<p>You are given <code>n</code> <code>points</code> in the plane that are all <strong>distinct</strong>, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>. A <strong>boomerang</strong> is a tuple of points <code>(i, j, k)</code> such that the distance between <code>i</code> and <code>j</code> equals the distance between <code>i</code> and <code>k</code> <strong>(the order of the tuple matters)</strong>.</p>

<p>Return <em>the number of boomerangs</em>.</p>

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

<pre>
<strong>Input:</strong> points = [[0,0],[1,0],[2,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]].
</pre>

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

<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> points = [[1,1]]
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>n == points.length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>points[i].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>
	<li>All the points are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int numberOfBoomerangs(vector<vector<int>>& points) {

        if (points.size() < 3)
        {
            return 0;
        }

        // for each element, check all the other elements for the distances, and then count the number of elements with the same distances
        unordered_map<int, int> distMap; 
        int count = 0;
        for (int i = 0; i < points.size(); i++)
        {
            for (int j = 0; j < points.size(); j++)
            {
                if (i == j)
                {
                    continue;
                }
                int dist = computeDistBeforeSqrt(points[i], points[j]);
                // std::cout << "dist: " << i << " " << j << " " << dist << std::endl;
                distMap[dist]++;
                if (distMap[dist] == 2)
                {
                    count += 2;
                }
                if (distMap[dist] > 2)
                {
                    count += (distMap[dist] * (distMap[dist] - 1))  - ((distMap[dist] - 1) * (distMap[dist] - 2));
                }
            }
            // for (auto elem : distMap)
            // {
            //     // std::cout << elem.first << " " << elem.second << std::endl;
            //     if (elem.second >= 2)
            //     {
            //         // if we have 2 elements, we can make 2 ways i.e (i, j, k) or (i, k, j)
            //         // if we have have 3 elements, 3 items and 2 slots, 3 choose 2
            //         count += elem.second * (elem.second - 1);
            //     }
            // }
            distMap.clear();
        }
        return count;
    }

    int computeDistBeforeSqrt(vector<int> pointA, vector<int> pointB)
    {
        return pow(pointB[0] - pointA[0], 2) + pow(pointB[1] - pointA[1], 2);
    }
};
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