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.InputStream;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.*;

public class SpecialPerm {
  public static void main(String[] args) throws IOException {
    InputReader in = new InputReader(System.in);
    PrintWriter pw = new PrintWriter(System.out);
    int t, n, st;

    t = in.nextInt();
    while(t-- > 0) {
      n = in.nextInt();
      if (n <= 3) {
        pw.println("-1");
        continue;
      } else {
        if (n % 2 == 0) st = n - 1;
        else st = n;
        for (int i = st; i > 0; i-=2) pw.print(i + " ");
        pw.print("4 2 ");
        if (st == n-1) st = n;
        else st = n - 1;
        for (int i = 6; i <= st; i+=2) pw.print(i + " ");
        pw.println();
      }
    }
    pw.close();
  }

  static class InputReader {
    BufferedReader br;
    StringTokenizer st;
    public InputReader(InputStream inputStream) {
      br = new BufferedReader(new InputStreamReader(inputStream));
      st = null;
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }
}