Problem: 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

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

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".

Examples

Input

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


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON3):

Solution:
if __name__ == "__main__":
    inputs = input()
    c = [-1]*len(inputs)
    stack = []
    ans, count = 0, 1
    for index, item in enumerate(inputs):
        if item == "(":
            stack.append(index)
        else:
            if stack:
                x = stack.pop()
                if x:
                    c[index] = x if c[x-1] == -1 else c[x-1]
                else:
                    c[index] = x
                tmp = index - c[index] + 1
                if ans < tmp: 
                    ans, count = tmp, 1;
                elif ans == tmp:
                    count += 1
    print(ans, count)