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:
#code by aanchaltiwari
#practice
s=input()
n=len(s)
valid=[-1]*n
freq=[0]*(n+1)
stack=[]
extension=[-1]*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]>=0:
                extension[i]=extension[index-1]
            length=i-extension[i]+1
            freq[length]+=1
f=0
for i in range(n,0,-1):
    if freq[i]:
        print(i,freq[i])
        f=1
        break
if f==0:
    print(0,1)