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 task_B;
import java.util.Scanner;
public class Task_B {
	public static Scanner scan = new Scanner(System.in);
	
	public static void main(String[] args) {
		
		
		
		/*int a1 = 2; //010
		 int b1 = 0;//101
		 System.out.println(a1&b1); //  0
		             
		int a2 = 3; //100
		int b2 = 2; //101
		System.out.println(a2 & b2); //  2 */
		int n = scan.nextInt();
		int[] a = new int[n-1];
		int[] b = new int[n-1];
		int[] t = new int[n];
		boolean f = true;
		for (int i = 0; i  < n-1; i++) {
			a[i] = scan.nextInt();
		}
		for (int i = 0; i  < n-1; i++) {
			b[i] = scan.nextInt();
		}
		for (int i = 0; i <= 3; i++) {
			for (int j= 0; j <= 3; j++) {
				if (a[0] == (i | j) && b[0] == (i & j)) {
					t[0] = i;
					t[1] = j;
				} else {
					f = false;
				}
			}
		}
		if (f = true) {
			for (int i = 1; i < n-1; i++) {
				if (f = false) {
					break;
				}
				for (int j = 0; j <= 3; j++) {
					if ((a[i] == (t[i] | j)) &&( b[i] == (t[i] & j))) {
						t[i+1] = j;
						f = true;
					} else f = false; 
				}
		}
	}
		if (f == false) {
			int c = t[0];
			t[0] = t[1];
			t[1] = c;
			if ((a[0] == (t[0] | t[1])) &&( b[0] == (t[0] & t[1]))) {
				f = true;
			}
			for (int i = 0; i < n-1; i++) {
				if (f == true) {
				for (int j = 0; j <= 3; j++) {
					if ((a[i] == (t[i] | j)) &&( b[i] == (t[i] & j))) {
						t[i+1] = j;
						f = true;
						break;
					} else f = false; 
				}
			}
		}
		} 
		if (f == true) {
			System.out.println("YES");
			for (int i = 0; i < n; i++) {
				System.out.print(t[i] + " ");
			}
		} else System.out.println("NO");
	}
}
