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:
for T in range(int(input())):

    n = int(input())
    x = list(map(int, input().split(" ")))
    b = [0]
    for i in x:
        b.append(i)

    vis = [False for cnt_used in range(2*n + 1)]
    a = [0 for cnt_a in range(2*n + 1)]

    set_elem_b = True
    for i in range(1, n+1):
        num = int(b[i])
        if not vis[num]:
            vis[num] = True
        else:
            set_elem_b = False
            break
    if not set_elem_b:
        print(-1)
        continue
    find = False
    for i in range(1, n+1):
        find = False
        for j in range(1, 2*n+1):
            if not vis[j] and j > b[i]:
                vis[j] = True
                a[i*2-1] = b[i]
                a[i*2] = j
                find = True
                break
        if not find:
            break
    if not find:
        print(-1)
        continue
    for i in range(1, 2*n+1):
        print(a[i], end = ' ')
    print()