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

queries = int(sys.stdin.readline())

for query in range(queries):
    length = int(sys.stdin.readline())
    arr = [int(x) for x in sys.stdin.readline().strip().split()]
    mx = arr[0]
    ans_arr = [0] * (length*2)
    arr_ins = [x for x in range(length*2,0,-1)]
    for el in arr:
        del arr_ins[arr_ins.index(el)]
    for pos in range(length):
        ans_arr[pos*2] = arr[pos]
        ins_pos = len(arr_ins)-1        
        while ins_pos >= 0 and arr_ins[ins_pos] < arr[pos]:
            ins_pos -= 1
        if ins_pos == -1:
            ans_arr = ['-1']
            break
        else:
            ans_arr[pos*2+1] = arr_ins[ins_pos]
            del arr_ins[ins_pos]
    #print(arr_ins)
    print(" ".join(map(str,ans_arr)))