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 = list(input())

cnt = 0
start = 0
end = 0
longest = 0
lvl = 0
i = 0
# ))(
# )((())))(()())
while i < len(s):
    if s[i] == "(":
        lvl = 0
        start = i
        end = i
        while end < len(s):
            if s[end] == "(":
                lvl += 1
            elif s[end] == ")":
                lvl -= 1

            # print(start,end,i,lvl)
            if lvl < 0: break
            if lvl == 0:
                if end - start +1 == longest:
                    cnt += 1
                elif end - start +1 > longest:
                    cnt = 1
                    longest = end - start + 1
                i = end
                end += 1
                # print(start, end, end - start + 1, longest)

            else:
                end += 1

    elif s[i] == ")":
        lvl -= 1
    i += 1

if cnt == 0:
    print("0 1")
else:
    print(f"{longest} {cnt}")
