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 atexit
import io
import sys
import math
from collections import defaultdict,Counter

# _INPUT_LINES = sys.stdin.read().splitlines()
# input = iter(_INPUT_LINES).__next__
# _OUTPUT_BUFFER = io.StringIO()
# sys.stdout = _OUTPUT_BUFFER

# @atexit.register
# def write():
#     sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())

# sys.stdout=open("CP2/output.txt",'w')
# sys.stdin=open("CP2/input.txt",'r')

# m=pow(10,9)+7
t=int(input())
for i in range(t):
    n=int(input())
    b=list(map(int,input().split()))
    visit=[0]*(2*n+1)
    for j in b:
        visit[j]=1
    l=[2]*n
    flag=0
    for j in range(n):
        if b[j]+1>2*n:
            flag=1
            break
        if visit[b[j]+1]==0:
            l[j]=b[j]+1
            visit[b[j]+1]=1
        else:
            p=b[j]+2
            while p<=2*n and visit[p]==1:
                p+=1
            if p>2*n:
                flag=1
                break
            l[j]=p
            visit[p]=1

    if visit.count(0)!=1 or flag==1:
        print(-1)
        continue
    for j in range(n):
        print(b[j],l[j],end=' ')
    print()