Problem: You are given a positive integer n, it is guaranteed that n is even (i.e. divisible by 2).

You want to construct the array a of length n such that: 

  * The first n/2 elements of a are even (divisible by 2); 
  * the second n/2 elements of a are odd (not divisible by 2); 
  * all elements of a are distinct and positive; 
  * the sum of the first half equals to the sum of the second half (∑_{i=1}^{n/2} a_i = ∑_{i=n/2 + 1}^{n} a_i). 



If there are multiple answers, you can print any. It is not guaranteed that the answer exists.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the length of the array. It is guaranteed that that n is even (i.e. divisible by 2).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — "NO" (without quotes), if there is no suitable answer for the given test case or "YES" in the first line and any suitable array a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) satisfying conditions from the problem statement on the second line.

Example

Input


5
2
4
6
8
10


Output


NO
YES
2 4 1 5
NO
YES
2 4 6 8 1 3 5 11
NO

Solution (in JAVA):

Solution:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while(t-->0){
		    int n = s.nextInt();
		    int k = s.nextInt();
		    int[] a = new int[n];
		    for(int i=0;i<n;i++) a[i]=s.nextInt();
		    int[] min = new int[n/2];
		    int[] max = new int[n/2];
		    HashMap<Integer,Integer> map = new HashMap<>();
		    for(int i=0;i<(n/2);i++){
		        int tt = a[i]+a[n-1-i];
		        map.put(tt,map.getOrDefault(tt,0)+1);
		        min[i]=Math.min(a[i],a[n-1-i])+1;
		        max[i]=Math.max(a[i],a[n-1-i])+k;
		    }
		    Arrays.sort(min);
		    Arrays.sort(max);
		    int[] mapl = new int[2*k+1];
		    int[] mapu = new int[2*k+1];
		    int j=0;
		    for(int i=2;i<=2*k;i++){
		        while(j<(n/2)&&i==min[j]) j++;
		        mapl[i]=(n/2)-j;
		        if(j==n/2) break;
		    }
		    j=(n/2);
		    for(int i=2*k;i>=2;i--){
		        while(j>0&&i==max[j-1]) j--;
		        mapu[i] = j;
		        if(j==0) break;
		    }
		    int ans=n/2;
		    for(int i=2;i<=2*k;i++){
		        ans = Math.min(ans,(n/2)-map.getOrDefault(i,0)+mapl[i]+mapu[i]);
		    }
		    System.out.println(ans);
		}
	}
}