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()

start = 0
cnt = 0
max_size = 0
max_cnt = 0
for i in range(0, len(s)):
    c = s[i]
    if c == '(':
        cnt += 1;
    else:
        cnt -= 1
    if cnt == 0:
        size = i - start + 1
        if size > max_size:
            max_size = size
            max_cnt = 1
        elif size == max_size:
            max_cnt += 1
    elif cnt < 0:
        start = i + 1
        cnt = 0
if max_size == 0:
    print("0 1")
else:
    print(max_size, max_cnt)