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 Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0){
			int n=sc.nextInt(),k=sc.nextInt();
			int arr[]=new int[n];
			int c[]=new int[2*k+1];
			for(int i=0;i<n;i++){
				arr[i]=sc.nextInt();
			}
			for(int i=0;i<n/2;i++){
				int x=i,y=n-i-1;
				int min=Math.min(arr[x], arr[y])+1;
				int max=Math.max(arr[x], arr[y])+k;
				int mid=arr[x]+arr[y];
				c[1]+=2;
				c[min]--;
				c[mid]--;
				if(mid!=2*k){
					c[mid+1]++;
				}
				if(max!=2*k){
					c[max+1]++;
				}
			}
			int ans=2*n;
			for(int i=1;i<=2*k;i++){
				c[i]+=c[i-1];
				ans=Math.min(ans, c[i]);
			}
			System.out.println(ans);
		}
	}
}