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>.
sp = []
lmax = 0
l = 0
s = input()
k = 0
for i in range(len(s)):
    a = s[i]
    if a == '(':
        sp.append(a)
        l += 1
    elif len(sp) == 0 or sp[-1] != '(':
        sp = []
    else:
        sp.pop(-1)
        if len(sp) == 0:
            k += 1
            lmax = max(l, lmax)

if k == 0:
    print(0, 1)
else:
    print(lmax, k)