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 
# t = int(input())
# n, k = map(int, input().split())
# a = list(map(int, input().split()))
# from collections import deque

#import copy
#import collections
#import sys

t = int(input())
for T in range(t):
    n = int(input())
    if n==2 or n==3:
        print(-1)
        continue
    if n==4:
        print(3,1,4,2)
        continue
    # except 6,7,11
    # i can represent all number as 4x+5y
    if n==6:
        print("5 3 6 2 4 1")
        continue
    if n==7:
        print("5 1 3 6 2 4 7")
        continue
    if n==11:
        print("5 1 3 6 2 4 7 9 11 8 10")
        continue
    x = 0
    while (n-4*x) % 5 != 0:
        x+=1
    y = (n-4*x) // 5
    class ay:
        def __init__(self):
            self.n = 1
        def add4(self):
            n = self.n
            print(n+1, n+3, n, n+2, end=' ')
            self.n += 4
        def add5(self):
            n = self.n
            print(n, n+3, n+1, n+4, n+2, end=' ')
            self.n += 5
    ayc = ay()
    for i in range(x): ayc.add4()
    for i in range(y): ayc.add5()
    print()
