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.util.*;

public class A {

	static boolean used[] = null;
	static int[] a = null;
	static ArrayList<Integer>[] gr = null;

	public static void main(String[] args) {

		try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {

			int n = Integer.parseInt(reader.readLine());
			a = new int[n - 1];
			String line[] = reader.readLine().split(" ");
			for(int i = 0; i < n - 1; i++) {
				a[i] = Integer.parseInt(line[i]);
			}
			int[] b = new int[n - 1];
			line = reader.readLine().split(" ");
			for(int i = 0; i < n - 1; i++) {
				b[i] = Integer.parseInt(line[i]);
				if(b[i] > a[i]) {
					System.out.println("NO");
					return;
				}
			}
			int[] ans = new int[n];
			boolean mb = true;
			for(int f = 0; f <= 3; f++) {
				for(int i = 0; i < n; i++) {
					ans[i] = -1;
				}
				ans[0] = f;
				mb = true;
				for(int i = 0; i < n - 1; i++) {
					HashSet<Integer> s = new HashSet<>();
					for(int num = 0; num <= 3; num++) {
						if((num | ans[i]) == a[i]) {
							s.add(num);
						}
					}
					for(int num : s) {
						if((num & ans[i]) == b[i]) {
							ans[i + 1] = num;
							break;
						}
					}
					if(ans[i + 1] == -1) {
						mb = false;
					}
				}
				if(! mb)
					continue;
				else
					break;
			}
			if(! mb) {
				System.out.println("No");
				return;
			}
			System.out.println("Yes");
			for(int i : ans) {
				System.out.print(i + " ");
			}

			//System.out.println("Yes");

		} catch(IOException e) {
		}

	}

	static int count = 0;
	public static void dfs(int pos) {
		used[pos] = true;
		a[pos] = count++;
		for(int i : gr[pos]) {
			if(! used[i]) {
				dfs(i);
			}
		}
		count--;
	}

	static class Pair implements Comparable<Pair> {

		int a, b;

		Pair(int a, int b) {
			this.a = a;
			this.b = b;
		}

		void getEl() {

		}

		@Override
		public int compareTo(Pair o) {

			return 0;
		}

	}

}
