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.util.Scanner;
import java.util.*;

public class Solution {

    public static final String IMPOSSIBLE = "IMPOSSIBLE";

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);

        int t = input.nextInt();

        for(int u=0; u < t; u++) {
            int n = input.nextInt();

            if (!((n & 3) == 0)) {
                System.out.println("NO");
            } else {

                long[] a = new long[n];

                long evens = 0;
                long valEven = 2;
                for(int i=0; i < (n/2); i++) {
                    a[i] = valEven;
                    evens += a[i];
                    valEven += 2;
                }

                int val = 1;
                long odds = 0;
                for(int i=(n/2); i < n; i++) {
                    if (i == n - 1) {
                        break;
                    }
                    a[i] = val;
                    odds += a[i];
                    val+= 2;
                }

                a[n-1] = evens - odds;

                System.out.println("YES");

                for(int i=0; i < n; i++) {
                    if (i == 0)
                        System.out.print(a[i]);
                    else
                        System.out.print(" " + a[i]);
                }
                System.out.println("");
            }
        }
    }

}