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:
def res(n,l):
   l1=[]
   d={}
   for j in range(1,2*n+1):
      if j not in l:
         l1.append(j)
   for i in l:
      for j in l1:
         if j>i:
            d[i]=j
            l1.remove(j)
            break
   if len(l1)!=0:
      return False
   else:
      return d


t=int(input())
for i in range(t):
   n=int(input())
   l=[int(x) for x in input().split()]
   x=res(n,l)
   if x==False:
      print("-1")
   else:
      for k in l:
         print(k,x[k],end=" ")
      print("\n")