Find the palindrome

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Even newborns know that a palindrome is a string of letters that reads the same way from left to right and from right to left. For example, the words madam, anna, and racecar are palindromes, while the words elephant and penguin are not.

Zenyk is given a string \(s\) consisting of \(n\) lowercase English letters.

Your task is to help him calculate the length of the longest substring that is a palindrome.

Input

The first line contains a single integer \(n\) — the length of the string.

The second line contains the string \(s\), which consists of \(n\) lowercase English letters.

Output

In a single line, output one integer — the length of the longest substring of the string \(s\) that is a palindrome.

Constraints

\(1 \le n \le 7 \cdot 10^3\).

Samples