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
		BufferedReader b=  new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(b.readLine());
		StringBuilder str = new StringBuilder();
		while(t--!=0){
		    
		    String[] in = b.readLine().split(" ");
		    int n = Integer.parseInt(in[0]);
		    int k = Integer.parseInt(in[1]);
		    
		    in = b.readLine().split(" ");
		    int[] arr = new int[n];
		    for(int i=0;i<n;i++){
		        arr[i] = Integer.parseInt(in[i]);
		    }
		    
		    long[] sum = new  long[n];
		    long[] maxS = new long[n];
		    long[] minS = new long[n];
		    
		  
		    long[] cnt = new long[2*k+1];     // pairs whose sum is x
		    for(int i=0;i<n/2;i++){
		        sum[i] = arr[i]+arr[n-i-1];
		        maxS[i] = k+Math.max(arr[i],arr[n-i-1]);
		        minS[i] = Math.min(arr[i],arr[n-i-1])+1;
		        
		        cnt[(int)sum[i]]++;
		    }
		    long[] pref = new long[2*k+2]; // pairs whose sum is x after atmost     // 1 modification
		    for(int i=0;i<n/2;i++){
		        pref[(int)minS[i]]+=1;
		        pref[(int)maxS[i]+1]-=1;
		    }
		    for(int i=2;i<=2*k+1;i++){
		        pref[i]+= pref[i-1];
		    }
		    long[] dono = new long[2*k+1];      // pairs whose sum is x after both     // mod
		    
		    for(int i =2;i<2*k+1;i++){
		        dono[i] = (long)(n/2-pref[i]);
		    }
		  //  System.out.println(map.get(2)+" "+map.get(3));
		    long ans = Long.MAX_VALUE;
		  //  System.out.println(toSum);
		    for(int i=2;i<2*k+1;i++){
		        ans = Math.min(ans,pref[i]-cnt[i]+(dono[i]*2));
		    }
		    str.append(ans+"\n");
		  
		}
		System.out.print(str);
	}
}