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>.
st = []
s = input()
dp = [0] * (len(s) + 1)
for i, c in enumerate(s, 1):
    if c == '(':
        st.append(i)
    elif len(st):
        j = st.pop()
        dp[i] = dp[j - 1] + i - j + 1
res = max(dp)
if res == 0:
    count = 1
else:
    count = dp.count(res)
print(res, count)