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().strip()

max_string = 0
total_max_strings = 0
stack = [None]*len(s)
arr = [None]*len(s)
top = -1

for (index, bracket) in enumerate(s):
    if bracket == '(':
        top += 1
        if arr[index-1] != None:
            stack[top] = arr[index-1]
        else:
            stack[top] = index
    elif top > -1:
        temp_len = index - stack[top] + 1

        if max_string < temp_len:
            max_string = temp_len
            total_max_strings = 1
        elif max_string == temp_len:
            total_max_strings += 1

        arr[index] = stack[top]
        top -= 1

print(max_string, total_max_strings or 1)