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.*;

import static java.lang.Math.*;

public class Tester {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt(), alast, blast;
        List<Integer> A = new ArrayList<>(), B = new ArrayList<>(), result = new ArrayList<>();
        for (int i = 0; i < n-1; i++) { A.add(s.nextInt()); }
        for (int i = 0; i < n-1; i++) { B.add(s.nextInt()); }
        int[] ret = getAandB(A.get(0), B.get(0));
        if (ret[0]==-1||ret[1]==-1){ System.out.println("NO");return; }
        for (int i = 1; i < n-1; i++) {
            if (i==1){
                int[] tmp = getAandB(A.get(1), B.get(1));
                if (tmp[0]==-1||tmp[1]==-1){System.out.println("NO");return; }
                if (ret[0]==tmp[0]){
                    result.add(ret[1]);
                    result.add(ret[0]);
                    result.add(tmp[1]);
                }
                else if (ret[1]==tmp[0]){
                    result.add(ret[0]);
                    result.add(ret[1]);
                    result.add(tmp[1]);
                }
                else{ System.out.println("NO");return; }
            }
            else {
                ret = getAandB(A.get(i), B.get(i));
                if (ret[0]==-1||ret[1]==-1){ System.out.println("NO");return; }
                if (result.get(result.size()-1)==ret[0]){result.add(ret[1]);}
                else{ System.out.println("NO");return; }
            }
        }
        System.out.println("YES");
        print(result);
    }

    static void print(List<Integer> v) {
        for (int i = 0; i < v.size(); i++) {
            System.out.print(v.get(i)+" ");
        }
    }

    static int[] getAandB(int x, int y) {
        int[] ret = {-1, -1};
        for (int a = 0; a <= 3; a++)
        {
            for (int b = 0; b <= 3; b++) {
                int q = a & b, w = a | b;
                if ((w == x)&& (q == y))
                {
                    ret[0] = b;
                    ret[1] = a;
                    return ret;
                }
            }
        }
        return ret;
    }

}