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()

c = 0
a = []
d = 0
m = -1
for i in s:
    if i == '(':
        a.append('(');
    else:
        if (len(a) == 0):
            if (c>m):
                m = c
                d = 1
            elif c==m:
                d += 1
            c = 0
        else:
            c += 1
            a.pop()
if (c>m):
    m = c
    d = 1
elif c==m:
    d += 1
if(m!=0):
    print(2*m,d)
else:
    print(0,1)
