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()
stack = []
ong = 0
ans = 0
ansi = 1
for i in data:
    #print i, ong
    #print stack
    if i == '(':
        stack.append(ong)
        ong = 0
    else:
        if len(stack):
            x = stack.pop()
            ong += (x+2)
            if ong>ans:
                ans = ong
                ansi = 1
            elif ong == ans:
                ansi += 1
        else:
            ong = 0
print ans, ansi