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:
def main():
    m = cnt = 1
    stack = [1]
    for c in input():
        if c == '(':
            stack.append(1)
        else:
            if len(stack) < 2:
                stack[0] = 1
            else:
                x = stack.pop() + stack.pop() + 1
                if m < x:
                    m, cnt = x, 1
                elif m == x:
                    cnt += 1
                stack.append(x)
    print(m - 1, cnt)


if __name__ == '__main__':
    main()