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>.
n, m, length = 0, 0, 0
s = input()
d = [-1] * 1000006
stack = []

max_length = 0
count = 1

for i in range(len(s)):
    if not stack or s[i] == '(':
        stack.append(i)
        continue

    pos = stack[-1]

    if s[pos] == '(':
        if d[pos - 1] != -1:
            d[i] = d[pos - 1]
        else:
            d[i] = pos

        length = i - d[i] + 1
        if length == max_length:
            count += 1
        elif length > max_length:
            max_length = length
            count = 1

    stack.pop()

print(max_length, count)

     	     	 	 	 	 			 		    	