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
end=-1
i=0
lst=[]

for i in sorted(list(dic.keys())):
    lst.append([i,dic[i]])
total=[]
new=[]
for i in range(len(lst)):
    if i==0 or lst[i][0]>lst[i-1][1]:
        new.append(lst[i])
lst=new
for i in range(len(lst)):
    if lst[i][0]==end+1:
        res+=lst[i][1]-lst[i][0]+1
        end=lst[i][1]

    else:
        total.append(res)
        res=lst[i][1]-lst[i][0]+1
        end=lst[i][1]

total.append(res)
if not total:
    t=0
else:
    t=max(total)
if t==0:
    print(0,1)
else:
    print(t,total.count(t))