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__":
    s = input()
    a0,a1 = 0,1
    l = r = maxlen = cnt = 0
    for i in s:
        if i == '(':
            l += 1
        else:
            r += 1
        if l == r:
            if 2*l > maxlen:
                maxlen = 2*l
                cnt = 1
            elif 2*l == maxlen:
                cnt += 1
        elif r > l:
            l = r = 0
    if maxlen > a0:
        a0,a1 = maxlen,cnt
    for i in s[::-1]:
        if i == '(':
            l += 1
        else:
            r += 1
        if l == r:
            if 2*l > maxlen:
                maxlen = 2*l
                cnt = 1
            elif 2*l == maxlen:
                cnt += 1
        elif r > l:
            l = r = 0
    if maxlen > a0:
        a0,a1 = maxlen,cnt
    print(a0,a1)