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:

for i in range(int(input())):
	n = int(input())
	b_array = list(map(int, input().split()))
	a_array = sorted(list(set(list(map(int, range(1, 2*n+1)))) - set(b_array)))
	sorted_array = sorted(list(map(list, list(zip(b_array, list(map(int, range(n))))))))
	#print(sorted_array)
	final_array = [0]*(2*n)
	state = True
	for j in range(2*n):
		if j % 2 == 0:
			final_array[j] = b_array[int(j/2)]
		else:
			final_array[j] = 0
	#print(final_array)
	#print(a_array)
	#print(sorted_array)
	for j in range(n):
		if sorted_array[j][0] < a_array[j]:
			final_array[2*sorted_array[j][1]+1] = a_array[j]
		else:
			print(-1)
			state = False
			break
	if state == True:
		for j in range(n-1):
			
			while True:
				k = 2
				p = -1
				while ((j*2)+1+k < 2*n):
					if ((final_array[j*2] < final_array[(j*2)+1+k])  and  (final_array[(j*2)+k] < final_array[(j*2)+1]) and (final_array[(j*2)+1] > final_array[(j*2)+1+k])):
						p = (j*2)+1+k
					k+=2

				if p != -1:
					final_array[(j*2)+1], final_array[p] = final_array[p], final_array[(j*2)+1]
				else:
					break

		print(' '.join(list(map(str, final_array))))