Dominant Character
Contest: Codeforces Round 754 (Div. 2)
Difficulty rating: 1400
Tags: brute force, greedy, implementation, strings

Ashish has a string $$$s$$$ of length $$$n$$$ containing only characters 'a', 'b' and 'c'.

He wants to find the length of the smallest substring, which satisfies the following conditions:

- Length of the substring is at least $$$2$$$
- 'a' occurs strictly more times in this substring than 'b'
- 'a' occurs strictly more times in this substring than 'c'

Ashish is busy planning his next Codeforces round. Help him solve the problem.

A string $$$a$$$ is a substring of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

Input format:
The first line contains a single integer $$$t$$$ $$$(1 \le t \le 10^{5})$$$  — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ $$$(2 \le n \le 10^{6})$$$  — the length of the string $$$s$$$.

The second line of each test case contains a string $$$s$$$ consisting only of characters 'a', 'b' and 'c'.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^{6}$$$.

Output format:
For each test case, output the length of the smallest substring which satisfies the given conditions or print $$$-1$$$ if there is no such substring.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
Consider the first test case. In the substring "aa", 'a' occurs twice, while 'b' and 'c' occur zero times. Since 'a' occurs strictly more times than 'b' and 'c', the substring "aa" satisfies the condition and the answer is $$$2$$$. The substring "a" also satisfies this condition, however its length is not at least $$$2$$$.

In the second test case, it can be shown that in none of the substrings of "cbabb" does 'a' occur strictly more times than 'b' and 'c' each.

In the third test case, "cacabccc", the length of the smallest substring that satisfies the conditions is $$$3$$$.

Example input:
3
2
aa
5
cbabb
8
cacabccc

Example output:
2
-1
3

Editorial:
Tl;dr: The following are all the possible minimal substrings (there aren't that many) which satisfy the given conditions: "aa", "aba", "aca", "abca", "acba", "abbacca", "accabba". Any other string that satisfies the condition contains at least one of these as a substring, and hence is not the optimal substring for the answer.
Claim: If a substring exists which satisfies the given conditions, then the length of the shortest such substring is at most $$$7$$$. Otherwise the solution does not exist.
Proof: Let us consider that the solution exists. We will try to prove this by breaking this into the following cases:
Case 1: There exist two such "a" whose distance is less than or equal to $$$2$$$, where distance is the absolute difference of their indices.
• In this case where there are two such "a" whose distance is less than $$$2$$$, then either these two "a" are present consecutive or there is only one single letter between these two "a". All these minimal substrings are "aa", "aba" and "aca"which satisfies all the given conditions.
Hence we can say that the shortest length of such substring that satisfies the given conditions is at most $$$3$$$ in this case.
Case 2: There exists no two such "a" whose distance is less than or equal to $$$2$$$.
• In this case all the consecutive occurrences of "a" are present at a distance at least $$$3$$$. Then in order for the number of "a" to be bigger than that of "b" and "c" the string must look like "a??a??a??a??a".
• Let us define "??" as a block. Now if there is any block consisting of different characters $$$i.e$$$ "bc" or "cb" then the substring "a??a" will satisfy all the given conditions and hence the minimal length will be $$$4$$$.
• Notice that there must be at least one block of "bb" and atleast one block of "cc", otherwise "a" will not be in a majority. Hence, there must exist 2 consecutive blocks equal to "bb" and "cc" or "cc" and "bb" in the string (otherwise all blocks would be of the same character). Hence we can pick the substring "abbacca" or "accabba" which satisfies the given conditions. The minimal length is, therefore, $$$7$$$ in this case.
Therefore we can say that the shortest length of such substring that satisfies the given conditions is at most $$$7$$$ in this case.
Thus, it suffices to only check all substrings of length up to $$$7$$$ and find the smallest among them that satisfies the given conditions (or report that it does not exist).
Time Complexity: $$$\mathcal{O}(7 \cdot n)$$$