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 sys

t=int(sys.stdin.readline())

for i in range(t):
	n=int(sys.stdin.readline())

	b=[int(j) for j in sys.stdin.readline().split()]

	arr=[]

	# perm=[]

	# for p in range(1,2*n+1):
	# 	perm.append(p+1)

	tot=2*n

	mark=[0]*tot

	for g in range(n):
		mark[b[g]-1]=1

	ans=True

	for h in range(n):
		done=0
		for k in range(2*n):
			if(mark[k]==0 and k+1>b[h]):
				mark[k]=1
				tmp=[b[h],k+1]
				tmp.sort()
				arr.append(tmp)
				done=1
				break
		
		if(done==0):
			ans=False
			break

	if(ans==True):
		for w in range(n):
			print(arr[w][0],end=" ")
			print(arr[w][1],end=" ")

		print()
	else:
		print(-1)