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>.
# import sys
# sys.stdin = open('D:\\codes\\ccdsap prepare\\in.txt', 'r')
# sys.stdout = open('D:\\codes\\ccdsap prepare\\out.txt', 'w')

s = input()
st = []
count = -sys.maxsize
thisdict = {}
for i in range(0, len(s)):
    if s[i] == '(':
        st.append(i)
    elif len(st) == 1:
        count = max(count, i - st[len(st) - 1] + 1)
        if count in thisdict:
            thisdict[count] = thisdict[count] + 1
        else:
            thisdict[count] = 1
        st.pop()
    elif len(st) != 0:
        st.pop()
if count == -sys.maxsize:
    print("0 1")
else:
    print(count, thisdict[count])
