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()
stack=[]
b=0
c=0
for i in a:
    if i=="(":
        b+=1
    else:
        c+=1
    if b==c:
        stack.append(2*b)
        b=0
        c=0
    if b<0:
        b=0
    if c<0 or c>b:
        c=0
    print(b,c)
print(max(stack),len(stack))