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 _ in range(T):
    a=int(input())
    A=list(map(int,input().split()))
    DP=[0 for i in range((2*a)+1)]
    flag=0
    for i in A:
        if(i>(2*a)):
            flag=1
        else:
            DP[i]=1

    if(flag==1):
        print(-1)
        continue

    else:
        mv=a
        B=[]
        for i in range(a):
            flag=0
            b=A[i]
            B.append(b)
            for j in range(b,(2*a)+1):
                if(DP[j]==0):
                    flag=1
                    B.append(j)
                    DP[j]=1
                    break
            if(flag==0):
                B=[-1]
                break
            

        for i in B[:len(B)-1]:
            print(i,end=" ")

        print(B[len(B)-1])