Identifier
Mp00105:
Binary words
—complement⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ 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 => 011
010 => 101 => 101 => 110
011 => 100 => 010 => 001
100 => 011 => 011 => 101
101 => 010 => 100 => 010
110 => 001 => 001 => 100
111 => 000 => 000 => 000
0000 => 1111 => 1111 => 1111
0001 => 1110 => 1110 => 0111
0010 => 1101 => 1101 => 1110
0011 => 1100 => 0110 => 0011
0100 => 1011 => 1011 => 1101
0101 => 1010 => 1100 => 0110
0110 => 1001 => 0101 => 1010
0111 => 1000 => 0010 => 0001
1000 => 0111 => 0111 => 1011
1001 => 0110 => 1010 => 0101
1010 => 0101 => 1001 => 1100
1011 => 0100 => 0100 => 0010
1100 => 0011 => 0011 => 1001
1101 => 0010 => 1000 => 0100
1110 => 0001 => 0001 => 1000
1111 => 0000 => 0000 => 0000
00000 => 11111 => 11111 => 11111
00001 => 11110 => 11110 => 01111
00010 => 11101 => 11101 => 11110
00011 => 11100 => 01110 => 00111
00100 => 11011 => 11011 => 11101
00101 => 11010 => 11100 => 01110
00110 => 11001 => 01101 => 10110
00111 => 11000 => 00110 => 00011
01000 => 10111 => 10111 => 11011
01001 => 10110 => 11010 => 01101
01010 => 10101 => 11001 => 11100
01011 => 10100 => 01100 => 00110
01100 => 10011 => 01011 => 10101
01101 => 10010 => 10100 => 01010
01110 => 10001 => 00101 => 10010
01111 => 10000 => 00010 => 00001
10000 => 01111 => 01111 => 10111
10001 => 01110 => 10110 => 01011
10010 => 01101 => 10101 => 11010
10011 => 01100 => 01010 => 00101
10100 => 01011 => 10011 => 11001
10101 => 01010 => 11000 => 01100
10110 => 01001 => 01001 => 10100
10111 => 01000 => 00100 => 00010
11000 => 00111 => 00111 => 10011
11001 => 00110 => 10010 => 01001
11010 => 00101 => 10001 => 11000
11011 => 00100 => 01000 => 00100
11100 => 00011 => 00011 => 10001
11101 => 00010 => 10000 => 01000
11110 => 00001 => 00001 => 10000
11111 => 00000 => 00000 => 00000
000000 => 111111 => 111111 => 111111
000001 => 111110 => 111110 => 011111
000010 => 111101 => 111101 => 111110
000011 => 111100 => 011110 => 001111
000100 => 111011 => 111011 => 111101
000101 => 111010 => 111100 => 011110
000110 => 111001 => 011101 => 101110
000111 => 111000 => 001110 => 000111
001000 => 110111 => 110111 => 111011
001001 => 110110 => 111010 => 011101
001010 => 110101 => 111001 => 111100
001011 => 110100 => 011100 => 001110
001100 => 110011 => 011011 => 101101
001101 => 110010 => 101100 => 010110
001110 => 110001 => 001101 => 100110
001111 => 110000 => 000110 => 000011
010000 => 101111 => 101111 => 110111
010001 => 101110 => 110110 => 011011
010010 => 101101 => 110101 => 111010
010011 => 101100 => 011010 => 001101
010100 => 101011 => 110011 => 111001
010101 => 101010 => 111000 => 011100
010110 => 101001 => 011001 => 101100
010111 => 101000 => 001100 => 000110
011000 => 100111 => 010111 => 101011
011001 => 100110 => 101010 => 010101
011010 => 100101 => 101001 => 110100
011011 => 100100 => 010100 => 001010
011100 => 100011 => 001011 => 100101
011101 => 100010 => 100100 => 010010
011110 => 100001 => 000101 => 100010
011111 => 100000 => 000010 => 000001
100000 => 011111 => 011111 => 101111
100001 => 011110 => 101110 => 010111
100010 => 011101 => 101101 => 110110
100011 => 011100 => 010110 => 001011
100100 => 011011 => 101011 => 110101
100101 => 011010 => 110100 => 011010
100110 => 011001 => 010101 => 101010
>>> Load all 3017 entries. <<<
100111 => 011000 => 001010 => 000101
101000 => 010111 => 100111 => 110011
101001 => 010110 => 110010 => 011001
101010 => 010101 => 110001 => 111000
101011 => 010100 => 011000 => 001100
101100 => 010011 => 010011 => 101001
101101 => 010010 => 101000 => 010100
101110 => 010001 => 001001 => 100100
101111 => 010000 => 000100 => 000010
110000 => 001111 => 001111 => 100111
110001 => 001110 => 100110 => 010011
110010 => 001101 => 100101 => 110010
110011 => 001100 => 010010 => 001001
110100 => 001011 => 100011 => 110001
110101 => 001010 => 110000 => 011000
110110 => 001001 => 010001 => 101000
110111 => 001000 => 001000 => 000100
111000 => 000111 => 000111 => 100011
111001 => 000110 => 100010 => 010001
111010 => 000101 => 100001 => 110000
111011 => 000100 => 010000 => 001000
111100 => 000011 => 000011 => 100001
111101 => 000010 => 100000 => 010000
111110 => 000001 => 000001 => 100000
111111 => 000000 => 000000 => 000000
0000000 => 1111111 => 1111111 => 1111111
0000001 => 1111110 => 1111110 => 0111111
0000010 => 1111101 => 1111101 => 1111110
0000011 => 1111100 => 0111110 => 0011111
0000100 => 1111011 => 1111011 => 1111101
0000101 => 1111010 => 1111100 => 0111110
0000110 => 1111001 => 0111101 => 1011110
0000111 => 1111000 => 0011110 => 0001111
0001000 => 1110111 => 1110111 => 1111011
0001001 => 1110110 => 1111010 => 0111101
0001010 => 1110101 => 1111001 => 1111100
0001011 => 1110100 => 0111100 => 0011110
0001100 => 1110011 => 0111011 => 1011101
0001101 => 1110010 => 1011100 => 0101110
0001110 => 1110001 => 0011101 => 1001110
0001111 => 1110000 => 0001110 => 0000111
0010000 => 1101111 => 1101111 => 1110111
0010001 => 1101110 => 1110110 => 0111011
0010010 => 1101101 => 1110101 => 1111010
0010011 => 1101100 => 0111010 => 0011101
0010100 => 1101011 => 1110011 => 1111001
0010101 => 1101010 => 1111000 => 0111100
0010110 => 1101001 => 0111001 => 1011100
0010111 => 1101000 => 0011100 => 0001110
0011000 => 1100111 => 0110111 => 1011011
0011001 => 1100110 => 1011010 => 0101101
0011010 => 1100101 => 1011001 => 1101100
0011011 => 1100100 => 0101100 => 0010110
0011100 => 1100011 => 0011011 => 1001101
0011101 => 1100010 => 1001100 => 0100110
0011110 => 1100001 => 0001101 => 1000110
0011111 => 1100000 => 0000110 => 0000011
0100000 => 1011111 => 1011111 => 1101111
0100001 => 1011110 => 1101110 => 0110111
0100010 => 1011101 => 1101101 => 1110110
0100011 => 1011100 => 0110110 => 0011011
0100100 => 1011011 => 1101011 => 1110101
0100101 => 1011010 => 1110100 => 0111010
0100110 => 1011001 => 0110101 => 1011010
0100111 => 1011000 => 0011010 => 0001101
0101000 => 1010111 => 1100111 => 1110011
0101001 => 1010110 => 1110010 => 0111001
0101010 => 1010101 => 1110001 => 1111000
0101011 => 1010100 => 0111000 => 0011100
0101100 => 1010011 => 0110011 => 1011001
0101101 => 1010010 => 1011000 => 0101100
0101110 => 1010001 => 0011001 => 1001100
0101111 => 1010000 => 0001100 => 0000110
0110000 => 1001111 => 0101111 => 1010111
0110001 => 1001110 => 1010110 => 0101011
0110010 => 1001101 => 1010101 => 1101010
0110011 => 1001100 => 0101010 => 0010101
0110100 => 1001011 => 1010011 => 1101001
0110101 => 1001010 => 1101000 => 0110100
0110110 => 1001001 => 0101001 => 1010100
0110111 => 1001000 => 0010100 => 0001010
0111000 => 1000111 => 0010111 => 1001011
0111001 => 1000110 => 1001010 => 0100101
0111010 => 1000101 => 1001001 => 1100100
0111011 => 1000100 => 0100100 => 0010010
0111100 => 1000011 => 0001011 => 1000101
0111101 => 1000010 => 1000100 => 0100010
0111110 => 1000001 => 0000101 => 1000010
0111111 => 1000000 => 0000010 => 0000001
1000000 => 0111111 => 0111111 => 1011111
1000001 => 0111110 => 1011110 => 0101111
1000010 => 0111101 => 1011101 => 1101110
1000011 => 0111100 => 0101110 => 0010111
1000100 => 0111011 => 1011011 => 1101101
1000101 => 0111010 => 1101100 => 0110110
1000110 => 0111001 => 0101101 => 1010110
1000111 => 0111000 => 0010110 => 0001011
1001000 => 0110111 => 1010111 => 1101011
1001001 => 0110110 => 1101010 => 0110101
1001010 => 0110101 => 1101001 => 1110100
1001011 => 0110100 => 0110100 => 0011010
1001100 => 0110011 => 0101011 => 1010101
1001101 => 0110010 => 1010100 => 0101010
1001110 => 0110001 => 0010101 => 1001010
1001111 => 0110000 => 0001010 => 0000101
1010000 => 0101111 => 1001111 => 1100111
1010001 => 0101110 => 1100110 => 0110011
1010010 => 0101101 => 1100101 => 1110010
1010011 => 0101100 => 0110010 => 0011001
1010100 => 0101011 => 1100011 => 1110001
1010101 => 0101010 => 1110000 => 0111000
1010110 => 0101001 => 0110001 => 1011000
1010111 => 0101000 => 0011000 => 0001100
1011000 => 0100111 => 0100111 => 1010011
1011001 => 0100110 => 1010010 => 0101001
1011010 => 0100101 => 1010001 => 1101000
1011011 => 0100100 => 0101000 => 0010100
1011100 => 0100011 => 0010011 => 1001001
1011101 => 0100010 => 1001000 => 0100100
1011110 => 0100001 => 0001001 => 1000100
1011111 => 0100000 => 0000100 => 0000010
1100000 => 0011111 => 0011111 => 1001111
1100001 => 0011110 => 1001110 => 0100111
1100010 => 0011101 => 1001101 => 1100110
1100011 => 0011100 => 0100110 => 0010011
1100100 => 0011011 => 1001011 => 1100101
1100101 => 0011010 => 1100100 => 0110010
1100110 => 0011001 => 0100101 => 1010010
1100111 => 0011000 => 0010010 => 0001001
1101000 => 0010111 => 1000111 => 1100011
1101001 => 0010110 => 1100010 => 0110001
1101010 => 0010101 => 1100001 => 1110000
1101011 => 0010100 => 0110000 => 0011000
1101100 => 0010011 => 0100011 => 1010001
1101101 => 0010010 => 1010000 => 0101000
1101110 => 0010001 => 0010001 => 1001000
1101111 => 0010000 => 0001000 => 0000100
1110000 => 0001111 => 0001111 => 1000111
1110001 => 0001110 => 1000110 => 0100011
1110010 => 0001101 => 1000101 => 1100010
1110011 => 0001100 => 0100010 => 0010001
1110100 => 0001011 => 1000011 => 1100001
1110101 => 0001010 => 1100000 => 0110000
1110110 => 0001001 => 0100001 => 1010000
1110111 => 0001000 => 0010000 => 0001000
1111000 => 0000111 => 0000111 => 1000011
1111001 => 0000110 => 1000010 => 0100001
1111010 => 0000101 => 1000001 => 1100000
1111011 => 0000100 => 0100000 => 0010000
1111100 => 0000011 => 0000011 => 1000001
1111101 => 0000010 => 1000000 => 0100000
1111110 => 0000001 => 0000001 => 1000000
1111111 => 0000000 => 0000000 => 0000000
00000000 => 11111111 => 11111111 => 11111111
00000001 => 11111110 => 11111110 => 01111111
00000010 => 11111101 => 11111101 => 11111110
00000011 => 11111100 => 01111110 => 00111111
00000100 => 11111011 => 11111011 => 11111101
00000101 => 11111010 => 11111100 => 01111110
00000110 => 11111001 => 01111101 => 10111110
00000111 => 11111000 => 00111110 => 00011111
00001000 => 11110111 => 11110111 => 11111011
00001001 => 11110110 => 11111010 => 01111101
00001010 => 11110101 => 11111001 => 11111100
00001011 => 11110100 => 01111100 => 00111110
00001100 => 11110011 => 01111011 => 10111101
00001101 => 11110010 => 10111100 => 01011110
00001110 => 11110001 => 00111101 => 10011110
00001111 => 11110000 => 00011110 => 00001111
00010000 => 11101111 => 11101111 => 11110111
00010001 => 11101110 => 11110110 => 01111011
00010010 => 11101101 => 11110101 => 11111010
00010011 => 11101100 => 01111010 => 00111101
00010100 => 11101011 => 11110011 => 11111001
00010101 => 11101010 => 11111000 => 01111100
00010110 => 11101001 => 01111001 => 10111100
00010111 => 11101000 => 00111100 => 00011110
00011000 => 11100111 => 01110111 => 10111011
00011001 => 11100110 => 10111010 => 01011101
00011010 => 11100101 => 10111001 => 11011100
00011011 => 11100100 => 01011100 => 00101110
00011100 => 11100011 => 00111011 => 10011101
00011101 => 11100010 => 10011100 => 01001110
00011110 => 11100001 => 00011101 => 10001110
00011111 => 11100000 => 00001110 => 00000111
00100000 => 11011111 => 11011111 => 11101111
00100001 => 11011110 => 11101110 => 01110111
00100010 => 11011101 => 11101101 => 11110110
00100011 => 11011100 => 01110110 => 00111011
00100100 => 11011011 => 11101011 => 11110101
00100101 => 11011010 => 11110100 => 01111010
00100110 => 11011001 => 01110101 => 10111010
00100111 => 11011000 => 00111010 => 00011101
00101000 => 11010111 => 11100111 => 11110011
00101001 => 11010110 => 11110010 => 01111001
00101010 => 11010101 => 11110001 => 11111000
00101011 => 11010100 => 01111000 => 00111100
00101100 => 11010011 => 01110011 => 10111001
00101101 => 11010010 => 10111000 => 01011100
00101110 => 11010001 => 00111001 => 10011100
00101111 => 11010000 => 00011100 => 00001110
00110000 => 11001111 => 01101111 => 10110111
00110001 => 11001110 => 10110110 => 01011011
00110010 => 11001101 => 10110101 => 11011010
00110011 => 11001100 => 01011010 => 00101101
00110100 => 11001011 => 10110011 => 11011001
00110101 => 11001010 => 11011000 => 01101100
00110110 => 11001001 => 01011001 => 10101100
00110111 => 11001000 => 00101100 => 00010110
00111000 => 11000111 => 00110111 => 10011011
00111001 => 11000110 => 10011010 => 01001101
00111010 => 11000101 => 10011001 => 11001100
00111011 => 11000100 => 01001100 => 00100110
00111100 => 11000011 => 00011011 => 10001101
00111101 => 11000010 => 10001100 => 01000110
00111110 => 11000001 => 00001101 => 10000110
00111111 => 11000000 => 00000110 => 00000011
01000000 => 10111111 => 10111111 => 11011111
01000001 => 10111110 => 11011110 => 01101111
01000010 => 10111101 => 11011101 => 11101110
01000011 => 10111100 => 01101110 => 00110111
01000100 => 10111011 => 11011011 => 11101101
01000101 => 10111010 => 11101100 => 01110110
01000110 => 10111001 => 01101101 => 10110110
01000111 => 10111000 => 00110110 => 00011011
01001000 => 10110111 => 11010111 => 11101011
01001001 => 10110110 => 11101010 => 01110101
01001010 => 10110101 => 11101001 => 11110100
01001011 => 10110100 => 01110100 => 00111010
01001100 => 10110011 => 01101011 => 10110101
01001101 => 10110010 => 10110100 => 01011010
01001110 => 10110001 => 00110101 => 10011010
01001111 => 10110000 => 00011010 => 00001101
01010000 => 10101111 => 11001111 => 11100111
01010001 => 10101110 => 11100110 => 01110011
01010010 => 10101101 => 11100101 => 11110010
01010011 => 10101100 => 01110010 => 00111001
01010100 => 10101011 => 11100011 => 11110001
01010101 => 10101010 => 11110000 => 01111000
01010110 => 10101001 => 01110001 => 10111000
01010111 => 10101000 => 00111000 => 00011100
01011000 => 10100111 => 01100111 => 10110011
01011001 => 10100110 => 10110010 => 01011001
01011010 => 10100101 => 10110001 => 11011000
01011011 => 10100100 => 01011000 => 00101100
01011100 => 10100011 => 00110011 => 10011001
01011101 => 10100010 => 10011000 => 01001100
01011110 => 10100001 => 00011001 => 10001100
01011111 => 10100000 => 00001100 => 00000110
01100000 => 10011111 => 01011111 => 10101111
01100001 => 10011110 => 10101110 => 01010111
01100010 => 10011101 => 10101101 => 11010110
01100011 => 10011100 => 01010110 => 00101011
01100100 => 10011011 => 10101011 => 11010101
01100101 => 10011010 => 11010100 => 01101010
01100110 => 10011001 => 01010101 => 10101010
01100111 => 10011000 => 00101010 => 00010101
01101000 => 10010111 => 10100111 => 11010011
01101001 => 10010110 => 11010010 => 01101001
01101010 => 10010101 => 11010001 => 11101000
01101011 => 10010100 => 01101000 => 00110100
01101100 => 10010011 => 01010011 => 10101001
01101101 => 10010010 => 10101000 => 01010100
01101110 => 10010001 => 00101001 => 10010100
01101111 => 10010000 => 00010100 => 00001010
01110000 => 10001111 => 00101111 => 10010111
01110001 => 10001110 => 10010110 => 01001011
01110010 => 10001101 => 10010101 => 11001010
01110011 => 10001100 => 01001010 => 00100101
01110100 => 10001011 => 10010011 => 11001001
01110101 => 10001010 => 11001000 => 01100100
01110110 => 10001001 => 01001001 => 10100100
01110111 => 10001000 => 00100100 => 00010010
01111000 => 10000111 => 00010111 => 10001011
01111001 => 10000110 => 10001010 => 01000101
01111010 => 10000101 => 10001001 => 11000100
01111011 => 10000100 => 01000100 => 00100010
01111100 => 10000011 => 00001011 => 10000101
01111101 => 10000010 => 10000100 => 01000010
01111110 => 10000001 => 00000101 => 10000010
01111111 => 10000000 => 00000010 => 00000001
10000000 => 01111111 => 01111111 => 10111111
10000001 => 01111110 => 10111110 => 01011111
10000010 => 01111101 => 10111101 => 11011110
10000011 => 01111100 => 01011110 => 00101111
10000100 => 01111011 => 10111011 => 11011101
10000101 => 01111010 => 11011100 => 01101110
10000110 => 01111001 => 01011101 => 10101110
10000111 => 01111000 => 00101110 => 00010111
10001000 => 01110111 => 10110111 => 11011011
10001001 => 01110110 => 11011010 => 01101101
10001010 => 01110101 => 11011001 => 11101100
10001011 => 01110100 => 01101100 => 00110110
10001100 => 01110011 => 01011011 => 10101101
10001101 => 01110010 => 10101100 => 01010110
10001110 => 01110001 => 00101101 => 10010110
10001111 => 01110000 => 00010110 => 00001011
10010000 => 01101111 => 10101111 => 11010111
10010001 => 01101110 => 11010110 => 01101011
10010010 => 01101101 => 11010101 => 11101010
10010011 => 01101100 => 01101010 => 00110101
10010100 => 01101011 => 11010011 => 11101001
10010101 => 01101010 => 11101000 => 01110100
10010110 => 01101001 => 01101001 => 10110100
10010111 => 01101000 => 00110100 => 00011010
10011000 => 01100111 => 01010111 => 10101011
10011001 => 01100110 => 10101010 => 01010101
10011010 => 01100101 => 10101001 => 11010100
10011011 => 01100100 => 01010100 => 00101010
10011100 => 01100011 => 00101011 => 10010101
10011101 => 01100010 => 10010100 => 01001010
10011110 => 01100001 => 00010101 => 10001010
10011111 => 01100000 => 00001010 => 00000101
10100000 => 01011111 => 10011111 => 11001111
10100001 => 01011110 => 11001110 => 01100111
10100010 => 01011101 => 11001101 => 11100110
10100011 => 01011100 => 01100110 => 00110011
10100100 => 01011011 => 11001011 => 11100101
10100101 => 01011010 => 11100100 => 01110010
10100110 => 01011001 => 01100101 => 10110010
10100111 => 01011000 => 00110010 => 00011001
10101000 => 01010111 => 11000111 => 11100011
10101001 => 01010110 => 11100010 => 01110001
10101010 => 01010101 => 11100001 => 11110000
10101011 => 01010100 => 01110000 => 00111000
10101100 => 01010011 => 01100011 => 10110001
10101101 => 01010010 => 10110000 => 01011000
10101110 => 01010001 => 00110001 => 10011000
10101111 => 01010000 => 00011000 => 00001100
10110000 => 01001111 => 01001111 => 10100111
10110001 => 01001110 => 10100110 => 01010011
10110010 => 01001101 => 10100101 => 11010010
10110011 => 01001100 => 01010010 => 00101001
10110100 => 01001011 => 10100011 => 11010001
10110101 => 01001010 => 11010000 => 01101000
10110110 => 01001001 => 01010001 => 10101000
10110111 => 01001000 => 00101000 => 00010100
10111000 => 01000111 => 00100111 => 10010011
10111001 => 01000110 => 10010010 => 01001001
10111010 => 01000101 => 10010001 => 11001000
10111011 => 01000100 => 01001000 => 00100100
10111100 => 01000011 => 00010011 => 10001001
10111101 => 01000010 => 10001000 => 01000100
10111110 => 01000001 => 00001001 => 10000100
10111111 => 01000000 => 00000100 => 00000010
11000000 => 00111111 => 00111111 => 10011111
11000001 => 00111110 => 10011110 => 01001111
11000010 => 00111101 => 10011101 => 11001110
11000011 => 00111100 => 01001110 => 00100111
11000100 => 00111011 => 10011011 => 11001101
11000101 => 00111010 => 11001100 => 01100110
11000110 => 00111001 => 01001101 => 10100110
11000111 => 00111000 => 00100110 => 00010011
11001000 => 00110111 => 10010111 => 11001011
11001001 => 00110110 => 11001010 => 01100101
11001010 => 00110101 => 11001001 => 11100100
11001011 => 00110100 => 01100100 => 00110010
11001100 => 00110011 => 01001011 => 10100101
11001101 => 00110010 => 10100100 => 01010010
11001110 => 00110001 => 00100101 => 10010010
11001111 => 00110000 => 00010010 => 00001001
11010000 => 00101111 => 10001111 => 11000111
11010001 => 00101110 => 11000110 => 01100011
11010010 => 00101101 => 11000101 => 11100010
11010011 => 00101100 => 01100010 => 00110001
11010100 => 00101011 => 11000011 => 11100001
11010101 => 00101010 => 11100000 => 01110000
11010110 => 00101001 => 01100001 => 10110000
11010111 => 00101000 => 00110000 => 00011000
11011000 => 00100111 => 01000111 => 10100011
11011001 => 00100110 => 10100010 => 01010001
11011010 => 00100101 => 10100001 => 11010000
11011011 => 00100100 => 01010000 => 00101000
11011100 => 00100011 => 00100011 => 10010001
11011101 => 00100010 => 10010000 => 01001000
11011110 => 00100001 => 00010001 => 10001000
11011111 => 00100000 => 00001000 => 00000100
11100000 => 00011111 => 00011111 => 10001111
11100001 => 00011110 => 10001110 => 01000111
11100010 => 00011101 => 10001101 => 11000110
11100011 => 00011100 => 01000110 => 00100011
11100100 => 00011011 => 10001011 => 11000101
11100101 => 00011010 => 11000100 => 01100010
11100110 => 00011001 => 01000101 => 10100010
11100111 => 00011000 => 00100010 => 00010001
11101000 => 00010111 => 10000111 => 11000011
11101001 => 00010110 => 11000010 => 01100001
11101010 => 00010101 => 11000001 => 11100000
11101011 => 00010100 => 01100000 => 00110000
11101100 => 00010011 => 01000011 => 10100001
11101101 => 00010010 => 10100000 => 01010000
11101110 => 00010001 => 00100001 => 10010000
11101111 => 00010000 => 00010000 => 00001000
11110000 => 00001111 => 00001111 => 10000111
11110001 => 00001110 => 10000110 => 01000011
11110010 => 00001101 => 10000101 => 11000010
11110011 => 00001100 => 01000010 => 00100001
11110100 => 00001011 => 10000011 => 11000001
11110101 => 00001010 => 11000000 => 01100000
11110110 => 00001001 => 01000001 => 10100000
11110111 => 00001000 => 00100000 => 00010000
11111000 => 00000111 => 00000111 => 10000011
11111001 => 00000110 => 10000010 => 01000001
11111010 => 00000101 => 10000001 => 11000000
11111011 => 00000100 => 01000000 => 00100000
11111100 => 00000011 => 00000011 => 10000001
11111101 => 00000010 => 10000000 => 01000000
11111110 => 00000001 => 00000001 => 10000000
11111111 => 00000000 => 00000000 => 00000000
000000000 => 111111111 => 111111111 => 111111111
000000001 => 111111110 => 111111110 => 011111111
000000010 => 111111101 => 111111101 => 111111110
000000011 => 111111100 => 011111110 => 001111111
000000100 => 111111011 => 111111011 => 111111101
000000101 => 111111010 => 111111100 => 011111110
000000110 => 111111001 => 011111101 => 101111110
000000111 => 111111000 => 001111110 => 000111111
000001000 => 111110111 => 111110111 => 111111011
000001001 => 111110110 => 111111010 => 011111101
000001010 => 111110101 => 111111001 => 111111100
000001011 => 111110100 => 011111100 => 001111110
000001100 => 111110011 => 011111011 => 101111101
000001101 => 111110010 => 101111100 => 010111110
000001110 => 111110001 => 001111101 => 100111110
000001111 => 111110000 => 000111110 => 000011111
000010000 => 111101111 => 111101111 => 111110111
000010001 => 111101110 => 111110110 => 011111011
000010010 => 111101101 => 111110101 => 111111010
000010011 => 111101100 => 011111010 => 001111101
000010100 => 111101011 => 111110011 => 111111001
000010101 => 111101010 => 111111000 => 011111100
000010110 => 111101001 => 011111001 => 101111100
000010111 => 111101000 => 001111100 => 000111110
000011000 => 111100111 => 011110111 => 101111011
000011001 => 111100110 => 101111010 => 010111101
000011010 => 111100101 => 101111001 => 110111100
000011011 => 111100100 => 010111100 => 001011110
000011100 => 111100011 => 001111011 => 100111101
000011101 => 111100010 => 100111100 => 010011110
000011110 => 111100001 => 000111101 => 100011110
000011111 => 111100000 => 000011110 => 000001111
000100000 => 111011111 => 111011111 => 111101111
000100001 => 111011110 => 111101110 => 011110111
000100010 => 111011101 => 111101101 => 111110110
000100011 => 111011100 => 011110110 => 001111011
000100100 => 111011011 => 111101011 => 111110101
000100101 => 111011010 => 111110100 => 011111010
000100110 => 111011001 => 011110101 => 101111010
000100111 => 111011000 => 001111010 => 000111101
000101000 => 111010111 => 111100111 => 111110011
000101001 => 111010110 => 111110010 => 011111001
000101010 => 111010101 => 111110001 => 111111000
000101011 => 111010100 => 011111000 => 001111100
000101100 => 111010011 => 011110011 => 101111001
000101101 => 111010010 => 101111000 => 010111100
000101110 => 111010001 => 001111001 => 100111100
000101111 => 111010000 => 000111100 => 000011110
000110000 => 111001111 => 011101111 => 101110111
000110001 => 111001110 => 101110110 => 010111011
000110010 => 111001101 => 101110101 => 110111010
000110011 => 111001100 => 010111010 => 001011101
000110100 => 111001011 => 101110011 => 110111001
000110101 => 111001010 => 110111000 => 011011100
000110110 => 111001001 => 010111001 => 101011100
000110111 => 111001000 => 001011100 => 000101110
000111000 => 111000111 => 001110111 => 100111011
000111001 => 111000110 => 100111010 => 010011101
000111010 => 111000101 => 100111001 => 110011100
000111011 => 111000100 => 010011100 => 001001110
000111100 => 111000011 => 000111011 => 100011101
000111101 => 111000010 => 100011100 => 010001110
000111110 => 111000001 => 000011101 => 100001110
000111111 => 111000000 => 000001110 => 000000111
001000000 => 110111111 => 110111111 => 111011111
001000001 => 110111110 => 111011110 => 011101111
001000010 => 110111101 => 111011101 => 111101110
001000011 => 110111100 => 011101110 => 001110111
001000100 => 110111011 => 111011011 => 111101101
001000101 => 110111010 => 111101100 => 011110110
001000110 => 110111001 => 011101101 => 101110110
001000111 => 110111000 => 001110110 => 000111011
001001000 => 110110111 => 111010111 => 111101011
001001001 => 110110110 => 111101010 => 011110101
001001010 => 110110101 => 111101001 => 111110100
001001011 => 110110100 => 011110100 => 001111010
001001100 => 110110011 => 011101011 => 101110101
001001101 => 110110010 => 101110100 => 010111010
001001110 => 110110001 => 001110101 => 100111010
001001111 => 110110000 => 000111010 => 000011101
001010000 => 110101111 => 111001111 => 111100111
001010001 => 110101110 => 111100110 => 011110011
001010010 => 110101101 => 111100101 => 111110010
001010011 => 110101100 => 011110010 => 001111001
001010100 => 110101011 => 111100011 => 111110001
001010101 => 110101010 => 111110000 => 011111000
001010110 => 110101001 => 011110001 => 101111000
001010111 => 110101000 => 001111000 => 000111100
001011000 => 110100111 => 011100111 => 101110011
001011001 => 110100110 => 101110010 => 010111001
001011010 => 110100101 => 101110001 => 110111000
001011011 => 110100100 => 010111000 => 001011100
001011100 => 110100011 => 001110011 => 100111001
001011101 => 110100010 => 100111000 => 010011100
001011110 => 110100001 => 000111001 => 100011100
001011111 => 110100000 => 000011100 => 000001110
001100000 => 110011111 => 011011111 => 101101111
001100001 => 110011110 => 101101110 => 010110111
001100010 => 110011101 => 101101101 => 110110110
001100011 => 110011100 => 010110110 => 001011011
001100100 => 110011011 => 101101011 => 110110101
001100101 => 110011010 => 110110100 => 011011010
001100110 => 110011001 => 010110101 => 101011010
001100111 => 110011000 => 001011010 => 000101101
001101000 => 110010111 => 101100111 => 110110011
001101001 => 110010110 => 110110010 => 011011001
001101010 => 110010101 => 110110001 => 111011000
001101011 => 110010100 => 011011000 => 001101100
001101100 => 110010011 => 010110011 => 101011001
001101101 => 110010010 => 101011000 => 010101100
001101110 => 110010001 => 001011001 => 100101100
001101111 => 110010000 => 000101100 => 000010110
001110000 => 110001111 => 001101111 => 100110111
001110001 => 110001110 => 100110110 => 010011011
001110010 => 110001101 => 100110101 => 110011010
001110011 => 110001100 => 010011010 => 001001101
001110100 => 110001011 => 100110011 => 110011001
001110101 => 110001010 => 110011000 => 011001100
001110110 => 110001001 => 010011001 => 101001100
001110111 => 110001000 => 001001100 => 000100110
001111000 => 110000111 => 000110111 => 100011011
001111001 => 110000110 => 100011010 => 010001101
001111010 => 110000101 => 100011001 => 110001100
001111011 => 110000100 => 010001100 => 001000110
001111100 => 110000011 => 000011011 => 100001101
001111101 => 110000010 => 100001100 => 010000110
001111110 => 110000001 => 000001101 => 100000110
001111111 => 110000000 => 000000110 => 000000011
010000000 => 101111111 => 101111111 => 110111111
010000001 => 101111110 => 110111110 => 011011111
010000010 => 101111101 => 110111101 => 111011110
010000011 => 101111100 => 011011110 => 001101111
010000100 => 101111011 => 110111011 => 111011101
010000101 => 101111010 => 111011100 => 011101110
010000110 => 101111001 => 011011101 => 101101110
010000111 => 101111000 => 001101110 => 000110111
010001000 => 101110111 => 110110111 => 111011011
010001001 => 101110110 => 111011010 => 011101101
010001010 => 101110101 => 111011001 => 111101100
010001011 => 101110100 => 011101100 => 001110110
010001100 => 101110011 => 011011011 => 101101101
010001101 => 101110010 => 101101100 => 010110110
010001110 => 101110001 => 001101101 => 100110110
010001111 => 101110000 => 000110110 => 000011011
010010000 => 101101111 => 110101111 => 111010111
010010001 => 101101110 => 111010110 => 011101011
010010010 => 101101101 => 111010101 => 111101010
010010011 => 101101100 => 011101010 => 001110101
010010100 => 101101011 => 111010011 => 111101001
010010101 => 101101010 => 111101000 => 011110100
010010110 => 101101001 => 011101001 => 101110100
010010111 => 101101000 => 001110100 => 000111010
010011000 => 101100111 => 011010111 => 101101011
010011001 => 101100110 => 101101010 => 010110101
010011010 => 101100101 => 101101001 => 110110100
010011011 => 101100100 => 010110100 => 001011010
010011100 => 101100011 => 001101011 => 100110101
010011101 => 101100010 => 100110100 => 010011010
010011110 => 101100001 => 000110101 => 100011010
010011111 => 101100000 => 000011010 => 000001101
010100000 => 101011111 => 110011111 => 111001111
010100001 => 101011110 => 111001110 => 011100111
010100010 => 101011101 => 111001101 => 111100110
010100011 => 101011100 => 011100110 => 001110011
010100100 => 101011011 => 111001011 => 111100101
010100101 => 101011010 => 111100100 => 011110010
010100110 => 101011001 => 011100101 => 101110010
010100111 => 101011000 => 001110010 => 000111001
010101000 => 101010111 => 111000111 => 111100011
010101001 => 101010110 => 111100010 => 011110001
010101010 => 101010101 => 111100001 => 111110000
010101011 => 101010100 => 011110000 => 001111000
010101100 => 101010011 => 011100011 => 101110001
010101101 => 101010010 => 101110000 => 010111000
010101110 => 101010001 => 001110001 => 100111000
010101111 => 101010000 => 000111000 => 000011100
010110000 => 101001111 => 011001111 => 101100111
010110001 => 101001110 => 101100110 => 010110011
010110010 => 101001101 => 101100101 => 110110010
010110011 => 101001100 => 010110010 => 001011001
010110100 => 101001011 => 101100011 => 110110001
010110101 => 101001010 => 110110000 => 011011000
010110110 => 101001001 => 010110001 => 101011000
010110111 => 101001000 => 001011000 => 000101100
010111000 => 101000111 => 001100111 => 100110011
010111001 => 101000110 => 100110010 => 010011001
010111010 => 101000101 => 100110001 => 110011000
010111011 => 101000100 => 010011000 => 001001100
010111100 => 101000011 => 000110011 => 100011001
010111101 => 101000010 => 100011000 => 010001100
010111110 => 101000001 => 000011001 => 100001100
010111111 => 101000000 => 000001100 => 000000110
011000000 => 100111111 => 010111111 => 101011111
011000001 => 100111110 => 101011110 => 010101111
011000010 => 100111101 => 101011101 => 110101110
011000011 => 100111100 => 010101110 => 001010111
011000100 => 100111011 => 101011011 => 110101101
011000101 => 100111010 => 110101100 => 011010110
011000110 => 100111001 => 010101101 => 101010110
011000111 => 100111000 => 001010110 => 000101011
011001000 => 100110111 => 101010111 => 110101011
011001001 => 100110110 => 110101010 => 011010101
011001010 => 100110101 => 110101001 => 111010100
011001011 => 100110100 => 011010100 => 001101010
011001100 => 100110011 => 010101011 => 101010101
011001101 => 100110010 => 101010100 => 010101010
011001110 => 100110001 => 001010101 => 100101010
011001111 => 100110000 => 000101010 => 000010101
011010000 => 100101111 => 101001111 => 110100111
011010001 => 100101110 => 110100110 => 011010011
011010010 => 100101101 => 110100101 => 111010010
011010011 => 100101100 => 011010010 => 001101001
011010100 => 100101011 => 110100011 => 111010001
011010101 => 100101010 => 111010000 => 011101000
011010110 => 100101001 => 011010001 => 101101000
011010111 => 100101000 => 001101000 => 000110100
011011000 => 100100111 => 010100111 => 101010011
011011001 => 100100110 => 101010010 => 010101001
011011010 => 100100101 => 101010001 => 110101000
011011011 => 100100100 => 010101000 => 001010100
011011100 => 100100011 => 001010011 => 100101001
011011101 => 100100010 => 100101000 => 010010100
011011110 => 100100001 => 000101001 => 100010100
011011111 => 100100000 => 000010100 => 000001010
011100000 => 100011111 => 001011111 => 100101111
011100001 => 100011110 => 100101110 => 010010111
011100010 => 100011101 => 100101101 => 110010110
011100011 => 100011100 => 010010110 => 001001011
011100100 => 100011011 => 100101011 => 110010101
011100101 => 100011010 => 110010100 => 011001010
011100110 => 100011001 => 010010101 => 101001010
011100111 => 100011000 => 001001010 => 000100101
011101000 => 100010111 => 100100111 => 110010011
011101001 => 100010110 => 110010010 => 011001001
011101010 => 100010101 => 110010001 => 111001000
011101011 => 100010100 => 011001000 => 001100100
011101100 => 100010011 => 010010011 => 101001001
011101101 => 100010010 => 101001000 => 010100100
011101110 => 100010001 => 001001001 => 100100100
011101111 => 100010000 => 000100100 => 000010010
011110000 => 100001111 => 000101111 => 100010111
011110001 => 100001110 => 100010110 => 010001011
011110010 => 100001101 => 100010101 => 110001010
011110011 => 100001100 => 010001010 => 001000101
011110100 => 100001011 => 100010011 => 110001001
011110101 => 100001010 => 110001000 => 011000100
011110110 => 100001001 => 010001001 => 101000100
011110111 => 100001000 => 001000100 => 000100010
011111000 => 100000111 => 000010111 => 100001011
011111001 => 100000110 => 100001010 => 010000101
011111010 => 100000101 => 100001001 => 110000100
011111011 => 100000100 => 010000100 => 001000010
011111100 => 100000011 => 000001011 => 100000101
011111101 => 100000010 => 100000100 => 010000010
011111110 => 100000001 => 000000101 => 100000010
011111111 => 100000000 => 000000010 => 000000001
100000000 => 011111111 => 011111111 => 101111111
100000001 => 011111110 => 101111110 => 010111111
100000010 => 011111101 => 101111101 => 110111110
100000011 => 011111100 => 010111110 => 001011111
100000100 => 011111011 => 101111011 => 110111101
100000101 => 011111010 => 110111100 => 011011110
100000110 => 011111001 => 010111101 => 101011110
100000111 => 011111000 => 001011110 => 000101111
100001000 => 011110111 => 101110111 => 110111011
100001001 => 011110110 => 110111010 => 011011101
100001010 => 011110101 => 110111001 => 111011100
100001011 => 011110100 => 011011100 => 001101110
100001100 => 011110011 => 010111011 => 101011101
100001101 => 011110010 => 101011100 => 010101110
100001110 => 011110001 => 001011101 => 100101110
100001111 => 011110000 => 000101110 => 000010111
100010000 => 011101111 => 101101111 => 110110111
100010001 => 011101110 => 110110110 => 011011011
100010010 => 011101101 => 110110101 => 111011010
100010011 => 011101100 => 011011010 => 001101101
100010100 => 011101011 => 110110011 => 111011001
100010101 => 011101010 => 111011000 => 011101100
100010110 => 011101001 => 011011001 => 101101100
100010111 => 011101000 => 001101100 => 000110110
100011000 => 011100111 => 010110111 => 101011011
100011001 => 011100110 => 101011010 => 010101101
100011010 => 011100101 => 101011001 => 110101100
100011011 => 011100100 => 010101100 => 001010110
100011100 => 011100011 => 001011011 => 100101101
100011101 => 011100010 => 100101100 => 010010110
100011110 => 011100001 => 000101101 => 100010110
100011111 => 011100000 => 000010110 => 000001011
100100000 => 011011111 => 101011111 => 110101111
100100001 => 011011110 => 110101110 => 011010111
100100010 => 011011101 => 110101101 => 111010110
100100011 => 011011100 => 011010110 => 001101011
100100100 => 011011011 => 110101011 => 111010101
100100101 => 011011010 => 111010100 => 011101010
100100110 => 011011001 => 011010101 => 101101010
100100111 => 011011000 => 001101010 => 000110101
100101000 => 011010111 => 110100111 => 111010011
100101001 => 011010110 => 111010010 => 011101001
100101010 => 011010101 => 111010001 => 111101000
100101011 => 011010100 => 011101000 => 001110100
100101100 => 011010011 => 011010011 => 101101001
100101101 => 011010010 => 101101000 => 010110100
100101110 => 011010001 => 001101001 => 100110100
100101111 => 011010000 => 000110100 => 000011010
100110000 => 011001111 => 010101111 => 101010111
100110001 => 011001110 => 101010110 => 010101011
100110010 => 011001101 => 101010101 => 110101010
100110011 => 011001100 => 010101010 => 001010101
100110100 => 011001011 => 101010011 => 110101001
100110101 => 011001010 => 110101000 => 011010100
100110110 => 011001001 => 010101001 => 101010100
100110111 => 011001000 => 001010100 => 000101010
100111000 => 011000111 => 001010111 => 100101011
100111001 => 011000110 => 100101010 => 010010101
100111010 => 011000101 => 100101001 => 110010100
100111011 => 011000100 => 010010100 => 001001010
100111100 => 011000011 => 000101011 => 100010101
100111101 => 011000010 => 100010100 => 010001010
100111110 => 011000001 => 000010101 => 100001010
100111111 => 011000000 => 000001010 => 000000101
101000000 => 010111111 => 100111111 => 110011111
101000001 => 010111110 => 110011110 => 011001111
101000010 => 010111101 => 110011101 => 111001110
101000011 => 010111100 => 011001110 => 001100111
101000100 => 010111011 => 110011011 => 111001101
101000101 => 010111010 => 111001100 => 011100110
101000110 => 010111001 => 011001101 => 101100110
101000111 => 010111000 => 001100110 => 000110011
101001000 => 010110111 => 110010111 => 111001011
101001001 => 010110110 => 111001010 => 011100101
101001010 => 010110101 => 111001001 => 111100100
101001011 => 010110100 => 011100100 => 001110010
101001100 => 010110011 => 011001011 => 101100101
101001101 => 010110010 => 101100100 => 010110010
101001110 => 010110001 => 001100101 => 100110010
101001111 => 010110000 => 000110010 => 000011001
101010000 => 010101111 => 110001111 => 111000111
101010001 => 010101110 => 111000110 => 011100011
101010010 => 010101101 => 111000101 => 111100010
101010011 => 010101100 => 011100010 => 001110001
101010100 => 010101011 => 111000011 => 111100001
101010101 => 010101010 => 111100000 => 011110000
101010110 => 010101001 => 011100001 => 101110000
101010111 => 010101000 => 001110000 => 000111000
101011000 => 010100111 => 011000111 => 101100011
101011001 => 010100110 => 101100010 => 010110001
101011010 => 010100101 => 101100001 => 110110000
101011011 => 010100100 => 010110000 => 001011000
101011100 => 010100011 => 001100011 => 100110001
101011101 => 010100010 => 100110000 => 010011000
101011110 => 010100001 => 000110001 => 100011000
101011111 => 010100000 => 000011000 => 000001100
101100000 => 010011111 => 010011111 => 101001111
101100001 => 010011110 => 101001110 => 010100111
101100010 => 010011101 => 101001101 => 110100110
101100011 => 010011100 => 010100110 => 001010011
101100100 => 010011011 => 101001011 => 110100101
101100101 => 010011010 => 110100100 => 011010010
101100110 => 010011001 => 010100101 => 101010010
101100111 => 010011000 => 001010010 => 000101001
101101000 => 010010111 => 101000111 => 110100011
101101001 => 010010110 => 110100010 => 011010001
101101010 => 010010101 => 110100001 => 111010000
101101011 => 010010100 => 011010000 => 001101000
101101100 => 010010011 => 010100011 => 101010001
101101101 => 010010010 => 101010000 => 010101000
101101110 => 010010001 => 001010001 => 100101000
101101111 => 010010000 => 000101000 => 000010100
101110000 => 010001111 => 001001111 => 100100111
101110001 => 010001110 => 100100110 => 010010011
101110010 => 010001101 => 100100101 => 110010010
101110011 => 010001100 => 010010010 => 001001001
101110100 => 010001011 => 100100011 => 110010001
101110101 => 010001010 => 110010000 => 011001000
101110110 => 010001001 => 010010001 => 101001000
101110111 => 010001000 => 001001000 => 000100100
101111000 => 010000111 => 000100111 => 100010011
101111001 => 010000110 => 100010010 => 010001001
101111010 => 010000101 => 100010001 => 110001000
101111011 => 010000100 => 010001000 => 001000100
101111100 => 010000011 => 000010011 => 100001001
101111101 => 010000010 => 100001000 => 010000100
101111110 => 010000001 => 000001001 => 100000100
101111111 => 010000000 => 000000100 => 000000010
110000000 => 001111111 => 001111111 => 100111111
110000001 => 001111110 => 100111110 => 010011111
110000010 => 001111101 => 100111101 => 110011110
110000011 => 001111100 => 010011110 => 001001111
110000100 => 001111011 => 100111011 => 110011101
110000101 => 001111010 => 110011100 => 011001110
110000110 => 001111001 => 010011101 => 101001110
110000111 => 001111000 => 001001110 => 000100111
110001000 => 001110111 => 100110111 => 110011011
110001001 => 001110110 => 110011010 => 011001101
110001010 => 001110101 => 110011001 => 111001100
110001011 => 001110100 => 011001100 => 001100110
110001100 => 001110011 => 010011011 => 101001101
110001101 => 001110010 => 101001100 => 010100110
110001110 => 001110001 => 001001101 => 100100110
110001111 => 001110000 => 000100110 => 000010011
110010000 => 001101111 => 100101111 => 110010111
110010001 => 001101110 => 110010110 => 011001011
110010010 => 001101101 => 110010101 => 111001010
110010011 => 001101100 => 011001010 => 001100101
110010100 => 001101011 => 110010011 => 111001001
110010101 => 001101010 => 111001000 => 011100100
110010110 => 001101001 => 011001001 => 101100100
110010111 => 001101000 => 001100100 => 000110010
110011000 => 001100111 => 010010111 => 101001011
110011001 => 001100110 => 101001010 => 010100101
110011010 => 001100101 => 101001001 => 110100100
110011011 => 001100100 => 010100100 => 001010010
110011100 => 001100011 => 001001011 => 100100101
110011101 => 001100010 => 100100100 => 010010010
110011110 => 001100001 => 000100101 => 100010010
110011111 => 001100000 => 000010010 => 000001001
110100000 => 001011111 => 100011111 => 110001111
110100001 => 001011110 => 110001110 => 011000111
110100010 => 001011101 => 110001101 => 111000110
110100011 => 001011100 => 011000110 => 001100011
110100100 => 001011011 => 110001011 => 111000101
110100101 => 001011010 => 111000100 => 011100010
110100110 => 001011001 => 011000101 => 101100010
110100111 => 001011000 => 001100010 => 000110001
110101000 => 001010111 => 110000111 => 111000011
110101001 => 001010110 => 111000010 => 011100001
110101010 => 001010101 => 111000001 => 111100000
110101011 => 001010100 => 011100000 => 001110000
110101100 => 001010011 => 011000011 => 101100001
110101101 => 001010010 => 101100000 => 010110000
110101110 => 001010001 => 001100001 => 100110000
110101111 => 001010000 => 000110000 => 000011000
110110000 => 001001111 => 010001111 => 101000111
110110001 => 001001110 => 101000110 => 010100011
110110010 => 001001101 => 101000101 => 110100010
110110011 => 001001100 => 010100010 => 001010001
110110100 => 001001011 => 101000011 => 110100001
110110101 => 001001010 => 110100000 => 011010000
110110110 => 001001001 => 010100001 => 101010000
110110111 => 001001000 => 001010000 => 000101000
110111000 => 001000111 => 001000111 => 100100011
110111001 => 001000110 => 100100010 => 010010001
110111010 => 001000101 => 100100001 => 110010000
110111011 => 001000100 => 010010000 => 001001000
110111100 => 001000011 => 000100011 => 100010001
110111101 => 001000010 => 100010000 => 010001000
110111110 => 001000001 => 000010001 => 100001000
110111111 => 001000000 => 000001000 => 000000100
111000000 => 000111111 => 000111111 => 100011111
111000001 => 000111110 => 100011110 => 010001111
111000010 => 000111101 => 100011101 => 110001110
111000011 => 000111100 => 010001110 => 001000111
111000100 => 000111011 => 100011011 => 110001101
111000101 => 000111010 => 110001100 => 011000110
111000110 => 000111001 => 010001101 => 101000110
111000111 => 000111000 => 001000110 => 000100011
111001000 => 000110111 => 100010111 => 110001011
111001001 => 000110110 => 110001010 => 011000101
111001010 => 000110101 => 110001001 => 111000100
111001011 => 000110100 => 011000100 => 001100010
111001100 => 000110011 => 010001011 => 101000101
111001101 => 000110010 => 101000100 => 010100010
111001110 => 000110001 => 001000101 => 100100010
111001111 => 000110000 => 000100010 => 000010001
111010000 => 000101111 => 100001111 => 110000111
111010001 => 000101110 => 110000110 => 011000011
111010010 => 000101101 => 110000101 => 111000010
111010011 => 000101100 => 011000010 => 001100001
111010100 => 000101011 => 110000011 => 111000001
111010101 => 000101010 => 111000000 => 011100000
111010110 => 000101001 => 011000001 => 101100000
111010111 => 000101000 => 001100000 => 000110000
111011000 => 000100111 => 010000111 => 101000011
111011001 => 000100110 => 101000010 => 010100001
111011010 => 000100101 => 101000001 => 110100000
111011011 => 000100100 => 010100000 => 001010000
111011100 => 000100011 => 001000011 => 100100001
111011101 => 000100010 => 100100000 => 010010000
111011110 => 000100001 => 000100001 => 100010000
111011111 => 000100000 => 000010000 => 000001000
111100000 => 000011111 => 000011111 => 100001111
111100001 => 000011110 => 100001110 => 010000111
111100010 => 000011101 => 100001101 => 110000110
111100011 => 000011100 => 010000110 => 001000011
111100100 => 000011011 => 100001011 => 110000101
111100101 => 000011010 => 110000100 => 011000010
111100110 => 000011001 => 010000101 => 101000010
111100111 => 000011000 => 001000010 => 000100001
111101000 => 000010111 => 100000111 => 110000011
111101001 => 000010110 => 110000010 => 011000001
111101010 => 000010101 => 110000001 => 111000000
111101011 => 000010100 => 011000000 => 001100000
111101100 => 000010011 => 010000011 => 101000001
111101101 => 000010010 => 101000000 => 010100000
111101110 => 000010001 => 001000001 => 100100000
111101111 => 000010000 => 000100000 => 000010000
111110000 => 000001111 => 000001111 => 100000111
111110001 => 000001110 => 100000110 => 010000011
111110010 => 000001101 => 100000101 => 110000010
111110011 => 000001100 => 010000010 => 001000001
111110100 => 000001011 => 100000011 => 110000001
111110101 => 000001010 => 110000000 => 011000000
111110110 => 000001001 => 010000001 => 101000000
111110111 => 000001000 => 001000000 => 000100000
111111000 => 000000111 => 000000111 => 100000011
111111001 => 000000110 => 100000010 => 010000001
111111010 => 000000101 => 100000001 => 110000000
111111011 => 000000100 => 010000000 => 001000000
111111100 => 000000011 => 000000011 => 100000001
111111101 => 000000010 => 100000000 => 010000000
111111110 => 000000001 => 000000001 => 100000000
111111111 => 000000000 => 000000000 => 000000000
1010101010 => 0101010101 => 1111000001 => 1111100000
1010101100 => 0101010011 => 0111000011 => 1011100001
1010110010 => 0101001101 => 1011000101 => 1101100010
1010110100 => 0101001011 => 1011000011 => 1101100001
1010111000 => 0101000111 => 0011000111 => 1001100011
1011001010 => 0100110101 => 1101001001 => 1110100100
1011001100 => 0100110011 => 0101001011 => 1010100101
1011010010 => 0100101101 => 1101000101 => 1110100010
1011010100 => 0100101011 => 1101000011 => 1110100001
1011011000 => 0100100111 => 0101000111 => 1010100011
1011100010 => 0100011101 => 1001001101 => 1100100110
1011100100 => 0100011011 => 1001001011 => 1100100101
1011101000 => 0100010111 => 1001000111 => 1100100011
1011110000 => 0100001111 => 0001001111 => 1000100111
1100101010 => 0011010101 => 1110010001 => 1111001000
1100101100 => 0011010011 => 0110010011 => 1011001001
1100110010 => 0011001101 => 1010010101 => 1101001010
1100110100 => 0011001011 => 1010010011 => 1101001001
1100111000 => 0011000111 => 0010010111 => 1001001011
1101001010 => 0010110101 => 1110001001 => 1111000100
1101001100 => 0010110011 => 0110001011 => 1011000101
1101010010 => 0010101101 => 1110000101 => 1111000010
1101010100 => 0010101011 => 1110000011 => 1111000001
1101011000 => 0010100111 => 0110000111 => 1011000011
1101100010 => 0010011101 => 1010001101 => 1101000110
1101100100 => 0010011011 => 1010001011 => 1101000101
1101101000 => 0010010111 => 1010000111 => 1101000011
1101110000 => 0010001111 => 0010001111 => 1001000111
1110001010 => 0001110101 => 1100011001 => 1110001100
1110001100 => 0001110011 => 0100011011 => 1010001101
1110010010 => 0001101101 => 1100010101 => 1110001010
1110010100 => 0001101011 => 1100010011 => 1110001001
1110011000 => 0001100111 => 0100010111 => 1010001011
1110100010 => 0001011101 => 1100001101 => 1110000110
1110100100 => 0001011011 => 1100001011 => 1110000101
1110101000 => 0001010111 => 1100000111 => 1110000011
1110110000 => 0001001111 => 0100001111 => 1010000111
1111000010 => 0000111101 => 1000011101 => 1100001110
1111000100 => 0000111011 => 1000011011 => 1100001101
1111001000 => 0000110111 => 1000010111 => 1100001011
1111010000 => 0000101111 => 1000001111 => 1100000111
1111100000 => 0000011111 => 0000011111 => 1000001111
101010101010 => 010101010101 => 111110000001 => 111111000000
101010101100 => 010101010011 => 011110000011 => 101111000001
101010110010 => 010101001101 => 101110000101 => 110111000010
101010110100 => 010101001011 => 101110000011 => 110111000001
101010111000 => 010101000111 => 001110000111 => 100111000011
101011001010 => 010100110101 => 110110001001 => 111011000100
101011001100 => 010100110011 => 010110001011 => 101011000101
101011010010 => 010100101101 => 110110000101 => 111011000010
101011010100 => 010100101011 => 110110000011 => 111011000001
101011011000 => 010100100111 => 010110000111 => 101011000011
101011100010 => 010100011101 => 100110001101 => 110011000110
101011100100 => 010100011011 => 100110001011 => 110011000101
101011101000 => 010100010111 => 100110000111 => 110011000011
101011110000 => 010100001111 => 000110001111 => 100011000111
101100101010 => 010011010101 => 111010010001 => 111101001000
101100101100 => 010011010011 => 011010010011 => 101101001001
101100110010 => 010011001101 => 101010010101 => 110101001010
101100110100 => 010011001011 => 101010010011 => 110101001001
101100111000 => 010011000111 => 001010010111 => 100101001011
101101001010 => 010010110101 => 111010001001 => 111101000100
101101001100 => 010010110011 => 011010001011 => 101101000101
101101010010 => 010010101101 => 111010000101 => 111101000010
101101010100 => 010010101011 => 111010000011 => 111101000001
101101011000 => 010010100111 => 011010000111 => 101101000011
101101100010 => 010010011101 => 101010001101 => 110101000110
101101100100 => 010010011011 => 101010001011 => 110101000101
101101101000 => 010010010111 => 101010000111 => 110101000011
101101110000 => 010010001111 => 001010001111 => 100101000111
101110001010 => 010001110101 => 110010011001 => 111001001100
101110001100 => 010001110011 => 010010011011 => 101001001101
101110010010 => 010001101101 => 110010010101 => 111001001010
101110010100 => 010001101011 => 110010010011 => 111001001001
101110011000 => 010001100111 => 010010010111 => 101001001011
101110100010 => 010001011101 => 110010001101 => 111001000110
101110100100 => 010001011011 => 110010001011 => 111001000101
101110101000 => 010001010111 => 110010000111 => 111001000011
101110110000 => 010001001111 => 010010001111 => 101001000111
101111000010 => 010000111101 => 100010011101 => 110001001110
101111000100 => 010000111011 => 100010011011 => 110001001101
101111001000 => 010000110111 => 100010010111 => 110001001011
101111010000 => 010000101111 => 100010001111 => 110001000111
101111100000 => 010000011111 => 000010011111 => 100001001111
110010101010 => 001101010101 => 111100100001 => 111110010000
110010101100 => 001101010011 => 011100100011 => 101110010001
110010110010 => 001101001101 => 101100100101 => 110110010010
110010110100 => 001101001011 => 101100100011 => 110110010001
110010111000 => 001101000111 => 001100100111 => 100110010011
110011001010 => 001100110101 => 110100101001 => 111010010100
110011001100 => 001100110011 => 010100101011 => 101010010101
110011010010 => 001100101101 => 110100100101 => 111010010010
110011010100 => 001100101011 => 110100100011 => 111010010001
110011011000 => 001100100111 => 010100100111 => 101010010011
110011100010 => 001100011101 => 100100101101 => 110010010110
110011100100 => 001100011011 => 100100101011 => 110010010101
110011101000 => 001100010111 => 100100100111 => 110010010011
110011110000 => 001100001111 => 000100101111 => 100010010111
110100101010 => 001011010101 => 111100010001 => 111110001000
110100101100 => 001011010011 => 011100010011 => 101110001001
110100110010 => 001011001101 => 101100010101 => 110110001010
110100110100 => 001011001011 => 101100010011 => 110110001001
110100111000 => 001011000111 => 001100010111 => 100110001011
110101001010 => 001010110101 => 111100001001 => 111110000100
110101001100 => 001010110011 => 011100001011 => 101110000101
110101010010 => 001010101101 => 111100000101 => 111110000010
110101010100 => 001010101011 => 111100000011 => 111110000001
110101011000 => 001010100111 => 011100000111 => 101110000011
110101100010 => 001010011101 => 101100001101 => 110110000110
110101100100 => 001010011011 => 101100001011 => 110110000101
110101101000 => 001010010111 => 101100000111 => 110110000011
110101110000 => 001010001111 => 001100001111 => 100110000111
110110001010 => 001001110101 => 110100011001 => 111010001100
110110001100 => 001001110011 => 010100011011 => 101010001101
110110010010 => 001001101101 => 110100010101 => 111010001010
110110010100 => 001001101011 => 110100010011 => 111010001001
110110011000 => 001001100111 => 010100010111 => 101010001011
110110100010 => 001001011101 => 110100001101 => 111010000110
110110100100 => 001001011011 => 110100001011 => 111010000101
110110101000 => 001001010111 => 110100000111 => 111010000011
110110110000 => 001001001111 => 010100001111 => 101010000111
110111000010 => 001000111101 => 100100011101 => 110010001110
110111000100 => 001000111011 => 100100011011 => 110010001101
110111001000 => 001000110111 => 100100010111 => 110010001011
110111010000 => 001000101111 => 100100001111 => 110010000111
110111100000 => 001000011111 => 000100011111 => 100010001111
111000101010 => 000111010101 => 111000110001 => 111100011000
111000101100 => 000111010011 => 011000110011 => 101100011001
111000110010 => 000111001101 => 101000110101 => 110100011010
111000110100 => 000111001011 => 101000110011 => 110100011001
111000111000 => 000111000111 => 001000110111 => 100100011011
111001001010 => 000110110101 => 111000101001 => 111100010100
111001001100 => 000110110011 => 011000101011 => 101100010101
111001010010 => 000110101101 => 111000100101 => 111100010010
111001010100 => 000110101011 => 111000100011 => 111100010001
111001011000 => 000110100111 => 011000100111 => 101100010011
111001100010 => 000110011101 => 101000101101 => 110100010110
111001100100 => 000110011011 => 101000101011 => 110100010101
111001101000 => 000110010111 => 101000100111 => 110100010011
111001110000 => 000110001111 => 001000101111 => 100100010111
111010001010 => 000101110101 => 111000011001 => 111100001100
111010001100 => 000101110011 => 011000011011 => 101100001101
111010010010 => 000101101101 => 111000010101 => 111100001010
111010010100 => 000101101011 => 111000010011 => 111100001001
111010011000 => 000101100111 => 011000010111 => 101100001011
111010100010 => 000101011101 => 111000001101 => 111100000110
111010100100 => 000101011011 => 111000001011 => 111100000101
111010101000 => 000101010111 => 111000000111 => 111100000011
111010110000 => 000101001111 => 011000001111 => 101100000111
111011000010 => 000100111101 => 101000011101 => 110100001110
111011000100 => 000100111011 => 101000011011 => 110100001101
111011001000 => 000100110111 => 101000010111 => 110100001011
111011010000 => 000100101111 => 101000001111 => 110100000111
111011100000 => 000100011111 => 001000011111 => 100100001111
111100001010 => 000011110101 => 110000111001 => 111000011100
111100001100 => 000011110011 => 010000111011 => 101000011101
111100010010 => 000011101101 => 110000110101 => 111000011010
111100010100 => 000011101011 => 110000110011 => 111000011001
111100011000 => 000011100111 => 010000110111 => 101000011011
111100100010 => 000011011101 => 110000101101 => 111000010110
111100100100 => 000011011011 => 110000101011 => 111000010101
111100101000 => 000011010111 => 110000100111 => 111000010011
111100110000 => 000011001111 => 010000101111 => 101000010111
111101000010 => 000010111101 => 110000011101 => 111000001110
111101000100 => 000010111011 => 110000011011 => 111000001101
111101001000 => 000010110111 => 110000010111 => 111000001011
111101010000 => 000010101111 => 110000001111 => 111000000111
111101100000 => 000010011111 => 010000011111 => 101000001111
111110000010 => 000001111101 => 100000111101 => 110000011110
111110000100 => 000001111011 => 100000111011 => 110000011101
111110001000 => 000001110111 => 100000110111 => 110000011011
111110010000 => 000001101111 => 100000101111 => 110000010111
111110100000 => 000001011111 => 100000011111 => 110000001111
111111000000 => 000000111111 => 000000111111 => 100000011111
10110111100000 => 01001000011111 => 00010100011111 => 10001010001111
10111011100000 => 01000100011111 => 00100100011111 => 10010010001111
10111100110000 => 01000011001111 => 01000100101111 => 10100010010111
10111101100000 => 01000010011111 => 01000100011111 => 10100010001111
10111111000000 => 01000000111111 => 00000100111111 => 10000010011111
11001111100000 => 00110000011111 => 00001001011111 => 10000100101111
11010111100000 => 00101000011111 => 00011000011111 => 10001100001111
11011001110000 => 00100110001111 => 00101000101111 => 10010100010111
11011011100000 => 00100100011111 => 00101000011111 => 10010100001111
11011101100000 => 00100010011111 => 01001000011111 => 10100100001111
11011111000000 => 00100000111111 => 00001000111111 => 10000100011111
11100110011000 => 00011001100111 => 01010001010111 => 10101000101011
11100110110000 => 00011001001111 => 01010001001111 => 10101000100111
11100111100000 => 00011000011111 => 00010001011111 => 10001000101111
11101011100000 => 00010100011111 => 00110000011111 => 10011000001111
11101100110000 => 00010011001111 => 01010000101111 => 10101000010111
11101111000000 => 00010000111111 => 00010000111111 => 10001000011111
11110001110000 => 00001110001111 => 00100001101111 => 10010000110111
11110011100000 => 00001100011111 => 00100001011111 => 10010000101111
11110111000000 => 00001000111111 => 00100000111111 => 10010000011111
11111000001100 => 00000111110011 => 01000001111011 => 10100000111101
11111000011000 => 00000111100111 => 01000001110111 => 10100000111011
11111000110000 => 00000111001111 => 01000001101111 => 10100000110111
11111001100000 => 00000110011111 => 01000001011111 => 10100000101111
11111011000000 => 00000100111111 => 01000000111111 => 10100000011111
11111110000000 => 00000001111111 => 00000001111111 => 10000000111111
1010101010101010 => 0101010101010101 => 1111111000000001 => 1111111100000000
1011111011000000 => 0100000100111111 => 0100001000111111 => 1010000100011111
1111111111 => 0000000000 => 0000000000 => 0000000000
1111111110 => 0000000001 => 0000000001 => 1000000000
1111111101 => 0000000010 => 1000000000 => 0100000000
1111111100 => 0000000011 => 0000000011 => 1000000001
1111111011 => 0000000100 => 0100000000 => 0010000000
1111111010 => 0000000101 => 1000000001 => 1100000000
1111111001 => 0000000110 => 1000000010 => 0100000001
1111111000 => 0000000111 => 0000000111 => 1000000011
1111110110 => 0000001001 => 0100000001 => 1010000000
1111110101 => 0000001010 => 1100000000 => 0110000000
1111110100 => 0000001011 => 1000000011 => 1100000001
1111110011 => 0000001100 => 0100000010 => 0010000001
1111110010 => 0000001101 => 1000000101 => 1100000010
1111110001 => 0000001110 => 1000000110 => 0100000011
1111110000 => 0000001111 => 0000001111 => 1000000111
1111101110 => 0000010001 => 0010000001 => 1001000000
1111101101 => 0000010010 => 1010000000 => 0101000000
1111101011 => 0000010100 => 0110000000 => 0011000000
1111101010 => 0000010101 => 1100000001 => 1110000000
1111101000 => 0000010111 => 1000000111 => 1100000011
1111100111 => 0000011000 => 0010000010 => 0001000001
1111100100 => 0000011011 => 1000001011 => 1100000101
1111100010 => 0000011101 => 1000001101 => 1100000110
1111100001 => 0000011110 => 1000001110 => 0100000111
1111011110 => 0000100001 => 0001000001 => 1000100000
1111011011 => 0000100100 => 0101000000 => 0010100000
1111011010 => 0000100101 => 1010000001 => 1101000000
1111011000 => 0000100111 => 0100000111 => 1010000011
1111010111 => 0000101000 => 0011000000 => 0001100000
1111010100 => 0000101011 => 1100000011 => 1110000001
1111010001 => 0000101110 => 1100000110 => 0110000011
1111001110 => 0000110001 => 0010000101 => 1001000010
1111001100 => 0000110011 => 0100001011 => 1010000101
1111001001 => 0000110110 => 1100001010 => 0110000101
1111000101 => 0000111010 => 1100001100 => 0110000110
1111000011 => 0000111100 => 0100001110 => 0010000111
1111000001 => 0000111110 => 1000011110 => 0100001111
1111000000 => 0000111111 => 0000111111 => 1000011111
1110111110 => 0001000001 => 0000100001 => 1000010000
1110111101 => 0001000010 => 1000100000 => 0100010000
1110111100 => 0001000011 => 0001000011 => 1000100001
1110111011 => 0001000100 => 0100100000 => 0010010000
1110110111 => 0001001000 => 0010100000 => 0001010000
1110101111 => 0001010000 => 0001100000 => 0000110000
1110101110 => 0001010001 => 0011000001 => 1001100000
1110101101 => 0001010010 => 1011000000 => 0101100000
1110101010 => 0001010101 => 1110000001 => 1111000000
1110100101 => 0001011010 => 1110000100 => 0111000010
1110100011 => 0001011100 => 0110000110 => 0011000011
1110100001 => 0001011110 => 1100001110 => 0110000111
1110100000 => 0001011111 => 1000011111 => 1100001111
1110011001 => 0001100110 => 1010001010 => 0101000101
1110010110 => 0001101001 => 0110001001 => 1011000100
1110010011 => 0001101100 => 0110001010 => 0011000101
1110010000 => 0001101111 => 1000101111 => 1100010111
1110001101 => 0001110010 => 1010001100 => 0101000110
1110001011 => 0001110100 => 0110001100 => 0011000110
1110001000 => 0001110111 => 1000110111 => 1100011011
1110000111 => 0001111000 => 0010001110 => 0001000111
1110000110 => 0001111001 => 0100011101 => 1010001110
1110000101 => 0001111010 => 1100011100 => 0110001110
1110000100 => 0001111011 => 1000111011 => 1100011101
1110000011 => 0001111100 => 0100011110 => 0010001111
1110000010 => 0001111101 => 1000111101 => 1100011110
1110000001 => 0001111110 => 1000111110 => 0100011111
1110000000 => 0001111111 => 0001111111 => 1000111111
1101111110 => 0010000001 => 0000010001 => 1000001000
1101111101 => 0010000010 => 1000010000 => 0100001000
1101111011 => 0010000100 => 0100010000 => 0010001000
1101101111 => 0010010000 => 0001010000 => 0000101000
1101101100 => 0010010011 => 0101000011 => 1010100001
1101101010 => 0010010101 => 1101000001 => 1110100000
1101101001 => 0010010110 => 1101000010 => 0110100001
1101100110 => 0010011001 => 0101000101 => 1010100010
1101100001 => 0010011110 => 1010001110 => 0101000111
1101100000 => 0010011111 => 0100011111 => 1010001111
1101011111 => 0010100000 => 0000110000 => 0000011000
1101011010 => 0010100101 => 1011000001 => 1101100000
1101011001 => 0010100110 => 1011000010 => 0101100001
1101010101 => 0010101010 => 1111000000 => 0111100000
1101010011 => 0010101100 => 0111000010 => 0011100001
1101010001 => 0010101110 => 1110000110 => 0111000011
1101001101 => 0010110010 => 1011000100 => 0101100010
1101001011 => 0010110100 => 0111000100 => 0011100010
1101001001 => 0010110110 => 1110001010 => 0111000101
1101001000 => 0010110111 => 1100010111 => 1110001011
1101000111 => 0010111000 => 0011000110 => 0001100011
1101000110 => 0010111001 => 0110001101 => 1011000110
1101000101 => 0010111010 => 1110001100 => 0111000110
1101000010 => 0010111101 => 1100011101 => 1110001110
1101000001 => 0010111110 => 1100011110 => 0110001111
1100111111 => 0011000000 => 0000010010 => 0000001001
1100111110 => 0011000001 => 0000100101 => 1000010010
1100111100 => 0011000011 => 0001001011 => 1000100101
1100111001 => 0011000110 => 1001001010 => 0100100101
1100110101 => 0011001010 => 1101001000 => 0110100100
1100110011 => 0011001100 => 0101001010 => 0010100101
1100110001 => 0011001110 => 1010010110 => 0101001011
1100101101 => 0011010010 => 1011001000 => 0101100100
1100101011 => 0011010100 => 0111001000 => 0011100100
1100101001 => 0011010110 => 1110010010 => 0111001001
1100101000 => 0011010111 => 1100100111 => 1110010011
1100100111 => 0011011000 => 0011001010 => 0001100101
1100100110 => 0011011001 => 0110010101 => 1011001010
1100100101 => 0011011010 => 1110010100 => 0111001010
1100100100 => 0011011011 => 1100101011 => 1110010101
1100100011 => 0011011100 => 0110010110 => 0011001011
1100100010 => 0011011101 => 1100101101 => 1110010110
1100100001 => 0011011110 => 1100101110 => 0110010111
1100100000 => 0011011111 => 1001011111 => 1100101111
1100011101 => 0011100010 => 1001001100 => 0100100110
1100011011 => 0011100100 => 0101001100 => 0010100110
1100011010 => 0011100101 => 1010011001 => 1101001100
1100011001 => 0011100110 => 1010011010 => 0101001101
1100011000 => 0011100111 => 0100110111 => 1010011011
1100010111 => 0011101000 => 0011001100 => 0001100110
1100010101 => 0011101010 => 1110011000 => 0111001100
1100010011 => 0011101100 => 0110011010 => 0011001101
1100010010 => 0011101101 => 1100110101 => 1110011010
1100010001 => 0011101110 => 1100110110 => 0110011011
1100001111 => 0011110000 => 0001001110 => 0000100111
1100001110 => 0011110001 => 0010011101 => 1001001110
1100001100 => 0011110011 => 0100111011 => 1010011101
1100001011 => 0011110100 => 0110011100 => 0011001110
1100001010 => 0011110101 => 1100111001 => 1110011100
1100000111 => 0011111000 => 0010011110 => 0001001111
1100000101 => 0011111010 => 1100111100 => 0110011110
1100000011 => 0011111100 => 0100111110 => 0010011111
1100000001 => 0011111110 => 1001111110 => 0100111111
1100000000 => 0011111111 => 0011111111 => 1001111111
1011111111 => 0100000000 => 0000000100 => 0000000010
1011111110 => 0100000001 => 0000001001 => 1000000100
1011111101 => 0100000010 => 1000001000 => 0100000100
1011111011 => 0100000100 => 0100001000 => 0010000100
1011111000 => 0100000111 => 0000100111 => 1000010011
1011101111 => 0100010000 => 0001001000 => 0000100100
1011101110 => 0100010001 => 0010010001 => 1001001000
1011101100 => 0100010011 => 0100100011 => 1010010001
1011101010 => 0100010101 => 1100100001 => 1110010000
1011100101 => 0100011010 => 1100100100 => 0110010010
1011100011 => 0100011100 => 0100100110 => 0010010011
1011100001 => 0100011110 => 1001001110 => 0100100111
1011100000 => 0100011111 => 0010011111 => 1001001111
1011011111 => 0100100000 => 0000101000 => 0000010100
1011011110 => 0100100001 => 0001010001 => 1000101000
1011011001 => 0100100110 => 1010100010 => 0101010001
1011010110 => 0100101001 => 0110100001 => 1011010000
1011010011 => 0100101100 => 0110100010 => 0011010001
1011010001 => 0100101110 => 1101000110 => 0110100011
1011010000 => 0100101111 => 1010001111 => 1101000111
1011001110 => 0100110001 => 0010100101 => 1001010010
1011001101 => 0100110010 => 1010100100 => 0101010010
1011001011 => 0100110100 => 0110100100 => 0011010010
1011001001 => 0100110110 => 1101001010 => 0110100101
1011001000 => 0100110111 => 1010010111 => 1101001011
1011000110 => 0100111001 => 0101001101 => 1010100110
1011000101 => 0100111010 => 1101001100 => 0110100110
1011000100 => 0100111011 => 1010011011 => 1101001101
1011000000 => 0100111111 => 0100111111 => 1010011111
1010111111 => 0101000000 => 0000011000 => 0000001100
1010111110 => 0101000001 => 0000110001 => 1000011000
1010111100 => 0101000011 => 0001100011 => 1000110001
1010111010 => 0101000101 => 1001100001 => 1100110000
1010111001 => 0101000110 => 1001100010 => 0100110001
1010110101 => 0101001010 => 1101100000 => 0110110000
1010110011 => 0101001100 => 0101100010 => 0010110001
1010101110 => 0101010001 => 0011100001 => 1001110000
1010101101 => 0101010010 => 1011100000 => 0101110000
1010101011 => 0101010100 => 0111100000 => 0011110000
1010101001 => 0101010110 => 1111000010 => 0111100001
1010101000 => 0101010111 => 1110000111 => 1111000011
1010100111 => 0101011000 => 0011100010 => 0001110001
1010100110 => 0101011001 => 0111000101 => 1011100010
1010100101 => 0101011010 => 1111000100 => 0111100010
1010100011 => 0101011100 => 0111000110 => 0011100011
1010100010 => 0101011101 => 1110001101 => 1111000110
1010011101 => 0101100010 => 1001100100 => 0100110010
1010011100 => 0101100011 => 0011001011 => 1001100101
1010011011 => 0101100100 => 0101100100 => 0010110010
1010011010 => 0101100101 => 1011001001 => 1101100100
1010011000 => 0101100111 => 0110010111 => 1011001011
1010010111 => 0101101000 => 0011100100 => 0001110010
1010010110 => 0101101001 => 0111001001 => 1011100100
1010010101 => 0101101010 => 1111001000 => 0111100100
1010010100 => 0101101011 => 1110010011 => 1111001001
1010010011 => 0101101100 => 0111001010 => 0011100101
1010001111 => 0101110000 => 0001100110 => 0000110011
1010001110 => 0101110001 => 0011001101 => 1001100110
1010001101 => 0101110010 => 1011001100 => 0101100110
1010001100 => 0101110011 => 0110011011 => 1011001101
1010001011 => 0101110100 => 0111001100 => 0011100110
1010001010 => 0101110101 => 1110011001 => 1111001100
1010000000 => 0101111111 => 1001111111 => 1100111111
1001111111 => 0110000000 => 0000001010 => 0000000101
1001111110 => 0110000001 => 0000010101 => 1000001010
1001111100 => 0110000011 => 0000101011 => 1000010101
1001111000 => 0110000111 => 0001010111 => 1000101011
1001110110 => 0110001001 => 0100101001 => 1010010100
1001110100 => 0110001011 => 1001010011 => 1100101001
1001110011 => 0110001100 => 0100101010 => 0010010101
1001110010 => 0110001101 => 1001010101 => 1100101010
1001110001 => 0110001110 => 1001010110 => 0100101011
1001101101 => 0110010010 => 1010101000 => 0101010100
1001101100 => 0110010011 => 0101010011 => 1010101001
1001101011 => 0110010100 => 0110101000 => 0011010100
1001101010 => 0110010101 => 1101010001 => 1110101000
1001101001 => 0110010110 => 1101010010 => 0110101001
1001101000 => 0110010111 => 1010100111 => 1101010011
1001100111 => 0110011000 => 0010101010 => 0001010101
1001100110 => 0110011001 => 0101010101 => 1010101010
1001100101 => 0110011010 => 1101010100 => 0110101010
1001100100 => 0110011011 => 1010101011 => 1101010101
1001100011 => 0110011100 => 0101010110 => 0010101011
1001100000 => 0110011111 => 0101011111 => 1010101111
1001011111 => 0110100000 => 0000110100 => 0000011010
1001011110 => 0110100001 => 0001101001 => 1000110100
1001011101 => 0110100010 => 1001101000 => 0100110100
1001011100 => 0110100011 => 0011010011 => 1001101001
1001011011 => 0110100100 => 0101101000 => 0010110100
1001011001 => 0110100110 => 1011010010 => 0101101001
1001011000 => 0110100111 => 0110100111 => 1011010011
1001010111 => 0110101000 => 0011101000 => 0001110100
1001010110 => 0110101001 => 0111010001 => 1011101000
1001010101 => 0110101010 => 1111010000 => 0111101000
1001010100 => 0110101011 => 1110100011 => 1111010001
1001010011 => 0110101100 => 0111010010 => 0011101001
1001010010 => 0110101101 => 1110100101 => 1111010010
1001010000 => 0110101111 => 1101001111 => 1110100111
1001001111 => 0110110000 => 0001101010 => 0000110101
1001001110 => 0110110001 => 0011010101 => 1001101010
1001001101 => 0110110010 => 1011010100 => 0101101010
1001001100 => 0110110011 => 0110101011 => 1011010101
1001001011 => 0110110100 => 0111010100 => 0011101010
1001001010 => 0110110101 => 1110101001 => 1111010100
1001001000 => 0110110111 => 1101010111 => 1110101011
1001000110 => 0110111001 => 0110101101 => 1011010110
1001000100 => 0110111011 => 1101011011 => 1110101101
1001000000 => 0110111111 => 1010111111 => 1101011111
1000111111 => 0111000000 => 0000010110 => 0000001011
1000111110 => 0111000001 => 0000101101 => 1000010110
1000111101 => 0111000010 => 1000101100 => 0100010110
1000111100 => 0111000011 => 0001011011 => 1000101101
1000111011 => 0111000100 => 0100101100 => 0010010110
1000111010 => 0111000101 => 1001011001 => 1100101100
1000111001 => 0111000110 => 1001011010 => 0100101101
1000111000 => 0111000111 => 0010110111 => 1001011011
1000110111 => 0111001000 => 0010101100 => 0001010110
1000110110 => 0111001001 => 0101011001 => 1010101100
1000110101 => 0111001010 => 1101011000 => 0110101100
1000110100 => 0111001011 => 1010110011 => 1101011001
1000110011 => 0111001100 => 0101011010 => 0010101101
1000110010 => 0111001101 => 1010110101 => 1101011010
1000101111 => 0111010000 => 0001101100 => 0000110110
1000101110 => 0111010001 => 0011011001 => 1001101100
1000101101 => 0111010010 => 1011011000 => 0101101100
1000101100 => 0111010011 => 0110110011 => 1011011001
1000101011 => 0111010100 => 0111011000 => 0011101100
1000101010 => 0111010101 => 1110110001 => 1111011000
1000100111 => 0111011000 => 0011011010 => 0001101101
1000100110 => 0111011001 => 0110110101 => 1011011010
1000100101 => 0111011010 => 1110110100 => 0111011010
1000100000 => 0111011111 => 1011011111 => 1101101111
1000011111 => 0111100000 => 0000101110 => 0000010111
1000011110 => 0111100001 => 0001011101 => 1000101110
1000011011 => 0111100100 => 0101011100 => 0010101110
1000011000 => 0111100111 => 0101110111 => 1010111011
1000010111 => 0111101000 => 0011011100 => 0001101110
1000010110 => 0111101001 => 0110111001 => 1011011100
1000001111 => 0111110000 => 0001011110 => 0000101111
1000001110 => 0111110001 => 0010111101 => 1001011110
1000001010 => 0111110101 => 1101111001 => 1110111100
1000001000 => 0111110111 => 1011110111 => 1101111011
1000000111 => 0111111000 => 0010111110 => 0001011111
1000000110 => 0111111001 => 0101111101 => 1010111110
1000000100 => 0111111011 => 1011111011 => 1101111101
1000000011 => 0111111100 => 0101111110 => 0010111111
1000000010 => 0111111101 => 1011111101 => 1101111110
1000000001 => 0111111110 => 1011111110 => 0101111111
1000000000 => 0111111111 => 0111111111 => 1011111111
10000000000 => 01111111111 => 01111111111 => 10111111111
10000000010 => 01111111101 => 10111111101 => 11011111110
10000000110 => 01111111001 => 01011111101 => 10101111110
10000001110 => 01111110001 => 00101111101 => 10010111110
10000011110 => 01111100001 => 00010111101 => 10001011110
10000111110 => 01111000001 => 00001011101 => 10000101110
10001111110 => 01110000001 => 00000101101 => 10000010110
10011111110 => 01100000001 => 00000010101 => 10000001010
10111111110 => 01000000001 => 00000001001 => 10000000100
11111111110 => 00000000001 => 00000000001 => 10000000000
100000000000 => 011111111111 => 011111111111 => 101111111111
100000000010 => 011111111101 => 101111111101 => 110111111110
100000111110 => 011111000001 => 000010111101 => 100001011110
101111111110 => 010000000001 => 000000001001 => 100000000100
111111111110 => 000000000001 => 000000000001 => 100000000000
100001011110 => 011110100001 => 000110111001 => 100011011100
100101111110 => 011010000001 => 000001101001 => 100000110100
110111111110 => 001000000001 => 000000010001 => 100000001000
100000001000 => 011111110111 => 101111110111 => 110111111011
10000010000 => 01111101111 => 10111101111 => 11011110111
10000100010 => 01111011101 => 11011101101 => 11101110110
100010011110 => 011101100001 => 000110110101 => 100011011010
100001101110 => 011110010001 => 001010111001 => 100101011100
110011111110 => 001100000001 => 000000100101 => 100000010010
10111011110 => 01000100001 => 00010010001 => 10001001000
11110111110 => 00001000001 => 00001000001 => 10000100000
111011111110 => 000100000001 => 000000100001 => 100000010000
10000100100 => 01111011011 => 11011101011 => 11101110101
100000101010 => 011111010101 => 111011110001 => 111101111000
100010001110 => 011101110001 => 001101101101 => 100110110110
100100011110 => 011011100001 => 000110101101 => 100011010110
100010101110 => 011101010001 => 001110110001 => 100111011000
100001110110 => 011110001001 => 010010111001 => 101001011100
101010111110 => 010101000001 => 000011100001 => 100001110000
100111011110 => 011000100001 => 000100101001 => 100010010100
10111101110 => 01000010001 => 00100010001 => 10010001000
111101111110 => 000010000001 => 000001000001 => 100000100000
100000100000 => 011111011111 => 101111011111 => 110111101111
10001000100 => 01110111011 => 11011011011 => 11101101101
100010010110 => 011101101001 => 011101101001 => 101110110100
101000011110 => 010111100001 => 000110011101 => 100011001110
100011001110 => 011100110001 => 001010110101 => 100101011010
100010110110 => 011101001001 => 010110110001 => 101011011000
100001111010 => 011110000101 => 100010111001 => 110001011100
110000111110 => 001111000001 => 000010011101 => 100001001110
100101101110 => 011010010001 => 001011010001 => 100101101000
11011101110 => 00100010001 => 00100100001 => 10010010000
111110111110 => 000001000001 => 000010000001 => 100001000000
10010000000 => 01101111111 => 10101111111 => 11010111111
10001001000 => 01110110111 => 11011010111 => 11101101011
100010001010 => 011101110101 => 111011011001 => 111101101100
100001010010 => 011110101101 => 111011100101 => 111101110010
110000011110 => 001111100001 => 000100111101 => 100010011110
101000101110 => 010111010001 => 001110011001 => 100111001100
100101001110 => 011010110001 => 001110100101 => 100111010010
100100110110 => 011011001001 => 010110101001 => 101011010100
100011010110 => 011100101001 => 011010110001 => 101101011000
100010111010 => 011101000101 => 100110110001 => 110011011000
100001111100 => 011110000011 => 000010111011 => 100001011101
10101010110 => 01010101001 => 01111000001 => 10111100000
101101011110 => 010010100001 => 000110100001 => 100011010000
101011101110 => 010100010001 => 001001100001 => 100100110000
100111110110 => 011000001001 => 010000101001 => 101000010100
11111110110 => 00000001001 => 01000000001 => 10100000000
111111011110 => 000000100001 => 000100000001 => 100010000000
100010000000 => 011101111111 => 101101111111 => 110110111111
10010001000 => 01101110111 => 11010110111 => 11101011011
110000001110 => 001111110001 => 001001111101 => 100100111110
100010101010 => 011101010101 => 111101100001 => 111110110000
101000110110 => 010111001001 => 010110011001 => 101011001100
100110001110 => 011001110001 => 001010101101 => 100101010110
100101010110 => 011010101001 => 011110100001 => 101111010000
100100111010 => 011011000101 => 100110101001 => 110011010100
100011100110 => 011100011001 => 010010110101 => 101001011010
100010111100 => 011101000011 => 000110110011 => 100011011001
11111111010 => 00000000101 => 10000000001 => 11000000000
111111101110 => 000000010001 => 001000000001 => 100100000000
0111111111 => 1000000000 => 0000000010 => 0000000001
0111111101 => 1000000010 => 1000000100 => 0100000010
0111111001 => 1000000110 => 1000001010 => 0100000101
0111110001 => 1000001110 => 1000010110 => 0100001011
0111100001 => 1000011110 => 1000101110 => 0100010111
0111000001 => 1000111110 => 1001011110 => 0100101111
0110000001 => 1001111110 => 1010111110 => 0101011111
0100000001 => 1011111110 => 1101111110 => 0110111111
0000000001 => 1111111110 => 1111111110 => 0111111111
01111111111 => 10000000000 => 00000000010 => 00000000001
01111111101 => 10000000010 => 10000000100 => 01000000010
0111111011 => 1000000100 => 0100000100 => 0010000010
01111111001 => 10000000110 => 10000001010 => 01000000101
0111110101 => 1000001010 => 1100001000 => 0110000100
01111110001 => 10000001110 => 10000010110 => 01000001011
0111101001 => 1000010110 => 1100010010 => 0110001001
01111100001 => 10000011110 => 10000101110 => 01000010111
0111010001 => 1000101110 => 1100100110 => 0110010011
01111000001 => 10000111110 => 10001011110 => 01000101111
0110100001 => 1001011110 => 1101001110 => 0110100111
01110000001 => 10001111110 => 10010111110 => 01001011111
0101000001 => 1010111110 => 1110011110 => 0111001111
01100000001 => 10011111110 => 10101111110 => 01010111111
0010000001 => 1101111110 => 1110111110 => 0111011111
01000000001 => 10111111110 => 11011111110 => 01101111111
00000000001 => 11111111110 => 11111111110 => 01111111111
0101010101 => 1010101010 => 1111100000 => 0111110000
0101010011 => 1010101100 => 0111100010 => 0011110001
0101001101 => 1010110010 => 1011100100 => 0101110010
0101001011 => 1010110100 => 0111100100 => 0011110010
0101000111 => 1010111000 => 0011100110 => 0001110011
0100110101 => 1011001010 => 1101101000 => 0110110100
0100110011 => 1011001100 => 0101101010 => 0010110101
0100101101 => 1011010010 => 1011101000 => 0101110100
0100101011 => 1011010100 => 0111101000 => 0011110100
0100100111 => 1011011000 => 0011101010 => 0001110101
0100011101 => 1011100010 => 1001101100 => 0100110110
0100011011 => 1011100100 => 0101101100 => 0010110110
0100010111 => 1011101000 => 0011101100 => 0001110110
0100001111 => 1011110000 => 0001101110 => 0000110111
0011010101 => 1100101010 => 1110110000 => 0111011000
0011010011 => 1100101100 => 0110110010 => 0011011001
0011001101 => 1100110010 => 1010110100 => 0101011010
0011001011 => 1100110100 => 0110110100 => 0011011010
0011000111 => 1100111000 => 0010110110 => 0001011011
0010110101 => 1101001010 => 1101110000 => 0110111000
0010110011 => 1101001100 => 0101110010 => 0010111001
0010101101 => 1101010010 => 1011110000 => 0101111000
0010101011 => 1101010100 => 0111110000 => 0011111000
0010100111 => 1101011000 => 0011110010 => 0001111001
0010011101 => 1101100010 => 1001110100 => 0100111010
0010011011 => 1101100100 => 0101110100 => 0010111010
0010010111 => 1101101000 => 0011110100 => 0001111010
0010001111 => 1101110000 => 0001110110 => 0000111011
0001110101 => 1110001010 => 1100111000 => 0110011100
0001110011 => 1110001100 => 0100111010 => 0010011101
0001101101 => 1110010010 => 1010111000 => 0101011100
0001101011 => 1110010100 => 0110111000 => 0011011100
0001100111 => 1110011000 => 0010111010 => 0001011101
0001011101 => 1110100010 => 1001111000 => 0100111100
0001011011 => 1110100100 => 0101111000 => 0010111100
0001010111 => 1110101000 => 0011111000 => 0001111100
0001001111 => 1110110000 => 0001111010 => 0000111101
0000111101 => 1111000010 => 1000111100 => 0100011110
0000111011 => 1111000100 => 0100111100 => 0010011110
0000110111 => 1111001000 => 0010111100 => 0001011110
0000101111 => 1111010000 => 0001111100 => 0000111110
0000011111 => 1111100000 => 0000111110 => 0000011111
010101010101 => 101010101010 => 111111000000 => 011111100000
010101010011 => 101010101100 => 011111000010 => 001111100001
010101001101 => 101010110010 => 101111000100 => 010111100010
010101001011 => 101010110100 => 011111000100 => 001111100010
010101000111 => 101010111000 => 001111000110 => 000111100011
010100110101 => 101011001010 => 110111001000 => 011011100100
010100110011 => 101011001100 => 010111001010 => 001011100101
010100101101 => 101011010010 => 101111001000 => 010111100100
010100101011 => 101011010100 => 011111001000 => 001111100100
010100100111 => 101011011000 => 001111001010 => 000111100101
010100011101 => 101011100010 => 100111001100 => 010011100110
010100011011 => 101011100100 => 010111001100 => 001011100110
010100010111 => 101011101000 => 001111001100 => 000111100110
010100001111 => 101011110000 => 000111001110 => 000011100111
010011010101 => 101100101010 => 111011010000 => 011101101000
010011010011 => 101100101100 => 011011010010 => 001101101001
010011001101 => 101100110010 => 101011010100 => 010101101010
010011001011 => 101100110100 => 011011010100 => 001101101010
010011000111 => 101100111000 => 001011010110 => 000101101011
010010110101 => 101101001010 => 110111010000 => 011011101000
010010110011 => 101101001100 => 010111010010 => 001011101001
010010101101 => 101101010010 => 101111010000 => 010111101000
010010101011 => 101101010100 => 011111010000 => 001111101000
010010100111 => 101101011000 => 001111010010 => 000111101001
010010011101 => 101101100010 => 100111010100 => 010011101010
010010011011 => 101101100100 => 010111010100 => 001011101010
010010010111 => 101101101000 => 001111010100 => 000111101010
010010001111 => 101101110000 => 000111010110 => 000011101011
010001110101 => 101110001010 => 110011011000 => 011001101100
010001110011 => 101110001100 => 010011011010 => 001001101101
010001101101 => 101110010010 => 101011011000 => 010101101100
010001101011 => 101110010100 => 011011011000 => 001101101100
010001100111 => 101110011000 => 001011011010 => 000101101101
010001011101 => 101110100010 => 100111011000 => 010011101100
010001011011 => 101110100100 => 010111011000 => 001011101100
010001010111 => 101110101000 => 001111011000 => 000111101100
010001001111 => 101110110000 => 000111011010 => 000011101101
010000111101 => 101111000010 => 100011011100 => 010001101110
010000111011 => 101111000100 => 010011011100 => 001001101110
010000110111 => 101111001000 => 001011011100 => 000101101110
010000101111 => 101111010000 => 000111011100 => 000011101110
010000011111 => 101111100000 => 000011011110 => 000001101111
001101010101 => 110010101010 => 111101100000 => 011110110000
001101010011 => 110010101100 => 011101100010 => 001110110001
001101001101 => 110010110010 => 101101100100 => 010110110010
001101001011 => 110010110100 => 011101100100 => 001110110010
001101000111 => 110010111000 => 001101100110 => 000110110011
001100110101 => 110011001010 => 110101101000 => 011010110100
001100110011 => 110011001100 => 010101101010 => 001010110101
001100101101 => 110011010010 => 101101101000 => 010110110100
001100101011 => 110011010100 => 011101101000 => 001110110100
001100100111 => 110011011000 => 001101101010 => 000110110101
001100011101 => 110011100010 => 100101101100 => 010010110110
001100011011 => 110011100100 => 010101101100 => 001010110110
001100010111 => 110011101000 => 001101101100 => 000110110110
001100001111 => 110011110000 => 000101101110 => 000010110111
001011010101 => 110100101010 => 111011100000 => 011101110000
001011010011 => 110100101100 => 011011100010 => 001101110001
001011001101 => 110100110010 => 101011100100 => 010101110010
001011001011 => 110100110100 => 011011100100 => 001101110010
001011000111 => 110100111000 => 001011100110 => 000101110011
001010110101 => 110101001010 => 110111100000 => 011011110000
001010110011 => 110101001100 => 010111100010 => 001011110001
001010101101 => 110101010010 => 101111100000 => 010111110000
001010101011 => 110101010100 => 011111100000 => 001111110000
001010100111 => 110101011000 => 001111100010 => 000111110001
001010011101 => 110101100010 => 100111100100 => 010011110010
001010011011 => 110101100100 => 010111100100 => 001011110010
001010010111 => 110101101000 => 001111100100 => 000111110010
001010001111 => 110101110000 => 000111100110 => 000011110011
001001110101 => 110110001010 => 110011101000 => 011001110100
001001110011 => 110110001100 => 010011101010 => 001001110101
001001101101 => 110110010010 => 101011101000 => 010101110100
001001101011 => 110110010100 => 011011101000 => 001101110100
001001100111 => 110110011000 => 001011101010 => 000101110101
001001011101 => 110110100010 => 100111101000 => 010011110100
001001011011 => 110110100100 => 010111101000 => 001011110100
001001010111 => 110110101000 => 001111101000 => 000111110100
001001001111 => 110110110000 => 000111101010 => 000011110101
001000111101 => 110111000010 => 100011101100 => 010001110110
001000111011 => 110111000100 => 010011101100 => 001001110110
001000110111 => 110111001000 => 001011101100 => 000101110110
001000101111 => 110111010000 => 000111101100 => 000011110110
001000011111 => 110111100000 => 000011101110 => 000001110111
000111010101 => 111000101010 => 111001110000 => 011100111000
000111010011 => 111000101100 => 011001110010 => 001100111001
000111001101 => 111000110010 => 101001110100 => 010100111010
000111001011 => 111000110100 => 011001110100 => 001100111010
000111000111 => 111000111000 => 001001110110 => 000100111011
000110110101 => 111001001010 => 110101110000 => 011010111000
000110110011 => 111001001100 => 010101110010 => 001010111001
000110101101 => 111001010010 => 101101110000 => 010110111000
000110101011 => 111001010100 => 011101110000 => 001110111000
000110100111 => 111001011000 => 001101110010 => 000110111001
000110011101 => 111001100010 => 100101110100 => 010010111010
000110011011 => 111001100100 => 010101110100 => 001010111010
000110010111 => 111001101000 => 001101110100 => 000110111010
000110001111 => 111001110000 => 000101110110 => 000010111011
000101110101 => 111010001010 => 110011110000 => 011001111000
000101110011 => 111010001100 => 010011110010 => 001001111001
000101101101 => 111010010010 => 101011110000 => 010101111000
000101101011 => 111010010100 => 011011110000 => 001101111000
000101100111 => 111010011000 => 001011110010 => 000101111001
000101011101 => 111010100010 => 100111110000 => 010011111000
000101011011 => 111010100100 => 010111110000 => 001011111000
000101010111 => 111010101000 => 001111110000 => 000111111000
000101001111 => 111010110000 => 000111110010 => 000011111001
000100111101 => 111011000010 => 100011110100 => 010001111010
000100111011 => 111011000100 => 010011110100 => 001001111010
000100110111 => 111011001000 => 001011110100 => 000101111010
000100101111 => 111011010000 => 000111110100 => 000011111010
000100011111 => 111011100000 => 000011110110 => 000001111011
000011110101 => 111100001010 => 110001111000 => 011000111100
000011110011 => 111100001100 => 010001111010 => 001000111101
000011101101 => 111100010010 => 101001111000 => 010100111100
000011101011 => 111100010100 => 011001111000 => 001100111100
000011100111 => 111100011000 => 001001111010 => 000100111101
000011011101 => 111100100010 => 100101111000 => 010010111100
000011011011 => 111100100100 => 010101111000 => 001010111100
000011010111 => 111100101000 => 001101111000 => 000110111100
000011001111 => 111100110000 => 000101111010 => 000010111101
000010111101 => 111101000010 => 100011111000 => 010001111100
000010111011 => 111101000100 => 010011111000 => 001001111100
000010110111 => 111101001000 => 001011111000 => 000101111100
000010101111 => 111101010000 => 000111111000 => 000011111100
000010011111 => 111101100000 => 000011111010 => 000001111101
000001111101 => 111110000010 => 100001111100 => 010000111110
000001111011 => 111110000100 => 010001111100 => 001000111110
000001110111 => 111110001000 => 001001111100 => 000100111110
000001101111 => 111110010000 => 000101111100 => 000010111110
000001011111 => 111110100000 => 000011111100 => 000001111110
000000111111 => 111111000000 => 000001111110 => 000000111111
11010101010 => 00101010101 => 11110000001 => 11111000000
11010101100 => 00101010011 => 01110000011 => 10111000001
10101010100 => 01010101011 => 11110000011 => 11111000001
111111111111 => 000000000000 => 000000000000 => 000000000000
111110000001 => 000001111110 => 100000111110 => 010000011111
111110100101 => 000001011010 => 111000000100 => 011100000010
111001100001 => 000110011110 => 101000101110 => 010100010111
111000011001 => 000111100110 => 101000111010 => 010100011101
111000000111 => 000111111000 => 001000111110 => 000100011111
111000110001 => 000111001110 => 101000110110 => 010100011011
111000100101 => 000111011010 => 111000110100 => 011100011010
111011000001 => 000100111110 => 101000011110 => 010100001111
111011100101 => 000100011010 => 110010000100 => 011001000010
111010010001 => 000101101110 => 111000010110 => 011100001011
111010011101 => 000101100010 => 100110000100 => 010011000010
111010000101 => 000101111010 => 111000011100 => 011100001110
111010110101 => 000101001010 => 110110000000 => 011011000000
100111100001 => 011000011110 => 100010101110 => 010001010111
100110011001 => 011001100110 => 101010101010 => 010101010101
100110001101 => 011001110010 => 101010101100 => 010101010110
100110110001 => 011001001110 => 101010100110 => 010101010011
100110100101 => 011001011010 => 111010100100 => 011101010010
100001111001 => 011110000110 => 100010111010 => 010001011101
100001100111 => 011110011000 => 001010111010 => 000101011101
100001101101 => 011110010010 => 101010111000 => 010101011100
100000011111 => 011111100000 => 000010111110 => 000001011111
100000110111 => 011111001000 => 001010111100 => 000101011110
100000100101 => 011111011010 => 111011110100 => 011101111010
100011011001 => 011100100110 => 101010110010 => 010101011001
100011000111 => 011100111000 => 001010110110 => 000101011011
100011001101 => 011100110010 => 101010110100 => 010101011010
100011110001 => 011100001110 => 100010110110 => 010001011011
100011100101 => 011100011010 => 110010110100 => 011001011010
100010010111 => 011101101000 => 001110110100 => 000111011010
100010011101 => 011101100010 => 100110110100 => 010011011010
100010000101 => 011101111010 => 111011011100 => 011101101110
100010110101 => 011101001010 => 110110110000 => 011011011000
101101100001 => 010010011110 => 101010001110 => 010101000111
101100011001 => 010011100110 => 101010011010 => 010101001101
101100110001 => 010011001110 => 101010010110 => 010101001011
101100100101 => 010011011010 => 111010010100 => 011101001010
101111000001 => 010000111110 => 100010011110 => 010001001111
101110010111 => 010001101000 => 001100100100 => 000110010010
101110010001 => 010001101110 => 110010010110 => 011001001011
101110000101 => 010001111010 => 110010011100 => 011001001110
101110110101 => 010001001010 => 110100100000 => 011010010000
101001011111 => 010110100000 => 000011100100 => 000001110010
101001011001 => 010110100110 => 101110010010 => 010111001001
101001001101 => 010110110010 => 101110010100 => 010111001010
101001110111 => 010110001000 => 001001100100 => 000100110010
101001110001 => 010110001110 => 100110010110 => 010011001011
101000010111 => 010111101000 => 001110011100 => 000111001110
101000011101 => 010111100010 => 100110011100 => 010011001110
101000110101 => 010111001010 => 110110011000 => 011011001100
101011010001 => 010100101110 => 110110000110 => 011011000011
101011000101 => 010100111010 => 110110001100 => 011011000110
101011110101 => 010100001010 => 110001100000 => 011000110000
101010010101 => 010101101010 => 111110001000 => 011111000100
0000000000 => 1111111111 => 1111111111 => 1111111111
0000000110 => 1111111001 => 0111111101 => 1011111110
0000011000 => 1111100111 => 0111110111 => 1011111011
0000011110 => 1111100001 => 0001111101 => 1000111110
0000010010 => 1111101101 => 1111110101 => 1111111010
0001100000 => 1110011111 => 0111011111 => 1011101111
0001100110 => 1110011001 => 0101110101 => 1010111010
0001111000 => 1110000111 => 0001110111 => 1000111011
0001111110 => 1110000001 => 0000011101 => 1000001110
0001110010 => 1110001101 => 1001110101 => 1100111010
0001001110 => 1110110001 => 0011110101 => 1001111010
0001000010 => 1110111101 => 1111011101 => 1111101110
0001011010 => 1110100101 => 1011110001 => 1101111000
0110000000 => 1001111111 => 0101111111 => 1010111111
0110000110 => 1001111001 => 0101011101 => 1010101110
0110011000 => 1001100111 => 0101010111 => 1010101011
0110011110 => 1001100001 => 0001010101 => 1000101010
0110010010 => 1001101101 => 1101010101 => 1110101010
0111100000 => 1000011111 => 0001011111 => 1000101111
0111100110 => 1000011001 => 0100010101 => 1010001010
0111111000 => 1000000111 => 0000010111 => 1000001011
0111111110 => 1000000001 => 0000000101 => 1000000010
0111110010 => 1000001101 => 1000010101 => 1100001010
0111001000 => 1000110111 => 1001010111 => 1100101011
0111000010 => 1000111101 => 1001011101 => 1100101110
0100100000 => 1011011111 => 1101011111 => 1110101111
0100100110 => 1011011001 => 0111010101 => 1011101010
0100111000 => 1011000111 => 0011010111 => 1001101011
0100111110 => 1011000001 => 0000110101 => 1000011010
0100110010 => 1011001101 => 1011010101 => 1101101010
0100001000 => 1011110111 => 1101110111 => 1110111011
0100001110 => 1011110001 => 0011011101 => 1001101110
0100000010 => 1011111101 => 1101111101 => 1110111110
0100011010 => 1011100101 => 1011011001 => 1101101100
0101101000 => 1010010111 => 1011000111 => 1101100011
0101100010 => 1010011101 => 1011001101 => 1101100110
0101001010 => 1010110101 => 1111001001 => 1111100100
000000000000 => 111111111111 => 111111111111 => 111111111111
000000000110 => 111111111001 => 011111111101 => 101111111110
000000011000 => 111111100111 => 011111110111 => 101111111011
000000011110 => 111111100001 => 000111111101 => 100011111110
000001100000 => 111110011111 => 011111011111 => 101111101111
000001100110 => 111110011001 => 010111110101 => 101011111010
000001111000 => 111110000111 => 000111110111 => 100011111011
000001111110 => 111110000001 => 000001111101 => 100000111110
000001001000 => 111110110111 => 111111010111 => 111111101011
000001000010 => 111110111101 => 111111011101 => 111111101110
000110000000 => 111001111111 => 011101111111 => 101110111111
000110000110 => 111001111001 => 010111011101 => 101011101110
000110011000 => 111001100111 => 010111010111 => 101011101011
000110011110 => 111001100001 => 000101110101 => 100010111010
000110010010 => 111001101101 => 110111010101 => 111011101010
000111100000 => 111000011111 => 000111011111 => 100011101111
000111100110 => 111000011001 => 010001110101 => 101000111010
000111111000 => 111000000111 => 000001110111 => 100000111011
000111111110 => 111000000001 => 000000011101 => 100000001110
000111110010 => 111000001101 => 100001110101 => 110000111010
000111001000 => 111000110111 => 100111010111 => 110011101011
000111001110 => 111000110001 => 001001110101 => 100100111010
000111011010 => 111000100101 => 101001110001 => 110100111000
000100100000 => 111011011111 => 111101011111 => 111110101111
000100111000 => 111011000111 => 001111010111 => 100111101011
000100111110 => 111011000001 => 000011110101 => 100001111010
000100110010 => 111011001101 => 101111010101 => 110111101010
000100011010 => 111011100101 => 101111011001 => 110111101100
000101101000 => 111010010111 => 101111000111 => 110111100011
000101101110 => 111010010001 => 001011110001 => 100101111000
000101100010 => 111010011101 => 101111001101 => 110111100110
000101111010 => 111010000101 => 100011110001 => 110001111000
000101001010 => 111010110101 => 111111001001 => 111111100100
011000000000 => 100111111111 => 010111111111 => 101011111111
011000000110 => 100111111001 => 010101111101 => 101010111110
011000011000 => 100111100111 => 010101110111 => 101010111011
011000011110 => 100111100001 => 000101011101 => 100010101110
011001100000 => 100110011111 => 010101011111 => 101010101111
011001100110 => 100110011001 => 010101010101 => 101010101010
011001111000 => 100110000111 => 000101010111 => 100010101011
011001111110 => 100110000001 => 000001010101 => 100000101010
011001110010 => 100110001101 => 100101010101 => 110010101010
011001011010 => 100110100101 => 101101010001 => 110110101000
011110000000 => 100001111111 => 000101111111 => 100010111111
011110000110 => 100001111001 => 010001011101 => 101000101110
011110011000 => 100001100111 => 010001010111 => 101000101011
011110011110 => 100001100001 => 000100010101 => 100010001010
011110010010 => 100001101101 => 110001010101 => 111000101010
011111100000 => 100000011111 => 000001011111 => 100000101111
011111100110 => 100000011001 => 010000010101 => 101000001010
011111111000 => 100000000111 => 000000010111 => 100000001011
011111111110 => 100000000001 => 000000000101 => 100000000010
011111001000 => 100000110111 => 100001010111 => 110000101011
011111000010 => 100000111101 => 100001011101 => 110000101110
011100111000 => 100011000111 => 001001010111 => 100100101011
011100001110 => 100011110001 => 001001011101 => 100100101110
011100011010 => 100011100101 => 101001011001 => 110100101100
011101101000 => 100010010111 => 101001000111 => 110100100011
011101100010 => 100010011101 => 101001001101 => 110100100110
011101001010 => 100010110101 => 111001001001 => 111100100100
010010011000 => 101101100111 => 011101010111 => 101110101011
010010011110 => 101101100001 => 000111010101 => 100011101010
010011100110 => 101100011001 => 010011010101 => 101001101010
010011111000 => 101100000111 => 000011010111 => 100001101011
010011110010 => 101100001101 => 100011010101 => 110001101010
010011001000 => 101100110111 => 101101010111 => 110110101011
010011011010 => 101100100101 => 101011010001 => 110101101000
010000100000 => 101111011111 => 110111011111 => 111011101111
010000111110 => 101111000001 => 000011011101 => 100001101110
010001101000 => 101110010111 => 101101100111 => 110110110011
010001101110 => 101110010001 => 001011011001 => 100101101100
010001111010 => 101110000101 => 100011011001 => 110001101100
010110100110 => 101001011001 => 011011000101 => 101101100010
010110111000 => 101001000111 => 001011000111 => 100101100011
010110110010 => 101001001101 => 101011000101 => 110101100010
010110001000 => 101001110111 => 101100110111 => 110110011011
010110001110 => 101001110001 => 001011001101 => 100101100110
010110011010 => 101001100101 => 101011001001 => 110101100100
010111101000 => 101000010111 => 100011000111 => 110001100011
010111100010 => 101000011101 => 100011001101 => 110001100110
010111001010 => 101000110101 => 110011001001 => 111001100100
010100101000 => 101011010111 => 111100100111 => 111110010011
010100101110 => 101011010001 => 001111001001 => 100111100100
010100111010 => 101011000101 => 100111001001 => 110011100100
010101101010 => 101010010101 => 110111000001 => 111011100000
0010101010 => 1101010101 => 1111100001 => 1111110000
0010101000 => 1101010111 => 1111000111 => 1111100011
0010101100 => 1101010011 => 0111100011 => 1011110001
0010110100 => 1101001011 => 1011100011 => 1101110001
0011010100 => 1100101011 => 1101100011 => 1110110001
0001010100 => 1110101011 => 1111100011 => 1111110001
0101010100 => 1010101011 => 1111000011 => 1111100001
00101010101 => 11010101010 => 11111100000 => 01111110000
00101010111 => 11010101000 => 00111110000 => 00011111000
0010101110 => 1101010001 => 0011110001 => 1001111000
00101010011 => 11010101100 => 01111100010 => 00111110001
0010100000 => 1101011111 => 1110011111 => 1111001111
00101011011 => 11010100100 => 01011110000 => 00101111000
0010111100 => 1101000011 => 0001110011 => 1000111001
00101001011 => 11010110100 => 01111100100 => 00111110010
00101101011 => 11010010100 => 01101110000 => 00110111000
0011110100 => 1100001011 => 1000110011 => 1100011001
00100101011 => 11011010100 => 01111101000 => 00111110100
0000010100 => 1111101011 => 1111110011 => 1111111001
00110101011 => 11001010100 => 01110110000 => 00111011000
0111010100 => 1000101011 => 1100100011 => 1110010001
00010101011 => 11101010100 => 01111110000 => 00111111000
01010101011 => 10101010100 => 01111100000 => 00111110000
0000000010 => 1111111101 => 1111111101 => 1111111110
0000001110 => 1111110001 => 0011111101 => 1001111110
0000111110 => 1111000001 => 0000111101 => 1000011110
0011111110 => 1100000001 => 0000001101 => 1000000110
00000000000 => 11111111111 => 11111111111 => 11111111111
00000000010 => 11111111101 => 11111111101 => 11111111110
0000000100 => 1111111011 => 1111111011 => 1111111101
00000000110 => 11111111001 => 01111111101 => 10111111110
0000001010 => 1111110101 => 1111111001 => 1111111100
0000010110 => 1111101001 => 0111111001 => 1011111100
0000101110 => 1111010001 => 0011111001 => 1001111100
0001011110 => 1110100001 => 0001111001 => 1000111100
0010111110 => 1101000001 => 0000111001 => 1000011100
0101111110 => 1010000001 => 0000011001 => 1000001100
00111111110 => 11000000001 => 00000001101 => 10000000110
0010110010 => 1101001101 => 1011100101 => 1101110010
0010111000 => 1101000111 => 0011100111 => 1001110011
0011001010 => 1100110101 => 1101101001 => 1110110100
0011001100 => 1100110011 => 0101101011 => 1010110101
0011010010 => 1100101101 => 1101100101 => 1110110010
0011011000 => 1100100111 => 0101100111 => 1010110011
0011100010 => 1100011101 => 1001101101 => 1100110110
0011100100 => 1100011011 => 1001101011 => 1100110101
0011101000 => 1100010111 => 1001100111 => 1100110011
0011110000 => 1100001111 => 0001101111 => 1000110111
0100101010 => 1011010101 => 1111010001 => 1111101000
0100101100 => 1011010011 => 0111010011 => 1011101001
0100110100 => 1011001011 => 1011010011 => 1101101001
0101001100 => 1010110011 => 0111001011 => 1011100101
0101010010 => 1010101101 => 1111000101 => 1111100010
0101011000 => 1010100111 => 0111000111 => 1011100011
0101100100 => 1010011011 => 1011001011 => 1101100101
0101110000 => 1010001111 => 0011001111 => 1001100111
0110001010 => 1001110101 => 1101011001 => 1110101100
0110001100 => 1001110011 => 0101011011 => 1010101101
0110010100 => 1001101011 => 1101010011 => 1110101001
0110100010 => 1001011101 => 1101001101 => 1110100110
0110100100 => 1001011011 => 1101001011 => 1110100101
0110101000 => 1001010111 => 1101000111 => 1110100011
0110110000 => 1001001111 => 0101001111 => 1010100111
0111000100 => 1000111011 => 1001011011 => 1100101101
0111010000 => 1000101111 => 1001001111 => 1100100111
001010101010 => 110101010101 => 111111000001 => 111111100000
001010101100 => 110101010011 => 011111000011 => 101111100001
001010111000 => 110101000111 => 001111000111 => 100111100011
001011001010 => 110100110101 => 110111001001 => 111011100100
001011010010 => 110100101101 => 110111000101 => 111011100010
001011010100 => 110100101011 => 110111000011 => 111011100001
001011100010 => 110100011101 => 100111001101 => 110011100110
001011100100 => 110100011011 => 100111001011 => 110011100101
001011101000 => 110100010111 => 100111000111 => 110011100011
001100101010 => 110011010101 => 111011010001 => 111101101000
001100110010 => 110011001101 => 101011010101 => 110101101010
001100110100 => 110011001011 => 101011010011 => 110101101001
001100111000 => 110011000111 => 001011010111 => 100101101011
001101001010 => 110010110101 => 111011001001 => 111101100100
001101010010 => 110010101101 => 111011000101 => 111101100010
001101010100 => 110010101011 => 111011000011 => 111101100001
001101011000 => 110010100111 => 011011000111 => 101101100011
001101100010 => 110010011101 => 101011001101 => 110101100110
001101100100 => 110010011011 => 101011001011 => 110101100101
001101101000 => 110010010111 => 101011000111 => 110101100011
001110001010 => 110001110101 => 110011011001 => 111001101100
001110010010 => 110001101101 => 110011010101 => 111001101010
001110010100 => 110001101011 => 110011010011 => 111001101001
001110100010 => 110001011101 => 110011001101 => 111001100110
001110100100 => 110001011011 => 110011001011 => 111001100101
001110101000 => 110001010111 => 110011000111 => 111001100011
001111000010 => 110000111101 => 100011011101 => 110001101110
001111000100 => 110000111011 => 100011011011 => 110001101101
001111001000 => 110000110111 => 100011010111 => 110001101011
001111010000 => 110000101111 => 100011001111 => 110001100111
001111100000 => 110000011111 => 000011011111 => 100001101111
010010101010 => 101101010101 => 111110100001 => 111111010000
010010101100 => 101101010011 => 011110100011 => 101111010001
010010110100 => 101101001011 => 101110100011 => 110111010001
010011001010 => 101100110101 => 110110101001 => 111011010100
010011010010 => 101100101101 => 110110100101 => 111011010010
010011010100 => 101100101011 => 110110100011 => 111011010001
010011100010 => 101100011101 => 100110101101 => 110011010110
010011100100 => 101100011011 => 100110101011 => 110011010101
010011101000 => 101100010111 => 100110100111 => 110011010011
010100101010 => 101011010101 => 111110010001 => 111111001000
010100101100 => 101011010011 => 011110010011 => 101111001001
010100110100 => 101011001011 => 101110010011 => 110111001001
010100111000 => 101011000111 => 001110010111 => 100111001011
010101001010 => 101010110101 => 111110001001 => 111111000100
010101010010 => 101010101101 => 111110000101 => 111111000010
010101010100 => 101010101011 => 111110000011 => 111111000001
010101011000 => 101010100111 => 011110000111 => 101111000011
010110001010 => 101001110101 => 110110011001 => 111011001100
010110010010 => 101001101101 => 110110010101 => 111011001010
010110010100 => 101001101011 => 110110010011 => 111011001001
010110100010 => 101001011101 => 110110001101 => 111011000110
010110101000 => 101001010111 => 110110000111 => 111011000011
010111000010 => 101000111101 => 100110011101 => 110011001110
010111000100 => 101000111011 => 100110011011 => 110011001101
010111001000 => 101000110111 => 100110010111 => 110011001011
010111010000 => 101000101111 => 100110001111 => 110011000111
010111100000 => 101000011111 => 000110011111 => 100011001111
011000101010 => 100111010101 => 111010110001 => 111101011000
011000110010 => 100111001101 => 101010110101 => 110101011010
011000110100 => 100111001011 => 101010110011 => 110101011001
011001001010 => 100110110101 => 111010101001 => 111101010100
011001010010 => 100110101101 => 111010100101 => 111101010010
011001010100 => 100110101011 => 111010100011 => 111101010001
011001100010 => 100110011101 => 101010101101 => 110101010110
011001100100 => 100110011011 => 101010101011 => 110101010101
011001101000 => 100110010111 => 101010100111 => 110101010011
011010001010 => 100101110101 => 111010011001 => 111101001100
011010010010 => 100101101101 => 111010010101 => 111101001010
011010010100 => 100101101011 => 111010010011 => 111101001001
011010011000 => 100101100111 => 011010010111 => 101101001011
011010100010 => 100101011101 => 111010001101 => 111101000110
011010101000 => 100101010111 => 111010000111 => 111101000011
011011000010 => 100100111101 => 101010011101 => 110101001110
011011000100 => 100100111011 => 101010011011 => 110101001101
011011001000 => 100100110111 => 101010010111 => 110101001011
011011010000 => 100100101111 => 101010001111 => 110101000111
011100010010 => 100011101101 => 110010110101 => 111001011010
011100010100 => 100011101011 => 110010110011 => 111001011001
011100100010 => 100011011101 => 110010101101 => 111001010110
011100100100 => 100011011011 => 110010101011 => 111001010101
011100101000 => 100011010111 => 110010100111 => 111001010011
011101000010 => 100010111101 => 110010011101 => 111001001110
011101000100 => 100010111011 => 110010011011 => 111001001101
011101001000 => 100010110111 => 110010010111 => 111001001011
011101010000 => 100010101111 => 110010001111 => 111001000111
011110000010 => 100001111101 => 100010111101 => 110001011110
011110000100 => 100001111011 => 100010111011 => 110001011101
011110001000 => 100001110111 => 100010110111 => 110001011011
011110010000 => 100001101111 => 100010101111 => 110001010111
011110100000 => 100001011111 => 100010011111 => 110001001111
01000100010 => 10111011101 => 11101101101 => 11110110110
01000010001 => 10111101110 => 11101110110 => 01110111011
01000001000 => 10111110111 => 11011110111 => 11101111011
01010101010 => 10101010101 => 11111000001 => 11111100000
01001001000 => 10110110111 => 11101010111 => 11110101011
01000100001 => 10111011110 => 11101101110 => 01110110111
01000010000 => 10111101111 => 11011101111 => 11101110111
00100001000 => 11011110111 => 11101110111 => 11110111011
00100010000 => 11011101111 => 11101101111 => 11110110111
00010000010 => 11101111101 => 11110111101 => 11111011110
00010000100 => 11101111011 => 11110111011 => 11111011101
00010001000 => 11101110111 => 11110110111 => 11111011011
00010010000 => 11101101111 => 11110101111 => 11111010111
00000100000 => 11111011111 => 11111011111 => 11111101111
10101010101010101010 => 01010101010101010101 => 11111111100000000001 => 11111111110000000000
0100000000 => 1011111111 => 1011111111 => 1101111111
0101111111 => 1010000000 => 0000001100 => 0000000110
01000000000 => 10111111111 => 10111111111 => 11011111111
0100000101 => 1011111010 => 1110111100 => 0111011110
0100001011 => 1011110100 => 0111011100 => 0011101110
0110111111 => 1001000000 => 0000010100 => 0000001010
01011111111 => 10100000000 => 00000001100 => 00000000110
0101010110 => 1010101001 => 0111100001 => 1011110000
0101011001 => 1010100110 => 1011100010 => 0101110001
0101011010 => 1010100101 => 1011100001 => 1101110000
0101100101 => 1010011010 => 1101100100 => 0110110010
0101100110 => 1010011001 => 0101100101 => 1010110010
0101101001 => 1010010110 => 1101100010 => 0110110001
0101101010 => 1010010101 => 1101100001 => 1110110000
0101101100 => 1010010011 => 0101100011 => 1010110001
0101110001 => 1010001110 => 1001100110 => 0100110011
0101110010 => 1010001101 => 1001100101 => 1100110010
0101110100 => 1010001011 => 1001100011 => 1100110001
0101111000 => 1010000111 => 0001100111 => 1000110011
0110010101 => 1001101010 => 1110101000 => 0111010100
0110010110 => 1001101001 => 0110101001 => 1011010100
0110011001 => 1001100110 => 1010101010 => 0101010101
0110011010 => 1001100101 => 1010101001 => 1101010100
0110011100 => 1001100011 => 0010101011 => 1001010101
0110100101 => 1001011010 => 1110100100 => 0111010010
0110101001 => 1001010110 => 1110100010 => 0111010001
0110101010 => 1001010101 => 1110100001 => 1111010000
0110101100 => 1001010011 => 0110100011 => 1011010001
0110110001 => 1001001110 => 1010100110 => 0101010011
0110110010 => 1001001101 => 1010100101 => 1101010010
0110110100 => 1001001011 => 1010100011 => 1101010001
0110111000 => 1001000111 => 0010100111 => 1001010011
0111000101 => 1000111010 => 1100101100 => 0110010110
0111000110 => 1000111001 => 0100101101 => 1010010110
0111001001 => 1000110110 => 1100101010 => 0110010101
0111001100 => 1000110011 => 0100101011 => 1010010101
0111010010 => 1000101101 => 1100100101 => 1110010010
0111011000 => 1000100111 => 0100100111 => 1010010011
0111100010 => 1000011101 => 1000101101 => 1100010110
0111100100 => 1000011011 => 1000101011 => 1100010101
0111101000 => 1000010111 => 1000100111 => 1100010011
0111110000 => 1000001111 => 0000101111 => 1000010111
010101010110 => 101010101001 => 011111000001 => 101111100000
010101011001 => 101010100110 => 101111000010 => 010111100001
010101011010 => 101010100101 => 101111000001 => 110111100000
010101011100 => 101010100011 => 001111000011 => 100111100001
010101100101 => 101010011010 => 110111000100 => 011011100010
010101101001 => 101010010110 => 110111000010 => 011011100001
010101110100 => 101010001011 => 100111000011 => 110011100001
010101111000 => 101010000111 => 000111000111 => 100011100011
010110010101 => 101001101010 => 111011001000 => 011101100100
010110010110 => 101001101001 => 011011001001 => 101101100100
010110011001 => 101001100110 => 101011001010 => 010101100101
010110011100 => 101001100011 => 001011001011 => 100101100101
010110100101 => 101001011010 => 111011000100 => 011101100010
010110101001 => 101001010110 => 111011000010 => 011101100001
010110101010 => 101001010101 => 111011000001 => 111101100000
010110110100 => 101001001011 => 101011000011 => 110101100001
010111000101 => 101000111010 => 110011001100 => 011001100110
010111000110 => 101000111001 => 010011001101 => 101001100110
010111001001 => 101000110110 => 110011001010 => 011001100101
010111001100 => 101000110011 => 010011001011 => 101001100101
010111010001 => 101000101110 => 110011000110 => 011001100011
010111010010 => 101000101101 => 110011000101 => 111001100010
010111010100 => 101000101011 => 110011000011 => 111001100001
010111011000 => 101000100111 => 010011000111 => 101001100011
010111100001 => 101000011110 => 100011001110 => 010001100111
010111100100 => 101000011011 => 100011001011 => 110001100101
010111110000 => 101000001111 => 000011001111 => 100001100111
011001010101 => 100110101010 => 111101010000 => 011110101000
011001010110 => 100110101001 => 011101010001 => 101110101000
011001011001 => 100110100110 => 101101010010 => 010110101001
011001011100 => 100110100011 => 001101010011 => 100110101001
011001100101 => 100110011010 => 110101010100 => 011010101010
011001101001 => 100110010110 => 110101010010 => 011010101001
011001101100 => 100110010011 => 010101010011 => 101010101001
011001110001 => 100110001110 => 100101010110 => 010010101011
011001110100 => 100110001011 => 100101010011 => 110010101001
011010010101 => 100101101010 => 111101001000 => 011110100100
011010010110 => 100101101001 => 011101001001 => 101110100100
011010011010 => 100101100101 => 101101001001 => 110110100100
011010011100 => 100101100011 => 001101001011 => 100110100101
011010100101 => 100101011010 => 111101000100 => 011110100010
011010100110 => 100101011001 => 011101000101 => 101110100010
011010101001 => 100101010110 => 111101000010 => 011110100001
011010101010 => 100101010101 => 111101000001 => 111110100000
011010101100 => 100101010011 => 011101000011 => 101110100001
011010110010 => 100101001101 => 101101000101 => 110110100010
011010110100 => 100101001011 => 101101000011 => 110110100001
011010111000 => 100101000111 => 001101000111 => 100110100011
011011000101 => 100100111010 => 110101001100 => 011010100110
011011000110 => 100100111001 => 010101001101 => 101010100110
011011001001 => 100100110110 => 110101001010 => 011010100101
011011001010 => 100100110101 => 110101001001 => 111010100100
011011001100 => 100100110011 => 010101001011 => 101010100101
011011010001 => 100100101110 => 110101000110 => 011010100011
011011010010 => 100100101101 => 110101000101 => 111010100010
011011010100 => 100100101011 => 110101000011 => 111010100001
011011011000 => 100100100111 => 010101000111 => 101010100011
011011100001 => 100100011110 => 100101001110 => 010010100111
011011100010 => 100100011101 => 100101001101 => 110010100110
011011100100 => 100100011011 => 100101001011 => 110010100101
011011101000 => 100100010111 => 100101000111 => 110010100011
011011110000 => 100100001111 => 000101001111 => 100010100111
011100010110 => 100011101001 => 011001011001 => 101100101100
011100011001 => 100011100110 => 101001011010 => 010100101101
011100011100 => 100011100011 => 001001011011 => 100100101101
011100101001 => 100011010110 => 111001010010 => 011100101001
011100101010 => 100011010101 => 111001010001 => 111100101000
011100101100 => 100011010011 => 011001010011 => 101100101001
011100110001 => 100011001110 => 101001010110 => 010100101011
011100110100 => 100011001011 => 101001010011 => 110100101001
011101000101 => 100010111010 => 111001001100 => 011100100110
011101001001 => 100010110110 => 111001001010 => 011100100101
011101010001 => 100010101110 => 111001000110 => 011100100011
011101010010 => 100010101101 => 111001000101 => 111100100010
011101010100 => 100010101011 => 111001000011 => 111100100001
011101011000 => 100010100111 => 011001000111 => 101100100011
011101100001 => 100010011110 => 101001001110 => 010100100111
011101100100 => 100010011011 => 101001001011 => 110100100101
011101110000 => 100010001111 => 001001001111 => 100100100111
011110001001 => 100001110110 => 110001011010 => 011000101101
011110001100 => 100001110011 => 010001011011 => 101000101101
011110100001 => 100001011110 => 110001001110 => 011000100111
011110100010 => 100001011101 => 110001001101 => 111000100110
011110100100 => 100001011011 => 110001001011 => 111000100101
011110101000 => 100001010111 => 110001000111 => 111000100011
011110110000 => 100001001111 => 010001001111 => 101000100111
011111000001 => 100000111110 => 100001011110 => 010000101111
011111000100 => 100000111011 => 100001011011 => 110000101101
011111010000 => 100000101111 => 100001001111 => 110000100111
0100000100 => 1011111011 => 1101111011 => 1110111101
0011100110 => 1100011001 => 0100110101 => 1010011010
0011101010 => 1100010101 => 1100110001 => 1110011000
0011101100 => 1100010011 => 0100110011 => 1010011001
0001101110 => 1110010001 => 0010111001 => 1001011100
0010110110 => 1101001001 => 0101110001 => 1010111000
0011110010 => 1100001101 => 1000110101 => 1100011010
0001110110 => 1110001001 => 0100111001 => 1010011100
0100111010 => 1011000101 => 1001101001 => 1100110100
0011111000 => 1100000111 => 0000110111 => 1000011011
0001111010 => 1110000101 => 1000111001 => 1100011100
0100111100 => 1011000011 => 0001101011 => 1000110101
0001111100 => 1110000011 => 0000111011 => 1000011101
001111000110 => 110000111001 => 010001101101 => 101000110110
100111001100 => 011000110011 => 010010101011 => 101001010101
001111001100 => 110000110011 => 010001101011 => 101000110101
001011010110 => 110100101001 => 011011100001 => 101101110000
001111010100 => 110000101011 => 110001100011 => 111000110001
000111010110 => 111000101001 => 011001110001 => 101100111000
001011011010 => 110100100101 => 101011100001 => 110101110000
100111011000 => 011000100111 => 010010100111 => 101001010011
001111011000 => 110000100111 => 010001100111 => 101000110011
100011011100 => 011100100011 => 001010110011 => 100101011001
010011011100 => 101100100011 => 001011010011 => 100101101001
000111011100 => 111000100011 => 001001110011 => 100100111001
000011011110 => 111100100001 => 000101111001 => 100010111100
001101100110 => 110010011001 => 010101100101 => 101010110010
001101101010 => 110010010101 => 110101100001 => 111010110000
100101101100 => 011010010011 => 010110100011 => 101011010001
001101101100 => 110010010011 => 010101100011 => 101010110001
001111100010 => 110000011101 => 100001101101 => 110000110110
100111100100 => 011000011011 => 100010101011 => 110001010101
001111100100 => 110000011011 => 100001101011 => 110000110101
010011101010 => 101100010101 => 110011010001 => 111001101000
001011101010 => 110100010101 => 110011100001 => 111001110000
100111101000 => 011000010111 => 100010100111 => 110001010011
001111101000 => 110000010111 => 100001100111 => 110000110011
000111101010 => 111000010101 => 110001110001 => 111000111000
100011101100 => 011100010011 => 010010110011 => 101001011001
010011101100 => 101100010011 => 010011010011 => 101001101001
000111101100 => 111000010011 => 010001110011 => 101000111001
000011101110 => 111100010001 => 001001111001 => 100100111100
101001110100 => 010110001011 => 100110010011 => 110011001001
001101110010 => 110010001101 => 100101100101 => 110010110010
100101110100 => 011010001011 => 100110100011 => 110011010001
001101110100 => 110010001011 => 100101100011 => 110010110001
001011110010 => 110100001101 => 100011100101 => 110001110010
100111110000 => 011000001111 => 000010101111 => 100001010111
001111110000 => 110000001111 => 000001101111 => 100000110111
100011110100 => 011100001011 => 100010110011 => 110001011001
010011110100 => 101100001011 => 100011010011 => 110001101001
001011110100 => 110100001011 => 100011100011 => 110001110001
000111110100 => 111000001011 => 100001110011 => 110000111001
110001111000 => 001110000111 => 000100110111 => 100010011011
101001111000 => 010110000111 => 000110010111 => 100011001011
001001111010 => 110110000101 => 100011101001 => 110001110100
100101111000 => 011010000111 => 000110100111 => 100011010011
001101111000 => 110010000111 => 000101100111 => 100010110011
100011111000 => 011100000111 => 000010110111 => 100001011011
001011111000 => 110100000111 => 000011100111 => 100001110011
000011111010 => 111100000101 => 100001111001 => 110000111100
010001111100 => 101110000011 => 000011011011 => 100001101101
001001111100 => 110110000011 => 000011101011 => 100001110101
000101111100 => 111010000011 => 000011110011 => 100001111001
000011111100 => 111100000011 => 000001111011 => 100000111101
0000000101 => 1111111010 => 1111111100 => 0111111110
0000001101 => 1111110010 => 1011111100 => 0101111110
0000011101 => 1111100010 => 1001111100 => 0100111110
0001111101 => 1110000010 => 1000011100 => 0100001110
00000001101 => 11111110010 => 10111111100 => 01011111110
0000101101 => 1111010010 => 1011111000 => 0101111100
0010111101 => 1101000010 => 1000111000 => 0100011100
0101111101 => 1010000010 => 1000011000 => 0100001100
11111111101 => 00000000010 => 10000000000 => 01000000000
100101010101 => 011010101010 => 111110100000 => 011111010000
100101011001 => 011010100110 => 101110100010 => 010111010001
100101100101 => 011010011010 => 110110100100 => 011011010010
100101101001 => 011010010110 => 110110100010 => 011011010001
100101110001 => 011010001110 => 100110100110 => 010011010011
100110101001 => 011001010110 => 111010100010 => 011101010001
100111000101 => 011000111010 => 110010101100 => 011001010110
100111001001 => 011000110110 => 110010101010 => 011001010101
101001010101 => 010110101010 => 111110010000 => 011111001000
101001101001 => 010110010110 => 110110010010 => 011011001001
101010100101 => 010101011010 => 111110000100 => 011111000010
101010101001 => 010101010110 => 111110000010 => 011111000001
101011001001 => 010100110110 => 110110001010 => 011011000101
101011100001 => 010100011110 => 100110001110 => 010011000111
101100010101 => 010011101010 => 111010011000 => 011101001100
101101000101 => 010010111010 => 111010001100 => 011101000110
101101001001 => 010010110110 => 111010001010 => 011101000101
101101010001 => 010010101110 => 111010000110 => 011101000011
101110100001 => 010001011110 => 110010001110 => 011001000111
110001010101 => 001110101010 => 111100110000 => 011110011000
110001011001 => 001110100110 => 101100110010 => 010110011001
110001100101 => 001110011010 => 110100110100 => 011010011010
110001101001 => 001110010110 => 110100110010 => 011010011001
110001110001 => 001110001110 => 100100110110 => 010010011011
110010010101 => 001101101010 => 111100101000 => 011110010100
110010011001 => 001101100110 => 101100101010 => 010110010101
110010100101 => 001101011010 => 111100100100 => 011110010010
110010101001 => 001101010110 => 111100100010 => 011110010001
110011000101 => 001100111010 => 110100101100 => 011010010110
110011001001 => 001100110110 => 110100101010 => 011010010101
110011010001 => 001100101110 => 110100100110 => 011010010011
110011100001 => 001100011110 => 100100101110 => 010010010111
110100010101 => 001011101010 => 111100011000 => 011110001100
110100100101 => 001011011010 => 111100010100 => 011110001010
110100101001 => 001011010110 => 111100010010 => 011110001001
110101000101 => 001010111010 => 111100001100 => 011110000110
110101001001 => 001010110110 => 111100001010 => 011110000101
110101010001 => 001010101110 => 111100000110 => 011110000011
110110000101 => 001001111010 => 110100011100 => 011010001110
110110001001 => 001001110110 => 110100011010 => 011010001101
110110010001 => 001001101110 => 110100010110 => 011010001011
110110100001 => 001001011110 => 110100001110 => 011010000111
110111000001 => 001000111110 => 100100011110 => 010010001111
111000010101 => 000111101010 => 111000111000 => 011100011100
111000101001 => 000111010110 => 111000110010 => 011100011001
111001000101 => 000110111010 => 111000101100 => 011100010110
111001001001 => 000110110110 => 111000101010 => 011100010101
111010001001 => 000101110110 => 111000011010 => 011100001101
111010100001 => 000101011110 => 111000001110 => 011100000111
111100000101 => 000011111010 => 110000111100 => 011000011110
111100010001 => 000011101110 => 110000110110 => 011000011011
111101000001 => 000010111110 => 110000011110 => 011000001111
0011110001 => 1100001110 => 1000110110 => 0100011011
110101000011 => 001010111100 => 011100001110 => 001110000111
110011000011 => 001100111100 => 010100101110 => 001010010111
110000111100 => 001111000011 => 000100111011 => 100010011101
110000001111 => 001111110000 => 000100111110 => 000010011111
111010000011 => 000101111100 => 011000011110 => 001100001111
111000011100 => 000111100011 => 001000111011 => 100100011101
001111000011 => 110000111100 => 010001101110 => 001000110111
111100000011 => 000011111100 => 010000111110 => 001000011111
000111110001 => 111000001110 => 100001110110 => 010000111011
001111100001 => 110000011110 => 100001101110 => 010000110111
01111110101 => 10000001010 => 11000001000 => 01100000100
0011101101 => 1100010010 => 1010011000 => 0101001100
0011011001 => 1100100110 => 1010110010 => 0101011001
0001000001 => 1110111110 => 1111011110 => 0111101111
0111010101 => 1000101010 => 1110010000 => 0111001000
0111010011 => 1000101100 => 0110010010 => 0011001001
0111001101 => 1000110010 => 1010010100 => 0101001010
0011110101 => 1100001010 => 1100011000 => 0110001100
0011110011 => 1100001100 => 0100011010 => 0010001101
0000111111 => 1111000000 => 0000011110 => 0000001111
110101010011 => 001010101100 => 011110000010 => 001111000001
110100110011 => 001011001100 => 010110001010 => 001011000101
110011010011 => 001100101100 => 011010010010 => 001101001001
110110010011 => 001001101100 => 011010001010 => 001101000101
111001010011 => 000110101100 => 011100010010 => 001110001001
111010010011 => 000101101100 => 011100001010 => 001110000101
11111110010 => 00000001101 => 10000000101 => 11000000010
0001110100 => 1110001011 => 1001110011 => 1100111001
0001101100 => 1110010011 => 0101110011 => 1010111001
0001011100 => 1110100011 => 0011110011 => 1001111001
0001101010 => 1110010101 => 1101110001 => 1110111000
0000111010 => 1111000101 => 1001111001 => 1100111100
0101000110 => 1010111001 => 0111001101 => 1011100110
0010100110 => 1101011001 => 0111100101 => 1011110010
0100010110 => 1011101001 => 0111011001 => 1011101100
0010010110 => 1101101001 => 0111101001 => 1011110100
0001010110 => 1110101001 => 0111110001 => 1011111000
0000110110 => 1111001001 => 0101111001 => 1010111100
0010001110 => 1101110001 => 0011101101 => 1001110110
000111010100 => 111000101011 => 110011100011 => 111001110001
000110110100 => 111001001011 => 101011100011 => 110101110001
010001110100 => 101110001011 => 100110110011 => 110011011001
001001110100 => 110110001011 => 100111010011 => 110011101001
000011110100 => 111100001011 => 100011110011 => 110001111001
001001011100 => 110110100011 => 001111010011 => 100111101001
000101011100 => 111010100011 => 001111100011 => 100111110001
000010111100 => 111101000011 => 000111110011 => 100011111001
000111010010 => 111000101101 => 110011100101 => 111001110010
010001110010 => 101110001101 => 100110110101 => 110011011010
001001110010 => 110110001101 => 100111010101 => 110011101010
000011110010 => 111100001101 => 100011110101 => 110001111010
000111001010 => 111000110101 => 110011101001 => 111001110100
000110101010 => 111001010101 => 111011100001 => 111101110000
010001101010 => 101110010101 => 110110110001 => 111011011000
001001101010 => 110110010101 => 110111010001 => 111011101000
000101101010 => 111010010101 => 110111100001 => 111011110000
000011101010 => 111100010101 => 110011110001 => 111001111000
010100011010 => 101011100101 => 101110011001 => 110111001100
010001011010 => 101110100101 => 101110110001 => 110111011000
000011011010 => 111100100101 => 101011110001 => 110101111000
010000111010 => 101111000101 => 100110111001 => 110011011100
010101000110 => 101010111001 => 011110001101 => 101111000110
001101000110 => 110010111001 => 011011001101 => 101101100110
010100100110 => 101011011001 => 011110010101 => 101111001010
010010100110 => 101101011001 => 011110100101 => 101111010010
001010100110 => 110101011001 => 011111000101 => 101111100010
000110100110 => 111001011001 => 011011100101 => 101101110010
010100010110 => 101011101001 => 011110011001 => 101111001100
001100010110 => 110011101001 => 011011011001 => 101101101100
010010010110 => 101101101001 => 011110101001 => 101111010100
001010010110 => 110101101001 => 011111001001 => 101111100100
010001010110 => 101110101001 => 011110110001 => 101111011000
001001010110 => 110110101001 => 011111010001 => 101111101000
000101010110 => 111010101001 => 011111100001 => 101111110000
000011010110 => 111100101001 => 011011110001 => 101101111000
010100001110 => 101011110001 => 001110011101 => 100111001110
001100001110 => 110011110001 => 001011011101 => 100101101110
001010001110 => 110101110001 => 001111001101 => 100111100110
010001001110 => 101110110001 => 001110110101 => 100111011010
001001001110 => 110110110001 => 001111010101 => 100111101010
000101001110 => 111010110001 => 001111100101 => 100111110010
000011001110 => 111100110001 => 001011110101 => 100101111010
001000101110 => 110111010001 => 001111011001 => 100111101100
000100101110 => 111011010001 => 001111101001 => 100111110100
000010101110 => 111101010001 => 001111110001 => 100111111000
010000011110 => 101111100001 => 000110111101 => 100011011110
000100011110 => 111011100001 => 000111101101 => 100011110110
000010011110 => 111101100001 => 000111110101 => 100011111010
000001011110 => 111110100001 => 000111111001 => 100011111100
000000111110 => 111111000001 => 000011111101 => 100001111110
0110111001 => 1001000110 => 1001010010 => 0100101001
0001101001 => 1110010110 => 1101110010 => 0110111001
00000101101 => 11111010010 => 10111111000 => 01011111100
00000010101 => 11111101010 => 11111111000 => 01111111100
0000010001 => 1111101110 => 1111110110 => 0111111011
10000000001 => 01111111110 => 10111111110 => 01011111111
11000000001 => 00111111110 => 10011111110 => 01001111111
11100000001 => 00011111110 => 10001111110 => 01000111111
11110000001 => 00001111110 => 10000111110 => 01000011111
11111000001 => 00000111110 => 10000011110 => 01000001111
11111100001 => 00000011110 => 10000001110 => 01000000111
11111110001 => 00000001110 => 10000000110 => 01000000011
11111111001 => 00000000110 => 10000000010 => 01000000001
11111111111 => 00000000000 => 00000000000 => 00000000000
0110011011 => 1001100100 => 0101010100 => 0010101010
0100111011 => 1011000100 => 0100110100 => 0010011010
0110010011 => 1001101100 => 0110101010 => 0011010101
0110110011 => 1001001100 => 0101010010 => 0010101001
0101110011 => 1010001100 => 0100110010 => 0010011001
0110010111 => 1001101000 => 0011010100 => 0001101010
0100110111 => 1011001000 => 0010110100 => 0001011010
0110100111 => 1001011000 => 0011010010 => 0001101001
0101100111 => 1010011000 => 0010110010 => 0001011001
0101001111 => 1010110000 => 0001110010 => 0000111001
100100111001 => 011011000110 => 100110101010 => 010011010101
101000111001 => 010111000110 => 100110011010 => 010011001101
100110011011 => 011001100100 => 010101010100 => 001010101010
100100011011 => 011011100100 => 010110101100 => 001011010110
101100011011 => 010011100100 => 010101001100 => 001010100110
101000011011 => 010111100100 => 010110011100 => 001011001110
100100111011 => 011011000100 => 010011010100 => 001001101010
101000111011 => 010111000100 => 010011001100 => 001001100110
100101111011 => 011010000100 => 010001101000 => 001000110100
100110010011 => 011001101100 => 011010101010 => 001101010101
101110010011 => 010001101100 => 011001001010 => 001100100101
101100010011 => 010011101100 => 011010011010 => 001101001101
100110110011 => 011001001100 => 010101010010 => 001010101001
100100110011 => 011011001100 => 010110101010 => 001011010101
101100110011 => 010011001100 => 010101001010 => 001010100101
101000110011 => 010111001100 => 010110011010 => 001011001101
100101110011 => 011010001100 => 010011010010 => 001001101001
101001110011 => 010110001100 => 010011001010 => 001001100101
100110100011 => 011001011100 => 011010100110 => 001101010011
101100100011 => 010011011100 => 011010010110 => 001101001011
100101100011 => 011010011100 => 010110100110 => 001011010011
101001100011 => 010110011100 => 010110010110 => 001011001011
101011000011 => 010100111100 => 010110001110 => 001011000111
100110010111 => 011001101000 => 001101010100 => 000110101010
101100010111 => 010011101000 => 001101001100 => 000110100110
100100110111 => 011011001000 => 001011010100 => 000101101010
101000110111 => 010111001000 => 001011001100 => 000101100110
100110100111 => 011001011000 => 001101010010 => 000110101001
101100100111 => 010011011000 => 001101001010 => 000110100101
100101100111 => 011010011000 => 001011010010 => 000101101001
101001100111 => 010110011000 => 001011001010 => 000101100101
100101101111 => 011010010000 => 000101101000 => 000010110100
100110101010 => 011001010101 => 111010100001 => 111101010000
101001101010 => 010110010101 => 110110010001 => 111011001000
100101101010 => 011010010101 => 110110100001 => 111011010000
100011101010 => 011100010101 => 110010110001 => 111001011000
101010011010 => 010101100101 => 101110001001 => 110111000100
100110011010 => 011001100101 => 101010101001 => 110101010100
101001011010 => 010110100101 => 101110010001 => 110111001000
100101011010 => 011010100101 => 101110100001 => 110111010000
101000111010 => 010111000101 => 100110011001 => 110011001100
101010100110 => 010101011001 => 011110000101 => 101111000010
100110100110 => 011001011001 => 011010100101 => 101101010010
101001100110 => 010110011001 => 010110010101 => 101011001010
100101100110 => 011010011001 => 010110100101 => 101011010010
101010010110 => 010101101001 => 011110001001 => 101111000100
100110010110 => 011001101001 => 011010101001 => 101101010100
101001010110 => 010110101001 => 011110010001 => 101111001000
101010001110 => 010101110001 => 001110001101 => 100111000110
100011101001 => 011100010110 => 110010110010 => 011001011001
100011010101 => 011100101010 => 111010110000 => 011101011000
100100110101 => 011011001010 => 110110101000 => 011011010100
100001110101 => 011110001010 => 110010111000 => 011001011100
101010001101 => 010101110010 => 101110001100 => 010111000110
100101001101 => 011010110010 => 101110100100 => 010111010010
101000101101 => 010111010010 => 101110011000 => 010111001100
100100101101 => 011011010010 => 101110101000 => 010111010100
100010101101 => 011101010010 => 101110110000 => 010111011000
101010100011 => 010101011100 => 011110000110 => 001111000011
100011100011 => 011100011100 => 010010110110 => 001001011011
101010010011 => 010101101100 => 011110001010 => 001111000101
101001010011 => 010110101100 => 011110010010 => 001111001001
100101010011 => 011010101100 => 011110100010 => 001111010001
100011010011 => 011100101100 => 011010110010 => 001101011001
100010110011 => 011101001100 => 010110110010 => 001011011001
100001110011 => 011110001100 => 010010111010 => 001001011101
101010001011 => 010101110100 => 011110001100 => 001111000110
100110001011 => 011001110100 => 011010101100 => 001101010110
101001001011 => 010110110100 => 011110010100 => 001111001010
100101001011 => 011010110100 => 011110100100 => 001111010010
100011001011 => 011100110100 => 011010110100 => 001101011010
101000101011 => 010111010100 => 011110011000 => 001111001100
100100101011 => 011011010100 => 011110101000 => 001111010100
100010101011 => 011101010100 => 011110110000 => 001111011000
100001101011 => 011110010100 => 011010111000 => 001101011100
100010011011 => 011101100100 => 010110110100 => 001011011010
100001011011 => 011110100100 => 010110111000 => 001011011100
100000111011 => 011111000100 => 010010111100 => 001001011110
100010100111 => 011101011000 => 001110110010 => 000111011001
100001010111 => 011110101000 => 001110111000 => 000111011100
101000001111 => 010111110000 => 000110011110 => 000011001111
100010001111 => 011101110000 => 000110110110 => 000011011011
100001001111 => 011110110000 => 000110111010 => 000011011101
100000101111 => 011111010000 => 000110111100 => 000011011110
01110111101 => 10001000010 => 10001001000 => 01000100100
01111011101 => 10000100010 => 10010001000 => 01001000100
01111101111 => 10000010000 => 00010000100 => 00001000010
10111110111 => 01000001000 => 00100001000 => 00010000100
10111101111 => 01000010000 => 00010001000 => 00001000100
11011110111 => 00100001000 => 00100010000 => 00010001000
11011101111 => 00100010000 => 00010010000 => 00001001000
11101111011 => 00010000100 => 01000100000 => 00100010000
11101101101 => 00010010010 => 10101000000 => 01010100000
0000001100 => 1111110011 => 0111111011 => 1011111101
0000110011 => 1111001100 => 0101111010 => 0010111101
0011001111 => 1100110000 => 0001011010 => 0000101101
0000000011 => 1111111100 => 0111111110 => 0011111111
0000110101 => 1111001010 => 1101111000 => 0110111100
0010000010 => 1101111101 => 1110111101 => 1111011110
0111001011 => 1000110100 => 0110010100 => 0011001010
0111110111 => 1000001000 => 0010000100 => 0001000010
11000000000 => 00111111111 => 00111111111 => 10011111111
0110001011 => 1001110100 => 0110101100 => 0011010110
0110000111 => 1001111000 => 0010101110 => 0001010111
110000111001 => 001111000110 => 100100111010 => 010010011101
110000110101 => 001111001010 => 110100111000 => 011010011100
110010001101 => 001101110010 => 101100101100 => 010110010110
110100001101 => 001011110010 => 101100011100 => 010110001110
110000101101 => 001111010010 => 101100111000 => 010110011100
110000011101 => 001111100010 => 100100111100 => 010010011110
011100100011 => 100011011100 => 011001010110 => 001100101011
011010010011 => 100101101100 => 011101001010 => 001110100101
011100010011 => 100011101100 => 011001011010 => 001100101101
011000110011 => 100111001100 => 010101011010 => 001010101101
010110001011 => 101001110100 => 011011001100 => 001101100110
011010001011 => 100101110100 => 011101001100 => 001110100110
011100001011 => 100011110100 => 011001011100 => 001100101110
011000101011 => 100111010100 => 011101011000 => 001110101100
011000011011 => 100111100100 => 010101011100 => 001010101110
101110000011 => 010001111100 => 010010011110 => 001001001111
110100100011 => 001011011100 => 011100010110 => 001110001011
110010010011 => 001101101100 => 011100101010 => 001110010101
110100010011 => 001011101100 => 011100011010 => 001110001101
110000110011 => 001111001100 => 010100111010 => 001010011101
101100001011 => 010011110100 => 011010011100 => 001101001110
110010001011 => 001101110100 => 011100101100 => 001110010110
110100001011 => 001011110100 => 011100011100 => 001110001110
111000001011 => 000111110100 => 011000111100 => 001100011110
110000101011 => 001111010100 => 011100111000 => 001110011100
110000011011 => 001111100100 => 010100111100 => 001010011110
001110000111 => 110001111000 => 001001101110 => 000100110111
110000100111 => 001111011000 => 001100111010 => 000110011101
110000010111 => 001111101000 => 001100111100 => 000110011110
0011010110 => 1100101001 => 0110110001 => 1011011000
0100110110 => 1011001001 => 0101101001 => 1010110100
0110001110 => 1001110001 => 0010101101 => 1001010110
0101001110 => 1010110001 => 0011100101 => 1001110010
0011001110 => 1100110001 => 0010110101 => 1001011010
0100011110 => 1011100001 => 0001101101 => 1000110110
0010011110 => 1101100001 => 0001110101 => 1000111010
001110101010 => 110001010101 => 111001100001 => 111100110000
001110011010 => 110001100101 => 101001101001 => 110100110100
001101011010 => 110010100101 => 101101100001 => 110110110000
011000111010 => 100111000101 => 100101011001 => 110010101100
001100111010 => 110011000101 => 100101101001 => 110010110100
001010111010 => 110101000101 => 100111100001 => 110011110000
000110111010 => 111001000101 => 100101110001 => 110010111000
001110100110 => 110001011001 => 011001100101 => 101100110010
001110010110 => 110001101001 => 011001101001 => 101100110100
001101010110 => 110010101001 => 011101100001 => 101110110000
010011010110 => 101100101001 => 011011010001 => 101101101000
011000110110 => 100111001001 => 010101011001 => 101010101100
010100110110 => 101011001001 => 010111001001 => 101011100100
001100110110 => 110011001001 => 010101101001 => 101010110100
010010110110 => 101101001001 => 010111010001 => 101011101000
001010110110 => 110101001001 => 010111100001 => 101011110000
000110110110 => 111001001001 => 010101110001 => 101010111000
010001110110 => 101110001001 => 010011011001 => 101001101100
011010001110 => 100101110001 => 001101001101 => 100110100110
001110001110 => 110001110001 => 001001101101 => 100100110110
001011001110 => 110100110001 => 001011100101 => 100101110010
001100101110 => 110011010001 => 001101101001 => 100110110100
010010101110 => 101101010001 => 001111010001 => 100111101000
001010101110 => 110101010001 => 001111100001 => 100111110000
000110101110 => 111001010001 => 001101110001 => 100110111000
001001101110 => 110110010001 => 001011101001 => 100101110100
010100011110 => 101011100001 => 000111001101 => 100011100110
001100011110 => 110011100001 => 000101101101 => 100010110110
001010011110 => 110101100001 => 000111100101 => 100011110010
010001011110 => 101110100001 => 000111011001 => 100011101100
001001011110 => 110110100001 => 000111101001 => 100011110100
000101011110 => 111010100001 => 000111110001 => 100011111000
001000111110 => 110111000001 => 000011101101 => 100001110110
000010111110 => 111101000001 => 000011111001 => 100001111100
0101000000 => 1010111111 => 1100111111 => 1110011111
0001010000 => 1110101111 => 1111001111 => 1111100111
0001000100 => 1110111011 => 1111011011 => 1111101101
0001010101 => 1110101010 => 1111110000 => 0111111000
0110001001 => 1001110110 => 1101011010 => 0110101101
0101011011 => 1010100100 => 0101110000 => 0010111000
0110101011 => 1001010100 => 0111010000 => 0011101000
0111101111 => 1000010000 => 0001000100 => 0000100010
011010010000 => 100101101111 => 110100101111 => 111010010111
011010000100 => 100101111011 => 110100111011 => 111010011101
011011011011 => 100100100100 => 010101010000 => 001010101000
011101101011 => 100010010100 => 011010010000 => 001101001000
011001101111 => 100110010000 => 000101010100 => 000010101010
0111000000 => 1000111111 => 0010111111 => 1001011111
0111111100 => 1000000011 => 0000001011 => 1000000101
0010000000 => 1101111111 => 1101111111 => 1110111111
01100000000 => 10011111111 => 01011111111 => 10101111111
0111111010 => 1000000101 => 1000001001 => 1100000100
101101010011 => 010010101100 => 011101000010 => 001110100001
101011010011 => 010100101100 => 011011000010 => 001101100001
100111010011 => 011000101100 => 011001010010 => 001100101001
110010110011 => 001101001100 => 010110010010 => 001011001001
101010110011 => 010101001100 => 010111000010 => 001011100001
110101001011 => 001010110100 => 011110000100 => 001111000010
101101001011 => 010010110100 => 011101000100 => 001110100010
110011001011 => 001100110100 => 011010010100 => 001101001010
101011001011 => 010100110100 => 011011000100 => 001101100010
100111001011 => 011000110100 => 011001010100 => 001100101010
110100101011 => 001011010100 => 011110001000 => 001111000100
101100101011 => 010011010100 => 011101001000 => 001110100100
110010101011 => 001101010100 => 011110010000 => 001111001000
101010101011 => 010101010100 => 011111000000 => 001111100000
100110101011 => 011001010100 => 011101010000 => 001110101000
110001101011 => 001110010100 => 011010011000 => 001101001100
101001101011 => 010110010100 => 011011001000 => 001101100100
100101101011 => 011010010100 => 011011010000 => 001101101000
100011101011 => 011100010100 => 011001011000 => 001100101100
110100011011 => 001011100100 => 010110001100 => 001011000110
110010011011 => 001101100100 => 010110010100 => 001011001010
101010011011 => 010101100100 => 010111000100 => 001011100010
110001011011 => 001110100100 => 010110011000 => 001011001100
101001011011 => 010110100100 => 010111001000 => 001011100100
100101011011 => 011010100100 => 010111010000 => 001011101000
100011011011 => 011100100100 => 010101011000 => 001010101100
100010111011 => 011101000100 => 010011011000 => 001001101100
110100100111 => 001011011000 => 001110001010 => 000111000101
110010100111 => 001101011000 => 001110010010 => 000111001001
101010100111 => 010101011000 => 001111000010 => 000111100001
110100010111 => 001011101000 => 001110001100 => 000111000110
110010010111 => 001101101000 => 001110010100 => 000111001010
101010010111 => 010101101000 => 001111000100 => 000111100010
110001010111 => 001110101000 => 001110011000 => 000111001100
101001010111 => 010110101000 => 001111001000 => 000111100100
100101010111 => 011010101000 => 001111010000 => 000111101000
100011010111 => 011100101000 => 001101011000 => 000110101100
100010110111 => 011101001000 => 001011011000 => 000101101100
0000001111 => 1111110000 => 0001111110 => 0000111111
0011111111 => 1100000000 => 0000000110 => 0000000011
00000000111 => 11111111000 => 00111111110 => 00011111111
0000010111 => 1111101000 => 0011111100 => 0001111110
00000011111 => 11111100000 => 00001111110 => 00000111111
00001111111 => 11110000000 => 00000011110 => 00000001111
00111111111 => 11000000000 => 00000000110 => 00000000011
10110000000 => 01001111111 => 01001111111 => 10100111111
0011111100 => 1100000011 => 0000011011 => 1000001101
00111111100 => 11000000011 => 00000011011 => 10000001101
0011011100 => 1100100011 => 0010110011 => 1001011001
0001111001 => 1110000110 => 1000111010 => 0100011101
011000111100 => 100111000011 => 000101011011 => 100010101101
010100111100 => 101011000011 => 000111001011 => 100011100101
001100111001 => 110011000110 => 100101101010 => 010010110101
001100111100 => 110011000011 => 000101101011 => 100010110101
010010111100 => 101101000011 => 000111010011 => 100011101001
001010111100 => 110101000011 => 000111100011 => 100011110001
000110111100 => 111001000011 => 000101110011 => 100010111001
001110110001 => 110001001110 => 101001100110 => 010100110011
001110110010 => 110001001101 => 101001100101 => 110100110010
001110110100 => 110001001011 => 101001100011 => 110100110001
001110111000 => 110001000111 => 001001100111 => 100100110011
001101101001 => 110010010110 => 110101100010 => 011010110001
001001111001 => 110110000110 => 100011101010 => 010001110101
001101110001 => 110010001110 => 100101100110 => 010010110011
001011100101 => 110100011010 => 110011100100 => 011001110010
001011101001 => 110100010110 => 110011100010 => 011001110001
000011111001 => 111100000110 => 100001111010 => 010000111101
001011110001 => 110100001110 => 100011100110 => 010001110011
000111100011 => 111000011100 => 010001110110 => 001000111011
000111100101 => 111000011010 => 110001110100 => 011000111010
000111101001 => 111000010110 => 110001110010 => 011000111001
111000101011 => 000111010100 => 011100011000 => 001110001100
111001001011 => 000110110100 => 011100010100 => 001110001010
101110001011 => 010001110100 => 011001001100 => 001100100110
110110001011 => 001001110100 => 011010001100 => 001101000110
111010001011 => 000101110100 => 011100001100 => 001110000110
111000001110 => 000111110001 => 001000111101 => 100100011110
001011011001 => 110100100110 => 101011100010 => 010101110001
001101100011 => 110010011100 => 010101100110 => 001010110011
001110010011 => 110001101100 => 011001101010 => 001100110101
001110011001 => 110001100110 => 101001101010 => 010100110101
001110011100 => 110001100011 => 001001101011 => 100100110101
001110100101 => 110001011010 => 111001100100 => 011100110010
11101000001 => 00010111110 => 11000011110 => 01100001111
11100100000 => 00011011111 => 10001011111 => 11000101111
11111000000 => 00000111111 => 00000111111 => 10000011111
10001000001 => 01110111110 => 11011011110 => 01101101111
11001000000 => 00110111111 => 10010111111 => 11001011111
00111000000 => 11000111111 => 00110111111 => 10011011111
100110111000 => 011001000111 => 001010100111 => 100101010011
101100100110 => 010011011001 => 011010010101 => 101101001010
111000100110 => 000111011001 => 011000110101 => 101100011010
110100010110 => 001011101001 => 011100011001 => 101110001100
110010001110 => 001101110001 => 001100101101 => 100110010110
100110011100 => 011001100011 => 001010101011 => 100101010101
100110101100 => 011001010011 => 011010100011 => 101101010001
100110110100 => 011001001011 => 101010100011 => 110101010001
0000101011 => 1111010100 => 0111111000 => 0011111100
0001000111 => 1110111000 => 0011110110 => 0001111011
0000100111 => 1111011000 => 0011111010 => 0001111101
0001001010 => 1110110101 => 1111101001 => 1111110100
0000100100 => 1111011011 => 1111101011 => 1111110101
0000100010 => 1111011101 => 1111101101 => 1111110110
0011000000 => 1100111111 => 0110111111 => 1011011111
0101010111 => 1010101000 => 0011110000 => 0001111000
111000010110 => 000111101001 => 011000111001 => 101100011100
100100111100 => 011011000011 => 000110101011 => 100011010101
110100011010 => 001011100101 => 101100011001 => 110110001100
111000011010 => 000111100101 => 101000111001 => 110100011100
101100011100 => 010011100011 => 001010011011 => 100101001101
110010011100 => 001101100011 => 001100101011 => 100110010101
110011001110 => 001100110001 => 001010010101 => 100101001010
111100001110 => 000011110001 => 001000011101 => 100100001110
110011111000 => 001100000111 => 000010010111 => 100001001011
111111100000 => 000000011111 => 000000011111 => 100000001111
0101110101 => 1010001010 => 1100110000 => 0110011000
11111100000 => 00000011111 => 00000011111 => 10000001111
00111110000 => 11000001111 => 00001101111 => 10000110111
100010101100 => 011101010011 => 011101100011 => 101110110001
100010111000 => 011101000111 => 001101100111 => 100110110011
100011001010 => 011100110101 => 110101101001 => 111010110100
100011100010 => 011100011101 => 100101101101 => 110010110110
110000110010 => 001111001101 => 101001110101 => 110100111010
111000001010 => 000111110101 => 110001111001 => 111000111100
110000011010 => 001111100101 => 101001111001 => 110100111100
110000010110 => 001111101001 => 011001111001 => 101100111100
111100000010 => 000011111101 => 100001111101 => 110000111110
111110000000 => 000001111111 => 000001111111 => 100000111111
11111111100 => 00000000011 => 00000000011 => 10000000001
11010000001 => 00101111110 => 11000111110 => 01100011111
0011010001 => 1100101110 => 1101100110 => 0110110011
01010000000 => 10101111111 => 11001111111 => 11100111111
110001001101 => 001110110010 => 101100110100 => 010110011010
0000101000 => 1111010111 => 1111100111 => 1111110011
0010001000 => 1101110111 => 1110110111 => 1111011011
000000001010 => 111111110101 => 111111111001 => 111111111100
000000101000 => 111111010111 => 111111100111 => 111111110011
000000100010 => 111111011101 => 111111101101 => 111111110110
000010100000 => 111101011111 => 111110011111 => 111111001111
000010101010 => 111101010101 => 111111100001 => 111111110000
000010001000 => 111101110111 => 111110110111 => 111111011011
000010000010 => 111101111101 => 111110111101 => 111111011110
001010000000 => 110101111111 => 111001111111 => 111100111111
001010001010 => 110101110101 => 111110011001 => 111111001100
001010101000 => 110101010111 => 111110000111 => 111111000011
001010100010 => 110101011101 => 111110001101 => 111111000110
001000100000 => 110111011111 => 111011011111 => 111101101111
001000101010 => 110111010101 => 111110110001 => 111111011000
001000001000 => 110111110111 => 111011110111 => 111101111011
001000000010 => 110111111101 => 111011111101 => 111101111110
001001010010 => 110110101101 => 111110100101 => 111111010010
001001000110 => 110110111001 => 011110101101 => 101111010110
101000000000 => 010111111111 => 100111111111 => 110011111111
101000001010 => 010111110101 => 111001111001 => 111100111100
101000101000 => 010111010111 => 111001100111 => 111100110011
101000100010 => 010111011101 => 111001101101 => 111100110110
101010100000 => 010101011111 => 111000011111 => 111100001111
101010001000 => 010101110111 => 111000110111 => 111100011011
101010000010 => 010101111101 => 111000111101 => 111100011110
100010101000 => 011101010111 => 111011000111 => 111101100011
100010100010 => 011101011101 => 111011001101 => 111101100110
100101100000 => 011010011111 => 011010011111 => 101101001111
100101001000 => 011010110111 => 111010010111 => 111101001011
100101000010 => 011010111101 => 111010011101 => 111101001110
110110110110 => 001001001001 => 010101000001 => 101010100000
110101101110 => 001010010001 => 001011000001 => 100101100000
111011101010 => 000100010101 => 110010000001 => 111001000000
111011010110 => 000100101001 => 011010000001 => 101101000000
111010101110 => 000101010001 => 001110000001 => 100111000000
111001011110 => 000110100001 => 000110001001 => 100011000100
111101100110 => 000010011001 => 010100000101 => 101010000010
10000111111 => 01111000000 => 00000101110 => 00000010111
10000001111 => 01111110000 => 00010111110 => 00001011111
10000000111 => 01111111000 => 00101111110 => 00010111111
111100111000 => 000011000111 => 001000010111 => 100100001011
100100110010 => 011011001101 => 101101010101 => 110110101010
100101001010 => 011010110101 => 111101001001 => 111110100100
100101100010 => 011010011101 => 101101001101 => 110110100110
100101101000 => 011010010111 => 101101000111 => 110110100011
100110010010 => 011001101101 => 110101010101 => 111010101010
100111000010 => 011000111101 => 100101011101 => 110010101110
100111001000 => 011000110111 => 100101010111 => 110010101011
011010000110 => 100101111001 => 011010011101 => 101101001110
011011011110 => 100100100001 => 000101010001 => 100010101000
00100000000 => 11011111111 => 11011111111 => 11101111111
101011111111 => 010100000000 => 000000011000 => 000000001100
111010111111 => 000101000000 => 000001100000 => 000000110000
101110111111 => 010001000000 => 000001001000 => 000000100100
111110101111 => 000001010000 => 000110000000 => 000011000000
101010101111 => 010101010000 => 000111100000 => 000011110000
111011101111 => 000100010000 => 000100100000 => 000010010000
101111101111 => 010000010000 => 000100001000 => 000010000100
111111101011 => 000000010100 => 011000000000 => 001100000000
101011101011 => 010100010100 => 011001100000 => 001100110000
111010101011 => 000101010100 => 011110000000 => 001111000000
101110101011 => 010001010100 => 011100100000 => 001110010000
111110111011 => 000001000100 => 010010000000 => 001001000000
101010111011 => 010101000100 => 010011100000 => 001001110000
111011111011 => 000100000100 => 010000100000 => 001000010000
101111111011 => 010000000100 => 010000001000 => 001000000100
111001011011 => 000110100100 => 010110001000 => 001011000100
101101011011 => 010010100100 => 010110100000 => 001011010000
100111011011 => 011000100100 => 010100101000 => 001010010100
111111111010 => 000000000101 => 100000000001 => 110000000000
101011111010 => 010100000101 => 100001100001 => 110000110000
111010111010 => 000101000101 => 100110000001 => 110011000000
101110111010 => 010001000101 => 100100100001 => 110010010000
111110101010 => 000001010101 => 111000000001 => 111100000000
101111101010 => 010000010101 => 110000100001 => 111000010000
101110101110 => 010001010001 => 001100100001 => 100110010000
111110010110 => 000001101001 => 011000001001 => 101100000100
101111010110 => 010000101001 => 011000100001 => 101100010000
111001110110 => 000110001001 => 010010001001 => 101001000100
101101110110 => 010010001001 => 010010100001 => 101001010000
101100010000 => 010011101111 => 101001101111 => 110100110111
100011010000 => 011100101111 => 101011001111 => 110101100111
110011000110 => 001100111001 => 010100101101 => 101010010110
110011000010 => 001100111101 => 101001011101 => 110100101110
110001001110 => 001110110001 => 001100110101 => 100110011010
110001101100 => 001110010011 => 010100110011 => 101010011001
110001100110 => 001110011001 => 010100110101 => 101010011010
110001100010 => 001110011101 => 101001101101 => 110100110110
110001110010 => 001110001101 => 100100110101 => 110010011010
111001000110 => 000110111001 => 011000101101 => 101100010110
111001000010 => 000110111101 => 110001011101 => 111000101110
111000010010 => 000111101101 => 110001110101 => 111000111010
111100011010 => 000011100101 => 101000011001 => 110100001100
110001001011 => 001110110100 => 011100110100 => 001110011010
110010010110 => 001101101001 => 011100101001 => 101110010100
110110000110 => 001001111001 => 010100011101 => 101010001110
111100000110 => 000011111001 => 010000111101 => 101000011110
110100001110 => 001011110001 => 001100011101 => 100110001110
11111010001 => 00000101110 => 11000000110 => 01100000011
10010101101 => 01101010010 => 10111010000 => 01011101000
0010010000 => 1101101111 => 1110101111 => 1111010111
010110100011 => 101001011100 => 011011000110 => 001101100011
011001001011 => 100110110100 => 011101010100 => 001110101010
011001100011 => 100110011100 => 010101010110 => 001010101011
0010100101 => 1101011010 => 1111100100 => 0111110010
0010110111 => 1101001000 => 0010111000 => 0001011100
0001001101 => 1110110010 => 1011110100 => 0101111010
11111111000 => 00000000111 => 00000000111 => 10000000011
0001010011 => 1110101100 => 0111110010 => 0011111001
0110101101 => 1001010010 => 1011010000 => 0101101000
0110011101 => 1001100010 => 1001010100 => 0100101010
0110001111 => 1001110000 => 0001010110 => 0000101011
0101101011 => 1010010100 => 0110110000 => 0011011000
0101011101 => 1010100010 => 1001110000 => 0100111000
0100111101 => 1011000010 => 1000110100 => 0100011010
0011000011 => 1100111100 => 0101101110 => 0010110111
0011011011 => 1100100100 => 0101011000 => 0010101100
111111011011 => 000000100100 => 010100000000 => 001010000000
111101101111 => 000010010000 => 000101000000 => 000010100000
111101111011 => 000010000100 => 010001000000 => 001000100000
110110111111 => 001001000000 => 000001010000 => 000000101000
110110011011 => 001001100100 => 010101000100 => 001010100010
110111101111 => 001000010000 => 000100010000 => 000010001000
110111111011 => 001000000100 => 010000010000 => 001000001000
110101101011 => 001010010100 => 011011000000 => 001101100000
001111111111 => 110000000000 => 000000000110 => 000000000011
001100111111 => 110011000000 => 000001011010 => 000000101101
000011111111 => 111100000000 => 000000011110 => 000000001111
000000110011 => 111111001100 => 010111111010 => 001011111101
000000001111 => 111111110000 => 000111111110 => 000011111111
000000000011 => 111111111100 => 011111111110 => 001111111111
011011111111 => 100100000000 => 000000010100 => 000000001010
011001111011 => 100110000100 => 010001010100 => 001000101010
011110111111 => 100001000000 => 000001000100 => 000000100010
011110011011 => 100001100100 => 010100010100 => 001010001010
011111101111 => 100000010000 => 000100000100 => 000010000010
011111111011 => 100000000100 => 010000000100 => 001000000010
11100000000 => 00011111111 => 00011111111 => 10001111111
11110000000 => 00001111111 => 00001111111 => 10000111111
11111110000 => 00000001111 => 00000001111 => 10000000111
11111001000 => 00000110111 => 10000010111 => 11000001011
111111110110 => 000000001001 => 010000000001 => 101000000000
111101011010 => 000010100101 => 101100000001 => 110110000000
110000000000 => 001111111111 => 001111111111 => 100111111111
110001011010 => 001110100101 => 101100110001 => 110110011000
110110011110 => 001001100001 => 000101000101 => 100010100010
110111100110 => 001000011001 => 010001000101 => 101000100010
110111011010 => 001000100101 => 101001000001 => 110100100000
110100100110 => 001011011001 => 011100010101 => 101110001010
110101111010 => 001010000101 => 100011000001 => 110001100000
0010000111 => 1101111000 => 0011101110 => 0001110111
11110101010 => 00001010101 => 11100000001 => 11110000000
0111011111 => 1000100000 => 0000100100 => 0000010010
01010111111 => 10101000000 => 00000111000 => 00000011100
110011001000 => 001100110111 => 101001010111 => 110100101011
110110001000 => 001001110111 => 101000110111 => 110100011011
111001001000 => 000110110111 => 110001010111 => 111000101011
111100001000 => 000011110111 => 100001110111 => 110000111011
11111101010 => 00000010101 => 11000000001 => 11100000000
10111011111 => 01000100000 => 00001001000 => 00000100100
11101010101 => 00010101010 => 11110000000 => 01111000000
11111011101 => 00000100010 => 10010000000 => 01001000000
11111100100 => 00000011011 => 10000001011 => 11000000101
11110010000 => 00001101111 => 10000101111 => 11000010111
110010010010 => 001101101101 => 111001010101 => 111100101010
110001001010 => 001110110101 => 111001101001 => 111100110100
0000110000 => 1111001111 => 0111101111 => 1011110111
001110000100 => 110001111011 => 100110111011 => 110011011101
101001011100 => 010110100011 => 001110010011 => 100111001001
001000100101 => 110111011010 => 111110110100 => 011111011010
001010000101 => 110101111010 => 111110011100 => 011111001110
00000101011 => 11111010100 => 01111111000 => 00111111100
0000111000 => 1111000111 => 0011110111 => 1001111011
100111000110 => 011000111001 => 010010101101 => 101001010110
101101000110 => 010010111001 => 011010001101 => 101101000110
100111010010 => 011000101101 => 110010100101 => 111001010010
100101110010 => 011010001101 => 100110100101 => 110011010010
110110000010 => 001001111101 => 101000111101 => 110100011110
110100001010 => 001011110101 => 111000111001 => 111100011100
11101010110 => 00010101001 => 01110000001 => 10111000000
110010000010 => 001101111101 => 110010111101 => 111001011110
10000010001 => 01111101110 => 11011110110 => 01101111011
0000000111111110 => 1111111000000001 => 0000000111111101 => 1000000011111110
00000000011111111110 => 11111111100000000001 => 00000000011111111101 => 10000000001111111110
111111100010 => 000000011101 => 100000001101 => 110000000110
111000000010 => 000111111101 => 100011111101 => 110001111110
111111101000 => 000000010111 => 100000000111 => 110000000011
111010000000 => 000101111111 => 100001111111 => 110000111111
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 back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
This is the word obtained by moving the last letter to the beginnig.
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