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 1.0
import sys, re, math
from collections import deque, defaultdict, Counter, OrderedDict
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from heapq import heappush, heappop, heapify, nlargest, nsmallest
def STR(): return list(input())
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
def sortListWithIndex(listOfTuples, idx):   return (sorted(listOfTuples, key=lambda x: x[idx]))
def sortDictWithVal(passedDic):
    temp = sorted(passedDic.items(), key=lambda kv: (kv[1], kv[0]))
    toret = {}
    for tup in temp:
        toret[tup[0]] = tup[1]
    return toret
def sortDictWithKey(passedDic):
    return dict(OrderedDict(sorted(passedDic.items())))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

t = INT()

while(t!=0):
    n = INT()
    l = []
    if(n%2==0):
        for i in range(n-1, 0, -2):
            l.append(i)
        l.append(4)
        l.append(2)
        for i in range(6, n+1, 2):
            l.append(i)
    else:
        for i in range(n, 0, -2):
            l.append(i)
        l.append(4)
        l.append(2)
        for i in range(6, n+1, 2):
            l.append(i)
    if(n==1 or n==2 or n==3):
        print(-1)
    else:
        print(*l)
    t-=1