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()
cnt = ans = 0
n = len(s)
st = [-1]
for i in range(n):
    if s[i]=='(': st.append(i)
    else:
        if st[-1]==-1 or s[st[-1]]==')': st.append(i)
        else:
            st.pop()
            if i-st[-1]>ans:
                ans = i-st[-1]
                cnt = 1
            elif i-st[-1]==ans: cnt += 1
if ans==0: cnt = 1
print(ans,cnt)