A15136. Palindromic Indices

You are given a palindromic string $s$ of length $n$ .

You have to count the number of indices $i$ $(1 \le i \le n)$ such that the string after removing $s_i$ from $s$ still remains a palindrome.

For example, consider $s$ = "aba"

1. If we remove $s_1$ from $s$ , the string becomes "ba" which is not a palindrome.
2. If we remove $s_2$ from $s$ , the string becomes "aa" which is a palindrome.
3. If we remove $s_3$ from $s$ , the string becomes "ab" which is not a palindrome.

A palindrome is a string that reads the same backward as forward. For example, "abba", "a", "fef" are palindromes whereas "codeforces", "acd", "xy" are not.

The input consists of multiple test cases. The first line of the input contains a single integer $t$ $(1 \leq t \leq 10^3)$ — the number of test cases. Description of the test cases follows.

The first line of each testcase contains a single integer $n$ $(2 \leq n \leq 10^5)$ — the length of string $s$ .

The second line of each test case contains a string $s$ consisting of lowercase English letters. It is guaranteed that $s$ is a palindrome.

It is guaranteed that sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output a single integer — the number of indices $i$ $(1 \le i \le n)$ such that the string after removing $s_i$ from $s$ still remains a palindrome.

The first test case is described in the statement.

In the second test case, the indices $i$ that result in palindrome after removing $s_i$ are $3, 4, 5, 6$ . Hence the answer is $4$ .

In the third test case, removal of any of the indices results in "d" which is a palindrome. Hence the answer is $2$ .