<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:

        def countPoints(p1, p2):

            x1, y1 = p1
            x2, y2 = p2

            if x1 != x2:
                prek = y1 - y2 
                preb = x1 * y2 - x2 * y1
                prec = x1 - x2
                a = gcd(prek, preb, prec)
                k, b, c = prek // a, preb // a, prec // a
                if k < 0 or (k == 0 and b < 0):
                    k, b, c = -k, -b, -c
            else:
                k, b, c = float('inf'), x1, 0
            
            cache[(k, b, c)] = cache.get((k, b, c), 0) + 1
            return cache[(k, b, c)]

        l = len(points)

        if l == 1:
            return 1

        max_num = 0
        for i in range(l):
            cache = {}
            for j in range(i + 1, l):
                max_num = max(max_num, countPoints(points[i], points[j]) + 1)
        
        return max_num
                
16663