<p>A sequence of numbers is called an <strong>arithmetic progression</strong> if the difference between any two consecutive elements is the same.</p>

<p>Given an array of numbers <code>arr</code>, return <code>true</code> <em>if the array can be rearranged to form an <strong>arithmetic progression</strong>. Otherwise, return</em> <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= arr.length &lt;= 1000</code></li>
	<li><code>-10<sup>6</sup> &lt;= arr[i] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution {
 public:
  bool canMakeArithmeticProgression(vector<int>& arr) {
    const int n = arr.size();
    const int mx = ranges::max(arr);
    const int mn = ranges::min(arr);
    const int range = mx - mn;
    if (range % (n - 1) != 0)
      return false;
    const int diff = range / (n - 1);
    if (diff == 0)
      return true;

    unordered_set<int> seen;

    for (const int a : arr) {
      if ((a - mn) % diff != 0)
        return false;
      if (!seen.insert(a).second)
        return false;
    }

    return true;
  }
};
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