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:
s = input()
a = []
for i in range(len(s)):
    if len(a) != 0 and s[a[-1]] == '(' and s[i] == ')':
        a.pop()
    else:
        a.append(i)
if len(a) == len(s):
    print(0, 1)
elif len(a) == 0:
    print(len(s), 1)
else:
    b = [a[0] - 0]
    for i in range(len(a) - 1):
        b.append(a[i + 1] - a[i] - 1)
    b.append(len(s) - a[-1] - 1)
    m = max(b)
    print(m, b.count(m))