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>.
from collections import defaultdict

if __name__ == "__main__":
    a = input()
    dic = defaultdict(int)
    l = r = max_len = 0
    from collections import defaultdict

if __name__ == "__main__":
    a = input()
    dic = defaultdict(int)
    dic1 = 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
    l1 = r1 = max_len1 = 0
    a = a[::-1]
    for i in a:
        if i == "(":
            l1 += 1
        else:
            r1 += 1
        if l1 == r1:
            max_len1 = max(max_len1,2*r1)
            dic1[max_len1] += 1
        elif r1 < l1:
            l1 = r1 = 0
    if max_len == 0 and max_len1 == 0:
        print(0,1)
    else:
        if max_len > max_len1:
            print(max_len,dic[max_len])
        elif max_len < max_len1:
            print(max_len1,dic1[max_len1])
        else:
            print(max_len,max(dic[max_len],dic1[max_len1]))
            