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 = []
early = [-1] * n
corrs = [-1] * n

for i in range(n):
    if s[i] == '(':
        stack.append(i)
    else:
        if stack:
            corrs[i] = early[i] = stack.pop()
            if early[i] and s[early[i] - 1] == ')' and early[early[i] - 1] != -1:
                early[i] = early[early[i] - 1]
        else:
            early[i] = corrs[i] = -1
 
# print(list(s))
# print(corrs)
# print(early)
 
record = 0
count = 0
 
for i in range(n):
    if early[i] == -1:
        continue
    length = i - early[i] + 1
    if length > record:
        record = length
        count = 1
    elif length == record:
        count += 1
if record == 0:
    print(0, 1)
else:
    print(record, count)