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 x1[200001], x2[200001], x3[200001];
int main() {
  int q;
  cin >> q;
  for (int qq = 0; qq < q; qq++) {
    long long n, k;
    cin >> n >> k;
    int arr[n];
    vector<int> x1(k * 2 + 2), x2(k * 2 + 2), x3(k * 2 + 2);
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
      if (i >= n / 2) {
        x1[arr[i] + arr[n - i - 1]]++;
        x2[min(arr[i], arr[n - i - 1]) + 1]++;
        x2[max(arr[i], arr[n - i - 1]) + k + 1]--;
      }
    }
    int res = 1e9;
    for (int i = 2; i <= k * 2; i++) {
      x2[i] += x2[i - 1];
      x3[i] = n / 2 - x2[i];
      res = min(res, x2[i] - x1[i] + (x3[i] * 2));
    }
    cout << res << endl;
  }
}