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 j in range(t):
    n = int(input())
    
    values = [0]*(2*n+2)
    b = list(map(int, input().split()))
    
    a = [0]*(2*n+2)
    
    #print(a,b)
    
    for i in range(n):
        a[2*i] = b[i]
        values[b[i]] = 1
        

    for i in range(n):
        check = False
        
        if b[i] >= 2*n:
            break
        
        if values[b[i]+1] == 0:
            #print("Entered direct")
            values[b[i]+1] = 1
            a[2*i+1] = b[i]+1
            check = True
            
        else:
            for p in range(b[i]+1,2*n+1):
                if values[p]==0:
                    a[2*i+1] = p
                    values[p] = 1
                    check = True
                    break
                    
            if check == False:
                break
                
        if check == False:
            break
    
    #print(a)
    success = True
    for i in range(2*n):
        if a[i] > 2*n or a[i] == 0:
            success = False
            break
            
    if success == False:
        print(-1)
        
    else:
        for i in range(2*n):
            print(a[i],end = ' ')
            
        print()