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
# sys.stdin = open("test.txt", 'r')

for _ in range(int(input())):
    n = int(input())
    b = list(map(int, input().split()))
    p = list(range(1, 2*n+1))
    inb = set(b)
    a = {}
    for i, v in enumerate(b):
        if v == 2*n:
            print(-1)
            break
        c = [z for z in p[p.index(v)+1:] if z not in inb]
        if len(c) == 0:
            print(-1)
            break
        i += 1
        a[2 * i-1] = v
        a[2*i] = c[0]
        p.remove(v)
        p.remove(c[0])
    else:
        string = ''
        for i in range(1, 2*n+1):
            string += str(a[i]) + ' '
        print(string)