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() {
  long long int t, n, i, j, s, sum, x, s2;
  while (scanf("%lld", &t) == 1) {
    for (i = 1; i <= t; i++) {
      scanf("%lld", &n);
      x = n / 2;
      if (x % 2 == 0) {
        s = 0;
        sum = 1;
        s2 = 1;
        printf("YES\n");
        for (j = 1; j < n; j++) {
          if (j <= n / 2) {
            printf("%lld ", 2 * j);
            s = s + 2 * j;
          } else if (j == (n / 2 + 1))
            printf("1 ");
          else {
            printf("%lld ", sum + 2);
            sum += 2;
            s2 += sum;
          }
        }
        printf("%lld\n", s - s2);
      } else
        printf("NO\n");
    }
  }
  return 0;
}