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 sys
import copy
input=sys.stdin.buffer.readline

t=int(input())
while t:
	t-=1
	n=int(input())
	arr=list(map(int,input().split()))
	arr1=copy.deepcopy(arr)
	arr1.sort()
	if arr1[0]==1:
		if max(arr)+1<=2*n:
			ans=[]
			for i in range(n):
				ans.append(arr[i])
				for j in range(arr[i]+1,2*n+1):
					if j not in arr1:
						ans.append(j)
						arr1.append(j)
						break
			if len(set(ans))!=2*n:
				print("-1")
			else:
				for x in ans:
					print(x,end=' ')
				print()
		else:
			print("-1")
	else:
		print("-1")