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>.
s = input()

stack = []
max_length = 0
count = 1

for i in range(len(s)):
    if s[i] == '(':
        stack.append(i)
    elif len(stack) > 0:
        if s[stack[-1]] == '(':
            stack.pop()
            length = i - (stack[-1] if len(stack) > 0 else -1)
            if length > max_length:
                max_length = length
                count = 1
            elif length == max_length:
                count += 1
        else:
            stack.append(i)

if max_length == 0:
    print("0 1")
else:
    print(max_length, count)

  		  					  			   	  	   	  	