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:
/*
 -> Written by <-
   -----------
  |J_O_B_E_E_L|
  |___________|
  |    ___    |
  |   (^_^)   |
  |  /( | )\  |
  |____|_|____|
*/

import java.util.*;


import java.io.*;

  
public class Test {
	
	public static void main(String[] args) throws Exception {
		int t=sc.nextInt();
		while(t-->0) {
			int x=sc.nextInt(); int k=sc.nextInt();
			int [] arr=sc.nextIntArray(x);
			int ans=Integer.MAX_VALUE;
			int [] overlap=new int [(k<<1)+2];
			for(int i=0;i<x>>1;i++) {
				int min=Math.min(arr[i], arr[x-i-1]);
				int max=Math.max(arr[i], arr[x-i-1]);
				overlap[1]+=2;
				overlap[min+1]--;
				overlap[max+min]--;
				overlap[min+max+1]++;
				overlap[max+k+1]++;
			}
			int sum=0;
			for(int i=1;i<overlap.length;i++) {
				sum+=overlap[i];
				ans=Math.min(ans, sum);
			}
			pw.println(ans);
		}
		pw.flush();
		pw.close();
	}
    static class Scanner {
    	 
        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;
 
        public Scanner(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }
 
        public boolean hasNextByte() {
            if (curbuf >= lenbuf) {
                curbuf = 0;
                try {
                    lenbuf = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return false;
            }
            return true;
        }
 
        private int readByte() {
            if (hasNextByte())
                return buffer[curbuf++];
            else
                return -1;
        }
 
        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
 
        private void skip() {
            while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                curbuf++;
        }
 
        public boolean hasNext() {
            skip();
            return hasNextByte();
        }
 
        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (!isSpaceChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
 
        public int nextInt() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }
 
        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
 
        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
        
        public Long [] nextSortedLongArray(int n) {
        	Long [] a=new Long[n];
        	for(int i=0;i<n;i++) a[i]=sc.nextLong();
        	Arrays.sort(a);
        	return a;
        }
        public Integer [] nextSortedIntegerArray(int n) {
        	Integer [] a=new Integer[n];
        	for(int i=0;i<n;i++) a[i]=sc.nextInt();
        	Arrays.sort(a);
        	return a;
        }
 
    }
 


   
	static PrintWriter pw=new PrintWriter(System.out);
	static Scanner sc=new Scanner(System.in);
 
}