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>.
s = input().strip()
n = len(s)

# Initialize a stack to keep track of opening brackets
stack = []

# Initialize an array to store the length of the longest valid bracket sequence ending at each index
dp = [0] * n

# Iterate through the input string
for i in range(n):
    if s[i] == '(':
        stack.append(i)
    elif stack:
        j = stack.pop()
        length = i - j + 1
        if j > 0:
            length += dp[j - 1]
        dp[i] = length

# Find the maximum length of a valid bracket sequence in the dp array
max_length = max(dp)

# Count the number of sequences with the maximum length
count = dp.count(max_length)

# Output the result
print(max_length, count)
