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.io.*;
import java.util.*;

public class Main {

    private void solve() {
        int n = nextInt();
        int len = n-1;
        int[] a = new int[len];
        int[] b = new int[len];
        int[][] t = new int[n][4];
        int[] print = new int[n];
        for (int i = 0; i < len; i++) {
            a[i] = nextInt();
            print[i]=-1;
        }
        print[len]=-1;
        for (int i = 0; i < len; i++) {
            b[i] = nextInt();
            if (a[i]<b[i]){
                System.out.println("NO");
                System.exit(0);
            }
        }
        for (int i = 0; i < len; i++) {
            for (int j = 0; j < 4; j++) {
                for (int k = 0; k < 4; k++) {
                    if ((a[i] == (j|k)) && (b[i] == (j & k))){
                        t[i][j]++;
                        t[i+1][k]++;
                        if(t[i][j]==2){
                            for (int l = 0; l < 4; l++) {
                                if ((a[i-1] == (l|j)) && (b[i-1] == (l & j))){
                                    print[i - 1] = l;
                                    print[i] = j;
                                    print[i+1] = k;
                                    break;
                                }
                            }
                        }
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            if (print[i]==-1){
                System.out.println("NO");
                System.exit(0);
            }
        }
        System.out.println("YES");
        for (int i = 0; i < n; i++) {
            System.out.print(print[i]+" ");
        }
    }
    public static void main(String[] args) {
        new Main().run();
    }

    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    private void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            //br = new BufferedReader(new FileReader("birthday.in"));
            //out = new PrintWriter(new FileWriter("birthday.out"));
            solve();
            br.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    private int nextInt() {
        return Integer.parseInt(next());
    }

    private String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
                return "END_OF_FILE";
            }
        }
        return st.nextToken();
    }
}