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:
import java.math.BigInteger;
import java.util.*;
public class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		for(int t=sc.nextInt();t>0;t--) {
			int n=sc.nextInt();
			if(n%4==0) {
				System.out.println("YES");
			}else {
				System.out.println("NO");
				continue;
			}
			int a[]=new int[n];
			int x=0;//下标
			for(int i=2;i<=n;i=i+2) {
				a[x]=i;
				x++;
			}for(int i=1;i<n-1;i=i+2) {
				a[x]=i;
				x++;
			}
			a[x]=a[n/2-1]+n/2-1;
			for(int i=0;i<n;i++) {
				System.out.print(a[i]+" ");
			}
			System.out.println();
		}
	}
}