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
 

** For More Input/Output Examples Use 'Expected Output' option **