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.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.StringTokenizer;

import static java.lang.Math.*;
import static java.util.Arrays.copyOf;
import static java.util.Arrays.fill;
import static java.util.Arrays.sort;
import static java.util.Collections.reverseOrder;
import static java.util.Collections.sort;
import static java.util.Comparator.comparing;
import static java.util.Comparator.comparingInt;


public class Main {
    FastScanner in;
    PrintWriter out;

    private void solve() throws IOException {
        int n = in.nextInt();
        int[] a = new int[n - 1];
        int[] b = new int[n - 1];
        int[] t = new int[n];
        for (int i = 0; i < n - 1; i++)
            a[i] = in.nextInt();
        for (int i = 0; i < n - 1; i++)
            b[i] = in.nextInt();
        int x, y, x1, y1;
        boolean bool;
        for (int k = 0; k < n - 2; k++) {
            bool = false;
            for (int i = 0; i <= 3; i++) {
                if (bool)
                    break;
                for (int j = 0; j <= 3; j++) {
                    if (bool)
                        break;
                    x = i | j;
                    y = i & j;
                    if (x == a[k] && y == b[k])
                        for (int l = 0; l <= 3; l++) {
                            if (bool)
                                break;
                            x1 = j | l;
                            y1 = j & l;
                            if (x1 == a[k + 1] && y1 == b[k + 1]) {
                                t[k] = i;
                                t[k + 1] = j;
                                t[k + 2] = l;
                                bool = true;
                            }

                        }
                }
            }
            if (!bool) {
                out.println("NO");
                return;
            }
        }
        out.println("YES");
        for (int i = 0; i < n; i++)
            out.print(t[i] + " ");
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

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

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }

    }

    private void run() throws IOException {
        in = new FastScanner(System.in);
        //in = new FastScanner(new FileInputStream("input.txt"));
        out = new PrintWriter(System.out);
        //out = new PrintWriter(new FileOutputStream("output.txt"));

        solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}