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;
  while (t--) {
    int n, k;
    cin >> n >> k;
    vector<int> v(n), one(2 * k + 1);
    unordered_map<int, int> zero;
    for (int i = 0; i < n; i++) cin >> v[i];
    for (int i = 0; i < n / 2; i++) {
      if (zero.find(v[i] + v[n - i - 1]) == zero.end())
        zero[v[i] + v[n - i - 1]] = 0;
      zero[v[i] + v[n - i - 1]]++;
      int l = min(v[i], v[n - i - 1]) + 1, r = max(v[i], v[n - i - 1]) + k;
      one[l] += 1;
      if (r + 1 <= 2 * k) one[r + 1] -= 1;
    }
    int ans = INT_MAX;
    for (int i = 1; i <= 2 * k; i++) one[i] += one[i - 1];
    for (int i = 2; i <= 2 * k; i++) {
      int z = 0, o = 0, t = 0;
      if (zero.find(i) != zero.end()) z = zero[i];
      o = one[i] - z;
      t = n / 2 - o - z;
      ans = min(ans, o + 2 * t);
    }
    cout << ans << "\n";
  }
  return 0;
}