<p>Given an array of <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents a point on the <strong>X-Y</strong> plane, return <em>the maximum number of points that lie on the same straight line</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane1.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane2.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= points.length &lt;= 300</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 <code>points</code> are <strong>unique</strong>.</li>
</ul>

from collections import defaultdict

class Solution:

    def is_same_line(self, point1, point2, point3):
        x1, y1 = tuple(point1)
        x2, y2 = tuple(point2)
        x3, y3 = tuple(point3)
        return (x3 - x1) * (y2 - y1) == (y3 - y1) * (x2 - x1)

    def maxPoints(self, points: List[List[int]]) -> int:
        if len(points) < 3:
            return len(points)
        collinears = defaultdict(list)
        pairs = [(i1, i2) for i1 in range(len(points)) for i2 in range(i1 + 1, len(points))]
        while pairs:
            i1, i2 = pairs.pop()
            for i3 in range(i2 + 1, len(points)):
                if self.is_same_line(points[i1], points[i2], points[i3]):
                    collinears[(i1, i2)].append(i3)
                    try:
                        pairs.remove((i1, i3))
                    except ValueError:
                        pass
                    try:
                        pairs.remove((i2, i3))
                    except ValueError:
                        pass
        if len(collinears) == 0:
            return 2
        return 2 + max(len(v) for v in collinears.values())

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