0111111101
1000000000 => 0111111111 => 0111111111 => 1111111110
10000000000 => 01111111111 => 01111111111 => 11111111110
10000000010 => 01111111101 => 10111111101 => 01111111011
10000000110 => 01111111001 => 01011111101 => 10111111010
10000001110 => 01111110001 => 00101111101 => 01011111010
10000011110 => 01111100001 => 00010111101 => 00101111010
10000111110 => 01111000001 => 00001011101 => 00010111010
10001111110 => 01110000001 => 00000101101 => 00001011010
10011111110 => 01100000001 => 00000010101 => 00000101010
10111111110 => 01000000001 => 00000001001 => 00000010010
11111111110 => 00000000001 => 00000000001 => 00000000010
100000000000 => 011111111111 => 011111111111 => 111111111110
100000000010 => 011111111101 => 101111111101 => 011111111011
100000111110 => 011111000001 => 000010111101 => 000101111010
101111111110 => 010000000001 => 000000001001 => 000000010010
111111111110 => 000000000001 => 000000000001 => 000000000010
100001011110 => 011110100001 => 000110111001 => 001101110010
100101111110 => 011010000001 => 000001101001 => 000011010010
110111111110 => 001000000001 => 000000010001 => 000000100010
100000001000 => 011111110111 => 101111110111 => 011111101111
10000010000 => 01111101111 => 10111101111 => 01111011111
10000100010 => 01111011101 => 11011101101 => 10111011011
100010011110 => 011101100001 => 000110110101 => 001101101010
110011111110 => 001100000001 => 000000100101 => 000001001010
10111011110 => 01000100001 => 00010010001 => 00100100010
11110111110 => 00001000001 => 00001000001 => 00010000010
111011111110 => 000100000001 => 000000100001 => 000001000010
10000100100 => 01111011011 => 11011101011 => 10111010111
100000101010 => 011111010101 => 111011110001 => 110111100011
100010001110 => 011101110001 => 001101101101 => 011011011010
100100011110 => 011011100001 => 000110101101 => 001101011010
100010101110 => 011101010001 => 001110110001 => 011101100010
100001110110 => 011110001001 => 010010111001 => 100101110010
101010111110 => 010101000001 => 000011100001 => 000111000010
100111011110 => 011000100001 => 000100101001 => 001001010010
10111101110 => 01000010001 => 00100010001 => 01000100010
111101111110 => 000010000001 => 000001000001 => 000010000010
100000100000 => 011111011111 => 101111011111 => 011110111111
10001000100 => 01110111011 => 11011011011 => 10110110111
100010010110 => 011101101001 => 011101101001 => 111011010010
101000011110 => 010111100001 => 000110011101 => 001100111010
100011001110 => 011100110001 => 001010110101 => 010101101010
100010110110 => 011101001001 => 010110110001 => 101101100010
110000111110 => 001111000001 => 000010011101 => 000100111010
100101101110 => 011010010001 => 001011010001 => 010110100010
11011101110 => 00100010001 => 00100100001 => 01001000010
111110111110 => 000001000001 => 000010000001 => 000100000010
10010000000 => 01101111111 => 10101111111 => 01011111111
10001001000 => 01110110111 => 11011010111 => 10110101111
100010001010 => 011101110101 => 111011011001 => 110110110011
100001010010 => 011110101101 => 111011100101 => 110111001011
110000011110 => 001111100001 => 000100111101 => 001001111010
101000101110 => 010111010001 => 001110011001 => 011100110010
100101001110 => 011010110001 => 001110100101 => 011101001010
100100110110 => 011011001001 => 010110101001 => 101101010010
100011010110 => 011100101001 => 011010110001 => 110101100010
100010111010 => 011101000101 => 100110110001 => 001101100011
100001111100 => 011110000011 => 000010111011 => 000101110110
10101010110 => 01010101001 => 01111000001 => 11110000010
101101011110 => 010010100001 => 000110100001 => 001101000010
101011101110 => 010100010001 => 001001100001 => 010011000010
100111110110 => 011000001001 => 010000101001 => 100001010010
11111110110 => 00000001001 => 01000000001 => 10000000010
111111011110 => 000000100001 => 000100000001 => 001000000010
100010000000 => 011101111111 => 101101111111 => 011011111111
10100000000 => 01011111111 => 10011111111 => 00111111111
10010001000 => 01101110111 => 11010110111 => 10101101111
110000001110 => 001111110001 => 001001111101 => 010011111010
100100011010 => 011011100101 => 101101011001 => 011010110011
100010101010 => 011101010101 => 111101100001 => 111011000011
101000110110 => 010111001001 => 010110011001 => 101100110010
100110001110 => 011001110001 => 001010101101 => 010101011010
100101010110 => 011010101001 => 011110100001 => 111101000010
100100111010 => 011011000101 => 100110101001 => 001101010011
100011100110 => 011100011001 => 010010110101 => 100101101010
100011011010 => 011100100101 => 101010110001 => 010101100011
100010111100 => 011101000011 => 000110110011 => 001101100110
11111111010 => 00000000101 => 10000000001 => 00000000011
111111101110 => 000000010001 => 001000000001 => 010000000010
0111111111 => 1000000000 => 0000000010 => 0000000100
0111111101 => 1000000010 => 1000000100 => 0000001001
0111111001 => 1000000110 => 1000001010 => 0000010101
0111110001 => 1000001110 => 1000010110 => 0000101101
0111100001 => 1000011110 => 1000101110 => 0001011101
0111000001 => 1000111110 => 1001011110 => 0010111101
0110000001 => 1001111110 => 1010111110 => 0101111101
0100000001 => 1011111110 => 1101111110 => 1011111101
0000000001 => 1111111110 => 1111111110 => 1111111101
01111111111 => 10000000000 => 00000000010 => 00000000100
01111111101 => 10000000010 => 10000000100 => 00000001001
0111111011 => 1000000100 => 0100000100 => 1000001000
01111111001 => 10000000110 => 10000001010 => 00000010101
0111110101 => 1000001010 => 1100001000 => 1000010001
01111110001 => 10000001110 => 10000010110 => 00000101101
0111101001 => 1000010110 => 1100010010 => 1000100101
01111100001 => 10000011110 => 10000101110 => 00001011101
0111010001 => 1000101110 => 1100100110 => 1001001101
01111000001 => 10000111110 => 10001011110 => 00010111101
0110100001 => 1001011110 => 1101001110 => 1010011101
01110000001 => 10001111110 => 10010111110 => 00101111101
0101000001 => 1010111110 => 1110011110 => 1100111101
01100000001 => 10011111110 => 10101111110 => 01011111101
0010000001 => 1101111110 => 1110111110 => 1101111101
01000000001 => 10111111110 => 11011111110 => 10111111101
00000000001 => 11111111110 => 11111111110 => 11111111101
0101010101 => 1010101010 => 1111100000 => 1111000001
0101010011 => 1010101100 => 0111100010 => 1111000100
0101001101 => 1010110010 => 1011100100 => 0111001001
0101001011 => 1010110100 => 0111100100 => 1111001000
0101000111 => 1010111000 => 0011100110 => 0111001100
0100110101 => 1011001010 => 1101101000 => 1011010001
0100110011 => 1011001100 => 0101101010 => 1011010100
0100101101 => 1011010010 => 1011101000 => 0111010001
0100101011 => 1011010100 => 0111101000 => 1111010000
0100100111 => 1011011000 => 0011101010 => 0111010100
0100011101 => 1011100010 => 1001101100 => 0011011001
0100011011 => 1011100100 => 0101101100 => 1011011000
0100010111 => 1011101000 => 0011101100 => 0111011000
0100001111 => 1011110000 => 0001101110 => 0011011100
0011010101 => 1100101010 => 1110110000 => 1101100001
0011010011 => 1100101100 => 0110110010 => 1101100100
0011001101 => 1100110010 => 1010110100 => 0101101001
0011001011 => 1100110100 => 0110110100 => 1101101000
0011000111 => 1100111000 => 0010110110 => 0101101100
0010110101 => 1101001010 => 1101110000 => 1011100001
0010110011 => 1101001100 => 0101110010 => 1011100100
0010101101 => 1101010010 => 1011110000 => 0111100001
0010101011 => 1101010100 => 0111110000 => 1111100000
0010100111 => 1101011000 => 0011110010 => 0111100100
0010011101 => 1101100010 => 1001110100 => 0011101001
0010011011 => 1101100100 => 0101110100 => 1011101000
0010010111 => 1101101000 => 0011110100 => 0111101000
0010001111 => 1101110000 => 0001110110 => 0011101100
0001110101 => 1110001010 => 1100111000 => 1001110001
0001110011 => 1110001100 => 0100111010 => 1001110100
0001101101 => 1110010010 => 1010111000 => 0101110001
0001101011 => 1110010100 => 0110111000 => 1101110000
0001100111 => 1110011000 => 0010111010 => 0101110100
0001011101 => 1110100010 => 1001111000 => 0011110001
0001011011 => 1110100100 => 0101111000 => 1011110000
0001010111 => 1110101000 => 0011111000 => 0111110000
0001001111 => 1110110000 => 0001111010 => 0011110100
0000111101 => 1111000010 => 1000111100 => 0001111001
0000111011 => 1111000100 => 0100111100 => 1001111000
0000110111 => 1111001000 => 0010111100 => 0101111000
0000101111 => 1111010000 => 0001111100 => 0011111000
0000011111 => 1111100000 => 0000111110 => 0001111100
010101010101 => 101010101010 => 111111000000 => 111110000001
010101010011 => 101010101100 => 011111000010 => 111110000100
010101001101 => 101010110010 => 101111000100 => 011110001001
010101001011 => 101010110100 => 011111000100 => 111110001000
010101000111 => 101010111000 => 001111000110 => 011110001100
010100110101 => 101011001010 => 110111001000 => 101110010001
010100110011 => 101011001100 => 010111001010 => 101110010100
010100101101 => 101011010010 => 101111001000 => 011110010001
010100101011 => 101011010100 => 011111001000 => 111110010000
010100100111 => 101011011000 => 001111001010 => 011110010100
010100011101 => 101011100010 => 100111001100 => 001110011001
010100011011 => 101011100100 => 010111001100 => 101110011000
010100010111 => 101011101000 => 001111001100 => 011110011000
010100001111 => 101011110000 => 000111001110 => 001110011100
010011010101 => 101100101010 => 111011010000 => 110110100001
010011010011 => 101100101100 => 011011010010 => 110110100100
010011001101 => 101100110010 => 101011010100 => 010110101001
010011001011 => 101100110100 => 011011010100 => 110110101000
010011000111 => 101100111000 => 001011010110 => 010110101100
010010110101 => 101101001010 => 110111010000 => 101110100001
010010110011 => 101101001100 => 010111010010 => 101110100100
010010101101 => 101101010010 => 101111010000 => 011110100001
010010101011 => 101101010100 => 011111010000 => 111110100000
010010100111 => 101101011000 => 001111010010 => 011110100100
010010011101 => 101101100010 => 100111010100 => 001110101001
010010011011 => 101101100100 => 010111010100 => 101110101000
010010010111 => 101101101000 => 001111010100 => 011110101000
010010001111 => 101101110000 => 000111010110 => 001110101100
010001110101 => 101110001010 => 110011011000 => 100110110001
010001110011 => 101110001100 => 010011011010 => 100110110100
010001101101 => 101110010010 => 101011011000 => 010110110001
010001101011 => 101110010100 => 011011011000 => 110110110000
010001100111 => 101110011000 => 001011011010 => 010110110100
010001011101 => 101110100010 => 100111011000 => 001110110001
010001011011 => 101110100100 => 010111011000 => 101110110000
010001010111 => 101110101000 => 001111011000 => 011110110000
010001001111 => 101110110000 => 000111011010 => 001110110100
010000111101 => 101111000010 => 100011011100 => 000110111001
010000111011 => 101111000100 => 010011011100 => 100110111000
010000110111 => 101111001000 => 001011011100 => 010110111000
010000101111 => 101111010000 => 000111011100 => 001110111000
010000011111 => 101111100000 => 000011011110 => 000110111100
001101010101 => 110010101010 => 111101100000 => 111011000001
001101010011 => 110010101100 => 011101100010 => 111011000100
001101001101 => 110010110010 => 101101100100 => 011011001001
001101001011 => 110010110100 => 011101100100 => 111011001000
001101000111 => 110010111000 => 001101100110 => 011011001100
001100110101 => 110011001010 => 110101101000 => 101011010001
001100110011 => 110011001100 => 010101101010 => 101011010100
001100101101 => 110011010010 => 101101101000 => 011011010001
001100101011 => 110011010100 => 011101101000 => 111011010000
001100100111 => 110011011000 => 001101101010 => 011011010100
001100011101 => 110011100010 => 100101101100 => 001011011001
001100011011 => 110011100100 => 010101101100 => 101011011000
001100010111 => 110011101000 => 001101101100 => 011011011000
001100001111 => 110011110000 => 000101101110 => 001011011100
001011010101 => 110100101010 => 111011100000 => 110111000001
001011010011 => 110100101100 => 011011100010 => 110111000100
001011001101 => 110100110010 => 101011100100 => 010111001001
001011001011 => 110100110100 => 011011100100 => 110111001000
001011000111 => 110100111000 => 001011100110 => 010111001100
001010110101 => 110101001010 => 110111100000 => 101111000001
001010110011 => 110101001100 => 010111100010 => 101111000100
001010101101 => 110101010010 => 101111100000 => 011111000001
001010101011 => 110101010100 => 011111100000 => 111111000000
001010100111 => 110101011000 => 001111100010 => 011111000100
001010011101 => 110101100010 => 100111100100 => 001111001001
001010011011 => 110101100100 => 010111100100 => 101111001000
001010010111 => 110101101000 => 001111100100 => 011111001000
001010001111 => 110101110000 => 000111100110 => 001111001100
001001110101 => 110110001010 => 110011101000 => 100111010001
001001110011 => 110110001100 => 010011101010 => 100111010100
001001101101 => 110110010010 => 101011101000 => 010111010001
001001101011 => 110110010100 => 011011101000 => 110111010000
001001100111 => 110110011000 => 001011101010 => 010111010100
001001011101 => 110110100010 => 100111101000 => 001111010001
001001011011 => 110110100100 => 010111101000 => 101111010000
001001010111 => 110110101000 => 001111101000 => 011111010000
001001001111 => 110110110000 => 000111101010 => 001111010100
001000111101 => 110111000010 => 100011101100 => 000111011001
001000111011 => 110111000100 => 010011101100 => 100111011000
001000110111 => 110111001000 => 001011101100 => 010111011000
001000101111 => 110111010000 => 000111101100 => 001111011000
001000011111 => 110111100000 => 000011101110 => 000111011100
000111010101 => 111000101010 => 111001110000 => 110011100001
000111010011 => 111000101100 => 011001110010 => 110011100100
000111001101 => 111000110010 => 101001110100 => 010011101001
000111001011 => 111000110100 => 011001110100 => 110011101000
000111000111 => 111000111000 => 001001110110 => 010011101100
000110110101 => 111001001010 => 110101110000 => 101011100001
000110110011 => 111001001100 => 010101110010 => 101011100100
000110101101 => 111001010010 => 101101110000 => 011011100001
000110101011 => 111001010100 => 011101110000 => 111011100000
000110100111 => 111001011000 => 001101110010 => 011011100100
000110011101 => 111001100010 => 100101110100 => 001011101001
000110011011 => 111001100100 => 010101110100 => 101011101000
000110010111 => 111001101000 => 001101110100 => 011011101000
000110001111 => 111001110000 => 000101110110 => 001011101100
000101110101 => 111010001010 => 110011110000 => 100111100001
000101110011 => 111010001100 => 010011110010 => 100111100100
000101101101 => 111010010010 => 101011110000 => 010111100001
000101101011 => 111010010100 => 011011110000 => 110111100000
000101100111 => 111010011000 => 001011110010 => 010111100100
000101011101 => 111010100010 => 100111110000 => 001111100001
000101011011 => 111010100100 => 010111110000 => 101111100000
000101010111 => 111010101000 => 001111110000 => 011111100000
000101001111 => 111010110000 => 000111110010 => 001111100100
000100111101 => 111011000010 => 100011110100 => 000111101001
000100111011 => 111011000100 => 010011110100 => 100111101000
000100110111 => 111011001000 => 001011110100 => 010111101000
000100101111 => 111011010000 => 000111110100 => 001111101000
000100011111 => 111011100000 => 000011110110 => 000111101100
000011110101 => 111100001010 => 110001111000 => 100011110001
000011110011 => 111100001100 => 010001111010 => 100011110100
000011101101 => 111100010010 => 101001111000 => 010011110001
000011101011 => 111100010100 => 011001111000 => 110011110000
000011100111 => 111100011000 => 001001111010 => 010011110100
000011011101 => 111100100010 => 100101111000 => 001011110001
000011011011 => 111100100100 => 010101111000 => 101011110000
000011010111 => 111100101000 => 001101111000 => 011011110000
000011001111 => 111100110000 => 000101111010 => 001011110100
000010111101 => 111101000010 => 100011111000 => 000111110001
000010111011 => 111101000100 => 010011111000 => 100111110000
000010110111 => 111101001000 => 001011111000 => 010111110000
000010101111 => 111101010000 => 000111111000 => 001111110000
000010011111 => 111101100000 => 000011111010 => 000111110100
000001111101 => 111110000010 => 100001111100 => 000011111001
000001111011 => 111110000100 => 010001111100 => 100011111000
000001110111 => 111110001000 => 001001111100 => 010011111000
000001101111 => 111110010000 => 000101111100 => 001011111000
000001011111 => 111110100000 => 000011111100 => 000111111000
000000111111 => 111111000000 => 000001111110 => 000011111100
11010101010 => 00101010101 => 11110000001 => 11100000011
11010101100 => 00101010011 => 01110000011 => 11100000110
10101010100 => 01010101011 => 11110000011 => 11100000111
111111111111 => 000000000000 => 000000000000 => 000000000000
111110000001 => 000001111110 => 100000111110 => 000001111101
111110100101 => 000001011010 => 111000000100 => 110000001001
111001100001 => 000110011110 => 101000101110 => 010001011101
111000011001 => 000111100110 => 101000111010 => 010001110101
111000000111 => 000111111000 => 001000111110 => 010001111100
111000110001 => 000111001110 => 101000110110 => 010001101101
111000100101 => 000111011010 => 111000110100 => 110001101001
111011000001 => 000100111110 => 101000011110 => 010000111101
111011100101 => 000100011010 => 110010000100 => 100100001001
111010011101 => 000101100010 => 100110000100 => 001100001001
111010000101 => 000101111010 => 111000011100 => 110000111001
100111100001 => 011000011110 => 100010101110 => 000101011101
100110011001 => 011001100110 => 101010101010 => 010101010101
100110000111 => 011001111000 => 001010101110 => 010101011100
100110001101 => 011001110010 => 101010101100 => 010101011001
100110110001 => 011001001110 => 101010100110 => 010101001101
100110100101 => 011001011010 => 111010100100 => 110101001001
100001111001 => 011110000110 => 100010111010 => 000101110101
100001100111 => 011110011000 => 001010111010 => 010101110100
100001101101 => 011110010010 => 101010111000 => 010101110001
100000011111 => 011111100000 => 000010111110 => 000101111100
100000100101 => 011111011010 => 111011110100 => 110111101001
100011011001 => 011100100110 => 101010110010 => 010101100101
100011000111 => 011100111000 => 001010110110 => 010101101100
100011001101 => 011100110010 => 101010110100 => 010101101001
100011110001 => 011100001110 => 100010110110 => 000101101101
100011100101 => 011100011010 => 110010110100 => 100101101001
100010010111 => 011101101000 => 001110110100 => 011101101000
100010011101 => 011101100010 => 100110110100 => 001101101001
100010000101 => 011101111010 => 111011011100 => 110110111001
100010110101 => 011101001010 => 110110110000 => 101101100001
101101100001 => 010010011110 => 101010001110 => 010100011101
101100011001 => 010011100110 => 101010011010 => 010100110101
101100000111 => 010011111000 => 001010011110 => 010100111100
101100110001 => 010011001110 => 101010010110 => 010100101101
101100100101 => 010011011010 => 111010010100 => 110100101001
101111000001 => 010000111110 => 100010011110 => 000100111101
101110010111 => 010001101000 => 001100100100 => 011001001000
101110000101 => 010001111010 => 110010011100 => 100100111001
101001011111 => 010110100000 => 000011100100 => 000111001000
101001011001 => 010110100110 => 101110010010 => 011100100101
101001000111 => 010110111000 => 001110010110 => 011100101100
101001001101 => 010110110010 => 101110010100 => 011100101001
101001110111 => 010110001000 => 001001100100 => 010011001000
101001110001 => 010110001110 => 100110010110 => 001100101101
101000010111 => 010111101000 => 001110011100 => 011100111000
101000011101 => 010111100010 => 100110011100 => 001100111001
101000110101 => 010111001010 => 110110011000 => 101100110001
101011000101 => 010100111010 => 110110001100 => 101100011001
101010010101 => 010101101010 => 111110001000 => 111100010001
0000000000 => 1111111111 => 1111111111 => 1111111111
0000000110 => 1111111001 => 0111111101 => 1111111010
0000011000 => 1111100111 => 0111110111 => 1111101110
0000011110 => 1111100001 => 0001111101 => 0011111010
0000010010 => 1111101101 => 1111110101 => 1111101011
0001100000 => 1110011111 => 0111011111 => 1110111110
0001100110 => 1110011001 => 0101110101 => 1011101010
0001111000 => 1110000111 => 0001110111 => 0011101110
0001111110 => 1110000001 => 0000011101 => 0000111010
0001110010 => 1110001101 => 1001110101 => 0011101011
0001001110 => 1110110001 => 0011110101 => 0111101010
0001000010 => 1110111101 => 1111011101 => 1110111011
0001011010 => 1110100101 => 1011110001 => 0111100011
0110000000 => 1001111111 => 0101111111 => 1011111110
0110000110 => 1001111001 => 0101011101 => 1010111010
0110011000 => 1001100111 => 0101010111 => 1010101110
0110011110 => 1001100001 => 0001010101 => 0010101010
0110010010 => 1001101101 => 1101010101 => 1010101011
0111100000 => 1000011111 => 0001011111 => 0010111110
0111100110 => 1000011001 => 0100010101 => 1000101010
0111111000 => 1000000111 => 0000010111 => 0000101110
0111111110 => 1000000001 => 0000000101 => 0000001010
0111110010 => 1000001101 => 1000010101 => 0000101011
0111001000 => 1000110111 => 1001010111 => 0010101111
0111000010 => 1000111101 => 1001011101 => 0010111011
0100100000 => 1011011111 => 1101011111 => 1010111111
0100100110 => 1011011001 => 0111010101 => 1110101010
0100111000 => 1011000111 => 0011010111 => 0110101110
0100111110 => 1011000001 => 0000110101 => 0001101010
0100110010 => 1011001101 => 1011010101 => 0110101011
0100001000 => 1011110111 => 1101110111 => 1011101111
0100001110 => 1011110001 => 0011011101 => 0110111010
0100000010 => 1011111101 => 1101111101 => 1011111011
0100011010 => 1011100101 => 1011011001 => 0110110011
0101101000 => 1010010111 => 1011000111 => 0110001111
0101100010 => 1010011101 => 1011001101 => 0110011011
0101001010 => 1010110101 => 1111001001 => 1110010011
000000000000 => 111111111111 => 111111111111 => 111111111111
000000000110 => 111111111001 => 011111111101 => 111111111010
000000011000 => 111111100111 => 011111110111 => 111111101110
000000011110 => 111111100001 => 000111111101 => 001111111010
000001100000 => 111110011111 => 011111011111 => 111110111110
000001100110 => 111110011001 => 010111110101 => 101111101010
000001111000 => 111110000111 => 000111110111 => 001111101110
000001111110 => 111110000001 => 000001111101 => 000011111010
000001001000 => 111110110111 => 111111010111 => 111110101111
000001000010 => 111110111101 => 111111011101 => 111110111011
000110000000 => 111001111111 => 011101111111 => 111011111110
000110000110 => 111001111001 => 010111011101 => 101110111010
000110011000 => 111001100111 => 010111010111 => 101110101110
000110011110 => 111001100001 => 000101110101 => 001011101010
000110010010 => 111001101101 => 110111010101 => 101110101011
000111100000 => 111000011111 => 000111011111 => 001110111110
000111100110 => 111000011001 => 010001110101 => 100011101010
000111111000 => 111000000111 => 000001110111 => 000011101110
000111111110 => 111000000001 => 000000011101 => 000000111010
000111110010 => 111000001101 => 100001110101 => 000011101011
000111001000 => 111000110111 => 100111010111 => 001110101111
000111001110 => 111000110001 => 001001110101 => 010011101010
000111011010 => 111000100101 => 101001110001 => 010011100011
000100100000 => 111011011111 => 111101011111 => 111010111111
000100111000 => 111011000111 => 001111010111 => 011110101110
000100111110 => 111011000001 => 000011110101 => 000111101010
000100110010 => 111011001101 => 101111010101 => 011110101011
000100011010 => 111011100101 => 101111011001 => 011110110011
000101101000 => 111010010111 => 101111000111 => 011110001111
000101101110 => 111010010001 => 001011110001 => 010111100010
000101100010 => 111010011101 => 101111001101 => 011110011011
000101111010 => 111010000101 => 100011110001 => 000111100011
000101001010 => 111010110101 => 111111001001 => 111110010011
011000000000 => 100111111111 => 010111111111 => 101111111110
011000000110 => 100111111001 => 010101111101 => 101011111010
011000011000 => 100111100111 => 010101110111 => 101011101110
011000011110 => 100111100001 => 000101011101 => 001010111010
011001100000 => 100110011111 => 010101011111 => 101010111110
011001100110 => 100110011001 => 010101010101 => 101010101010
011001111000 => 100110000111 => 000101010111 => 001010101110
011001111110 => 100110000001 => 000001010101 => 000010101010
011001110010 => 100110001101 => 100101010101 => 001010101011
011001011010 => 100110100101 => 101101010001 => 011010100011
011110000000 => 100001111111 => 000101111111 => 001011111110
011110000110 => 100001111001 => 010001011101 => 100010111010
011110011000 => 100001100111 => 010001010111 => 100010101110
011110011110 => 100001100001 => 000100010101 => 001000101010
011110010010 => 100001101101 => 110001010101 => 100010101011
011111100000 => 100000011111 => 000001011111 => 000010111110
011111100110 => 100000011001 => 010000010101 => 100000101010
011111111000 => 100000000111 => 000000010111 => 000000101110
011111111110 => 100000000001 => 000000000101 => 000000001010
011111001000 => 100000110111 => 100001010111 => 000010101111
011111000010 => 100000111101 => 100001011101 => 000010111011
011100111000 => 100011000111 => 001001010111 => 010010101110
011100001110 => 100011110001 => 001001011101 => 010010111010
011100011010 => 100011100101 => 101001011001 => 010010110011
011101101000 => 100010010111 => 101001000111 => 010010001111
011101100010 => 100010011101 => 101001001101 => 010010011011
011101001010 => 100010110101 => 111001001001 => 110010010011
010010011000 => 101101100111 => 011101010111 => 111010101110
010010011110 => 101101100001 => 000111010101 => 001110101010
010011100110 => 101100011001 => 010011010101 => 100110101010
010011111000 => 101100000111 => 000011010111 => 000110101110
010011110010 => 101100001101 => 100011010101 => 000110101011
010011001000 => 101100110111 => 101101010111 => 011010101111
010011011010 => 101100100101 => 101011010001 => 010110100011
010000100000 => 101111011111 => 110111011111 => 101110111111
010000111110 => 101111000001 => 000011011101 => 000110111010
010001101000 => 101110010111 => 101101100111 => 011011001111
010001101110 => 101110010001 => 001011011001 => 010110110010
010001111010 => 101110000101 => 100011011001 => 000110110011
010110100110 => 101001011001 => 011011000101 => 110110001010
010110111000 => 101001000111 => 001011000111 => 010110001110
010110110010 => 101001001101 => 101011000101 => 010110001011
010110001000 => 101001110111 => 101100110111 => 011001101111
010110001110 => 101001110001 => 001011001101 => 010110011010
010110011010 => 101001100101 => 101011001001 => 010110010011
010111101000 => 101000010111 => 100011000111 => 000110001111
010111100010 => 101000011101 => 100011001101 => 000110011011
010111001010 => 101000110101 => 110011001001 => 100110010011
010100101000 => 101011010111 => 111100100111 => 111001001111
010100101110 => 101011010001 => 001111001001 => 011110010010
010100111010 => 101011000101 => 100111001001 => 001110010011
010101101010 => 101010010101 => 110111000001 => 101110000011
0010101010 => 1101010101 => 1111100001 => 1111000011
0010101000 => 1101010111 => 1111000111 => 1110001111
0010101100 => 1101010011 => 0111100011 => 1111000110
0010110100 => 1101001011 => 1011100011 => 0111000111
0011010100 => 1100101011 => 1101100011 => 1011000111
0001010100 => 1110101011 => 1111100011 => 1111000111
0101010100 => 1010101011 => 1111000011 => 1110000111
00101010101 => 11010101010 => 11111100000 => 11111000001
00101010111 => 11010101000 => 00111110000 => 01111100000
0010101110 => 1101010001 => 0011110001 => 0111100010
00101010011 => 11010101100 => 01111100010 => 11111000100
0010100000 => 1101011111 => 1110011111 => 1100111111
00101011011 => 11010100100 => 01011110000 => 10111100000
0010111100 => 1101000011 => 0001110011 => 0011100110
00101001011 => 11010110100 => 01111100100 => 11111001000
00101101011 => 11010010100 => 01101110000 => 11011100000
0011110100 => 1100001011 => 1000110011 => 0001100111
00100101011 => 11011010100 => 01111101000 => 11111010000
0000010100 => 1111101011 => 1111110011 => 1111100111
00110101011 => 11001010100 => 01110110000 => 11101100000
0111010100 => 1000101011 => 1100100011 => 1001000111
00010101011 => 11101010100 => 01111110000 => 11111100000
01010101011 => 10101010100 => 01111100000 => 11111000000
0000000010 => 1111111101 => 1111111101 => 1111111011
0000001110 => 1111110001 => 0011111101 => 0111111010
0000111110 => 1111000001 => 0000111101 => 0001111010
0011111110 => 1100000001 => 0000001101 => 0000011010
00000000000 => 11111111111 => 11111111111 => 11111111111
00000000010 => 11111111101 => 11111111101 => 11111111011
0000000100 => 1111111011 => 1111111011 => 1111110111
00000000110 => 11111111001 => 01111111101 => 11111111010
0000001010 => 1111110101 => 1111111001 => 1111110011
00000001110 => 11111110001 => 00111111101 => 01111111010
0000010110 => 1111101001 => 0111111001 => 1111110010
00000011110 => 11111100001 => 00011111101 => 00111111010
0000101110 => 1111010001 => 0011111001 => 0111110010
00000111110 => 11111000001 => 00001111101 => 00011111010
0001011110 => 1110100001 => 0001111001 => 0011110010
00001111110 => 11110000001 => 00000111101 => 00001111010
0010111110 => 1101000001 => 0000111001 => 0001110010
00011111110 => 11100000001 => 00000011101 => 00000111010
0101111110 => 1010000001 => 0000011001 => 0000110010
00111111110 => 11000000001 => 00000001101 => 00000011010
01111111110 => 10000000001 => 00000000101 => 00000001010
0010110010 => 1101001101 => 1011100101 => 0111001011
0010111000 => 1101000111 => 0011100111 => 0111001110
0011001010 => 1100110101 => 1101101001 => 1011010011
0011001100 => 1100110011 => 0101101011 => 1011010110
0011010010 => 1100101101 => 1101100101 => 1011001011
0011011000 => 1100100111 => 0101100111 => 1011001110
0011100010 => 1100011101 => 1001101101 => 0011011011
0011100100 => 1100011011 => 1001101011 => 0011010111
0011101000 => 1100010111 => 1001100111 => 0011001111
0011110000 => 1100001111 => 0001101111 => 0011011110
0100101010 => 1011010101 => 1111010001 => 1110100011
0100101100 => 1011010011 => 0111010011 => 1110100110
0100110100 => 1011001011 => 1011010011 => 0110100111
0101001100 => 1010110011 => 0111001011 => 1110010110
0101010010 => 1010101101 => 1111000101 => 1110001011
0101011000 => 1010100111 => 0111000111 => 1110001110
0101100100 => 1010011011 => 1011001011 => 0110010111
0101110000 => 1010001111 => 0011001111 => 0110011110
0110001010 => 1001110101 => 1101011001 => 1010110011
0110001100 => 1001110011 => 0101011011 => 1010110110
0110010100 => 1001101011 => 1101010011 => 1010100111
0110100010 => 1001011101 => 1101001101 => 1010011011
0110100100 => 1001011011 => 1101001011 => 1010010111
0110101000 => 1001010111 => 1101000111 => 1010001111
0110110000 => 1001001111 => 0101001111 => 1010011110
0111000100 => 1000111011 => 1001011011 => 0010110111
0111010000 => 1000101111 => 1001001111 => 0010011111
001010101010 => 110101010101 => 111111000001 => 111110000011
001010101100 => 110101010011 => 011111000011 => 111110000110
001010110010 => 110101001101 => 101111000101 => 011110001011
001010110100 => 110101001011 => 101111000011 => 011110000111
001010111000 => 110101000111 => 001111000111 => 011110001110
001011001010 => 110100110101 => 110111001001 => 101110010011
001011010010 => 110100101101 => 110111000101 => 101110001011
001011010100 => 110100101011 => 110111000011 => 101110000111
001011100010 => 110100011101 => 100111001101 => 001110011011
001011100100 => 110100011011 => 100111001011 => 001110010111
001011101000 => 110100010111 => 100111000111 => 001110001111
001100101010 => 110011010101 => 111011010001 => 110110100011
001100110010 => 110011001101 => 101011010101 => 010110101011
001100110100 => 110011001011 => 101011010011 => 010110100111
001100111000 => 110011000111 => 001011010111 => 010110101110
001101001010 => 110010110101 => 111011001001 => 110110010011
001101010010 => 110010101101 => 111011000101 => 110110001011
001101010100 => 110010101011 => 111011000011 => 110110000111
001101011000 => 110010100111 => 011011000111 => 110110001110
001101100010 => 110010011101 => 101011001101 => 010110011011
001101100100 => 110010011011 => 101011001011 => 010110010111
001101101000 => 110010010111 => 101011000111 => 010110001111
001110001010 => 110001110101 => 110011011001 => 100110110011
001110010010 => 110001101101 => 110011010101 => 100110101011
001110010100 => 110001101011 => 110011010011 => 100110100111
001110100010 => 110001011101 => 110011001101 => 100110011011
001110100100 => 110001011011 => 110011001011 => 100110010111
001110101000 => 110001010111 => 110011000111 => 100110001111
001111000010 => 110000111101 => 100011011101 => 000110111011
001111000100 => 110000111011 => 100011011011 => 000110110111
001111001000 => 110000110111 => 100011010111 => 000110101111
001111010000 => 110000101111 => 100011001111 => 000110011111
001111100000 => 110000011111 => 000011011111 => 000110111110
010010101010 => 101101010101 => 111110100001 => 111101000011
010010101100 => 101101010011 => 011110100011 => 111101000110
010010110010 => 101101001101 => 101110100101 => 011101001011
010010110100 => 101101001011 => 101110100011 => 011101000111
010011001010 => 101100110101 => 110110101001 => 101101010011
010011010010 => 101100101101 => 110110100101 => 101101001011
010011010100 => 101100101011 => 110110100011 => 101101000111
010011100010 => 101100011101 => 100110101101 => 001101011011
010011100100 => 101100011011 => 100110101011 => 001101010111
010011101000 => 101100010111 => 100110100111 => 001101001111
010100101010 => 101011010101 => 111110010001 => 111100100011
010100101100 => 101011010011 => 011110010011 => 111100100110
010100110010 => 101011001101 => 101110010101 => 011100101011
010100110100 => 101011001011 => 101110010011 => 011100100111
010100111000 => 101011000111 => 001110010111 => 011100101110
010101001010 => 101010110101 => 111110001001 => 111100010011
010101010010 => 101010101101 => 111110000101 => 111100001011
010101010100 => 101010101011 => 111110000011 => 111100000111
010101011000 => 101010100111 => 011110000111 => 111100001110
010101100010 => 101010011101 => 101110001101 => 011100011011
010101100100 => 101010011011 => 101110001011 => 011100010111
010110001010 => 101001110101 => 110110011001 => 101100110011
010110010010 => 101001101101 => 110110010101 => 101100101011
010110010100 => 101001101011 => 110110010011 => 101100100111
010110100010 => 101001011101 => 110110001101 => 101100011011
010110100100 => 101001011011 => 110110001011 => 101100010111
010110101000 => 101001010111 => 110110000111 => 101100001111
010111000010 => 101000111101 => 100110011101 => 001100111011
010111000100 => 101000111011 => 100110011011 => 001100110111
010111001000 => 101000110111 => 100110010111 => 001100101111
010111010000 => 101000101111 => 100110001111 => 001100011111
010111100000 => 101000011111 => 000110011111 => 001100111110
011000101010 => 100111010101 => 111010110001 => 110101100011
011000110010 => 100111001101 => 101010110101 => 010101101011
011000110100 => 100111001011 => 101010110011 => 010101100111
011001001010 => 100110110101 => 111010101001 => 110101010011
011001010010 => 100110101101 => 111010100101 => 110101001011
011001010100 => 100110101011 => 111010100011 => 110101000111
011001100010 => 100110011101 => 101010101101 => 010101011011
011001100100 => 100110011011 => 101010101011 => 010101010111
011001101000 => 100110010111 => 101010100111 => 010101001111
011010001010 => 100101110101 => 111010011001 => 110100110011
011010010010 => 100101101101 => 111010010101 => 110100101011
011010010100 => 100101101011 => 111010010011 => 110100100111
011010011000 => 100101100111 => 011010010111 => 110100101110
011010100010 => 100101011101 => 111010001101 => 110100011011
011010100100 => 100101011011 => 111010001011 => 110100010111
011010101000 => 100101010111 => 111010000111 => 110100001111
011011000010 => 100100111101 => 101010011101 => 010100111011
011011000100 => 100100111011 => 101010011011 => 010100110111
011011001000 => 100100110111 => 101010010111 => 010100101111
011011010000 => 100100101111 => 101010001111 => 010100011111
011100001010 => 100011110101 => 110010111001 => 100101110011
011100010010 => 100011101101 => 110010110101 => 100101101011
011100010100 => 100011101011 => 110010110011 => 100101100111
011100100010 => 100011011101 => 110010101101 => 100101011011
011100100100 => 100011011011 => 110010101011 => 100101010111
011100101000 => 100011010111 => 110010100111 => 100101001111
011101000010 => 100010111101 => 110010011101 => 100100111011
011101000100 => 100010111011 => 110010011011 => 100100110111
011101001000 => 100010110111 => 110010010111 => 100100101111
011101010000 => 100010101111 => 110010001111 => 100100011111
011110000010 => 100001111101 => 100010111101 => 000101111011
011110000100 => 100001111011 => 100010111011 => 000101110111
011110001000 => 100001110111 => 100010110111 => 000101101111
011110010000 => 100001101111 => 100010101111 => 000101011111
011110100000 => 100001011111 => 100010011111 => 000100111111
01000100010 => 10111011101 => 11101101101 => 11011011011
01000010001 => 10111101110 => 11101110110 => 11011101101
01000001000 => 10111110111 => 11011110111 => 10111101111
01010101010 => 10101010101 => 11111000001 => 11110000011
01001001000 => 10110110111 => 11101010111 => 11010101111
01000100001 => 10111011110 => 11101101110 => 11011011101
01000010000 => 10111101111 => 11011101111 => 10111011111
00100001000 => 11011110111 => 11101110111 => 11011101111
00100010000 => 11011101111 => 11101101111 => 11011011111
00010000010 => 11101111101 => 11110111101 => 11101111011
00010000100 => 11101111011 => 11110111011 => 11101110111
00010001000 => 11101110111 => 11110110111 => 11101101111
00010010000 => 11101101111 => 11110101111 => 11101011111
00000100000 => 11111011111 => 11111011111 => 11110111111
10101010101010101010 => 01010101010101010101 => 11111111100000000001 => 11111111000000000011
0100000000 => 1011111111 => 1011111111 => 0111111111
0100011111 => 1011100000 => 0000110110 => 0001101100
0101111111 => 1010000000 => 0000001100 => 0000011000
01000000000 => 10111111111 => 10111111111 => 01111111111
0100001011 => 1011110100 => 0111011100 => 1110111000
0100101111 => 1011010000 => 0001110100 => 0011101000
0110111111 => 1001000000 => 0000010100 => 0000101000
01011111111 => 10100000000 => 00000001100 => 00000011000
0101010110 => 1010101001 => 0111100001 => 1111000010
0101011001 => 1010100110 => 1011100010 => 0111000101
0101011010 => 1010100101 => 1011100001 => 0111000011
0101100101 => 1010011010 => 1101100100 => 1011001001
0101100110 => 1010011001 => 0101100101 => 1011001010
0101101001 => 1010010110 => 1101100010 => 1011000101
0101101010 => 1010010101 => 1101100001 => 1011000011
0101101100 => 1010010011 => 0101100011 => 1011000110
0101110001 => 1010001110 => 1001100110 => 0011001101
0101110010 => 1010001101 => 1001100101 => 0011001011
0101111000 => 1010000111 => 0001100111 => 0011001110
0110010101 => 1001101010 => 1110101000 => 1101010001
0110010110 => 1001101001 => 0110101001 => 1101010010
0110011001 => 1001100110 => 1010101010 => 0101010101
0110011010 => 1001100101 => 1010101001 => 0101010011
0110011100 => 1001100011 => 0010101011 => 0101010110
0110100101 => 1001011010 => 1110100100 => 1101001001
0110101001 => 1001010110 => 1110100010 => 1101000101
0110101010 => 1001010101 => 1110100001 => 1101000011
0110101100 => 1001010011 => 0110100011 => 1101000110
0110110001 => 1001001110 => 1010100110 => 0101001101
0110110010 => 1001001101 => 1010100101 => 0101001011
0110110100 => 1001001011 => 1010100011 => 0101000111
0110111000 => 1001000111 => 0010100111 => 0101001110
0111000101 => 1000111010 => 1100101100 => 1001011001
0111000110 => 1000111001 => 0100101101 => 1001011010
0111001001 => 1000110110 => 1100101010 => 1001010101
0111001010 => 1000110101 => 1100101001 => 1001010011
0111001100 => 1000110011 => 0100101011 => 1001010110
0111010010 => 1000101101 => 1100100101 => 1001001011
0111011000 => 1000100111 => 0100100111 => 1001001110
0111100100 => 1000011011 => 1000101011 => 0001010111
0111110000 => 1000001111 => 0000101111 => 0001011110
010101010110 => 101010101001 => 011111000001 => 111110000010
010101011001 => 101010100110 => 101111000010 => 011110000101
010101011010 => 101010100101 => 101111000001 => 011110000011
010101011100 => 101010100011 => 001111000011 => 011110000110
010101100101 => 101010011010 => 110111000100 => 101110001001
010101101001 => 101010010110 => 110111000010 => 101110000101
010101110010 => 101010001101 => 100111000101 => 001110001011
010101111000 => 101010000111 => 000111000111 => 001110001110
010110010101 => 101001101010 => 111011001000 => 110110010001
010110010110 => 101001101001 => 011011001001 => 110110010010
010110011001 => 101001100110 => 101011001010 => 010110010101
010110011100 => 101001100011 => 001011001011 => 010110010110
010110100101 => 101001011010 => 111011000100 => 110110001001
010110101001 => 101001010110 => 111011000010 => 110110000101
010110101010 => 101001010101 => 111011000001 => 110110000011
010110101100 => 101001010011 => 011011000011 => 110110000110
010110110100 => 101001001011 => 101011000011 => 010110000111
010111000101 => 101000111010 => 110011001100 => 100110011001
010111000110 => 101000111001 => 010011001101 => 100110011010
010111001001 => 101000110110 => 110011001010 => 100110010101
010111001100 => 101000110011 => 010011001011 => 100110010110
010111010010 => 101000101101 => 110011000101 => 100110001011
010111010100 => 101000101011 => 110011000011 => 100110000111
010111011000 => 101000100111 => 010011000111 => 100110001110
010111100001 => 101000011110 => 100011001110 => 000110011101
010111110000 => 101000001111 => 000011001111 => 000110011110
011001010101 => 100110101010 => 111101010000 => 111010100001
011001010110 => 100110101001 => 011101010001 => 111010100010
011001011001 => 100110100110 => 101101010010 => 011010100101
011001011100 => 100110100011 => 001101010011 => 011010100110
011001100101 => 100110011010 => 110101010100 => 101010101001
011001101001 => 100110010110 => 110101010010 => 101010100101
011001101100 => 100110010011 => 010101010011 => 101010100110
011001110001 => 100110001110 => 100101010110 => 001010101101
011010010101 => 100101101010 => 111101001000 => 111010010001
011010010110 => 100101101001 => 011101001001 => 111010010010
011010011010 => 100101100101 => 101101001001 => 011010010011
011010011100 => 100101100011 => 001101001011 => 011010010110
011010100101 => 100101011010 => 111101000100 => 111010001001
011010100110 => 100101011001 => 011101000101 => 111010001010
011010101001 => 100101010110 => 111101000010 => 111010000101
011010101010 => 100101010101 => 111101000001 => 111010000011
011010101100 => 100101010011 => 011101000011 => 111010000110
011010110010 => 100101001101 => 101101000101 => 011010001011
011010110100 => 100101001011 => 101101000011 => 011010000111
011010111000 => 100101000111 => 001101000111 => 011010001110
011011000101 => 100100111010 => 110101001100 => 101010011001
011011000110 => 100100111001 => 010101001101 => 101010011010
011011001001 => 100100110110 => 110101001010 => 101010010101
011011001010 => 100100110101 => 110101001001 => 101010010011
011011001100 => 100100110011 => 010101001011 => 101010010110
011011010010 => 100100101101 => 110101000101 => 101010001011
011011010100 => 100100101011 => 110101000011 => 101010000111
011011011000 => 100100100111 => 010101000111 => 101010001110
011011100001 => 100100011110 => 100101001110 => 001010011101
011011101000 => 100100010111 => 100101000111 => 001010001111
011011110000 => 100100001111 => 000101001111 => 001010011110
011100010110 => 100011101001 => 011001011001 => 110010110010
011100011001 => 100011100110 => 101001011010 => 010010110101
011100011100 => 100011100011 => 001001011011 => 010010110110
011100101001 => 100011010110 => 111001010010 => 110010100101
011100101010 => 100011010101 => 111001010001 => 110010100011
011100101100 => 100011010011 => 011001010011 => 110010100110
011100110001 => 100011001110 => 101001010110 => 010010101101
011101000101 => 100010111010 => 111001001100 => 110010011001
011101001001 => 100010110110 => 111001001010 => 110010010101
011101001100 => 100010110011 => 011001001011 => 110010010110
011101010010 => 100010101101 => 111001000101 => 110010001011
011101010100 => 100010101011 => 111001000011 => 110010000111
011101011000 => 100010100111 => 011001000111 => 110010001110
011101100001 => 100010011110 => 101001001110 => 010010011101
011101110000 => 100010001111 => 001001001111 => 010010011110
011110001010 => 100001110101 => 110001011001 => 100010110011
011110001100 => 100001110011 => 010001011011 => 100010110110
011110100100 => 100001011011 => 110001001011 => 100010010111
011110110000 => 100001001111 => 010001001111 => 100010011110
011111000001 => 100000111110 => 100001011110 => 000010111101
0100000100 => 1011111011 => 1101111011 => 1011110111
0011100110 => 1100011001 => 0100110101 => 1001101010
0011101010 => 1100010101 => 1100110001 => 1001100011
0011101100 => 1100010011 => 0100110011 => 1001100110
0010110110 => 1101001001 => 0101110001 => 1011100010
0011110010 => 1100001101 => 1000110101 => 0001101011
0001110110 => 1110001001 => 0100111001 => 1001110010
0100111010 => 1011000101 => 1001101001 => 0011010011
0010111010 => 1101000101 => 1001110001 => 0011100011
0011111000 => 1100000111 => 0000110111 => 0001101110
0100111100 => 1011000011 => 0001101011 => 0011010110
0001111100 => 1110000011 => 0000111011 => 0001110110
001111000110 => 110000111001 => 010001101101 => 100011011010
001111001010 => 110000110101 => 110001101001 => 100011010011
100111001100 => 011000110011 => 010010101011 => 100101010110
001111001100 => 110000110011 => 010001101011 => 100011010110
001011010110 => 110100101001 => 011011100001 => 110111000010
001111010010 => 110000101101 => 110001100101 => 100011001011
001111010100 => 110000101011 => 110001100011 => 100011000111
000111010110 => 111000101001 => 011001110001 => 110011100010
001011011010 => 110100100101 => 101011100001 => 010111000011
100111011000 => 011000100111 => 010010100111 => 100101001110
001111011000 => 110000100111 => 010001100111 => 100011001110
100011011100 => 011100100011 => 001010110011 => 010101100110
010011011100 => 101100100011 => 001011010011 => 010110100110
000111011100 => 111000100011 => 001001110011 => 010011100110
001101100110 => 110010011001 => 010101100101 => 101011001010
001101101010 => 110010010101 => 110101100001 => 101011000011
100101101100 => 011010010011 => 010110100011 => 101101000110
001101101100 => 110010010011 => 010101100011 => 101011000110
001111100010 => 110000011101 => 100001101101 => 000011011011
010011101010 => 101100010101 => 110011010001 => 100110100011
001011101010 => 110100010101 => 110011100001 => 100111000011
001111101000 => 110000010111 => 100001100111 => 000011001111
000111101010 => 111000010101 => 110001110001 => 100011100011
100011101100 => 011100010011 => 010010110011 => 100101100110
010011101100 => 101100010011 => 010011010011 => 100110100110
001011101100 => 110100010011 => 010011100011 => 100111000110
000111101100 => 111000010011 => 010001110011 => 100011100110
000011101110 => 111100010001 => 001001111001 => 010011110010
101001110100 => 010110001011 => 100110010011 => 001100100111
001101110010 => 110010001101 => 100101100101 => 001011001011
100101110100 => 011010001011 => 100110100011 => 001101000111
001101110100 => 110010001011 => 100101100011 => 001011000111
001011110010 => 110100001101 => 100011100101 => 000111001011
100111110000 => 011000001111 => 000010101111 => 000101011110
001111110000 => 110000001111 => 000001101111 => 000011011110
110001111000 => 001110000111 => 000100110111 => 001001101110
101001111000 => 010110000111 => 000110010111 => 001100101110
100101111000 => 011010000111 => 000110100111 => 001101001110
001101111000 => 110010000111 => 000101100111 => 001011001110
100011111000 => 011100000111 => 000010110111 => 000101101110
001011111000 => 110100000111 => 000011100111 => 000111001110
000011111010 => 111100000101 => 100001111001 => 000011110011
010001111100 => 101110000011 => 000011011011 => 000110110110
001001111100 => 110110000011 => 000011101011 => 000111010110
000101111100 => 111010000011 => 000011110011 => 000111100110
000011111100 => 111100000011 => 000001111011 => 000011110110
0000000101 => 1111111010 => 1111111100 => 1111111001
0000011101 => 1111100010 => 1001111100 => 0011111001
0001111101 => 1110000010 => 1000011100 => 0000111001
0000001001 => 1111110110 => 1111111010 => 1111110101
0010111101 => 1101000010 => 1000111000 => 0001110001
11111111101 => 00000000010 => 10000000000 => 00000000001
100101010101 => 011010101010 => 111110100000 => 111101000001
100101011001 => 011010100110 => 101110100010 => 011101000101
100101100101 => 011010011010 => 110110100100 => 101101001001
100101101001 => 011010010110 => 110110100010 => 101101000101
100101110001 => 011010001110 => 100110100110 => 001101001101
100110101001 => 011001010110 => 111010100010 => 110101000101
100111000101 => 011000111010 => 110010101100 => 100101011001
100111001001 => 011000110110 => 110010101010 => 100101010101
101001010101 => 010110101010 => 111110010000 => 111100100001
101001101001 => 010110010110 => 110110010010 => 101100100101
101010100101 => 010101011010 => 111110000100 => 111100001001
101010101001 => 010101010110 => 111110000010 => 111100000101
101011001001 => 010100110110 => 110110001010 => 101100010101
101011100001 => 010100011110 => 100110001110 => 001100011101
101100010101 => 010011101010 => 111010011000 => 110100110001
101101000101 => 010010111010 => 111010001100 => 110100011001
101101001001 => 010010110110 => 111010001010 => 110100010101
110001010101 => 001110101010 => 111100110000 => 111001100001
110001011001 => 001110100110 => 101100110010 => 011001100101
110001100101 => 001110011010 => 110100110100 => 101001101001
110001101001 => 001110010110 => 110100110010 => 101001100101
110001110001 => 001110001110 => 100100110110 => 001001101101
110010010101 => 001101101010 => 111100101000 => 111001010001
110010011001 => 001101100110 => 101100101010 => 011001010101
110010100101 => 001101011010 => 111100100100 => 111001001001
110010101001 => 001101010110 => 111100100010 => 111001000101
110011000101 => 001100111010 => 110100101100 => 101001011001
110011001001 => 001100110110 => 110100101010 => 101001010101
110011100001 => 001100011110 => 100100101110 => 001001011101
110100010101 => 001011101010 => 111100011000 => 111000110001
110100100101 => 001011011010 => 111100010100 => 111000101001
110100101001 => 001011010110 => 111100010010 => 111000100101
110101000101 => 001010111010 => 111100001100 => 111000011001
110101001001 => 001010110110 => 111100001010 => 111000010101
110110000101 => 001001111010 => 110100011100 => 101000111001
110111000001 => 001000111110 => 100100011110 => 001000111101
111000010101 => 000111101010 => 111000111000 => 110001110001
111000101001 => 000111010110 => 111000110010 => 110001100101
111001000101 => 000110111010 => 111000101100 => 110001011001
111001001001 => 000110110110 => 111000101010 => 110001010101
111100000101 => 000011111010 => 110000111100 => 100001111001
0111000011 => 1000111100 => 0100101110 => 1001011100
0011110001 => 1100001110 => 1000110110 => 0001101101
110101000011 => 001010111100 => 011100001110 => 111000011100
110100000111 => 001011111000 => 001100011110 => 011000111100
110011000011 => 001100111100 => 010100101110 => 101001011100
110110000011 => 001001111100 => 010100011110 => 101000111100
110000111100 => 001111000011 => 000100111011 => 001001110110
110000001111 => 001111110000 => 000100111110 => 001001111100
011100000111 => 100011111000 => 001001011110 => 010010111100
111001000011 => 000110111100 => 011000101110 => 110001011100
111010000011 => 000101111100 => 011000011110 => 110000111100
111000011100 => 000111100011 => 001000111011 => 010001110110
001111000011 => 110000111100 => 010001101110 => 100011011100
011110000011 => 100001111100 => 010001011110 => 100010111100
111100000011 => 000011111100 => 010000111110 => 100001111100
000111110001 => 111000001110 => 100001110110 => 000011101101
001111100001 => 110000011110 => 100001101110 => 000011011101
01111110101 => 10000001010 => 11000001000 => 10000010001
0011101101 => 1100010010 => 1010011000 => 0100110001
0011011001 => 1100100110 => 1010110010 => 0101100101
0111010101 => 1000101010 => 1110010000 => 1100100001
0111010011 => 1000101100 => 0110010010 => 1100100100
0111001101 => 1000110010 => 1010010100 => 0100101001
0111000111 => 1000111000 => 0010010110 => 0100101100
0011110011 => 1100001100 => 0100011010 => 1000110100
0111100011 => 1000011100 => 0100010110 => 1000101100
0000111111 => 1111000000 => 0000011110 => 0000111100
110101010011 => 001010101100 => 011110000010 => 111100000100
110100110011 => 001011001100 => 010110001010 => 101100010100
110100001111 => 001011110000 => 000110001110 => 001100011100
110011010011 => 001100101100 => 011010010010 => 110100100100
110011000111 => 001100111000 => 001010010110 => 010100101100
110110010011 => 001001101100 => 011010001010 => 110100010100
110001110011 => 001110001100 => 010010011010 => 100100110100
110011100011 => 001100011100 => 010010010110 => 100100101100
110111000011 => 001000111100 => 010010001110 => 100100011100
110000011111 => 001111100000 => 000010011110 => 000100111100
111001010011 => 000110101100 => 011100010010 => 111000100100
111010010011 => 000101101100 => 011100001010 => 111000010100
111000110011 => 000111001100 => 010100011010 => 101000110100
111001100011 => 000110011100 => 010100010110 => 101000101100
111011000011 => 000100111100 => 010100001110 => 101000011100
111110000011 => 000001111100 => 010000011110 => 100000111100
11111110010 => 00000001101 => 10000000101 => 00000001011
0001110100 => 1110001011 => 1001110011 => 0011100111
0001101100 => 1110010011 => 0101110011 => 1011100110
0100011100 => 1011100011 => 0011011011 => 0110110110
0001011100 => 1110100011 => 0011110011 => 0111100110
0000111100 => 1111000011 => 0001111011 => 0011110110
0001101010 => 1110010101 => 1101110001 => 1011100011
0010011010 => 1101100101 => 1011101001 => 0111010011
0000111010 => 1111000101 => 1001111001 => 0011110011
0101000110 => 1010111001 => 0111001101 => 1110011010
0010100110 => 1101011001 => 0111100101 => 1111001010
0100010110 => 1011101001 => 0111011001 => 1110110010
0010010110 => 1101101001 => 0111101001 => 1111010010
0001010110 => 1110101001 => 0111110001 => 1111100010
0000110110 => 1111001001 => 0101111001 => 1011110010
0010001110 => 1101110001 => 0011101101 => 0111011010
000111010100 => 111000101011 => 110011100011 => 100111000111
000110110100 => 111001001011 => 101011100011 => 010111000111
010001110100 => 101110001011 => 100110110011 => 001101100111
001001110100 => 110110001011 => 100111010011 => 001110100111
000011110100 => 111100001011 => 100011110011 => 000111100111
001001011100 => 110110100011 => 001111010011 => 011110100110
000101011100 => 111010100011 => 001111100011 => 011111000110
000010111100 => 111101000011 => 000111110011 => 001111100110
000111010010 => 111000101101 => 110011100101 => 100111001011
000110110010 => 111001001101 => 101011100101 => 010111001011
010001110010 => 101110001101 => 100110110101 => 001101101011
001001110010 => 110110001101 => 100111010101 => 001110101011
000011110010 => 111100001101 => 100011110101 => 000111101011
000111001010 => 111000110101 => 110011101001 => 100111010011
000110101010 => 111001010101 => 111011100001 => 110111000011
010001101010 => 101110010101 => 110110110001 => 101101100011
001001101010 => 110110010101 => 110111010001 => 101110100011
000101101010 => 111010010101 => 110111100001 => 101111000011
000011101010 => 111100010101 => 110011110001 => 100111100011
010100011010 => 101011100101 => 101110011001 => 011100110011
001100011010 => 110011100101 => 101011011001 => 010110110011
010010011010 => 101101100101 => 101110101001 => 011101010011
001010011010 => 110101100101 => 101111001001 => 011110010011
000110011010 => 111001100101 => 101011101001 => 010111010011
010001011010 => 101110100101 => 101110110001 => 011101100011
001001011010 => 110110100101 => 101111010001 => 011110100011
000101011010 => 111010100101 => 101111100001 => 011111000011
000011011010 => 111100100101 => 101011110001 => 010111100011
010000111010 => 101111000101 => 100110111001 => 001101110011
010101000110 => 101010111001 => 011110001101 => 111100011010
001101000110 => 110010111001 => 011011001101 => 110110011010
010100100110 => 101011011001 => 011110010101 => 111100101010
010010100110 => 101101011001 => 011110100101 => 111101001010
001010100110 => 110101011001 => 011111000101 => 111110001010
000110100110 => 111001011001 => 011011100101 => 110111001010
010100010110 => 101011101001 => 011110011001 => 111100110010
001100010110 => 110011101001 => 011011011001 => 110110110010
010010010110 => 101101101001 => 011110101001 => 111101010010
001010010110 => 110101101001 => 011111001001 => 111110010010
010001010110 => 101110101001 => 011110110001 => 111101100010
001001010110 => 110110101001 => 011111010001 => 111110100010
000101010110 => 111010101001 => 011111100001 => 111111000010
000011010110 => 111100101001 => 011011110001 => 110111100010
010100001110 => 101011110001 => 001110011101 => 011100111010
001100001110 => 110011110001 => 001011011101 => 010110111010
001010001110 => 110101110001 => 001111001101 => 011110011010
010001001110 => 101110110001 => 001110110101 => 011101101010
001001001110 => 110110110001 => 001111010101 => 011110101010
000101001110 => 111010110001 => 001111100101 => 011111001010
000011001110 => 111100110001 => 001011110101 => 010111101010
001000101110 => 110111010001 => 001111011001 => 011110110010
000100101110 => 111011010001 => 001111101001 => 011111010010
000010101110 => 111101010001 => 001111110001 => 011111100010
010000011110 => 101111100001 => 000110111101 => 001101111010
000100011110 => 111011100001 => 000111101101 => 001111011010
000010011110 => 111101100001 => 000111110101 => 001111101010
000001011110 => 111110100001 => 000111111001 => 001111110010
000000111110 => 111111000001 => 000011111101 => 000111111010
0110111001 => 1001000110 => 1001010010 => 0010100101
00000010101 => 11111101010 => 11111111000 => 11111110001
0000010001 => 1111101110 => 1111110110 => 1111101101
00000001001 => 11111110110 => 11111111010 => 11111110101
10000000001 => 01111111110 => 10111111110 => 01111111101
11000000001 => 00111111110 => 10011111110 => 00111111101
11100000001 => 00011111110 => 10001111110 => 00011111101
11110000001 => 00001111110 => 10000111110 => 00001111101
11111000001 => 00000111110 => 10000011110 => 00000111101
11111100001 => 00000011110 => 10000001110 => 00000011101
11111110001 => 00000001110 => 10000000110 => 00000001101
11111111001 => 00000000110 => 10000000010 => 00000000101
11111111111 => 00000000000 => 00000000000 => 00000000000
0110011011 => 1001100100 => 0101010100 => 1010101000
0100111011 => 1011000100 => 0100110100 => 1001101000
0110010011 => 1001101100 => 0110101010 => 1101010100
0110110011 => 1001001100 => 0101010010 => 1010100100
0101110011 => 1010001100 => 0100110010 => 1001100100
0110010111 => 1001101000 => 0011010100 => 0110101000
0100110111 => 1011001000 => 0010110100 => 0101101000
0110100111 => 1001011000 => 0011010010 => 0110100100
0101100111 => 1010011000 => 0010110010 => 0101100100
0101001111 => 1010110000 => 0001110010 => 0011100100
100100111001 => 011011000110 => 100110101010 => 001101010101
101000111001 => 010111000110 => 100110011010 => 001100110101
100110011011 => 011001100100 => 010101010100 => 101010101000
101100011011 => 010011100100 => 010101001100 => 101010011000
100100111011 => 011011000100 => 010011010100 => 100110101000
101000111011 => 010111000100 => 010011001100 => 100110011000
100101111011 => 011010000100 => 010001101000 => 100011010000
100110010011 => 011001101100 => 011010101010 => 110101010100
101110010011 => 010001101100 => 011001001010 => 110010010100
101100010011 => 010011101100 => 011010011010 => 110100110100
100110110011 => 011001001100 => 010101010010 => 101010100100
100100110011 => 011011001100 => 010110101010 => 101101010100
101100110011 => 010011001100 => 010101001010 => 101010010100
101000110011 => 010111001100 => 010110011010 => 101100110100
100101110011 => 011010001100 => 010011010010 => 100110100100
101001110011 => 010110001100 => 010011001010 => 100110010100
100110100011 => 011001011100 => 011010100110 => 110101001100
101100100011 => 010011011100 => 011010010110 => 110100101100
100101100011 => 011010011100 => 010110100110 => 101101001100
101101100011 => 010010011100 => 010101000110 => 101010001100
101001100011 => 010110011100 => 010110010110 => 101100101100
101011100011 => 010100011100 => 010011000110 => 100110001100
101101000011 => 010010111100 => 011010001110 => 110100011100
101011000011 => 010100111100 => 010110001110 => 101100011100
100110010111 => 011001101000 => 001101010100 => 011010101000
101100010111 => 010011101000 => 001101001100 => 011010011000
100100110111 => 011011001000 => 001011010100 => 010110101000
101000110111 => 010111001000 => 001011001100 => 010110011000
100110100111 => 011001011000 => 001101010010 => 011010100100
100100100111 => 011011011000 => 001110101010 => 011101010100
101100100111 => 010011011000 => 001101001010 => 011010010100
101000100111 => 010111011000 => 001110011010 => 011100110100
100101100111 => 011010011000 => 001011010010 => 010110100100
101001100111 => 010110011000 => 001011001010 => 010110010100
100101000111 => 011010111000 => 001110100110 => 011101001100
101101000111 => 010010111000 => 001101000110 => 011010001100
101011000111 => 010100111000 => 001011000110 => 010110001100
101010000111 => 010101111000 => 001110001110 => 011100011100
100100101111 => 011011010000 => 000111010100 => 001110101000
101000101111 => 010111010000 => 000111001100 => 001110011000
100101101111 => 011010010000 => 000101101000 => 001011010000
100101001111 => 011010110000 => 000111010010 => 001110100100
101001001111 => 010110110000 => 000111001010 => 001110010100
101010001111 => 010101110000 => 000111000110 => 001110001100
100110101010 => 011001010101 => 111010100001 => 110101000011
101001101010 => 010110010101 => 110110010001 => 101100100011
100101101010 => 011010010101 => 110110100001 => 101101000011
100011101010 => 011100010101 => 110010110001 => 100101100011
101010011010 => 010101100101 => 101110001001 => 011100010011
100110011010 => 011001100101 => 101010101001 => 010101010011
101001011010 => 010110100101 => 101110010001 => 011100100011
100101011010 => 011010100101 => 101110100001 => 011101000011
101000111010 => 010111000101 => 100110011001 => 001100110011
101010100110 => 010101011001 => 011110000101 => 111100001010
100110100110 => 011001011001 => 011010100101 => 110101001010
101001100110 => 010110011001 => 010110010101 => 101100101010
100101100110 => 011010011001 => 010110100101 => 101101001010
101010010110 => 010101101001 => 011110001001 => 111100010010
100110010110 => 011001101001 => 011010101001 => 110101010010
101001010110 => 010110101001 => 011110010001 => 111100100010
101010001110 => 010101110001 => 001110001101 => 011100011010
100011101001 => 011100010110 => 110010110010 => 100101100101
100011010101 => 011100101010 => 111010110000 => 110101100001
100100110101 => 011011001010 => 110110101000 => 101101010001
100001110101 => 011110001010 => 110010111000 => 100101110001
101010001101 => 010101110010 => 101110001100 => 011100011001
100101001101 => 011010110010 => 101110100100 => 011101001001
101000101101 => 010111010010 => 101110011000 => 011100110001
100100101101 => 011011010010 => 101110101000 => 011101010001
100010101101 => 011101010010 => 101110110000 => 011101100001
101010100011 => 010101011100 => 011110000110 => 111100001100
100011100011 => 011100011100 => 010010110110 => 100101101100
101001010011 => 010110101100 => 011110010010 => 111100100100
100010110011 => 011101001100 => 010110110010 => 101101100100
100001110011 => 011110001100 => 010010111010 => 100101110100
101010001011 => 010101110100 => 011110001100 => 111100011000
100110001011 => 011001110100 => 011010101100 => 110101011000
101001001011 => 010110110100 => 011110010100 => 111100101000
100101001011 => 011010110100 => 011110100100 => 111101001000
101000101011 => 010111010100 => 011110011000 => 111100110000
100100101011 => 011011010100 => 011110101000 => 111101010000
100010101011 => 011101010100 => 011110110000 => 111101100000
100001011011 => 011110100100 => 010110111000 => 101101110000
101000001111 => 010111110000 => 000110011110 => 001100111100
100100001111 => 011011110000 => 000110101110 => 001101011100
100010001111 => 011101110000 => 000110110110 => 001101101100
100001001111 => 011110110000 => 000110111010 => 001101110100
01110111101 => 10001000010 => 10001001000 => 00010010001
01111011101 => 10000100010 => 10010001000 => 00100010001
01111101111 => 10000010000 => 00010000100 => 00100001000
10111110111 => 01000001000 => 00100001000 => 01000010000
10111101111 => 01000010000 => 00010001000 => 00100010000
11011110111 => 00100001000 => 00100010000 => 01000100000
11011101111 => 00100010000 => 00010010000 => 00100100000
11101111011 => 00010000100 => 01000100000 => 10001000000
0000001100 => 1111110011 => 0111111011 => 1111110110
0000110011 => 1111001100 => 0101111010 => 1011110100
0011001111 => 1100110000 => 0001011010 => 0010110100
0000000011 => 1111111100 => 0111111110 => 1111111100
0001101111 => 1110010000 => 0001011100 => 0010111000
0010000010 => 1101111101 => 1110111101 => 1101111011
0111001011 => 1000110100 => 0110010100 => 1100101000
0111110111 => 1000001000 => 0010000100 => 0100001000
11000000000 => 00111111111 => 00111111111 => 01111111110
0110000111 => 1001111000 => 0010101110 => 0101011100
110000111001 => 001111000110 => 100100111010 => 001001110101
110000110101 => 001111001010 => 110100111000 => 101001110001
110010001101 => 001101110010 => 101100101100 => 011001011001
110100001101 => 001011110010 => 101100011100 => 011000111001
110000101101 => 001111010010 => 101100111000 => 011001110001
110000011101 => 001111100010 => 100100111100 => 001001111001
011100100011 => 100011011100 => 011001010110 => 110010101100
011010010011 => 100101101100 => 011101001010 => 111010010100
011100010011 => 100011101100 => 011001011010 => 110010110100
011000110011 => 100111001100 => 010101011010 => 101010110100
011010001011 => 100101110100 => 011101001100 => 111010011000
011100001011 => 100011110100 => 011001011100 => 110010111000
011000101011 => 100111010100 => 011101011000 => 111010110000
101110000011 => 010001111100 => 010010011110 => 100100111100
111000100011 => 000111011100 => 011000110110 => 110001101100
110100010011 => 001011101100 => 011100011010 => 111000110100
111000010011 => 000111101100 => 011000111010 => 110001110100
110000110011 => 001111001100 => 010100111010 => 101001110100
110100001011 => 001011110100 => 011100011100 => 111000111000
110000101011 => 001111010100 => 011100111000 => 111001110000
001110000111 => 110001111000 => 001001101110 => 010011011100
010110000111 => 101001111000 => 001011001110 => 010110011100
011010000111 => 100101111000 => 001101001110 => 011010011100
011000100111 => 100111011000 => 001101011010 => 011010110100
110010000111 => 001101111000 => 001100101110 => 011001011100
110000100111 => 001111011000 => 001100111010 => 011001110100
110000010111 => 001111101000 => 001100111100 => 011001111000
011000001111 => 100111110000 => 000101011110 => 001010111100
0011011010 => 1100100101 => 1010110001 => 0101100011
0011010110 => 1100101001 => 0110110001 => 1101100010
0100110110 => 1011001001 => 0101101001 => 1011010010
0110001110 => 1001110001 => 0010101101 => 0101011010
0101001110 => 1010110001 => 0011100101 => 0111001010
0011001110 => 1100110001 => 0010110101 => 0101101010
0100011110 => 1011100001 => 0001101101 => 0011011010
0010011110 => 1101100001 => 0001110101 => 0011101010
001110101010 => 110001010101 => 111001100001 => 110011000011
001110011010 => 110001100101 => 101001101001 => 010011010011
001101011010 => 110010100101 => 101101100001 => 011011000011
011000111010 => 100111000101 => 100101011001 => 001010110011
001100111010 => 110011000101 => 100101101001 => 001011010011
010010111010 => 101101000101 => 100111010001 => 001110100011
001010111010 => 110101000101 => 100111100001 => 001111000011
000110111010 => 111001000101 => 100101110001 => 001011100011
001110100110 => 110001011001 => 011001100101 => 110011001010
001110010110 => 110001101001 => 011001101001 => 110011010010
001101010110 => 110010101001 => 011101100001 => 111011000010
010011010110 => 101100101001 => 011011010001 => 110110100010
011000110110 => 100111001001 => 010101011001 => 101010110010
010100110110 => 101011001001 => 010111001001 => 101110010010
001100110110 => 110011001001 => 010101101001 => 101011010010
010010110110 => 101101001001 => 010111010001 => 101110100010
001010110110 => 110101001001 => 010111100001 => 101111000010
000110110110 => 111001001001 => 010101110001 => 101011100010
010001110110 => 101110001001 => 010011011001 => 100110110010
011010001110 => 100101110001 => 001101001101 => 011010011010
001110001110 => 110001110001 => 001001101101 => 010011011010
001011001110 => 110100110001 => 001011100101 => 010111001010
010010101110 => 101101010001 => 001111010001 => 011110100010
001010101110 => 110101010001 => 001111100001 => 011111000010
010100011110 => 101011100001 => 000111001101 => 001110011010
001100011110 => 110011100001 => 000101101101 => 001011011010
010001011110 => 101110100001 => 000111011001 => 001110110010
000101011110 => 111010100001 => 000111110001 => 001111100010
001000111110 => 110111000001 => 000011101101 => 000111011010
000010111110 => 111101000001 => 000011111001 => 000111110010
0101000000 => 1010111111 => 1100111111 => 1001111111
0001010000 => 1110101111 => 1111001111 => 1110011111
0001000100 => 1110111011 => 1111011011 => 1110110111
0001010101 => 1110101010 => 1111110000 => 1111100001
0101011011 => 1010100100 => 0101110000 => 1011100000
0001001011 => 1110110100 => 0111110100 => 1111101000
0110101011 => 1001010100 => 0111010000 => 1110100000
0111101111 => 1000010000 => 0001000100 => 0010001000
011010010000 => 100101101111 => 110100101111 => 101001011111
011010000100 => 100101111011 => 110100111011 => 101001110111
011011011011 => 100100100100 => 010101010000 => 101010100000
011101101011 => 100010010100 => 011010010000 => 110100100000
011001101111 => 100110010000 => 000101010100 => 001010101000
0111000000 => 1000111111 => 0010111111 => 0101111110
0111111100 => 1000000011 => 0000001011 => 0000010110
0010000000 => 1101111111 => 1101111111 => 1011111111
0111111010 => 1000000101 => 1000001001 => 0000010011
101101010011 => 010010101100 => 011101000010 => 111010000100
101011010011 => 010100101100 => 011011000010 => 110110000100
100111010011 => 011000101100 => 011001010010 => 110010100100
110010110011 => 001101001100 => 010110010010 => 101100100100
101010110011 => 010101001100 => 010111000010 => 101110000100
100011110011 => 011100001100 => 010001011010 => 100010110100
110101001011 => 001010110100 => 011110000100 => 111100001000
101101001011 => 010010110100 => 011101000100 => 111010001000
110011001011 => 001100110100 => 011010010100 => 110100101000
101011001011 => 010100110100 => 011011000100 => 110110001000
100111001011 => 011000110100 => 011001010100 => 110010101000
110100101011 => 001011010100 => 011110001000 => 111100010000
101100101011 => 010011010100 => 011101001000 => 111010010000
110010101011 => 001101010100 => 011110010000 => 111100100000
101010101011 => 010101010100 => 011111000000 => 111110000000
100110101011 => 011001010100 => 011101010000 => 111010100000
110001101011 => 001110010100 => 011010011000 => 110100110000
101001101011 => 010110010100 => 011011001000 => 110110010000
100101101011 => 011010010100 => 011011010000 => 110110100000
100011101011 => 011100010100 => 011001011000 => 110010110000
110100011011 => 001011100100 => 010110001100 => 101100011000
110010011011 => 001101100100 => 010110010100 => 101100101000
101010011011 => 010101100100 => 010111000100 => 101110001000
110001011011 => 001110100100 => 010110011000 => 101100110000
101001011011 => 010110100100 => 010111001000 => 101110010000
100101011011 => 011010100100 => 010111010000 => 101110100000
100011011011 => 011100100100 => 010101011000 => 101010110000
110000111011 => 001111000100 => 010010011100 => 100100111000
100010111011 => 011101000100 => 010011011000 => 100110110000
100001111011 => 011110000100 => 010001011100 => 100010111000
100111000111 => 011000111000 => 001001010110 => 010010101100
110100100111 => 001011011000 => 001110001010 => 011100010100
110010100111 => 001101011000 => 001110010010 => 011100100100
101010100111 => 010101011000 => 001111000010 => 011110000100
110001100111 => 001110011000 => 001010011010 => 010100110100
100011100111 => 011100011000 => 001001011010 => 010010110100
110100010111 => 001011101000 => 001110001100 => 011100011000
110010010111 => 001101101000 => 001110010100 => 011100101000
101010010111 => 010101101000 => 001111000100 => 011110001000
110001010111 => 001110101000 => 001110011000 => 011100110000
101001010111 => 010110101000 => 001111001000 => 011110010000
100101010111 => 011010101000 => 001111010000 => 011110100000
100011010111 => 011100101000 => 001101011000 => 011010110000
110000110111 => 001111001000 => 001010011100 => 010100111000
100010110111 => 011101001000 => 001011011000 => 010110110000
100001110111 => 011110001000 => 001001011100 => 010010111000
101100001111 => 010011110000 => 000101001110 => 001010011100
110010001111 => 001101110000 => 000110010110 => 001100101100
100110001111 => 011001110000 => 000101010110 => 001010101100
110001001111 => 001110110000 => 000110011010 => 001100110100
100011001111 => 011100110000 => 000101011010 => 001010110100
110000101111 => 001111010000 => 000110011100 => 001100111000
100001101111 => 011110010000 => 000101011100 => 001010111000
101000011111 => 010111100000 => 000011001110 => 000110011100
100100011111 => 011011100000 => 000011010110 => 000110101100
100010011111 => 011101100000 => 000011011010 => 000110110100
100001011111 => 011110100000 => 000011011100 => 000110111000
100000111111 => 011111000000 => 000001011110 => 000010111100
0000001111 => 1111110000 => 0001111110 => 0011111100
0011111111 => 1100000000 => 0000000110 => 0000001100
00000000111 => 11111111000 => 00111111110 => 01111111100
0000010111 => 1111101000 => 0011111100 => 0111111000
00000011111 => 11111100000 => 00001111110 => 00011111100
00001111111 => 11110000000 => 00000011110 => 00000111100
00111111111 => 11000000000 => 00000000110 => 00000001100
0011111100 => 1100000011 => 0000011011 => 0000110110
00111111100 => 11000000011 => 00000011011 => 00000110110
0011011100 => 1100100011 => 0010110011 => 0101100110
0001111001 => 1110000110 => 1000111010 => 0001110101
011000111100 => 100111000011 => 000101011011 => 001010110110
010100111100 => 101011000011 => 000111001011 => 001110010110
001100111001 => 110011000110 => 100101101010 => 001011010101
001100111100 => 110011000011 => 000101101011 => 001011010110
010010111100 => 101101000011 => 000111010011 => 001110100110
001010111100 => 110101000011 => 000111100011 => 001111000110
000110111100 => 111001000011 => 000101110011 => 001011100110
001110110001 => 110001001110 => 101001100110 => 010011001101
001110110010 => 110001001101 => 101001100101 => 010011001011
001110110100 => 110001001011 => 101001100011 => 010011000111
001110111000 => 110001000111 => 001001100111 => 010011001110
001101101001 => 110010010110 => 110101100010 => 101011000101
001001111001 => 110110000110 => 100011101010 => 000111010101
001101110001 => 110010001110 => 100101100110 => 001011001101
001011100101 => 110100011010 => 110011100100 => 100111001001
001011101001 => 110100010110 => 110011100010 => 100111000101
000011111001 => 111100000110 => 100001111010 => 000011110101
001011110001 => 110100001110 => 100011100110 => 000111001101
000111100011 => 111000011100 => 010001110110 => 100011101100
000111100101 => 111000011010 => 110001110100 => 100011101001
111000101011 => 000111010100 => 011100011000 => 111000110000
111001001011 => 000110110100 => 011100010100 => 111000101000
101110001011 => 010001110100 => 011001001100 => 110010011000
110110001011 => 001001110100 => 011010001100 => 110100011000
111010001011 => 000101110100 => 011100001100 => 111000011000
101111000011 => 010000111100 => 010001001110 => 100010011100
111000001110 => 000111110001 => 001000111101 => 010001111010
001011011001 => 110100100110 => 101011100010 => 010111000101
001101100011 => 110010011100 => 010101100110 => 101011001100
001110010011 => 110001101100 => 011001101010 => 110011010100
001110011001 => 110001100110 => 101001101010 => 010011010101
001110011100 => 110001100011 => 001001101011 => 010011010110
001110100101 => 110001011010 => 111001100100 => 110011001001
11101000001 => 00010111110 => 11000011110 => 10000111101
11100100000 => 00011011111 => 10001011111 => 00010111111
11111000000 => 00000111111 => 00000111111 => 00001111110
10001000001 => 01110111110 => 11011011110 => 10110111101
11001000000 => 00110111111 => 10010111111 => 00101111111
00111000000 => 11000111111 => 00110111111 => 01101111110
100110111000 => 011001000111 => 001010100111 => 010101001110
101100100110 => 010011011001 => 011010010101 => 110100101010
111000100110 => 000111011001 => 011000110101 => 110001101010
110100010110 => 001011101001 => 011100011001 => 111000110010
110010001110 => 001101110001 => 001100101101 => 011001011010
100110011100 => 011001100011 => 001010101011 => 010101010110
100110101100 => 011001010011 => 011010100011 => 110101000110
0000101011 => 1111010100 => 0111111000 => 1111110000
0001000111 => 1110111000 => 0011110110 => 0111101100
0000100111 => 1111011000 => 0011111010 => 0111110100
0001001010 => 1110110101 => 1111101001 => 1111010011
0000100100 => 1111011011 => 1111101011 => 1111010111
0000100010 => 1111011101 => 1111101101 => 1111011011
0011000000 => 1100111111 => 0110111111 => 1101111110
0101010111 => 1010101000 => 0011110000 => 0111100000
111000010110 => 000111101001 => 011000111001 => 110001110010
100100111100 => 011011000011 => 000110101011 => 001101010110
110100011010 => 001011100101 => 101100011001 => 011000110011
111000011010 => 000111100101 => 101000111001 => 010001110011
101100011100 => 010011100011 => 001010011011 => 010100110110
110010011100 => 001101100011 => 001100101011 => 011001010110
110011001110 => 001100110001 => 001010010101 => 010100101010
111100001110 => 000011110001 => 001000011101 => 010000111010
110011111000 => 001100000111 => 000010010111 => 000100101110
111111100000 => 000000011111 => 000000011111 => 000000111110
0101110101 => 1010001010 => 1100110000 => 1001100001
11111100000 => 00000011111 => 00000011111 => 00000111110
00111110000 => 11000001111 => 00001101111 => 00011011110
100010101100 => 011101010011 => 011101100011 => 111011000110
100010110010 => 011101001101 => 101101100101 => 011011001011
100010111000 => 011101000111 => 001101100111 => 011011001110
100011001010 => 011100110101 => 110101101001 => 101011010011
100011100010 => 011100011101 => 100101101101 => 001011011011
110000110010 => 001111001101 => 101001110101 => 010011101011
111000001010 => 000111110101 => 110001111001 => 100011110011
110000011010 => 001111100101 => 101001111001 => 010011110011
110000010110 => 001111101001 => 011001111001 => 110011110010
111100000010 => 000011111101 => 100001111101 => 000011111011
111110000000 => 000001111111 => 000001111111 => 000011111110
11111111100 => 00000000011 => 00000000011 => 00000000110
11010000001 => 00101111110 => 11000111110 => 10001111101
01010000000 => 10101111111 => 11001111111 => 10011111111
110001001101 => 001110110010 => 101100110100 => 011001101001
0000101000 => 1111010111 => 1111100111 => 1111001111
0010001000 => 1101110111 => 1110110111 => 1101101111
000000001010 => 111111110101 => 111111111001 => 111111110011
000000101000 => 111111010111 => 111111100111 => 111111001111
000000100010 => 111111011101 => 111111101101 => 111111011011
000010100000 => 111101011111 => 111110011111 => 111100111111
000010101010 => 111101010101 => 111111100001 => 111111000011
000010001000 => 111101110111 => 111110110111 => 111101101111
000010000010 => 111101111101 => 111110111101 => 111101111011
001010000000 => 110101111111 => 111001111111 => 110011111111
001010001010 => 110101110101 => 111110011001 => 111100110011
001010101000 => 110101010111 => 111110000111 => 111100001111
001010100010 => 110101011101 => 111110001101 => 111100011011
001000100000 => 110111011111 => 111011011111 => 110110111111
001000101010 => 110111010101 => 111110110001 => 111101100011
001000001000 => 110111110111 => 111011110111 => 110111101111
001000000010 => 110111111101 => 111011111101 => 110111111011
001001010010 => 110110101101 => 111110100101 => 111101001011
001001000110 => 110110111001 => 011110101101 => 111101011010
101000000000 => 010111111111 => 100111111111 => 001111111111
101000001010 => 010111110101 => 111001111001 => 110011110011
101000101000 => 010111010111 => 111001100111 => 110011001111
101000100010 => 010111011101 => 111001101101 => 110011011011
101010100000 => 010101011111 => 111000011111 => 110000111111
101010001000 => 010101110111 => 111000110111 => 110001101111
101010000010 => 010101111101 => 111000111101 => 110001111011
100010101000 => 011101010111 => 111011000111 => 110110001111
100010100010 => 011101011101 => 111011001101 => 110110011011
100101100000 => 011010011111 => 011010011111 => 110100111110
100101001000 => 011010110111 => 111010010111 => 110100101111
100101000010 => 011010111101 => 111010011101 => 110100111011
110110110110 => 001001001001 => 010101000001 => 101010000010
110101101110 => 001010010001 => 001011000001 => 010110000010
111011101010 => 000100010101 => 110010000001 => 100100000011
111011010110 => 000100101001 => 011010000001 => 110100000010
111010101110 => 000101010001 => 001110000001 => 011100000010
111001011110 => 000110100001 => 000110001001 => 001100010010
111101100110 => 000010011001 => 010100000101 => 101000001010
10000111111 => 01111000000 => 00000101110 => 00001011100
10000001111 => 01111110000 => 00010111110 => 00101111100
10000000111 => 01111111000 => 00101111110 => 01011111100
111100111000 => 000011000111 => 001000010111 => 010000101110
100100110010 => 011011001101 => 101101010101 => 011010101011
100101001010 => 011010110101 => 111101001001 => 111010010011
100101100010 => 011010011101 => 101101001101 => 011010011011
100101101000 => 011010010111 => 101101000111 => 011010001111
100110010010 => 011001101101 => 110101010101 => 101010101011
100111000010 => 011000111101 => 100101011101 => 001010111011
100111001000 => 011000110111 => 100101010111 => 001010101111
011010000110 => 100101111001 => 011010011101 => 110100111010
011011011110 => 100100100001 => 000101010001 => 001010100010
00100000000 => 11011111111 => 11011111111 => 10111111111
101011111111 => 010100000000 => 000000011000 => 000000110000
111010111111 => 000101000000 => 000001100000 => 000011000000
101110111111 => 010001000000 => 000001001000 => 000010010000
111110101111 => 000001010000 => 000110000000 => 001100000000
101010101111 => 010101010000 => 000111100000 => 001111000000
111011101111 => 000100010000 => 000100100000 => 001001000000
101111101111 => 010000010000 => 000100001000 => 001000010000
111111101011 => 000000010100 => 011000000000 => 110000000000
101011101011 => 010100010100 => 011001100000 => 110011000000
111010101011 => 000101010100 => 011110000000 => 111100000000
101110101011 => 010001010100 => 011100100000 => 111001000000
111110111011 => 000001000100 => 010010000000 => 100100000000
101010111011 => 010101000100 => 010011100000 => 100111000000
111011111011 => 000100000100 => 010000100000 => 100001000000
101111111011 => 010000000100 => 010000001000 => 100000010000
111001011011 => 000110100100 => 010110001000 => 101100010000
101101011011 => 010010100100 => 010110100000 => 101101000000
100111011011 => 011000100100 => 010100101000 => 101001010000
111111111010 => 000000000101 => 100000000001 => 000000000011
101011111010 => 010100000101 => 100001100001 => 000011000011
111010111010 => 000101000101 => 100110000001 => 001100000011
101110111010 => 010001000101 => 100100100001 => 001001000011
111110101010 => 000001010101 => 111000000001 => 110000000011
101111101010 => 010000010101 => 110000100001 => 100001000011
100111001010 => 011000110101 => 110010101001 => 100101010011
101110101110 => 010001010001 => 001100100001 => 011001000010
111110010110 => 000001101001 => 011000001001 => 110000010010
101111010110 => 010000101001 => 011000100001 => 110001000010
111001110110 => 000110001001 => 010010001001 => 100100010010
101101110110 => 010010001001 => 010010100001 => 100101000010
101100010000 => 010011101111 => 101001101111 => 010011011111
100011010000 => 011100101111 => 101011001111 => 010110011111
110011000110 => 001100111001 => 010100101101 => 101001011010
110011000010 => 001100111101 => 101001011101 => 010010111011
110001001110 => 001110110001 => 001100110101 => 011001101010
110001101100 => 001110010011 => 010100110011 => 101001100110
110001100110 => 001110011001 => 010100110101 => 101001101010
110001100010 => 001110011101 => 101001101101 => 010011011011
111001000110 => 000110111001 => 011000101101 => 110001011010
111001000010 => 000110111101 => 110001011101 => 100010111011
111000010010 => 000111101101 => 110001110101 => 100011101011
111100011010 => 000011100101 => 101000011001 => 010000110011
100111000011 => 011000111100 => 010010101110 => 100101011100
110001001011 => 001110110100 => 011100110100 => 111001101000
110001000111 => 001110111000 => 001100110110 => 011001101100
110010010110 => 001101101001 => 011100101001 => 111001010010
110110000110 => 001001111001 => 010100011101 => 101000111010
111100000110 => 000011111001 => 010000111101 => 100001111010
110100001110 => 001011110001 => 001100011101 => 011000111010
11111010001 => 00000101110 => 11000000110 => 10000001101
010011100011 => 101100011100 => 010011010110 => 100110101100
011001001011 => 100110110100 => 011101010100 => 111010101000
011001100011 => 100110011100 => 010101010110 => 101010101100
011011000011 => 100100111100 => 010101001110 => 101010011100
110001100011 => 001110011100 => 010100110110 => 101001101100
0010100101 => 1101011010 => 1111100100 => 1111001001
0010110111 => 1101001000 => 0010111000 => 0101110000
0010011111 => 1101100000 => 0000111010 => 0001110100
0001001101 => 1110110010 => 1011110100 => 0111101001
11111111000 => 00000000111 => 00000000111 => 00000001110
0001010011 => 1110101100 => 0111110010 => 1111100100
0110101101 => 1001010010 => 1011010000 => 0110100001
0110011101 => 1001100010 => 1001010100 => 0010101001
0110001111 => 1001110000 => 0001010110 => 0010101100
0101101011 => 1010010100 => 0110110000 => 1101100000
0101011101 => 1010100010 => 1001110000 => 0011100001
0100111101 => 1011000010 => 1000110100 => 0001101001
0011000011 => 1100111100 => 0101101110 => 1011011100
0011011011 => 1100100100 => 0101011000 => 1010110000
0001111011 => 1110000100 => 0100011100 => 1000111000
111111011011 => 000000100100 => 010100000000 => 101000000000
111101101111 => 000010010000 => 000101000000 => 001010000000
111101111011 => 000010000100 => 010001000000 => 100010000000
110110111111 => 001001000000 => 000001010000 => 000010100000
110110011011 => 001001100100 => 010101000100 => 101010001000
110111101111 => 001000010000 => 000100010000 => 001000100000
110111111011 => 001000000100 => 010000010000 => 100000100000
110101101011 => 001010010100 => 011011000000 => 110110000000
001111111111 => 110000000000 => 000000000110 => 000000001100
001100111111 => 110011000000 => 000001011010 => 000010110100
000011111111 => 111100000000 => 000000011110 => 000000111100
000000110011 => 111111001100 => 010111111010 => 101111110100
000000001111 => 111111110000 => 000111111110 => 001111111100
000000000011 => 111111111100 => 011111111110 => 111111111100
011011111111 => 100100000000 => 000000010100 => 000000101000
011001111011 => 100110000100 => 010001010100 => 100010101000
011110111111 => 100001000000 => 000001000100 => 000010001000
011110011011 => 100001100100 => 010100010100 => 101000101000
011111101111 => 100000010000 => 000100000100 => 001000001000
011111111011 => 100000000100 => 010000000100 => 100000001000
11100000000 => 00011111111 => 00011111111 => 00111111110
11110000000 => 00001111111 => 00001111111 => 00011111110
11111110000 => 00000001111 => 00000001111 => 00000011110
11111001000 => 00000110111 => 10000010111 => 00000101111
111111110110 => 000000001001 => 010000000001 => 100000000010
111101011010 => 000010100101 => 101100000001 => 011000000011
110000000000 => 001111111111 => 001111111111 => 011111111110
110001011010 => 001110100101 => 101100110001 => 011001100011
110110011110 => 001001100001 => 000101000101 => 001010001010
110111100110 => 001000011001 => 010001000101 => 100010001010
110111011010 => 001000100101 => 101001000001 => 010010000011
110100100110 => 001011011001 => 011100010101 => 111000101010
110101111010 => 001010000101 => 100011000001 => 000110000011
0010000111 => 1101111000 => 0011101110 => 0111011100
0011100111 => 1100011000 => 0010011010 => 0100110100
11110101010 => 00001010101 => 11100000001 => 11000000011
0111011111 => 1000100000 => 0000100100 => 0001001000
01010111111 => 10101000000 => 00000111000 => 00001110000
110011001000 => 001100110111 => 101001010111 => 010010101111
110110001000 => 001001110111 => 101000110111 => 010001101111
111001001000 => 000110110111 => 110001010111 => 100010101111
111100001000 => 000011110111 => 100001110111 => 000011101111
11111101010 => 00000010101 => 11000000001 => 10000000011
10111011111 => 01000100000 => 00001001000 => 00010010000
11101010101 => 00010101010 => 11110000000 => 11100000001
11111100100 => 00000011011 => 10000001011 => 00000010111
11110010000 => 00001101111 => 10000101111 => 00001011111
110100100010 => 001011011101 => 111000101101 => 110001011011
110010010010 => 001101101101 => 111001010101 => 110010101011
110001001010 => 001110110101 => 111001101001 => 110011010011
0000110000 => 1111001111 => 0111101111 => 1111011110
001110000100 => 110001111011 => 100110111011 => 001101110111
101001011100 => 010110100011 => 001110010011 => 011100100110
0000100001 => 1111011110 => 1111101110 => 1111011101
001000100101 => 110111011010 => 111110110100 => 111101101001
001010000101 => 110101111010 => 111110011100 => 111100111001
00000101011 => 11111010100 => 01111111000 => 11111110000
0000111000 => 1111000111 => 0011110111 => 0111101110
100111000110 => 011000111001 => 010010101101 => 100101011010
101101000110 => 010010111001 => 011010001101 => 110100011010
100111010010 => 011000101101 => 110010100101 => 100101001011
100101110010 => 011010001101 => 100110100101 => 001101001011
00000010001 => 11111101110 => 11111110110 => 11111101101
110110000010 => 001001111101 => 101000111101 => 010001111011
110100001010 => 001011110101 => 111000111001 => 110001110011
11101010110 => 00010101001 => 01110000001 => 11100000010
110010000010 => 001101111101 => 110010111101 => 100101111011
10000010001 => 01111101110 => 11011110110 => 10111101101
0000000111111110 => 1111111000000001 => 0000000111111101 => 0000001111111010
00000000011111111110 => 11111111100000000001 => 00000000011111111101 => 00000000111111111010
111111100010 => 000000011101 => 100000001101 => 000000011011
111000000010 => 000111111101 => 100011111101 => 000111111011
111111101000 => 000000010111 => 100000000111 => 000000001111
111010000000 => 000101111111 => 100001111111 => 000011111111
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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.
For instance, to compute $\phi(4154223)$, the sequence of words is
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 $w_{i+1} < v_k$.
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.
Map
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
This is the word obtained by moving the first letter to the end.
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