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:
testcases=int(input())
masterlist=[]
for i in range(testcases):
    input()
    tempseq=list(map(int,input().split(" ")))
    masterlist.append(tuple(tempseq))
def lexicographer(tup):
    buildlist=[]
    for i in range(len(tup)):
            val=tup[i]
            buildlist.append(val)
            run=True
            orig=val+1
            while run==True:
                if orig in buildlist or orig in tup:
                    orig+=1
                else:
                    buildlist.append(orig)
                    run=False
    maxim=max(buildlist)
    for i in range(1,maxim):
        if i not in buildlist:
            return [-1]
    return buildlist
for sequence in masterlist:
    ans=lexicographer(sequence)
    str=""
    for i in ans:
        str+="{} ".format(i)
    print(str)