Double Lexicographically Minimum

2000ms

262144K

Description:

You are given a string $$$s$$$. You can reorder the characters to form a string $$$t$$$. Define $$$t_{\mathrm{max}}$$$ to be the lexicographical maximum of $$$t$$$ and $$$t$$$ in reverse order.

Given $$$s$$$ determine the lexicographically minimum value of $$$t_{\mathrm{max}}$$$ over all reorderings $$$t$$$ of $$$s$$$.

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 $$$b$$$.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases. Descriptions of test cases follow.

The first and only line of each test case contains a string $$$s$$$ ($$$1 \leq |s| \leq 10^5$$$). $$$s$$$ consists of only lowercase English letters.

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

Output:

For each test case print the lexicographically minimum value of $$$t_{\mathrm{max}}$$$ over all reorderings $$$t$$$ of $$$s$$$.

Sample Input:

12
a
aab
abb
abc
aabb
aabbb
aaabb
abbb
abbbb
abbcc
eaga
ffcaba

Sample Output:

a
aba
bab
bca
abba
abbba
ababa
bbab
bbabb
bbcca
agea
acffba

Note:

For the first test case, there is only one reordering of $$$s$$$, namely "a".

For the second test case, there are three reorderings of $$$s$$$.

$$$t = \mathtt{aab}$$$: $$$t_{\mathrm{max}} = \max(\mathtt{aab}, \mathtt{baa}) = \mathtt{baa}$$$
$$$t = \mathtt{aba}$$$: $$$t_{\mathrm{max}} = \max(\mathtt{aba}, \mathtt{aba}) = \mathtt{aba}$$$
$$$t = \mathtt{baa}$$$: $$$t_{\mathrm{max}} = \max(\mathtt{baa}, \mathtt{aab}) = \mathtt{baa}$$$

The lexicographical minimum of $$$t_{\mathrm{max}}$$$ over all cases is "aba".

Informação

Provedor Codeforces

Código CF1799C