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>.
def ii(): return int(input())
def si(): return input()
def mi(): return map(int,input().split())
def msi(): return map(str,input().split())
def li(): return list(mi())

s=si()
stack,dp,c=[],[0]*(len(s)),[0]*(len(s))
for i in range(len(s)):
    if s[i]=='(':
        stack.append(i)
        c[i]=-1
        
    else:
        if stack:
            c[i]=i-stack[-1]+1
            if c[stack[-1]-1]!=-1:
                c[i]+=c[stack[-1]-1]
                
            stack.pop()
            
        else:
            c[i]=-1
            
if max(c)==0:
    print(0,1)
    
else:
    print(max(c),c.count(max(c)))
    #print(*c)