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 bisect import bisect_right

t = int(input())
for _ in range(t):
    n = int(input())
    b = [ int(x) for x in input().split()]
    arr = [False]*(2*n+1)
    result = [0]*(n*2)
    for i, val in enumerate(b):
        result[i*2] = val
        arr[val] = True

    arr[0] = True
    arr = [ i for (i, v) in enumerate(arr) if v==False]
    arr = sorted(arr)

    err = False
    for i in range(n):
        j = bisect_right(arr, result[i*2])
        if j==len(arr):
            err = True
            break
        result[2*i+1] = arr[j]
        arr.pop(j)

    if err:
        print("-1")
    else:
        print(" ".join(map(str, result)))