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 = []
max_len = 0
curr_len = 0
count = 1

for bracket in brackets:
    if bracket == '(':
        stack.append(bracket)
    elif stack:
        stack.pop()
        curr_len += 2
        if not stack:
            if curr_len == max_len:
                count += 1
            max_len = max(max_len, curr_len)
    else:
        curr_len = 0

print(max_len, count)
   					  	 	      			 		 		 		