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()

i = 0
degree = 0
maxLen, maxCnt = 0, 1
prev = {}

while i < len(s):
    degree += 1 if s[i] == '(' else -1
    if degree in prev and s[prev[degree] + 1] == '(':
        curLen = i - prev[degree]
        if curLen > maxLen:
            maxLen = curLen
            maxCnt = 1
        elif curLen == maxLen:
            maxCnt += 1
    prev[degree] = i
    i += 1

print(maxLen, maxCnt)
