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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.lang.String;

import static java.lang.Math.*;

public class Main {
    long mod = (long) 1e9 + 7;

    void run() throws IOException {
        int n = nextInt();
        int[] a = new int[n - 1];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
        }
        int[] b = new int[n - 1];
        for (int i = 0; i < b.length; i++) {
            b[i] = nextInt();
        }
        int[] t = new int[n];
        int countno = 0;
        for (int i = 0; i < 4; i++) {
            t = new int[n];
            t[0] = i;
            boolean yes = false;
            for (int j = 0; j < a.length; j++) {
                int[] first = new int[2];
                int[] second = new int[2];
                int[] third = new int[2];
                if (t[j] == 1) first[1] = 1;
                if (t[j] == 2) first[0] = 1;
                if (t[j] == 3) {
                    first[0] = first[1] = 1;
                }
                if (a[j] == 1) second[1] = 1;
                if (a[j] == 2) second[0] = 1;
                if (a[j] == 3) {
                    second[0] = second[1] = 1;
                }
                if (b[j] == 1) third[1] = 1;
                if (b[j] == 2) third[0] = 1;
                if (b[j] == 3) {
                    third[0] = third[1] = 1;
                }
                int[] ans = new int[2];
                for (int e = 0; e < 2; e++) {
                    if (first[e] == 0 && second[e] == 0 && third[e] == 0) ans[e] = 0;
                    else if (first[e] == 0 && second[e] == 0 && third[e] == 1) {
                        yes = true;
                        countno++;
                        break;
                    } else if (first[e] == 0 && second[e] == 1 && third[e] == 0) ans[e] = 1;
                    else if (first[e] == 0 && second[e] == 1 && third[e] == 1) {
                        yes = true;
                        countno++;
                        break;
                    } else if (first[e] == 1 && second[e] == 0 && third[e] == 0) {
                        yes = true;
                        countno++;
                        break;
                    } else if (first[e] == 1 && second[e] == 0 && third[e] == 1) {
                        yes = true;
                        countno++;
                        break;
                    } else if (first[e] == 1 && second[e] == 1 && third[e] == 0) ans[e] = 0;
                    else if (first[e] == 1 && second[e] == 1 && third[e] == 1) ans[e] = 1;
                }
                if (yes) break;
                int k = 0;
                if (ans[0] == 1) k += 2;
                if (ans[1] == 1) k++;
                t[j + 1] = k;
            }
            if (!yes) break;
        }
        if (countno < 4) {
            pw.println("YES");
            for (int i = 0; i < t.length; i++) {
                pw.print(t[i] + " ");
            }
        } else {
            pw.println("NO");
        }
        pw.close();
    }

    class Point {
        long x;
        int y;

        public Point(long a, int b) {
            x = a;
            y = b;
        }
    }

    class PointComp implements Comparator<Point> {

        @Override
        public int compare(Point o1, Point o2) {
            if (o1.x == o2.x) return Integer.compare(o1.y, o2.y);
            return Long.compare(o1.x, o2.x);
        }
    }

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);

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

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

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

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

    public Main() throws FileNotFoundException {
    }

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


}