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>.
brack = input()
l = len(brack)
s = []
longest = 0
num = 1
for i in range(l):
    if(brack[i] == '('):
        s.append(i)
    elif(brack[i] == '(' and s):
        temp = i-s.pop()+1
        if(temp > longest):
            longest = temp
            num = 1
        elif(temp == longest):
            num += 1
print(longest, num)