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:
import heapq

def solve(n,t):
    remainingCandidates = sorted(list(set([a for a in range(1,2*n + 1)]) - set(t) - set([x for x in range(1, sorted(t)[0], 1)])))

    if len(remainingCandidates) != n:
        return -1
    else:
        used = [False]*len(remainingCandidates)
        ans = []
        for i,x in enumerate(t):
            ans.append(x)
            for j,y in enumerate(remainingCandidates):
                if y > x and not used[j]:
                    ans.append(y)
                    used[j] = True
                    break
            if len(ans) % 2 != 0:
                return -1
        return " ".join(str(x) for x in ans)


for i in range(int(input())):
    n = int(input())
    t = list(map(int, input().split()))
    print(solve(n,t))