<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>

from collections import defaultdict
from math import sqrt
class Solution:
    def numberOfBoomerangs(self, points: List[List[int]]) -> int:
        nr_of_points = defaultdict(dict)

        for i in range(len(points)):
            for j in range(i + 1, len(points)):
                distance = sqrt(pow(points[i][0] - points[j][0], 2) + pow(points[i][1] - points[j][1], 2))
                nr_of_points[i][distance] = nr_of_points[i].get(distance, 0) + 1
                nr_of_points[j][distance] = nr_of_points[j].get(distance, 0) + 1
                
        boomerangs = 0
        for distance_mapping in nr_of_points.values():
            for value in distance_mapping.values():
                if value > 1:
                    boomerangs += value * (value - 1)
        return boomerangs 
29800