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())
import heapq
for _ in range(t):
    n = int(input())
    B = list(map(int, input().split()))
    if 1 not in set(B):
        print(-1)
        continue
    d = {}
    A = [0]*(2*n)
    for i in range(n):
        A[2*i] = B[i]
        d[B[i]] = 2*i+1
    #print(id)
    flag = True
    ids = []
    heapq.heapify(ids)
    for i in range(1, 2*n+1):
        if i in d:
            heapq.heappush(ids, d[i])
        else:
            if not ids:
                flag = False
                break
            id = heapq.heappop(ids)
            if A[id-1] > i:
                flag = False
                break
            else:
                A[id] = i
    if flag:
        print(*A)
    else:
        print(-1)