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 sys import stdin,stderr
def rl():
    return [int(w) for w in stdin.readline().split()]

def solve(n, b):
    f = [True for i in range(2*n+1)]
    for x in b:
        if not f[x]:
            return [-1]
        f[x] = False
    a = []
    for x in b:
        a.append(x)
        for y in range(x+1, 2*n+1):
            if f[y]:
                a.append(y)
                f[y] = False
                break
        else:
            return [-1]
    return a

t, = rl()
for _ in range(t):
    print(*solve(rl()[0], rl()))