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 sys import exit
from bisect import bisect

def iis(): return map(int, input().split())
def ii(): return int(input())
def liis():	return list(map(int, input().split()))

t = ii()
for _ in range(t):
	n = ii()
	b = liis()
	todos = []
	duplas = []
	for i in range(1, 2*n+1):
		if i not in b:
			todos.append(i)
	flag = False
	for i in b:
		a = bisect(todos, i)
		if a >= len(todos): 
			flag = True
			break
		duplas.append([i, todos[a]])
		todos[a] = -1
		todos = sorted(todos)
	if flag:
		print(-1)
	else:
		for dupla in duplas:
			print(" ".join(map(str, dupla)), end=" ")
		print()