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 
import java.util.*;
import java.io.*;

public class Main {

  public static void main(String[] args) throws Exception {
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);

    int TT = Integer.parseInt(in.readLine());
    int currTT = 0;
    StringBuilder output = new StringBuilder();

    while (currTT++ < TT) {
      int n = Integer.parseInt(in.readLine());

      if (n < 4) {
        output.append("-1");
      } else {
        for (int i = (n % 2 == 0) ? n - 1 : n; i >= 1; i -= 2) {
          output.append(i + " ");
        }
        output.append("4 2 ");
        for (int i = 6; i <= n; i += 2) {
          output.append(i + " ");
        }
      }

      output.append("\n");
    }

    out.print(output);

    in.close();
    out.close();
  }

}