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:
a,b = 0,1

l = [-1]

for i,c in enumerate(input()):

    if c == '(':

        l.append(i)

    elif len(l) > 1:

        l.pop()

        minl = i - l[-1]

        if a < minl:

            a,b = minl,1

        elif a == minl:

            b += 1

    else:

        l[0] = i

print(a, b)



# Made By Mostafa_Khaled