400. Longest Well-Formed Parentheses

0

Hard

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

Input Format

Enter the number of test cases followed by the input string for each test case.

Output Format

Print the length of the longest well-formed parentheses substring for each test case.

Example

Input

2 (() )()())

Output

2 4

Constraints

1<=T<=1000 1<=Length(S)<=1000
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