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:
from sys import stdin
import math
from bisect import bisect_right

def inp():
	return stdin.readline().strip()

def binSearch(a, d):
    res = bisect_right(a, d)
    if res >= len(a):
        return(-1)
    else:
        return(a[res])
t = int(inp())
for _ in range(t):
    n = int(inp())
    b = [int(x) for x in inp().split()]
    ar = [int(x+1) for x in range(2*n) if x+1 not in b]
    ans = []
    for i in b:
        c = binSearch(ar, i)
        if c == -1:
            print(-1)
            break
        else:
            ar.remove(c)
            ans.append(min(i, c))
            ans.append(max(i, c))
    else:
        print(*ans)