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 enum


s=input()
n = len(s)
dp = [0] * n
st, ans = 0, 0

for (idx, v) in enumerate(s):
    if  v == '(':
        st += 1
    else:
        if st == 0:
            continue
        else:
            st -= 1
            dp[idx] = 2
            if idx - 1 >= 0 and s[idx - 1] == ')':
                dp[idx] = max(dp[idx], dp[idx - 1] + 2)
            if idx - 2 >= 0 and s[idx - 2] == ')':
                dp[idx] = max(dp[idx], dp[idx - 2] + 2)
            
ans = max(dp)

if ans == 0:
    print("0 1")
else:
    print(ans, dp.count(ans))

    
