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 = lambda: sys.stdin.readline().rstrip()
from bisect import bisect_left as bl, bisect_right as br
for _ in range(int(input())):
    n=int(input())
    a=[int(i) for i in input().split()]
    b=[0]*(n*2)
    for i in range(0,2*n,2):
        b[i]=a[i//2]
    st=set([i for i in range(1,2*n+1)])
    for i in a:
        st.remove(i)
    st=list(st)
    st.sort()
    flag=1
    for i in range(1,2*n,2):
        z=br(st,b[i-1])
        if z==len(st):
            flag=0
            break
        b[i]=st.pop(z)
    if flag==0:
        print(-1)
        continue
    for i in range(0,(2*n)-1,2):
        if b[i]>b[i+1] : b[i],b[i+1]=b[i+1],b[i]
    print(*b)