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())
M=[]
    
def fonction(n,L):
    if max(L)>=2*n:
        return -1
    elif len(set(L))!=len(L):
           return -1
    else:
        res=list()
        D=list()
        for k in L:
            j=k
            ra=[D[i][1] for i in range(len(D))]
            while(( j in ra) or (j in L)) and (j<=2*n):
                j+=1
            D.append((k,j))
            res.append(k)
            res.append(j)
        if sorted(res)==[k for k in range(1,2*n+1)]:
            return res
        else:
            return -1
                
    

for i in range(t):
    n=int(input())
    L=[int(x) for x in input().split()]
    M.append(fonction(n,L))
for k in M:
    if type(k)==list:
        dh=" ".join([str(i) for i in k])
        for x in dh.split()[:-1]:
            print(int(x) , end =" ")
        print(int(dh.split()[-1]))
        
    else:
        print(k)