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;

public class Main {
  private static void printBalancedArray(int n) {
    if ((n / 2) % 2 != 0)
      System.out.println("NO");
    else {
      System.out.println("YES");
      int[] a            = new int[n];
      int   evenNumber   = 2;
      int   oddNumber    = 1;
      int   leftSideSum  = 0;
      int   rightSideSum = 0;
      int   i            = 0;
      for (; i < n / 2; i++, evenNumber += 2) {
        leftSideSum = leftSideSum + evenNumber;
        a[i]        = evenNumber;
      }//end for - i
      for (; i < n - 1; i++, oddNumber += 2) {
        rightSideSum = rightSideSum + oddNumber;
        a[i]         = oddNumber;
      }//end for - i
      a[n - 1] = leftSideSum - rightSideSum;
      for (int j = 0; j < n; j++)
        System.out.print(a[j] + " ");
      System.out.println();
    }//end if - else
  }// end printBalancedArray
  
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int     t  = sc.nextInt();
    for (int i = 0; i < t; i++)
      printBalancedArray(sc.nextInt());
  }//end main
}// end Main - class