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:

def get_rank(input):
  indices = list(range(len(input)))
  indices.sort(key=lambda x: input[x])
  output = [0] * len(indices)
  for i, x in enumerate(indices):
    output[x] = i
  return output

cases = int(raw_input().strip())
for case in range(cases):
  n = int(raw_input().strip())
  b = map(int, raw_input().strip().split(" "))
  a = [0 for i in xrange(2 * n)]
  for i in range(n):
    a[i * 2] = b[i]
  perm = sorted(list(set(xrange(1, 2 * n + 1)) - set(b)))
  rank = get_rank(b)
  for i in range(n):
    a[i * 2 + 1] = perm[rank[i]]
  possible = True
  for i in range(n):
    if b[i] != min(a[i * 2], a[i * 2 + 1]):
      possible = False
      break
  if not possible:
    print "-1"
  else:
    for i in range(n):
      min_possible = a[i * 2 + 1]
      min_j = i
      for j in range(i + 1, n):
        if a[j * 2 + 1] > a[i * 2] and min_possible > a[j * 2 + 1]:
          min_possible = a[j * 2 + 1]
          min_j = j
      if min_j != i:
        a[i * 2 + 1], a[min_j * 2 + 1] = a[min_j * 2 + 1], a[i * 2 + 1]
    print ' '.join(map(str, a))