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>.
def solve(a):

    stack = []
    longest = 0
    count = 1
    
    for i in range(len(a)):
        current = a[i]
        stack.append(i)

        if current == ')':
            if len(stack) >= 2:
                if a[stack[-2]] == '(' and a[stack[-1]] == ')':
                    stack.pop()
                    stack.pop()
                    curr = i - stack[-1]
                    
                    if curr > longest:
                        longest = curr
                        count = 1
                    elif curr == longest:
                        count += 1 

    return [longest, count]

if __name__ == '__main__':
 
    a = list(input())

    print(*solve(a))