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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

/**
 * http://codeforces.com/contest/1343/problem/D
 */
public class TaskD {

    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int T = in.nextInt();
        StringBuilder res = new StringBuilder();
        for(int t=0;t<T;t++){
            final int n = in.nextInt();
            final int k = in.nextInt();
            final int []a = in.readIntArr(n);
            int result = solutionDP(n, k, a);
            res.append(result).append('\n');
        }
        out.printf("%s",res.toString());
        out.close();
        in.close();
    }


    private static int solutionDP(int n, int k, int [] a){
        int [] dp = new int[2*k+2];

        for(int i=0;i<n/2;i++){
            int min = Math.min(a[i], a[n-i-1]);
            int max = Math.max(a[i], a[n-i-1]);
            int left = min+1;
            int right = max+k;
            int m = min+max;
            dp[left]++;
            dp[m]++;
            dp[m+1]--;
            dp[right+1]--;
        }
        int pref = dp[0];
        int result = n;
        for(int i=1;i<dp.length;i++){
            result = Math.min(result, n-pref);
            pref+=dp[i];
        }
        return result;
    }


    private static int solutionBF(int n, int k, int[] a) {

        Map<Integer, int[]> m = new HashMap<>();

        for(int i=0;i<n/2;i++){
            int value = a[i]+a[n-i-1];
            int [] count  = m.get(value);
            if(count==null){
                count=new int[1];
                m.put(value,count);
            }
            count[0]++;
        }

        int min = n;
        for(int value=2;value<=2*k;value++){
            int count = 0;
            for(int i=0;i<n/2;i++){
                if((a[i]+a[n-i-1])==value){
                    continue;
                }

                if(a[i]<value&&a[i]+k>=value){
                    count+=1;
                    continue;
                }
                if(a[n-i-1]<value&&a[n-i-1]+k>=value){
                    count+=1;
                    continue;
                }
                count+=2;
            }
            min=Math.min(min,count);
        }

        return min;
    }

    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        long nextLong() {
            return Long.parseLong(next());
        }

    }
}