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:
from collections import Counter
s = input()
n = len(s)
d = []
c = dict()
for i in range(n):
    if s[i] == ')': 
        if len(d) == 0: 
            continue
        c[i] = i - d[-1] + 1 + c.get(d.pop() - 1, 0)
    else:
        d.append(i)

if len(c) == 0:
    print(0, 1)
else:
    res = Counter(c.values())
    m = max(res.keys())
    print(m, res[m])