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 Counter
s = input()
dp = [0] * len(s)

# dp[i] = dp[i-1] + 2 + dp[i-dp[i-1]-2] if s[i] == ')' and s[i-dp[i-1]-1] == '(' else 0 

for i in range(1, len(s)):
    if s[i] == '(':
        dp[i] = 0
    else:
        if s[i-dp[i-1]-1] == '(':
            dp[i] = dp[i-1] + 2
            if i-dp[i-1]-2 >= 0:
                dp[i] += dp[i-dp[i-1]-2]
        else:
            dp[i] = 0
cnt = Counter(dp)
if cnt[0] == len(s):
    print(0, 1)
else :
    print(max(cnt), cnt[max(cnt)])