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 feb20 {

//	            ***                          ++                      
//             +=-==+                      +++=-                     
//            +-:---==+                   *+=----=                   
//           +-:------==+               ++=------==                  
//           =-----------=++=========================                
//          +--:::::---:-----============-=======+++====             
//          +---:..:----::-===============-======+++++++++           
//          =---:...---:-===================---===++++++++++         
//          +----:...:-=======================--==+++++++++++        
//          +-:------====================++===---==++++===+++++      
//         +=-----======================+++++==---==+==-::=++**+     
//        +=-----================---=======++=========::.:-+*****    
//       +==::-====================--:  --:-====++=+===:..-=+*****   
//       +=---=====================-...  :=..:-=+++++++++===++*****  
//       +=---=====+=++++++++++++++++=-:::::-====+++++++++++++*****+ 
//      +=======++++++++++++=+++++++============++++++=======+****** 
//      +=====+++++++++++++++++++++++++==++++==++++++=:...  . .+**** 
//     ++====++++++++++++++++++++++++++++++++++++++++-.     ..-+**** 
//     +======++++++++++++++++++++++++++++++++===+====:.    ..:=++++ 
//     +===--=====+++++++++++++++++++++++++++=========-::....::-=++* 
//     ====--==========+++++++==+++===++++===========--:::....:=++*  
//     ====---===++++=====++++++==+++=======-::--===-:.  ....:-+++   
//     ==--=--====++++++++==+++++++++++======--::::...::::::-=+++    
//     ===----===++++++++++++++++++++============--=-==----==+++     
//     =--------====++++++++++++++++=====================+++++++     
//     =---------=======++++++++====+++=================++++++++     
//     -----------========+++++++++++++++=================+++++++    
//     =----------==========++++++++++=====================++++++++  
//     =====------==============+++++++===================+++==+++++ 
//     =======------==========================================++++++

	// created by : Nitesh Gupta

	public static void main(String[] args) throws Exception {
//		first();
//		sec();
//		third();
//		four();
		fif();
//			six();
	}

	private static void sec() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		StringBuilder sb = new StringBuilder();

		int n = Integer.parseInt(scn[0]);
		long s = Integer.parseInt(scn[1]);
		long val = s / n;
		long left = s - val * n;

		long[] arr = new long[n];
		long max = 1;
		long min = s;

		for (int i = 0; i < n; i++) {
			arr[i] = val;
			if (left-- > 0) {
				arr[i] += 1;
			}
			max = Math.max(max, arr[i]);
			min = Math.min(min, arr[i]);
		}
		long np = max - 2;
		if (np > 0) {

		} else {
			if (max == 2 && min == max) {
				np = 1;
			} else if (min == 1) {
				np = -1;
			} else {
				np = max + 1;
			}
		}
		if (np == -1) {
			sb.append("NO");
		} else {
			sb.append("YES\n");
			for (long ele : arr)
				sb.append(ele + " ");
			sb.append("\n");
			sb.append(np);
		}
		System.out.println(sb);
		return;
	}

	private static void third() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		int t = Integer.parseInt(scn[0]);
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			scn = (br.readLine()).trim().split(" ");
			int n0 = Integer.parseInt(scn[0]);
			int n1 = Integer.parseInt(scn[1]);
			int n2 = Integer.parseInt(scn[2]);
			StringBuilder ab = new StringBuilder();
			if (n0 != 0) {
				for (int i = 0; i < n0 + 1; i++) {
					ab.append("0");
				}
			}
			int len = ab.length();
			int i = 0;
			for (i = 0; i < n1; i++) {
				if (i % 2 == 0) {
					ab.append("1");

				} else {
					ab.append("0");
				}
			}
			if (len == 0 && n1 != 0) {
				if (i % 2 == 0) {
					ab.append("1");

				} else {
					ab.append("0");
				}
			}

			len = ab.length();
			if (n2 != 0) {

				if (len == 0) {
					for (i = 0; i < n2 + 1; i++) {
						ab.append("1");
					}
				} else if (ab.charAt(len - 1) == '0') {
					ab.setCharAt(len - 1, '1');
					for (i = 1; i < n2; i++) {
						ab.append("1");
					}
					ab.append('0');
				} else {
					for (i = 0; i < n2; i++) {
						ab.append("1");
					}
				}
			}
			sb.append(ab + "\n");
		}
		System.out.println(sb);
		return;
	}

	private static void four() throws Exception {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		int t = Integer.parseInt(scn[0]);
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			scn = (br.readLine()).trim().split(" ");
			int n = Integer.parseInt(scn[0]);
			int[] arr = new int[n + 1];
			PriorityQueue<pair> pq = new PriorityQueue<>((a, b) -> {
				if (a.size == b.size) {
					return a.l - b.l;
				}
				return -a.size + b.size;
			});

			pq.add(new pair(1, n));

			int num = 1;
			while (!pq.isEmpty()) {
				pair p = pq.poll();
				if (p.l > p.r)
					continue;

				int mid = 0;
				if ((p.r - p.l + 1) % 2 == 1) {
					mid = (p.l + p.r) / 2;

				} else {
					mid = (p.l + p.r - 1) / 2;
				}

				arr[mid] = num;
				num += 1;
				int right = mid - 1;
				int left = mid + 1;

				if (right >= p.l)
					pq.add(new pair(p.l, right));

				if (p.r >= left)
					pq.add(new pair(left, p.r));

			}
			for (int i = 1; i <= n; i++) {
				if (arr[i] == 0) {
					arr[i] = num;
					num += 1;
				}
				sb.append(arr[i] + " ");
			}

			sb.append("\n");
		}
		System.out.println(sb);
		return;
	}

	static class pair {
		int l, r, size;

		pair(int a, int b) {
			l = a;
			r = b;
			size = (r - l + 1);
		}

	}

	private static void fif() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		int t = Integer.parseInt(scn[0]);
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			scn = (br.readLine()).trim().split(" ");
			int n = Integer.parseInt(scn[0]);
			int[] arr = new int[n + 1];
			for (int i = 1; i <= n; i++)
				arr[i] = i;

			int[] ans = new int[n + 1];
			for (int i = 1; i <= n; i += 4) {
				int rem = n - i + 1;
				if (rem >= 8) {
					int idx = i;
					ans[idx++] = arr[i + 1];
					ans[idx++] = arr[i + 3];
					ans[idx++] = arr[i];
					ans[idx++] = arr[i + 2];
				} else if (rem >= 7) {

					int idx = i;
					ans[idx++] = arr[i + 1];
					ans[idx++] = arr[i + 3];
					ans[idx++] = arr[i];
					ans[idx++] = arr[i + 4];
					ans[idx++] = arr[i + 6];
					ans[idx++] = arr[i + 2];
					ans[idx++] = arr[i + 5];

				} else if (rem >= 6) {

					int idx = i;
					ans[idx++] = arr[i + 1];
					ans[idx++] = arr[i + 3];
					ans[idx++] = arr[i];
					ans[idx++] = arr[i + 4];
					ans[idx++] = arr[i + 2];
					ans[idx++] = arr[i + 5];

				} else if (rem >= 5) {

					int idx = i;
					ans[idx++] = arr[i + 1];
					ans[idx++] = arr[i + 3];
					ans[idx++] = arr[i];
					ans[idx++] = arr[i + 4];
					ans[idx++] = arr[i + 2];

				} else if (rem >= 4) {

					int idx = i;
					ans[idx++] = arr[i + 1];
					ans[idx++] = arr[i + 3];
					ans[idx++] = arr[i];
					ans[idx++] = arr[i + 2];

				}
			}
			boolean can = true;
			if(n<4){
				sb.append("-1");
			} else {
				for (int i = 1; i <= n; i++)
					sb.append(ans[i] + " ");
			}			sb.append("\n");
		}
		System.out.println(sb);
		return;
	}

	private static void six() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		int t = Integer.parseInt(scn[0]);
		StringBuilder sb = new StringBuilder();

		while (t-- > 0) {
			scn = (br.readLine()).trim().split(" ");
			int n = Integer.parseInt(scn[0]);
			long[] arr = new long[n];
			scn = (br.readLine()).trim().split(" ");
			for (int i = 0; i < n; i++) {
				arr[i] = Long.parseLong(scn[i]);
			}

			sb.append("\n");
		}
		System.out.println(sb);
		return;
	}

	public static void sort(long[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			long temp = arr[i];
			arr[i] = arr[idx];
			arr[idx] = temp;
		}
		Arrays.sort(arr);
	}

	public static void print(long[][] dp) {
		for (long[] a : dp) {
			for (long ele : a) {
				System.out.print(ele + " ");
			}
			System.out.println();
		}
	}

}
