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>.
stack = [-1]

string = input()
maxlength  =-1
count = 0
for i in range(len(string)):
    
    if string[i] == "(":
        stack.append(i)
    else:
        ind = stack.pop()
       
        if not stack:
            stack.append(i)
        else:
            if maxlength<(i-ind+1):
                maxlength = i-ind+1
                count = 1
            elif maxlength == (i-ind+1):
                count+=1
        
if maxlength!=-1:
    print(maxlength,count)
else:
    print(0,1)

            
            
            

