Problem: Given are two sequences A and B, both of length N. A and B are each sorted in the ascending order. Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

* 1\leq N \leq 2 \times 10^5
* 1\leq A_i,B_i \leq N
* A and B are each sorted in the ascending order.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


Output

If there exist no reorderings that satisfy the condition, print `No`.

If there exists a reordering that satisfies the condition, print `Yes` on the first line. After that, print a reordering of B on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

Examples

Input

6
1 1 1 2 2 3
1 1 1 2 2 3


Output

Yes
2 2 3 1 1 1


Input

3
1 1 2
1 1 3


Output

No


Input

4
1 1 2 3
1 2 3 3


Output

Yes
3 3 1 2

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class Main {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int n = Integer.parseInt(bf.readLine());
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		int[] array = new int[n];
 		for(int j =0;j<n;j++){
 			array[j] = Integer.parseInt(st.nextToken());
 		}
 		StringTokenizer st1 = new StringTokenizer(bf.readLine());
 		int[] newarray = new int[n];
 		for(int j = 0;j<n;j++){
 			newarray[n-1-j] = Integer.parseInt(st1.nextToken());
 		}
 		int start = Integer.MAX_VALUE;
 		int end = -1;
 		int val = 0;
 		for(int j =0;j<n;j++){
 			if (array[j] == newarray[j]){
 				start = Math.min(start,  j);
 				val = array[j];
 				end = Math.max(end,  j);
 			}
 		}
 		
 		int curr = 0;
 		ArrayList<Integer> indices = new ArrayList<Integer>();
 		for(int j = 0;j<n;j++){
 			if ((j < start || j > end) && array[j]!= val && newarray[j]!= val){
 				indices.add(j);
 			}
 		}
 		if (indices.size() >= end-start+1){
 			out.println("Yes");
 			for(int j = start;j<=end;j++){
 				//swap indices.get(j-start) and j
 				int temp = newarray[j];
 				newarray[j] = newarray[indices.get(j-start)];
 				newarray[indices.get(j-start)] = temp;
 			}
 			for(int j : newarray){
 				out.print(j + " ");
 			}
 			out.println();
 		}
 		else{
 			out.println("No");
 		}
 		
 		
 		
 		out.println();
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is