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.Collections;
import java.util.Scanner;
import java.util.Vector;

public class NewClass {

                 public static void main(String[] args) {
                                  Scanner ob = new Scanner(System.in);
                                  int t = ob.nextInt();
                                  for (int T = 1; T <= t; T++) {
                                                   int n = ob.nextInt();
                                                   if (n % 4 == 0) {
                                                                    System.out.println("YES");
                                                                    Vector v1 = new Vector();
                                                                    Vector v2 = new Vector();
                                                                    int count = 0;
                                                                    for (int i = 2; i <= n; i += 2) {
                                                                                     v1.add(i);
                                                                                     count++;
                                                                                     v2.add(i - 1);
                                                                    }
                                                                    v2.set(v2.size() - 1, (int) v2.get(v2.size() - 1) + count);
                                                                    //  System.out.println(v1);
                                                                    // System.out.println(v2);
                                                                    for (int i = 0; i < n / 2; i++) {
                                                                                     System.out.print(v1.get(i) + " ");
                                                                    }
                                                                    for (int i = 0; i < n / 2; i++) {
                                                                                     System.out.print(v2.get(i) + " ");
                                                                    }
                                                                    System.out.println();
                                                   } else {
                                                                    System.out.println("NO");
                                                   }

                                  }
                 }

}