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>.

n=input()
stack=[]
count=0
maxi=0
u_max=0
for i in n:
    if i=='(':
        stack.append(i)
    if i==')':
        if len(stack)>0 and stack[-1]=='(':
            stack.pop()
            maxi+=2
        if maxi==u_max:
            count+=1
        if maxi>u_max:
            count=1
    
        if len(stack)==0:
            maxi=0
if u_max==0:
    print(u_max,'1')
else:
    print(u_max,count)