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>.
from collections import defaultdict
s = [0] + list(input())
n = len(s)
dp = [0] * n
g = defaultdict(int)
for i in range(1, n):
    if s[i] == ')':
        if s[i - 1] == '(':
            if i - 2 >= 0:
                dp[i] = dp[i - 2] + 2
        else:
            if i - dp[i - 1] + 1 >= 0 and s[i - dp[i - 1] - 1] == '(':
                if i - dp[i - 1] - 2 >= 0:
                    dp[i] += dp[i - dp[i - 1] - 2] + 2 + dp[i - 1]
    g[dp[i]] += 1
ans_k, ans_v = -1, -1
for k, v in g.items():
    if k > ans_k:
        ans_k = k
        ans_v = v
if ans_k <= 0:
    print(0, 1)
else:
    print(ans_k, ans_v)