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()

lst=[]
mx=0
arrmax=[]
for i in s:
    if(i==")" and len(lst)==0):
        continue
    else:
        if(i=="("):
            lst.append("(")
        elif(i==")"):
            mx+=2
            del lst[-1]
            if(len(lst)==0):
                arrmax.append(mx)
                mx=0
if(len(arrmax)!=0):
    m=max(arrmax)
    cont=0
    for i in arrmax:
        if(i==m):
            cont+=1
    print(m,cont)
else:
    print(0,1)

