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())
elt=[]
for i in range(t):
    n=int(input())
    l=[]
    c=[]
    chaine=input()
    el=chaine.split(" ")
    for e in el:
        l.append(int(e))
        c.append(int(e))
    elt.append((n,c,l))
for n,c,l in elt:    
    for k in range(2*n):
        m=0
        if k+1 not in l:
            g=0
            for p in c:
               if k+1>p:
                   l.insert(l.index(p)+1,k+1)
                   c.remove(p)
                   g=1
                   break
                   
            if g==0:
                m=-1
                print(-1)
                break
    if m==0: 
        for g in l:
            print(g,end=' ')
        print('')