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>.
l=input()
l1=[]
l2=[]
ans=0
count=1
for i in range(len(l)):
    if l[i]=="(":
        if l1==[]:
            l1.append(i)
            l2.append(i)
        else:
            l1.append(i)
    else:
        if l1!=[]:
            l1.pop()
            if l1==[]:
                l2.append(i)
                if len(l2)==2 and l2[1]-l2[0]>ans:
                    ans=l2[1]-l2[0]
                    l2=[]
                    count=1
                elif len(l2)==2 and l2[1]-l2[0]==ans:
                    l2=[]
                    count+=1
print(str(ans+1)+" "+str(count))

