<p>Given the coordinates of four points in 2D space <code>p1</code>, <code>p2</code>, <code>p3</code> and <code>p4</code>, return <code>true</code> <em>if the four points construct a square</em>.</p>

<p>The coordinate of a point <code>p<sub>i</sub></code> is represented as <code>[x<sub>i</sub>, y<sub>i</sub>]</code>. The input is <strong>not</strong> given in any order.</p>

<p>A <strong>valid square</strong> has four equal sides with positive length and four equal angles (90-degree angles).</p>

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

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
<strong>Output:</strong> true
</pre>

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

<pre>
<strong>Input:</strong> p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
<strong>Output:</strong> false
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
<strong>Output:</strong> true
</pre>

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

<ul>
	<li><code>p1.length == p2.length == p3.length == p4.length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
 public:
  bool validSquare(vector<int>& p1, vector<int>& p2,  //
                   vector<int>& p3, vector<int>& p4) {
    unordered_set<int> distSet;
    vector<vector<int>> points{p1, p2, p3, p4};

    for (int i = 0; i < 4; ++i)
      for (int j = i + 1; j < 4; ++j)
        distSet.insert(dist(points[i], points[j]));

    return !distSet.contains(0) && distSet.size() == 2;
  }

 private:
  int dist(vector<int>& p1, vector<int>& p2) {
    return (p1[0] - p2[0]) * (p1[0] - p2[0]) +
           (p1[1] - p2[1]) * (p1[1] - p2[1]);
  }
};
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