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.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class D {
    public static void main(String[] args) {
        FastReader reader = new FastReader();
        BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
        int t;
        try {
            t = reader.nextInt();
            for (int i = 0; i < t; i++) {
                int n, k;
                n = reader.nextInt();
                k = reader.nextInt();

                int a[] = new int[n];

                for (int j = 0; j < n; j++) {
                    a[j] = reader.nextInt();
                }

                if (n == 2 || k == 1) {
                    log.write("0\n");
                    log.flush();
                    continue;
                }

                int sum[] = new int[n / 2];
                int max[] = new int[n / 2];
                int min[] = new int[n / 2];

                int value[] = new int[2 * k + 1];

                for (int j = 0; j < n / 2; j++) {
                    sum[j] = a[j] + a[n - 1 - j];
                    max[j] = sum[j] + (k - Math.min(a[j], a[n - 1 -j]));
                    min[j] = sum[j] - (Math.max(a[j], a[n - 1 - j]) - 1);

                    // 1 to min - 1 increase by 2
                    value[1] += 2;
                    if (min[j] != 2 * k) {
                        value[min[j]] -= 2;
                    }

                    // min to max increase by 1
                    value[min[j]] += 1;
                    if (max[j] != 2 * k) {
                        value[max[j] + 1] -= 1;
                    }

                    // max + 1 to 2 *k increase by 2
                    if (max[j] != 2 * k) {
                        value[max[j] + 1] += 2;
                    }
                }

                // Update the array
                int ans = Integer.MAX_VALUE;
                for (int j = 2; j <= 2 * k; j++) {
                    value[j] += value[j - 1];
                    if (value[j] < ans) {
                        ans = value[j];
                    }
                }

                for (int j = 0; j < n / 2; j++) {
                    value[sum[j]]--;
                    if (value[sum[j]] < ans) {
                        ans = value[sum[j]];
                    }
                }

                log.write(ans + "\n");
                log.flush();
            }
            log.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (Exception e) {
            e.printStackTrace();
        }
        return str;
    }
}