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 = list(input())

stack_o = [-1]

l = 0

m = 0
check = 0
count = 1

for i,item in enumerate(s):
    if item == '(':
        stack_o.append(i)
    elif item == ')':
        if len(stack_o)>1:
            del stack_o[-1]
            l = i - stack_o[-1]
            if l == m:
                count += 1
            elif l>m:
                count = 1
                m = l
        else:
            stack_o[0] = i
print(m,count)