You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.

For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.

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Input

The first and the only line contain one integer n (1 ≤ n ≤ 10^5).

Output

If there is no solution, output "NO" in the first line. 

If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.

Examples

Input


3


Output


YES
1 4 5 2 3 6 

Input


4


Output


NO

Note

Example from the statement is shown for the first example. 

It can be proved that there is no solution in the second example.
import java.io.*;
import java.util.*;
import java.lang.*;

public class zeroarray
{
	public static void main (String[] args)throws IOException
	{
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    int n=Integer.parseInt(br.readLine());
	    int a[]=new int[2*n];
	    if(n%2==1)
	    {
	        System.out.println("YES");int p=1;int count;int i;
	        for(i=0,count=1;i<2*n;i++)
	        {
	            if(count<=n)
	            {
	            a[i]=p;
	            p++;
	            if(i<(n))
	            {
	                a[i+n]=p;
	                p++;
	                i=i+n;
	            }
	            else if(i>(n))
	            {
	                a[i-n]=p;
	                p++;
	                i=i-n;
	            }
	         count++;   
	            
	        }
	        else 
	        break;
	        }
	        for(i=0;i<2*n;i++)
	        {
	            System.out.print(a[i]+" ");
	        }
	    }
	    else
	    System.out.println("NO");
	   
    }
}