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:
# N, M, P = map(int, input().split())
# A = list(map(int, input().split()))
T = int(input())
for t in range(T):
	N = int(input())
	B = list(map(int, input().split()))
	S = set(B)
	out = []
	for n in range(2*N):
		if n%2 == 0:
			out.append(str(B[n//2]))
		else:
			curr = B[(n-1)//2]
			fl = 0
			for i in range(1, (N*2)+1):
				if i > curr and i not in S:
					out.append(str(i))
					S.add(i)
					fl = 1
					break
			if fl == 0:
				break
	if fl == 0:
		print(-1)
	else:
		print(" ".join(out))