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 math
import heapq
import collections
fast_reader = sys.stdin.readline
fast_writer = sys.stdout.write
def input():
	return fast_reader().strip()
def print(*argv):
	fast_writer(' '.join((str(i)) for i in argv))
	fast_writer('\n')
def printspace(*argv):
	fast_writer(' '.join((str(i)) for i in argv))
	fast_writer(' ')
def inputnum():
    return(int(input()))
def inputnums():
    return(map(int,input().split()))
def inputlist():
    return(list(map(int,input().split())))
def inputstring():
    return([x for x in input()])
def inputstringnum():
    return([ord(x)-ord('a') for x in input()])
def inputmatrixchar(rows):
    arr2d = [[j for j in input().strip()] for i in range(rows)] 
    return arr2d
def inputmatrixint(rows):
    arr2d = []
    for _ in range(rows):
        arr2d.append([int(i) for i in input().split()])
    return arr2d
    
t = int(input())
for q in range(t):
    n = inputnum()
    b = inputlist()
    s = []
    ans = []
    for i in range(1, 2*n + 1):
        if i not in b:
            s.append(i)
    for i in range(n):
        ans.append(b[i])
        for j in range(n):
            if s[j] > b[i]:
                ans.append(s[j])
                s[j] = -1
                break
    s.sort()
    if s[n-1] != -1:
        print(-1)
    else:
        print(*ans)