Longest Valid Parentheses

Given a string consisting only of the characters '(' and ')', determine the length of the longest well-formed (i.e., valid) parentheses substring.

A substring is considered valid if every opening parenthesis '\(' has a corresponding closing parenthesis '\)' and the pairs are properly nested. In other words, the substring must satisfy the rules of balanced parentheses.

For example, if the input is ((), the longest valid substring is () with a length of 2.

Note: When a mathematical formula is necessary, please use LaTeX format. For this problem, if needed, the length calculation can be thought of as \(i - j\), where \(i\) and \(j\) are indices in the string.

inputFormat

The input consists of a single line containing a string composed solely of the characters '(' and ')'.

outputFormat

The output is a single integer representing the length of the longest valid (well-formed) parentheses substring.

(()

2