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:
import copy
for i in range(int(input())):
    n=int(input())
    l=[int(j) for j in input().split()][:n]
    l1=list(set(list(range(1,2*n+1))).difference(set(l)))
    t=copy.deepcopy(l)
    l1.sort()
    m=-1
    for k in range(n):
        h=-1
        for j in range(n):
            if(l1[j]>t[k]):
                if l1[j] not in l:
                    a=l.index(t[k])
                    l.insert(a+1,l1[j])
                    h=1
                    break
        if(h==-1):
            print("-1")
            m=1
            break
    if(m==-1):
        for k in l:
            print(k,end=" ")
        print()