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 = []
mx = 0
m = 0
ns = 0
for i in s:
    if st:
        if i == ')':
            st.pop()
            m+=1
        elif i=='(':
            st.append(i)
    else:
        if i=='(':
            st.append(i)
        else:
            if m>mx:
                mx = m
                ns = 1
            elif m==mx:
                ns+=1
            m = 0
    #print(st)
    #print(m)
if m>mx:
    mx = m
    ns = 1
elif m==mx:
    ns+=1

if mx==0:
    ns = 1
print(2*mx,ns)
        