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>.
# LUOGU_RID: 101907434
s = input()
t = []
a = [0] * len(s)
for i, c in enumerate(s):
    if c == '(':
        t += i,
    elif t:
        a[t.pop()] = a[i] = 1
a = ''.join(map(str, a)).split('0')
if max(a):
    print(len(max(a)), a.count(max(a)))
else:
    print('0 1')