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 Solution {

    private static final String NO = "NO";
    private static final String YES = "YES";
    public static BufferedWriter bw;
    public static FR sc;
    private static final int MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        sc = new FR();
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = 1;
        t = sc.i();
        while (t > 0) {
            t--;
            int n = sc.i();
            int ans = solve(n);
            bw.write("\n");
        }
        bw.close();

    }

    private static int solve(int n) throws IOException {
        int ans = 1;
        if (n < 4) {
            if (n > 1) {
                ans = -1;
            }
            bw.write(ans +" ");
            return ans;
        }
        for (int i = n; i > 0; i--) {
            if (i % 2 == 1) {
                bw.write(i + " ");
            }
        }
        bw.write(4 + " " + 2 + " ");
        for (int i = 6; i <= n; i += 2) {
            bw.write(i + " ");

        }
        return 0;
    }


}

class FR {
    BufferedReader br;
    StringTokenizer st;

    public FR() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String s() {
        if (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {

            }
        }
        return st.nextToken();
    }

    public int i() {
        return Integer.parseInt(s());
    }

    public Integer[] ia(int n) {
        Integer[] a = new Integer[n];
        for (int i = 0; i < n; i++) {
            a[i] = i();
        }
        return a;
    }

    public long[] la(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = l();
        }
        return a;
    }

    public String[] sa(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = s();
        }
        return a;
    }

    public long l() {
        return Long.parseLong(s());
    }
}
