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()
longest=0 
count=0
i=0
l=[]
c=0
while i<len(s):
    if s[i]=="(":
        l.append(")")
        i+=1
        continue 
    else:
        if len(l)==0:
            c=0
            i+=1 
            continue
        j=i 
        while l and j<len(s) and s[j]==")" and s[j]==l[-1]:
            c+=1 
            j+=1 
            l.pop()
        if c>longest:
            longest=c 
            count=1
        elif c==longest:
            count+=1 
        #print(c,count)
        i=j 
if longest==0:
    print("0 1")
else:
    print(2*longest,count)
        
            
        