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:
def solve():
    n = eval(input())
    b = input().split()
    vis = [0 for i in range(0, 420)]
    a = [0 for i in range(0, 400)]
    pos = 0
    flag = True
    for x in b:
        vis[int(x)] = 1
    for x in b:
        y = int(x)
        pos += 1
        a[2 * pos - 1] = y
        ok = False
        for j in range(y + 1, 2 * n + 1):
            if vis[j] == 0:
                vis[j] = 1
                a[pos * 2] = j
                ok = True
                break

        if ok == False:
            flag = False
            break
    if flag == False:
        print(-1)
    else:
        for i in range(1, 2 * n + 1):
            print(a[i], end=" ")
        print("")


t = eval(input())
while t:
    solve()
    t -= 1