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()
ans=0
count=1
stack=[]
c=[-1]*len(s)
d=[-1]*len(s)
for i,el in enumerate(s):
    if el=="(":
        stack.append(i)
    else:
        if not stack:
            d[i]=-1
            c[i]=-1
        else:
            d[i]=stack.pop()
            
            pos=d[i]-1
            if pos>=0 and s[pos]=="(" and c[pos]!=-1:
                if c[pos]+i-d[i]+1>ans:
                    ans=c[pos]+i-d[i]+1
                    count=1
                elif c[pos]+i-d[i]+1==ans:
                    count+=1
                c[i]=c[pos]+i-d[i]+1
            else:
                
                c[i]=i-d[i]+1
                if ans<c[i]:
                    ans=c[i]
                    count=1
                elif ans==c[i]:
                    count+=1                    
print(ans,count)