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 i in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    b = []
    d = 0
    for i in range(1, 2*n+1):
        if i not in a:
            b.append(i)
    b.sort()
    c = []
    i = 0
    j = 0
    while(len(b) > 0):
        if(b[-1] < a[i]):
            d = 1
            break
        else:
            if(b[j] > a[i]):
                c.append(a[i])
                c.append(b[j])
                a.remove(a[i])
                b.remove(b[j])
                j = 0
            else:
                j += 1
        if(j == len(b)):
            break
    if(d == 1):
        print(-1)
    else:
        print(*c)