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
import bisect

def metod(x):
    if t[x] == "A":
        w = a
    else:
        w = b
    for i in range(x + 1, len(t)-1):
        if t[i] != t[i - 1]:
            if t[i] == "A":
                w+=a
            else:
                w+=b
    return w

 
def morzermorzer():
    n =  int(input())
    w = list(map(int, input().split()))
    isk = []
    for i in range(1, 2 * n + 1):
        if i not in w:
            isk.append(i)
    isk.sort()
    ans = [0 for i in range(2*n)]
    for i in range(n):
        ans[i * 2] = w[i]
    fl = 0
    for i in range(n - 1):
        ind = bisect.bisect(isk, w[i])
        if ind != n - i:
            r = isk[ind]
            del isk[ind]
            ans[i * 2 + 1] = r
        else:
            print(-1)
            return 0
    if isk[-1] < w[-1]:
        print(-1)
        return 0
    else:
        ans[-1] = isk[-1]
        print(*ans)
        
for morzer in range(int(input())): 
    morzermorzer()