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;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
long long int gcd(long long int x, long long int y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
long long int lcm(long long int a, long long int b) {
  return (a * b) / gcd(a, b);
}
long long int logx(long long int base, long long int num) {
  int cnt = 0;
  while (num != 1) {
    num /= base;
    ++cnt;
  }
  return cnt;
}
vector<long long int> vin(long long int n) {
  vector<long long int> a(n);
  for (long long int i = 0; i < n; i++) cin >> a[i];
  return a;
}
void out(vector<long long int> a) {
  for (int i = 0; i < (long long int)a.size(); i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
void in(long long int *a, long long int n) {
  for (long long int i = 0; i < n; i++) cin >> a[i];
}
void out(long long int *a, long long int n) {
  for (long long int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << '\n';
}
void out1(vector<long long int> v) {
  for (long long int i = 0; i < (long long int)v.size(); i++) {
    cout << v[i] << " ";
  }
  cout << endl;
}
const long long int MAXN = (long long int)(1 * 1e6 + 5), level = 22;
void solve() {
  long long int n;
  cin >> n;
  if ((n / 2) % 2)
    cout << "NO\n";
  else {
    long long int x = 2;
    long long int y = 1;
    cout << "YES\n";
    for (long long int i = 0; i < n / 2; i++) {
      cout << x << " ";
      x += 2;
    }
    for (long long int i = 0; i < n / 2 - 1; i++) {
      cout << y << " ";
      y += 2;
    }
    n /= 2;
    cout << 2 * (n * (n + 1) / 2) - (n - 1) * (n - 1) << '\n';
  }
}
int main() {
  fast();
  long long int t = 1;
  cin >> t;
  for (long long int i = 0; i < t; i++) {
    solve();
  }
}