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 PYTHON):

Solution:
from sys import stdin
s = raw_input()
stack = []
match = [False] * (len(s) + 1)
for i, c in enumerate(s):
    if c == ')':
        if not stack:
            stack = []
        else:
            l = stack.pop()
            match[l] = True
            match[i] = True
    else:
        stack.append(i)
maxlen = 0 
occr = 1 
prev = -1
for i in range(len(s) + 1): 
    if not match[i]:
        l = i - prev - 1 
        if l > maxlen:
            maxlen = l 
            occr = 1 
        elif l == maxlen and l != 0:
            occr += 1
        prev = i 
print maxlen, occr