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()
br = []
count = 0
longest = 0
cur = 0

br.append(-1)

for i in range(len(s)):
    if (s[i] == '('):
        br.append(i)
    elif (s[i] == ')'):
        if len(br) != 0:
            br.pop()

        if (len(br) != 0):
            if i-br[-1] > longest:
                longest = i-br[-1]
                count = 1
            elif i-br[-1] == longest:
                count += 1
        else:
            br.append(i)

if (longest == 0):
    count = 1

print(longest, count, sep=' ')
