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:
string=input()
index=[-1]
count=1
ma=0
for i in range(len(string)):
    #print(index)
    if(string[i]=='('):
        index.append(i)
    elif(len(index)>1):
        index.pop()
        n=i-index[-1]
        if(ma<n):
            ma=n
            count=1
        elif(ma==n):
            count+=1
    else:
        index[0]=i
print(str(ma),'',str(count))