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 defaultdict

t = int(input())

for _ in range(t):
    n = int(input())
    b = list(map(int, input().split()))
    b = list(map(lambda x: x-1, b))
    flag = [False]*(2*n)
    
    for bi in b:
        flag[bi] = True
        
    pair = defaultdict(int)
    f = True
    
    for bi in b:
        for i in range(bi+1, 2*n):
            if not flag[i]:
                pair[bi] = i
                flag[i] = True
                break
        else:
            f = False
    
    if not f:
        print(-1)
        continue

    ans = []
    
    for bi in b:
        ans.append(min(bi, pair[bi]))
        ans.append(max(bi, pair[bi]))
    
    ans = list(map(lambda x: x+1, ans))
    
    print(*ans)