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>.
string = input()
stack = []
num = int(0)
lis = {}
right_bracket = string.count(')')
for i in list(string):
    if i is '(':
        stack.append(i)
    elif i is ')':
        if len(stack) > 0:
            stack.pop()
            num += 1
            right_bracket -= 1
            if right_bracket == 0:
                try:
                    lis[num*2] += 1
                except:
                    lis[num*2] = 1
                    break
        else:
            try:
                    lis[num*2] += 1
            except:
                    lis[num*2] = 1 
            num = 0
if len(stack) == 0 and num>0 and right_bracket != 0:
    try:
        lis[num*2] += 1
    except:
        lis[num*2] = 1 
if len(lis):
    max_key = max(lis, key = lambda k: k)
    print(max_key, end=" ")
    print(lis[max_key])
else:
    print("0 1")