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:
n=int(input())
for i in range(n):
    a_l=int(input())
    l=list(map(int,input().split()))
    
    temp=[0]*((max(l)*2)+1)
    dicti={}
    flag=False
    for j in range(a_l):
        if(l[j]>=a_l*2):
            flag=True
            break
    
    if((1 not in l) or flag==True):
        print(-1)

    else:
        for j in range(a_l):
            temp[l[j]]=1

        
        for j in range(a_l):
        
            for k in range(l[j]+1,len(temp)):
                if(temp[k]==0):
                    dicti[l[j]]=k
                    temp[k]=1
                    break

        
        
        sum=0
        for a in dicti:
            sum+=a+dicti[a]

        
        if(sum==(((a_l*2)*(a_l*2+1))/2)):
            for j in range(a_l):
                print(l[j],end=" ")
                print(dicti[l[j]],end=" ")
        else:
            print(-1)