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:
t=int(input())
for ii in range(t):
    n=int(input())
    flag=True
    a=[int(i) for i in input().split()]
    t=n*2
    b=[0]*(t+1)
    c=[]
    for i in a:
        if i==t:
            flag=False
            break
        b[i]=1
    if flag==False:
        print(-1)
    else:
        for i in a:
            c.append(i)
            j=i+1 
            while b[j]==1:
                if j==t and b[j]==1:
                    flag=False
                    break
                j+=1
            if flag==False:
                print(-1)
                break
            c.append(j)
            b[j]=1
        for i in c:
            if flag==True : print(i,end=' ')
        if flag==True:print()