Phase Shift
Description
There was a string $s$ which was supposed to be encrypted. For this reason, all $26$ lowercase English letters were arranged in a circle in some order, afterwards, each letter in $s$ was replaced with the one that follows in clockwise order, in that way the string $t$ was obtained.
You are given a string $t$. Determine the lexicographically smallest string $s$ that could be a prototype of the given string $t$.
A string $a$ is lexicographically smaller than a string $b$ of the same length if and only if:
- 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 the input contains a single integer $t$ ($1 \le t \le 3 \cdot 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains one integer $n$ ($1 \le n \le 10^5$) — the length of the string $t$.
The next line contains the string $t$ of the length $n$, containing lowercase English letters.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
For each test case, output a single line containing the lexicographically smallest string $s$ which could be a prototype of $t$.
Input
The first line of the input contains a single integer $t$ ($1 \le t \le 3 \cdot 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains one integer $n$ ($1 \le n \le 10^5$) — the length of the string $t$.
The next line contains the string $t$ of the length $n$, containing lowercase English letters.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
Output
For each test case, output a single line containing the lexicographically smallest string $s$ which could be a prototype of $t$.
5
1
a
2
ba
10
codeforces
26
abcdefghijklmnopqrstuvwxyz
26
abcdefghijklmnopqrstuvwxzy
b
ac
abcdebfadg
bcdefghijklmnopqrstuvwxyza
bcdefghijklmnopqrstuvwxyaz
Note
In the first test case, we couldn't have the string "a", since the letter a would transit to itself. Lexicographically the second string "b" is suitable as an answer.
In the second test case, the string "aa" is not suitable, since a would transit to itself. "ab" is not suitable, since the circle would be closed with $2$ letters, but it must contain all $26$. The next string "ac" is suitable.
Below you can see the schemes for the first three test cases. The non-involved letters are skipped, they can be arbitrary placed in the gaps.
