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
t, = map(int, input().split())
for _ in range(t):
    N = int(input())
    B = list(map(int, input().split()))
    vs = set(B)
    cc = 0
    for i in range(2*N, 0, -1):
#        print(i)
        if i in vs:
            cc -= 1
        else:
            cc += 1
        if cc < 0:
            print(-1)
            break
    else:
        rs = []
        for b in B:
            rs.append(b)
            for i in range(b+1, 2*N+1):
                if i not in vs:
                    rs.append(i)
                    vs.add(i)
                    break
        print(*rs)