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 sys
input = sys.stdin.readline
for j in range(int(input())):
    n = int(input())
    b = list(map(int, input().split(" ")))
    save = b.copy()
    temp = set(b)
    c =[]
    for k in range(1, 2*n+1):
        if k not in temp:
            c.append(k)
    b.sort()
    c.sort()
    ansDict = {}
    ans = 0
    for lol in range(n):
        if(b[lol]>c[lol]):
            ans = -1
    for sad in range(n):
        mini = max(c)
        for f in c:
            if(f<mini and f>save[sad]):
                mini = f
        
        ansDict[save[sad]] = mini
        c.remove(mini)
    if(ans==-1):
        print(-1)
    else:
        ans = []
        for go in range(n):
            ans.append(str(save[go]))
            ans.append(str(ansDict[save[go]]))
        print(" ".join(ans))