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.util.*;

public class div3636b {
public static void main(String[] args) {
Scanner scan=new Scanner(System.in);
	
	long test=scan.nextLong();
	while(test>0){
		long n=scan.nextLong();
		long sum=1;
		long sum1=0;
		long s1=0;
		long s2=0;
		if(n%4==0){
			System.out.println("YES");
			long a[]=new long[(int)n];
			for(int i=0;i<n/2;i++){
		a[i]=2*(i+1);
		System.out.print(a[i]+" ");
		s1=s1+a[i];
			}
			a[(int)n/2]=1;
			System.out.print(1+" ");
			s2=1;
			for(int j=(int)n/2+1;j<n-1;j++){
				a[j]=a[j-1]+2;
				System.out.print(a[j]+" ");
				sum1=sum1++;

				s2=s2+a[j];
			}
			a[(int)n-1]=s1-s2;
			System.out.print(a[(int)n-1]+" ");

			
			
		}
		else{
			System.out.print("NO");
		}

		test--;
		System.out.println();
	}
}
}