Longest valid Parentheses

[madHEYsiaOYO]

Given a string S consisting of opening and closing parenthesis '(' and ')'. Find length of the longest valid parenthesis substring.

Input:
First line contains number of test cases T. Each test case have one line string S of character '(' and ')' of length N.

Constraints:
1 <= T <= 500
1 <= N <= 105

Example:
Input:
2
((()
)()())

Output:
2
4

Explanation:
Testcase 1: Longest valid balanced parantheses is () and its length is 2.