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:
a=int(input())
for i in range(a):
    n=int(input())
    z=list(map(int,input().split()))
    t=[0 for i in range(3*max(z))]
    ans=[]
    for i in range(len(z)):
        if(t[z[i]]==0):
            t[z[i]]=1
    for i in range(len(z)):
        ans.append(z[i])
        for j in range(z[i]+1,len(t)):
            if(t[j]==0):
                t[j]=1
                ans.append(j)
                break;
    
    t=sorted(ans)
    flag=0
    for i in range(len(t)):
        if(t[i]!=i+1):
            flag=1
            break;
    if(flag==1):
        print(-1)
    else:
        print(' '.join(map(str,ans)))