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())
while(t):
    t=t-1
    n = int(input())
    b = [int(s) for s in input().split()]
    dic = [0]*((2*n)+1)
    for i in b:
        dic[i] = 1
    
    x = (2*n)+1
    a = []
    ans = 1
    # print(dic)
    for i in b:
        flag = 0
        # print(i)
        for j in range(i+1,x):
            if dic[j] == 0:
                # print("         {}".format(j))
                n = j
                dic[j] = 1
                flag = 1
                break
        # print(flag)
        # print(n)
        # print(dic)

        if flag == 0:
            ans = -1
            break
        else:
            a.append(i)
            a.append(n)
    
    if ans == 1:
        for i in a:
            print(i,end=" ")
        print()
    else:
        print(ans)