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 MOD = 1000000007;
const long long MAX = 2e4 + 7;
const long long dx[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const long long dy[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
float prob(long long w, long long h, long long l, long long u, long long r,
           long long d, long long i, long long j) {
  if (i == h && j == w)
    return (float)1;
  else if ((r == w && d == h) || (l == 1 && u == 1))
    return (float)0;
  else if (i >= u && i <= d && j >= l && j <= r)
    return (float)0;
  else if (i == h) {
    if (d == h && j < l)
      return (float)0;
    else
      return (float)1;
  } else if (j == w) {
    if (r == w && i < u)
      return (float)0;
    else
      return (float)1;
  } else if ((i > d && j > l) || (i > u && j > r))
    return (float)1;
  else if (i == u - 1 && j >= l && j <= r) {
    if (r == w)
      return (float)0;
    else
      return pow(0.5, r - j + 1);
  } else if (j == l - 1 && i >= u && i <= d) {
    if (d == h)
      return (float)0;
    else
      return pow(0.5, d - i + 1);
  } else
    return 0.5 * (prob(w, h, l, u, r, d, i + 1, j) +
                  prob(w, h, l, u, r, d, i, j + 1));
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  cin >> t;
  for (long long ii = 0; ii < t; ii++) {
    long long n;
    cin >> n;
    if (n % 4 != 0)
      cout << "NO"
           << "\n";
    else {
      cout << "YES"
           << "\n";
      for (long long i = 0; i < n / 2; i++) cout << 2 * (i + 1) << " ";
      for (long long i = 0; i < n / 2 - 1; i++) cout << 2 * (i + 1) - 1 << " ";
      cout << n + (n / 2) - 1 << "\n";
    }
  }
  return 0;
}