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

t = int(sys.stdin.readline())
for _ in range(t):
    n = int(sys.stdin.readline())

    sq = []
    bq = [int(b) for b in sys.stdin.readline().split()]
    aq = [True] * (2*n+1)
    for b in bq:
        aq[b] = False
    for b in bq:
        sq.append(b)
        j = b+1
        while j <= 2*n:
            if aq[j]:
                aq[j] = False
                sq.append(j)
                break
            j+=1
        else:
            print(-1)
            break
    else:
        sys.stdout.write(str(sq[0]))
        for s in sq[1:]:
            sys.stdout.write(" ")
            sys.stdout.write(str(s))
        sys.stdout.write("\n")