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()
st=[]
n=len(s) 
cnt=0
li=dict()
for i in range(n):
    if(s[i]=='('):
        st.append(s[i])
    elif(len(st)>0 and s[i]==')'):
        st.pop()
        cnt+=2 
        
    if(len(st)==0 and cnt>0):
        try :
            li[cnt]+=1 
        except KeyError:
            li[cnt]=0 
            li[cnt]+=1 
        cnt=0 
val=0
jind=-1
for j in li.keys():
    if(li[j]>0 and j > jind):
        val=li[j] 
        jind=j 
        
print(jind , val) if(jind!=-1) else print(0 , 1)
    