A permutation of length n is an array p=[p_1,p_2,...,p_n], which contains every integer from 1 to n (inclusive) and, moreover, each number appears exactly once. For example, p=[3,1,4,2,5] is a permutation of length 5.

For a given number n (n ≥ 2), find a permutation p in which absolute difference (that is, the absolute value of difference) of any two neighboring (adjacent) elements is between 2 and 4, inclusive. Formally, find such permutation p that 2 ≤ |p_i - p_{i+1}| ≤ 4 for each i (1 ≤ i < n).

Print any such permutation for the given integer n or determine that it does not exist.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases in the input. Then t test cases follow.

Each test case is described by a single line containing an integer n (2 ≤ n ≤ 1000).

Output

Print t lines. Print a permutation that meets the given requirements. If there are several such permutations, then print any of them. If no such permutation exists, print -1.

Example

Input


6
10
2
4
6
7
13


Output


9 6 10 8 4 7 3 1 5 2 
-1
3 1 4 2 
5 3 6 2 4 1 
5 1 3 6 2 4 7 
13 9 7 11 8 4 1 3 5 2 6 10 12 
#include <bits/stdc++.h>
using namespace std;
long long int power(long long int x, unsigned long long int y) {
  long long int res = 1;
  while (y > 0) {
    if (y & 1) {
      res = res * x;
    }
    y = y >> 1;
    x = x * x;
  }
  return res;
}
long long int powermod(long long int x, unsigned long long int y,
                       long long int p) {
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) {
      res = (res * x) % p;
    }
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
int32_t main() {
  long long int T;
  cin >> T;
  vector<long long int> odd, even;
  while (T--) {
    long long int n;
    cin >> n;
    for (long long int i = (long long int)(1); i < (long long int)(n + 1);
         i++) {
      if (i % 2 == 0)
        even.push_back(i);
      else
        odd.push_back(i);
    }
    if (n <= 3) {
      cout << "-1\n";
      odd.clear();
      even.clear();
      continue;
    }
    sort((odd).begin(), (odd).end(), greater<long long int>());
    sort((even).begin(), (even).end());
    swap(even[0], even[1]);
    for (long long int i = (long long int)(0); i < (long long int)(odd.size());
         i++) {
      cout << odd[i] << " ";
    }
    for (long long int i = (long long int)(0); i < (long long int)(even.size());
         i++) {
      cout << even[i] << " ";
    }
    cout << "\n";
    odd.clear();
    even.clear();
  }
  return 0;
}
