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>.
lst = []
m, _max, count = 0, 0, 0
for i in input():
    if i == '(':
        lst.append(i)
    else:
        for j in range(len(lst) - 1, -1, -1):
            if lst[j] == '(':
                lst[j] += ')'
                break
        else:
            lst.append(')')
lst.append(')')

for i in range(len(lst)):
    if len(lst[i]) == 1:
        if m > _max:
            _max = m
            count = 1
        elif m == _max and m > 0:
            count += 1
        m = 0
    else:
        m += 2

print(lst)
print(_max, count)
