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.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;

public class TaskB {

	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		BufferedWriter br = new BufferedWriter(new OutputStreamWriter(System.out));
		int t = Integer.parseInt(in.nextLine());
		while (t-- > 0) {
			StringBuilder sb = new StringBuilder();
			int n = in.nextInt();
			long[] ans = new long[n];
			if (n % 4 != 0) {
				System.out.println("NO");
				continue;
			}
			long sum = 2, sum2 = 1;
			ans[0] = 2;
			for (int i = 1; i < n / 2; i++) {
				ans[i] = ans[i - 1] + 2;
				sum += ans[i];
			}
			ans[n / 2] = 1;
			for (int i = (n / 2) + 1; i < n; i++) {
				ans[i] = ans[i - 1] + 2;
				sum2 += ans[i];
				if (i == n - 1)
					sum2 -= ans[i];
			}
			ans[n - 1] = (sum - sum2);
			System.out.println("YES");
			for (int i = 0; i < n; i++) {
				if (i == n - 1) {
					System.out.println(String.valueOf(ans[i]));
				} else {
					System.out.print(String.valueOf(ans[i]) + " ");
				}
			}
			br.write(System.lineSeparator());
			br.flush();
		}
	}

	private static void shuffleArray(int[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			int tmp = arr[i];
			int randomPos = rnd.nextInt(n);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}

	private static void shuffleArray(long[] arr) {
		int n = arr.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			long tmp = arr[i];
			int randomPos = i + rnd.nextInt(n - i);
			arr[i] = arr[randomPos];
			arr[randomPos] = tmp;
		}
	}
}

class Graph {

	private Map<Integer, List<Integer>> adjVertices;
	private String status;

	public void addCity(int city) {
		adjVertices.putIfAbsent(city, new ArrayList<>());
	}

	public void addEdge(int city1, int city2) {
		adjVertices.get(city1).add(city2);
		adjVertices.get(city2).add(city1);
	}

	public void setStatus(String status) {
		this.status = status;
	}

	public Map<Integer, List<Integer>> getCities() {
		return adjVertices;
	}
}