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())
for x in range(t):
    n = int(input())
    arr = list(map(int, input().split()))
    count = 0
    a = 0
    out = []
    fail = False
    while(a < n):
        out.append(arr[a])
        count = out[-1]
        while(count < 2*n):
            count+=1
            if (not count in arr) and (not count in out):
                if count > arr[a]:
                    out.append(count)
                    count = 2*n + 10
        if(out[-1] == arr[a]):
            fail = True
            a = 2*n + 1
        a+=1
    if fail:
        print(int(-1))
    else:
        print(*out)