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:
# -*- coding: utf-8 -*-
"""
Created on Sat Feb 29 05:27:25 2020

@author: hp
"""

t = int(input())
for i in range(t):
    n = int(input())
    lst = [int(j) for j in input().split()]
    a=[0]*2*n
    y = True
    for j in range(n):
        a[2*j] = lst[j]
    for j in range(n):
        x = a[2*j] + 1
        z = True
        k=0
        while(z==True):
            if(x+k not in a):
                a[2*j+1]=x+k
                z =False
            k+=1
    for j in range(2*n):
        if(j+1 not in a):
            y = False
            break
    if(y==False):
        print(-1)
    else:
        for j in a:
            print(j,end=" ")