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:
def Input():
    tem = input().split()
    ans = []
    for it in tem:
        ans.append(int(it))
    return ans
from collections import Counter
T = Input()[0]

def solve(n, b):
    m = 2*n
    a = []
    for i in range(n):
        a.append([b[i],i])
    a.sort(reverse=True)
    vis=[0 for i in range(m+1)]
    ans=[0 for i in range(m)]
    for i in range(n):
        vis[a[i][0]]=1
    for i in range(n):
        flag = False
        big_a = None
        for j in range(m,a[i][0],-1):
            if vis[j]==0:
                flag = True
                big_a = j
                vis[j]=1
                break
        if flag:
            ans[2*a[i][1]]=a[i][0]
            ans[2*a[i][1]+1]=big_a
        else:
            return [-1]
    for i in range(1,m,2):
        for j in range(i+2,m,2):
            if ans[j]<ans[i] and ans[j]>ans[i-1] and ans[i]>ans[j-1]:
                ans[i],ans[j]=ans[j],ans[i]
                
    return ans

for tt in range(T):
    n = Input()[0]
    b = Input()
    ans=solve(n,b)
    if ans[0]==-1:
        print(-1)
    else:
        print(ans[0],end='')
        for i in range(1,2*n):
            print('',ans[i],end='')
        print()