A14687. Mirror in the String

You have a string $s_1 s_2 \ldots s_n$ and you stand on the left of the string looking right. You want to choose an index $k$ ( $1 \le k \le n$ ) and place a mirror after the $k$ -th letter, so that what you see is $s_1 s_2 \ldots s_k s_k s_{k - 1} \ldots s_1$ . What is the lexicographically smallest string you can see?

A string $a$ is lexicographically smaller than a string $b$ if and only if one of the following holds:

- $a$ is a prefix of $b$ , but $a \ne b$ ;
- in the first position where $a$ and $b$ differ, the string $a$ has a letter that appears earlier in the alphabet than the corresponding letter in $b$ .

The first line of input contains one integer $t$ ( $1 \leq t \leq 10\,000$ ): the number of test cases.

The next $t$ lines contain the description of the test cases, two lines per a test case.

In the first line you are given one integer $n$ ( $1 \leq n \leq 10^5$ ): the length of the string.

The second line contains the string $s$ consisting of $n$ lowercase English characters.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case print the lexicographically smallest string you can see.

In the first test case choose $k = 1$ to obtain "cc".

In the second test case choose $k = 3$ to obtain "cbaabc".

In the third test case choose $k = 1$ to obtain "aa".

In the fourth test case choose $k = 1$ to obtain "bb".