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:
def solve(m, b):
    d=dict()
    y=dict()
    for i in range(m):
        d[b[i]]=0
        
    for k in d.keys():
        x=k+1
        while x in d.keys() or x in y.keys():
            x+=1
        if (x>2*m):
            return -1
        d[k]=x
        y[x]=k
    
    for i in range(m):
        print(b[i], d[b[i]], end=" ")
    print()
        
    return 1

for _ in range(int(input())):
    m=int(input())
    b=list(map(int, input().split()))
    
    if (solve(m, b)==-1):
        print(-1)