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 PYTHON):

Solution:
from bisect import bisect
for _ in range(input()):
    n = input()
    a = map(int,raw_input().split())
    if 1 not in a or 2*n in a:
        print -1
        continue
    l = []
    for i in range(1,2*n+1):
        if i not in a:
            l.append(i)
    d = {}
    f = 0
    for i in range(n):
        p = bisect(l,a[i])
        if p==len(l):
            f = 1
            break
        d[a[i]] = l[p]
        l.remove(l[p])
    if f==1:
        print -1
        continue
    for i in range(n):
        print a[i],d[a[i]],
    print