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 _ in range(N):
    n = int(input())
    b = list(map(int, input().split()))
    a = [-1] * 2*n

    pos = list(filter(lambda x: x not in b, range(1, 2*n + 1)))

    f = True

    for i, el in enumerate(b):
        a[2*i] = el

        st, end = 0, len(pos)
        new_idx = (st + end) // 2
        idx = None
        min_pos = 2*n + 1

        while new_idx != idx:
            idx = new_idx
            cur = pos[idx]
            if cur < el:
                st = idx
            else:
                min_pos = min(min_pos, cur)
                end = idx
            new_idx = (st + end) // 2

        try:
            pos.remove(min_pos)
            a[2*i + 1] = min_pos
        except Exception:
            f = False
            break

    if f:
        print(*a)
    else:
        print(-1)