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>.
    s = input()
     
    n = len(s)
     
    stack = []
    early = [-1] * n
    corrs = [-1] * n
     
    for i in range(n):
        if s[i] == '(':
            stack.append(i)
        else:
            if stack:
                corrs[i] = early[i] = stack.pop()
                if early[i] and s[early[i] - 1] == ')' and early[early[i] - 1] != -1:
                    early[i] = early[early[i] - 1]
            else:
                early[i] = corrs[i] = -1
     
    # print(list(s))
    # print(corrs)
    # print(early)
     
    record = 0
    count = 0
     
    for i in range(n):
        if early[i] == -1:
            continue
        length = i - early[i] + 1
        if length > record:
            record = length
            count = 1
        elif length == record:
            count += 1
    if record == 0:
        print(0, 1)
    else:
        print(record, count)