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:trueExplanation: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:falseExplanation:There is no way to reorder the elements to obtain an arithmetic progression.

**Constraints:**

`2 <= arr.length <= 1000`

`-10`

^{6}<= arr[i] <= 10^{6}

class Solution {
public boolean canMakeArithmeticProgression(int[] arr) {
}
}