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())
    b = [int(x) for x in input().split()]
    d = sorted(b)
    c = []
    j = 0
    for i in range(1, 2 * n + 1):
        if j < len(d) and i == d[j]:
            j += 1
        else:
            c.append(i)

    j = 0
    out = []
    for val in b:
        out.append(val)
        while j < len(c):
            if c[j] > val:
                out.append(c[j])
                c[j] = -1
                j = 0
                break
            else:
                j += 1
        else:
            print(-1)
            break
    else:
        print(' '.join(map(str, out)))