Problem: You are given an array a consisting of n integers (it is guaranteed that n is even, i.e. divisible by 2). All a_i does not exceed some integer k.

Your task is to replace the minimum number of elements (replacement is the following operation: choose some index i from 1 to n and replace a_i with some integer in range [1; k]) to satisfy the following conditions:

  * after all replacements, all a_i are positive integers not greater than k; 
  * for all i from 1 to n/2 the following equation is true: a_i + a_{n - i + 1} = x, where x should be the same for all n/2 pairs of elements. 



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 first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 2 ⋅ 10^5) — the length of a and the maximum possible value of some a_i correspondingly. It is guratanteed that n is even (i.e. divisible by 2). The second line of the test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the i-th element of a.

It is guaranteed that the sum of n (as well as the sum of k) over all test cases does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ k ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer — the minimum number of elements you have to replace in a to satisfy the conditions from the problem statement.

Example

Input


4
4 2
1 2 1 2
4 3
1 2 2 1
8 7
6 1 1 7 6 3 4 6
6 6
5 2 6 1 3 4


Output


0
1
4
2

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;
    }
  }
}