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:
nn = int(input())
for tt in range(nn):
    total = []
    num = int(input())
    arr = []
    arr1 = str(input())
    arr1 = arr1.split()
    dicts = {}
    last = 2 * num
    for i in arr1:
        kt = int(i)
        arr.append( int(i) )
        dicts[kt] = 1 
    ans = []
    flag = 0 
    for i in arr:
        ans.append(i)
        while True:
            i += 1 
            if i > last:
                flag = 1 
                break
            if i not in dicts:
                dicts[i] = 1 
                ans.append(i)
                break
        if flag == 1:
            break
    if flag == 1:
        print(-1)
    else:
        strs = ""
        for i in ans:
            strs += str(i)
            strs += " "
        print(strs)