Given a string S consisting only of opening and closing parenthesis 'ie '('  and ')', find out the length of the longest valid substring.

NOTE: Length of smallest the valid substring ( ) is 2.

Input
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. 
The first line of each test case contains a string S consisting only of ( and ).

Output

Print out the length of the longest valid substring.

Constraints
1 <= T <= 100
0 <   S  <= 110

Examples 

Input
4
(()(
()()((
((()()())))
()(())(

Output
2
4
10
6

Explanation:
Test Case 1: (()(
The longest valid substring is "()". Length = 2
Test Case 2: ()()((
The longest valid substring is "()()". Length = 4
Test Case 3: ((()()())))
The longest valid substring is "((()()()))". Length = 10
​Test Case 4: ()(())(
The longest valid substring is "()(())". Length = 6

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