#描述#
This is yet another problem dealing with regular bracket sequences.

We should remind you that a bracket sequence is called regular, if by inserting ‘+’ and ‘1’ into it we can get a correct mathematical expression. For example, sequences “(())()”, “()” and “(()(()))” are regular, while “)(“, “(()” and “(()))(“ are not.

You are given a string of “(“ and “)” characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.

#格式#
##输入格式##
There are T test cases(2≤T≤20).
The only line of each test case contains a non-empty string, consisting of “(“ and “)” characters. Its length does not exceed 10^6.

##输出格式##
For each test case Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

#样例1#
##样例输入1##

)((())))(()())
))(

##样例输出1##

6 2
0 1    

#限制#
500ms
32768KB

#提示#

#来源#