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 __Solution {


    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

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

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;

    void init() throws FileNotFoundException {


        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }

        tok = new StringTokenizer("");
    }

    void run() {
        try {
            long timeStart = System.currentTimeMillis();

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeStart));
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }


    String readLine() throws IOException {
        return in.readLine();
    }


    String delimiter = " ";

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine) return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }


    void solve() throws IOException {
        int n =readInt();
        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] = readInt();
        }
        for(int i = 0 ; i < n - 1; ++i)
        {
            b[i] = readInt();
        }
        boolean first = false;
        boolean next = false;
        firstci:
        for(int c = 0; c < 4; ++c)
        {
            for(int x = 0; x < 4; ++x)
            {
                int g = c|x;
                int k = c&x;
                if(a[0] == g & k == b[0])
                {
                    t[0] = c;
                    t[1] = x;
                    first = true;
                    break firstci;
                }
            }
        }
        if(first) {
            for(int i = 2; i < n; ++i)
            {
                next = false;
                for(int c = 0; c < 4; ++c)
                {
                    int g = t[i - 1]|c;
                    int k = t[i - 1]&c;
                    if(g == a[i - 1] & k == b[i -1])
                    {
                        t[i] = c;
                        next = true;
                        break;
                    }
                }
                if(!next){break;}
            }
            if(next)
            {
                out.println("YES");
                for(int i = 0; i < n; ++i)
                {
                    out.print(t[i] + " ");
                }
            }
            else{out.println("NO");}
        } else {out.println("NO");}

    }
    }
