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()
top=-1
d={}
c=0
for j in range(len(s)):
    if top == -1 and s[j] ==')':
        c=0
        continue
    if s[j] == '(':
        top=top+1
    else:
        top=top-1
        c=c+1
        if c in d:
            d[c]=d[c]+1
        else:
            d[c]=1
if(len(d)==0):
    print(0,1)
else:
    k=sorted(d)[-1]
    print(2*k,d[k])