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>.
'''input
)((())))(()())
'''
s = input().lstrip(')')
max_len = 0
num_max = 1
counts = {}

for i, c in enumerate(s):
    if c == '(':
        counts[i] = 0
        for start_pos in counts:
            counts[start_pos] += 1
    else:
        for start_pos in list(counts.keys()):
            counts[start_pos] -= 1
            if counts[start_pos] == 0:
                l = i - start_pos + 1
                if l > max_len:
                    max_len = l
                    num_max = 1
                elif l == max_len:
                    num_max += 1
            elif counts[start_pos] < 0:
                del counts[start_pos]

print(max_len, num_max)
