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:
import collections

n = list(input())
stack_b = [0]
stack_pos = [0]
length = 0
lenarray = [0]
counter = 0

for i in range(len(n)):
    if n[i] == "(":
        stack_b.append(i + 1)
        stack_pos.append(i + 1)
    else:
        if len(stack_b) > 1:
            stack_b.pop()
            stack_pos.pop()
            lenarray.append(i + 1 - stack_pos[-1])
        else:
            stack_pos.append(i + 1)

print(max(lenarray), collections.Counter(lenarray)[max(lenarray)])