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;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long t, a[200010], s[400020];
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    for (long long i = 0; i < 2 * k + 2; i++) s[i] = 0;
    for (long long i = 0; i < n; i++) cin >> a[i];
    for (long long i = 0; i < n / 2; i++) {
      if (a[i] > a[n - 1 - i]) swap(a[i], a[n - 1 - i]);
      s[0] += 2;
      s[a[i] + 1]--;
      s[a[i] + a[n - 1 - i]]--;
      s[a[i] + a[n - 1 - i] + 1]++;
      s[k + a[n - 1 - i] + 1]++;
    }
    long long out = 1e9, p = 0;
    for (long long i = 0; i < 2 * k + 1; i++) {
      p += s[i];
      if (i >= 2) out = min(out, p);
    }
    cout << out << '\n';
  }
  return 0;
}