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 heapq as hq

t = int(input())
for _ in range(t):
	n = int(input())
	b = list(map(int, input().split()))
	sb = sorted([(b[i]-1, i) for i in range(n)]) + [(2*n+1, -1)]
	a = [0]*(2*n)
	pos = []
	ind = 0
	for i in range(2*n):
		if i < sb[ind][0]:
			if len(pos) == 0:
				a = ["-1"]
				break
			p = hq.heappop(pos)
			a[p] = str(i+1)
		else:
			p = 2*sb[ind][1]
			a[p] = str(i+1)
			hq.heappush(pos, p+1)
			ind += 1
	print(" ".join(a))