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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Nikita Mikhailov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.readInt();
            int hn = n / 2;
            int k = in.readInt();

            int[] aR = in.readInts(n / 2);
            int[] bR = new int[n / 2];
            int[] tmp = in.readInts(n / 2);

            for (int i = 0; i < n / 2; i++) {
                bR[i] = tmp[n / 2 - 1 - i];
            }


            int RANGE = 2 * k + 100;
            int[] oneChangeCnt = new int[RANGE];
            int[] noChangeCnt = new int[RANGE];

            for (int i = 0; i < hn; i++) {
                int a = Math.max(aR[i], bR[i]);
                int b = Math.min(aR[i], bR[i]);


                noChangeCnt[a + b]++;

                int leftGrInc = b + 1;
                int rightGrInc = a + k;

                oneChangeCnt[leftGrInc]++;
                oneChangeCnt[rightGrInc + 1]--;
            }

            MinMaxCounter<Integer> mmc = new MinMaxCounter<>();
            int oneChangeCounter = 0;
            for (int i = 0; i < RANGE; i++) {
                int noChange = noChangeCnt[i];
                oneChangeCounter += oneChangeCnt[i];

                int oneChange = oneChangeCounter - noChange;

                int twoChange = n / 2 - noChange - oneChange;

                mmc.min(oneChange + 2 * twoChange);
            }

            out.println(mmc.get());
        }

    }

    static class MinMaxCounter<T extends Comparable<T>> {
        private T value;
        private boolean init;

        public MinMaxCounter(T startValue) {
            init = true;
            value = startValue;
        }

        public MinMaxCounter() {
            init = false;
        }

        public void min(T a) {
            if (init) {
                value = value.compareTo(a) < 0 ? value : a;
            } else {
                value = a;
                init = true;
            }
        }

        public T get() {
            if (init) {
                return value;
            } else {
                return null;
            }
        }

    }

    static class FastScanner {
        private StringTokenizer st;
        private BufferedReader in;

        public FastScanner(final InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public String readToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int readInt() {
            return Integer.parseInt(readToken());
        }

        public int[] readInts(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = readInt();
            }
            return res;
        }

        public String next() {
            return readToken();
        }

    }
}