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>.
ch=input()
l=[]
l.append(-1)
a=0
n=1
m=0
for i in range(len(ch)):
    if(ch[i]=="(" ):
        l.append(i)
    elif(len(l)>1 ):
        l.pop()
        a=i-l[-1]    
        if(a>m):
            n=1
            m=a
        elif(a==m):
            n+=1
    else:
        l[0]=i      
print(m,n)

