Identifier
Mp00316:
Binary words
—inverse Foata bijection⟶
Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Images
0 => 0 => 1 => 1
1 => 1 => 0 => 0
00 => 00 => 11 => 11
01 => 01 => 10 => 10
10 => 10 => 01 => 01
11 => 11 => 00 => 00
000 => 000 => 111 => 111
001 => 001 => 110 => 110
010 => 100 => 011 => 011
011 => 011 => 100 => 010
100 => 010 => 101 => 101
101 => 101 => 010 => 100
110 => 110 => 001 => 001
111 => 111 => 000 => 000
0000 => 0000 => 1111 => 1111
0001 => 0001 => 1110 => 1110
0010 => 1000 => 0111 => 0111
0011 => 0011 => 1100 => 0110
0100 => 0100 => 1011 => 1011
0101 => 1001 => 0110 => 1010
0110 => 1100 => 0011 => 0011
0111 => 0111 => 1000 => 0010
1000 => 0010 => 1101 => 1101
1001 => 0101 => 1010 => 1100
1010 => 0110 => 1001 => 0101
1011 => 1011 => 0100 => 0100
1100 => 1010 => 0101 => 1001
1101 => 1101 => 0010 => 1000
1110 => 1110 => 0001 => 0001
1111 => 1111 => 0000 => 0000
00000 => 00000 => 11111 => 11111
00001 => 00001 => 11110 => 11110
00010 => 10000 => 01111 => 01111
00011 => 00011 => 11100 => 01110
00100 => 01000 => 10111 => 10111
00101 => 10001 => 01110 => 10110
00110 => 11000 => 00111 => 00111
00111 => 00111 => 11000 => 00110
01000 => 00100 => 11011 => 11011
01001 => 01001 => 10110 => 11010
01010 => 01100 => 10011 => 01011
01011 => 10011 => 01100 => 01010
01100 => 10100 => 01011 => 10011
01101 => 11001 => 00110 => 10010
01110 => 11100 => 00011 => 00011
01111 => 01111 => 10000 => 00010
10000 => 00010 => 11101 => 11101
10001 => 00101 => 11010 => 11100
10010 => 00110 => 11001 => 01101
10011 => 01011 => 10100 => 01100
10100 => 10010 => 01101 => 10101
10101 => 01101 => 10010 => 10100
10110 => 01110 => 10001 => 00101
10111 => 10111 => 01000 => 00100
11000 => 01010 => 10101 => 11001
11001 => 10101 => 01010 => 11000
11010 => 10110 => 01001 => 01001
11011 => 11011 => 00100 => 01000
11100 => 11010 => 00101 => 10001
11101 => 11101 => 00010 => 10000
11110 => 11110 => 00001 => 00001
11111 => 11111 => 00000 => 00000
000000 => 000000 => 111111 => 111111
000001 => 000001 => 111110 => 111110
000010 => 100000 => 011111 => 011111
000011 => 000011 => 111100 => 011110
000100 => 010000 => 101111 => 101111
000101 => 100001 => 011110 => 101110
000110 => 110000 => 001111 => 001111
000111 => 000111 => 111000 => 001110
001000 => 001000 => 110111 => 110111
001001 => 010001 => 101110 => 110110
001010 => 011000 => 100111 => 010111
001011 => 100011 => 011100 => 010110
001100 => 101000 => 010111 => 100111
001101 => 110001 => 001110 => 100110
001110 => 111000 => 000111 => 000111
001111 => 001111 => 110000 => 000110
010000 => 000100 => 111011 => 111011
010001 => 001001 => 110110 => 111010
010010 => 001100 => 110011 => 011011
010011 => 010011 => 101100 => 011010
010100 => 100100 => 011011 => 101011
010101 => 011001 => 100110 => 101010
010110 => 011100 => 100011 => 001011
010111 => 100111 => 011000 => 001010
011000 => 010100 => 101011 => 110011
011001 => 101001 => 010110 => 110010
011010 => 101100 => 010011 => 010011
011011 => 110011 => 001100 => 010010
011100 => 110100 => 001011 => 100011
011101 => 111001 => 000110 => 100010
011110 => 111100 => 000011 => 000011
011111 => 011111 => 100000 => 000010
100000 => 000010 => 111101 => 111101
100001 => 000101 => 111010 => 111100
100010 => 000110 => 111001 => 011101
100011 => 001011 => 110100 => 011100
100100 => 100010 => 011101 => 101101
100101 => 001101 => 110010 => 101100
100110 => 001110 => 110001 => 001101
>>> Load all 1063 entries. <<<
100111 => 010111 => 101000 => 001100
101000 => 010010 => 101101 => 110101
101001 => 100101 => 011010 => 110100
101010 => 100110 => 011001 => 010101
101011 => 011011 => 100100 => 010100
101100 => 110010 => 001101 => 100101
101101 => 011101 => 100010 => 100100
101110 => 011110 => 100001 => 000101
101111 => 101111 => 010000 => 000100
110000 => 001010 => 110101 => 111001
110001 => 010101 => 101010 => 111000
110010 => 010110 => 101001 => 011001
110011 => 101011 => 010100 => 011000
110100 => 011010 => 100101 => 101001
110101 => 101101 => 010010 => 101000
110110 => 101110 => 010001 => 001001
110111 => 110111 => 001000 => 001000
111000 => 101010 => 010101 => 110001
111001 => 110101 => 001010 => 110000
111010 => 110110 => 001001 => 010001
111011 => 111011 => 000100 => 010000
111100 => 111010 => 000101 => 100001
111101 => 111101 => 000010 => 100000
111110 => 111110 => 000001 => 000001
111111 => 111111 => 000000 => 000000
0000000 => 0000000 => 1111111 => 1111111
0000001 => 0000001 => 1111110 => 1111110
0000010 => 1000000 => 0111111 => 0111111
0000011 => 0000011 => 1111100 => 0111110
0000100 => 0100000 => 1011111 => 1011111
0000101 => 1000001 => 0111110 => 1011110
0000110 => 1100000 => 0011111 => 0011111
0000111 => 0000111 => 1111000 => 0011110
0001000 => 0010000 => 1101111 => 1101111
0001001 => 0100001 => 1011110 => 1101110
0001010 => 0110000 => 1001111 => 0101111
0001011 => 1000011 => 0111100 => 0101110
0001100 => 1010000 => 0101111 => 1001111
0001101 => 1100001 => 0011110 => 1001110
0001110 => 1110000 => 0001111 => 0001111
0001111 => 0001111 => 1110000 => 0001110
0010000 => 0001000 => 1110111 => 1110111
0010001 => 0010001 => 1101110 => 1110110
0010010 => 0011000 => 1100111 => 0110111
0010011 => 0100011 => 1011100 => 0110110
0010100 => 1001000 => 0110111 => 1010111
0010101 => 0110001 => 1001110 => 1010110
0010110 => 0111000 => 1000111 => 0010111
0010111 => 1000111 => 0111000 => 0010110
0011000 => 0101000 => 1010111 => 1100111
0011001 => 1010001 => 0101110 => 1100110
0011010 => 1011000 => 0100111 => 0100111
0011011 => 1100011 => 0011100 => 0100110
0011100 => 1101000 => 0010111 => 1000111
0011101 => 1110001 => 0001110 => 1000110
0011110 => 1111000 => 0000111 => 0000111
0011111 => 0011111 => 1100000 => 0000110
0100000 => 0000100 => 1111011 => 1111011
0100001 => 0001001 => 1110110 => 1111010
0100010 => 0001100 => 1110011 => 0111011
0100011 => 0010011 => 1101100 => 0111010
0100100 => 1000100 => 0111011 => 1011011
0100101 => 0011001 => 1100110 => 1011010
0100110 => 0011100 => 1100011 => 0011011
0100111 => 0100111 => 1011000 => 0011010
0101000 => 0100100 => 1011011 => 1101011
0101001 => 1001001 => 0110110 => 1101010
0101010 => 1001100 => 0110011 => 0101011
0101011 => 0110011 => 1001100 => 0101010
0101100 => 1100100 => 0011011 => 1001011
0101101 => 0111001 => 1000110 => 1001010
0101110 => 0111100 => 1000011 => 0001011
0101111 => 1001111 => 0110000 => 0001010
0110000 => 0010100 => 1101011 => 1110011
0110001 => 0101001 => 1010110 => 1110010
0110010 => 0101100 => 1010011 => 0110011
0110011 => 1010011 => 0101100 => 0110010
0110100 => 0110100 => 1001011 => 1010011
0110101 => 1011001 => 0100110 => 1010010
0110110 => 1011100 => 0100011 => 0010011
0110111 => 1100111 => 0011000 => 0010010
0111000 => 1010100 => 0101011 => 1100011
0111001 => 1101001 => 0010110 => 1100010
0111010 => 1101100 => 0010011 => 0100011
0111011 => 1110011 => 0001100 => 0100010
0111100 => 1110100 => 0001011 => 1000011
0111101 => 1111001 => 0000110 => 1000010
0111110 => 1111100 => 0000011 => 0000011
0111111 => 0111111 => 1000000 => 0000010
1000000 => 0000010 => 1111101 => 1111101
1000001 => 0000101 => 1111010 => 1111100
1000010 => 0000110 => 1111001 => 0111101
1000011 => 0001011 => 1110100 => 0111100
1000100 => 1000010 => 0111101 => 1011101
1000101 => 0001101 => 1110010 => 1011100
1000110 => 0001110 => 1110001 => 0011101
1000111 => 0010111 => 1101000 => 0011100
1001000 => 0100010 => 1011101 => 1101101
1001001 => 1000101 => 0111010 => 1101100
1001010 => 1000110 => 0111001 => 0101101
1001011 => 0011011 => 1100100 => 0101100
1001100 => 1100010 => 0011101 => 1001101
1001101 => 0011101 => 1100010 => 1001100
1001110 => 0011110 => 1100001 => 0001101
1001111 => 0101111 => 1010000 => 0001100
1010000 => 0010010 => 1101101 => 1110101
1010001 => 0100101 => 1011010 => 1110100
1010010 => 0100110 => 1011001 => 0110101
1010011 => 1001011 => 0110100 => 0110100
1010100 => 0110010 => 1001101 => 1010101
1010101 => 1001101 => 0110010 => 1010100
1010110 => 1001110 => 0110001 => 0010101
1010111 => 0110111 => 1001000 => 0010100
1011000 => 1010010 => 0101101 => 1100101
1011001 => 1100101 => 0011010 => 1100100
1011010 => 1100110 => 0011001 => 0100101
1011011 => 0111011 => 1000100 => 0100100
1011100 => 1110010 => 0001101 => 1000101
1011101 => 0111101 => 1000010 => 1000100
1011110 => 0111110 => 1000001 => 0000101
1011111 => 1011111 => 0100000 => 0000100
1100000 => 0001010 => 1110101 => 1111001
1100001 => 0010101 => 1101010 => 1111000
1100010 => 0010110 => 1101001 => 0111001
1100011 => 0101011 => 1010100 => 0111000
1100100 => 0011010 => 1100101 => 1011001
1100101 => 0101101 => 1010010 => 1011000
1100110 => 0101110 => 1010001 => 0011001
1100111 => 1010111 => 0101000 => 0011000
1101000 => 1001010 => 0110101 => 1101001
1101001 => 0110101 => 1001010 => 1101000
1101010 => 0110110 => 1001001 => 0101001
1101011 => 1011011 => 0100100 => 0101000
1101100 => 0111010 => 1000101 => 1001001
1101101 => 1011101 => 0100010 => 1001000
1101110 => 1011110 => 0100001 => 0001001
1101111 => 1101111 => 0010000 => 0001000
1110000 => 0101010 => 1010101 => 1110001
1110001 => 1010101 => 0101010 => 1110000
1110010 => 1010110 => 0101001 => 0110001
1110011 => 1101011 => 0010100 => 0110000
1110100 => 1011010 => 0100101 => 1010001
1110101 => 1101101 => 0010010 => 1010000
1110110 => 1101110 => 0010001 => 0010001
1110111 => 1110111 => 0001000 => 0010000
1111000 => 1101010 => 0010101 => 1100001
1111001 => 1110101 => 0001010 => 1100000
1111010 => 1110110 => 0001001 => 0100001
1111011 => 1111011 => 0000100 => 0100000
1111100 => 1111010 => 0000101 => 1000001
1111101 => 1111101 => 0000010 => 1000000
1111110 => 1111110 => 0000001 => 0000001
1111111 => 1111111 => 0000000 => 0000000
00000000 => 00000000 => 11111111 => 11111111
00000001 => 00000001 => 11111110 => 11111110
00000010 => 10000000 => 01111111 => 01111111
00000011 => 00000011 => 11111100 => 01111110
00000100 => 01000000 => 10111111 => 10111111
00000101 => 10000001 => 01111110 => 10111110
00000110 => 11000000 => 00111111 => 00111111
00000111 => 00000111 => 11111000 => 00111110
00001000 => 00100000 => 11011111 => 11011111
00001001 => 01000001 => 10111110 => 11011110
00001010 => 01100000 => 10011111 => 01011111
00001011 => 10000011 => 01111100 => 01011110
00001100 => 10100000 => 01011111 => 10011111
00001101 => 11000001 => 00111110 => 10011110
00001110 => 11100000 => 00011111 => 00011111
00001111 => 00001111 => 11110000 => 00011110
00010000 => 00010000 => 11101111 => 11101111
00010001 => 00100001 => 11011110 => 11101110
00010010 => 00110000 => 11001111 => 01101111
00010011 => 01000011 => 10111100 => 01101110
00010100 => 10010000 => 01101111 => 10101111
00010101 => 01100001 => 10011110 => 10101110
00010110 => 01110000 => 10001111 => 00101111
00010111 => 10000111 => 01111000 => 00101110
00011000 => 01010000 => 10101111 => 11001111
00011001 => 10100001 => 01011110 => 11001110
00011010 => 10110000 => 01001111 => 01001111
00011011 => 11000011 => 00111100 => 01001110
00011100 => 11010000 => 00101111 => 10001111
00011101 => 11100001 => 00011110 => 10001110
00011110 => 11110000 => 00001111 => 00001111
00011111 => 00011111 => 11100000 => 00001110
00100000 => 00001000 => 11110111 => 11110111
00100001 => 00010001 => 11101110 => 11110110
00100010 => 00011000 => 11100111 => 01110111
00100011 => 00100011 => 11011100 => 01110110
00100100 => 10001000 => 01110111 => 10110111
00100101 => 00110001 => 11001110 => 10110110
00100110 => 00111000 => 11000111 => 00110111
00100111 => 01000111 => 10111000 => 00110110
00101000 => 01001000 => 10110111 => 11010111
00101001 => 10010001 => 01101110 => 11010110
00101010 => 10011000 => 01100111 => 01010111
00101011 => 01100011 => 10011100 => 01010110
00101100 => 11001000 => 00110111 => 10010111
00101101 => 01110001 => 10001110 => 10010110
00101110 => 01111000 => 10000111 => 00010111
00101111 => 10001111 => 01110000 => 00010110
00110000 => 00101000 => 11010111 => 11100111
00110001 => 01010001 => 10101110 => 11100110
00110010 => 01011000 => 10100111 => 01100111
00110011 => 10100011 => 01011100 => 01100110
00110100 => 01101000 => 10010111 => 10100111
00110101 => 10110001 => 01001110 => 10100110
00110110 => 10111000 => 01000111 => 00100111
00110111 => 11000111 => 00111000 => 00100110
00111000 => 10101000 => 01010111 => 11000111
00111001 => 11010001 => 00101110 => 11000110
00111010 => 11011000 => 00100111 => 01000111
00111011 => 11100011 => 00011100 => 01000110
00111100 => 11101000 => 00010111 => 10000111
00111101 => 11110001 => 00001110 => 10000110
00111110 => 11111000 => 00000111 => 00000111
00111111 => 00111111 => 11000000 => 00000110
01000000 => 00000100 => 11111011 => 11111011
01000001 => 00001001 => 11110110 => 11111010
01000010 => 00001100 => 11110011 => 01111011
01000011 => 00010011 => 11101100 => 01111010
01000100 => 10000100 => 01111011 => 10111011
01000101 => 00011001 => 11100110 => 10111010
01000110 => 00011100 => 11100011 => 00111011
01000111 => 00100111 => 11011000 => 00111010
01001000 => 01000100 => 10111011 => 11011011
01001001 => 10001001 => 01110110 => 11011010
01001010 => 10001100 => 01110011 => 01011011
01001011 => 00110011 => 11001100 => 01011010
01001100 => 11000100 => 00111011 => 10011011
01001101 => 00111001 => 11000110 => 10011010
01001110 => 00111100 => 11000011 => 00011011
01001111 => 01001111 => 10110000 => 00011010
01010000 => 00100100 => 11011011 => 11101011
01010001 => 01001001 => 10110110 => 11101010
01010010 => 01001100 => 10110011 => 01101011
01010011 => 10010011 => 01101100 => 01101010
01010100 => 01100100 => 10011011 => 10101011
01010101 => 10011001 => 01100110 => 10101010
01010110 => 10011100 => 01100011 => 00101011
01010111 => 01100111 => 10011000 => 00101010
01011000 => 10100100 => 01011011 => 11001011
01011001 => 11001001 => 00110110 => 11001010
01011010 => 11001100 => 00110011 => 01001011
01011011 => 01110011 => 10001100 => 01001010
01011100 => 11100100 => 00011011 => 10001011
01011101 => 01111001 => 10000110 => 10001010
01011110 => 01111100 => 10000011 => 00001011
01011111 => 10011111 => 01100000 => 00001010
01100000 => 00010100 => 11101011 => 11110011
01100001 => 00101001 => 11010110 => 11110010
01100010 => 00101100 => 11010011 => 01110011
01100011 => 01010011 => 10101100 => 01110010
01100100 => 00110100 => 11001011 => 10110011
01100101 => 01011001 => 10100110 => 10110010
01100110 => 01011100 => 10100011 => 00110011
01100111 => 10100111 => 01011000 => 00110010
01101000 => 10010100 => 01101011 => 11010011
01101001 => 01101001 => 10010110 => 11010010
01101010 => 01101100 => 10010011 => 01010011
01101011 => 10110011 => 01001100 => 01010010
01101100 => 01110100 => 10001011 => 10010011
01101101 => 10111001 => 01000110 => 10010010
01101110 => 10111100 => 01000011 => 00010011
01101111 => 11001111 => 00110000 => 00010010
01110000 => 01010100 => 10101011 => 11100011
01110001 => 10101001 => 01010110 => 11100010
01110010 => 10101100 => 01010011 => 01100011
01110011 => 11010011 => 00101100 => 01100010
01110100 => 10110100 => 01001011 => 10100011
01110101 => 11011001 => 00100110 => 10100010
01110110 => 11011100 => 00100011 => 00100011
01110111 => 11100111 => 00011000 => 00100010
01111000 => 11010100 => 00101011 => 11000011
01111001 => 11101001 => 00010110 => 11000010
01111010 => 11101100 => 00010011 => 01000011
01111011 => 11110011 => 00001100 => 01000010
01111100 => 11110100 => 00001011 => 10000011
01111101 => 11111001 => 00000110 => 10000010
01111110 => 11111100 => 00000011 => 00000011
01111111 => 01111111 => 10000000 => 00000010
10000000 => 00000010 => 11111101 => 11111101
10000001 => 00000101 => 11111010 => 11111100
10000010 => 00000110 => 11111001 => 01111101
10000011 => 00001011 => 11110100 => 01111100
10000100 => 10000010 => 01111101 => 10111101
10000101 => 00001101 => 11110010 => 10111100
10000110 => 00001110 => 11110001 => 00111101
10000111 => 00010111 => 11101000 => 00111100
10001000 => 01000010 => 10111101 => 11011101
10001001 => 10000101 => 01111010 => 11011100
10001010 => 10000110 => 01111001 => 01011101
10001011 => 00011011 => 11100100 => 01011100
10001100 => 11000010 => 00111101 => 10011101
10001101 => 00011101 => 11100010 => 10011100
10001110 => 00011110 => 11100001 => 00011101
10001111 => 00101111 => 11010000 => 00011100
10010000 => 00100010 => 11011101 => 11101101
10010001 => 01000101 => 10111010 => 11101100
10010010 => 01000110 => 10111001 => 01101101
10010011 => 10001011 => 01110100 => 01101100
10010100 => 01100010 => 10011101 => 10101101
10010101 => 10001101 => 01110010 => 10101100
10010110 => 10001110 => 01110001 => 00101101
10010111 => 00110111 => 11001000 => 00101100
10011000 => 10100010 => 01011101 => 11001101
10011001 => 11000101 => 00111010 => 11001100
10011010 => 11000110 => 00111001 => 01001101
10011011 => 00111011 => 11000100 => 01001100
10011100 => 11100010 => 00011101 => 10001101
10011101 => 00111101 => 11000010 => 10001100
10011110 => 00111110 => 11000001 => 00001101
10011111 => 01011111 => 10100000 => 00001100
10100000 => 00010010 => 11101101 => 11110101
10100001 => 00100101 => 11011010 => 11110100
10100010 => 00100110 => 11011001 => 01110101
10100011 => 01001011 => 10110100 => 01110100
10100100 => 00110010 => 11001101 => 10110101
10100101 => 01001101 => 10110010 => 10110100
10100110 => 01001110 => 10110001 => 00110101
10100111 => 10010111 => 01101000 => 00110100
10101000 => 10010010 => 01101101 => 11010101
10101001 => 01100101 => 10011010 => 11010100
10101010 => 01100110 => 10011001 => 01010101
10101011 => 10011011 => 01100100 => 01010100
10101100 => 01110010 => 10001101 => 10010101
10101101 => 10011101 => 01100010 => 10010100
10101110 => 10011110 => 01100001 => 00010101
10101111 => 01101111 => 10010000 => 00010100
10110000 => 01010010 => 10101101 => 11100101
10110001 => 10100101 => 01011010 => 11100100
10110010 => 10100110 => 01011001 => 01100101
10110011 => 11001011 => 00110100 => 01100100
10110100 => 10110010 => 01001101 => 10100101
10110101 => 11001101 => 00110010 => 10100100
10110110 => 11001110 => 00110001 => 00100101
10110111 => 01110111 => 10001000 => 00100100
10111000 => 11010010 => 00101101 => 11000101
10111001 => 11100101 => 00011010 => 11000100
10111010 => 11100110 => 00011001 => 01000101
10111011 => 01111011 => 10000100 => 01000100
10111100 => 11110010 => 00001101 => 10000101
10111101 => 01111101 => 10000010 => 10000100
10111110 => 01111110 => 10000001 => 00000101
10111111 => 10111111 => 01000000 => 00000100
11000000 => 00001010 => 11110101 => 11111001
11000001 => 00010101 => 11101010 => 11111000
11000010 => 00010110 => 11101001 => 01111001
11000011 => 00101011 => 11010100 => 01111000
11000100 => 00011010 => 11100101 => 10111001
11000101 => 00101101 => 11010010 => 10111000
11000110 => 00101110 => 11010001 => 00111001
11000111 => 01010111 => 10101000 => 00111000
11001000 => 10001010 => 01110101 => 11011001
11001001 => 00110101 => 11001010 => 11011000
11001010 => 00110110 => 11001001 => 01011001
11001011 => 01011011 => 10100100 => 01011000
11001100 => 00111010 => 11000101 => 10011001
11001101 => 01011101 => 10100010 => 10011000
11001110 => 01011110 => 10100001 => 00011001
11001111 => 10101111 => 01010000 => 00011000
11010000 => 01001010 => 10110101 => 11101001
11010001 => 10010101 => 01101010 => 11101000
11010010 => 10010110 => 01101001 => 01101001
11010011 => 01101011 => 10010100 => 01101000
11010100 => 10011010 => 01100101 => 10101001
11010101 => 01101101 => 10010010 => 10101000
11010110 => 01101110 => 10010001 => 00101001
11010111 => 10110111 => 01001000 => 00101000
11011000 => 11001010 => 00110101 => 11001001
11011001 => 01110101 => 10001010 => 11001000
11011010 => 01110110 => 10001001 => 01001001
11011011 => 10111011 => 01000100 => 01001000
11011100 => 01111010 => 10000101 => 10001001
11011101 => 10111101 => 01000010 => 10001000
11011110 => 10111110 => 01000001 => 00001001
11011111 => 11011111 => 00100000 => 00001000
11100000 => 00101010 => 11010101 => 11110001
11100001 => 01010101 => 10101010 => 11110000
11100010 => 01010110 => 10101001 => 01110001
11100011 => 10101011 => 01010100 => 01110000
11100100 => 01011010 => 10100101 => 10110001
11100101 => 10101101 => 01010010 => 10110000
11100110 => 10101110 => 01010001 => 00110001
11100111 => 11010111 => 00101000 => 00110000
11101000 => 01101010 => 10010101 => 11010001
11101001 => 10110101 => 01001010 => 11010000
11101010 => 10110110 => 01001001 => 01010001
11101011 => 11011011 => 00100100 => 01010000
11101100 => 10111010 => 01000101 => 10010001
11101101 => 11011101 => 00100010 => 10010000
11101110 => 11011110 => 00100001 => 00010001
11101111 => 11101111 => 00010000 => 00010000
11110000 => 10101010 => 01010101 => 11100001
11110001 => 11010101 => 00101010 => 11100000
11110010 => 11010110 => 00101001 => 01100001
11110011 => 11101011 => 00010100 => 01100000
11110100 => 11011010 => 00100101 => 10100001
11110101 => 11101101 => 00010010 => 10100000
11110110 => 11101110 => 00010001 => 00100001
11110111 => 11110111 => 00001000 => 00100000
11111000 => 11101010 => 00010101 => 11000001
11111001 => 11110101 => 00001010 => 11000000
11111010 => 11110110 => 00001001 => 01000001
11111011 => 11111011 => 00000100 => 01000000
11111100 => 11111010 => 00000101 => 10000001
11111101 => 11111101 => 00000010 => 10000000
11111110 => 11111110 => 00000001 => 00000001
11111111 => 11111111 => 00000000 => 00000000
000000000 => 000000000 => 111111111 => 111111111
000000001 => 000000001 => 111111110 => 111111110
000000010 => 100000000 => 011111111 => 011111111
000000011 => 000000011 => 111111100 => 011111110
000000100 => 010000000 => 101111111 => 101111111
000000101 => 100000001 => 011111110 => 101111110
000000110 => 110000000 => 001111111 => 001111111
000000111 => 000000111 => 111111000 => 001111110
000001000 => 001000000 => 110111111 => 110111111
000001001 => 010000001 => 101111110 => 110111110
000001010 => 011000000 => 100111111 => 010111111
000001011 => 100000011 => 011111100 => 010111110
000001100 => 101000000 => 010111111 => 100111111
000001101 => 110000001 => 001111110 => 100111110
000001110 => 111000000 => 000111111 => 000111111
000001111 => 000001111 => 111110000 => 000111110
000010000 => 000100000 => 111011111 => 111011111
000010001 => 001000001 => 110111110 => 111011110
000010010 => 001100000 => 110011111 => 011011111
000010011 => 010000011 => 101111100 => 011011110
000010100 => 100100000 => 011011111 => 101011111
000010101 => 011000001 => 100111110 => 101011110
000010110 => 011100000 => 100011111 => 001011111
000010111 => 100000111 => 011111000 => 001011110
000011000 => 010100000 => 101011111 => 110011111
000011001 => 101000001 => 010111110 => 110011110
000011010 => 101100000 => 010011111 => 010011111
000011011 => 110000011 => 001111100 => 010011110
000011100 => 110100000 => 001011111 => 100011111
000011101 => 111000001 => 000111110 => 100011110
000011110 => 111100000 => 000011111 => 000011111
000011111 => 000011111 => 111100000 => 000011110
000100000 => 000010000 => 111101111 => 111101111
000100001 => 000100001 => 111011110 => 111101110
000100010 => 000110000 => 111001111 => 011101111
000100011 => 001000011 => 110111100 => 011101110
000100100 => 100010000 => 011101111 => 101101111
000100101 => 001100001 => 110011110 => 101101110
000100110 => 001110000 => 110001111 => 001101111
000100111 => 010000111 => 101111000 => 001101110
000101000 => 010010000 => 101101111 => 110101111
000101001 => 100100001 => 011011110 => 110101110
000101010 => 100110000 => 011001111 => 010101111
000101011 => 011000011 => 100111100 => 010101110
000101100 => 110010000 => 001101111 => 100101111
000101101 => 011100001 => 100011110 => 100101110
000101110 => 011110000 => 100001111 => 000101111
000101111 => 100001111 => 011110000 => 000101110
000110000 => 001010000 => 110101111 => 111001111
000110001 => 010100001 => 101011110 => 111001110
000110010 => 010110000 => 101001111 => 011001111
000110011 => 101000011 => 010111100 => 011001110
000110100 => 011010000 => 100101111 => 101001111
000110101 => 101100001 => 010011110 => 101001110
000110110 => 101110000 => 010001111 => 001001111
000110111 => 110000111 => 001111000 => 001001110
000111000 => 101010000 => 010101111 => 110001111
000111001 => 110100001 => 001011110 => 110001110
000111010 => 110110000 => 001001111 => 010001111
000111011 => 111000011 => 000111100 => 010001110
000111100 => 111010000 => 000101111 => 100001111
000111101 => 111100001 => 000011110 => 100001110
000111110 => 111110000 => 000001111 => 000001111
000111111 => 000111111 => 111000000 => 000001110
001000000 => 000001000 => 111110111 => 111110111
001000001 => 000010001 => 111101110 => 111110110
001000010 => 000011000 => 111100111 => 011110111
001000011 => 000100011 => 111011100 => 011110110
001000100 => 100001000 => 011110111 => 101110111
001000101 => 000110001 => 111001110 => 101110110
001000110 => 000111000 => 111000111 => 001110111
001000111 => 001000111 => 110111000 => 001110110
001001000 => 010001000 => 101110111 => 110110111
001001001 => 100010001 => 011101110 => 110110110
001001010 => 100011000 => 011100111 => 010110111
001001011 => 001100011 => 110011100 => 010110110
001001100 => 110001000 => 001110111 => 100110111
001001101 => 001110001 => 110001110 => 100110110
001001110 => 001111000 => 110000111 => 000110111
001001111 => 010001111 => 101110000 => 000110110
001010000 => 001001000 => 110110111 => 111010111
001010001 => 010010001 => 101101110 => 111010110
001010010 => 010011000 => 101100111 => 011010111
001010011 => 100100011 => 011011100 => 011010110
001010100 => 011001000 => 100110111 => 101010111
001010101 => 100110001 => 011001110 => 101010110
001010110 => 100111000 => 011000111 => 001010111
001010111 => 011000111 => 100111000 => 001010110
001011000 => 101001000 => 010110111 => 110010111
001011001 => 110010001 => 001101110 => 110010110
001011010 => 110011000 => 001100111 => 010010111
001011011 => 011100011 => 100011100 => 010010110
001011100 => 111001000 => 000110111 => 100010111
001011101 => 011110001 => 100001110 => 100010110
001011110 => 011111000 => 100000111 => 000010111
001011111 => 100011111 => 011100000 => 000010110
001100000 => 000101000 => 111010111 => 111100111
001100001 => 001010001 => 110101110 => 111100110
001100010 => 001011000 => 110100111 => 011100111
001100011 => 010100011 => 101011100 => 011100110
001100100 => 001101000 => 110010111 => 101100111
001100101 => 010110001 => 101001110 => 101100110
001100110 => 010111000 => 101000111 => 001100111
001100111 => 101000111 => 010111000 => 001100110
001101000 => 100101000 => 011010111 => 110100111
001101001 => 011010001 => 100101110 => 110100110
001101010 => 011011000 => 100100111 => 010100111
001101011 => 101100011 => 010011100 => 010100110
001101100 => 011101000 => 100010111 => 100100111
001101101 => 101110001 => 010001110 => 100100110
001101110 => 101111000 => 010000111 => 000100111
001101111 => 110001111 => 001110000 => 000100110
001110000 => 010101000 => 101010111 => 111000111
001110001 => 101010001 => 010101110 => 111000110
001110010 => 101011000 => 010100111 => 011000111
001110011 => 110100011 => 001011100 => 011000110
001110100 => 101101000 => 010010111 => 101000111
001110101 => 110110001 => 001001110 => 101000110
001110110 => 110111000 => 001000111 => 001000111
001110111 => 111000111 => 000111000 => 001000110
001111000 => 110101000 => 001010111 => 110000111
001111001 => 111010001 => 000101110 => 110000110
001111010 => 111011000 => 000100111 => 010000111
001111011 => 111100011 => 000011100 => 010000110
001111100 => 111101000 => 000010111 => 100000111
001111101 => 111110001 => 000001110 => 100000110
001111110 => 111111000 => 000000111 => 000000111
001111111 => 001111111 => 110000000 => 000000110
010000000 => 000000100 => 111111011 => 111111011
010000001 => 000001001 => 111110110 => 111111010
010000010 => 000001100 => 111110011 => 011111011
010000011 => 000010011 => 111101100 => 011111010
010000100 => 100000100 => 011111011 => 101111011
010000101 => 000011001 => 111100110 => 101111010
010000110 => 000011100 => 111100011 => 001111011
010000111 => 000100111 => 111011000 => 001111010
010001000 => 010000100 => 101111011 => 110111011
010001001 => 100001001 => 011110110 => 110111010
010001010 => 100001100 => 011110011 => 010111011
010001011 => 000110011 => 111001100 => 010111010
010001100 => 110000100 => 001111011 => 100111011
010001101 => 000111001 => 111000110 => 100111010
010001110 => 000111100 => 111000011 => 000111011
010001111 => 001001111 => 110110000 => 000111010
010010000 => 001000100 => 110111011 => 111011011
010010001 => 010001001 => 101110110 => 111011010
010010010 => 010001100 => 101110011 => 011011011
010010011 => 100010011 => 011101100 => 011011010
010010100 => 011000100 => 100111011 => 101011011
010010101 => 100011001 => 011100110 => 101011010
010010110 => 100011100 => 011100011 => 001011011
010010111 => 001100111 => 110011000 => 001011010
010011000 => 101000100 => 010111011 => 110011011
010011001 => 110001001 => 001110110 => 110011010
010011010 => 110001100 => 001110011 => 010011011
010011011 => 001110011 => 110001100 => 010011010
010011100 => 111000100 => 000111011 => 100011011
010011101 => 001111001 => 110000110 => 100011010
010011110 => 001111100 => 110000011 => 000011011
010011111 => 010011111 => 101100000 => 000011010
010100000 => 000100100 => 111011011 => 111101011
010100001 => 001001001 => 110110110 => 111101010
010100010 => 001001100 => 110110011 => 011101011
010100011 => 010010011 => 101101100 => 011101010
010100100 => 001100100 => 110011011 => 101101011
010100101 => 010011001 => 101100110 => 101101010
010100110 => 010011100 => 101100011 => 001101011
010100111 => 100100111 => 011011000 => 001101010
010101000 => 100100100 => 011011011 => 110101011
010101001 => 011001001 => 100110110 => 110101010
010101010 => 011001100 => 100110011 => 010101011
010101011 => 100110011 => 011001100 => 010101010
010101100 => 011100100 => 100011011 => 100101011
010101101 => 100111001 => 011000110 => 100101010
010101110 => 100111100 => 011000011 => 000101011
010101111 => 011001111 => 100110000 => 000101010
010110000 => 010100100 => 101011011 => 111001011
010110001 => 101001001 => 010110110 => 111001010
010110010 => 101001100 => 010110011 => 011001011
010110011 => 110010011 => 001101100 => 011001010
010110100 => 101100100 => 010011011 => 101001011
010110101 => 110011001 => 001100110 => 101001010
010110110 => 110011100 => 001100011 => 001001011
010110111 => 011100111 => 100011000 => 001001010
010111000 => 110100100 => 001011011 => 110001011
010111001 => 111001001 => 000110110 => 110001010
010111010 => 111001100 => 000110011 => 010001011
010111011 => 011110011 => 100001100 => 010001010
010111100 => 111100100 => 000011011 => 100001011
010111101 => 011111001 => 100000110 => 100001010
010111110 => 011111100 => 100000011 => 000001011
010111111 => 100111111 => 011000000 => 000001010
011000000 => 000010100 => 111101011 => 111110011
011000001 => 000101001 => 111010110 => 111110010
011000010 => 000101100 => 111010011 => 011110011
011000011 => 001010011 => 110101100 => 011110010
011000100 => 000110100 => 111001011 => 101110011
011000101 => 001011001 => 110100110 => 101110010
011000110 => 001011100 => 110100011 => 001110011
011000111 => 010100111 => 101011000 => 001110010
011001000 => 100010100 => 011101011 => 110110011
011001001 => 001101001 => 110010110 => 110110010
011001010 => 001101100 => 110010011 => 010110011
011001011 => 010110011 => 101001100 => 010110010
011001100 => 001110100 => 110001011 => 100110011
011001101 => 010111001 => 101000110 => 100110010
011001110 => 010111100 => 101000011 => 000110011
011001111 => 101001111 => 010110000 => 000110010
011010000 => 010010100 => 101101011 => 111010011
011010001 => 100101001 => 011010110 => 111010010
011010010 => 100101100 => 011010011 => 011010011
011010011 => 011010011 => 100101100 => 011010010
011010100 => 100110100 => 011001011 => 101010011
011010101 => 011011001 => 100100110 => 101010010
011010110 => 011011100 => 100100011 => 001010011
011010111 => 101100111 => 010011000 => 001010010
011011000 => 110010100 => 001101011 => 110010011
011011001 => 011101001 => 100010110 => 110010010
011011010 => 011101100 => 100010011 => 010010011
011011011 => 101110011 => 010001100 => 010010010
011011100 => 011110100 => 100001011 => 100010011
011011101 => 101111001 => 010000110 => 100010010
011011110 => 101111100 => 010000011 => 000010011
011011111 => 110011111 => 001100000 => 000010010
011100000 => 001010100 => 110101011 => 111100011
011100001 => 010101001 => 101010110 => 111100010
011100010 => 010101100 => 101010011 => 011100011
011100011 => 101010011 => 010101100 => 011100010
011100100 => 010110100 => 101001011 => 101100011
011100101 => 101011001 => 010100110 => 101100010
011100110 => 101011100 => 010100011 => 001100011
011100111 => 110100111 => 001011000 => 001100010
011101000 => 011010100 => 100101011 => 110100011
011101001 => 101101001 => 010010110 => 110100010
011101010 => 101101100 => 010010011 => 010100011
011101011 => 110110011 => 001001100 => 010100010
011101100 => 101110100 => 010001011 => 100100011
011101101 => 110111001 => 001000110 => 100100010
011101110 => 110111100 => 001000011 => 000100011
011101111 => 111001111 => 000110000 => 000100010
011110000 => 101010100 => 010101011 => 111000011
011110001 => 110101001 => 001010110 => 111000010
011110010 => 110101100 => 001010011 => 011000011
011110011 => 111010011 => 000101100 => 011000010
011110100 => 110110100 => 001001011 => 101000011
011110101 => 111011001 => 000100110 => 101000010
011110110 => 111011100 => 000100011 => 001000011
011110111 => 111100111 => 000011000 => 001000010
011111000 => 111010100 => 000101011 => 110000011
011111001 => 111101001 => 000010110 => 110000010
011111010 => 111101100 => 000010011 => 010000011
011111011 => 111110011 => 000001100 => 010000010
011111100 => 111110100 => 000001011 => 100000011
011111101 => 111111001 => 000000110 => 100000010
011111110 => 111111100 => 000000011 => 000000011
011111111 => 011111111 => 100000000 => 000000010
100000000 => 000000010 => 111111101 => 111111101
100000001 => 000000101 => 111111010 => 111111100
100000010 => 000000110 => 111111001 => 011111101
100000011 => 000001011 => 111110100 => 011111100
100000100 => 100000010 => 011111101 => 101111101
100000101 => 000001101 => 111110010 => 101111100
100000110 => 000001110 => 111110001 => 001111101
100000111 => 000010111 => 111101000 => 001111100
100001000 => 010000010 => 101111101 => 110111101
100001001 => 100000101 => 011111010 => 110111100
100001010 => 100000110 => 011111001 => 010111101
100001011 => 000011011 => 111100100 => 010111100
100001100 => 110000010 => 001111101 => 100111101
100001101 => 000011101 => 111100010 => 100111100
100001110 => 000011110 => 111100001 => 000111101
100001111 => 000101111 => 111010000 => 000111100
100010000 => 001000010 => 110111101 => 111011101
100010001 => 010000101 => 101111010 => 111011100
100010010 => 010000110 => 101111001 => 011011101
100010011 => 100001011 => 011110100 => 011011100
100010100 => 011000010 => 100111101 => 101011101
100010101 => 100001101 => 011110010 => 101011100
100010110 => 100001110 => 011110001 => 001011101
100010111 => 000110111 => 111001000 => 001011100
100011000 => 101000010 => 010111101 => 110011101
100011001 => 110000101 => 001111010 => 110011100
100011010 => 110000110 => 001111001 => 010011101
100011011 => 000111011 => 111000100 => 010011100
100011100 => 111000010 => 000111101 => 100011101
100011101 => 000111101 => 111000010 => 100011100
100011110 => 000111110 => 111000001 => 000011101
100011111 => 001011111 => 110100000 => 000011100
100100000 => 000100010 => 111011101 => 111101101
100100001 => 001000101 => 110111010 => 111101100
100100010 => 001000110 => 110111001 => 011101101
100100011 => 010001011 => 101110100 => 011101100
100100100 => 001100010 => 110011101 => 101101101
100100101 => 010001101 => 101110010 => 101101100
100100110 => 010001110 => 101110001 => 001101101
100100111 => 100010111 => 011101000 => 001101100
100101000 => 100100010 => 011011101 => 110101101
100101001 => 011000101 => 100111010 => 110101100
100101010 => 011000110 => 100111001 => 010101101
100101011 => 100011011 => 011100100 => 010101100
100101100 => 011100010 => 100011101 => 100101101
100101101 => 100011101 => 011100010 => 100101100
100101110 => 100011110 => 011100001 => 000101101
100101111 => 001101111 => 110010000 => 000101100
100110000 => 010100010 => 101011101 => 111001101
100110001 => 101000101 => 010111010 => 111001100
100110010 => 101000110 => 010111001 => 011001101
100110011 => 110001011 => 001110100 => 011001100
100110100 => 101100010 => 010011101 => 101001101
100110101 => 110001101 => 001110010 => 101001100
100110110 => 110001110 => 001110001 => 001001101
100110111 => 001110111 => 110001000 => 001001100
100111000 => 110100010 => 001011101 => 110001101
100111001 => 111000101 => 000111010 => 110001100
100111010 => 111000110 => 000111001 => 010001101
100111011 => 001111011 => 110000100 => 010001100
100111100 => 111100010 => 000011101 => 100001101
100111101 => 001111101 => 110000010 => 100001100
100111110 => 001111110 => 110000001 => 000001101
100111111 => 010111111 => 101000000 => 000001100
101000000 => 000010010 => 111101101 => 111110101
101000001 => 000100101 => 111011010 => 111110100
101000010 => 000100110 => 111011001 => 011110101
101000011 => 001001011 => 110110100 => 011110100
101000100 => 000110010 => 111001101 => 101110101
101000101 => 001001101 => 110110010 => 101110100
101000110 => 001001110 => 110110001 => 001110101
101000111 => 010010111 => 101101000 => 001110100
101001000 => 100010010 => 011101101 => 110110101
101001001 => 001100101 => 110011010 => 110110100
101001010 => 001100110 => 110011001 => 010110101
101001011 => 010011011 => 101100100 => 010110100
101001100 => 001110010 => 110001101 => 100110101
101001101 => 010011101 => 101100010 => 100110100
101001110 => 010011110 => 101100001 => 000110101
101001111 => 100101111 => 011010000 => 000110100
101010000 => 010010010 => 101101101 => 111010101
101010001 => 100100101 => 011011010 => 111010100
101010010 => 100100110 => 011011001 => 011010101
101010011 => 011001011 => 100110100 => 011010100
101010100 => 100110010 => 011001101 => 101010101
101010101 => 011001101 => 100110010 => 101010100
101010110 => 011001110 => 100110001 => 001010101
101010111 => 100110111 => 011001000 => 001010100
101011000 => 110010010 => 001101101 => 110010101
101011001 => 011100101 => 100011010 => 110010100
101011010 => 011100110 => 100011001 => 010010101
101011011 => 100111011 => 011000100 => 010010100
101011100 => 011110010 => 100001101 => 100010101
101011101 => 100111101 => 011000010 => 100010100
101011110 => 100111110 => 011000001 => 000010101
101011111 => 011011111 => 100100000 => 000010100
101100000 => 001010010 => 110101101 => 111100101
101100001 => 010100101 => 101011010 => 111100100
101100010 => 010100110 => 101011001 => 011100101
101100011 => 101001011 => 010110100 => 011100100
101100100 => 010110010 => 101001101 => 101100101
101100101 => 101001101 => 010110010 => 101100100
101100110 => 101001110 => 010110001 => 001100101
101100111 => 110010111 => 001101000 => 001100100
101101000 => 011010010 => 100101101 => 110100101
101101001 => 101100101 => 010011010 => 110100100
101101010 => 101100110 => 010011001 => 010100101
101101011 => 110011011 => 001100100 => 010100100
101101100 => 101110010 => 010001101 => 100100101
101101101 => 110011101 => 001100010 => 100100100
101101110 => 110011110 => 001100001 => 000100101
101101111 => 011101111 => 100010000 => 000100100
101110000 => 101010010 => 010101101 => 111000101
101110001 => 110100101 => 001011010 => 111000100
101110010 => 110100110 => 001011001 => 011000101
101110011 => 111001011 => 000110100 => 011000100
101110100 => 110110010 => 001001101 => 101000101
101110101 => 111001101 => 000110010 => 101000100
101110110 => 111001110 => 000110001 => 001000101
101110111 => 011110111 => 100001000 => 001000100
101111000 => 111010010 => 000101101 => 110000101
101111001 => 111100101 => 000011010 => 110000100
101111010 => 111100110 => 000011001 => 010000101
101111011 => 011111011 => 100000100 => 010000100
101111100 => 111110010 => 000001101 => 100000101
101111101 => 011111101 => 100000010 => 100000100
101111110 => 011111110 => 100000001 => 000000101
101111111 => 101111111 => 010000000 => 000000100
110000000 => 000001010 => 111110101 => 111111001
110000001 => 000010101 => 111101010 => 111111000
110000010 => 000010110 => 111101001 => 011111001
110000011 => 000101011 => 111010100 => 011111000
110000100 => 000011010 => 111100101 => 101111001
110000101 => 000101101 => 111010010 => 101111000
110000110 => 000101110 => 111010001 => 001111001
110000111 => 001010111 => 110101000 => 001111000
110001000 => 100001010 => 011110101 => 110111001
110001001 => 000110101 => 111001010 => 110111000
110001010 => 000110110 => 111001001 => 010111001
110001011 => 001011011 => 110100100 => 010111000
110001100 => 000111010 => 111000101 => 100111001
110001101 => 001011101 => 110100010 => 100111000
110001110 => 001011110 => 110100001 => 000111001
110001111 => 010101111 => 101010000 => 000111000
110010000 => 010001010 => 101110101 => 111011001
110010001 => 100010101 => 011101010 => 111011000
110010010 => 100010110 => 011101001 => 011011001
110010011 => 001101011 => 110010100 => 011011000
110010100 => 100011010 => 011100101 => 101011001
110010101 => 001101101 => 110010010 => 101011000
110010110 => 001101110 => 110010001 => 001011001
110010111 => 010110111 => 101001000 => 001011000
110011000 => 110001010 => 001110101 => 110011001
110011001 => 001110101 => 110001010 => 110011000
110011010 => 001110110 => 110001001 => 010011001
110011011 => 010111011 => 101000100 => 010011000
110011100 => 001111010 => 110000101 => 100011001
110011101 => 010111101 => 101000010 => 100011000
110011110 => 010111110 => 101000001 => 000011001
110011111 => 101011111 => 010100000 => 000011000
110100000 => 001001010 => 110110101 => 111101001
110100001 => 010010101 => 101101010 => 111101000
110100010 => 010010110 => 101101001 => 011101001
110100011 => 100101011 => 011010100 => 011101000
110100100 => 010011010 => 101100101 => 101101001
110100101 => 100101101 => 011010010 => 101101000
110100110 => 100101110 => 011010001 => 001101001
110100111 => 011010111 => 100101000 => 001101000
110101000 => 011001010 => 100110101 => 110101001
110101001 => 100110101 => 011001010 => 110101000
110101010 => 100110110 => 011001001 => 010101001
110101011 => 011011011 => 100100100 => 010101000
110101100 => 100111010 => 011000101 => 100101001
110101101 => 011011101 => 100100010 => 100101000
110101110 => 011011110 => 100100001 => 000101001
110101111 => 101101111 => 010010000 => 000101000
110110000 => 101001010 => 010110101 => 111001001
110110001 => 110010101 => 001101010 => 111001000
110110010 => 110010110 => 001101001 => 011001001
110110011 => 011101011 => 100010100 => 011001000
110110100 => 110011010 => 001100101 => 101001001
110110101 => 011101101 => 100010010 => 101001000
110110110 => 011101110 => 100010001 => 001001001
110110111 => 101110111 => 010001000 => 001001000
110111000 => 111001010 => 000110101 => 110001001
110111001 => 011110101 => 100001010 => 110001000
110111010 => 011110110 => 100001001 => 010001001
110111011 => 101111011 => 010000100 => 010001000
110111100 => 011111010 => 100000101 => 100001001
110111101 => 101111101 => 010000010 => 100001000
110111110 => 101111110 => 010000001 => 000001001
110111111 => 110111111 => 001000000 => 000001000
111000000 => 000101010 => 111010101 => 111110001
111000001 => 001010101 => 110101010 => 111110000
111000010 => 001010110 => 110101001 => 011110001
111000011 => 010101011 => 101010100 => 011110000
111000100 => 001011010 => 110100101 => 101110001
111000101 => 010101101 => 101010010 => 101110000
111000110 => 010101110 => 101010001 => 001110001
111000111 => 101010111 => 010101000 => 001110000
111001000 => 001101010 => 110010101 => 110110001
111001001 => 010110101 => 101001010 => 110110000
111001010 => 010110110 => 101001001 => 010110001
111001011 => 101011011 => 010100100 => 010110000
111001100 => 010111010 => 101000101 => 100110001
111001101 => 101011101 => 010100010 => 100110000
111001110 => 101011110 => 010100001 => 000110001
111001111 => 110101111 => 001010000 => 000110000
111010000 => 100101010 => 011010101 => 111010001
111010001 => 011010101 => 100101010 => 111010000
111010010 => 011010110 => 100101001 => 011010001
111010011 => 101101011 => 010010100 => 011010000
111010100 => 011011010 => 100100101 => 101010001
111010101 => 101101101 => 010010010 => 101010000
111010110 => 101101110 => 010010001 => 001010001
111010111 => 110110111 => 001001000 => 001010000
111011000 => 011101010 => 100010101 => 110010001
111011001 => 101110101 => 010001010 => 110010000
111011010 => 101110110 => 010001001 => 010010001
111011011 => 110111011 => 001000100 => 010010000
111011100 => 101111010 => 010000101 => 100010001
111011101 => 110111101 => 001000010 => 100010000
111011110 => 110111110 => 001000001 => 000010001
111011111 => 111011111 => 000100000 => 000010000
111100000 => 010101010 => 101010101 => 111100001
111100001 => 101010101 => 010101010 => 111100000
111100010 => 101010110 => 010101001 => 011100001
111100011 => 110101011 => 001010100 => 011100000
111100100 => 101011010 => 010100101 => 101100001
111100101 => 110101101 => 001010010 => 101100000
111100110 => 110101110 => 001010001 => 001100001
111100111 => 111010111 => 000101000 => 001100000
111101000 => 101101010 => 010010101 => 110100001
111101001 => 110110101 => 001001010 => 110100000
111101010 => 110110110 => 001001001 => 010100001
111101011 => 111011011 => 000100100 => 010100000
111101100 => 110111010 => 001000101 => 100100001
111101101 => 111011101 => 000100010 => 100100000
111101110 => 111011110 => 000100001 => 000100001
111101111 => 111101111 => 000010000 => 000100000
111110000 => 110101010 => 001010101 => 111000001
111110001 => 111010101 => 000101010 => 111000000
111110010 => 111010110 => 000101001 => 011000001
111110011 => 111101011 => 000010100 => 011000000
111110100 => 111011010 => 000100101 => 101000001
111110101 => 111101101 => 000010010 => 101000000
111110110 => 111101110 => 000010001 => 001000001
111110111 => 111110111 => 000001000 => 001000000
111111000 => 111101010 => 000010101 => 110000001
111111001 => 111110101 => 000001010 => 110000000
111111010 => 111110110 => 000001001 => 010000001
111111011 => 111111011 => 000000100 => 010000000
111111100 => 111111010 => 000000101 => 100000001
111111101 => 111111101 => 000000010 => 100000000
111111110 => 111111110 => 000000001 => 000000001
111111111 => 111111111 => 000000000 => 000000000
1111111110 => 1111111110 => 0000000001 => 0000000001
1101111110 => 1011111110 => 0100000001 => 0000001001
1011111110 => 0111111110 => 1000000001 => 0000000101
1010111110 => 1001111110 => 0110000001 => 0000010101
1001111110 => 0011111110 => 1100000001 => 0000001101
1001011110 => 1000111110 => 0111000001 => 0000101101
1000111110 => 0001111110 => 1110000001 => 0000011101
1000101110 => 1000011110 => 0111100001 => 0001011101
1000011110 => 0000111110 => 1111000001 => 0000111101
1000010110 => 1000001110 => 0111110001 => 0010111101
1000001110 => 0000011110 => 1111100001 => 0001111101
1000001010 => 1000000110 => 0111111001 => 0101111101
1000000110 => 0000001110 => 1111110001 => 0011111101
1000000100 => 1000000010 => 0111111101 => 1011111101
1000000010 => 0000000110 => 1111111001 => 0111111101
1000000000 => 0000000010 => 1111111101 => 1111111101
10000000000 => 00000000010 => 11111111101 => 11111111101
10000000010 => 00000000110 => 11111111001 => 01111111101
10000000110 => 00000001110 => 11111110001 => 00111111101
10000001110 => 00000011110 => 11111100001 => 00011111101
10000011110 => 00000111110 => 11111000001 => 00001111101
10000111110 => 00001111110 => 11110000001 => 00000111101
10001111110 => 00011111110 => 11100000001 => 00000011101
10011111110 => 00111111110 => 11000000001 => 00000001101
10111111110 => 01111111110 => 10000000001 => 00000000101
11111111110 => 11111111110 => 00000000001 => 00000000001
0111111111 => 0111111111 => 1000000000 => 0000000010
0111111101 => 1111111001 => 0000000110 => 1000000010
0111111001 => 1111101001 => 0000010110 => 1100000010
0111110001 => 1110101001 => 0001010110 => 1110000010
0111100001 => 1010101001 => 0101010110 => 1111000010
0100000001 => 0000001001 => 1111110110 => 1111111010
0000000001 => 0000000001 => 1111111110 => 1111111110
01111111111 => 01111111111 => 10000000000 => 00000000010
01111111101 => 11111111001 => 00000000110 => 10000000010
0111111011 => 1111110011 => 0000001100 => 0100000010
0111101001 => 1101101001 => 0010010110 => 1101000010
0111010001 => 0110101001 => 1001010110 => 1110100010
0010000001 => 0000010001 => 1111101110 => 1111110110
01000000001 => 00000001001 => 11111110110 => 11111111010
00000000001 => 00000000001 => 11111111110 => 11111111110
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.
See Mp00096Foata bijection.
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.
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