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)
st = []
en = [0]*n
for i in range(n):
    if s[i] == '(':
        st.append(i)
    elif st:
        en[st.pop()] = i

ans = 0
mx = 0
cnt = 1
pen = 0
i = 0
while i < n:
    if en[i]:
        ta = en[i]-i+1
        if i == pen+1:
            ans += ta
        else:
            ans = ta
        if ans > mx:
            mx = ans
            cnt = 1
        elif ans == mx:
            cnt += 1
        pen = en[i]
        i = en[i]+1
    else:
        i += 1
print(mx,cnt)