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.util.*;
public class Main {
    public static int n;
    public static int[] a, b;
    public static int and(int i, int j) {
        return i & j;
    }
    public static int or(int i, int j) {
        return i | j;
    }
    public static String check(int i, String res) {
        int A = res.charAt(res.length() - 2) - '0';
        int B = res.charAt(res.length() - 1) - '0';
        boolean flag = or(A, B) == a[i] && and(A, B) == b[i];
        if (!flag) {
            return null;
        }
        if (i == n - 2) {
            return res;
        }
        if (i > 1 && i < n - 2) {
            if (a[i] == a[i + 1] && b[i] == b[i + 1]) {
                return check(i + 1, res + res.charAt(res.length() - 2));
            }
            if (b[i] == b[i + 1] && b[i] == 0) {
                if (a[i] == 1 && a[i + 1] == 2) {
                    return check(i + 1, res + "2");
                }
                if (a[i] == 2 && a[i + 1] == 3) {
                    return check(i + 1, res + "1");
                }
                if (a[i] == 3 && a[i + 1] == 0) {
                    return check(i + 1, res + "0");
                }
            }
        }
        for (int x = 0; x <= 3; x++) {
            String str = check(i + 1, res + x);
            if (str != null) {
                return str;
            }
        }
        return null;
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        a = new int[n - 1];
        b = new int[n - 1];
        for (int i = 0; i < a.length; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < b.length; i++) {
            b[i] = in.nextInt();
        }
        boolean flag = false;
        for (int i = 0; i <= 3; i++) {
            if (flag) break;
            for (int j = 0; j <= 3; j++) {
                String str = check(0, i + "" + j);
                if (str != null) {
                    System.out.println("YES");
                    for (char c : str.toCharArray()) {
                        System.out.print(c + " ");
                    }
                    flag = true;
                    break;
                }
            }
        }
        if (!flag) System.out.println("NO");
    }
}