Problem: You are given a sequence b_1, b_2, …, b_n. Find the lexicographically minimal permutation a_1, a_2, …, a_{2n} such that b_i = min(a_{2i-1}, a_{2i}), or determine that it is impossible.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case consists of one integer n — the number of elements in the sequence b (1 ≤ n ≤ 100).

The second line of each test case consists of n different integers b_1, …, b_n — elements of the sequence b (1 ≤ b_i ≤ 2n).

It is guaranteed that the sum of n by all test cases doesn't exceed 100.

Output

For each test case, if there is no appropriate permutation, print one number -1.

Otherwise, print 2n integers a_1, …, a_{2n} — required lexicographically minimal permutation of numbers from 1 to 2n.

Example

Input


5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8


Output


1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

Solution (in PYTHON3):

Solution:
whatever=int(input())
for i in range (whatever) :
    k=int(input())
    bs=list(map(int,input().split()))
    a=[0]*2*k
    avail=[]
    for t in range (1,(2*k)+1) :
        if t not in bs :
            avail.append(t)
    avail=sorted(avail)
    for l in range (0,(2*k),2) :
        a[l]=bs[int(l/2)]
        flag=0   
        for hello in avail  :
            if hello>bs[int(l/2)] and flag==0 :
                a[l+1]=hello
                avail.remove(hello)
                flag=1
    if 0 in a :
        print (-1)
    else :
        print (*a)