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 main():
    for _ in range(int(input())):
        n = int(input()) 
        a = list(map(int,input().split()))
        
        t = 0
        ans = []
        used = [0] * (2 * n + 1)
        for i in range(n):
            used[a[i]] += 1
            if used[a[i]] == 2:
                t = 1
                ans = -1
                break
            
        if t:
            print(-1)
            continue
        
        var = []
        for i in range(1, 2 * n + 1):
            if not used[i]:
                var.append(i)
        
        ans = []
        used = [0] * (2 * n + 1)    
        for i in range(n):
            cur = a[i]
            add = -1
            for j in range(n):
                if var[j] > cur and not used[var[j]]:
                    add = var[j]
                    used[var[j]] = 1
                    break
            if add == -1:
                t = 1
                break
            ans.append(cur)
            ans.append(var[j])
            
        if t:
            print(-1)
            continue
        print(*ans)
                
                    
                    
                    
                
            


main()