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 MAXN = 1e6 + 5;
long long n, m, t;
long long v[MAXN];
long long cha[MAXN];
int main() {
  cin >> t;
  while (t--) {
    cin >> n >> m;
    for (long long i = 1; i <= n; i++) scanf("%lld", &v[i]);
    for (long long i = 1; i <= 2 * m + 1; i++) cha[i] = 0;
    map<long long, long long> ma;
    for (long long i = 1; i <= n / 2; i++) {
      long long tmp = v[i] + v[n - i + 1], maxm = max(v[i], v[n - i + 1]),
                minm = min(v[i], v[n - i + 1]);
      cha[2] += 2, cha[minm + 1] -= 2;
      cha[maxm + m + 1] += 2, cha[2 * m + 1] -= 2;
      cha[minm + 1]++, cha[maxm + m + 1]--;
      cha[tmp]--, cha[tmp + 1]++;
    }
    long long tmp = 0;
    long long ans = 1e9;
    for (long long i = 2; i <= m * 2; i++) {
      tmp += cha[i];
      ans = min(tmp, ans);
    }
    cout << ans << endl;
  }
}