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=e=[None]*(10*6+1)  #s=start, f=frequency, e=extension
f=[0]*(10*6+1)
stack=[]
st=input()
mx=0
for i in range(len(st)):
    if st[i]=='(':
        stack.append(i)
    else:
        if stack==[]:
            s[i]=e[i]=-1
        else:
            idx=stack.pop()
            s[i]=e[i]=idx
            if idx-1>=0 and st[idx-1]==')' and s[idx-1]>=0:
                e[i]=e[idx-1]
            l=i-e[i]+1
            f[l]+=1
            mx=max(mx,l)
f[0]=1
print(mx,f[mx])