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 n, k;
int a[200005];
int cnt[400005];
int cv[400005];
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    memset(cnt, 0, sizeof(cnt));
    memset(cv, 0, sizeof(cv));
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for (int i = 1; i * 2 <= n; i++) {
      cnt[a[i] + a[n - i + 1]]++;
      cv[min(a[i], a[n - i + 1]) + 1]++, cv[max(a[i], a[n - i + 1]) + k + 1]--;
    }
    for (int i = 3; i <= 2 * k; i++) cv[i] += cv[i - 1];
    int ans = 200005;
    for (int x = 2; x <= 2 * k; x++) {
      ans = min(ans, n - cnt[x] - cv[x]);
    }
    printf("%d\n", ans);
  }
  return 0;
}