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()
left = 0
ans = 0
current = 0
res = {}
for i in range(len(s)):
    if s[i] == '(' and i != len(s) - 1:
        left += 1
    else:
        if left > 0:
            current += 2
            left -= 1
        if left == 0 or i == len(s) - 1:
            if current in res:
                res[current] += 1
            else:
                res[current] = 1
            ans = max(ans, current)
            current = 0

if ans == 0:
    print('0 1')
else:
    print('%d %d' %(ans, res[ans]))