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 OutWriter out;
    static InReader in;

    public static void main(String args[]) throws IOException {
        in = new InReader();
        out = new OutWriter();
        int n = in.nextInt();
        int t[][] = new int[n][2];
        int a[][] = new int[n - 1][2];
        int b[][] = new int[n - 1][2];
        for (int i = 0; i < n - 1; i++) {
            int x = in.nextInt();
            if (x % 2 == 0) {
                a[i][0] = 0;
            } else {
                a[i][0] = 1;
            }
            if (x >= 2) {
                a[i][1] = 1;
            }
        }
        for (int i = 0; i < n - 1; i++) {
            int x = in.nextInt();
            if (x % 2 == 0) {
                b[i][0] = 0;
            } else {
                b[i][0] = 1;
            }
            if (x >= 2) {
                b[i][1] = 1;
            }
        }
        boolean flag = true;
        for (int x = 0; x <= 3; x++) {
            if (x % 2 == 0) {
                t[0][0] = 0;
            } else {
                t[0][0] = 1;
            }
            if (x >= 2) {
                t[0][1] = 1;
            } else {
                t[0][1] = 0;
            }
            flag =true;
            for (int i = 1; i < n; i++) {
                for (int j = 0; j < 2; j++) {
                    if (a[i-1][j] == 0 && b[i-1][j] == 1) {
                        flag = false;
                        break;
                    }
                    if (a[i-1][j] == 0) {
                        if (t[i - 1][j] == 1) {
                            flag = false;
                            break;
                        } else {
                            t[i][j] = 0;
                        }
                    }
                    if (b[i-1][j] == 1) {
                        if (t[i - 1][j] == 0) {
                            flag = false;
                            break;
                        } else {
                            t[i][j] = 1;
                        }
                    }
                    if (a[i-1][j] == 1 && b[i-1][j] == 0) {
                        t[i][j] = t[i - 1][j] ^ 1;
                    }
                }

            }
            if (flag) {
                int ans[] = new int[n];
                for (int i = 0; i < n; i++) {
                    ans[i] = t[i][0] + t[i][1] * 2;
                }
                for (int i = 0; i < n - 1; i++) {
                    if (!((ans[i] | ans[i + 1]) == a[i][0] + a[i][1] * 2 && (ans[i] & ans[i + 1]) == b[i][0] + b[i][1] * 2)) {
                        flag = false;
                    }
                }
                if (flag) {
                    out.println("Yes");
                    for (int i = 0; i < n; i++) {
                        out.prints(ans[i]);
                    }
                    break;
                }
            }
        }
        if (!flag) {
            out.println("No");
        }


        out.close();

    }


    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    static class Pair implements Comparable<Pair> {
        int x;
        int y;


        Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            if (x - o.x != 0) {
                return x - o.x;
            } else {
                if (y - o.y != 0) {
                    return -1;
                } else {
                    return 0;
                }
            }
        }
    }


    static class InReader {
        BufferedReader in;

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

        InReader() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        StringTokenizer token = new StringTokenizer("");

        void update() throws IOException {
            if (!token.hasMoreTokens()) {
                String a = in.readLine();
                if (a != null) {
                    token = new StringTokenizer(a);
                }
            }
        }

        int nextInt() throws IOException {
            update();
            return Integer.parseInt(token.nextToken());
        }

        long nextLong() throws IOException {
            update();
            return Long.parseLong(token.nextToken());
        }

        double nextDouble() throws IOException {
            update();
            return Double.parseDouble(token.nextToken());
        }

        boolean hasNext() throws IOException {
            update();
            return token.hasMoreTokens();
        }

        String next() throws IOException {
            update();
            return token.nextToken();
        }
    }

    static class OutWriter {
        PrintWriter out;

        OutWriter() {
            out = new PrintWriter(System.out);
        }

        OutWriter(String name) throws IOException {
            out = new PrintWriter(new FileWriter(name));
        }

        StringBuilder cout = new StringBuilder();

        <T> void print(T a) {
            cout.append(a);
        }

        <T> void println(T a) {
            cout.append(a);
            cout.append('\n');
        }

        <T> void prints(T a) {
            cout.append(a);
            cout.append(' ');
        }

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