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()
op = 0
count = 0
longest = 0
cur = 0

for b in s:
    if (b == '('):
        op += 1
    elif (b == ')') and op > 0:
        cur += 2
        op -=1
        if cur > longest:
            longest = cur
            count = 1
        elif cur == longest:
            count += 1
    else:
        cur = 0

if (longest == 0):
    count = 1

print(longest, count, sep=' ')
