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:
a, b = [], []

for i, x in enumerate(input()):
    if x == '(':
        b.append(i)
    elif b:
        j = b.pop()
        
        while a and a[-1][0] > j:
            a.pop()
        
        if a and a[-1][1] == j - 1:
            a.append((a.pop()[0], i))
        else:
            a.append((j, i))

m, n = 0, 1

for x in a:
    l = x[1] - x[0] + 1
    if l > m:
        m, n = l, 1
    elif l == m:
        n += 1

print(m, n)