Longest Balanced Parentheses

You are given a string s consisting only of the characters '(' and ')'. Your task is to determine the length of the longest substring that forms a balanced parentheses sequence.

A balanced parentheses sequence is defined recursively as follows:

• An empty string is balanced.
• If S is balanced, then (S) is balanced.
• If S and T are balanced, then their concatenation ST is balanced.

If no balanced substring exists, the answer should be 0.

You may use the following mathematical expression for balanced sequences: \( \text{if } S \text{ is balanced, then } (S) \text{ is balanced} \).

inputFormat

The input consists of a single string s provided via standard input. The string contains only the characters '(' and ')'.

Example Input:

()()

outputFormat

Output the length of the longest balanced parentheses substring. The output should be printed to standard output.

Example Output:

4

## sample

()

2