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:
"""
from collections import Counter

t=int(input())
for i in range(t):
    n = int(input())
    nums = list(map(int, input().split()))
    c = Counter(nums)
    ans = 0
    for i,j in c.items():
        ans += j//i
        c[i] = j%i
    print(c)
    print(ans)"""


"""
from functools import lru_cache

@lru_cache(maxsize=None)
def findMinMax(s):
    if len(s)==1:
        return int(s[0])**2
    return int(s[0])*int(s[-1])



t = int(input())
for i in range(t):
    a,k = list(map(int, input().split()))
    for i in range(k-1):
        l = "".join(sorted(str(a)))
        if "0" in l:
            break
        else:
            a += findMinMax(l)
    print(a)"""

t = int(input())
for i in range(t):
    n = int(input())
    nums = list(map(int, input().split()))
    ans = [0]*(2*n)
    for i in range(0,n*2,2):
        ans[i] = nums[i//2]
    left = sorted(set(range(1,2*n+1))-set(nums))
    for j in range(1,n*2, 2):
        for k in left:
            if k > ans[j-1]:
                ans[j]=k
                left.remove(k)
                break
    if 0 in ans:
        print(-1)
    else:
        print(" ".join(list(map(str, ans))))