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:
from collections import defaultdict
for  _ in range(int(input())):
        N = int(input())
        List = [int(x) for x in input().split()]
        Dict = defaultdict(int)
        for i in List:
                Dict[i] = 1
        Res = []
        flag = 0
        for i in range(N):
                Res.append(List[i])
                if(List[i] == 2*N):
                        flag = 1
                        print(-1)
                        break
                for j in range(List[i]+1,2*N+1):
                        if(Dict[j]==0):
                                Res.append(j)
                                Dict[j] = 1
                                break
                        elif(j==2*N and Dict[j] == 1):
                                flag = 1
                                print(-1)
                                break
                if(flag==1):
                        break
        if(flag == 0):
                print(*Res)