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 = []
longest = 0
subs = 0
curr = 0
for bracket in s:
    if bracket == '(':
        stack.append(1)
    else:
        if not stack:
            continue
        elif stack[-1] == 1:
            stack.pop()
            curr += 2
            if not stack:
                longest = max(longest, curr)
                curr = 0
                subs += 1
if subs == 0:
    print("0 1")
else:
    print(longest, end = " ")
    print(subs)