human
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 
 ... Give me a Python code to 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?
assistant
#Here is Python code to 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.

#!/usr/bin/python3
import sys
 
readline = sys.stdin.readline
 
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))
 
# def solve():
#     n, x = nm()
#     d = nl()*2
#     f = [x*(x+1)//2 for x in d]
#     for i in range(2*n-1):
#         f[i+1] += f[i]
#     l = -1
#     s = sum(d[:n])
#     ans = 0
#     for r in range(n, 2*n):
#         s += d[r]
#         # print(s)
#         while s > x:
#             l += 1
#             s -= d[l]
#         # print(l, r, s, f[r] - f[l] + d[l]*(d[l]+1)//2 - (d[l]-x+s)*(d[l]-x+s+1)//2)
#         ans = max(ans, f[r] - f[l] + d[l]*(d[l]+1)//2 - (d[l]-x+s)*(d[l]-x+s+1)//2)
#     print(ans)
 
#     return
 
# solve()

"Codeforces Round #319 (Div. 2)"
"B. Modulo Sum"
# n,m=nm()
# a=nl()
# te=set()
# tt=[]
# f=1
# for i in a:
#     for j in te:
#         q=(j+i)%m
#         tt.append(q)
#     tt.append(i%m)
#     if 0 in tt:
#         f=0
#         break
#     while len(tt)>0:
#         q=tt.pop()
#         te.add(q)
# if f==0:
#     print("YES")
# else:
#     print("NO")
    
"Codeforces Round #638 (Div. 2)"
"D. Phoenix and Science"
# t=ni()
# for i in range(t):
#     n=ni()
#     q=1
#     z=[]
#     tq=1
#     while tq<n:
#         z.append(q)
#         # print(q,tq)
#         q=q*2
#         tq+=q
#     # print(z)
#     tq=tq-q
#     if n-tq!=0:
#         z.append(n-tq)
#     z.sort()
#     # print(z)
#     print(len(z)-1)
#     for j in range(1,len(z)):
#         print(z[j]-z[j-1],end=" ")
#     print()
"Educational Codeforces Round 72 (Rated for Div. 2)"
"B. Zmei Gorynich"
# from math import ceil
# t=ni()
# for i in range(t):
#     n,x=nm()
#     maxd=0
#     maxdh=-int(1e9)
#     for j in range(n):
#         di,hi=nm()
#         if maxd<di:
#             maxd=di
#         if maxdh<(di-hi):
#             maxdh=di-hi
#     ans=-1
#     if maxd<x and maxdh<1:
#         print(ans)
#     elif maxd>=x:
#         print(1)
#     elif maxd<x and maxdh>0:
#        ...