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>.
################################################################################
bracket=input()

# bracket=')((())))(()())'
# bracket='))('
# bracket='()(())()'
# bracket='((((()((('
################################################################################
n=len(bracket)

regular=[0 for i in range(n)]
stack=[]
for i,s in enumerate(bracket):
    if s=='(':
        stack.append(i)
    else:
        if len(stack)>0:
            regular[i]=1
            j=stack.pop()
            regular[j]=1

longs=[0 for i in range(n)]
long=0
for i,r in enumerate(regular):
    if r:
        long+=1
        longs[i]=long
    else:
        long=0

max_regular=max(longs)
if max_regular==0:
    print('0 1')
else:
    out=str(max_regular)+' '+str(longs.count(max_regular))
    print(out)
