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())
for hh in range(0,t):
    n=int(input())
    if n<4:
        print(-1)
    else:
        li=[]
        count4=n//4
        for i in range(0,count4):
            if i%2==0:
                li.append(4*i+3)
                li.append(4*i+1)
                li.append(4*i+4)
                li.append(4*i+2)
            else:
                li.append(4*i+2)
                li.append(4*i+4)
                li.append(4*i+1)
                li.append(4*i+3)
        tot=count4*4
        # if count4%2==1:
        #     # second
        #     arr=[]
        #     arr.append(tot+2)
        #     arr.append(tot+4)
        #     arr.append(tot+1)
        #     arr.append(tot+3)
        #     for i in range(0,n%4):
        #         li.append(arr[i])
        # else:
        #     # first
        #     arr=[]
        #     arr.append(tot+3)
        #     arr.append(tot+1)
        #     arr.append(tot+4)
        #     arr.append(tot+2)
        #     for i in range(0,n%4):
        #         li.append(arr[i])
        if(tot<n):
            tot+=1
            vall=tot
            for i in range(0,len(li)-1):
                if abs(li[i]-vall)>=2 and abs(li[i+1]-vall)>=2:
                    if abs(li[i]-vall)<=4 and abs(li[i+1]-vall)<=4:
                        li.insert(i+1,vall)
        if(tot<n):
            tot+=1
            vall=tot
            for i in range(0,len(li)-1):
                if abs(li[i]-vall)>=2 and abs(li[i+1]-vall)>=2:
                    if abs(li[i]-vall)<=4 and abs(li[i+1]-vall)<=4:
                        li.insert(i+1,vall)
        if(tot<n):
            tot+=1
            vall=tot
            for i in range(0,len(li)-1):
                if abs(li[i]-vall)>=2 and abs(li[i+1]-vall)>=2:
                    if abs(li[i]-vall)<=4 and abs(li[i+1]-vall)<=4:
                        li.insert(i+1,vall)
        
        print(*li)
        

# 3 1 4 2 6 8 5 7 11 9 12 10 14 16 13 15
# 3 1 4 2 7 6
# 5 6 7 8
# 7 5 8 6
# 9 10 11 12
# 13 14 15 16

# 2 4 1 3

# 1 4 2 6 3 5



        

        
