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:
t = int(input())
for _ in range(t):
  n = int(input())
  a = list(map(int,input().split()))
  b = sorted(a)
  used = [0 for i in range(2*n+1)]
  flg = 1
  for i in range(n):
    if b[i] > i*2+1:
      print(-1)
      flg = 0
      break
    used[b[i]] = 1
  if flg == 0:
    continue
  ans = []
  for i in range(n):
    ans.append(a[i])
    for j in range(a[i],2*n+1):
      if used[j] == 0:
        ans.append(j)
        used[j] = 1
        break
  print(*ans)