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='))('
################################################################################
n=len(bracket)
long=[0 for i in range(n)]

pn=0
start=0
for i,s in enumerate(bracket):
    if s=='(':
        pn+=1
    if s==')':
        pn=pn-1

    if pn==0:
        long[i]=i-start+1
        strat=i+1

    if pn==-1:
        pn=0
        start=i+1

max_regular=max(long)
if max_regular==0:
    print('0 1')
else:

    out=str(max_regular)+' '+str(long.count(max_regular))
    print(out)
