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:
s = input()
n = len(s)
dem1_max = 0
dem2_max = 1
A = [-1]
for i in range(n):
    if s[i] == "(":
        A.append(i)        
    elif len(A) > 1: 
        x = A.pop()
        u  = i - A[-1]
        if u == dem1_max:
            dem2_max += 1
        elif u >= dem1_max:
            dem1_max = u
            dem2_max = 1        
    else:
        A[0] = i
print("{} {}".format(dem1_max,dem2_max))