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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Submit {
    public static void main(String arfs[]) throws IOException{
        process();
    }
    public static void process() throws IOException{
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(in.readLine());
        for(int t=0;t<T;t++){
            StringTokenizer st=new StringTokenizer(in.readLine()," ");
            int n=Integer.parseInt(st.nextToken());
            int k=Integer.parseInt(st.nextToken());
            int arr[]=new int[n+1];
            st=new StringTokenizer(in.readLine()," ");
            for(int i=1;i<=n;i++)
                arr[i]=Integer.parseInt(st.nextToken());
            HashMap<Integer,Integer> map=new HashMap<>();
            HashMap<Integer,Integer> g=new HashMap<>();
            int p[]=new int[2*k+2];
            for(int i=1;i<=n/2;i++) {
                if(!map.containsKey(arr[i] + arr[n - i + 1]))
                    map.put(arr[i] + arr[n - i + 1], 1);
                else
                    map.put(arr[i] + arr[n - i + 1],map.get(arr[i] + arr[n - i + 1])+1);
                int a=1+Math.min(arr[i],arr[n-i+1]);
                int b=k+Math.max(arr[i],arr[n-i+1]);
                p[a]++;
                p[b+1]--;
            }
            for(int i=2;i<=2*k;i++)
                p[i]+=p[i-1];
            int ans=Integer.MAX_VALUE;
            int zero=0;
            int one=0;
            int two=0;
            int pair=n/2;
            for(int i=2;i<=2*k;i++){
                if(map.containsKey(i))
                    zero=map.get(i);
                else
                    zero=0;
                one=Math.abs(p[i]-zero);
                two=Math.abs(pair-(zero+one));
                ans=Math.min(ans,one+(two*2));
            }
            System.out.println(ans);
        }
    }
}