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.*;
import java.text.*;
import java.math.*;
import static java.lang.Integer.*;
import static java.lang.Double.*;
import java.lang.Math.*;

public class G {

	public static FastIO file = new FastIO();

	public static int ntc, ctc;
	public static final long MOD = 1000000007L; //998244353L;
	public static final int N = 200005, dx[] = { 0, 1, 0, -1 }, dy[] = { 1, 0, -1, 0 };

	public void run() throws Exception {
		ntc = nextInt();
		for (ctc = 1; ctc <= ntc; ++ctc)
			solve();
		file.out.flush();
		file.out.close();
	}

	public static void solve() {
		int n = nextInt();
		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
		for (int i = 0; i < n; i++) graph.add(new ArrayList<>());
		for (int i = 0; i < n; i++) {
			for (int j = i + 1; j < n; j++) {
				if (Math.abs(i - j) >= 2 && Math.abs(i - j) <= 4) {
					graph.get(i).add(j);
					graph.get(j).add(i);
				}
			}
		}
//		for (int i = 0; i < n; i++) {
//			println(i + " " + graph.get(i));
//		}
		boolean done = false;
		for (int start = 0; start < n; start++) {
			int[] order = new int[n];
			boolean[] vis = new boolean[n];
			int cur = start;
			vis[cur] = true;
			order[0] = start + 1;
			boolean works = true;
			for (int i = 1; i < n; i++) {
				boolean found = false;
				//if (cur < n / 2) {
					for (int j = graph.get(cur).size() - 1; j >= 0; j--) {
						if (!vis[graph.get(cur).get(j)]) {
							vis[graph.get(cur).get(j)] = true;
							found = true;
							cur = graph.get(cur).get(j);
							order[i] = cur + 1;
							break;
						}
					}
					if (!found) {
						for (int j = 0; j < graph.get(cur).size(); j++) {
							if (!vis[graph.get(cur).get(j)]) {
								vis[graph.get(cur).get(j)] = true;
								found = true;
								cur = graph.get(cur).get(j);
								order[i] = cur + 1;
								break;
							}
						}
					}
				//}
				//else {
//					for (int j = 0; j < graph.get(cur).size(); j++) {
//						if (!vis[graph.get(cur).get(j)]) {
//							vis[graph.get(cur).get(j)] = true;
//							found = true;
//							cur = graph.get(cur).get(j);
//							order[i] = cur + 1;
//							break;
//						}
//					}
//					if (!found) {
//						for (int j = graph.get(cur).size() - 1; j >= 0; j--) {
//							if (!vis[graph.get(cur).get(j)]) {
//								vis[graph.get(cur).get(j)] = true;
//								found = true;
//								cur = graph.get(cur).get(j);
//								order[i] = cur + 1;
//								break;
//							}
//						}
//					}
			//	}
			//	println(found + " " + cur);
				if (!found) {
					works = false;
					break;
				}
			}
			//println(Arrays.toString(order));
			if (works) {
				done = true;
				for (int i = 0; i < n; i++) {
					if (i > 0) print(" ");
					print(order[i]);
				}
				println("");
				break;
			}
		}
		if (!done) println("-1");
	}

	public static long mod(long n, long mod) {
		return (n % mod + mod) % mod;
	}

	public static long pow(long n, long p, long mod) {
		long ret = 1L;
		while (p > 0) {
			if (p % 2 != 0L)
				ret = mod(ret * n, mod);
			n = mod(n * n, mod);
			p >>= 1L;
		}
		return ret;
	}

	public static long pow(long n, long p) {
		long ret = 1L;
		while (p > 0) {
			if (p % 2 != 0L)
				ret *= n;
			n *= n;
			p >>= 1L;
		}
		return ret;
	}

	public static long gcd(long x, long y) {
		while (x != 0) {
			long tmp = x;
			x = y % x;
			y = tmp;
		}
		return y;
	}

	public static long lcm(long x, long y) {
		return x / gcd(x, y) * y;
	}

	public static boolean isPrime(int n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		return true;
	}

	public static class Pair<A, B> implements Comparable {
		public A fi;
		public B se;

		public Pair(A fi, B se) {
			this.fi = fi;
			this.se = se;
		}

		@Override
		public boolean equals(Object o) {
			if (this == o)
				return true;
			if (o == null || getClass() != o.getClass())
				return false;
			Pair<?, ?> p = (Pair<?, ?>) o;
			if (!fi.equals(p.fi))
				return false;
			return se.equals(p.se);
		}

		@Override
		public int hashCode() {
			return 31 * fi.hashCode() + se.hashCode();
		}

		@Override
		public String toString() {
			return fi.toString() + " " + se.toString();
		}

		public static <A, B> Pair<A, B> of(A a, B b) {
			return new Pair<A, B>(a, b);
		}

		public int compareTo(Object o) {
			Pair<?, ?> p = (Pair<?, ?>) o;
			if (fi.equals(p.fi))
				return ((Comparable) se).compareTo(p.se);
			return ((Comparable) fi).compareTo(p.fi);
		}
	}

	public static String next() {
		return file.next();
	}

	public static int nextInt() {
		return file.nextInt();
	}

	public static long nextLong() {
		return file.nextLong();
	}

	public static double nextDouble() {
		return file.nextDouble();
	}

	public static String nextLine() {
		return file.nextLine();
	}

	public static void print(Object o) {
		file.out.print(o);
	}

	public static void println(Object o) {
		file.out.println(o);
	}

	public static void printf(String s, Object... o) {
		file.out.printf(s, o);
	}

	public static class FastIO {
		BufferedReader br;
		StringTokenizer st;
		PrintWriter out;

		public FastIO() {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		}

		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;
		}

		void print(Object o) {
			out.print(o);
		}

		void println(Object o) {
			out.println(o);
		}

		void printf(String s, Object... o) {
			out.printf(s, o);
		}
	}

	public static void main(String[] args) throws Exception {
		new G().run();
	}
}
