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 sys
input = sys.stdin.readline
 
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

tests = inp()
testcount = 0
while testcount < tests:
    n = inp()
    b = inlt()
    if 1 not in b or 2*n in b:
        print(-1)
    else:
        arr = []
        for elem in b:
            i = 1
            while i < 4*n:
                if elem+i not in b and elem+i not in arr:
                    arr.append(elem+i)
                    i += 4*n
                else: i += 1
        string = ''
        i = 0
        while i < n:
            string += str(b[i]) + ' ' + str(arr[i]) + ' '
            i += 1
        if max(max(b),max(arr)) > 2*n:
            print(-1)
        else:
            print(string[:len(string)-1])
    testcount += 1