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 math import sqrt, factorial, ceil
from collections import Counter, defaultdict
from heapq import heapify, heapreplace, heappush, heappop
from bisect import bisect_left

t=int(stdin.readline())
while t:
    t-=1
    n=int(stdin.readline())
    b=list(map(int,stdin.readline().split()))
    a=[0]*(2*n)
    j=0
    r=[0]*(2*n+1)
    ans=1
    for i in range(0,2*n,2):
        a[i]=b[j]
        j+=1
        r[a[i]]=1
    for i in range(1,2*n,2):
        temp=a[i-1]+1
        while temp<=2*n:
            if r[temp]==0:
                a[i]=temp
                r[temp]=1
                break
            temp+=1
        if a[i]==0:
            ans=-1
            break
    if ans==1:
        print(*a)
    else:
        print(ans)