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>.
# @author: guoyc
# @date: 2018/7/20

s = input()

N = len(s)

dp = [0] * (N + 1)

ml = 0
cnt = 1

for i in range(1, N):
    if s[i] == '(':
        continue
    if s[i - 1] == '(':
        dp[i] = 2 + dp[i - 1]
    elif (i - 1) - dp[i - 1] >= 0:
        if s[(i - 1) - dp[i - 1]] == '(':
            dp[i] = dp[i - 1] + 2 + dp[(i - 1) - dp[i - 1] - 1]
    if dp[i] > ml:
        ml = dp[i]
        cnt = 1
    elif dp[i] == ml:
        cnt += 1

print(ml, cnt)
