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 longest_regular_substring(s):
    stack = []
    max_len = 0
    count = 1
    start = 0
    for i, c in enumerate(s):
        if c == '(':
            stack.append(i)
        else:
            if stack:
                stack.pop()
                if stack:
                    length = i - stack[-1]
                else:
                    length = i - start + 1
                if length > max_len:
                    max_len = length
                    count = 1
                elif length == max_len:
                    count += 1
            else:
                start = i + 1
    return max_len, count

s = input()
print(*longest_regular_substring(s))

	 	 	 	 			     					 			 		 	