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:
t = int(input())
for _ in range(t):
    n = int(input())
    a = [int(x) for x in input().split()]
    b = [None]*(2*n)
    c = set(a)
    d = set(range(1, 2*n+1))
    for i in range(len(a)):
        x = a[i]+1
        while x in c:
            x += 1
        else:
            q = 2*i
            w = 2*i+1
            b[q] = a[i]
            b[w] = x
            c.add(x)
    count = 1
    if c != d:
        print('-1')
    else:
        if count == 1 or 1:
            for i in range(len(b)):
                print(b[i], end=' ')
            print()