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

Q = int(input())
Query = []
for _ in range(Q):
    N = int(input())
    A = list(map(int, input().split()))
    Query.append((N, A))

for N, A in Query:
    S = set(A)
    C = set()
    for n in range(1, 2*N+1):
        if not n in S:
            C.add(n)
    
    ans = []
    for a in A:
        to = -1
        for n in range(a+1, 2*N+1):
            if n in C:
                to = n
                break
        if to == -1:
            ans = []
            break
        ans.append(a)
        ans.append(to)
        C.remove(to)
    
    if not ans:
        print(-1)
    else:
        print(*ans)