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 = list()
c  = 0
x  = 0
max = 0
for i in range(len(s)):
    if s[i] == '(':
        st.append(s[i])
    else:
        if st and st[-1] == '(':
            c+=2
            st.pop()
            if i == len(s)-1:
                if c > max:
                    max = c
                    x   = 1
                elif c>=1 and c == max:
                    x += 1
        else :
            if c > max:
                max = c
                x = 1
            elif c>=1 and c == max:
                x+= 1
            c = 0
if x >= 1:
    print(str(max)+' '+ str(x))
else:
    print('0 1')
            
