4466: C. Phase Shift

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 ≤ t ≤ 3⋅10⁴) — the number of test cases. The description of test cases follows.

The first line of each test case contains one integer n (1 ≤ n ≤ 10⁵) — 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⋅10⁵.

5
1
a
2
ba
10
codeforces
26
abcdefghijklmnopqrstuvwxyz
26
abcdefghijklmnopqrstuvwxzy

b
ac
abcdebfadg
bcdefghijklmnopqrstuvwxyza
bcdefghijklmnopqrstuvwxyaz

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.