<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>

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        slopes = []

        for i in range(len(points)):
            for j in range(i + 1, len(points)):
                (x1, y1) = points[i]
                (x2, y2) = points[j]

                # a x_1 + b y_1 + c = 0
                # a x_2 + b y_2 + c = 0
                # a (x_1 - x_2) + b (y_1 - y_2) = 0
                # b (y_1 - y_2) = a (x_2 - x_1)

                dy = y1 - y2 # a
                dx = x2 - x1 # b

                if dy < 0:
                    dy *= -1
                    dx *= -1

                c = 0 - dy * x1 - dx * y1

                slopes.append((dy, dx, c))

        best_count = 1

        for (a, b, c) in slopes:
            count = 0

            for (x, y) in points:
                if a * x + b * y + c == 0:
                    count += 1

            best_count = max(count, best_count)

        return best_count
21294