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()
a,b = 0,len(s)
while s[a]==')': a += 1
while s[b-1]=='(': b -= 1
if a==b: print(0,1); exit()

res,cnt,dic,st = 0,1,{},0
for i in range(a,b):
    if s[i]=='(': 
        if st not in dic: dic[st] = [i,i]
        st += 1
    else:
        if st in dic:
            if dic[st][-1]-dic[st][0]==res: cnt += 1
            elif dic[st][-1]-dic[st][0]>res: res = dic[st][-1]-dic[st][0]; cnt = 1
            del dic[st]
        if st:
            st -= 1
            dic[st][1] = i+1

for st in dic:
    if dic[st][-1]-dic[st][0]==res: cnt += 1
    elif dic[st][-1]-dic[st][0]>res: res = dic[st][-1]-dic[st][0]; cnt = 1
print(res,cnt)