Longest Valid Parentheses

Given a string s consisting only of the characters '(' and ')', determine the length of the longest valid (well-formed) parentheses substring. A valid substring is one where every opening parenthesis has a corresponding closing parenthesis and the parentheses are properly nested.

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

Note: The solution should read the input from standard input (stdin) and print the result to standard output (stdout).

inputFormat

A single line containing the string s, which contains only the characters '(' and ')'.

Example:

()(()))

outputFormat

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

Example:

4

## sample

()

2

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