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>.
l = list(input())
t = 0
max_so_far = 0
max_len_so_far = 0
times = 0
for i in l:
    if i is '(':
        t+=1
    elif i is ')':
        t-=1
        if t>=0:
            max_so_far += 2
        elif t<0:
            t = 0
            if max_so_far>max_len_so_far:
                max_len_so_far = max_so_far
                max_so_far = 0
                times = 1
            elif max_so_far > 0 and max_so_far == max_len_so_far:
                times += 1
                max_so_far = 0
if t == 0 and max_so_far>0:
    if max_so_far>max_len_so_far:
        max_len_so_far = max_so_far
        times = 1
    elif max_so_far == max_len_so_far:
        times += 1
if max_len_so_far == 0:
    print('0 1')
else:
    print(max_len_so_far,times)                
            
