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:
for p in range(int(input())):
  n=int(input())
  a=list(map(int,input().split()))
  b=[0]*(2*n)
  for i in a:
    b[i-1]+=1
  m=0
  c=[]
  for i in range(n):
    j=a[i]
    while(j<(2*n)):
      if b[j]==0:
        b[j]+=1
        c.append(j+1)
        m+=1
        break
      else:
        j+=1
  if m!=n:
    print(-1)
  else:
    for i in range(n):
      print(a[i],c[i],end=" ")