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.InputStreamReader;
import java.util.*;

public class D {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int tt = sc.nextInt();
        while (tt-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            int[] arr = sc.readArray(n);

            Map<Integer, Integer> map = new HashMap<>();
            List<Integer> minSums = new ArrayList<>();
            List<Integer> maxSums = new ArrayList<>();
            for (int i = 0, j = n - 1; i < j; ++i, --j) {
                int sum = arr[i] + arr[j];
                map.put(sum, 1 + map.getOrDefault(sum, 0));
                minSums.add(Math.min(arr[i], arr[j]) + 1);
                maxSums.add(Math.max(arr[i], arr[j]) + k);
            }

            Collections.sort(minSums);
            Collections.sort(maxSums);

            /*System.out.println(map);
            System.out.println(minSums);
            System.out.println(maxSums);*/
            int minChanges = n / 2;
            for (int sum : map.keySet()) {
                int pairsWithSum = map.get(sum);

                // find pairs with maxSum < sum
                int pairsWithLowerMaxSum = binarySearchLesserThanRightMostWithRepeat(maxSums, sum);

                // find pairs with minSum > sum
                int pairsWithHigherMinSum = binarySearchGreaterThanLeftMostWithRepeat(minSums, sum);

                int pairsWithBothChanges = pairsWithHigherMinSum + pairsWithLowerMaxSum;
                int remainingPairs = (n / 2) - pairsWithBothChanges;
                int pairsWithOneChange = Math.max(0, remainingPairs - pairsWithSum);
               /* System.out.print(sum +" -> ");
                System.out.print(", both : " + pairsWithBothChanges);
                System.out.print(", one : " + pairsWithOneChange);
                System.out.print(", ans : " + (pairsWithOneChange + 2 * pairsWithBothChanges));*/
                minChanges = Math.min(minChanges, pairsWithOneChange + 2 * pairsWithBothChanges);
            }

            System.out.println(minChanges);

           
        }
    }

    private static int binarySearchLesserThanRightMostWithRepeat(List<Integer> list, int key){

        //System.out.println("Searching for count smaller than " + key + " in " + list);
        int n = list.size();
        int idx = -1;
        int low = 0, high = n - 1;
        while(low <= high){
            int mid = (low + high) / 2;
            if(list.get(mid) < key){
                idx = mid;
                low = 1 + mid;
            }
            else
                high = mid - 1;
        }

        //System.out.println("ret : " + (1 + idx));
        return idx + 1;
    }
    private static int binarySearchGreaterThanLeftMostWithRepeat(List<Integer> list, int key){
        //System.out.println("Searching for count greater than " + key + " in " + list);
        int n = list.size();
        int idx = n;
        int low = 0, high = n - 1;
        while(low <= high){
            int mid = (low + high) / 2;

            if(list.get(mid) > key){
                idx = mid;
                high = mid - 1;
            }
            else
                low = 1 + mid;
        }

        //System.out.println("ret : " + (n - idx));
        return n - idx;
    }
    private static class FastReader {
        private final BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        int[] readArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextInt();

            return arr;
        }

        long[] readLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextLong();

            return arr;
        }

        double[] readDoubleArray(int n) {
            double[] arr = new double[n];
            for (int i = 0; i < n; ++i)
                arr[i] = nextDouble();
            return arr;
        }

    }
}