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 PYTHON):

Solution:
t=input()
from collections import Counter,defaultdict
for i in range(t):
    n=input()
    l=list(map(int,raw_input().split()))
    l1=[]
    c=Counter(l)
    d=defaultdict(int)
    ans=True
    for j in l:
        for k in range(j+1,201):
            if c[k]<>1 and d[k]<>1:
                l1.append(j)
                l1.append(k)
                d[j]=1
                d[k]=1
                break
    for j in range(1,max(l1)+1):
        if d[j]==0:
            ans=False
            break
    if ans==True:
        s=''
        for j in l1:
            s=s+str(j)+' '
        print s.rstrip(' ')
    else:
        print -1