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()
stack,c,l,ll=[-1],1,0,0
for i in range(len(s)):
    if s[i]=="(":
        stack.append(i)
    else:
        stack.pop()
        if stack:
            k=stack[-1]
            if i-stack[-1]>ll:
                ll=i-stack[-1]
                c=1
            elif i-stack[-1]==ll:
                c+=1
        else:
            stack.append(i)
print(ll,c)