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:
bracket_string = input()
stack = []
max_len = 0
max_len_count = 1
for i in range(len(bracket_string)):
    if bracket_string[i] == ')' and stack and bracket_string[stack[-1]] == '(':
        stack.pop()
        if stack:
            cur_left_index = stack[-1]
        else:
            cur_left_index = -1
        cur_len = i - cur_left_index
        if cur_len > max_len:
            max_len = cur_len
            max_len_count = 1
        elif cur_len == max_len:
            max_len_count += 1
    else:
        stack.append(i)
print(max_len, max_len_count)