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>.
s = input()
cnt = []
res = [0, 1]
for i in range(len(s)):
    if s[i] == ')':
        if len(cnt) == 0 or cnt[-1] == -1:
            cnt.append(-1)
            continue        
        elif cnt[-1] > 0:
            num = cnt.pop()
            if len(cnt) > 0 and cnt[-1] == 0:
                cnt.pop()
                cnt.append(num + 2)
            else:
                cnt.append(-1)
        else:
            cnt.pop()
            cnt.append(2)
        num = 0
        while len(cnt) > 0 and cnt[-1] > 0:
            num += cnt.pop()
        cnt.append(num)
        if cnt[-1] > res[0]:
            res = [cnt[-1], 1]
        elif cnt[-1] == res[0]:
            res[1] += 1
    else:
        cnt.append(0)
    
print('%d %d' %(res[0], res[1]))