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:
import sys

from collections import Counter


def solve(N, B):
    counts = Counter(B)
    if any(v > 1 for v in counts.values()):
        return -1
    # Want smallest permutation that is element-wise greater than B
    C = []
    for x in range(1, 2 * N + 1):
        if x not in counts:
            C.append(x)
    # Sorted B and C must be pairable
    if any(b > c for b, c in zip(sorted(B), C)):
        return -1

    # Brute force with early exit to find min permutation
    # This passed but I am not sure if it's the intended solution?
    def gen(index=0):
        if index == N:
            yield C
            return
        for c, i in sorted(zip(C[index:N], range(index, N))):
            if B[index] < c:
                C[index], C[i] = C[i], C[index]
                yield from gen(index + 1)
                # Turns out this is never reached! The first permutation will always succeed
                assert False
                C[index], C[i] = C[i], C[index]

    for sol in gen():
        A = []
        for b, c in zip(B, C):
            A.append(str(b))
            A.append(str(c))
        return " ".join(A)
    return -1


if __name__ == "__main__":
    input = sys.stdin.readline
    T = int(input())
    for t in range(T):
        N, = map(int, input().split())
        B = [int(x) for x in input().split()]
        ans = solve(N, B)
        print(ans)