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 PYTHON):

Solution:
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7

def ni():
    return int(raw_input())


def li():
    return map(int,raw_input().split())


def pn(n):
    stdout.write(str(n)+'\n')


def pa(arr):
    pr(' '.join(map(str,arr))+'\n')

# fast read function for total integer input

def inp():
    # this function returns whole input of
    # space/line seperated integers 
    # Use Ctrl+D to flush stdin.
    return map(int,stdin.read().split())
    
range = xrange # not for python 3.0+


for t in range(ni()):
    n=ni()
    l=li()
    d=Counter(l)
    arr=[]
    for i in range(1,2*n+1):
        if not d[i]:
            arr.append(i)
    f=0
    ans=[]
    for i in range(n):
        f1=0
        for j in arr:
            if j>l[i]:
                f1=1
                break
        if not f1:
            f=1
            break
        ans.append(l[i])
        ans.append(j)
        arr.remove(j)
    if f:
        pn(-1)
    else:
        pa(ans)