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.lang.*;
import java.io.*;

public class Solution{
  public static void main(String[] args) throws IOException{
    StringBuilder print = new StringBuilder();
    BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(input.readLine());
    while(t-- > 0){
      int n = Integer.parseInt(input.readLine());
      if(n < 4){
        print.append("-1\n");
        continue;
      }
      if(n == 4){
        print.append(four(0) + "\n");
      }
      if(n == 5){
        print.append(five(0) + "\n");
      }
      if(n == 6){
        print.append(six(0) + "\n");
      }
      if(n == 7){
        print.append(seven(0) + "\n");
      }
      if(n == 8){
        print.append(seven(0) + "8\n");
      }
      if(n == 9){
        print.append(five(0) + four(5) + "\n");
      }
      if(n == 10){
        print.append(six(0) + four(6) + "\n");
      }
      if(n == 11){
        print.append(seven(0) + four(7) + "\n");
      }
      if(n == 12){
        print.append(seven(0) + five(7) + "\n");
      }
      if(n == 13){
        print.append(seven(0) + six(7) + "\n");
      }
      if(n > 13){
        int fours = (n - 5)/4 - 1;
        int current = 5;
        print.append(five(0));
        for(int i = 0; i < fours; i ++){
          print.append(four(current));
          current += 4;
        }
        if((n - current) == 4){
          print.append(four(current) + "\n");
        }
        if((n - current) == 5){
          print.append(five(current) + "\n");
        }
        if((n - current) == 6){
          print.append(six(current) + "\n");
        }
        if((n - current) == 7){
          print.append(seven(current) + "\n");
        }
      }
    }
    System.out.println(print.toString());
  }
  public static String four(int num){
    String num1 = String.valueOf(num + 2);
    String num2 = String.valueOf(num + 4);
    String num3 = String.valueOf(num + 1);
    String num4 = String.valueOf(num + 3);
    String returnString = num1 + " " + num2 + " " + num3 + " " + num4 + " ";
    return(returnString);
  }
  public static String five(int num){
    String num1 = String.valueOf(num + 1);
    String num2 = String.valueOf(num + 4);
    String num3 = String.valueOf(num + 2);
    String num4 = String.valueOf(num + 5);
    String num5 = String.valueOf(num + 3);
    String returnString = num1 + " " + num2 + " " + num3 + " " + num4 + " " + num5 + " ";
    return(returnString);
  }
  public static String six(int num){
    String num1 = String.valueOf(num + 1);
    String num2 = String.valueOf(num + 4);
    String num3 = String.valueOf(num + 2);
    String num4 = String.valueOf(num + 6);
    String num5 = String.valueOf(num + 3);
    String num6 = String.valueOf(num + 5);
    String returnString = num1 + " " + num2 + " " + num3 + " " + num4 + " " + num5 + " " + num6 + " ";
    return(returnString);
  }
  public static String seven(int num){
    String num1 = String.valueOf(num + 1);
    String num2 = String.valueOf(num + 3);
    String num3 = String.valueOf(num + 7);
    String num4 = String.valueOf(num + 5);
    String num5 = String.valueOf(num + 2);
    String num6 = String.valueOf(num + 4);
    String num7 = String.valueOf(num + 6);
    String returnString = num1 + " " + num2 + " " + num3 + " " + num4 + " " + num5 + " " + num6 + " " +  num7 + " ";
    return(returnString);
  }
}
