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 find(st, num):
    mn = -1
    for i in st:
        if mn == -1:
            if i > num:
                mn = i
        else:
            if num < i < mn:
                mn = i

    return mn

def main():
    n = int(input())
    st = set()
    for i in range(1, (n * 2) + 1):
        st.add(i)
    lst = list(map(int, input().split()))
    for i in lst:
        if not i in st:
            break
        st.remove(i)
    line = ""
    for i in lst:
        elem = find(st, i)
        if elem == -1:
            print(-1)
            return
        line += str(i) + " " + str(elem) + " "
        st.remove(elem)
    print(line)






if __name__ == "__main__":
    t = int(input())
    for i in range(t):
        main()