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>.
n = list(input())
counter = 0
substringarray = []
lmax = 0
lmax_counter = 1
k = 0
while k < len(n):
    counter = 0
    for i in range(k, len(n)):
        if n[i] == "(":
            counter += 1
            substringarray.append(n[i])
#            print("a", counter, len(substringarray))
        else:
            counter -= 1
#            print("b", counter, len(substringarray))
            if counter < 0:
                counter = 0
                break
            else:
                substringarray.append(n[i])
#               print("b2", counter, len(substringarray))

        if counter == 0:
#           print("c", counter, len(substringarray))
            if lmax <= len(substringarray):
                if lmax == len(substringarray):
                    lmax_counter += 1
                else:
                    lmax = len(substringarray)
    k += 1
    substringarray = []

print(lmax, lmax_counter)