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 mi():return map(int,input().split())
def li():return list(mi())
def ii():return int(input())
def si():return input()
t=ii()
while(t):
    t-=1
    n=ii()
    a=li()
    b=a[:]
    b.sort()
    a1=[]
    l=0
    for i in range(1,2*n+1):
        if(l<len(b) and i==b[l]):
            l+=1
        else:
            a1.append(i)
    f=0
    m={}
    for i in range(n):
        if(b[i]>a1[i]):
            f=1
        m[b[i]]=a1[i]
    if(f):
        print('-1')
    else:
        for i in a:
            print(i,end=" ")
            for j in range(n):
                if(a1[j]>i):
                    print(a1[j],end=" ")
                    a1[j]=0
                    break
        print()