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 printA(b,n):
    a = []
    if 1 not in b:
        print("-1")
        return
    i = 0
    while i != n:
        curr = b[i]
        if curr not in a:
            a.append(curr)
        nextE = curr+1
        condN = True
        while condN ==  True:
            if nextE in b or nextE in a:
                condN = True
            else:
                condN  = False
                break
            while nextE in b:
                nextE+=1
            while nextE in a:
                nextE+=1

        a.append(nextE)
        #print(curr, nextE)
        i+=1
    newa = sorted(a)
    #print(a)
    for i in range(1,(2*n)+1):
        if i != newa[i-1]:
            print("-1")
            return
    print(*a)

if __name__ == "__main__":
    t = int(input())
    for i in range(t):
        n = int(input())
        b = list(map(int, input().split()))
        printA(b,n)