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 solve(N, B):
    A = [0] * (2 * N)
    check = [False] * (2 * N)
    flag = True
    for i in range(N):
        A[i*2] = B[i]
        check[B[i]-1] = True
    for i in range(N):
        tmp = A[i*2]
        for j in range(tmp, 2*N):
            if not check[j]:
                A[i*2+1] = j+1
                check[j] = True
                break
    for i in range(N):
        if A[2*i] > A[2*i+1]:
            flag = False
    if flag:
        print(" ".join(map(str, A)))
    else:
        print(-1)

def main():
    T = int(input())
    for i in range(T):
        N = int(input())
        B = list(map(int, input().split()))
        solve(N, B)
if __name__ == "__main__":
    main()