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)
st=[0]*n 
en=[0]*n
stk=[]
Fr=[0]*(n+1) 
mx=0 
l=0
for i in range(n): 
    #print(stk)
    if(s[i]=='('):
        stk.append(i) 
    else:
        if(len(stk)==0):
            st[i]=-1 
            
        else:
            en[i]=indx=st[i]=stk.pop()
            if(indx>0 and s[indx-1]==')' and st[indx-1]>=0):
                en[i]=en[indx-1]
            
            l=i-en[i] +1
            Fr[l]+=1
            mx=max(mx,l)
    
print(mx, Fr[mx])