Description

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.

Input

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.

Output

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".

Sample

Input

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

Output

6 2
0 1