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
input = sys.stdin.readline
t = int(input())
import bisect
for _ in range(t):
  n = int(input())
  a = list(map(int,input().split()))
  b = [0 for _ in range(2*n)]
  for x in a:
    b[x-1] = 1
  c = []
  for i in range(2*n):
    if b[i] == 0:
      c.append(i+1)
  try:
    d = []
    for x in a:
      bi = bisect.bisect_left(c,x)
      tmp = c[bi]
      del c[bi]
      d.append(tmp)
    #print(a)
    #print(d)
    ans = ''
    for i in range(n):
      ans += str(a[i])
      ans += ' '
      ans += str(d[i])
      if i != n-1:
        ans += ' '
    print(ans)
  except:
    print(-1)