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()

d = [-1] * len(s)
e = [-1] * len(s)

stack = []
for i, c in enumerate(s):
    if(c == "("):
        stack.append(i)
    else:
        if(len(stack) == 0):
            continue
        else:
            d[i] = stack.pop()
            e[i] = d[i]
            if(s[d[i] - 1] == ")" and e[d[i] - 1] != -1):
                e[i] = e[d[i] - 1]

best = 0
for i in range(len(s)):
    if(e[i] != -1):
        best = max(best, i - e[i] + 1)

count = 0
for i in range(len(s)):
    if(e[i] != -1 and best == i - e[i] + 1):
        count += 1


if(best == 0):
    print("0 1")
else:
    print(best, count)