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.util.Scanner;
public class zadacha1 {

	public static void main(String[] args) {
		Scanner reader = new Scanner(System.in);
		int n = reader.nextInt();
		int[] a = new int[n-1];
		int[] b = new int[n-1];
		int[] t = new int[n];
		for(int i = 0; i < n-1; i++) {
			int y = reader.nextInt();
			if(y == 0) {
				a[i] = 0;
			}
			if(y == 1) {
				a[i] = 1;
			}
			if(y == 2) {
				a[i] = 10;
			}
			if(y == 3) {
				a[i] = 11;
			}
		}
		for(int i = 0; i < n-1; i++) {
			int y = reader.nextInt();
			if(y == 0) {
				b[i] = 0;
			}
			if(y == 1) {
				b[i] = 1;
			}
			if(y == 2) {
				b[i] = 10;
			}
			if(y == 3) {
				b[i] = 11;
			}

		}
		t[0] = b[0]; t[1] = a[0];
		int yu = 1;
		for(int i = 1; i < n-1; i++) {
			for(int j = 0; j < 4; j++) {
				if(j == 0) {
					if((t[i] == a[i]) &&(0 == b[i])) {
						t[i+1] = 0;
						yu = 1;
						break;
					}
				}
				if(j == 1) {
					if(((t[i] + 1)/10 == a[i]/10)&&((t[i] + 1)%10 == a[i]%10)||((t[i] + 1)%10-1 == a[i]%10)) {
						if((t[i]%10 * 1 == b[i]%10)&&(b[i]/10 == 0)) {
							t[i+1] = 1;
							yu = 1;
							break;
						}
						
					}
				}
				if(j == 2) {
					if(((t[i] + 10)%10 == a[i]%10)&&((t[i] + 10)/10 == a[i]/10)||((t[i] + 10)/10-1 == a[i]/10)) {
						if((0 == b[i]%10)&&(b[i]/10 == t[i]/10)) {
							t[i+1] = 10;
							yu = 1;
							break;
						}
						
					}
				}
				if(j == 3) {
					if((((t[i] + 11)%10 == a[i]%10)||((t[i] + 11)%10-1 == a[i]%10))&&((t[i] + 11)/10 == a[i]/10)||((t[i] + 11)/10-1 == a[i]/10)) {
						if((t[i]%10 == b[i]%10)&&(b[i]/10 == t[i]/10)) {
							t[i+1] = 11;
							yu = 1;
							break;
						}
						
					}
				}
				yu = 0;
			}
			if(yu == 0) {
				break;
			}
		}
		if(yu==0) {
			System.out.println("NO");
		}
		else {
			System.out.println("YES");
			for(int i  = 0; i < n -1; i++) {
				if(t[i] == 10) {
					System.out.print(2 + " ");
				}
				else {
					if(t[i] == 11) {
						System.out.print(3 + " ");
					}
					else {
						System.out.print(t[i] + " ");
					}
				}
			}
			if(t[n-1] == 10) {
				System.out.println(2);
			}
			else {
				if(t[n-1] == 11) {
					System.out.println(3);
				}
				else {
					System.out.println(t[n-1]);
				}
			}
		}
	}

}