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 
# -*- coding: utf-8 -*-
import sys
import math
import os
import itertools
import string
import heapq
import _collections
from collections import Counter
from collections import defaultdict
from functools import lru_cache
import bisect
import re
import queue
from decimal import *


class Scanner():
    @staticmethod
    def int():
        return int(sys.stdin.readline().rstrip())

    @staticmethod
    def string():
        return sys.stdin.readline().rstrip()

    @staticmethod
    def map_int():
        return [int(x) for x in Scanner.string().split()]

    @staticmethod
    def string_list(n):
        return [Scanner.string() for i in range(n)]

    @staticmethod
    def int_list_list(n):
        return [Scanner.map_int() for i in range(n)]

    @staticmethod
    def int_cols_list(n):
        return [Scanner.int() for i in range(n)]


class Math():
    @staticmethod
    def gcd(a, b):
        if b == 0:
            return a
        return Math.gcd(b, a % b)

    @staticmethod
    def lcm(a, b):
        return (a * b) // Math.gcd(a, b)

    @staticmethod
    def divisor(n):
        res = []
        i = 1
        for i in range(1, int(n ** 0.5) + 1):
            if n % i == 0:
                res.append(i)
                if i != n // i:
                    res.append(n // i)
        return res

    @staticmethod
    def round_up(a, b):
        return -(-a // b)

    @staticmethod
    def is_prime(n):
        if n < 2:
            return False
        if n == 2:
            return True
        if n % 2 == 0:
            return False
        d = int(n ** 0.5) + 1
        for i in range(3, d + 1, 2):
            if n % i == 0:
                return False
        return True


def pop_count(x):
    x = x - ((x >> 1) & 0x5555555555555555)
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f
    x = x + (x >> 8)
    x = x + (x >> 16)
    x = x + (x >> 32)
    return x & 0x0000007f


MOD = int(1e09) + 7
INF = int(1e15)


def solve():
    N = Scanner.int()
    if N == 2 or N == 3:
        print(-1)
        return
    if N == 1:
        print(1)
        return
    ans = [0 for _ in range(N)]
    i = N // 2 - 1
    ans[i - 1] = 3
    ans[i] = 1
    ans[i + 1] = 4
    ans[i + 2] = 2
    i += 3
    for k in range(4, N):
        ans[i] = k + 1
        if k % 2 == 0:
            i -= k + 1
        else:
            i += k + 1
    print(*ans, sep=' ')


def main():
    # sys.stdin = open("sample.txt")
    T = Scanner.int()
    for _ in range(T):
        solve()


if __name__ == "__main__":
    main()
