<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 maxPoints(self, points: List[List[int]]) -> int:
        if len(points) <= 1:
            return len(points)
            
        slope_counter = defaultdict(set)
        for i in range(len(points)):
            for j in range(i+1, len(points)):
                x1, y1 = points[i]
                x2, y2 = points[j]
                if x1 == x2:
                    key = f"x-{x1}"
                    slope_counter[key].add(y1)
                    slope_counter[key].add(y2)
                elif y1 == y2:
                    key = f"y-{y1}"
                    slope_counter[key].add(x1)
                    slope_counter[key].add(x2)
                else:
                    slope = (y2 - y1) / float(x2 - x1)
                    intercept = y1 - slope * x1
                    key = f"{slope:.8f}-{intercept:.8f}"
                    slope_counter[key].add((x1, y1))
                    slope_counter[key].add((x2, y2))
        
        max_points = 0
        for key, value in slope_counter.items():
            max_points = max(max_points, len(value))
        
        return max_points
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