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 math
import atexit
import io
import sys
 
# input = sys.stdin.readline
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
 
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
 
def array_to_string(a):
    s = ""
    for i in a:
        s += str(i)
    return s
 
t = int(input())
while t>0:
    t = t-1
    n = int(input())
    b = list(map(int,input().split()))
    temp = [1 for i in range(4*n)]
    temp = [0] + temp
    a = [0 for i in range(2*n)]
    for i in range(n):
        temp[b[i]] = 0
        a[2*i] = b[i]
    # print("a",a)
    for i in range(n):
        num = b[i]
        for j in range(num+1,len(temp)):
            if temp[j] == 1:
                a[2*i+1] = j
                temp[j] = 0
                break
    if max(a)>2*n:
        print(-1)
        continue
    for i in a:
        print(i,end = " ")
    print()