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()
    ans0,ans1 = 0,1
    l = r = max_len = cnt = 0
    for i in a:
        if i == '(':
            l += 1
        else:
            r += 1
        if l == r:
            if 2*r > max_len:
                max_len = 2*r
                cnt = 1
            elif 2*r == max_len:
                cnt += 1
        elif r > l:
            l = r = 0
    if max_len > ans0:
        ans0,ans1 = max_len,cnt
    a = a[::-1]
    l = r = max_len = cnt = 0
    for i in a:
        if i == '(':
            l += 1
        else:
            r += 1
        if l == r:
            if 2*r > max_len:
                max_len = 2*r
                cnt = 1
            elif 2*r == max_len:
                cnt += 1
        elif r > l:
            l = r = 0
    if max_len > ans0:
        ans0,ans1 = max_len,cnt
    print(ans0,ans1)