Manipulating History

1000ms

262144K

Description:

As a human, she can erase history of its entirety. As a Bai Ze (Hakutaku), she can create history out of nothingness.

—Perfect Memento in Strict Sense

Keine has the ability to manipulate history.

The history of Gensokyo is a string $$$s$$$ of length $$$1$$$ initially. To fix the chaos caused by Yukari, she needs to do the following operations $$$n$$$ times, for the $$$i$$$-th time:

She chooses a non-empty substring $$$t_{2i-1}$$$ of $$$s$$$.
She replaces $$$t_{2i-1}$$$ with a non-empty string, $$$t_{2i}$$$. Note that the lengths of strings $$$t_{2i-1}$$$ and $$$t_{2i}$$$ can be different.

Note that if $$$t_{2i-1}$$$ occurs more than once in $$$s$$$, exactly one of them will be replaced.

For example, let $$$s=$$$"marisa", $$$t_{2i-1}=$$$"a", and $$$t_{2i}=$$$"z". After the operation, $$$s$$$ becomes "mzrisa" or "marisz".

After $$$n$$$ operations, Keine got the final string and an operation sequence $$$t$$$ of length $$$2n$$$. Just as Keine thinks she has finished, Yukari appears again and shuffles the order of $$$t$$$. Worse still, Keine forgets the initial history.

Help Keine find the initial history of Gensokyo!

Recall that a substring is a sequence of consecutive characters of the string. For example, for string "abc" its substrings are: "ab", "c", "bc" and some others. But the following strings are not its substring: "ac", "cba", "acb".

Hacks

You cannot make hacks in this problem.

Input:

Each test contains multiple test cases. The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 10^3$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n < 10 ^ 5$$$) — the number of operations.

The next $$$2n$$$ lines contains one non-empty string $$$t_{i}$$$ — the $$$i$$$-th string of the shuffled sequence $$$t$$$.

The next line contains one non-empty string $$$s$$$ — the final string.

It is guaranteed that the total length of given strings (including $$$t_i$$$ and $$$s$$$) over all test cases does not exceed $$$2 \cdot 10 ^ 5$$$. All given strings consist of lowercase English letters only.

It is guaranteed that the initial string exists. It can be shown that the initial string is unique.

Output:

For each test case, print the initial string in one line.

Sample Input:

2
2
a
ab
b
cd
acd
3
z
a
a
aa
yakumo
ran
yakumoran

Sample Output:

a
z

Note:

Test case 1:

Initially $$$s$$$ is "a".

In the first operation, Keine chooses "a", and replaces it with "ab". $$$s$$$ becomes "ab".
In the second operation, Keine chooses "b", and replaces it with "cd". $$$s$$$ becomes "acd".

So the final string is "acd", and $$$t=[$$$"a", "ab", "b", "cd"$$$]$$$ before being shuffled.

Test case 2:

Initially $$$s$$$ is "z".

In the first operation, Keine chooses "z", and replaces it with "aa". $$$s$$$ becomes "aa".
In the second operation, Keine chooses "a", and replaces it with "ran". $$$s$$$ becomes "aran".
In the third operation, Keine chooses "a", and replaces it with "yakumo". $$$s$$$ becomes "yakumoran".

So the final string is "yakumoran", and $$$t=[$$$"z", "aa", "a", "ran", "a", "yakumo"$$$]$$$ before being shuffled.

Informação

Provedor Codeforces

Código CF1688C