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.IOException;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.StringTokenizer;

public class TaskB {
    public static String doMain(Reader reader) throws IOException {
        MyReader in = new MyReader(reader);
        int n = in.nextInt();
        int[] a = in.readIntArray(n-1);
        int[] b = in.readIntArray(n-1);
        int run = 0;
        StringBuilder sb = new StringBuilder();
        for (int first = 0; first < 4; ++first) {
            int[] test = check(a, b, first);
            if (test == null) {
                continue;
            }
            sb.append("YES\n");
            for (int k : test) {
                sb.append(k + " ");
            }
            return sb.toString();
        }
        return "NO";
    }

    private static int[] check(int[] a, int[] b, int g) {
        int[] ans = new int[a.length + 1];
        ans[0] = g;
        here:
        for (int i = 0; i < a.length; ++i) {
            for (int next = 0; next < 4; ++next) {
                if ((ans[i] & next) == b[i] && (ans[i] | next) == a[i]) {
                    ans[i + 1] = next;
                    continue here;
                }
            }
            return null;
        }
        return ans;
    }

    public static void main(String[] args) throws IOException {
        String result = doMain(new InputStreamReader(System.in));
        System.out.println(result);
    }

    static class MyReader {
        BufferedReader bf;

        StringTokenizer st;

        String last;

        MyReader(Reader reader) throws IOException {
            bf = new BufferedReader(reader);
            readNextLine();
        }

        String nextToken() throws IOException {
            while (!st.hasMoreTokens()) {
                readNextLine();
            }
            return st.nextToken();
        }

        void readNextLine() throws IOException {
            last = bf.readLine();
            if (last == null) last = "";
            st = new StringTokenizer(last);
        }

        String nextLine() throws IOException {
            String s = last;
            readNextLine();
            return s;
        }

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

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

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

        int[] readIntArray(int n) throws IOException {
            int[] answer = new int[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextInt();
            }
            return answer;
        }

        long[] readLongArray(int n) throws IOException {
            long[] answer = new long[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextLong();
            }
            return answer;
        }

        double[] readDoubleArray(int n) throws IOException {
            double[] answer = new double[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextDouble();
            }
            return answer;
        }
    }
}
