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:
#!/usr/bin/env python

line = input()
s = [-1]
max = 0
n_max = 0
i = 0
for a in line:
    if a == '(':
        s.append(i)
    elif len(s) > 1:
        e = s.pop()
        d = i - s[-1]
        if d > max:
            max = d
            n_max = 1
        elif d == max:
            n_max += 1
    else:
        s[0] = i
    i =i + 1

if max == 0:
    print(0, 1)
else:
    print(max, n_max)