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()
n = len(s)
f = [0] * n
best, ans = 0, 1
for i in range(1, n):
    if s[i] == ")":
        j = i - f[i - 1] - 1
        if j >= 0 and s[j] == "(" and f[i - 1] == i - j - 1:
            f[i] = f[i - 1] + 2
        if j - 1 >= 0 and f[j - 1]:
            f[i] += f[j - 1]
        if f[i] > best:
            best = f[i]
            ans = 1
        elif f[i] == best:
            ans += 1
print(best, ans)