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 sys
import math

#to read string
get_string = lambda: sys.stdin.readline().strip()
#to read list of integers
get_list = lambda: list( map(int,sys.stdin.readline().strip().split()) )
#to read integers
get_int = lambda: int(sys.stdin.readline())
#to print fast
#pt = lambda x: sys.stdout.write(str(x)+'\n')

#--------------------------------WhiteHat010--------------------------------------#
for _ in range(get_int()):
    n = get_int()
    lst1 = get_list()
    lst2 = [i for i in range(1,2*n+1) if i not in lst1]
    res = [0]*(2*n)
    valid = True 
    for i in range(n):
        a = lst1[i]
        b = -1
        for j in range(n):
            if lst2[j] > a:
                b = lst2[j]
                lst2[j] = 0
                break
        if b == -1:
            valid = False
            break
        res[2*i],res[2*i+1] = a,b
    
    if valid: 
        print(*res)  
    else:
        print(-1)