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 sys
s = sys.stdin.readline().strip()
stack = []
dp = [0]*(len(s)+1)
for i in range(len(s)):
    if s[i] == ')':
        if stack:
            begin = stack.pop()
            dp[i] = dp[begin-1] + (i - begin + 1)
    else:
        stack.append(i)

mx = max(dp)
if mx == 0:
    print(0,1)
else:
    print(mx,dp.count(mx))