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>.
n = int(input())
s = input()
dp = [0] * n
stack = []

for i in range(n):
    if s[i] == '(':
        stack.append(i)
    elif stack:
        j = stack.pop()
        dp[i] = dp[j-1] + i - j + 1 if j > 0 else i + 1

print(max(dp.count(max(dp)), 1), max(dp))
