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:
from collections import defaultdict as dfd
for _ in range(int(input())):
    N = int(input())
    A = list(map(int,input().split()))
    C = dfd(int)
    for i in range(1,(2*N)+1):
        C[i] = 0
    for i in range(len(A)):
        C[A[i]] = 1
    B = []
    # print(C)
    for i in range(len(A)):
        B.append(A[i])
        z = 0
        temp = A[i]+1
        while(z!=1):
            if(C[temp]==0):
                C[temp]=1
                B.append(temp)
                z = 1
            else:
                temp+=1
            # print("Hello")
    res = 0
    for i in range(len(B)):
        if(B[i]>(2*N)):
            print(-1)
            res = 1
            break
    if(res==0):
        print(*B)