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>.
# https://codeforces.com/problemset/problem/5/C

bs = str(input())
res, count = 0, 0
stack = []
dp = [0]*len(bs)
for i in range(len(bs)):
    if bs[i] == '(':
        stack.append(i)
    else:
        if len(stack) == 0:
            continue
        last_left_b = stack.pop()
        if last_left_b > 0:
            dp[i] = i - last_left_b + 1 +dp[last_left_b-1]
        else:
            dp[i] = i - last_left_b + 1
        if dp[i] > res:
            res = dp[i]
            count = 1
        elif dp[i] == res:
            count += 1
if res == 0:
    print('0 1')
else:
    print(res, count)
