<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 fractions import Fraction
from dataclasses import dataclass

@dataclass
class Line:
    origin: tuple[int, int]
    slope: Fraction | None
    l: int = 2
    
    def contains(self, point: tuple[int, int]) -> bool:
        x, y = point
        x1, y1 = self.origin
        dx = x - x1
        dy = y - y1

        if dx == 0:
            return self.slope is None
        else:
            if self.slope is None:
                return False
            fr = Fraction(dy, dx)
            return fr == self.slope

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        lines = []
        best = min(2, len(points))

        for i, (x, y) in enumerate(points):
            for l in lines:
                if l.contains((x, y)):
                    l.l += 1
                    best = max(best, l.l)
            for (x1, y1) in points[:i]:
                dy = y - y1
                dx = x - x1
                if dx == 0:
                    slope = None
                else:
                    slope = Fraction(dy, dx)
                lines.append(Line((x1, y1), slope))
        
        # if len(points) == 7:
        #     print(*lines, sep="\n")
            
        return best
        
27160