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>.
init_brackets = tuple(input())

stack_id = [-1]
result = {0: 1}

for i, bracket in enumerate(init_brackets):
    if bracket == '(':
        stack_id.append(i)
    else:
        stack_id.pop()
        if stack_id:
            res = i - stack_id[-1]
            result[res] = result.get(res, 0) + 1
        else:
            stack_id.append(i)
 
max_res = max(result)
print(max_res, result[max_res])
						   						 		 			    	 	 	