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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t = sc.nextInt();
        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < t; i++) {
            int n = sc.nextInt();
            if (n%4!=0) ans.append("NO\n");
            else {
                ans.append("YES\n");
                long even = 0;
                long odd = 0;
                for (int i1 = 0, e=2; i1 < n / 2; i1++, e+=2) {
                    even += e;
                    ans.append(e).append(" ");
                }
                for (int i1 = 0, o=1; i1 < n / 2-1; i1++, o+=2) {
                    odd+=o;
                    ans.append(o).append(" ");
                }
                ans.append(even - odd).append("\n");
            }
        }
        System.out.println(ans);
    }


    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");

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

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

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

        public int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) {
                a[i]=nextInt();
            }
            return a;
        }

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

    }
}