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()
res1, res2 = 0, 1
from collections import defaultdict 
hm = defaultdict(lambda:-2)
hm[0] = -1
cur = 0
for i in range(len(s)):
    if s[i] == ')':
        cur -= 1
    else:
        cur += 1
    if hm[cur + 1] != -2:
        hm[cur + 1] = -2
    if hm[cur] != -2:
        tmp = i - hm[cur]
        if tmp > res1:
            res1 = tmp
            res2 = 1
        elif tmp == res1:
            res2 += 1
    else:
        hm[cur] = i 
print(res1, res2)