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>.
s = input()
n = len(s)

stack = []  # stack to keep track of opening brackets
max_len = 0  # maximum length of regular bracket sequence found so far
count = 1  # number of substrings with maximum length found so far

for i in range(n):
    if s[i] == '(':
        stack.append(i)  # push the index of opening bracket to stack
    elif stack:  # if stack is non-empty
        j = stack.pop()  # pop the index of opening bracket from stack
        if j > 0 and s[j-1] == ')' and max_len == i-j+1:  # another substring with same length found
            count += 1
        elif i-j+1 > max_len:  # new substring with longer length found
            max_len = i-j+1
            count = 1

if max_len == 0:
    print("0 1")
else:
    print(max_len, count)
