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 CPP):

Solution:
#include <bits/stdc++.h>
int main() {
  int t;
  std::cin >> t;
  for (int i = 0; i < t; i++) {
    int n, k;
    std::cin >> n >> k;
    int a[n];
    for (int j = 0; j < n; j++) {
      std::cin >> a[j];
    }
    int prefix[k * 2 + 2];
    int suffix[k * 2 + 2];
    for (int j = 0; j < k * 2 + 2; j++) {
      prefix[j] = 0;
      suffix[j] = 0;
    }
    for (int j = 0; j < n / 2; j++) {
      prefix[std::min(a[j], a[n - j - 1]) + 1] += 1;
      suffix[std::max(a[j], a[n - j - 1]) + k + 1] += 1;
      prefix[a[j] + a[n - j - 1]] += 1;
      suffix[a[j] + a[n - j - 1] + 1] += 1;
    }
    int counter = n;
    int minimum = INT_MAX;
    for (int j = 0; j < k * 2 + 2; j++) {
      counter -= prefix[j];
      counter += suffix[j];
      minimum = std::min(counter, minimum);
    }
    std::cout << minimum << std::endl;
  }
}