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.InputStreamReader;

public class BalancedArray {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int cases = Integer.parseInt(br.readLine());

        for (int i = 0; i < cases; i++) {
            int s = Integer.parseInt(br.readLine());

            int[] array1 = new int[s / 2];
            int[] array2 = new int[s / 2];

            if (s / 2 % 2 == 1) {
                System.out.println("NO");
                continue;
            } else {
                System.out.println("YES");
            }

            int sumEven = 0;
            int sumOdd = 0;

            int even = 2;
            int odd = 1;
            for (int j = 0; j < s / 2 - 1; j++) {
                array1[j] = even;
                array2[j] = odd;
                sumEven += even;
                sumOdd += odd;
                even += 2;
                odd += 2;
            }

            array1[s / 2 - 1] = even;
            array2[s / 2 - 1] = sumEven + even - sumOdd;


            print(array1);
            print(array2);
        }
    }

    public static void print(int[] array) {
        for (int i = 0; i < array.length; i++) {
            System.out.print(array[i] + " ");
        }
    }
}