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;
int main(void) {
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (n < 4)
      cout << -1;
    else if (n == 4)
      cout << "3 1 4 2";
    else {
      if (n % 2 == 0) {
        int i;
        for (i = 1; i <= n / 2; i++) cout << 2 * i - 1 << " ";
        cout << 2 * (i - 1) - 4 << " ";
        int x = 2 * (i - 1) - 4;
        for (int i = n; i >= 1; i -= 2) {
          if (i != x) cout << i << " ";
        }
      } else {
        int j;
        for (j = 1; j <= (n / 2) + 1; j++) cout << 2 * j - 1 << " ";
        cout << 2 * (j - 1) - 4 << " ";
        int x = 2 * (j - 1) - 4;
        for (j = n - 1; j >= 1; j -= 2) {
          if (j != x) cout << j << " ";
        }
      }
    }
    cout << "\n";
  }
}
