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>.
if __name__ == '__main__':
    
    string = input()
    longest = 0
    count = 1
    stack = [-1]
    
    for i in range(len(string)):
        if string[i]=="(":
            stack.append(i)
        
        else:
            stack.pop()
            
            if not stack:
                stack.append(i)
            else:
                if longest<i-stack[-1]:
                    longest = i-stack[-1]
                    count = 0
                if longest==i-stack[-1]:
                    count+=1
                    
    
    print("{} {}".format(longest,count))
    