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:
for tc in range(int(input())):
    n = int(input())
    arr = []
    d = {}
    line = input().split()
    for i in range(1, (2*n)+1):
        d[i] = 1
    for i in range(n):
        arr.append(int(line[i]))
        d[arr[i]] = 0
    # print(d)
    b = []
    flag = 0
    for i in range(n):
        ele = arr[i]+1
        plus = 0
        while(ele <= (2*n)):
            plus += 1
            if d[ele] == 1:
                d[ele] = 0
                break
            ele += 1
        if ele > (2*n):
            flag = 1
            break
        b.append(arr[i]+plus)
    if flag == 1:
        print("-1")
        continue
    i = 0
    while(i < n):
        print(arr[i], end=" ")
        print(b[i], end=" ")
        i += 1
    print("")
    # print(arr, b)