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())
stack_b = [0]
stack_pos = [0]
length = 0
lenarray = []
counter = 0
len_max = 0

for i in range(len(n)):
    if n[i] == "(":
        stack_b.append(i + 1)
        stack_pos.append(i + 1)
    else:
        if len(stack_b) > 1:
            stack_b.pop()
            stack_pos.pop()
            tmp = stack_pos.pop()
            length = i + 1 - tmp
            lenarray.append(length)
            stack_pos.append(tmp)
        else:
            stack_pos.append(i + 1)


if lenarray:
    for k in lenarray:
        if k == max(lenarray):
            counter +=1
    print(max(lenarray), counter)
else:
    print("0 1")
