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
def main():
	for t in range(int(input())):
	    n = int(input())
	    s = [i for i in range(1,2*n+1)]
	    l = [int(j) for j in input().split()]
	    for i in range(n):
	    	s.remove(l[i])
	    z = list(zip(l, [i for i in range(n)]))
	    # z.sort()
	    s.sort()
	    ans = [0]*(2*n)
	    # print(z, s)
	    for i in range(n):
	    	num = z[i][0]
	    	# print(s, ans)
	    	for j in s:
	    		if j>num:
	    			ans[2*z[i][1]]=num
	    			ans[2*z[i][1]+1]=j
	    			s.remove(j)
	    			break
	    	else:
	    		print(-1)
	    		break
	    else:
	    	print(" ".join(map(str, ans)))
	    		# ans.append((z[i][0], s[i], z[i]))
	    		# ans.append(s[i])

    
main()