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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class BracketSequence {

    public static void main(String[] args) throws IOException {
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        String sequence = input.readLine();
        ArrayList<Integer> list = new ArrayList<Integer>();
        int length = 0;
        int count = 0;
        int last = -1;
        int index = 0;
        for (int i = 0; i < sequence.length(); i++) {
            if (sequence.charAt(i) == '(')
                list.add(i);
            else if(list.isEmpty())
                last = i;
            else {
                list.remove(list.size()-1);
                if(list.isEmpty())
                    index = i-last;
                else
                    index = i-list.get(list.size()-1);
                    
                if(index > length) {
                    length = index;
                    count = 1;
                } 
                else if (index == length)
                    count++;
            }
        }
        if(length == 0)
            System.out.println("0 1");
        else
            System.out.println(length + " " + count);
    }

}