<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

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        lines = defaultdict(int)
        ans = 0

        for i in range(len(points)):
            curLines = set()
            for j in range(i):
                x1, y1 = points[i]
                x2, y2 = points[j]
                dx = x2 - x1
                dy = y2 - y1
                z = dx * y2 - dy * x2

                if (dx != 0):
                    angle = Fraction(dy, dx)
                    y0 = Fraction(z, dx)
                    curLines.add((angle.numerator, angle.denominator, y0.numerator, y0.denominator))
                else: 
                    curLines.add((x1, 0, 0, 0))
            
            for line in curLines:
                lines[line] += 1

        # for count in lines.values():
        for key in lines: 
            ans = max(ans, lines[key])

        return ans + 1



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