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()
l = list()
cnt, maxl, maxc, doing = 0,0,0,True
for c in s:
    if l and c == ')':
        l.pop()
        cnt += 1
    if c == '(':
        l.append(c)
        cnt += 1
    if not l:
        if cnt > maxl:
            maxl = cnt
            maxc = 0
        maxc += (cnt == maxl)
        cnt = 0
        l = list()

print(maxl, maxc)