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 Solution {

    private static PrintWriter out;

    public static void main(String[] args) {
       FastScanner fs = new FastScanner();
       out = new PrintWriter(new BufferedOutputStream(System.out));
       
       int t = fs.nextInt();
 
        while (t-- > 0) {
            int n = fs.nextInt();
            solve(n);
        }

       out.close();
    }

    static void solve(int n) {
        if (n % 4 != 0) {
            out.println("NO");
            return;
        }
        out.println("YES");
        
        for (int i = 1; i <= n/2; ++i) {
            out.printf("%d ", i * 2);
        }
        for (int i = 1; i <= n/2 - 1; ++i) {
            out.printf("%d ", i * 2 - 1);
        }
     
        out.printf("%d\n", n - 1 + n/2);
    }
}

class FastScanner {
    private BufferedReader br;
    private StringTokenizer st;

    public FastScanner() {
        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;
    }
}