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 
"""Template for Python Competitive Programmers prepared by pa.n.ik, kabeer seth and Mayank Chaudhary """

# to use the print and division function of Python3
from __future__ import division, print_function

"""value of mod"""
MOD = 998244353
mod = 10**9 + 7

"""use resource"""
# import resource
# resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])

"""for factorial"""

def prepare_factorial():
    fact = [1]
    for i in range(1, 5005):
        fact.append((fact[-1] * i) % mod)
    ifact = [0] * 5005
    ifact[5004] = pow(fact[5004], mod - 2, mod)
    for i in range(5004, 0, -1):
        ifact[i - 1] = (i * ifact[i]) % mod

    return fact, ifact

"""uncomment next 4 lines while doing recursion based question"""
# import threading
# threading.stack_size(1<<27)
import sys
# sys.setrecursionlimit(10000)


"""uncomment modules according to your need"""
from bisect import bisect_left, bisect_right, insort
# from itertools import repeat
from math import floor, ceil, sqrt, degrees, atan, pi, log, sin, radians
from heapq import heappop, heapify, heappush
# from random import randint as rn
# from Queue import Queue as Q
from collections import Counter, defaultdict, deque
# from copy import deepcopy
# from decimal import *


def modinv(n, p):
    return pow(n, p - 2, p)

def ncr(n, r,  fact, ifact):    # for using this uncomment the lines calculating fact and ifact
    t = (fact[n] * (ifact[r]*ifact[n-r]) % mod)% mod
    return t


def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def input(): return sys.stdin.readline().strip()

"""*****************************************************************************************"""

def GCD(x, y):
    while (y):
        x, y = y, x % y
    return x

def lcm(x, y):
    return (x*y)//(GCD(x, y))

def get_xor(n):
    return [n,1,n+1,0][n%4]

def bin_pow(a, b):
    res = 1
    while b:
        if b&1:
            res = (res * a)
            b -= 1
        else:
            a = (a* a)
            b>>=1
    return res

""" ********************************************************************************************* """

def main():

    def solve(n):

        dq = deque()
        dq.append(3)
        dq.append(1)
        dq.append(4)
        dq.append(2)

        turn = 1
        for i in range(5, n+1):
            if turn&1:
                dq.append(i)
            else:
                dq.appendleft(i)
            turn ^= 1

        return list(dq)

    T = int(input())
    while T:
        n = int(input())
        if n<4:
            print(-1)
        else:
            ans = solve(n)
            print(*ans)
        T-=1

""" -------- Python 2 and 3 footer by Pajenegod and c1729 ---------"""

py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip
    range = xrange

import os, sys
from io import IOBase, BytesIO

BUFSIZE = 8192

class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0, 2), super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill(): pass
        return super(FastIO, self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill();
            self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.getvalue())
            self.truncate(0), self.seek(0)


class IOWrapper(IOBase):

    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            self.write = lambda s: self.buffer.write(s.encode('ascii'))
            self.read = lambda: self.buffer.read().decode('ascii')
            self.readline = lambda: self.buffer.readline().decode('ascii')


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

""" main function"""

if __name__ == '__main__':
    main()
    # threading.Thread(target=main).start()