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.*;
import java.util.*;

public class CF_636_Div3 {

	static class Reader {

		private InputStream mIs;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public Reader() {
			this(System.in);
		}

		public Reader(InputStream is) {
			mIs = is;
		}

		public int read() {
			if (numChars == -1) {
				throw new InputMismatchException();

			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = mIs.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String next() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] intArray(int n) {
			Reader r = new Reader();
			int arr[] = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = r.nextInt();
			}
			return arr;
		}

		public long[] longArray(int n) {
			Reader r = new Reader();
			long arr[] = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = r.nextInt();
			}
			return arr;
		}

		public void printArray(int arr[]) {
			PrintWriter out = new PrintWriter(System.out);
			for (int i = 0; i < arr.length; i++) {
				if (i == arr.length - 1)
					out.println(arr[i]);
				else
					out.print(arr[i] + " ");
			}
			out.close();
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}

	static Reader r = new Reader();

	private static void solve1() {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {
			long n = r.nextLong();

			long ans = 1;
			long sum = 1, num = 1;

			for (int i = 2; i <= Math.sqrt(n); i++) {
				num *= 2;
				sum += num;
				if (n % sum == 0) {
					ans = n / sum;
					break;
				}
			}

			res.append(ans).append("\n");
		}

		System.out.print(res);

	}

	static StringBuilder res;

	static boolean findDistinctOddSum(long n, long k) {
		boolean flag = false;
		if ((k * k) <= n && (n + k) % 2 == 0) {
			long val = 1;
			long sum = 0;
			for (int i = 1; i < k; i++) {
				res.append(val).append(" ");
				sum += val;
				val += 2;
			}
			res.append(n - sum).append(" ");
			flag = true;
		}
		return flag;
	}

	private static void solve2() {

		int t = r.nextInt();

		while (t-- > 0) {

			long n = r.nextLong();
			res = new StringBuilder();

			boolean flag = true;
			if (n / 2 % 2 != 0) {
				flag = false;
			} else {
				int even = 2;
				long sum = 0;
				for (int i = 1; i <= n / 2; i++) {
					res.append(even).append(" ");
					sum += even;
					even += 2;
				}
				if (!findDistinctOddSum(sum, n / 2)) {
					flag = false;
				}
			}

			if (flag) {
				System.out.println("YES");
				System.out.println(res);
			} else {
				System.out.println("NO");
			}
		}
	}

	private static void solve3() {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			res.append(false).append("\n");
		}

		System.out.print(res);

	}

	private static void solve4() {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			res.append(false).append("\n");
		}

		System.out.print(res);

	}

	private static void solve5() {

		int t = r.nextInt();
		StringBuilder res = new StringBuilder();

		while (t-- > 0) {

			int n = r.nextInt();

			long ans = 0;
			if (n % 3 == 0) {
				ans = n / 3;
			} else {
				for (int i = 3; i <= Math.sqrt(n); i++) {
					if (n % i == 0) {
						ans = i;
					}
				}
			}

			res.append(ans).append("\n");
		}

		System.out.print(res);

	}

	public static void main(String[] args) throws IOException {

//		solve1();

		solve2();

		// solve3();

		// solve4();

		// solve5();
	}

}