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.math.BigInteger;
import java.util.*;
                                 
public class Main {
                             
    static Scanner in;
         
//  static StreamTokenizer in;
//  static int nextInt() throws IOException {
//      in.nextToken();
//      return (int)in.nval;    
//  }
     
    Random rand = new Random();
     
    static long gcd(long a, long c) {
        BigInteger q = BigInteger.valueOf(a);
        BigInteger w = BigInteger.valueOf(c);
        q = q.gcd(w);
        return q.longValue();
    }
    static int[][] mat;
//    static boolean[][] used;

    public static void main(String args[]) throws IOException {
//      in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        PrintWriter out = new PrintWriter(System.out);
        in = new Scanner(System.in);            
	    int n = in.nextInt();
	    int[] a = new int[n-1];
	    int[] b = new int[n-1];
	    int[] c = new int[n];
	    for(int i = 0;i<n-1;i++) {
	    	a[i] = in.nextInt();
	    }
	    boolean fl = false;
	    for(int i = 0;i<n-1;i++) b[i] = in.nextInt();
	    for(int f = 0;f<4;f++) {
	    	c[0] = f;
	    	boolean flag = true;
	    	for(int i = 1;i<n;i++) {
	    		flag = false;
	    		for(int w = 0;w<4;w++) {
	    			int ans1 = c[i-1] & w;
	    			int ans2 = c[i-1] | w;
	    			if(ans1 == b[i-1] && ans2 == a[i-1]) {
	    				flag = true;
	    				c[i] = w;
	    				break;
	    			}
	    		}
    			if(!flag) break;
	    	}
	    	if(flag) {
	    		
	    		fl =true;
	    		break;
	    	}

	    }
	    if(!fl) {
	    	System.out.println("NO");
	    }else {
	    	System.out.println("YES");
	    	for(int i = 0;i<n;i++) {
	    		System.out.print(c[i]+" ");
	    	}
	    }
    }
}
                                 
class Pair implements Comparable{
	int a;
    int b;
    public Pair() {
        this.a=-1;
        this.b=-1;
    }
    public Pair(int a, int b) {
        this.a=a;
        this.b=b;
    }
    public int compareTo(Object arg0) {
        if(Integer.compare(this.a, ((Pair)arg0).a)==0) return Integer.compare(this.b, ((Pair)arg0).b);
            return Integer.compare(this.a, ((Pair)arg0).a);
    }
}