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:
from math import *
from collections import *
t = int(input())
for y in range(t):
	n = int(input())
	a = list(map(int,input().split()))
	ch = [0 for i in range(2*n+1)]
	b = [-1 for i in range(2*n)]
	for i in range(n):
		ch[a[i]] = 1
		b[2*i] = a[i]
	flag = 0
	for i in range(0,2*n,2):
		m = -1
		for j in range(b[i],2*n+1):
			if(ch[j] == 0):
				ch[j] = 1
				m = j
				break
		if(m == -1):
			flag = -1
			break
		b[i+1] = m
		#print(ch)
	if(flag == -1):
		print(-1)
	else:
		for i in b:
			print(i,end = " ")
		print()