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()
st = []
dp = [0]*(len(s))

for j, x in enumerate(s):
    if x == '(': st += [j]
    elif st: 
        i = st.pop()
        dp[j] = dp[i-1] + j - i + 1

ans = max(dp)
print(ans, dp.index(ans) + 2 - ans if ans else 1)