Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Images
0 => 0 => 0 => 0
1 => 1 => 1 => 1
00 => 00 => 00 => 00
01 => 01 => 10 => 10
10 => 10 => 01 => 01
11 => 11 => 11 => 11
000 => 000 => 000 => 000
001 => 001 => 100 => 010
010 => 100 => 010 => 100
011 => 011 => 101 => 101
100 => 010 => 001 => 001
101 => 101 => 110 => 110
110 => 110 => 011 => 011
111 => 111 => 111 => 111
0000 => 0000 => 0000 => 0000
0001 => 0001 => 1000 => 0010
0010 => 1000 => 0100 => 0100
0011 => 0011 => 1001 => 0101
0100 => 0100 => 0010 => 1000
0101 => 1001 => 1100 => 1010
0110 => 1010 => 0101 => 1001
0111 => 0111 => 1011 => 1011
1000 => 0010 => 0001 => 0001
1001 => 0101 => 1010 => 0110
1010 => 1100 => 0110 => 1100
1011 => 1011 => 1101 => 1101
1100 => 0110 => 0011 => 0011
1101 => 1101 => 1110 => 1110
1110 => 1110 => 0111 => 0111
1111 => 1111 => 1111 => 1111
00000 => 00000 => 00000 => 00000
00001 => 00001 => 10000 => 00010
00010 => 10000 => 01000 => 00100
00011 => 00011 => 10001 => 00101
00100 => 01000 => 00100 => 01000
00101 => 10001 => 11000 => 01010
00110 => 10010 => 01001 => 01001
00111 => 00111 => 10011 => 01011
01000 => 00100 => 00010 => 10000
01001 => 01001 => 10100 => 10010
01010 => 11000 => 01100 => 10100
01011 => 10011 => 11001 => 10101
01100 => 01010 => 00101 => 10001
01101 => 10101 => 11010 => 10110
01110 => 10110 => 01011 => 10011
01111 => 01111 => 10111 => 10111
10000 => 00010 => 00001 => 00001
10001 => 00101 => 10010 => 00110
10010 => 10100 => 01010 => 01100
10011 => 01011 => 10101 => 01101
10100 => 01100 => 00110 => 11000
10101 => 11001 => 11100 => 11010
10110 => 11010 => 01101 => 11001
10111 => 10111 => 11011 => 11011
11000 => 00110 => 00011 => 00011
11001 => 01101 => 10110 => 01110
11010 => 11100 => 01110 => 11100
11011 => 11011 => 11101 => 11101
11100 => 01110 => 00111 => 00111
11101 => 11101 => 11110 => 11110
11110 => 11110 => 01111 => 01111
11111 => 11111 => 11111 => 11111
000000 => 000000 => 000000 => 000000
000001 => 000001 => 100000 => 000010
000010 => 100000 => 010000 => 000100
000011 => 000011 => 100001 => 000101
000100 => 010000 => 001000 => 001000
000101 => 100001 => 110000 => 001010
000110 => 100010 => 010001 => 001001
000111 => 000111 => 100011 => 001011
001000 => 001000 => 000100 => 010000
001001 => 010001 => 101000 => 010010
001010 => 110000 => 011000 => 010100
001011 => 100011 => 110001 => 010101
001100 => 010010 => 001001 => 010001
001101 => 100101 => 110010 => 010110
001110 => 100110 => 010011 => 010011
001111 => 001111 => 100111 => 010111
010000 => 000100 => 000010 => 100000
010001 => 001001 => 100100 => 100010
010010 => 101000 => 010100 => 100100
010011 => 010011 => 101001 => 100101
010100 => 011000 => 001100 => 101000
010101 => 110001 => 111000 => 101010
010110 => 110010 => 011001 => 101001
010111 => 100111 => 110011 => 101011
011000 => 001010 => 000101 => 100001
011001 => 010101 => 101010 => 100110
011010 => 110100 => 011010 => 101100
011011 => 101011 => 110101 => 101101
011100 => 010110 => 001011 => 100011
011101 => 101101 => 110110 => 101110
011110 => 101110 => 010111 => 100111
011111 => 011111 => 101111 => 101111
100000 => 000010 => 000001 => 000001
100001 => 000101 => 100010 => 000110
100010 => 100100 => 010010 => 001100
100011 => 001011 => 100101 => 001101
100100 => 010100 => 001010 => 011000
100101 => 101001 => 110100 => 011010
100110 => 101010 => 010101 => 011001
>>> Load all 1053 entries. <<<
100111 => 010111 => 101011 => 011011
101000 => 001100 => 000110 => 110000
101001 => 011001 => 101100 => 110010
101010 => 111000 => 011100 => 110100
101011 => 110011 => 111001 => 110101
101100 => 011010 => 001101 => 110001
101101 => 110101 => 111010 => 110110
101110 => 110110 => 011011 => 110011
101111 => 101111 => 110111 => 110111
110000 => 000110 => 000011 => 000011
110001 => 001101 => 100110 => 001110
110010 => 101100 => 010110 => 011100
110011 => 011011 => 101101 => 011101
110100 => 011100 => 001110 => 111000
110101 => 111001 => 111100 => 111010
110110 => 111010 => 011101 => 111001
110111 => 110111 => 111011 => 111011
111000 => 001110 => 000111 => 000111
111001 => 011101 => 101110 => 011110
111010 => 111100 => 011110 => 111100
111011 => 111011 => 111101 => 111101
111100 => 011110 => 001111 => 001111
111101 => 111101 => 111110 => 111110
111110 => 111110 => 011111 => 011111
111111 => 111111 => 111111 => 111111
0000000 => 0000000 => 0000000 => 0000000
0000001 => 0000001 => 1000000 => 0000010
0000010 => 1000000 => 0100000 => 0000100
0000011 => 0000011 => 1000001 => 0000101
0000100 => 0100000 => 0010000 => 0001000
0000101 => 1000001 => 1100000 => 0001010
0000110 => 1000010 => 0100001 => 0001001
0000111 => 0000111 => 1000011 => 0001011
0001000 => 0010000 => 0001000 => 0010000
0001001 => 0100001 => 1010000 => 0010010
0001010 => 1100000 => 0110000 => 0010100
0001011 => 1000011 => 1100001 => 0010101
0001100 => 0100010 => 0010001 => 0010001
0001101 => 1000101 => 1100010 => 0010110
0001110 => 1000110 => 0100011 => 0010011
0001111 => 0001111 => 1000111 => 0010111
0010000 => 0001000 => 0000100 => 0100000
0010001 => 0010001 => 1001000 => 0100010
0010010 => 1010000 => 0101000 => 0100100
0010011 => 0100011 => 1010001 => 0100101
0010100 => 0110000 => 0011000 => 0101000
0010101 => 1100001 => 1110000 => 0101010
0010110 => 1100010 => 0110001 => 0101001
0010111 => 1000111 => 1100011 => 0101011
0011000 => 0010010 => 0001001 => 0100001
0011001 => 0100101 => 1010010 => 0100110
0011010 => 1100100 => 0110010 => 0101100
0011011 => 1001011 => 1100101 => 0101101
0011100 => 0100110 => 0010011 => 0100011
0011101 => 1001101 => 1100110 => 0101110
0011110 => 1001110 => 0100111 => 0100111
0011111 => 0011111 => 1001111 => 0101111
0100000 => 0000100 => 0000010 => 1000000
0100001 => 0001001 => 1000100 => 1000010
0100010 => 1001000 => 0100100 => 1000100
0100011 => 0010011 => 1001001 => 1000101
0100100 => 0101000 => 0010100 => 1001000
0100101 => 1010001 => 1101000 => 1001010
0100110 => 1010010 => 0101001 => 1001001
0100111 => 0100111 => 1010011 => 1001011
0101000 => 0011000 => 0001100 => 1010000
0101001 => 0110001 => 1011000 => 1010010
0101010 => 1110000 => 0111000 => 1010100
0101011 => 1100011 => 1110001 => 1010101
0101100 => 0110010 => 0011001 => 1010001
0101101 => 1100101 => 1110010 => 1010110
0101110 => 1100110 => 0110011 => 1010011
0101111 => 1001111 => 1100111 => 1010111
0110000 => 0001010 => 0000101 => 1000001
0110001 => 0010101 => 1001010 => 1000110
0110010 => 1010100 => 0101010 => 1001100
0110011 => 0101011 => 1010101 => 1001101
0110100 => 0110100 => 0011010 => 1011000
0110101 => 1101001 => 1110100 => 1011010
0110110 => 1101010 => 0110101 => 1011001
0110111 => 1010111 => 1101011 => 1011011
0111000 => 0010110 => 0001011 => 1000011
0111001 => 0101101 => 1010110 => 1001110
0111010 => 1101100 => 0110110 => 1011100
0111011 => 1011011 => 1101101 => 1011101
0111100 => 0101110 => 0010111 => 1000111
0111101 => 1011101 => 1101110 => 1011110
0111110 => 1011110 => 0101111 => 1001111
0111111 => 0111111 => 1011111 => 1011111
1000000 => 0000010 => 0000001 => 0000001
1000001 => 0000101 => 1000010 => 0000110
1000010 => 1000100 => 0100010 => 0001100
1000011 => 0001011 => 1000101 => 0001101
1000100 => 0100100 => 0010010 => 0011000
1000101 => 1001001 => 1100100 => 0011010
1000110 => 1001010 => 0100101 => 0011001
1000111 => 0010111 => 1001011 => 0011011
1001000 => 0010100 => 0001010 => 0110000
1001001 => 0101001 => 1010100 => 0110010
1001010 => 1101000 => 0110100 => 0110100
1001011 => 1010011 => 1101001 => 0110101
1001100 => 0101010 => 0010101 => 0110001
1001101 => 1010101 => 1101010 => 0110110
1001110 => 1010110 => 0101011 => 0110011
1001111 => 0101111 => 1010111 => 0110111
1010000 => 0001100 => 0000110 => 1100000
1010001 => 0011001 => 1001100 => 1100010
1010010 => 1011000 => 0101100 => 1100100
1010011 => 0110011 => 1011001 => 1100101
1010100 => 0111000 => 0011100 => 1101000
1010101 => 1110001 => 1111000 => 1101010
1010110 => 1110010 => 0111001 => 1101001
1010111 => 1100111 => 1110011 => 1101011
1011000 => 0011010 => 0001101 => 1100001
1011001 => 0110101 => 1011010 => 1100110
1011010 => 1110100 => 0111010 => 1101100
1011011 => 1101011 => 1110101 => 1101101
1011100 => 0110110 => 0011011 => 1100011
1011101 => 1101101 => 1110110 => 1101110
1011110 => 1101110 => 0110111 => 1100111
1011111 => 1011111 => 1101111 => 1101111
1100000 => 0000110 => 0000011 => 0000011
1100001 => 0001101 => 1000110 => 0001110
1100010 => 1001100 => 0100110 => 0011100
1100011 => 0011011 => 1001101 => 0011101
1100100 => 0101100 => 0010110 => 0111000
1100101 => 1011001 => 1101100 => 0111010
1100110 => 1011010 => 0101101 => 0111001
1100111 => 0110111 => 1011011 => 0111011
1101000 => 0011100 => 0001110 => 1110000
1101001 => 0111001 => 1011100 => 1110010
1101010 => 1111000 => 0111100 => 1110100
1101011 => 1110011 => 1111001 => 1110101
1101100 => 0111010 => 0011101 => 1110001
1101101 => 1110101 => 1111010 => 1110110
1101110 => 1110110 => 0111011 => 1110011
1101111 => 1101111 => 1110111 => 1110111
1110000 => 0001110 => 0000111 => 0000111
1110001 => 0011101 => 1001110 => 0011110
1110010 => 1011100 => 0101110 => 0111100
1110011 => 0111011 => 1011101 => 0111101
1110100 => 0111100 => 0011110 => 1111000
1110101 => 1111001 => 1111100 => 1111010
1110110 => 1111010 => 0111101 => 1111001
1110111 => 1110111 => 1111011 => 1111011
1111000 => 0011110 => 0001111 => 0001111
1111001 => 0111101 => 1011110 => 0111110
1111010 => 1111100 => 0111110 => 1111100
1111011 => 1111011 => 1111101 => 1111101
1111100 => 0111110 => 0011111 => 0011111
1111101 => 1111101 => 1111110 => 1111110
1111110 => 1111110 => 0111111 => 0111111
1111111 => 1111111 => 1111111 => 1111111
00000000 => 00000000 => 00000000 => 00000000
00000001 => 00000001 => 10000000 => 00000010
00000010 => 10000000 => 01000000 => 00000100
00000011 => 00000011 => 10000001 => 00000101
00000100 => 01000000 => 00100000 => 00001000
00000101 => 10000001 => 11000000 => 00001010
00000110 => 10000010 => 01000001 => 00001001
00000111 => 00000111 => 10000011 => 00001011
00001000 => 00100000 => 00010000 => 00010000
00001001 => 01000001 => 10100000 => 00010010
00001010 => 11000000 => 01100000 => 00010100
00001011 => 10000011 => 11000001 => 00010101
00001100 => 01000010 => 00100001 => 00010001
00001101 => 10000101 => 11000010 => 00010110
00001110 => 10000110 => 01000011 => 00010011
00001111 => 00001111 => 10000111 => 00010111
00010000 => 00010000 => 00001000 => 00100000
00010001 => 00100001 => 10010000 => 00100010
00010010 => 10100000 => 01010000 => 00100100
00010011 => 01000011 => 10100001 => 00100101
00010100 => 01100000 => 00110000 => 00101000
00010101 => 11000001 => 11100000 => 00101010
00010110 => 11000010 => 01100001 => 00101001
00010111 => 10000111 => 11000011 => 00101011
00011000 => 00100010 => 00010001 => 00100001
00011001 => 01000101 => 10100010 => 00100110
00011010 => 11000100 => 01100010 => 00101100
00011011 => 10001011 => 11000101 => 00101101
00011100 => 01000110 => 00100011 => 00100011
00011101 => 10001101 => 11000110 => 00101110
00011110 => 10001110 => 01000111 => 00100111
00011111 => 00011111 => 10001111 => 00101111
00100000 => 00001000 => 00000100 => 01000000
00100001 => 00010001 => 10001000 => 01000010
00100010 => 10010000 => 01001000 => 01000100
00100011 => 00100011 => 10010001 => 01000101
00100100 => 01010000 => 00101000 => 01001000
00100101 => 10100001 => 11010000 => 01001010
00100110 => 10100010 => 01010001 => 01001001
00100111 => 01000111 => 10100011 => 01001011
00101000 => 00110000 => 00011000 => 01010000
00101001 => 01100001 => 10110000 => 01010010
00101010 => 11100000 => 01110000 => 01010100
00101011 => 11000011 => 11100001 => 01010101
00101100 => 01100010 => 00110001 => 01010001
00101101 => 11000101 => 11100010 => 01010110
00101110 => 11000110 => 01100011 => 01010011
00101111 => 10001111 => 11000111 => 01010111
00110000 => 00010010 => 00001001 => 01000001
00110001 => 00100101 => 10010010 => 01000110
00110010 => 10100100 => 01010010 => 01001100
00110011 => 01001011 => 10100101 => 01001101
00110100 => 01100100 => 00110010 => 01011000
00110101 => 11001001 => 11100100 => 01011010
00110110 => 11001010 => 01100101 => 01011001
00110111 => 10010111 => 11001011 => 01011011
00111000 => 00100110 => 00010011 => 01000011
00111001 => 01001101 => 10100110 => 01001110
00111010 => 11001100 => 01100110 => 01011100
00111011 => 10011011 => 11001101 => 01011101
00111100 => 01001110 => 00100111 => 01000111
00111101 => 10011101 => 11001110 => 01011110
00111110 => 10011110 => 01001111 => 01001111
00111111 => 00111111 => 10011111 => 01011111
01000000 => 00000100 => 00000010 => 10000000
01000001 => 00001001 => 10000100 => 10000010
01000010 => 10001000 => 01000100 => 10000100
01000011 => 00010011 => 10001001 => 10000101
01000100 => 01001000 => 00100100 => 10001000
01000101 => 10010001 => 11001000 => 10001010
01000110 => 10010010 => 01001001 => 10001001
01000111 => 00100111 => 10010011 => 10001011
01001000 => 00101000 => 00010100 => 10010000
01001001 => 01010001 => 10101000 => 10010010
01001010 => 11010000 => 01101000 => 10010100
01001011 => 10100011 => 11010001 => 10010101
01001100 => 01010010 => 00101001 => 10010001
01001101 => 10100101 => 11010010 => 10010110
01001110 => 10100110 => 01010011 => 10010011
01001111 => 01001111 => 10100111 => 10010111
01010000 => 00011000 => 00001100 => 10100000
01010001 => 00110001 => 10011000 => 10100010
01010010 => 10110000 => 01011000 => 10100100
01010011 => 01100011 => 10110001 => 10100101
01010100 => 01110000 => 00111000 => 10101000
01010101 => 11100001 => 11110000 => 10101010
01010110 => 11100010 => 01110001 => 10101001
01010111 => 11000111 => 11100011 => 10101011
01011000 => 00110010 => 00011001 => 10100001
01011001 => 01100101 => 10110010 => 10100110
01011010 => 11100100 => 01110010 => 10101100
01011011 => 11001011 => 11100101 => 10101101
01011100 => 01100110 => 00110011 => 10100011
01011101 => 11001101 => 11100110 => 10101110
01011110 => 11001110 => 01100111 => 10100111
01011111 => 10011111 => 11001111 => 10101111
01100000 => 00001010 => 00000101 => 10000001
01100001 => 00010101 => 10001010 => 10000110
01100010 => 10010100 => 01001010 => 10001100
01100011 => 00101011 => 10010101 => 10001101
01100100 => 01010100 => 00101010 => 10011000
01100101 => 10101001 => 11010100 => 10011010
01100110 => 10101010 => 01010101 => 10011001
01100111 => 01010111 => 10101011 => 10011011
01101000 => 00110100 => 00011010 => 10110000
01101001 => 01101001 => 10110100 => 10110010
01101010 => 11101000 => 01110100 => 10110100
01101011 => 11010011 => 11101001 => 10110101
01101100 => 01101010 => 00110101 => 10110001
01101101 => 11010101 => 11101010 => 10110110
01101110 => 11010110 => 01101011 => 10110011
01101111 => 10101111 => 11010111 => 10110111
01110000 => 00010110 => 00001011 => 10000011
01110001 => 00101101 => 10010110 => 10001110
01110010 => 10101100 => 01010110 => 10011100
01110011 => 01011011 => 10101101 => 10011101
01110100 => 01101100 => 00110110 => 10111000
01110101 => 11011001 => 11101100 => 10111010
01110110 => 11011010 => 01101101 => 10111001
01110111 => 10110111 => 11011011 => 10111011
01111000 => 00101110 => 00010111 => 10000111
01111001 => 01011101 => 10101110 => 10011110
01111010 => 11011100 => 01101110 => 10111100
01111011 => 10111011 => 11011101 => 10111101
01111100 => 01011110 => 00101111 => 10001111
01111101 => 10111101 => 11011110 => 10111110
01111110 => 10111110 => 01011111 => 10011111
01111111 => 01111111 => 10111111 => 10111111
10000000 => 00000010 => 00000001 => 00000001
10000001 => 00000101 => 10000010 => 00000110
10000010 => 10000100 => 01000010 => 00001100
10000011 => 00001011 => 10000101 => 00001101
10000100 => 01000100 => 00100010 => 00011000
10000101 => 10001001 => 11000100 => 00011010
10000110 => 10001010 => 01000101 => 00011001
10000111 => 00010111 => 10001011 => 00011011
10001000 => 00100100 => 00010010 => 00110000
10001001 => 01001001 => 10100100 => 00110010
10001010 => 11001000 => 01100100 => 00110100
10001011 => 10010011 => 11001001 => 00110101
10001100 => 01001010 => 00100101 => 00110001
10001101 => 10010101 => 11001010 => 00110110
10001110 => 10010110 => 01001011 => 00110011
10001111 => 00101111 => 10010111 => 00110111
10010000 => 00010100 => 00001010 => 01100000
10010001 => 00101001 => 10010100 => 01100010
10010010 => 10101000 => 01010100 => 01100100
10010011 => 01010011 => 10101001 => 01100101
10010100 => 01101000 => 00110100 => 01101000
10010101 => 11010001 => 11101000 => 01101010
10010110 => 11010010 => 01101001 => 01101001
10010111 => 10100111 => 11010011 => 01101011
10011000 => 00101010 => 00010101 => 01100001
10011001 => 01010101 => 10101010 => 01100110
10011010 => 11010100 => 01101010 => 01101100
10011011 => 10101011 => 11010101 => 01101101
10011100 => 01010110 => 00101011 => 01100011
10011101 => 10101101 => 11010110 => 01101110
10011110 => 10101110 => 01010111 => 01100111
10011111 => 01011111 => 10101111 => 01101111
10100000 => 00001100 => 00000110 => 11000000
10100001 => 00011001 => 10001100 => 11000010
10100010 => 10011000 => 01001100 => 11000100
10100011 => 00110011 => 10011001 => 11000101
10100100 => 01011000 => 00101100 => 11001000
10100101 => 10110001 => 11011000 => 11001010
10100110 => 10110010 => 01011001 => 11001001
10100111 => 01100111 => 10110011 => 11001011
10101000 => 00111000 => 00011100 => 11010000
10101001 => 01110001 => 10111000 => 11010010
10101010 => 11110000 => 01111000 => 11010100
10101011 => 11100011 => 11110001 => 11010101
10101100 => 01110010 => 00111001 => 11010001
10101101 => 11100101 => 11110010 => 11010110
10101110 => 11100110 => 01110011 => 11010011
10101111 => 11001111 => 11100111 => 11010111
10110000 => 00011010 => 00001101 => 11000001
10110001 => 00110101 => 10011010 => 11000110
10110010 => 10110100 => 01011010 => 11001100
10110011 => 01101011 => 10110101 => 11001101
10110100 => 01110100 => 00111010 => 11011000
10110101 => 11101001 => 11110100 => 11011010
10110110 => 11101010 => 01110101 => 11011001
10110111 => 11010111 => 11101011 => 11011011
10111000 => 00110110 => 00011011 => 11000011
10111001 => 01101101 => 10110110 => 11001110
10111010 => 11101100 => 01110110 => 11011100
10111011 => 11011011 => 11101101 => 11011101
10111100 => 01101110 => 00110111 => 11000111
10111101 => 11011101 => 11101110 => 11011110
10111110 => 11011110 => 01101111 => 11001111
10111111 => 10111111 => 11011111 => 11011111
11000000 => 00000110 => 00000011 => 00000011
11000001 => 00001101 => 10000110 => 00001110
11000010 => 10001100 => 01000110 => 00011100
11000011 => 00011011 => 10001101 => 00011101
11000100 => 01001100 => 00100110 => 00111000
11000101 => 10011001 => 11001100 => 00111010
11000110 => 10011010 => 01001101 => 00111001
11000111 => 00110111 => 10011011 => 00111011
11001000 => 00101100 => 00010110 => 01110000
11001001 => 01011001 => 10101100 => 01110010
11001010 => 11011000 => 01101100 => 01110100
11001011 => 10110011 => 11011001 => 01110101
11001100 => 01011010 => 00101101 => 01110001
11001101 => 10110101 => 11011010 => 01110110
11001110 => 10110110 => 01011011 => 01110011
11001111 => 01101111 => 10110111 => 01110111
11010000 => 00011100 => 00001110 => 11100000
11010001 => 00111001 => 10011100 => 11100010
11010010 => 10111000 => 01011100 => 11100100
11010011 => 01110011 => 10111001 => 11100101
11010100 => 01111000 => 00111100 => 11101000
11010101 => 11110001 => 11111000 => 11101010
11010110 => 11110010 => 01111001 => 11101001
11010111 => 11100111 => 11110011 => 11101011
11011000 => 00111010 => 00011101 => 11100001
11011001 => 01110101 => 10111010 => 11100110
11011010 => 11110100 => 01111010 => 11101100
11011011 => 11101011 => 11110101 => 11101101
11011100 => 01110110 => 00111011 => 11100011
11011101 => 11101101 => 11110110 => 11101110
11011110 => 11101110 => 01110111 => 11100111
11011111 => 11011111 => 11101111 => 11101111
11100000 => 00001110 => 00000111 => 00000111
11100001 => 00011101 => 10001110 => 00011110
11100010 => 10011100 => 01001110 => 00111100
11100011 => 00111011 => 10011101 => 00111101
11100100 => 01011100 => 00101110 => 01111000
11100101 => 10111001 => 11011100 => 01111010
11100110 => 10111010 => 01011101 => 01111001
11100111 => 01110111 => 10111011 => 01111011
11101000 => 00111100 => 00011110 => 11110000
11101001 => 01111001 => 10111100 => 11110010
11101010 => 11111000 => 01111100 => 11110100
11101011 => 11110011 => 11111001 => 11110101
11101100 => 01111010 => 00111101 => 11110001
11101101 => 11110101 => 11111010 => 11110110
11101110 => 11110110 => 01111011 => 11110011
11101111 => 11101111 => 11110111 => 11110111
11110000 => 00011110 => 00001111 => 00001111
11110001 => 00111101 => 10011110 => 00111110
11110010 => 10111100 => 01011110 => 01111100
11110011 => 01111011 => 10111101 => 01111101
11110100 => 01111100 => 00111110 => 11111000
11110101 => 11111001 => 11111100 => 11111010
11110110 => 11111010 => 01111101 => 11111001
11110111 => 11110111 => 11111011 => 11111011
11111000 => 00111110 => 00011111 => 00011111
11111001 => 01111101 => 10111110 => 01111110
11111010 => 11111100 => 01111110 => 11111100
11111011 => 11111011 => 11111101 => 11111101
11111100 => 01111110 => 00111111 => 00111111
11111101 => 11111101 => 11111110 => 11111110
11111110 => 11111110 => 01111111 => 01111111
11111111 => 11111111 => 11111111 => 11111111
000000000 => 000000000 => 000000000 => 000000000
000000001 => 000000001 => 100000000 => 000000010
000000010 => 100000000 => 010000000 => 000000100
000000011 => 000000011 => 100000001 => 000000101
000000100 => 010000000 => 001000000 => 000001000
000000101 => 100000001 => 110000000 => 000001010
000000110 => 100000010 => 010000001 => 000001001
000000111 => 000000111 => 100000011 => 000001011
000001000 => 001000000 => 000100000 => 000010000
000001001 => 010000001 => 101000000 => 000010010
000001010 => 110000000 => 011000000 => 000010100
000001011 => 100000011 => 110000001 => 000010101
000001100 => 010000010 => 001000001 => 000010001
000001101 => 100000101 => 110000010 => 000010110
000001110 => 100000110 => 010000011 => 000010011
000001111 => 000001111 => 100000111 => 000010111
000010000 => 000100000 => 000010000 => 000100000
000010001 => 001000001 => 100100000 => 000100010
000010010 => 101000000 => 010100000 => 000100100
000010011 => 010000011 => 101000001 => 000100101
000010100 => 011000000 => 001100000 => 000101000
000010101 => 110000001 => 111000000 => 000101010
000010110 => 110000010 => 011000001 => 000101001
000010111 => 100000111 => 110000011 => 000101011
000011000 => 001000010 => 000100001 => 000100001
000011001 => 010000101 => 101000010 => 000100110
000011010 => 110000100 => 011000010 => 000101100
000011011 => 100001011 => 110000101 => 000101101
000011100 => 010000110 => 001000011 => 000100011
000011101 => 100001101 => 110000110 => 000101110
000011110 => 100001110 => 010000111 => 000100111
000011111 => 000011111 => 100001111 => 000101111
000100000 => 000010000 => 000001000 => 001000000
000100001 => 000100001 => 100010000 => 001000010
000100010 => 100100000 => 010010000 => 001000100
000100011 => 001000011 => 100100001 => 001000101
000100100 => 010100000 => 001010000 => 001001000
000100101 => 101000001 => 110100000 => 001001010
000100110 => 101000010 => 010100001 => 001001001
000100111 => 010000111 => 101000011 => 001001011
000101000 => 001100000 => 000110000 => 001010000
000101001 => 011000001 => 101100000 => 001010010
000101010 => 111000000 => 011100000 => 001010100
000101011 => 110000011 => 111000001 => 001010101
000101100 => 011000010 => 001100001 => 001010001
000101101 => 110000101 => 111000010 => 001010110
000101110 => 110000110 => 011000011 => 001010011
000101111 => 100001111 => 110000111 => 001010111
000110000 => 000100010 => 000010001 => 001000001
000110001 => 001000101 => 100100010 => 001000110
000110010 => 101000100 => 010100010 => 001001100
000110011 => 010001011 => 101000101 => 001001101
000110100 => 011000100 => 001100010 => 001011000
000110101 => 110001001 => 111000100 => 001011010
000110110 => 110001010 => 011000101 => 001011001
000110111 => 100010111 => 110001011 => 001011011
000111000 => 001000110 => 000100011 => 001000011
000111001 => 010001101 => 101000110 => 001001110
000111010 => 110001100 => 011000110 => 001011100
000111011 => 100011011 => 110001101 => 001011101
000111100 => 010001110 => 001000111 => 001000111
000111101 => 100011101 => 110001110 => 001011110
000111110 => 100011110 => 010001111 => 001001111
000111111 => 000111111 => 100011111 => 001011111
001000000 => 000001000 => 000000100 => 010000000
001000001 => 000010001 => 100001000 => 010000010
001000010 => 100010000 => 010001000 => 010000100
001000011 => 000100011 => 100010001 => 010000101
001000100 => 010010000 => 001001000 => 010001000
001000101 => 100100001 => 110010000 => 010001010
001000110 => 100100010 => 010010001 => 010001001
001000111 => 001000111 => 100100011 => 010001011
001001000 => 001010000 => 000101000 => 010010000
001001001 => 010100001 => 101010000 => 010010010
001001010 => 110100000 => 011010000 => 010010100
001001011 => 101000011 => 110100001 => 010010101
001001100 => 010100010 => 001010001 => 010010001
001001101 => 101000101 => 110100010 => 010010110
001001110 => 101000110 => 010100011 => 010010011
001001111 => 010001111 => 101000111 => 010010111
001010000 => 000110000 => 000011000 => 010100000
001010001 => 001100001 => 100110000 => 010100010
001010010 => 101100000 => 010110000 => 010100100
001010011 => 011000011 => 101100001 => 010100101
001010100 => 011100000 => 001110000 => 010101000
001010101 => 111000001 => 111100000 => 010101010
001010110 => 111000010 => 011100001 => 010101001
001010111 => 110000111 => 111000011 => 010101011
001011000 => 001100010 => 000110001 => 010100001
001011001 => 011000101 => 101100010 => 010100110
001011010 => 111000100 => 011100010 => 010101100
001011011 => 110001011 => 111000101 => 010101101
001011100 => 011000110 => 001100011 => 010100011
001011101 => 110001101 => 111000110 => 010101110
001011110 => 110001110 => 011000111 => 010100111
001011111 => 100011111 => 110001111 => 010101111
001100000 => 000010010 => 000001001 => 010000001
001100001 => 000100101 => 100010010 => 010000110
001100010 => 100100100 => 010010010 => 010001100
001100011 => 001001011 => 100100101 => 010001101
001100100 => 010100100 => 001010010 => 010011000
001100101 => 101001001 => 110100100 => 010011010
001100110 => 101001010 => 010100101 => 010011001
001100111 => 010010111 => 101001011 => 010011011
001101000 => 001100100 => 000110010 => 010110000
001101001 => 011001001 => 101100100 => 010110010
001101010 => 111001000 => 011100100 => 010110100
001101011 => 110010011 => 111001001 => 010110101
001101100 => 011001010 => 001100101 => 010110001
001101101 => 110010101 => 111001010 => 010110110
001101110 => 110010110 => 011001011 => 010110011
001101111 => 100101111 => 110010111 => 010110111
001110000 => 000100110 => 000010011 => 010000011
001110001 => 001001101 => 100100110 => 010001110
001110010 => 101001100 => 010100110 => 010011100
001110011 => 010011011 => 101001101 => 010011101
001110100 => 011001100 => 001100110 => 010111000
001110101 => 110011001 => 111001100 => 010111010
001110110 => 110011010 => 011001101 => 010111001
001110111 => 100110111 => 110011011 => 010111011
001111000 => 001001110 => 000100111 => 010000111
001111001 => 010011101 => 101001110 => 010011110
001111010 => 110011100 => 011001110 => 010111100
001111011 => 100111011 => 110011101 => 010111101
001111100 => 010011110 => 001001111 => 010001111
001111101 => 100111101 => 110011110 => 010111110
001111110 => 100111110 => 010011111 => 010011111
001111111 => 001111111 => 100111111 => 010111111
010000000 => 000000100 => 000000010 => 100000000
010000001 => 000001001 => 100000100 => 100000010
010000010 => 100001000 => 010000100 => 100000100
010000011 => 000010011 => 100001001 => 100000101
010000100 => 010001000 => 001000100 => 100001000
010000101 => 100010001 => 110001000 => 100001010
010000110 => 100010010 => 010001001 => 100001001
010000111 => 000100111 => 100010011 => 100001011
010001000 => 001001000 => 000100100 => 100010000
010001001 => 010010001 => 101001000 => 100010010
010001010 => 110010000 => 011001000 => 100010100
010001011 => 100100011 => 110010001 => 100010101
010001100 => 010010010 => 001001001 => 100010001
010001101 => 100100101 => 110010010 => 100010110
010001110 => 100100110 => 010010011 => 100010011
010001111 => 001001111 => 100100111 => 100010111
010010000 => 000101000 => 000010100 => 100100000
010010001 => 001010001 => 100101000 => 100100010
010010010 => 101010000 => 010101000 => 100100100
010010011 => 010100011 => 101010001 => 100100101
010010100 => 011010000 => 001101000 => 100101000
010010101 => 110100001 => 111010000 => 100101010
010010110 => 110100010 => 011010001 => 100101001
010010111 => 101000111 => 110100011 => 100101011
010011000 => 001010010 => 000101001 => 100100001
010011001 => 010100101 => 101010010 => 100100110
010011010 => 110100100 => 011010010 => 100101100
010011011 => 101001011 => 110100101 => 100101101
010011100 => 010100110 => 001010011 => 100100011
010011101 => 101001101 => 110100110 => 100101110
010011110 => 101001110 => 010100111 => 100100111
010011111 => 010011111 => 101001111 => 100101111
010100000 => 000011000 => 000001100 => 101000000
010100001 => 000110001 => 100011000 => 101000010
010100010 => 100110000 => 010011000 => 101000100
010100011 => 001100011 => 100110001 => 101000101
010100100 => 010110000 => 001011000 => 101001000
010100101 => 101100001 => 110110000 => 101001010
010100110 => 101100010 => 010110001 => 101001001
010100111 => 011000111 => 101100011 => 101001011
010101000 => 001110000 => 000111000 => 101010000
010101001 => 011100001 => 101110000 => 101010010
010101010 => 111100000 => 011110000 => 101010100
010101011 => 111000011 => 111100001 => 101010101
010101100 => 011100010 => 001110001 => 101010001
010101101 => 111000101 => 111100010 => 101010110
010101110 => 111000110 => 011100011 => 101010011
010101111 => 110001111 => 111000111 => 101010111
010110000 => 000110010 => 000011001 => 101000001
010110001 => 001100101 => 100110010 => 101000110
010110010 => 101100100 => 010110010 => 101001100
010110011 => 011001011 => 101100101 => 101001101
010110100 => 011100100 => 001110010 => 101011000
010110101 => 111001001 => 111100100 => 101011010
010110110 => 111001010 => 011100101 => 101011001
010110111 => 110010111 => 111001011 => 101011011
010111000 => 001100110 => 000110011 => 101000011
010111001 => 011001101 => 101100110 => 101001110
010111010 => 111001100 => 011100110 => 101011100
010111011 => 110011011 => 111001101 => 101011101
010111100 => 011001110 => 001100111 => 101000111
010111101 => 110011101 => 111001110 => 101011110
010111110 => 110011110 => 011001111 => 101001111
010111111 => 100111111 => 110011111 => 101011111
011000000 => 000001010 => 000000101 => 100000001
011000001 => 000010101 => 100001010 => 100000110
011000010 => 100010100 => 010001010 => 100001100
011000011 => 000101011 => 100010101 => 100001101
011000100 => 010010100 => 001001010 => 100011000
011000101 => 100101001 => 110010100 => 100011010
011000110 => 100101010 => 010010101 => 100011001
011000111 => 001010111 => 100101011 => 100011011
011001000 => 001010100 => 000101010 => 100110000
011001001 => 010101001 => 101010100 => 100110010
011001010 => 110101000 => 011010100 => 100110100
011001011 => 101010011 => 110101001 => 100110101
011001100 => 010101010 => 001010101 => 100110001
011001101 => 101010101 => 110101010 => 100110110
011001110 => 101010110 => 010101011 => 100110011
011001111 => 010101111 => 101010111 => 100110111
011010000 => 000110100 => 000011010 => 101100000
011010001 => 001101001 => 100110100 => 101100010
011010010 => 101101000 => 010110100 => 101100100
011010011 => 011010011 => 101101001 => 101100101
011010100 => 011101000 => 001110100 => 101101000
011010101 => 111010001 => 111101000 => 101101010
011010110 => 111010010 => 011101001 => 101101001
011010111 => 110100111 => 111010011 => 101101011
011011000 => 001101010 => 000110101 => 101100001
011011001 => 011010101 => 101101010 => 101100110
011011010 => 111010100 => 011101010 => 101101100
011011011 => 110101011 => 111010101 => 101101101
011011100 => 011010110 => 001101011 => 101100011
011011101 => 110101101 => 111010110 => 101101110
011011110 => 110101110 => 011010111 => 101100111
011011111 => 101011111 => 110101111 => 101101111
011100000 => 000010110 => 000001011 => 100000011
011100001 => 000101101 => 100010110 => 100001110
011100010 => 100101100 => 010010110 => 100011100
011100011 => 001011011 => 100101101 => 100011101
011100100 => 010101100 => 001010110 => 100111000
011100101 => 101011001 => 110101100 => 100111010
011100110 => 101011010 => 010101101 => 100111001
011100111 => 010110111 => 101011011 => 100111011
011101000 => 001101100 => 000110110 => 101110000
011101001 => 011011001 => 101101100 => 101110010
011101010 => 111011000 => 011101100 => 101110100
011101011 => 110110011 => 111011001 => 101110101
011101100 => 011011010 => 001101101 => 101110001
011101101 => 110110101 => 111011010 => 101110110
011101110 => 110110110 => 011011011 => 101110011
011101111 => 101101111 => 110110111 => 101110111
011110000 => 000101110 => 000010111 => 100000111
011110001 => 001011101 => 100101110 => 100011110
011110010 => 101011100 => 010101110 => 100111100
011110011 => 010111011 => 101011101 => 100111101
011110100 => 011011100 => 001101110 => 101111000
011110101 => 110111001 => 111011100 => 101111010
011110110 => 110111010 => 011011101 => 101111001
011110111 => 101110111 => 110111011 => 101111011
011111000 => 001011110 => 000101111 => 100001111
011111001 => 010111101 => 101011110 => 100111110
011111010 => 110111100 => 011011110 => 101111100
011111011 => 101111011 => 110111101 => 101111101
011111100 => 010111110 => 001011111 => 100011111
011111101 => 101111101 => 110111110 => 101111110
011111110 => 101111110 => 010111111 => 100111111
011111111 => 011111111 => 101111111 => 101111111
100000000 => 000000010 => 000000001 => 000000001
100000001 => 000000101 => 100000010 => 000000110
100000010 => 100000100 => 010000010 => 000001100
100000011 => 000001011 => 100000101 => 000001101
100000100 => 010000100 => 001000010 => 000011000
100000101 => 100001001 => 110000100 => 000011010
100000110 => 100001010 => 010000101 => 000011001
100000111 => 000010111 => 100001011 => 000011011
100001000 => 001000100 => 000100010 => 000110000
100001001 => 010001001 => 101000100 => 000110010
100001010 => 110001000 => 011000100 => 000110100
100001011 => 100010011 => 110001001 => 000110101
100001100 => 010001010 => 001000101 => 000110001
100001101 => 100010101 => 110001010 => 000110110
100001110 => 100010110 => 010001011 => 000110011
100001111 => 000101111 => 100010111 => 000110111
100010000 => 000100100 => 000010010 => 001100000
100010001 => 001001001 => 100100100 => 001100010
100010010 => 101001000 => 010100100 => 001100100
100010011 => 010010011 => 101001001 => 001100101
100010100 => 011001000 => 001100100 => 001101000
100010101 => 110010001 => 111001000 => 001101010
100010110 => 110010010 => 011001001 => 001101001
100010111 => 100100111 => 110010011 => 001101011
100011000 => 001001010 => 000100101 => 001100001
100011001 => 010010101 => 101001010 => 001100110
100011010 => 110010100 => 011001010 => 001101100
100011011 => 100101011 => 110010101 => 001101101
100011100 => 010010110 => 001001011 => 001100011
100011101 => 100101101 => 110010110 => 001101110
100011110 => 100101110 => 010010111 => 001100111
100011111 => 001011111 => 100101111 => 001101111
100100000 => 000010100 => 000001010 => 011000000
100100001 => 000101001 => 100010100 => 011000010
100100010 => 100101000 => 010010100 => 011000100
100100011 => 001010011 => 100101001 => 011000101
100100100 => 010101000 => 001010100 => 011001000
100100101 => 101010001 => 110101000 => 011001010
100100110 => 101010010 => 010101001 => 011001001
100100111 => 010100111 => 101010011 => 011001011
100101000 => 001101000 => 000110100 => 011010000
100101001 => 011010001 => 101101000 => 011010010
100101010 => 111010000 => 011101000 => 011010100
100101011 => 110100011 => 111010001 => 011010101
100101100 => 011010010 => 001101001 => 011010001
100101101 => 110100101 => 111010010 => 011010110
100101110 => 110100110 => 011010011 => 011010011
100101111 => 101001111 => 110100111 => 011010111
100110000 => 000101010 => 000010101 => 011000001
100110001 => 001010101 => 100101010 => 011000110
100110010 => 101010100 => 010101010 => 011001100
100110011 => 010101011 => 101010101 => 011001101
100110100 => 011010100 => 001101010 => 011011000
100110101 => 110101001 => 111010100 => 011011010
100110110 => 110101010 => 011010101 => 011011001
100110111 => 101010111 => 110101011 => 011011011
100111000 => 001010110 => 000101011 => 011000011
100111001 => 010101101 => 101010110 => 011001110
100111010 => 110101100 => 011010110 => 011011100
100111011 => 101011011 => 110101101 => 011011101
100111100 => 010101110 => 001010111 => 011000111
100111101 => 101011101 => 110101110 => 011011110
100111110 => 101011110 => 010101111 => 011001111
100111111 => 010111111 => 101011111 => 011011111
101000000 => 000001100 => 000000110 => 110000000
101000001 => 000011001 => 100001100 => 110000010
101000010 => 100011000 => 010001100 => 110000100
101000011 => 000110011 => 100011001 => 110000101
101000100 => 010011000 => 001001100 => 110001000
101000101 => 100110001 => 110011000 => 110001010
101000110 => 100110010 => 010011001 => 110001001
101000111 => 001100111 => 100110011 => 110001011
101001000 => 001011000 => 000101100 => 110010000
101001001 => 010110001 => 101011000 => 110010010
101001010 => 110110000 => 011011000 => 110010100
101001011 => 101100011 => 110110001 => 110010101
101001100 => 010110010 => 001011001 => 110010001
101001101 => 101100101 => 110110010 => 110010110
101001110 => 101100110 => 010110011 => 110010011
101001111 => 011001111 => 101100111 => 110010111
101010000 => 000111000 => 000011100 => 110100000
101010001 => 001110001 => 100111000 => 110100010
101010010 => 101110000 => 010111000 => 110100100
101010011 => 011100011 => 101110001 => 110100101
101010100 => 011110000 => 001111000 => 110101000
101010101 => 111100001 => 111110000 => 110101010
101010110 => 111100010 => 011110001 => 110101001
101010111 => 111000111 => 111100011 => 110101011
101011000 => 001110010 => 000111001 => 110100001
101011001 => 011100101 => 101110010 => 110100110
101011010 => 111100100 => 011110010 => 110101100
101011011 => 111001011 => 111100101 => 110101101
101011100 => 011100110 => 001110011 => 110100011
101011101 => 111001101 => 111100110 => 110101110
101011110 => 111001110 => 011100111 => 110100111
101011111 => 110011111 => 111001111 => 110101111
101100000 => 000011010 => 000001101 => 110000001
101100001 => 000110101 => 100011010 => 110000110
101100010 => 100110100 => 010011010 => 110001100
101100011 => 001101011 => 100110101 => 110001101
101100100 => 010110100 => 001011010 => 110011000
101100101 => 101101001 => 110110100 => 110011010
101100110 => 101101010 => 010110101 => 110011001
101100111 => 011010111 => 101101011 => 110011011
101101000 => 001110100 => 000111010 => 110110000
101101001 => 011101001 => 101110100 => 110110010
101101010 => 111101000 => 011110100 => 110110100
101101011 => 111010011 => 111101001 => 110110101
101101100 => 011101010 => 001110101 => 110110001
101101101 => 111010101 => 111101010 => 110110110
101101110 => 111010110 => 011101011 => 110110011
101101111 => 110101111 => 111010111 => 110110111
101110000 => 000110110 => 000011011 => 110000011
101110001 => 001101101 => 100110110 => 110001110
101110010 => 101101100 => 010110110 => 110011100
101110011 => 011011011 => 101101101 => 110011101
101110100 => 011101100 => 001110110 => 110111000
101110101 => 111011001 => 111101100 => 110111010
101110110 => 111011010 => 011101101 => 110111001
101110111 => 110110111 => 111011011 => 110111011
101111000 => 001101110 => 000110111 => 110000111
101111001 => 011011101 => 101101110 => 110011110
101111010 => 111011100 => 011101110 => 110111100
101111011 => 110111011 => 111011101 => 110111101
101111100 => 011011110 => 001101111 => 110001111
101111101 => 110111101 => 111011110 => 110111110
101111110 => 110111110 => 011011111 => 110011111
101111111 => 101111111 => 110111111 => 110111111
110000000 => 000000110 => 000000011 => 000000011
110000001 => 000001101 => 100000110 => 000001110
110000010 => 100001100 => 010000110 => 000011100
110000011 => 000011011 => 100001101 => 000011101
110000100 => 010001100 => 001000110 => 000111000
110000101 => 100011001 => 110001100 => 000111010
110000110 => 100011010 => 010001101 => 000111001
110000111 => 000110111 => 100011011 => 000111011
110001000 => 001001100 => 000100110 => 001110000
110001001 => 010011001 => 101001100 => 001110010
110001010 => 110011000 => 011001100 => 001110100
110001011 => 100110011 => 110011001 => 001110101
110001100 => 010011010 => 001001101 => 001110001
110001101 => 100110101 => 110011010 => 001110110
110001110 => 100110110 => 010011011 => 001110011
110001111 => 001101111 => 100110111 => 001110111
110010000 => 000101100 => 000010110 => 011100000
110010001 => 001011001 => 100101100 => 011100010
110010010 => 101011000 => 010101100 => 011100100
110010011 => 010110011 => 101011001 => 011100101
110010100 => 011011000 => 001101100 => 011101000
110010101 => 110110001 => 111011000 => 011101010
110010110 => 110110010 => 011011001 => 011101001
110010111 => 101100111 => 110110011 => 011101011
110011000 => 001011010 => 000101101 => 011100001
110011001 => 010110101 => 101011010 => 011100110
110011010 => 110110100 => 011011010 => 011101100
110011011 => 101101011 => 110110101 => 011101101
110011100 => 010110110 => 001011011 => 011100011
110011101 => 101101101 => 110110110 => 011101110
110011110 => 101101110 => 010110111 => 011100111
110011111 => 011011111 => 101101111 => 011101111
110100000 => 000011100 => 000001110 => 111000000
110100001 => 000111001 => 100011100 => 111000010
110100010 => 100111000 => 010011100 => 111000100
110100011 => 001110011 => 100111001 => 111000101
110100100 => 010111000 => 001011100 => 111001000
110100101 => 101110001 => 110111000 => 111001010
110100110 => 101110010 => 010111001 => 111001001
110100111 => 011100111 => 101110011 => 111001011
110101000 => 001111000 => 000111100 => 111010000
110101001 => 011110001 => 101111000 => 111010010
110101010 => 111110000 => 011111000 => 111010100
110101011 => 111100011 => 111110001 => 111010101
110101100 => 011110010 => 001111001 => 111010001
110101101 => 111100101 => 111110010 => 111010110
110101110 => 111100110 => 011110011 => 111010011
110101111 => 111001111 => 111100111 => 111010111
110110000 => 000111010 => 000011101 => 111000001
110110001 => 001110101 => 100111010 => 111000110
110110010 => 101110100 => 010111010 => 111001100
110110011 => 011101011 => 101110101 => 111001101
110110100 => 011110100 => 001111010 => 111011000
110110101 => 111101001 => 111110100 => 111011010
110110110 => 111101010 => 011110101 => 111011001
110110111 => 111010111 => 111101011 => 111011011
110111000 => 001110110 => 000111011 => 111000011
110111001 => 011101101 => 101110110 => 111001110
110111010 => 111101100 => 011110110 => 111011100
110111011 => 111011011 => 111101101 => 111011101
110111100 => 011101110 => 001110111 => 111000111
110111101 => 111011101 => 111101110 => 111011110
110111110 => 111011110 => 011101111 => 111001111
110111111 => 110111111 => 111011111 => 111011111
111000000 => 000001110 => 000000111 => 000000111
111000001 => 000011101 => 100001110 => 000011110
111000010 => 100011100 => 010001110 => 000111100
111000011 => 000111011 => 100011101 => 000111101
111000100 => 010011100 => 001001110 => 001111000
111000101 => 100111001 => 110011100 => 001111010
111000110 => 100111010 => 010011101 => 001111001
111000111 => 001110111 => 100111011 => 001111011
111001000 => 001011100 => 000101110 => 011110000
111001001 => 010111001 => 101011100 => 011110010
111001010 => 110111000 => 011011100 => 011110100
111001011 => 101110011 => 110111001 => 011110101
111001100 => 010111010 => 001011101 => 011110001
111001101 => 101110101 => 110111010 => 011110110
111001110 => 101110110 => 010111011 => 011110011
111001111 => 011101111 => 101110111 => 011110111
111010000 => 000111100 => 000011110 => 111100000
111010001 => 001111001 => 100111100 => 111100010
111010010 => 101111000 => 010111100 => 111100100
111010011 => 011110011 => 101111001 => 111100101
111010100 => 011111000 => 001111100 => 111101000
111010101 => 111110001 => 111111000 => 111101010
111010110 => 111110010 => 011111001 => 111101001
111010111 => 111100111 => 111110011 => 111101011
111011000 => 001111010 => 000111101 => 111100001
111011001 => 011110101 => 101111010 => 111100110
111011010 => 111110100 => 011111010 => 111101100
111011011 => 111101011 => 111110101 => 111101101
111011100 => 011110110 => 001111011 => 111100011
111011101 => 111101101 => 111110110 => 111101110
111011110 => 111101110 => 011110111 => 111100111
111011111 => 111011111 => 111101111 => 111101111
111100000 => 000011110 => 000001111 => 000001111
111100001 => 000111101 => 100011110 => 000111110
111100010 => 100111100 => 010011110 => 001111100
111100011 => 001111011 => 100111101 => 001111101
111100100 => 010111100 => 001011110 => 011111000
111100101 => 101111001 => 110111100 => 011111010
111100110 => 101111010 => 010111101 => 011111001
111100111 => 011110111 => 101111011 => 011111011
111101000 => 001111100 => 000111110 => 111110000
111101001 => 011111001 => 101111100 => 111110010
111101010 => 111111000 => 011111100 => 111110100
111101011 => 111110011 => 111111001 => 111110101
111101100 => 011111010 => 001111101 => 111110001
111101101 => 111110101 => 111111010 => 111110110
111101110 => 111110110 => 011111011 => 111110011
111101111 => 111101111 => 111110111 => 111110111
111110000 => 000111110 => 000011111 => 000011111
111110001 => 001111101 => 100111110 => 001111110
111110010 => 101111100 => 010111110 => 011111100
111110011 => 011111011 => 101111101 => 011111101
111110100 => 011111100 => 001111110 => 111111000
111110101 => 111111001 => 111111100 => 111111010
111110110 => 111111010 => 011111101 => 111111001
111110111 => 111110111 => 111111011 => 111111011
111111000 => 001111110 => 000111111 => 000111111
111111001 => 011111101 => 101111110 => 011111110
111111010 => 111111100 => 011111110 => 111111100
111111011 => 111111011 => 111111101 => 111111101
111111100 => 011111110 => 001111111 => 001111111
111111101 => 111111101 => 111111110 => 111111110
111111110 => 111111110 => 011111111 => 011111111
111111111 => 111111111 => 111111111 => 111111111
1111111110 => 1111111110 => 0111111111 => 0111111111
1111111101 => 1111111101 => 1111111110 => 1111111110
1111111001 => 0111111101 => 1011111110 => 0111111110
1111110001 => 0011111101 => 1001111110 => 0011111110
1111101110 => 1111110110 => 0111111011 => 1111110011
1111100001 => 0001111101 => 1000111110 => 0001111110
1111000001 => 0000111101 => 1000011110 => 0000111110
1110000001 => 0000011101 => 1000001110 => 0000011110
1100000001 => 0000001101 => 1000000110 => 0000001110
1001010110 => 1110100010 => 0111010001 => 0110101001
1000000001 => 0000000101 => 1000000010 => 0000000110
1000000000 => 0000000010 => 0000000001 => 0000000001
10000000000 => 00000000010 => 00000000001 => 00000000001
11111111110 => 11111111110 => 01111111111 => 01111111111
0111111101 => 1011111101 => 1101111110 => 1011111110
0111111001 => 0101111101 => 1010111110 => 1001111110
0111110001 => 0010111101 => 1001011110 => 1000111110
0111100001 => 0001011101 => 1000101110 => 1000011110
0111000001 => 0000101101 => 1000010110 => 1000001110
0110000001 => 0000010101 => 1000001010 => 1000000110
0100000001 => 0000001001 => 1000000100 => 1000000010
0000000001 => 0000000001 => 1000000000 => 0000000010
00000000001 => 00000000001 => 10000000000 => 00000000010
0000000110 => 1000000010 => 0100000001 => 0000001001
00000000110 => 10000000010 => 01000000001 => 00000001001
0101010110 => 1111000010 => 0111100001 => 1010101001
11111111101 => 11111111101 => 11111111110 => 11111111110
0010010110 => 1101000010 => 0110100001 => 0100101001
11000000001 => 00000001101 => 10000000110 => 00000001110
11111111001 => 01111111101 => 10111111110 => 01111111110
0000001100 => 0100000010 => 0010000001 => 0000010001
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.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.
See Mp00096Foata bijection.
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