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 = list(input())

sta = [0]*(len(s)+1)
ans = [0]*(len(s)+1)
head=0
ans1=0
ans2=1
for i in range(len(s)):
    if s[i]==')':
        if head==0:
            continue
        head-=1
        ans[i] = i-sta[head]+1+ans[sta[head]-1]
        if ans1==ans[i]:
            ans2+=1
        elif ans1<ans[i]:
            ans1=ans[i]
            ans2=1

    else:
        head+=1
        sta[head]=i
print(ans1,ans2)
