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>.
stack = []
ans = 0
count = 1
cur = 0
for i,c in enumerate(input()):
    if c == '(':
        cur += 1
        stack.append(i)
    else:
        if cur == 0:
            pass
        else:
            cur -= 1
            rl = i-stack.pop()+1
            if rl>ans:
                ans = rl
                count =1
            elif rl == ans:
                count +=1
print(ans, count)