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:

def STR(): return list(input())
def INT(): return int(input())
def MAP(): return map(int, input().split())
def MAP2():return map(float,input().split())
def LIST(): return list(map(int, input().split()))
def STRING(): return input()
import string
import sys
from heapq import heappop , heappush
from bisect import *
from collections import deque , Counter , defaultdict
from math import *
from itertools import permutations , accumulate
dx = [-1 , 1 , 0 , 0  ]
dy = [0 , 0  , 1  , - 1]
#visited = [[False for i in range(m)] for j in range(n)]
#sys.stdin = open(r'input.txt' , 'r')
#sys.stdout = open(r'output.txt' , 'w')
#for tt in range(INT()):


#CODE




for tt in range(INT()):
    n = INT()
    arr = LIST()
    freq = [0] * (2*n+1)
    for i in arr:
        freq[i] = 1
    #print(freq)
    flag = True
    ans = []
    for i in range(n):
        for j in range(arr[i] , 2*n+1):
            if j > arr[i] and freq[j] == 0:
                ans.append(arr[i])
                ans.append(j)
                freq[j] = 1
                break

    #print(ans)
    k = list(ans)
    if len(ans) < 2 * n :
        print('-1')
    else:
        ans.sort()
        for i in range(1 , 2 * n + 1):
            if (i != ans[i - 1]):
                flag = False
                break
        if flag:
            print(*k)
        else:
            print(-1)