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 tra[100006], tra1[100006];
int main() {
  long long t;
  cin >> t;
  while (t--) {
    long long n, k;
    cin >> n;
    long long str[n + 4], s[n + 4];
    long long sum = 0, m, l, r, type, j = 0, rev = 0;
    long long num = n;
    num = num * 2;
    long long s1[n + 4];
    long long a = n / 2;
    long long b = n / 2;
    long long sum2 = 0, q = 0, w = 0;
    for (int i = 1; i < num / 2; i += 2) {
      sum += i;
      s[q++] = i;
      a--;
      if (a == 0) break;
      s[q++] = num - i;
      sum += (num - i);
      a--;
      if (a == 0) break;
    }
    for (int i = 2; i < num / 2; i += 2) {
      sum2 += i;
      s1[w++] = i;
      b--;
      if (b == 0) break;
      s1[w++] = num - i;
      sum2 += (num - i);
      b--;
      if (b == 0) break;
    }
    if (sum == sum2 && b == 0 && a == 0) {
      cout << "YES" << endl;
      for (int i = 0; i < w; i++) cout << s1[i] << " ";
      for (int i = 0; i < q; i++) cout << s[i] << " ";
      cout << endl;
    } else {
      cout << "NO" << endl;
    }
  }
}