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()
arr = [-1]
longest_len = 0
count = 1
for j, k in enumerate(s):
    if k == '(':
        arr.append(j)
    elif len(arr) > 1:
        arr.pop()
        mini = j - arr[-1]
        if longest_len < mini:
            longest_len, count = mini, 1
        elif longest_len == mini:
            count += 1
    else:
        arr[0] = j

print(longest_len, count)