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 PYTHON):

Solution:
import math
import heapq
import sys
num = int(raw_input())
for i in range(num):
    n = int(raw_input())
    nums = [int(x) for x in raw_input().split(" ")]
    if 1 not in nums:
        print("-1")
        continue
    cur_set = set()
    for nn in nums:
        cur_set.add(nn)
    ans = []
    flag = 0
    for nn in nums:
        ans.append(str(nn))
        c = nn+1
        while c in cur_set and c<=2*n:
            c+=1
        if c>2*n:
            flag = 1
            break
        ans.append(str(c))
        cur_set.add(c)
    if flag == 1:
        print("-1")
        continue
    print(" ".join(ans))