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>.
string=input()
stack=[]
m=0
arr=[]
n=0
for i in string:
    flag=True
    if len(stack)>=1:
        if stack[-1]=='(' and i==')':
            m=m+1
            stack.pop()
            flag=False
        if m>0:
            arr+=(2*m,)
    if flag:
        stack+=(i,)
        if stack[-1]!='(':
            m=0
            n=n+1
if len(arr)>0:
    print(max(arr),n)
else:
    print(0,1)
