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>.
import collections

s = input()

M = 10 ** 6 + 5

dp = [0] * M

stack = collections.deque()

maxLen = 0
cnt = 0

for i, c in enumerate(s):
    if c == ")":
        if 0 == len(stack): continue
        tmp = stack.pop()
        if tmp:
            dp[i] = dp[tmp - 1] + i - tmp + 1
        else:
            dp[i] = i + 1
        if dp[i] > maxLen:
            maxLen = dp[i]
            cnt = 1
        elif dp[i] == maxLen:
            cnt += 1
    else:
        stack.append(i)
if not maxLen:
    cnt = 1
print(maxLen, end = " ")
print(cnt)