A sequence of numbers is called an arithmetic progression if the difference between any two consecutive elements is the same.

Given an array of numbers `arr`, return `true` if the array can be rearranged to form an arithmetic progression. Otherwise, return `false`.

Example 1:

    Input: arr = [3,5,1]
    Output: true
    Explanation: We can reorder the elements as [1,3,5] or [5,3,1] with differences 2 and -2 respectively, between each consecutive elements.

Example 2:

    Input: arr = [1,2,4]
    Output: false
    Explanation: There is no way to reorder the elements to obtain an arithmetic progression.

Constraints:

- `2 <= arr.length <= 1000`
- `-106 <= arr[i] <= 106`