When Masha came to math classes today, she saw two integer sequences of length n - 1 on the blackboard. Let's denote the elements of the first sequence as a_i (0 ≤ a_i ≤ 3), and the elements of the second sequence as b_i (0 ≤ b_i ≤ 3).

Masha became interested if or not there is an integer sequence of length n, which elements we will denote as t_i (0 ≤ t_i ≤ 3), so that for every i (1 ≤ i ≤ n - 1) the following is true: 

  * a_i = t_i | t_{i + 1} (where | denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR)) and 
  * b_i = t_i \& t_{i + 1} (where \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND)). 



The question appeared to be too difficult for Masha, so now she asked you to check whether such a sequence t_i of length n exists. If it exists, find such a sequence. If there are multiple such sequences, find any of them.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5) — the length of the sequence t_i. 

The second line contains n - 1 integers a_1, a_2, …, a_{n-1} (0 ≤ a_i ≤ 3) — the first sequence on the blackboard.

The third line contains n - 1 integers b_1, b_2, …, b_{n-1} (0 ≤ b_i ≤ 3) — the second sequence on the blackboard.

Output

In the first line print "YES" (without quotes), if there is a sequence t_i that satisfies the conditions from the statements, and "NO" (without quotes), if there is no such sequence.

If there is such a sequence, on the second line print n integers t_1, t_2, …, t_n (0 ≤ t_i ≤ 3) — the sequence that satisfies the statements conditions.

If there are multiple answers, print any of them.

Examples

Input

4
3 3 2
1 2 0


Output

YES
1 3 2 0 

Input

3
1 3
3 2


Output

NO

Note

In the first example it's easy to see that the sequence from output satisfies the given conditions: 

  * t_1 | t_2 = (01_2) | (11_2) = (11_2) = 3 = a_1 and t_1 \& t_2 = (01_2) \& (11_2) = (01_2) = 1 = b_1; 
  * t_2 | t_3 = (11_2) | (10_2) = (11_2) = 3 = a_2 and t_2 \& t_3 = (11_2) \& (10_2) = (10_2) = 2 = b_2; 
  * t_3 | t_4 = (10_2) | (00_2) = (10_2) = 2 = a_3 and t_3 \& t_4 = (10_2) \& (00_2) = (00_2) = 0 = b_3. 



In the second example there is no such sequence.
import java.util.ArrayList;
import java.util.Random;
import java.util.Scanner;

public class Main2 {

    private static ArrayList<Integer[]> solved = new ArrayList<>();

    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);

        Integer len = scan.nextInt();
        Integer[] a = new Integer[len-1];
        Integer[] b = new Integer[len-1];

        for(Integer i = 0; i < a.length; i++){
            a[i] = scan.nextInt();
        }

        for(Integer i = 0; i < b.length; i++){
            b[i] = scan.nextInt();
        }

        Integer[] solve = solve(len, a, b);

        for(Integer i = 0; i < solve.length; i++){
            System.out.print(solve[i]+" ");
        }

    }

    private static Integer[] solve(Integer len, Integer[] a, Integer b[]){

        boolean next = true;
        Integer[] arrToCheck = null;

        while(next){
            if(solved.size()<=120*len){
                arrToCheck = generateRandomArr(len);

                int count = 0;

                for(Integer i = 0; i < a.length; i++){
                    if(a[i]!=(arrToCheck[i]|arrToCheck[i+1]) || b[i]!=(arrToCheck[i]&arrToCheck[i+1])){
                        break;
                    }else{
                        count++;
                    }
                }

                if(count == a.length){
                    System.out.println("YES");
                    next = false;
                }else{
                    solved.add(arrToCheck);
                }
            }else{
                System.out.print("NO");
                arrToCheck = new Integer[0];
                break;
            }
        }

        return arrToCheck;

    }

    private static Integer[] generateRandomArr(Integer len){
        Integer[] result = new Integer[len];

        for(Integer i = 0; i < len; i++){
            result[i] = new Random().nextInt(4);
        }

        if(!isSolved(result)){
            return result;
        }else{
            return generateRandomArr(len);
        }
    }

    private static boolean isSolved(Integer[] arr){
        boolean result = false;

        for(Integer i = 0; i < solved.size(); i++){
            if(solved.get(i).equals(arr)){
                result = true;
                break;
            }
        }

        return result;
    }

}


/* private static Integer[] solve(Integer len, Integer[] a, Integer b[]){

        Integer[] arrToCheck = generateRandomArr(len);

        boolean next = false;

        for(Integer i = 0; i < a.length; i++){
            if(a[i]!=(arrToCheck[i]|arrToCheck[i+1]) || b[i]!=(arrToCheck[i]&arrToCheck[i+1])){
                next = true;
            }
        }

        if(next){
            solved.add(arrToCheck);
            return solve(len, a, b);
        }else{
            System.out.println("YES");
            return arrToCheck;
        }

    }*/