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>.
# cook your dish here
s = input()

st= []
c = 0
ma = 0
ma2 = 0
for i in s:
    if i == '(':
        st.append(i)
    else:
        if st != []:
            st.pop()
            ma2 += 1
            if st == []:
                c += 1
                if ma2 > ma:
                    ma = ma2
                ma2 = 0
            
if c == 0:
    print("0 1")
else:
    print(2*ma,c)
    