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:
t = int(input())
res = []
for i in range (t) :
    n = input()
    n = int(n)
    b = input().split()
    a=[0]*(2*n)
    for j in range (n) :
        b[j] = int(b[j])
    for j in range (n) :
        a[2*j]=b[j]
    index=1
    fuck = True
    for j in range (1,2*n+1) :
        if not j in a :
            flag = True
            for k in range (n) :
                if a[2*k+1]==0 and a[2*k]<j :
                    a[2*k+1]=j
                    flag = False
                    break
            if flag :
                fuck = False
                break
    if fuck :
        res.append(a)
    else :
        res.append([-1])
for i in range (t) :
    for j in range (len(res[i])) :
        print(res[i][j],end=" ")
    print()