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>.
string=input()
l=len(string)
s=[-1]*l
e=[-1]*l
F=[0]*(l+1)
stack=[]
maxi=0
for i in range(l):
    if string[i]=="(":
        stack.append(i)
    else:
        if len(stack)!=0:
            last_index=stack.pop()
            if last_index ==0:
                e[i]=0
                F[i-e[i]+1]+=1
                maxi=max(maxi,i-e[i]+1)
            else:
                if e[last_index-1]!=-1:
                    e[i]=e[last_index-1]
                    F[i-e[i]+1]+=1
                    maxi=max(maxi,i-e[i]+1)
                else:
                    e[i]=last_index
                    F[i-e[i]+1]+=1
                    maxi=max(maxi,i-e[i]+1)
if maxi==0:
    print(0,1)
else:
    print(maxi,F[maxi])
