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>.
inp=input();
st=[];
d=[-1]*len(inp);
c=[-1]*len(inp);
for i in range(len(inp)):
    if inp[i]=='(':
        st.append(i);
    else:
        if len(st)==0:
            d[i]=-1;
            c[i]=-1;
        else:
            d[i]=st.pop();
            c[i]=d[i];
            if inp[d[i]-1]==')' and c[d[i]-1]!=-1:
                c[i]=c[d[i]-1];

maxl=0;
n=1;
l=0;
for i in range(len(c)):
    if c[i]!=-1:
        l=i-c[i]+1;
        if l>maxl:
            maxl=l;
            n=1;
        elif l==maxl:
            n+=1;

print(*[maxl,n]);
