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 __ in range(int(input())):
	n = int(input())
	# a = [-1]*(n+1)
	b = [-1]*(2*n)
	a = [int(x) for x in input().split()]
	m1 = {}
	for i in range(n):
		m1[a[i]] = 1
		b[2*i] = a[i]
	for i in range(1,2*n,2):
		k = a[i//2]
		while k in m1:
			k += 1
		b[i] = k
		m1[k]=1
	#print(m1)
	f=0
	for x in b:
		if x > 2*n:
			f=1
			break
	if f == 1:
		print(-1)
	else:
		for x in b:
			print(x,end=' ')
		print()