378QAQ and Core
Description
378QAQ has a string $s$ of length $n$. Define the core of a string as the substring$^\dagger$ with maximum lexicographic$^\ddagger$ order.
For example, the core of "$\mathtt{bazoka}$" is "$\mathtt{zoka}$", and the core of "$\mathtt{aaa}$" is "$\mathtt{aaa}$".
378QAQ wants to rearrange the string $s$ so that the core is lexicographically minimum. Find the lexicographically minimum possible core over all rearrangements of $s$.
$^\dagger$ A substring of string $s$ is a continuous segment of letters from $s$. For example, "$\mathtt{defor}$", "$\mathtt{code}$" and "$\mathtt{o}$" are all substrings of "$\mathtt{codeforces}$" while "$\mathtt{codes}$" and "$\mathtt{aaa}$" are not.
$^\ddagger$ A string $p$ is lexicographically smaller than a string $q$ if and only if one of the following holds:
- $p$ is a prefix of $q$, but $p \ne q$; or
- in the first position where $p$ and $q$ differ, the string $p$ has a smaller element than the corresponding element in $q$ (when compared by their ASCII code).
For example, "$\mathtt{code}$" and "$\mathtt{coda}$" are both lexicographically smaller than "$\mathtt{codeforces}$" while "$\mathtt{codeforceston}$" and "$\mathtt{z}$" are not.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 10^5$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1\leq n\leq 10^6$) — the length of string $s$.
The next line of each test case contains the string $s$ of length $n$. The string $s$ consists of lowercase English letters.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.
For each test case, output the lexicographically minimum possible core over all rearrangements of $s$.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\leq t\leq 10^5$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($1\leq n\leq 10^6$) — the length of string $s$.
The next line of each test case contains the string $s$ of length $n$. The string $s$ consists of lowercase English letters.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^6$.
Output
For each test case, output the lexicographically minimum possible core over all rearrangements of $s$.
6
3
qaq
4
cccc
6
bazoka
6
zazzzz
7
ababbbb
7
ccbabcc
qaq
cccc
z
zzz
bbababb
cbcacbc
Note
In the first test case, all possible rearrangements and their corresponding cores are as follows:
- "$\mathtt{qaq}$", its core is "$\mathtt{qaq}$".
- "$\mathtt{aqq}$", its core is "$\mathtt{qq}$".
- "$\mathtt{qqa}$", its core is "$\mathtt{qqa}$".
So the core with the minimum lexicographic order in all rearrangement plans is "$\mathtt{qaq}$".