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())
for i in range(T):
    N=int(input())
    l=[0]*(N*2+1)
    f=0
    c=0
    b=[int(x) for x in input().split()]
    for j in range(0,len(b)):
        c=c+1
        l[c]=b[j]
        c=c+1
        if b.count(b[j]+1)==1 or l.count(b[j]+1)==1:
            m=b[j]+1
            while(True):
                m=m+1
                if b.count(m)==0 and l.count(m)==0:
                    break
                if m==(2*N):
                    f=1
                    break
            if f==1:
                break
            else:
                l[c]=m   
        else:
            l[c]=b[j]+1
    for j in range(1,2*N+1):
        if l.count(j)==0:
            f=1
            break
    if f==1:
        print(-1)
    else:
        l.pop(0)
        print(*l)