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.util.*;
import java.io.*;

public class ProblemD {
    public static void main(String[] args) {
        MyScanner s = new MyScanner();
        int cas = s.nextInt();
        for (int x = 0; x < cas; x++) {
            int n = s.nextInt();
            int k = s.nextInt();
            int[] ar = new int[n];
            ArrayList<Point> poin1 = new ArrayList<Point>();
            Point[] p = new Point[2*n];
            for (int i = 0; i < n; i++) {
                ar[i] = s.nextInt();
            }
            long sum = 0L + n;
            long min = sum;
            for (int i = 0; i < n/2; i++) {
                int a = ar[i];
                int b = ar[n-i-1];
                poin1.add(new Point(Math.min(a, b) + 1, -1));
                poin1.add(new Point(a+b, -1));
                poin1.add(new Point(a+b + 1, +1));
                poin1.add(new Point(Math.max(a, b) + k + 1, +1));
            }
            for (int i = 0; i < poin1.size(); i++) {
                p[i] = poin1.get(i);
            }
            Arrays.sort(p);
            for (int i = 0; i < p.length; i++) {
                sum += p[i].v;
                if (sum < min) {
                    min = sum;
                }
            }
            System.out.println(min);
        }
    }

    public static class Point  implements Comparable<Point>{
        public int x;
        public int v;

        public Point(int x, int v) {
            this.x = x;
            this.v = v;
        }

        public int compareTo(Point p) {
            int n =  this.x - p.x;
            if (n == 0) {
                return p.v - this.v;
            }
            else {
                return n;
            }
        }
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

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

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

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

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

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

    }
}