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()
n = len(s)
stack = []
valid = [-1 for i in range(n)]
freq = [0]*(n+1)
extension = [-1 for i in range(n)]
for i in range(n):
    if s[i] == "(":
        stack.append(i)
    else:
        if stack:
            index = stack.pop()
            valid[i] = index
            extension[i] = index
            if index-1 > 0 and s[index-1] == ")" and valid[index-1] != -1:
                extension[i] = extension[index-1]
            length = i-extension[i]+1
            freq[length] += 1
ans = 0
for i in range(n, -1, -1):
    if freq[i]:
        print(i, freq[i])
        break
else:
    print(0, 1)