<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:
    int calcDist(vector<int>& p1, vector<int>& p2){
        int x1 = p1[0];
        int x2 = p2[0];
        int y1 = p1[1];
        int y2 = p2[1];
        int distance = ((x2-x1)*(x2-x1)) + ((y2-y1)*(y2-y1));   // d^2 = x^2  +  y^2
        return distance;
    }

    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        unordered_set<int> distances;
        //Edge Distances
        distances.insert(calcDist(p1,p2));
        distances.insert(calcDist(p1,p3));
        distances.insert(calcDist(p1,p4));
        //Diagonal Diatances
        distances.insert(calcDist(p2,p3));
        distances.insert(calcDist(p2,p4));
        distances.insert(calcDist(p3,p4));

        //only 2 distances stored in the set, One for edges and One for diagonals
        if(distances.size()==2  && distances.count(0)==0)  
            return true;
        else
            return false;
    }
};
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