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:
for i in range(int(input())):
    n=int(input())
    nums=[int(i) for i in input().split()]
    check=set(nums)
    s=max(nums)
    l=[int(i)+1 if int(i)+1 not in check else 0 for i in range(2*n)]
    l=sorted(list(set(l)))
    l.remove(0)
    o=""
    b=0
    for i in nums:
        s=0
        while s<len(l) and l[s]<i:
            s+=1
        if s==len(l):
            b=1
            break
        else:
            o+=str(i)+" "+str(l[s])+" "
            l.remove(l[s])
    if b:
        print(-1)
    else:
        print(o[:-1])