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().strip())

debug = False

for t in range(T):
    N = int(input().strip())
    A = list(map(int, input().split()))
    
    totalSum = 2*N*(2*N+1)/2
    total=0
    d={}
    
    for a in A:
        d[a]=1
    B = []    
    for a in A: 
        B.append(a)
        total+=a
        x=a
        while True:
            x = x+1
            if x not in d:
                d[x]=1
                B.append(x)
                total+=x
                break
            
    if total==totalSum:
        print(*B)
    else:
        print(-1)