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:
te = int(input())
while te > 0:
    te -= 1
    n = int(input())
    B = list(map(int, input().split()))
    D = {}
    for i in B:
        D[i] = 1
    ans = []
    i = 0
    while i < n:
        ans.append(B[i])
        k = B[i]
        while k < 2*n:
            k += 1
            if D.get(k) is None:
                D[k] = 1
                ans.append(k)
                break
        i += 1    
    if len(ans) == 2*n:
        for i in ans:
            print(i, end=" ")  
    else:
        print(-1)             
    # print(D)