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>.
# Submitted using https://github.com/Nirlep5252/codeforces-cli
# >.<

s = input()
uwu = []
d = 0

for ch in s:
    if ch == "(":  # )
        d += 1
    else:
        d -= 1
    uwu.append(d)

# print(uwu)
start = -1
ans = 0
count = 0

for i, e in enumerate(uwu):
    if e == 0:
        x = i - start
        if start != -1:
            if x > ans:
                ans = x
                count = 1
            elif x == ans:
                count += 1
        start = i


if 0 not in uwu:
    print(0, 1)
else:
    print(ans + 2, count)

