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 practice;

import java.util.Scanner;
import java.util.Arrays;

public class FirstCode {

	public static void main(String[] args)  {
		Scanner scan = new Scanner(System.in);
		
		int t = scan.nextInt();
		
		for(int tt=0;tt<t;tt++) {
			int n = scan.nextInt();
			int k = scan.nextInt();
			int a[] = new int[2*k+2];
			for(int i=0;i<2*k+2;i++) {
				a[i] = 0;
			}
			
			int b[] = new int[n];
			for(int i=0;i<n;i++) {
				b[i] = scan.nextInt();
			}
			
			for(int i=0;i<n/2;i++) {
				int x = b[i];
				int y = b[n-1-i];
				
				int mn = (x+1 > y+1 ? y+1 : x+1);
				int mx = (x+k > y+k ? x+k : y+k);
				
				a[mn]++;
				a[mx+1]--;
				a[mx+1]+=2;
				a[k+k+1]-=2;
				a[2]+=2;
				a[mn]-=2;
				a[x+y]--;
				a[x+y+1]++;
			}
			
			int ans = n;
			
			for(int i=2;i<=k+k;i++) {
				a[i] += a[i-1];
				ans = (ans > a[i] ? a[i] : ans);
			}
			
			System.out.println(ans);
		}
		
		scan.close();
	}
	
	static int power(int a,int b,int m) {
		int res = 1;
		while(b > 0) {
			if((b&1) != 0) {
				res = res*a;
				res %= m;
			}
			a = a*a;
			a %= m;
			b = b/2;
		}
		return res;
	}
	

}