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 solve():
    brackets = input()

    stack = []
    stack.append(-1)
    num_valid, max_len = 1, 0

    for i in range(len(brackets)):
        if brackets[i] == "(":
            stack.append(i)
        
        else:
            if len(stack):
                stack.pop()
            
            if len(stack):
                if max_len == i - stack[-1]:
                    num_valid += 1
                elif i - stack[-1] > max_len:
                    max_len = i - stack[-1]

            else:
                stack.append(i)
    
    print(max_len, num_valid)
    

solve()
   				 				    	   			 				