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()
stack=[]
dic={}
n=len(s)
for i in range(n):
    if s[i]=='(':
        stack.append(i)
    else:
        if stack:
            dic[stack.pop()]=i
res=0
cur=1
i=0
lst=[]
for i in sorted(list(dic.keys())):
    lst.append([i,dic[i]])
for i in range(len(lst)):

    if lst[i][1]-lst[i][0]+1>res:
        res=lst[i][1]-lst[i][0]+1
        cur=1
    elif lst[i][1]-lst[i][0]+1==res:
        cur+=1
print(res,cur)