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:
testCases = int(input())
for i1 in range(testCases):
    length = int(input())
    taken = [False]*length*2
    b = list(map(int, input().split()))
    a = [0]*2*length
    for i2 in range(length):
        taken[b[i2] - 1] = True
        a[i2*2] = b[i2]
    if taken.index(True) > 0:
        print(-1)
    else:
        for i2 in range(length):
            for i3 in range(b[i2] , 2*length, 1):
                if not taken[i3]:
                    taken[i3] = True
                    a[(i2*2) + 1] = (i3 + 1)
                    break
        if 0 in a:
            print(-1)
        else:
            for i2 in a:
                print(i2,end=' ')
            print("")