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>.
a=str(input())
b=[]
c=0
d=1
e=0
f=0
for i in a:
    if i=='(':
        b.append(i)
    else:
        if len(b)!=0 and b[len(b)-1]=='(':
            b.pop()
            c=c+2
        else:
            if c==e:
                d=d+1
            if d>f:
                f=d
            if c>e:
                e=c
                c=0
                d=1
print(e,f)