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 javafx.util.Pair;
 
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.util.Map.Entry;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
 
public class abc {
		
		public static void main(String[] args) throws Exception {
			// TODO Auto-generated method stub
			InputReader s = new InputReader(System.in);
			PrintWriter p = new PrintWriter(System.out);
			int t = s.nextInt();
			while (t-- > 0) {
				int n=s.nextInt();
				int k=s.nextInt();
				int[] arr=new int[n];
				for(int i=0 ; i<arr.length ; i++) {
					arr[i]=s.nextInt();
				}
			int[] freq=new int[2*k+1];
			int i=0,j=arr.length-1;
			int[] pre=new int[2*k+1];
			while(i<j) {
				int sum=arr[i]+arr[j];
				freq[sum]++;
				int a=Math.min(arr[i],arr[n-i-1])+1;
				int b=Math.max(arr[i], arr[n-i-1])+k;
				pre[a]++;
				if(b+1<pre.length) {
					pre[b+1]--;
				}
				
				i++;
				j--;
			}
			for(i=1 ; i<pre.length ; i++) {
				pre[i]+=pre[i-1];
			}
			int ans=Integer.MAX_VALUE;
			for(i=0 ; i<pre.length ; i++) {
				int a=pre[i]-freq[i]+2*(n/2-pre[i]);
				ans=Math.min(ans, a);
			}
			System.out.println(ans);
			
			}
			p.flush();
			p.close();
		}
	 
		
		
		static int helper(int[][] arr , int pos) {
			
			helper(arr,pos);
			return -1;
		}
		
		
		
		static long power(long x, long y) 
	    { 
			long temp=0l; 
	        if( y == 0) 
	            return 1l; 
	        temp = power(x, y/2);  
	          
	        if (y%2 == 0) 
	            return temp*temp; 
	        else
	        { 
	            if(y > 0) 
	                return x * temp * temp; 
	            else
	                return (temp * temp) / x; 
	        } 
	    }  
		
		
		public static boolean helper(int[] arr1 , int[] arr2) {
			boolean[] temp=new boolean[3];
			if(arr1.length==0) return true;
			if(arr1[0]!=arr2[0]) return false;
			temp[arr1[0]+1]=true;
			for(int i=1 ; i<arr1.length ; i++) {
				
				if(arr1[i]==arr2[i]) {
					
				}else if(arr1[i]<arr2[i]) {
					if(!temp[2]) {
						return false;
					}
				}else {
					if(!temp[0]) {
						return false;
					}
				}
				temp[arr1[i]+1]=true;
			}
			return true;
		}
		
		
		
		static class Pair<T, V> {
			T first; // maximum distance Node
			V second; // distance of maximum distance node
	 
			// Constructor
			Pair(T first, V second) {
				this.first = first;
				this.second = second;
			}
		}
	 
		public static ArrayList Divisors(long n) {
			ArrayList<Long> div = new ArrayList<>();
	 
			for (long i = 1; i <= Math.sqrt(n); i++) {
				if (n % i == 0) {
					div.add(i);
	 
					if (n / i != i)
						div.add(n / i);
				}
			}
			return div;
		}
	 
		public static int BinarySearch(long[] a, long k) {
			int n = a.length;
			int i = 0, j = n - 1;
			int mid = 0;
	 
			if (k < a[0])
				return 0;
			else if (k >= a[n - 1])
				return n;
			else {
				while (j - i > 1) {
					mid = (i + j) / 2;
	 
					if (k >= a[mid])
						i = mid;
					else
						j = mid;
				}
			}
	 
			return i + 1;
		}
	 
		public static long GCD(long a, long b) {
			if (b == 0)
				return a;
			else
				return GCD(b, a % b);
		}
	 
		public static long LCM(long a, long b) {
			return (a * b) / GCD(a, b);
		}
	 
		static class InputReader {
	 
			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;
	 
			public InputReader(InputStream stream) {
				this.stream = stream;
			}
	 
			public int snext() {
				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++];
			}
	 
			static class pair implements Comparable<pair> {
				Integer x, y;
	 
				pair(int x, int y) {
					this.x = x;
					this.y = y;
				}
	 
				public int compareTo(pair o) {
					int result = x.compareTo(o.x);
					if (result == 0)
						result = y.compareTo(o.y);
	 
					return result;
				}
	 
				public String toString() {
					return x + " " + y;
				}
	 
				public boolean equals(Object o) {
					if (o instanceof pair) {
						pair p = (pair) o;
						return p.x - x == 0 && p.y - y == 0;
					}
					return false;
				}
	 
				public int hashCode() {
					return new Long(x).hashCode() * 31 + new Long(y).hashCode();
				}
			}
	 
			public int nextInt() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public long nextLong() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int[] nextIntArray(int n) {
				int a[] = new int[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}
	 
			public String readString() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public String nextLine() {
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}
	 
			public boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
	 
			public interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		}
	 
		static class CodeX {
			public static void sort(long arr[]) {
				merge_sort(arr, 0, arr.length - 1);
			}
	 
			private static void merge_sort(long A[], long start, long end) {
				if (start < end) {
					long mid = (start + end) / 2;
					merge_sort(A, start, mid);
					merge_sort(A, mid + 1, end);
					merge(A, start, mid, end);
				}
	 
			}
	 
			private static void merge(long A[], long start, long mid, long end) {
				long p = start, q = mid + 1;
				long Arr[] = new long[(int) (end - start + 1)];
				long k = 0;
	 
				for (int i = (int) start; i <= end; i++) {
					if (p > mid)
						Arr[(int) k++] = A[(int) q++];
	 
					else if (q > end)
						Arr[(int) k++] = A[(int) p++];
	 
					else if (A[(int) p] < A[(int) q])
						Arr[(int) k++] = A[(int) p++];
	 
					else
						Arr[(int) k++] = A[(int) q++];
				}
				for (int i = 0; i < k; i++) {
					A[(int) start++] = Arr[i];
				}
	 
			}
	 
		}
	 
	}