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:
data = raw_input()
table = []
ans = 0
ansnum = 1
num = 0
for i in xrange(0, len(data)):
    if data[i] == '(':
        table.append(num)
        num = 0
    else:
        if len(table):
            num += table.pop()+2
            if num>ans:
                ans = num
                ansnum = 1
            elif num == ans:
                ansnum += 1
        else:
            num = 0
print ans, ansnum