Score : $400$ points

Problem Statement

You are given $3$ binary strings $S_1, S_2, S_3$, each containing exactly $N$ 0's and $N$ 1's.

Find a binary string of length $2N+1$, which is a subsequence of all of the strings $S_1 + S_1, S_2 + S_2, S_3 + S_3$ ($s+t$ denotes the concatenation of strings $s$ and $t$ in order). It's guaranteed that under the constraints above such a string always exists.

Here a string $B$ is a subsequence of a string $A$ if $B$ can be obtained by removing zero or more characters from $A$ and concatenating the remaining characters without changing the order.

You will be given $T$ test cases. Solve each of them.

Constraints

• $1 \le T \le 10^5$
• $1\le N \le 10^5$
• $S_i$ is a binary string of length $2N$ consisting of $N$ 0's and $N$ 1's.
• The sum of $N$ over all test cases doesn't exceed $10^5$.

Input

Input is given from Standard Input in the following format. The first line of input is as follows:

$T$

Then, $T$ test cases follow, each of which is in the following format:

$N$

$S_1$

$S_2$

$S_3$

Output

For each test case, print any binary string of length $2N+1$, which is a subsequence of all of $S_1 + S_1, S_2 + S_2, S_3 + S_3$. If many such strings exist, you can print any.

2
1
01
01
10
2
0101
0011
1100

010
11011

In the first case, 010 is a subsequence of 0101, 0101, and 1010.

In the second case, 11011 is a subsequence of 01010101, 00110011, and 11001100.