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:
import math
from collections import Counter
for _ in range(int(input())):
    n=int(input())
    l=list(map(int,input().split()))
    ll=[]
    s=list(range(1,n+1))
    for i in l:
        ll.append(i)
        if i+1 not in ll and i+1 not in l:
            ll.append(i+1)
        else:
            j=i+2
            while j in ll or j in l:
                j+=1
            ll.append(j)
    d=Counter(ll)
    c=0
    for i in d:
        if i>2*n or d[i]>1:
            c=1
            #print(i,d[i],n,d,ll)
            break
    if c==1:
        print(-1)
    else:
        print(*ll)