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:
n = int(input())


for i in range(n):
    length = int(input())
    b = [int(i) for i in input().split()]
    c = list()
    final = list()
    pool = list()
    var = False
    for j in range(1, 2*length + 1):
        if j not in b:
            pool.append(j)

    for j in range(len(b)):
        var = False
        for k in range(len(pool)):
            if pool[k] > b[j]:
                var = pool[k]
                c.append(var)
                pool.remove(var)
                var = True
                break
        if not var:
            break

    if not var:
        print(-1)
        continue
    else:
        for j in range(len(b)):
            final.append(b[j])
            final.append(c[j])
        print(' '.join(map(str, final)))