Longest Balanced Parentheses Substring

Given a string S consisting solely of the characters ( and ), your task is to determine the length of the longest contiguous substring that forms a valid (i.e., balanced) parentheses sequence.

A valid sequence is defined as one in which every opening parenthesis ( is matched with a corresponding closing parenthesis ), and the pairs are properly nested. For instance, the substring "((()))" is perfectly balanced with a length of 6, while "<code())</code>" has a maximum balanced length of 2.

You may find it useful to consider the formula \( \text{length} = i - j \), where \( j \) denotes the index of the last unmatched parenthesis before a balanced substring starting right after it.

Read the input from stdin and output your answer to stdout.

inputFormat

A single line containing the string S composed only of the characters '(' and ')'.

outputFormat

A single integer representing the length of the longest balanced parentheses substring.## sample

(()))

4