<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(object):
  Point = namedtuple("Point", "x y")

  def _distance(self, p1, p2):
    return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y)

  def numberOfBoomerangs( self, points: list):
    size = len(points)
    points = [Solution.Point(x, y) for x, y in points]
    p2dist = [defaultdict(list) for _ in range(size)]
    for p1, p2 in itertools.combinations(range(size), 2):
      d = self._distance(points[p1], points[p2])
      p2dist[p1][d].append(p2)
      p2dist[p2][d].append(p1)

    for dt in p2dist:
      for vs in dt.values():
        vs.sort()

    ans = 0
    for i in range(size):
      for j in range(size):
        if j == i:
          continue
        d = self._distance(points[i], points[j])
        positions = p2dist[i][d]
        j_pos = bisect.bisect_left(positions, j)
        ans += len(positions) - (j_pos + 1)

    return ans * 2

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