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;
long long GCD(long long x, long long y) {
  if (y == 0) return x;
  return GCD(y, x % y);
}
long long LCM(long long x, long long y) { return (x * y) / (GCD(x, y)); }
long long LOGK(long long x, long long k) {
  if (x >= k) return 1 + LOGK(x / k, k);
  return 0;
}
long long MPOW(long long a, long long b, long long m) {
  if (b == 0) return 1;
  long long x = MPOW(a, b / 2, m);
  x = (x * x) % m;
  if (b % 2 == 1) x = (x * a) % m;
  return x;
}
long long MINV(long long a, long long m) { return MPOW(a, m - 2, m); }
class pnc {
  long long FACT_MAX, MODU;
  vector<long long> fact;

 public:
  pnc(long long n, long long m) {
    FACT_MAX = n;
    fact.resize(FACT_MAX);
    MODU = m;
    MFACT_INIT(MODU);
  }
  void MFACT_INIT(long long m) {
    fact[0] = 1;
    for (long long i = 1; i < FACT_MAX; ++i) fact[i] = (i * fact[i - 1]) % MODU;
  }
  long long MFACT(long long n) { return fact[n]; }
  long long PERM(long long n, long long r) {
    return (fact[n] * ::MINV(fact[n - r], MODU)) % MODU;
  }
  long long COMB(long long n, long long r) {
    return (PERM(n, r) * ::MINV(fact[r], MODU)) % MODU;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long test = 1;
  cin >> test;
  while (test--) {
    long long n;
    cin >> n;
    if ((n / 2) % 2 == 1) {
      cout << "NO"
           << "\n";
      continue;
    }
    cout << "YES"
         << "\n";
    long long total = 0;
    long long a = 2;
    for (long long i = 1; i <= n / 2; i++) {
      cout << a << ' ';
      total += a;
      a += 2;
    }
    long long total2 = 0;
    long long b = 1;
    for (long long i = 1; i < n / 2; i++) {
      cout << b << ' ';
      total2 += b;
      b += 2;
    }
    cout << total - total2 << "\n";
  }
}