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;
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (T i : v) os << i << ' ';
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& v) {
  for (T i : v) os << i << ' ';
  return os;
}
template <class T, class S>
ostream& operator<<(ostream& os, const pair<T, S>& v) {
  os << v.first << ' ' << v.second;
  return os;
}
template <class T, class S>
ostream& operator<<(ostream& os, const unordered_map<T, S>& v) {
  for (auto i : v) os << '(' << i.first << "=>" << i.second << ')' << ' ';
  return os;
}
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target( \
    "avx2,sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
clock_t time_p = clock();
void starboy1299() {
  time_p = clock() - time_p;
  cerr << "Time Taken : " << (float)(time_p) / CLOCKS_PER_SEC << "\n";
}
void solve() {
  long long n;
  cin >> n;
  long long half = n / 2;
  if (half % 2) {
    cout << "NO" << '\n';
    return;
  }
  cout << "YES" << '\n';
  long long sum = 0;
  for (long long i = 0; i < half; i++) {
    cout << (i + 1) * 2 << " ";
    sum += (i + 1) * 2;
  }
  long long sum2 = 0;
  for (long long i = 0; i < half - 1; i++) {
    cout << (i + 1) * 2 - 1 << " ";
    sum2 += (i + 1) * 2 - 1;
  }
  cout << sum - sum2 << '\n';
}
int32_t main() {
  fast();
  long long t;
  cin >> t;
  for (long long i = 1; i <= t; i++) {
    solve();
  }
}