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)
s1=[]
c=0
c1=1
k=[]
for i in range(n):
    if s[i]=='(':
        s1.append(['(',i])
    else:
        if s1:
            k=s1.pop()
            #print(i,k)
            if c==(i-k[1]+1):
                c1+=1
            elif c<(i-k[1]+1):
                c=(i-k[1]+1)
                
print(c,c1)