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 = [0] + list(map(str, input()))

n = len(s)
if len(s) == 0 or len(s) == 1: print("0")
dp = [0] * (n)
ans = 0
num = 1
for i in range(1, n):
    if s[i] == ")":
        if s[i-1] == "(":
            dp[i] = dp[i-2] + 2
        if s[i - 1] == ")":
            if s[i - dp[i - 1] - 1] == "(" and i - dp[i-1] - 1 >=0:
                dp[i] = dp[i - 1] + 2 + dp[i - dp[i - 1] - 2]

    if dp[i] > ans:
        ans = dp[i]
        num = 1
    elif dp[i] == ans:
        num += 1


print(ans, num)