<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
import math
class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        n = len(points)
        
        if n <= 2:
            return n
        D = defaultdict(lambda: 0)
        max_points = 0
        for i in range(n):
            for j in range(i):
                xa, ya = points[i]
                xb, yb = points[j]
                if xb == xa:
                    slope = "fuck"
                    intercept = xb
                else:
                    slope = (yb - ya) / (xb - xa)
                    intercept = yb - slope * xb
                    slope = f"{slope:.8f}"
                    intercept = f"{intercept:.8f}"
                    # print(slope)

                key = (slope, intercept)
                D[key] += 1
                max_points = max(max_points, D[key])

        print(max_points)
        return int(math.sqrt(max_points * 2)) + 1

        
                
                
                
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