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())
	arr = list(map(int,input().split()))
	s = set()
	for i in range(1,2*n +1):
		s.add(i)
	for i in arr:
		s.discard(i)
	a = []
	b = True
	for i in arr:
		if i+1>2*n:
			b = False
		else:
			if i+1 in s:
				a+=[i+1]
				s.discard(i+1)
			else:
				c = False
				for t in s:
					if t>i:
						a+=[t]
						s.discard(t)
						c = True
						break
				if not c:
					b = False
					break
	if not b:
		print(-1)
	else:
		for i in range(n):
			print(arr[i],a[i],end=" ")