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>.
brac_seq = list(input())
r = count = max = 0
max_count = 0

for b in brac_seq:
    
    if b == '(':
        r += 1
    
    if b == ')':
        if r < 1 and count > 0:
            if max < count:
                max = count
                max_count = 1
            if max == count :
                max_count += 1
                
            count = 0
        if r>0:
            r -= 1
            count += 2 
            
if max > 0 :
    print(str(max) + ' ' + str(max_count))
else:
    print ('0 1')