Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Images
=>
0=>0=>0
1=>1=>1
00=>00=>00
01=>01=>10
10=>10=>01
11=>11=>11
000=>000=>000
001=>001=>100
010=>100=>010
011=>011=>101
100=>010=>001
101=>101=>110
110=>110=>011
111=>111=>111
0000=>0000=>0000
0001=>0001=>1000
0010=>1000=>0100
0011=>0011=>1001
0100=>0100=>0010
0101=>1001=>1100
0110=>1010=>0101
0111=>0111=>1011
1000=>0010=>0001
1001=>0101=>1010
1010=>1100=>0110
1011=>1011=>1101
1100=>0110=>0011
1101=>1101=>1110
1110=>1110=>0111
1111=>1111=>1111
00000=>00000=>00000
00001=>00001=>10000
00010=>10000=>01000
00011=>00011=>10001
00100=>01000=>00100
00101=>10001=>11000
00110=>10010=>01001
00111=>00111=>10011
01000=>00100=>00010
01001=>01001=>10100
01010=>11000=>01100
01011=>10011=>11001
01100=>01010=>00101
01101=>10101=>11010
01110=>10110=>01011
01111=>01111=>10111
10000=>00010=>00001
10001=>00101=>10010
10010=>10100=>01010
10011=>01011=>10101
10100=>01100=>00110
10101=>11001=>11100
10110=>11010=>01101
10111=>10111=>11011
11000=>00110=>00011
11001=>01101=>10110
11010=>11100=>01110
11011=>11011=>11101
11100=>01110=>00111
11101=>11101=>11110
11110=>11110=>01111
11111=>11111=>11111
000000=>000000=>000000
000001=>000001=>100000
000010=>100000=>010000
000011=>000011=>100001
000100=>010000=>001000
000101=>100001=>110000
000110=>100010=>010001
000111=>000111=>100011
001000=>001000=>000100
001001=>010001=>101000
001010=>110000=>011000
001011=>100011=>110001
001100=>010010=>001001
001101=>100101=>110010
001110=>100110=>010011
001111=>001111=>100111
010000=>000100=>000010
010001=>001001=>100100
010010=>101000=>010100
010011=>010011=>101001
010100=>011000=>001100
010101=>110001=>111000
010110=>110010=>011001
010111=>100111=>110011
011000=>001010=>000101
011001=>010101=>101010
011010=>110100=>011010
011011=>101011=>110101
011100=>010110=>001011
011101=>101101=>110110
011110=>101110=>010111
011111=>011111=>101111
100000=>000010=>000001
100001=>000101=>100010
100010=>100100=>010010
100011=>001011=>100101
100100=>010100=>001010
100101=>101001=>110100
100110=>101010=>010101
100111=>010111=>101011
101000=>001100=>000110
101001=>011001=>101100
101010=>111000=>011100
101011=>110011=>111001
101100=>011010=>001101
101101=>110101=>111010
101110=>110110=>011011
101111=>101111=>110111
110000=>000110=>000011
110001=>001101=>100110
110010=>101100=>010110
110011=>011011=>101101
110100=>011100=>001110
110101=>111001=>111100
110110=>111010=>011101
110111=>110111=>111011
111000=>001110=>000111
111001=>011101=>101110
111010=>111100=>011110
111011=>111011=>111101
111100=>011110=>001111
111101=>111101=>111110
111110=>111110=>011111
111111=>111111=>111111
0000000=>0000000=>0000000
0000001=>0000001=>1000000
0000010=>1000000=>0100000
0000011=>0000011=>1000001
0000100=>0100000=>0010000
0000101=>1000001=>1100000
0000110=>1000010=>0100001
0000111=>0000111=>1000011
0001000=>0010000=>0001000
0001001=>0100001=>1010000
0001010=>1100000=>0110000
0001011=>1000011=>1100001
0001100=>0100010=>0010001
0001101=>1000101=>1100010
0001110=>1000110=>0100011
0001111=>0001111=>1000111
0010000=>0001000=>0000100
0010001=>0010001=>1001000
0010010=>1010000=>0101000
0010011=>0100011=>1010001
0010100=>0110000=>0011000
0010101=>1100001=>1110000
0010110=>1100010=>0110001
0010111=>1000111=>1100011
0011000=>0010010=>0001001
0011001=>0100101=>1010010
0011010=>1100100=>0110010
0011011=>1001011=>1100101
0011100=>0100110=>0010011
0011101=>1001101=>1100110
0011110=>1001110=>0100111
0011111=>0011111=>1001111
0100000=>0000100=>0000010
0100001=>0001001=>1000100
0100010=>1001000=>0100100
0100011=>0010011=>1001001
0100100=>0101000=>0010100
0100101=>1010001=>1101000
0100110=>1010010=>0101001
0100111=>0100111=>1010011
0101000=>0011000=>0001100
0101001=>0110001=>1011000
0101010=>1110000=>0111000
0101011=>1100011=>1110001
0101100=>0110010=>0011001
0101101=>1100101=>1110010
0101110=>1100110=>0110011
0101111=>1001111=>1100111
0110000=>0001010=>0000101
0110001=>0010101=>1001010
0110010=>1010100=>0101010
0110011=>0101011=>1010101
0110100=>0110100=>0011010
0110101=>1101001=>1110100
0110110=>1101010=>0110101
0110111=>1010111=>1101011
0111000=>0010110=>0001011
0111001=>0101101=>1010110
0111010=>1101100=>0110110
0111011=>1011011=>1101101
0111100=>0101110=>0010111
0111101=>1011101=>1101110
0111110=>1011110=>0101111
0111111=>0111111=>1011111
1000000=>0000010=>0000001
1000001=>0000101=>1000010
1000010=>1000100=>0100010
1000011=>0001011=>1000101
1000100=>0100100=>0010010
1000101=>1001001=>1100100
1000110=>1001010=>0100101
1000111=>0010111=>1001011
1001000=>0010100=>0001010
1001001=>0101001=>1010100
1001010=>1101000=>0110100
1001011=>1010011=>1101001
1001100=>0101010=>0010101
1001101=>1010101=>1101010
1001110=>1010110=>0101011
1001111=>0101111=>1010111
1010000=>0001100=>0000110
1010001=>0011001=>1001100
1010010=>1011000=>0101100
1010011=>0110011=>1011001
1010100=>0111000=>0011100
1010101=>1110001=>1111000
1010110=>1110010=>0111001
1010111=>1100111=>1110011
1011000=>0011010=>0001101
1011001=>0110101=>1011010
1011010=>1110100=>0111010
1011011=>1101011=>1110101
1011100=>0110110=>0011011
1011101=>1101101=>1110110
1011110=>1101110=>0110111
1011111=>1011111=>1101111
1100000=>0000110=>0000011
1100001=>0001101=>1000110
1100010=>1001100=>0100110
1100011=>0011011=>1001101
1100100=>0101100=>0010110
1100101=>1011001=>1101100
1100110=>1011010=>0101101
1100111=>0110111=>1011011
1101000=>0011100=>0001110
1101001=>0111001=>1011100
1101010=>1111000=>0111100
1101011=>1110011=>1111001
1101100=>0111010=>0011101
1101101=>1110101=>1111010
1101110=>1110110=>0111011
1101111=>1101111=>1110111
1110000=>0001110=>0000111
1110001=>0011101=>1001110
1110010=>1011100=>0101110
1110011=>0111011=>1011101
1110100=>0111100=>0011110
1110101=>1111001=>1111100
1110110=>1111010=>0111101
1110111=>1110111=>1111011
1111000=>0011110=>0001111
1111001=>0111101=>1011110
1111010=>1111100=>0111110
1111011=>1111011=>1111101
1111100=>0111110=>0011111
1111101=>1111101=>1111110
1111110=>1111110=>0111111
1111111=>1111111=>1111111
00000000=>00000000=>00000000
00000001=>00000001=>10000000
00000010=>10000000=>01000000
00000011=>00000011=>10000001
00000100=>01000000=>00100000
00000101=>10000001=>11000000
00000110=>10000010=>01000001
00000111=>00000111=>10000011
00001000=>00100000=>00010000
00001001=>01000001=>10100000
00001010=>11000000=>01100000
00001011=>10000011=>11000001
00001100=>01000010=>00100001
00001101=>10000101=>11000010
00001110=>10000110=>01000011
00001111=>00001111=>10000111
00010000=>00010000=>00001000
00010001=>00100001=>10010000
00010010=>10100000=>01010000
00010011=>01000011=>10100001
00010100=>01100000=>00110000
00010101=>11000001=>11100000
00010110=>11000010=>01100001
00010111=>10000111=>11000011
00011000=>00100010=>00010001
00011001=>01000101=>10100010
00011010=>11000100=>01100010
00011011=>10001011=>11000101
00011100=>01000110=>00100011
00011101=>10001101=>11000110
00011110=>10001110=>01000111
00011111=>00011111=>10001111
00100000=>00001000=>00000100
00100001=>00010001=>10001000
00100010=>10010000=>01001000
00100011=>00100011=>10010001
00100100=>01010000=>00101000
00100101=>10100001=>11010000
00100110=>10100010=>01010001
00100111=>01000111=>10100011
00101000=>00110000=>00011000
00101001=>01100001=>10110000
00101010=>11100000=>01110000
00101011=>11000011=>11100001
00101100=>01100010=>00110001
00101101=>11000101=>11100010
00101110=>11000110=>01100011
00101111=>10001111=>11000111
00110000=>00010010=>00001001
00110001=>00100101=>10010010
00110010=>10100100=>01010010
00110011=>01001011=>10100101
00110100=>01100100=>00110010
00110101=>11001001=>11100100
00110110=>11001010=>01100101
00110111=>10010111=>11001011
00111000=>00100110=>00010011
00111001=>01001101=>10100110
00111010=>11001100=>01100110
00111011=>10011011=>11001101
00111100=>01001110=>00100111
00111101=>10011101=>11001110
00111110=>10011110=>01001111
00111111=>00111111=>10011111
01000000=>00000100=>00000010
01000001=>00001001=>10000100
01000010=>10001000=>01000100
01000011=>00010011=>10001001
01000100=>01001000=>00100100
01000101=>10010001=>11001000
01000110=>10010010=>01001001
01000111=>00100111=>10010011
01001000=>00101000=>00010100
01001001=>01010001=>10101000
01001010=>11010000=>01101000
01001011=>10100011=>11010001
01001100=>01010010=>00101001
01001101=>10100101=>11010010
01001110=>10100110=>01010011
01001111=>01001111=>10100111
01010000=>00011000=>00001100
01010001=>00110001=>10011000
01010010=>10110000=>01011000
01010011=>01100011=>10110001
01010100=>01110000=>00111000
01010101=>11100001=>11110000
01010110=>11100010=>01110001
01010111=>11000111=>11100011
01011000=>00110010=>00011001
01011001=>01100101=>10110010
01011010=>11100100=>01110010
01011011=>11001011=>11100101
01011100=>01100110=>00110011
01011101=>11001101=>11100110
01011110=>11001110=>01100111
01011111=>10011111=>11001111
01100000=>00001010=>00000101
01100001=>00010101=>10001010
01100010=>10010100=>01001010
01100011=>00101011=>10010101
01100100=>01010100=>00101010
01100101=>10101001=>11010100
01100110=>10101010=>01010101
01100111=>01010111=>10101011
01101000=>00110100=>00011010
01101001=>01101001=>10110100
01101010=>11101000=>01110100
01101011=>11010011=>11101001
01101100=>01101010=>00110101
01101101=>11010101=>11101010
01101110=>11010110=>01101011
01101111=>10101111=>11010111
01110000=>00010110=>00001011
01110001=>00101101=>10010110
01110010=>10101100=>01010110
01110011=>01011011=>10101101
01110100=>01101100=>00110110
01110101=>11011001=>11101100
01110110=>11011010=>01101101
01110111=>10110111=>11011011
01111000=>00101110=>00010111
01111001=>01011101=>10101110
01111010=>11011100=>01101110
01111011=>10111011=>11011101
01111100=>01011110=>00101111
01111101=>10111101=>11011110
01111110=>10111110=>01011111
01111111=>01111111=>10111111
10000000=>00000010=>00000001
10000001=>00000101=>10000010
10000010=>10000100=>01000010
10000011=>00001011=>10000101
10000100=>01000100=>00100010
10000101=>10001001=>11000100
10000110=>10001010=>01000101
10000111=>00010111=>10001011
10001000=>00100100=>00010010
10001001=>01001001=>10100100
10001010=>11001000=>01100100
10001011=>10010011=>11001001
10001100=>01001010=>00100101
10001101=>10010101=>11001010
10001110=>10010110=>01001011
10001111=>00101111=>10010111
10010000=>00010100=>00001010
10010001=>00101001=>10010100
10010010=>10101000=>01010100
10010011=>01010011=>10101001
10010100=>01101000=>00110100
10010101=>11010001=>11101000
10010110=>11010010=>01101001
10010111=>10100111=>11010011
10011000=>00101010=>00010101
10011001=>01010101=>10101010
10011010=>11010100=>01101010
10011011=>10101011=>11010101
10011100=>01010110=>00101011
10011101=>10101101=>11010110
10011110=>10101110=>01010111
10011111=>01011111=>10101111
10100000=>00001100=>00000110
10100001=>00011001=>10001100
10100010=>10011000=>01001100
10100011=>00110011=>10011001
10100100=>01011000=>00101100
10100101=>10110001=>11011000
10100110=>10110010=>01011001
10100111=>01100111=>10110011
10101000=>00111000=>00011100
10101001=>01110001=>10111000
10101010=>11110000=>01111000
10101011=>11100011=>11110001
10101100=>01110010=>00111001
10101101=>11100101=>11110010
10101110=>11100110=>01110011
10101111=>11001111=>11100111
10110000=>00011010=>00001101
10110001=>00110101=>10011010
10110010=>10110100=>01011010
10110011=>01101011=>10110101
10110100=>01110100=>00111010
10110101=>11101001=>11110100
10110110=>11101010=>01110101
10110111=>11010111=>11101011
10111000=>00110110=>00011011
10111001=>01101101=>10110110
10111010=>11101100=>01110110
10111011=>11011011=>11101101
10111100=>01101110=>00110111
10111101=>11011101=>11101110
10111110=>11011110=>01101111
10111111=>10111111=>11011111
11000000=>00000110=>00000011
11000001=>00001101=>10000110
11000010=>10001100=>01000110
11000011=>00011011=>10001101
11000100=>01001100=>00100110
11000101=>10011001=>11001100
11000110=>10011010=>01001101
11000111=>00110111=>10011011
11001000=>00101100=>00010110
11001001=>01011001=>10101100
11001010=>11011000=>01101100
11001011=>10110011=>11011001
11001100=>01011010=>00101101
11001101=>10110101=>11011010
11001110=>10110110=>01011011
11001111=>01101111=>10110111
11010000=>00011100=>00001110
11010001=>00111001=>10011100
11010010=>10111000=>01011100
11010011=>01110011=>10111001
11010100=>01111000=>00111100
11010101=>11110001=>11111000
11010110=>11110010=>01111001
11010111=>11100111=>11110011
11011000=>00111010=>00011101
11011001=>01110101=>10111010
11011010=>11110100=>01111010
11011011=>11101011=>11110101
11011100=>01110110=>00111011
11011101=>11101101=>11110110
11011110=>11101110=>01110111
11011111=>11011111=>11101111
11100000=>00001110=>00000111
11100001=>00011101=>10001110
11100010=>10011100=>01001110
11100011=>00111011=>10011101
11100100=>01011100=>00101110
11100101=>10111001=>11011100
11100110=>10111010=>01011101
11100111=>01110111=>10111011
11101000=>00111100=>00011110
11101001=>01111001=>10111100
11101010=>11111000=>01111100
11101011=>11110011=>11111001
11101100=>01111010=>00111101
11101101=>11110101=>11111010
11101110=>11110110=>01111011
11101111=>11101111=>11110111
11110000=>00011110=>00001111
11110001=>00111101=>10011110
11110010=>10111100=>01011110
11110011=>01111011=>10111101
11110100=>01111100=>00111110
11110101=>11111001=>11111100
11110110=>11111010=>01111101
11110111=>11110111=>11111011
11111000=>00111110=>00011111
11111001=>01111101=>10111110
11111010=>11111100=>01111110
11111011=>11111011=>11111101
11111100=>01111110=>00111111
11111101=>11111101=>11111110
11111110=>11111110=>01111111
11111111=>11111111=>11111111
000000000=>000000000=>000000000
000000001=>000000001=>100000000
000000010=>100000000=>010000000
000000011=>000000011=>100000001
000000100=>010000000=>001000000
000000101=>100000001=>110000000
000000110=>100000010=>010000001
000000111=>000000111=>100000011
000001000=>001000000=>000100000
000001001=>010000001=>101000000
000001010=>110000000=>011000000
000001011=>100000011=>110000001
000001100=>010000010=>001000001
000001101=>100000101=>110000010
000001110=>100000110=>010000011
000001111=>000001111=>100000111
000010000=>000100000=>000010000
000010001=>001000001=>100100000
000010010=>101000000=>010100000
000010011=>010000011=>101000001
000010100=>011000000=>001100000
000010101=>110000001=>111000000
000010110=>110000010=>011000001
000010111=>100000111=>110000011
000011000=>001000010=>000100001
000011001=>010000101=>101000010
000011010=>110000100=>011000010
000011011=>100001011=>110000101
000011100=>010000110=>001000011
000011101=>100001101=>110000110
000011110=>100001110=>010000111
000011111=>000011111=>100001111
000100000=>000010000=>000001000
000100001=>000100001=>100010000
000100010=>100100000=>010010000
000100011=>001000011=>100100001
000100100=>010100000=>001010000
000100101=>101000001=>110100000
000100110=>101000010=>010100001
000100111=>010000111=>101000011
000101000=>001100000=>000110000
000101001=>011000001=>101100000
000101010=>111000000=>011100000
000101011=>110000011=>111000001
000101100=>011000010=>001100001
000101101=>110000101=>111000010
000101110=>110000110=>011000011
000101111=>100001111=>110000111
000110000=>000100010=>000010001
000110001=>001000101=>100100010
000110010=>101000100=>010100010
000110011=>010001011=>101000101
000110100=>011000100=>001100010
000110101=>110001001=>111000100
000110110=>110001010=>011000101
000110111=>100010111=>110001011
000111000=>001000110=>000100011
000111001=>010001101=>101000110
000111010=>110001100=>011000110
000111011=>100011011=>110001101
000111100=>010001110=>001000111
000111101=>100011101=>110001110
000111110=>100011110=>010001111
000111111=>000111111=>100011111
001000000=>000001000=>000000100
001000001=>000010001=>100001000
001000010=>100010000=>010001000
001000011=>000100011=>100010001
001000100=>010010000=>001001000
001000101=>100100001=>110010000
001000110=>100100010=>010010001
001000111=>001000111=>100100011
001001000=>001010000=>000101000
001001001=>010100001=>101010000
001001010=>110100000=>011010000
001001011=>101000011=>110100001
001001100=>010100010=>001010001
001001101=>101000101=>110100010
001001110=>101000110=>010100011
001001111=>010001111=>101000111
001010000=>000110000=>000011000
001010001=>001100001=>100110000
001010010=>101100000=>010110000
001010011=>011000011=>101100001
001010100=>011100000=>001110000
001010101=>111000001=>111100000
001010110=>111000010=>011100001
001010111=>110000111=>111000011
001011000=>001100010=>000110001
001011001=>011000101=>101100010
001011010=>111000100=>011100010
001011011=>110001011=>111000101
001011100=>011000110=>001100011
001011101=>110001101=>111000110
001011110=>110001110=>011000111
001011111=>100011111=>110001111
001100000=>000010010=>000001001
001100001=>000100101=>100010010
001100010=>100100100=>010010010
001100011=>001001011=>100100101
001100100=>010100100=>001010010
001100101=>101001001=>110100100
001100110=>101001010=>010100101
001100111=>010010111=>101001011
001101000=>001100100=>000110010
001101001=>011001001=>101100100
001101010=>111001000=>011100100
001101011=>110010011=>111001001
001101100=>011001010=>001100101
001101101=>110010101=>111001010
001101110=>110010110=>011001011
001101111=>100101111=>110010111
001110000=>000100110=>000010011
001110001=>001001101=>100100110
001110010=>101001100=>010100110
001110011=>010011011=>101001101
001110100=>011001100=>001100110
001110101=>110011001=>111001100
001110110=>110011010=>011001101
001110111=>100110111=>110011011
001111000=>001001110=>000100111
001111001=>010011101=>101001110
001111010=>110011100=>011001110
001111011=>100111011=>110011101
001111100=>010011110=>001001111
001111101=>100111101=>110011110
001111110=>100111110=>010011111
001111111=>001111111=>100111111
010000000=>000000100=>000000010
010000001=>000001001=>100000100
010000010=>100001000=>010000100
010000011=>000010011=>100001001
010000100=>010001000=>001000100
010000101=>100010001=>110001000
010000110=>100010010=>010001001
010000111=>000100111=>100010011
010001000=>001001000=>000100100
010001001=>010010001=>101001000
010001010=>110010000=>011001000
010001011=>100100011=>110010001
010001100=>010010010=>001001001
010001101=>100100101=>110010010
010001110=>100100110=>010010011
010001111=>001001111=>100100111
010010000=>000101000=>000010100
010010001=>001010001=>100101000
010010010=>101010000=>010101000
010010011=>010100011=>101010001
010010100=>011010000=>001101000
010010101=>110100001=>111010000
010010110=>110100010=>011010001
010010111=>101000111=>110100011
010011000=>001010010=>000101001
010011001=>010100101=>101010010
010011010=>110100100=>011010010
010011011=>101001011=>110100101
010011100=>010100110=>001010011
010011101=>101001101=>110100110
010011110=>101001110=>010100111
010011111=>010011111=>101001111
010100000=>000011000=>000001100
010100001=>000110001=>100011000
010100010=>100110000=>010011000
010100011=>001100011=>100110001
010100100=>010110000=>001011000
010100101=>101100001=>110110000
010100110=>101100010=>010110001
010100111=>011000111=>101100011
010101000=>001110000=>000111000
010101001=>011100001=>101110000
010101010=>111100000=>011110000
010101011=>111000011=>111100001
010101100=>011100010=>001110001
010101101=>111000101=>111100010
010101110=>111000110=>011100011
010101111=>110001111=>111000111
010110000=>000110010=>000011001
010110001=>001100101=>100110010
010110010=>101100100=>010110010
010110011=>011001011=>101100101
010110100=>011100100=>001110010
010110101=>111001001=>111100100
010110110=>111001010=>011100101
010110111=>110010111=>111001011
010111000=>001100110=>000110011
010111001=>011001101=>101100110
010111010=>111001100=>011100110
010111011=>110011011=>111001101
010111100=>011001110=>001100111
010111101=>110011101=>111001110
010111110=>110011110=>011001111
010111111=>100111111=>110011111
011000000=>000001010=>000000101
011000001=>000010101=>100001010
011000010=>100010100=>010001010
011000011=>000101011=>100010101
011000100=>010010100=>001001010
011000101=>100101001=>110010100
011000110=>100101010=>010010101
011000111=>001010111=>100101011
011001000=>001010100=>000101010
011001001=>010101001=>101010100
011001010=>110101000=>011010100
011001011=>101010011=>110101001
011001100=>010101010=>001010101
011001101=>101010101=>110101010
011001110=>101010110=>010101011
011001111=>010101111=>101010111
011010000=>000110100=>000011010
011010001=>001101001=>100110100
011010010=>101101000=>010110100
011010011=>011010011=>101101001
011010100=>011101000=>001110100
011010101=>111010001=>111101000
011010110=>111010010=>011101001
011010111=>110100111=>111010011
011011000=>001101010=>000110101
011011001=>011010101=>101101010
011011010=>111010100=>011101010
011011011=>110101011=>111010101
011011100=>011010110=>001101011
011011101=>110101101=>111010110
011011110=>110101110=>011010111
011011111=>101011111=>110101111
011100000=>000010110=>000001011
011100001=>000101101=>100010110
011100010=>100101100=>010010110
011100011=>001011011=>100101101
011100100=>010101100=>001010110
011100101=>101011001=>110101100
011100110=>101011010=>010101101
011100111=>010110111=>101011011
011101000=>001101100=>000110110
011101001=>011011001=>101101100
011101010=>111011000=>011101100
011101011=>110110011=>111011001
011101100=>011011010=>001101101
011101101=>110110101=>111011010
011101110=>110110110=>011011011
011101111=>101101111=>110110111
011110000=>000101110=>000010111
011110001=>001011101=>100101110
011110010=>101011100=>010101110
011110011=>010111011=>101011101
011110100=>011011100=>001101110
011110101=>110111001=>111011100
011110110=>110111010=>011011101
011110111=>101110111=>110111011
011111000=>001011110=>000101111
011111001=>010111101=>101011110
011111010=>110111100=>011011110
011111011=>101111011=>110111101
011111100=>010111110=>001011111
011111101=>101111101=>110111110
011111110=>101111110=>010111111
011111111=>011111111=>101111111
100000000=>000000010=>000000001
100000001=>000000101=>100000010
100000010=>100000100=>010000010
100000011=>000001011=>100000101
100000100=>010000100=>001000010
100000101=>100001001=>110000100
100000110=>100001010=>010000101
100000111=>000010111=>100001011
100001000=>001000100=>000100010
100001001=>010001001=>101000100
100001010=>110001000=>011000100
100001011=>100010011=>110001001
100001100=>010001010=>001000101
100001101=>100010101=>110001010
100001110=>100010110=>010001011
100001111=>000101111=>100010111
100010000=>000100100=>000010010
100010001=>001001001=>100100100
100010010=>101001000=>010100100
100010011=>010010011=>101001001
100010100=>011001000=>001100100
100010101=>110010001=>111001000
100010110=>110010010=>011001001
100010111=>100100111=>110010011
100011000=>001001010=>000100101
100011001=>010010101=>101001010
100011010=>110010100=>011001010
100011011=>100101011=>110010101
100011100=>010010110=>001001011
100011101=>100101101=>110010110
100011110=>100101110=>010010111
100011111=>001011111=>100101111
100100000=>000010100=>000001010
100100001=>000101001=>100010100
100100010=>100101000=>010010100
100100011=>001010011=>100101001
100100100=>010101000=>001010100
100100101=>101010001=>110101000
100100110=>101010010=>010101001
100100111=>010100111=>101010011
100101000=>001101000=>000110100
100101001=>011010001=>101101000
100101010=>111010000=>011101000
100101011=>110100011=>111010001
100101100=>011010010=>001101001
100101101=>110100101=>111010010
100101110=>110100110=>011010011
100101111=>101001111=>110100111
100110000=>000101010=>000010101
100110001=>001010101=>100101010
100110010=>101010100=>010101010
100110011=>010101011=>101010101
100110100=>011010100=>001101010
100110101=>110101001=>111010100
100110110=>110101010=>011010101
100110111=>101010111=>110101011
100111000=>001010110=>000101011
100111001=>010101101=>101010110
100111010=>110101100=>011010110
100111011=>101011011=>110101101
100111100=>010101110=>001010111
100111101=>101011101=>110101110
100111110=>101011110=>010101111
100111111=>010111111=>101011111
101000000=>000001100=>000000110
101000001=>000011001=>100001100
101000010=>100011000=>010001100
101000011=>000110011=>100011001
101000100=>010011000=>001001100
101000101=>100110001=>110011000
101000110=>100110010=>010011001
101000111=>001100111=>100110011
101001000=>001011000=>000101100
101001001=>010110001=>101011000
101001010=>110110000=>011011000
101001011=>101100011=>110110001
101001100=>010110010=>001011001
101001101=>101100101=>110110010
101001110=>101100110=>010110011
101001111=>011001111=>101100111
101010000=>000111000=>000011100
101010001=>001110001=>100111000
101010010=>101110000=>010111000
101010011=>011100011=>101110001
101010100=>011110000=>001111000
101010101=>111100001=>111110000
101010110=>111100010=>011110001
101010111=>111000111=>111100011
101011000=>001110010=>000111001
101011001=>011100101=>101110010
101011010=>111100100=>011110010
101011011=>111001011=>111100101
101011100=>011100110=>001110011
101011101=>111001101=>111100110
101011110=>111001110=>011100111
101011111=>110011111=>111001111
101100000=>000011010=>000001101
101100001=>000110101=>100011010
101100010=>100110100=>010011010
101100011=>001101011=>100110101
101100100=>010110100=>001011010
101100101=>101101001=>110110100
101100110=>101101010=>010110101
101100111=>011010111=>101101011
101101000=>001110100=>000111010
101101001=>011101001=>101110100
101101010=>111101000=>011110100
101101011=>111010011=>111101001
101101100=>011101010=>001110101
101101101=>111010101=>111101010
101101110=>111010110=>011101011
101101111=>110101111=>111010111
101110000=>000110110=>000011011
101110001=>001101101=>100110110
101110010=>101101100=>010110110
101110011=>011011011=>101101101
101110100=>011101100=>001110110
101110101=>111011001=>111101100
101110110=>111011010=>011101101
101110111=>110110111=>111011011
101111000=>001101110=>000110111
101111001=>011011101=>101101110
101111010=>111011100=>011101110
101111011=>110111011=>111011101
101111100=>011011110=>001101111
101111101=>110111101=>111011110
101111110=>110111110=>011011111
101111111=>101111111=>110111111
110000000=>000000110=>000000011
110000001=>000001101=>100000110
110000010=>100001100=>010000110
110000011=>000011011=>100001101
110000100=>010001100=>001000110
110000101=>100011001=>110001100
110000110=>100011010=>010001101
110000111=>000110111=>100011011
110001000=>001001100=>000100110
110001001=>010011001=>101001100
110001010=>110011000=>011001100
110001011=>100110011=>110011001
110001100=>010011010=>001001101
110001101=>100110101=>110011010
110001110=>100110110=>010011011
110001111=>001101111=>100110111
110010000=>000101100=>000010110
110010001=>001011001=>100101100
110010010=>101011000=>010101100
110010011=>010110011=>101011001
110010100=>011011000=>001101100
110010101=>110110001=>111011000
110010110=>110110010=>011011001
110010111=>101100111=>110110011
110011000=>001011010=>000101101
110011001=>010110101=>101011010
110011010=>110110100=>011011010
110011011=>101101011=>110110101
110011100=>010110110=>001011011
110011101=>101101101=>110110110
110011110=>101101110=>010110111
110011111=>011011111=>101101111
110100000=>000011100=>000001110
110100001=>000111001=>100011100
110100010=>100111000=>010011100
110100011=>001110011=>100111001
110100100=>010111000=>001011100
110100101=>101110001=>110111000
110100110=>101110010=>010111001
110100111=>011100111=>101110011
110101000=>001111000=>000111100
110101001=>011110001=>101111000
110101010=>111110000=>011111000
110101011=>111100011=>111110001
110101100=>011110010=>001111001
110101101=>111100101=>111110010
110101110=>111100110=>011110011
110101111=>111001111=>111100111
110110000=>000111010=>000011101
110110001=>001110101=>100111010
110110010=>101110100=>010111010
110110011=>011101011=>101110101
110110100=>011110100=>001111010
110110101=>111101001=>111110100
110110110=>111101010=>011110101
110110111=>111010111=>111101011
110111000=>001110110=>000111011
110111001=>011101101=>101110110
110111010=>111101100=>011110110
110111011=>111011011=>111101101
110111100=>011101110=>001110111
110111101=>111011101=>111101110
110111110=>111011110=>011101111
110111111=>110111111=>111011111
111000000=>000001110=>000000111
111000001=>000011101=>100001110
111000010=>100011100=>010001110
111000011=>000111011=>100011101
111000100=>010011100=>001001110
111000101=>100111001=>110011100
111000110=>100111010=>010011101
111000111=>001110111=>100111011
111001000=>001011100=>000101110
111001001=>010111001=>101011100
111001010=>110111000=>011011100
111001011=>101110011=>110111001
111001100=>010111010=>001011101
111001101=>101110101=>110111010
111001110=>101110110=>010111011
111001111=>011101111=>101110111
111010000=>000111100=>000011110
111010001=>001111001=>100111100
111010010=>101111000=>010111100
111010011=>011110011=>101111001
111010100=>011111000=>001111100
111010101=>111110001=>111111000
111010110=>111110010=>011111001
111010111=>111100111=>111110011
111011000=>001111010=>000111101
111011001=>011110101=>101111010
111011010=>111110100=>011111010
111011011=>111101011=>111110101
111011100=>011110110=>001111011
111011101=>111101101=>111110110
111011110=>111101110=>011110111
111011111=>111011111=>111101111
111100000=>000011110=>000001111
111100001=>000111101=>100011110
111100010=>100111100=>010011110
111100011=>001111011=>100111101
111100100=>010111100=>001011110
111100101=>101111001=>110111100
111100110=>101111010=>010111101
111100111=>011110111=>101111011
111101000=>001111100=>000111110
111101001=>011111001=>101111100
111101010=>111111000=>011111100
111101011=>111110011=>111111001
111101100=>011111010=>001111101
111101101=>111110101=>111111010
111101110=>111110110=>011111011
111101111=>111101111=>111110111
111110000=>000111110=>000011111
111110001=>001111101=>100111110
111110010=>101111100=>010111110
111110011=>011111011=>101111101
111110100=>011111100=>001111110
111110101=>111111001=>111111100
111110110=>111111010=>011111101
111110111=>111110111=>111111011
111111000=>001111110=>000111111
111111001=>011111101=>101111110
111111010=>111111100=>011111110
111111011=>111111011=>111111101
111111100=>011111110=>001111111
111111101=>111111101=>111111110
111111110=>111111110=>011111111
111111111=>111111111=>111111111
1010101010=>1111100000=>0111110000
1010110010=>1011100100=>0101110010
1010110100=>0111100100=>0011110010
1011001010=>1101101000=>0110110100
1011010010=>1011101000=>0101110100
1011010100=>0111101000=>0011110100
1100101010=>1110110000=>0111011000
1100110010=>1010110100=>0101011010
1101001010=>1101110000=>0110111000
1101010010=>1011110000=>0101111000
1101010100=>0111110000=>0011111000
1101101000=>0011110100=>0001111010
1110001010=>1100111000=>0110011100
1110010010=>1010111000=>0101011100
1110101000=>0011111000=>0001111100
1111010000=>0001111100=>0000111110
1111100000=>0000111110=>0000011111
101010101010=>111111000000=>011111100000
101010110010=>101111000100=>010111100010
101010110100=>011111000100=>001111100010
101011001010=>110111001000=>011011100100
101011010010=>101111001000=>010111100100
101011010100=>011111001000=>001111100100
101011101000=>001111001100=>000111100110
101100101010=>111011010000=>011101101000
101100110010=>101011010100=>010101101010
101100110100=>011011010100=>001101101010
101101001010=>110111010000=>011011101000
101101010010=>101111010000=>010111101000
101101010100=>011111010000=>001111101000
101101101000=>001111010100=>000111101010
101110001010=>110011011000=>011001101100
101110010010=>101011011000=>010101101100
101110101000=>001111011000=>000111101100
101111000100=>010011011100=>001001101110
101111010000=>000111011100=>000011101110
110010101010=>111101100000=>011110110000
110010110010=>101101100100=>010110110010
110010110100=>011101100100=>001110110010
110011001010=>110101101000=>011010110100
110011010010=>101101101000=>010110110100
110011010100=>011101101000=>001110110100
110011100100=>010101101100=>001010110110
110100101010=>111011100000=>011101110000
110100110010=>101011100100=>010101110010
110101001010=>110111100000=>011011110000
110101010010=>101111100000=>010111110000
110101010100=>011111100000=>001111110000
110101101000=>001111100100=>000111110010
110110001010=>110011101000=>011001110100
110110010010=>101011101000=>010101110100
110110101000=>001111101000=>000111110100
111000101010=>111001110000=>011100111000
111001001010=>110101110000=>011010111000
111001010010=>101101110000=>010110111000
111001010100=>011101110000=>001110111000
111010001010=>110011110000=>011001111000
111010010010=>101011110000=>010101111000
111010101000=>001111110000=>000111111000
111011010000=>000111110100=>000011111010
111100001010=>110001111000=>011000111100
111101010000=>000111111000=>000011111100
111110100000=>000011111100=>000001111110
1111111111=>1111111111=>1111111111
1111111110=>1111111110=>0111111111
1111111001=>0111111101=>1011111110
1111110000=>0001111110=>0000111111
1111101000=>0011111100=>0001111110
1111100001=>0001111101=>1000111110
1111011000=>0011111010=>0001111101
1111010001=>0011111001=>1001111100
1111001001=>0101111001=>1010111100
1111000101=>1001111001=>1100111100
1110111111=>1110111111=>1111011111
1110111000=>0011110110=>0001111011
1110110001=>0011110101=>1001111010
1110101010=>1111110000=>0111111000
1110101001=>0111110001=>1011111000
1110100101=>1011110001=>1101111000
1110100011=>0011110011=>1001111001
1110010101=>1101110001=>1110111000
1110010011=>0101110011=>1010111001
1110000111=>0001110111=>1000111011
1101111111=>1101111111=>1110111111
1101111110=>1110111110=>0111011111
1101101001=>0111101001=>1011110100
1101011111=>1110011111=>1111001111
1101011001=>0111100101=>1011110010
1101010101=>1111100001=>1111110000
1101010011=>0111100011=>1011110001
1101001101=>1011100101=>1101110010
1100110101=>1101101001=>1110110100
1100011101=>1001101101=>1100110110
1100001111=>0001101111=>1000110111
1011111110=>1101111110=>0110111111
1011100101=>1011011001=>1101101100
1011011111=>1101011111=>1110101111
1011011001=>0111010101=>1011101010
1011010101=>1111010001=>1111101000
1011001101=>1011010101=>1101101010
1011000111=>0011010111=>1001101011
1011000010=>1000110100=>0100011010
1011000001=>0000110101=>1000011010
1010110101=>1111001001=>1111100100
1010101000=>0011110000=>0001111000
1010100010=>1001110000=>0100111000
1010011101=>1011001101=>1101100110
1010010111=>1011000111=>1101100011
1010010100=>0110110000=>0011011000
1010010010=>1010110000=>0101011000
1010000101=>1000110001=>1100011000
1001111110=>1010111110=>0101011111
1001101101=>1101010101=>1110101010
1001100100=>0101010100=>0010101010
1001100010=>1001010100=>0100101010
1001100001=>0001010101=>1000101010
1001010101=>1110100001=>1111010000
1001010010=>1011010000=>0101101000
1000111110=>1001011110=>0100101111
1000110010=>1010010100=>0101001010
1000100101=>1010010001=>1101001000
1000011110=>1000101110=>0100010111
1000011001=>0100010101=>1010001010
1000001110=>1000010110=>0100001011
1000001101=>1000010101=>1100001010
1000000110=>1000001010=>0100000101
1000000100=>0100000100=>0010000010
1000000010=>1000000100=>0100000010
1000000001=>0000000101=>1000000010
1000000000=>0000000010=>0000000001
10000000000=>00000000010=>00000000001
11111111110=>11111111110=>01111111111
0111111111=>0111111111=>1011111111
0111111101=>1011111101=>1101111110
0111100001=>0001011101=>1000101110
0000000001=>0000000001=>1000000000
01111111111=>01111111111=>10111111111
0111101001=>0110111001=>1011011100
0110100001=>0001101001=>1000110100
0010000001=>0000010001=>1000001000
00000000001=>00000000001=>10000000000
0101010101=>1111000001=>1111100000
0101010011=>0111000011=>1011100001
0101000111=>0011000111=>1001100011
0100110011=>0101001011=>1010100101
0100101011=>1101000011=>1110100001
0100100111=>0101000111=>1010100011
0100001111=>0001001111=>1000100111
0011010101=>1110010001=>1111001000
0011010011=>0110010011=>1011001001
0011000111=>0010010111=>1001001011
0010101011=>1110000011=>1111000001
0010001111=>0010001111=>1001000111
0001110011=>0100011011=>1010001101
0001100111=>0100010111=>1010001011
0001010111=>1100000111=>1110000011
0001001111=>0100001111=>1010000111
0000011111=>0000011111=>1000001111
010101010101=>111110000001=>111111000000
010101010011=>011110000011=>101111000001
010101001101=>101110000101=>110111000010
010100101011=>110110000011=>111011000001
010100011101=>100110001101=>110011000110
010100010111=>100110000111=>110011000011
010100001111=>000110001111=>100011000111
010011010101=>111010010001=>111101001000
010011001101=>101010010101=>110101001010
010011000111=>001010010111=>100101001011
010010110011=>011010001011=>101101000101
010010101101=>111010000101=>111101000010
010010101011=>111010000011=>111101000001
010010010111=>101010000111=>110101000011
010010001111=>001010001111=>100101000111
010001110011=>010010011011=>101001001101
010001100111=>010010010111=>101001001011
010001001111=>010010001111=>101001000111
010000111101=>100010011101=>110001001110
010000110111=>100010010111=>110001001011
010000011111=>000010011111=>100001001111
001101010101=>111100100001=>111110010000
001101001101=>101100100101=>110110010010
001101001011=>101100100011=>110110010001
001101000111=>001100100111=>100110010011
001100110011=>010100101011=>101010010101
001100100111=>010100100111=>101010010011
001100010111=>100100100111=>110010010011
001100001111=>000100101111=>100010010111
001011010101=>111100010001=>111110001000
001011010011=>011100010011=>101110001001
001011001011=>101100010011=>110110001001
001011000111=>001100010111=>100110001011
001010101011=>111100000011=>111110000001
001010100111=>011100000111=>101110000011
001010011101=>101100001101=>110110000110
001010010111=>101100000111=>110110000011
001010001111=>001100001111=>100110000111
001001110011=>010100011011=>101010001101
001001100111=>010100010111=>101010001011
001001010111=>110100000111=>111010000011
001001001111=>010100001111=>101010000111
001000111011=>100100011011=>110010001101
001000110111=>100100010111=>110010001011
001000011111=>000100011111=>100010001111
000111010101=>111000110001=>111100011000
000111001101=>101000110101=>110100011010
000111001011=>101000110011=>110100011001
000111000111=>001000110111=>100100011011
000110110011=>011000101011=>101100010101
000110101101=>111000100101=>111100010010
000110010111=>101000100111=>110100010011
000110001111=>001000101111=>100100010111
000101110101=>111000011001=>111100001100
000101100111=>011000010111=>101100001011
000101011101=>111000001101=>111100000110
000101010111=>111000000111=>111100000011
000100111101=>101000011101=>110100001110
000100111011=>101000011011=>110100001101
000100110111=>101000010111=>110100001011
000100011111=>001000011111=>100100001111
000011110011=>010000111011=>101000011101
000011100111=>010000110111=>101000011011
000011001111=>010000101111=>101000010111
000010101111=>110000001111=>111000000111
000010011111=>010000011111=>101000001111
000001111101=>100000111101=>110000011110
000001110111=>100000110111=>110000011011
000001011111=>100000011111=>110000001111
000000111111=>000000111111=>100000011111
111111111111=>111111111111=>111111111111
111110011111=>011111011111=>101111101111
111110000001=>000001111101=>100000111110
111110100101=>101111110001=>110111111000
111001100001=>000101110101=>100010111010
111000011001=>010001110101=>101000111010
111000000111=>000001110111=>100000111011
111000110001=>001001110101=>100100111010
111000100101=>101001110001=>110100111000
111011000001=>000011110101=>100001111010
111011100101=>101111011001=>110111101100
111010010111=>101111000111=>110111100011
111010011101=>101111001101=>110111100110
111010000101=>100011110001=>110001111000
100111100111=>010101110111=>101010111011
100111100001=>000101011101=>100010101110
100110011001=>010101010101=>101010101010
100110000111=>000101010111=>100010101011
100110000001=>000001010101=>100000101010
100110110001=>001101010101=>100110101010
100001111001=>010001011101=>101000101110
100001100111=>010001010111=>101000101011
100001100001=>000100010101=>100010001010
100000011111=>000001011111=>100000101111
100000011001=>010000010101=>101000001010
100000000001=>000000000101=>100000000010
100000100101=>101000010001=>110100001000
100011011111=>100101011111=>110010101111
100011000111=>001001010111=>100100101011
100011110111=>100101110111=>110010111011
100011110001=>001001011101=>100100101110
100011100101=>101001011001=>110100101100
100010010111=>101001000111=>110100100011
100010011101=>101001001101=>110100100110
100010000101=>100010010001=>110001001000
101101100111=>011101010111=>101110101011
101101100001=>000111010101=>100011101010
101100011001=>010011010101=>101001101010
101100000111=>000011010111=>100001101011
101100110001=>001011010101=>100101101010
101100100101=>101011010001=>110101101000
101111011001=>011101110101=>101110111010
101111000001=>000011011101=>100001101110
101111100101=>101101111001=>110110111100
101110010111=>101101100111=>110110110011
101110011101=>101101101101=>110110110110
101110000101=>100011011001=>110001101100
101001011111=>101100011111=>110110001111
101001011001=>011011000101=>101101100010
101001000111=>001011000111=>100101100011
101001001101=>101011000101=>110101100010
101001110111=>101100110111=>110110011011
101001110001=>001011001101=>100101100110
101001111101=>101100111101=>110110011110
101000010111=>100011000111=>110001100011
101000011101=>100011001101=>110001100110
101000000101=>100000110001=>110000011000
101010010101=>110111000001=>111011100000
0000000000=>0000000000=>0000000000
0000011110=>1000001110=>0100000111
0001111110=>1000111110=>0100011111
0111111110=>1011111110=>0101111111
000000000000=>000000000000=>000000000000
0000000010=>1000000000=>0100000000
0000001110=>1000000110=>0100000011
0000111110=>1000011110=>0100001111
0011111110=>1001111110=>0100111111
00000000010=>10000000000=>01000000000
00000001110=>10000000110=>01000000011
00000111110=>10000011110=>01000001111
0010111110=>1100011110=>0110001111
00011111110=>10001111110=>01000111111
01111111110=>10111111110=>01011111111
0011100010=>1001001100=>0100100110
001010101100=>011110000010=>001111000001
001010110100=>011110000100=>001111000010
001011001100=>010110001010=>001011000101
001011010100=>011110001000=>001111000100
001011011000=>001110001010=>000111000101
001011100100=>010110001100=>001011000110
001011101000=>001110001100=>000111000110
001100101100=>011010010010=>001101001001
001100110100=>011010010100=>001101001010
001101001100=>010110010010=>001011001001
001101010100=>011110010000=>001111001000
001101011000=>001110010010=>000111001001
001101100100=>010110010100=>001011001010
001101101000=>001110010100=>000111001010
001110010100=>011010011000=>001101001100
001110100100=>010110011000=>001011001100
001110101000=>001110011000=>000111001100
010010101100=>011101000010=>001110100001
010010110100=>011101000100=>001110100010
010011001100=>010101001010=>001010100101
010011010100=>011101001000=>001110100100
010011011000=>001101001010=>000110100101
010011100100=>010101001100=>001010100110
010011101000=>001101001100=>000110100110
010100101100=>011011000010=>001101100001
010100110100=>011011000100=>001101100010
010101001100=>010111000010=>001011100001
010101010100=>011111000000=>001111100000
010101011000=>001111000010=>000111100001
010101100100=>010111000100=>001011100010
010101101000=>001111000100=>000111100010
010110001100=>010011001010=>001001100101
010110010100=>011011001000=>001101100100
010110011000=>001011001010=>000101100101
010110100100=>010111001000=>001011100100
010110101000=>001111001000=>000111100100
010111000100=>010011001100=>001001100110
010111001000=>001011001100=>000101100110
011000101100=>011001010010=>001100101001
011000110100=>011001010100=>001100101010
011001001100=>010101010010=>001010101001
011001010100=>011101010000=>001110101000
011001011000=>001101010010=>000110101001
011001100100=>010101010100=>001010101010
011001101000=>001101010100=>000110101010
011010001100=>010011010010=>001001101001
011010010100=>011011010000=>001101101000
011010011000=>001011010010=>000101101001
011010100100=>010111010000=>001011101000
011010101000=>001111010000=>000111101000
011011000100=>010011010100=>001001101010
011011001000=>001011010100=>000101101010
011100010100=>011001011000=>001100101100
011100100100=>010101011000=>001010101100
011100101000=>001101011000=>000110101100
011101000100=>010011011000=>001001101100
011101001000=>001011011000=>000101101100
0101110001=>0011001101=>1001100110
0110010101=>1101010001=>1110101000
0110011001=>0101010101=>1010101010
0110110001=>0011010101=>1001101010
011010010101=>110110100001=>111011010000
011010101001=>011110100001=>101111010000
011011010100=>011110101000=>001111010100
011100011001=>010010110101=>101001011010
011101100001=>000110110101=>100011011010
0000000101=>1000000001=>1100000000
0000001101=>1000000101=>1100000010
0001111101=>1000111101=>1100011110
00000001101=>10000000101=>11000000010
100101110001=>001101001101=>100110100110
101011100001=>000111001101=>100011100110
101110100001=>000111011001=>100011101100
0011000110=>1001001010=>0100100101
0001101001=>0110001001=>1011000100
0000010001=>0010000001=>1001000000
11111111111=>11111111111=>11111111111
101000111001=>010011001101=>101001100110
100100111001=>010101001101=>101010100110
100110100011=>001101010011=>100110101001
101001100011=>001011001011=>100101100101
100101100011=>001101001011=>100110100101
100110010011=>010101010011=>101010101001
101000110011=>010011001011=>101001100101
100100110011=>010101001011=>101010100101
101010000111=>000111000111=>100011100011
100101000111=>001101000111=>100110100011
101000100111=>010011000111=>101001100011
100100100111=>010101000111=>101010100011
100100010111=>100101000111=>110010100011
110101010101=>111111000001=>111111100000
110101011001=>011111000101=>101111100010
110101101001=>011111001001=>101111100100
110101110001=>001111001101=>100111100110
110110010101=>110111010001=>111011101000
110110101001=>011111010001=>101111101000
110110110001=>001111010101=>100111101010
110111010001=>001111011001=>100111101100
111001010101=>111011100001=>111101110000
111010010101=>110111100001=>111011110000
111010101001=>011111100001=>101111110000
111010110001=>001111100101=>100111110010
111011010001=>001111101001=>100111110100
111100010101=>110011110001=>111001111000
111100100101=>101011110001=>110101111000
111101010001=>001111110001=>100111111000
111101100001=>000111110101=>100011111010
111110100001=>000111111001=>100011111100
111111000001=>000011111101=>100001111110
0110010011=>0101010011=>1010101001
011100010011=>010010110011=>101001011001
011010001011=>100110100011=>110011010001
101100100011=>001011010011=>100101101001
101100010011=>010011010011=>101001101001
011100000111=>000010110111=>100001011011
0101000000=>0000011000=>0000001100
110011010101=>111011010001=>111101101000
110100110101=>110111001001=>111011100100
110001110101=>110011011001=>111001101100
110101010011=>011111000011=>101111100001
101000111011=>100110011011=>110011001101
110101000111=>001111000111=>100111100011
101100010111=>100110100111=>110011010011
101000110111=>100110010111=>110011001011
100100101111=>101010001111=>110101000111
0000000011=>0000000011=>1000000001
0000111111=>0000111111=>1000011111
0011111111=>0011111111=>1001111111
00000000011=>00000000011=>10000000001
00111111111=>00111111111=>10011111111
11011111111=>11011111111=>11101111111
0011111100=>0100111110=>0010011111
0011110011=>0100111011=>1010011101
0110100111=>0110100111=>1011010011
0110110011=>0110101011=>1011010101
0100101001=>0110100001=>1011010000
011010110111=>111010010111=>111101001011
011000100001=>000100101001=>100010010100
000110100001=>000110001001=>100011000100
010010100001=>000110100001=>100011010000
011100101111=>101011001111=>110101100111
011010000001=>000001101001=>100000110100
000100101001=>011010000001=>101101000000
010000101001=>011000100001=>101100010000
000110001001=>010010001001=>101001000100
010010001001=>010010100001=>101001010000
101011000011=>000111001011=>100011100101
101101000011=>000111010011=>100011101001
0001010101=>1110000001=>1111000000
0111010101=>1110110001=>1111011000
0001110111=>1000110111=>1100011011
0011110101=>1100111001=>1110011100
000000000101=>100000000001=>110000000000
010101110111=>111000110111=>111100011011
000001010101=>111000000001=>111100000000
011101010111=>111011000111=>111101100011
011101110101=>111011011001=>111101101100
011111011111=>101111011111=>110111101111
010011101111=>101001101111=>110100110111
110110100011=>001111010011=>100111101001
111000110101=>110011101001=>111001110100
111010100011=>001111100011=>100111110001
111101000011=>000111110011=>100011111001
000001111111=>000001111111=>100000111111
001111100101=>101001111001=>110100111100
011110100101=>101101110001=>110110111000
0110101011=>1110100011=>1111010001
0100111001=>0101001101=>1010100110
0101100011=>0011001011=>1001100101
000111011001=>011000110101=>101100011010
010011011001=>011010010101=>101101001010
011001000111=>001010100111=>100101010011
011101000011=>000110110011=>100011011001
0111011001=>0110110101=>1011011010
100100100001=>000101010001=>100010101000
0100010011=>0100100011=>1010010001
0101110011=>0110011011=>1011001101
0110100011=>0011010011=>1001101001
0101000011=>0001100011=>1000110001
0100110111=>1010010111=>1101001011
0101100111=>0110010111=>1011001011
0110101111=>1101001111=>1110100111
101001111011=>101100111011=>110110011101
101110110011=>011101101011=>101110110101
101100101111=>101101001111=>110110100111
101001101111=>101100101111=>110110010111
101011001111=>011100101111=>101110010111
0101000101=>1001100001=>1100110000
0110110101=>1110101001=>1111010100
0110001001=>0100101001=>1010010100
0111010011=>0110110011=>1011011001
010100000101=>100001100001=>110000110000
000101000101=>100110000001=>110011000000
010001000101=>100100100001=>110010010000
000001101001=>011000001001=>101100000100
011000001001=>010000101001=>101000010100
011001010011=>011010100011=>101101010001
0011011110=>1100101110=>0110010111
000111110101=>110001111001=>111000111100
0111001101=>1010110101=>1101011010
011101010101=>111101100001=>111110110000
011101010011=>011101100011=>101110110001
011100110101=>110101101001=>111010110100
001111010101=>111001110001=>111100111000
011101101001=>011101101001=>101110110100
011101011001=>011101100101=>101110110010
011110010101=>110101110001=>111010111000
011110101001=>011101110001=>101110111000
011111000101=>100101111001=>110010111100
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.
searching the database
Sorry, this map was not found in the database.