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
count = 0
cur_len = 0

for c in brackets:
    if c == '(':
        stack.append(c)
        cur_len += 1
    else:
        if stack:
            stack.pop()
            cur_len += 1
            if not stack:
                if cur_len > max_len:
                    max_len = cur_len
                    count = 1
                elif cur_len == max_len:
                    count += 1
        else:
            cur_len = 0
            

print(max_len, count)
	 			 	    		 		 			 	   				 	