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 stdin
from collections import deque
mod = 10**9 + 7
import sys
import random
# sys.setrecursionlimit(10**6)
from queue import PriorityQueue
# def rl():
#     return [int(w) for w in stdin.readline().split()]
from bisect import bisect_right
from bisect import bisect_left
from collections import defaultdict
from math import sqrt,factorial,gcd,log2,inf,ceil
# map(int,input().split())
# # l = list(map(int,input().split()))
# from itertools import permutations
import heapq
# input = lambda: sys.stdin.readline().rstrip()
input = lambda : sys.stdin.readline().rstrip()
from sys import stdin, stdout
from heapq import heapify, heappush, heappop
from itertools import permutations
from math import factorial as f

def ncr(x, y):
    return f(x) // (f(y) * f(x - y))

t = int(input())

for _ in range(t):

    n = int(input())
    l = list(map(int,input().split()))
    seti  = set(i for i in range(1,2*n+1))
    set1 = set(i for i in l)
    ans = []
    flag = 0
    ba = [i for i in range(1,2*n+1)]
    for i in range(n):

        z = l[i]
        if z not in seti:
            flag = 1
            break
        else:
            seti.remove(z)

            ans.append(z)
            ka = len(ans)
            for j in ba:
                if j>z and j in seti and j not in set1:
                    ans.append(j)
                    seti.remove(j)
                    break

            if len(ans) == ka:
                flag = 1
                break
    # print(ans)
    if flag == 1:
        print(-1)
    else:
        print(*ans)