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.io.*;
import java.util.*;
public class Main {
  public static void main(String[] args) throws IOException{
      BufferedReader b1 = new BufferedReader(new InputStreamReader(System.in));
      int t = Integer.parseInt(b1.readLine());
      while(t-->0) {
          int n = Integer.parseInt(b1.readLine());
          if(n < 4) {
              System.out.println("-1");
          }
          else {
              StringBuilder sb = new StringBuilder();
              int p = 2;
              for(int i = 0; i<n-(n%4); i++) {
                if(n % 4 == 2) {
                    if(i == (n-(n%4))-1) {
                        sb.append((n-1) + " ");
                    }
                }
                if(n % 4 == 3) {
                    if(i == (n-(n%4)) - 3) {
                        sb.append((n-1) + " ");
                    }
                    else if(i == (n-(n%4)) - 2) {
                        sb.append(n + " ");
                        sb.append((n-2) + " ");
                    }
                }
                if((i+1)%4 == 0) {
                    sb.append(p + " ");
                    p += 3;
                    continue;
                }
                if(p % 4 == 0) {
                    sb.append(p + " ");
                    p -= 3;
                }
                else {
                    sb.append(p + " ");
                    p += 2;
                }
              }   
              if(n % 4 == 1 || n % 4 == 2) {
                  sb.append(n);
                  System.out.println(sb);
              }
              else {
                  System.out.println(sb);
              }

          }    
      }
  }
}