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>.
if __name__ == "__main__":
    a = input()
    dic = defaultdict(int)
    l = r = max_len = 0
    for i in a:
        if i == "(":
            l += 1
        else:
            r += 1
        if l == r:
            max_len = max(max_len,2*r)
            dic[max_len] += 1
        elif r > l:
            l = r = 0
    l = r  = 0
    for i in a:
        if i == "(":
            l += 1
        else:
            r += 1
        if l == r:
            max_len = max(max_len,2*r)
            dic[max_len] += 1
        elif r < l:
            l = r = 0
    print(dic[max_len])