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.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
s=input()
temp={}
curr=0
ans=0
c=0
temp[0]=-1
for i,el in enumerate(s):
    if el=="(":
        curr+=1
        if curr not in temp:
            temp[curr]=i
    else:
        curr-=1
        if curr<0:
            temp={0:i}
            curr=0
        else:
            if curr in temp:
                ind=temp[curr]
                if i-ind>ans:
                    ans=i-ind
                    c=1
                elif i-ind==ans:
                    c+=1
            else:
                temp[curr]=i
print(ans,max(c,1))
                