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)

m = 0
c = 1
i = 0
while i < n:
    balanse = 0
    l = 0
    lm = 0
    while l + i < n:
        l += 1
        if s[l+i-1] == "(":
            balanse += 1
        elif s[l+i-1] == ")":
            balanse -= 1

        if balanse < 0:
            break
        elif balanse == 0:
            if l > m:
                lm = l
            elif l == m:
                c += 1

    if 0 != lm == m:
        c += 1
    elif lm > m:
        m = lm
        c = 1

    i += 1
print(m, c)
