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:
/**
 * Created by scott on 3/25/2015.
 */

import java.util.*;

public class Brackets {

    static Scanner console = new Scanner(System.in);

    public static void main(String[] args){
        int longest = 0;
        int count = 1;
        Stack<Integer> start = new Stack<Integer>();
        Stack<Integer> end = new Stack<Integer>();

        String line = console.next();

        for(int i = 0;i<line.length();i++){
            if(line.charAt(i) == ')'){

                if(start.size() > 0){
                    int curr = start.pop();
                    while(end.size() > 0 && end.peek() > curr){
                        end.pop();
                        end.pop();
                    }

                    int length = i - curr + 1;
                    if(end.size() > 0 && end.peek() == curr - 1){
                        int temp = end.pop();
                        length = length + end.peek();
                        end.push(temp);
                    }

                    if(length > longest){
                        longest = length;
                        count = 1;
                    }
                    else if(length == longest){
                        count++;
                    }

                    end.push(length);
                    end.push(i);
                }
                else{
                    end.clear();
                }
            }
            else{
                start.push(i);
            }
        }

        System.out.println(longest + " " + count);
    }
}