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)
stack = []
dp = [0 for i in range(0, n)]
max_size = 0
max_cnt = 0
for i in range(0, n):
    c = s[i]
    if c == '(':
        stack.append(i)
    else:
        if len(stack) > 0:
            prev = stack.pop()
            temp = dp[prev - 1] + i - prev + 1
            dp[i] = temp
            if temp > max_size:
                max_size = temp
                max_cnt = 1
            elif temp == max_size:
                max_cnt += 1
if max_size == 0:
    print("0 1")
else:
    print(max_size, max_cnt)