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()
balance = 0
stack = [(-(10 ** 9), -2), (balance, -1)]
maxlen = 0
cnt = 1
for i in range(len(s)):
    if s[i] == "(":
        balance += 1
    else:
        balance -= 1
    while stack[-1][0] > balance:
        stack.pop()
    if stack[-1][0] == balance:
        if i - stack[-1][1] > maxlen:
            maxlen = i - stack[-1][1]
            cnt = 1
        elif i - stack[-1][1] == maxlen:
            cnt += 1
    stack.append((balance, i))
print(maxlen, cnt)