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 {
    static class Writer {
        PrintWriter cout;

        Writer() throws IOException {
            cout = new PrintWriter(System.out);
        }

        Writer(String name) throws IOException {
            cout = new PrintWriter(new FileWriter(name));
        }

        StringBuilder out = new StringBuilder();

        void print(Object a) {
            out.append(a);
        }

        void close() {
            cout.print(out.toString());
            cout.close();
        }
    }

    static class Reader {
        BufferedReader in;

        Reader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        Reader(String name) throws IOException {
            in = new BufferedReader(new FileReader(name));
        }

        StringTokenizer tokin = new StringTokenizer("");

        String next() throws IOException {
            if (!tokin.hasMoreTokens()) {
                tokin = new StringTokenizer(in.readLine());
            }
            return tokin.nextToken();
        }

        boolean hasNext() throws IOException {
            if (!tokin.hasMoreTokens()) {
                String s = in.readLine();
                if (s != null) {
                    tokin = new StringTokenizer(s);
                    return true;
                } else {
                    return false;
                }
            } else {
                return true;
            }
        }

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

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

    static int a[], b[], n;

    public static void main(String args[]) throws IOException {
        Reader in = new Reader(/*"kek.txt"*/);
        Writer out = new Writer();
        n = in.nextInt();
        a = new int[n - 1];
        b = new int[n - 1];
        for (int i = 0; i < n - 1; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < n - 1; i++) {
            b[i] = in.nextInt();
        }
        boolean must = false;
        for (int t1 = 0; t1 < 4 && !must; t1++) {
            int t[] = new int[n];
            t[0] = t1;
            boolean must1 = true;
            for (int i = 0; i < n - 1; i++) {
                int j = 0;
                for (j = 0; j < 4; j++) {
                    if ((t[i] | j) == a[i] && (t[i] & j) == b[i]) {
                        t[i + 1] = j;
                        break;
                    }
                }
                if (j == 4) {
                    must1 = false;
                    break;
                }
            }
            if (must1) {
                out.print("YES\n");
                for (int i = 0; i < n; i++) {
                    out.print(t[i] + " ");
                }
                must = true;
                break;
            }
        }
        if (!must) {
            out.print("NO");
        }
        out.close();
    }
}