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.util.StringTokenizer;

public class Main {

    private static int[] a,b,t;
    private static int n;

    public static void main(String[] args) throws IOException{
        n = Reader.readint();
        a = new int[n];
        b = new int[n];
        t = new int[n + 1];
        for(int i = 1;i < n;i ++){
            a[i] = Reader.readint();
        }

        for(int i = 1;i < n;i ++){
            b[i] = Reader.readint();
        }

        if(dfs(1)){
            StringBuilder res = new StringBuilder();
            for(int i  = 1;i <= n;i ++){
                res.append(t[i]);
                if(i == n){
                    res.append('\n');
                }
                else{
                    res.append(' ');
                }
            }
            System.out.println("YES");
            System.out.print(res);
        }
        else{
            System.out.println("NO");
        }

    }

    private static boolean dfs(int pos){
        if(pos == n + 1){
            return true;
        }
        else if(pos == 1){
            for(int i = 0;i <= 3;i ++){
                t[1] = i;
                if(dfs(pos + 1))
                    return true;
            }
        }
        else{
            for(int i = 0;i <= 3;i ++){
                if((i & t[pos - 1]) == b[pos - 1] && (i | t[pos - 1]) == a[pos - 1]){
                    t[pos] = i;
                    if(dfs(pos + 1))
                        return true;
                }
            }
        }
        return false;
    }
}
class Reader{
    private static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
    private static StringTokenizer stringTokenizer = new StringTokenizer("");
    public static String readline() throws IOException{
        return bufferedReader.readLine();
    }
    static int readint() throws IOException{
        if(!stringTokenizer.hasMoreTokens()){
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());
        }
        return Integer.parseInt(stringTokenizer.nextToken());
    }

}