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>.
brackets = tuple(input())

stack = [-1]
max_res = 0
count = 1

for i, bracket in enumerate(brackets):
    if bracket == '(':
        stack.append(i)
    else:
        stack.pop()
        if stack:
            res = i - stack[-1]
            if res == max_res:
                count += 1
            max_res = max(res, max_res)
        else:
            stack.append(i)


print(max_res, count)
	 				  	   		 				 		 	   	 		