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()
index = [0]*len(string)
stack = list()
match = [("(",")")]
i = 0
n = 0
count = 0
max_n = 0
while i < len(string):
    if string[i] == "(":
        stack.append(i)
    else:
        if stack != [] and (string[stack[-1]], string[i]) in match:
            index[stack.pop()] = 1
            index[i] = 1
    i += 1
for i in index:
    if i == 0:
        n = 0
    else:
        n += 1
    if max_n == n:
        count += 1
    max_n = max(max_n, n)
if max_n == 0:
    count = 1
elif count == 0:
    count = 1
print(max_n, count)