Acacius and String
Contest: Codeforces Round 657 (Div. 2)
Difficulty rating: 1500
Tags: brute force, implementation, strings

Acacius is studying strings theory. Today he came with the following problem.

You are given a string $$$s$$$ of length $$$n$$$ consisting of lowercase English letters and question marks. It is possible to replace question marks with lowercase English letters in such a way that a string "abacaba" occurs as a substring in a resulting string exactly once?

Each question mark should be replaced with exactly one lowercase English letter. For example, string "a?b?c" can be transformed into strings "aabbc" and "azbzc", but can't be transformed into strings "aabc", "a?bbc" and "babbc".

Occurrence of a string $$$t$$$ of length $$$m$$$ in the string $$$s$$$ of length $$$n$$$ as a substring is a index $$$i$$$ ($$$1 \leq i \leq n - m + 1$$$) such that string $$$s[i..i+m-1]$$$ consisting of $$$m$$$ consecutive symbols of $$$s$$$ starting from $$$i$$$-th equals to string $$$t$$$. For example string "ababa" has two occurrences of a string "aba" as a substring with $$$i = 1$$$ and $$$i = 3$$$, but there are no occurrences of a string "aba" in the string "acba" as a substring.

Please help Acacius to check if it is possible to replace all question marks with lowercase English letters in such a way that a string "abacaba" occurs as a substring in a resulting string exactly once.

Input format:
First line of input contains an integer $$$T$$$ ($$$1 \leq T \leq 5000$$$), number of test cases. $$$T$$$ pairs of lines with test case descriptions follow.

The first line of a test case description contains a single integer $$$n$$$ ($$$7 \leq n \leq 50$$$), length of a string $$$s$$$.

The second line of a test case description contains string $$$s$$$ of length $$$n$$$ consisting of lowercase English letters and question marks.

Output format:
For each test case output an answer for it.

In case if there is no way to replace question marks in string $$$s$$$ with a lowercase English letters in such a way that there is exactly one occurrence of a string "abacaba" in the resulting string as a substring output "No".

Otherwise output "Yes" and in the next line output a resulting string consisting of $$$n$$$ lowercase English letters. If there are multiple possible strings, output any.

You may print every letter in "Yes" and "No" in any case you want (so, for example, the strings yEs, yes, Yes, and YES will all be recognized as positive answer).

Constraints:
Time limit: 1.0 s
Memory limit: 512.0 MB

Note:
In first example there is exactly one occurrence of a string "abacaba" in the string "abacaba" as a substring.

In second example seven question marks can be replaced with any seven lowercase English letters and with "abacaba" in particular.

In sixth example there are two occurrences of a string "abacaba" as a substring.

Example input:
6
7
abacaba
7
???????
11
aba?abacaba
11
abacaba?aba
15
asdf???f???qwer
11
abacabacaba

Example output:
Yes
abacaba
Yes
abacaba
Yes
abadabacaba
Yes
abacabadaba
No
No

Editorial:
At first, we will check if some string of length $$$n$$$ contains exactly one occurrence of "abacaba".
Lemma 1. This check can be done in $$$O(n)$$$ time.
Proof. We can try all the possible positions $$$i$$$ of a string $$$s$$$ and check whether $$$i$$$ is a starting position for a substring "abacaba". This check can be performed in a $$$O(1)$$$ time by checking if $$$s_{i + j} = t_j$$$ for all $$$j \in [0; 6]$$$ where string $$$t$$$ is "abacaba". So, overall complexity of such a check works in $$$n \cdot O(1) = O(n)$$$ time.
To solve the problem we will iterate over all positions $$$i$$$ and check whether there exists a valid string such that its single occurrence of a substring "abacaba" starts from position $$$i$$$. String $$$s$$$ has a single occurrence $$$i$$$ of a substring "abacaba" if and only if two following criteria are satisfied.
• $$$i$$$ is a occurrence of a substring "abacaba" in $$$s$$$.
• There are no occurrence $$$j$$$ of a substring "abacaba" in $$$s$$$ such that $$$i \neq j$$$.
First criterion can be checked directly. $$$i$$$ can be an occurrence of a substring "abacaba" in a resulting string if and only if for all $$$j \in [0; 6]$$$ $$$s_{i + j} = t_j$$$ or $$$s_{i + j} = '?'$$$.
To check the second criterion we need the following lemma.
Lemma 2. Question marks in string $$$s$$$ can be replaced with lowercase English letters in such a way that no new occurrences of "abacaba" will appear.
Proof. Let's replace all the questing marks with "z" letter. Any substring of $$$s$$$ that contained question mark will not become a occurrence of "abacaba" since "abacaba" does not contain "z".
So after fixing position of a single occurrence $$$i$$$ resulting string can be constructed directly.
This leads to a $$$O(n^2)$$$ solution. Refer to author's solution code for more details.