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 min_largest(arr, x):
    start = 0
    end = len(arr) - 1
    while start <= end:
        mid = start + (end - start) // 2
        if arr[mid] < x:
            start = mid + 1
        else:
            end = mid - 1
    result = start if start < len(arr) else -1
    return result


def permutation(arr, n):
    present = set(arr)
    missing = [i for i in range(1, 2*n+1) if i not in present]
    result = []
    for number in arr:
        result.append(number)
        temp = min_largest(missing, number)
        if temp == -1:
            return [-1]
        result.append(missing.pop(temp))
    return result


if __name__ == '__main__':
    T = int(input())
    for t in range(T):
        n = int(input())
        arr = list(map(int, input().split()))
        result = permutation(arr, n)
        for item in result:
            print(item, end=' ')
        print()
'''
5
1
1
2
4 1
3
4 1 3
4
2 3 4 5
5
1 5 7 2 8

1 2 
-1
4 5 1 2 3 6 
-1
1 3 5 6 7 9 2 4 8 10 

'''