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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;


import java.util.*;


public class Main {


    Set<Integer>set=new HashSet<>();
    public boolean canVisitAllRooms(List<List<Integer>> rooms) {

        List<Integer>s=new ArrayList<>(rooms.get(0));
        for (int i = 0; i < s.size(); i++) {
            set.add(s.get(i));
        }
        for (int i = 0; i < s.size(); i++) {
            for(int it:rooms.get(i)){
                if (!set.contains(it)){
                    s.add(it);
                    set.add(it);
                }
            }
        }

        return rooms.size()==set.size();


    }



    public static void main (String[]args) throws IOException {
        Scanner in = new Scanner(System.in);


        try (PrintWriter or = new PrintWriter(System.out)) {

            int t=in.nextInt();
            outer:
            while (t-->0){
               int n=in.nextInt();

               if ((n/2)%2==1)or.println("NO");
               else{
                   long[]a=new long[n];
                   int d=2;
                   long sum=0,sum2=0;
                   for (int i = 0; i < n/2; i++) {
                       a[i]=d;

                       sum+=(long)(d);
                       d+=2;
                   }
                   d=1;
                   for (int i = n/2; i <n-1 ; i++) {
                       a[i]=d;
                       sum2+=(long)(d);
                       d+=2;
                   }
                   a[n-1]=sum-sum2;
                   or.println("YES");
                   for(long k:a)or.print(k+" " );
                   or.println();
               }







            }








        }
    }




    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static int getlen(int r,int l,int a){
        return (r-l+1+1)/(a+1);
    }






    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++) {
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec) {
                        f *= 10;
                    }
                }
            }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}

class Pair implements Comparable<Pair> {
    int first, second;

    public Pair(int first, int second) {
        this.first = first;
        this.second = second;
    }


    @Override
    public int compareTo(Pair o) {
        if (first!=o.first)return first-o.first;
        return second-o.second;
    }
}

class Tempo {

    int first,second,third;

    public Tempo(int first, int second, int third) {
        this.first = first;
        this.second = second;
        this.third = third;
    }
}