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:
for _ in range(int(input())):

    n = int(input())
    arr = list(map(int,input().split()))

    tree = list(range(2*n+10))
    def find(st):
        if tree[st]!=st:
            tree[st] = find(tree[st])
        return tree[st]
    for c in arr:
        tree[find(c)] = find(c+1)

    ans = [0]*(2*n)
    for i in range(0,2*n,2):
        ans[i] = arr[i//2]
    f = True
    for i in range(1,2*n,2):
        d = ans[i-1]
        ans[i] = find(d)
        tree[ans[i]] = find(ans[i]+1)
        if ans[i]>2*n:
            f = False
            break
    if f:
        print(*ans)
    else:
        print(-1)