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 = []
ans = 0
cnt = 1
mx = 0
i = 0
start = 0
while i < len(s):
    if s[i] == '(':
        st.append(i)
    elif st and s[i] == ')':
        st.pop()
    else:
        ans = i-start
        if ans > mx:
            mx = ans
            cnt = 1
        elif ans == mx:
            cnt += 1
        start = i+1
    i += 1
if mx == 1:
    print(0,1)
else:
    print(mx,cnt)
