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>.
seq = input()

stack = []
max_len = 0
valid = 0

l = 0
for bracket in seq:
    if bracket == '(':
        stack.append('(')
        l += 1
        
    elif bracket == ')' and len(stack) == 0:
        l = 0
        
    else:
        stack.pop()
        l += 1
        
        if len(stack) == 0:
            valid += 1
            if max_len < l:
                max_len = l
                
            l = 0
            
if valid == 0:
    print('0 1')
    
else:
    print('{} {}'.format(max_len, valid))