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()
n=len(s)
c=[-1 for i in range(n)]
e=[-1 for i in range(n)]
st=[]
maxi=[0, 1]
for i in range(len(s)):
    if s[i]=="(":
        st.append(i)
    else:
        if len(st)==0:
            continue
        else:
            c[i]=e[i]=st.pop()
            if(c[i]>0 and c[c[i]-1]!=-1):
                e[i]=e[c[i]-1]
            l=i-e[i]+1
            if l>maxi[0]:
                maxi=[l, 1]
            elif l==maxi[0]:
                maxi[1]+=1
print(*maxi)    