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 Main {

	public static class FastReader {
		BufferedReader br;
		StringTokenizer root;
		
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (root == null || !root.hasMoreTokens()) {
				try {
					root = new StringTokenizer(br.readLine());
				} catch (Exception addd) {
					addd.printStackTrace();
				}
			}
			return root.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception addd) {
				addd.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	
	public static FastReader sc = new FastReader();
 
	static int mod = (int) (1e9+7),MAX=(int) (3e5);
	static List<Integer>[] edges ;
	static long[][] dp;
	public static void main(String[] args) {
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			int[] a = new int[n];
			for(int i=0;i<n;++i) a[i] = sc.nextInt();
			Map<Integer,Integer> map = new HashMap<>();
			// number of pairs which can make x sum by changing atmost one element
		    int[] pre = new int[2*k+2]; 
		    for(int i=0;i<n/2;++i) {
		    	int sum = a[i] + a[n-i-1];
		    	map.put(sum,map.getOrDefault(sum,0)+1);
		    	int min = Math.min(a[i],a[n-i-1]);
		    	int max = Math.max(a[i],a[n-i-1]);
		    	pre[min+1]++;
		    	pre[max+k+1]--;
		    }
		    int ans = n;
		    for(int i=2;i<=2*k;++i) {
		    	pre[i]+=pre[i-1];
		    	int changes = pre[i] - map.getOrDefault(i,0) + 2*(n/2-pre[i]);
		    	ans = Math.min(ans,changes);
		    }
		    out.println(ans);
		}
		out.close();

	}
	
	
	
}