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.*;

public class Solution {
    public static BufferedReader br;
    public static Print print=new Print();
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        int T = Integer.parseInt(br.readLine());
        for (int t = 0; t < T; t++) {
            solve();
        }
        print.close();
    }

    public static void solve()throws Exception {
        int N = Integer.parseInt(br.readLine());

        int half = N / 2;

        if (half % 2 != 0 ) {
            print.println("NO");
            return;
        }
        long evenSum = 0L;
        print.println("YES");
        for ( int i = 1; i <= half; i++ ) {
            int val = i*2;
            print.print(val + " ");
            evenSum += val;
        }
        long oddSum = 0L;
        for ( int i = 1; i <= half-1; i++ ) {
            int val = (i*2) - 1;
            print.print(val + " ");
            oddSum += val;
        }
        print.println(evenSum - oddSum);
        // System.out.println(evenSum + " " + (evenSum - oddSum));
    }
}
class Print
{
    private final BufferedWriter bw;
    public Print()
    {
        this.bw=new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public void print(Object object)throws IOException
    {
        bw.append(""+object);
    }
    public void println(Object object)throws IOException
    {
        print(object);
        bw.append("\n");
    }
    public void close()throws IOException
    {
        bw.close();
    }
}