An integer array `original` is transformed into a doubled array `changed` by appending twice the value of every element in `original`, and then randomly shuffling the resulting array.

Given an array `changed`, return `original` if `changed` is a doubled array. If `changed` is not a doubled array, return an empty array. The elements in `original` may be returned in any order.

Example 1:

    Input: changed = [1,3,4,2,6,8]
    Output: [1,3,4]
    Explanation: One possible original array could be [1,3,4]:
    - Twice the value of 1 is 1 * 2 = 2.
    - Twice the value of 3 is 3 * 2 = 6.
    - Twice the value of 4 is 4 * 2 = 8.
    Other original arrays could be [4,3,1] or [3,1,4].

Example 2:

    Input: changed = [6,3,0,1]
    Output: []
    Explanation: changed is not a doubled array.

Example 3:

    Input: changed = [1]
    Output: []
    Explanation: changed is not a doubled array.

Constraints:

- `1 <= changed.length <= 105`
- `0 <= changed[i] <= 105`