Your friend, a biochemistry major, tripped while carrying a tray of computer files through the lab. All of the files fell to the ground and broke. Your friend picked up all the file fragments and called you to ask for help putting them back together again.
Fortunately, all of the files on the tray were identical, all of them broke into exactly two fragments, and all of the file fragments were found. Unfortunately, the files didn't all break in the same place, and the fragments were completely mixed up by their fall to the floor.
You've translated the original binary fragments into strings of ASCII 1's and 0's, and you're planning to write a program to determine the bit pattern the files contained.
Input
Input will consist of a sequence of "file fragments", one per line. Each fragment consists of a string of ASCII 1's and 0's. Subsequent testcases are separated with a blank line.
Output
Output for each case is a single line of ASCII 1's and 0's giving the bit pattern of the original files. If there are 2N fragments in the input, it should be possible to concatenate these fragments together in pairs to make N copies of the output string. If there is no unique solution, any of the possible solutions may be output.
Your friend is certain that there were no more than 144 files on the tray, and that the files were all less than 256 bytes in size.
Sample Input
011
0111
01110
111
0111
10111
Sample Output
01110111
