Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON3):

Solution:
l=[-1]
#print(l)
maxi,count=0,0
for i,c in enumerate(input()):
    if c=='(':
        l.append(i)
        #print("After append:",l)
    else:
        if len(l)>1:
            l.pop()
            var=i-l[-1]
            #print("Popping time:",l,i,l[-1],var)
            if var>maxi:
                maxi=var
                count=1
            elif var==maxi:
                count+=1
        else:
            l[0]=i
            #print("In case:",l,i)
if maxi:
    print(maxi,count)
else:
    print(0,1)