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>.
a=input()
s=[-1]*len(a)
e=[-1]*len(a)
ans=[0]*(len(a)+1)
stack=[]
for i in range(len(a)):
    if a[i]=="(":
        stack.append(i)
    elif stack:
        k=stack.pop()
        s[i]=k
        e[i]=k
        if k-1>=0:
            if s[k-1]!=-1:
                e[i]=e[k-1]
        ans[i-e[i]+1]+=1
fin=""
for i in range(len(ans)):
    if ans[i]!=0:
        fin=str(i)+" "+str(ans[i])
if fin=="":
    print("0 1")
else:
    print(fin)
