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>
using namespace std;
int main() {
  int t;
  cin >> t;
  pair<bool, int> ans[t];
  for (int i = 0; i < t; i++) {
    int n;
    cin >> n;
    if (n % 4 == 0) {
      ans[i].first = 1;
      ans[i].second = n;
    } else {
      ans[i].first = 0;
    }
  }
  for (int i = 0; i < t; i++) {
    if (ans[i].first) {
      cout << "YES \n";
      for (int q = 2; q <= ans[i].second; q += 2) {
        cout << q << " ";
      }
      for (int q = 1; q <= ans[i].second - 2; q += 2) {
        cout << q << " ";
      }
      cout << ans[i].second + (ans[i].second / 2) - 1;
      cout << "\n";
    } else {
      cout << "NO \n";
    }
  }
  return 0;
}