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>.
string = input()
stack = ["("]
c = []
res = "("
init = string.find("(")+1

for i in range(init, len(string)):
    if string[i] == "(" and i >= init:
        stack.append("(")
        print(stack)
        res += "("

    elif string[i] == ")" and len(stack) != 0:
        stack.pop()
        res += ")"
        if len(stack) == 0:
            c.append(len(res))
            res = ""

if len(c) == 0:
    print(0, 1)
else:
    c.sort(reverse=True)
    x = c.count(c[0])
    print(c[0], x)