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 = [s[0]]
ans = cans = 0
tans = 0
for i in range(1,len(s)):
    if len(st) == 0:
        ans = max(ans,tans)
        if ans == tans and ans != 0:
            cans += 1
        else:
            cans = 0
        st.append(s[i])
    if s[i] == '(' and st[-1] == ')':
        st = []
        continue
    if s[i] == ')' and st[-1] == '(':
        tans += 2
        st.pop()
    else:
        st.append(s[i])
if ans == cans == 0:
    print(0,1)
else:
    print(ans,cans)