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;
const long long int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, m;
    cin >> n;
    m = n / 2;
    if (m % 2 == 1) {
      cout << "NO\n";
      continue;
    }
    cout << "YES\n";
    vector<long long int> even(m), pref(m);
    for (long long int i = 0, num = 2; i < m; i++, num += 2) {
      even[i] = num;
      if (i % 2 == 1) pref[i] = even[i] + even[i - 1];
    }
    set<long long int> u;
    vector<long long int> odd(m);
    for (long long int i = 1; i < m; i += 2) {
      long long int temp = pref[i];
      temp /= 2;
      long long int a = temp - 2, b = temp + 2;
      while (u.count(a) || u.count(b)) {
        a -= 2;
        b += 2;
      }
      odd[i - 1] = a;
      odd[i] = b;
      u.insert(a);
      u.insert(b);
    }
    for (long long int i = 0; i < m; i++) cout << even[i] << " ";
    for (long long int i = 0; i < m; i++) cout << odd[i] << " ";
    cout << "\n";
  }
  return 0;
}