Binary Literature
Description
A bitstring is a string that contains only the characters 0 and 1.
Koyomi Kanou is working hard towards her dream of becoming a writer. To practice, she decided to participate in the Binary Novel Writing Contest. The writing prompt for the contest consists of three bitstrings of length $2n$. A valid novel for the contest is a bitstring of length at most $3n$ that contains at least two of the three given strings as subsequences.
Koyomi has just received the three prompt strings from the contest organizers. Help her write a valid novel for the contest.
A string $a$ is a subsequence of a string $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero) characters.
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$).
Each of the following three lines contains a bitstring of length $2n$. It is guaranteed that these three strings are pairwise distinct.
It is guaranteed that the sum of $n$ across all test cases does not exceed $10^5$.
For each test case, print a single line containing a bitstring of length at most $3n$ that has at least two of the given bitstrings as subsequences.
It can be proven that under the constraints of the problem, such a bitstring always exists.
If there are multiple possible answers, you may output any of them.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$).
Each of the following three lines contains a bitstring of length $2n$. It is guaranteed that these three strings are pairwise distinct.
It is guaranteed that the sum of $n$ across all test cases does not exceed $10^5$.
Output
For each test case, print a single line containing a bitstring of length at most $3n$ that has at least two of the given bitstrings as subsequences.
It can be proven that under the constraints of the problem, such a bitstring always exists.
If there are multiple possible answers, you may output any of them.
Samples
2
1
00
11
01
3
011001
111010
010001
010
011001010
Note
In the first test case, the bitstrings 00 and 01 are subsequences of the output string: 010 and 010. Note that 11 is not a subsequence of the output string, but this is not required.
In the second test case all three input strings are subsequences of the output string: 011001010, 011001010 and 011001010.