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:
import bisect
import collections

t = int(input())
for test in range(t):
    canDo = True
    n = int(input()) # elements in sequence
    b = []
    a = list(range(1,2*n+1))
    for i in input().split():
        b.append(int(i))
        a.remove(int(i))
    a.sort()
    c = []
    for i, elem in enumerate(b):
        placeholder = bisect.bisect_left(a, elem)
        if placeholder == len(a):
            canDo = False
            break
        else:
            c.append(str(b[i]))
            c.append(str(a[placeholder]))
            del a[placeholder]
    if not canDo:
        print(-1)
        continue
    print(' '.join(c))