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.
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(f.readLine());
		int[] a = new int[n-1];
		int[] b = new int[n-1];
		
		StringTokenizer st = new StringTokenizer(f.readLine());
		for(int i = 0; i < n-1; i ++){
			a[i] = Integer.parseInt(st.nextToken());
		}
		
		st = new StringTokenizer(f.readLine());
		for(int i = 0; i < n-1; i ++){
			b[i] = Integer.parseInt(st.nextToken());
		}
		
		int last = -1;
		for(int start = 0; start < 4; start ++){
			last = start;
			boolean good = true;
			int[] ans = new int[n];
			ans[0] = last;
			for(int i = 0; i < n-1; i ++){
				int or1 = a[i]/2;
				int or0 = a[i]%2;
				int and1 = b[i]/2;
				int and0 = b[i]%2;
				int last1 = last/2;
				int last0 = last%2;
				int next1 = 0;
				int next0 = 0;
				
				if(last1 == 0){
					if(or1 == 0) next1 = 0;
					else next1 = 1;
					
					if(and1 == 1){
						good = false;
						break;
					}
				}
				else{
					if(and1 == 1) next1 = 1;
					else next1 = 0;
					
					if(or1 == 0){
						good = false;
						break;
					} 
				}
				
				if(last0 == 0){
					if(or0 == 0) next0 = 0;
					else next0 = 1;
					
					if(and0 == 1){
						good = false;
						break;
					} 
				}
				else{
					if(and0 == 1) next0 = 1;
					else next0 = 0;
					
					if(or0 == 0){
						good = false;
						break;
					} 
				}
				last = next1*2 + next0;
				ans[i] = last;
			}
			
			if(!good){
				continue;
			}
			else{
				System.out.println("YES");
				PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
				for(int i = 0; i < n; i ++){
					out.print(ans[i] + " ");
				}
				out.close();
				System.exit(0);
			}
		}
		
		System.out.println("NO");
	}
}