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.lang.*;
import java.io.*;
import java.math.*;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        public InputReader(InputStream st) {
            this.stream = st;
        } 
        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        } 
    }
    public static class Key {

        private final int x;
        private final int y;

        public Key(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Key)) return false;
            Key key = (Key) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

    }
    static class Pair{
        String s;
        int x;
        public Pair(String s,int x){
            this.s=s;
            this.x=x;
        }
    }
    static void dfs(int i,int p,int d){
        
    }
   
    static PrintWriter w = new PrintWriter(System.out);
    static long mod=998244353L,mod1=1000000007;
    static ArrayList<Integer> arr[];
    static Map<Key,Integer> map; 
    public static void main(String [] args){
        InputReader sc=new InputReader(System.in);
         int t=sc.ni();
       
        while(t-->0){
            int n=sc.ni();
            int k=sc.ni();
            int arr[]=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=sc.ni();
            }
            int p0[]=new int[2*k+5];
            int p1[]=new int[2*k+5];
            int p2[]=new int[2*k+5];
            for(int i=0;i<n/2;i++){
                int min=Math.min(arr[i],arr[n-i-1]);
                int max=Math.max(arr[i],arr[n-i-1]);
                int sum=min+max;
                p0[sum]++;
                if((min+1)<=(sum-1)){
                    p1[min+1]++;
                    p1[sum]--;
                }
                if((sum+1)<=(k+max)){
                    p1[sum+1]++;
                    p1[k+max+1]--;
                }
                if(min>=2){
                    p2[2]++;
                    p2[min+1]--;
                    
                }
                if(k>=(max+1)){
                    p2[k+max+1]++;
                    p2[2*k+1]--;
                }
            }
            int ans=Integer.MAX_VALUE;
            for(int i=1;i<2*k+5;i++){
                p1[i]+=p1[i-1];
                p2[i]+=p2[i-1];
            }
            //for(int i=2;i<=2*k;i++)w.println(p0[i]+" "+p1[i]+" "+p2[i]);
            for(int i=2;i<=2*k;i++){
                if((p0[i]+p1[i]+p2[i])==n/2){
                    ans=Math.min(ans,p1[i]+2*p2[i]);
                    //w.println("NUM"+i+" "+p1[i]+" "+p2[i]);
                }
            }
           w.println(ans);

        }
        w.close();
    }
}