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())
def closest_greater(num,a):
    for x in range(num,len(a)):
        if(a[x] == 1):
            a[x] = 0
            return x
    return -1

while(t>0):
    n = int(input())
    s = input()
    b = ['0']
    b= b+ s.split()
    a = [1]*(2*len(b) - 1)
    flag = 0
    ans = []
    for x in range(1,len(b)):
        a[int(b[x])]-=1
    for x in range(1,len(b)):
        current = int(b[x])
        ans.append(current)
        nex = closest_greater(current,a)
        if(nex == -1):
            flag = 1
            break
        else:
            a[nex] = 0
            ans.append(nex)
    if(flag == 1):
        print('-1')
    else:
        for x in ans:
            print(x,end=' ')
    t-=1