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>.
a = input()
open = -1
d = 0
f = 0
c = 0
for i in a:
    if i=='(':
        if open ==-1:
            open = 1
        else:
            open +=1    
    elif i==')':
        if open>0:
            if c<open:
                c = open
            open= open-1
    if open==0:
        f+=1
        if c*2>d:
            d = c*2
        open = -1
        c = 0
if d==0 and f==0:
    print(0,1)
else:
    print(d, f)