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>.
string = input()
stack = []
count = 0
maxVal = float('-inf')
for char in range(len(string)):
    if len(stack)==0:
        maxVal = char
        count = 1
        stack.append((string[char], char))
    elif stack[-1][0] == "(" and string[char] == ")":
        _, ind = stack.pop()
        temp = char - ind + 1
        if temp == maxVal:
            count +=1
        if temp > maxVal:
            count = 1
            maxVal = temp
    else:
        stack.append((string[char],char))
print(maxVal, count)
        