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()
n = len(s)

stack = []
c = [-1] * n
p = [-1] * n
for i in range(n):
    if s[i] == '(':
        stack.append(i)
        continue
    if not stack:
        continue
    j = stack.pop()
    p[i] = j
    c[i] = j
    if j > 0 and s[j - 1] == ')' and p[j - 1] != -1:
        c[i] = c[j - 1]


ans = 0
cnt = 1
for i in range(n):
    if c[i] == -1:
        continue
    now = i - c[i] + 1
    if now > ans:
        ans = now
        cnt = 0
    if now == ans:
        cnt += 1

print(ans, cnt)

