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:
/*
 *created by Kraken on 21-04-2020 at 19:44
 */
//package com.kraken.cf.cf636;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class D {

  public static void main(String[] args) {
    FastReader sc = new FastReader();
    long t = sc.nextInt();
    while (t-- > 0) {
      int n = sc.nextInt(), k = sc.nextInt();
      long[] x = new long[n];
      long[] cnt = new long[2 * k + 2];
      Map<Long, Integer> map = new HashMap<>();
      for (int i = 0; i < n; i++) x[i] = sc.nextInt();
      for (int i = 0; i < n / 2; i++) {
        long sum = x[i] + x[n - i - 1];
        if (map.containsKey(sum)) map.put(sum, map.get(sum) + 1);
        else map.put(sum, 1);
        long min = Math.min(x[i], x[n - i - 1]);
        long max = Math.max(x[i], x[n - i - 1]);
        cnt[(int) min + 1]++;
        cnt[(int) max + k + 1]--;
      }
      for (int i = 1; i < 2 * k + 1; i++) cnt[i] += cnt[i - 1];
      long ans = Long.MAX_VALUE;
//      System.out.println(map);
//      System.out.println(Arrays.toString(cnt));
      for (int i = 2; i <= 2 * k; i++) {
        long ta = 0;
        if (map.containsKey((long) i)) ta = cnt[i] - map.get((long) i) + (2 * (n / 2 - cnt[i]));
        else ta = cnt[i] + (2 * (n / 2 - cnt[i]));
        ans = Math.min(ta, ans);
      }
      System.out.println(ans);
    }
  }

  static class FastReader {

    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;
    }
  }
}