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 bisect
t = int(input())
for i in range(t):
    n = int(input())
    l = list(map(int,input().split()))
    l1 = []
    l2 = []
    c = 0
    l3 = sorted(l)
    for i in range(min(l)+1,2*n+1):
        if i not in l:
            l1.append(i)
    if len(l1) == 0:
        print(-1)
    else:
        for i in l:
            if len(l1) == 0:
                c+=1
                break
            w = bisect.bisect_left(l1,i)
            if w == len(l1):
                c+=1
                break
            l2.append(i)
            l2.append(l1[w])
            del l1[w]
        if c == 0:
            print(*l2)
        else:
            print(-1)