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()
q=[]
dp=[0]*(len(s)+1)
Max=1
c=0
for i in range(len(s)):
    if s[i]=="(":
        q.append(i)
    else:
        if q:
            temp=q.pop()
            dp[i]=dp[temp-1]+i-temp+1
            Max=max(dp[i],Max)
if Max==1:
    print("0 1")
else:
    for i in range(len(dp)):
        if dp[i]==Max:
            c=c+1
    print(Max,c)