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()
st = []
pairs = []
pair = 0
count = 0
for char in s:
    if char == '(':
        st.append(char)
    elif char == ')' and len(st) != 0:
        st.pop()
        pair += 2
        if len(st) == 0:
            count += 1
            pairs.append(pair)
            pair = 0
if count == 0:
    print(0, 1)
else:
    print(max(pairs), count)