<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:
        cache = {}
        for index in range(len(points)):
            for pairindex in range(index+1,len(points)):
                x1,y1 = points[index]
                x2,y2 = points[pairindex]
                if x2 >x1:
                    grad = (y2-y1)/(x2-x1)
                    intercept = y2-grad*x2
                if x2 < x1:
                    grad = (y1-y2)/(x1-x2)
                    intercept = y2-grad*x2
                if x2 == x1:
                    grad = None
                    intercept = x2
                key = str(grad) + "," +str(intercept)
                if key not in cache:
                    cache[key] = [[x1,y1],[x2,y2]]
                else:
                    if [x1,y1] not in cache[key]:
                        cache[key].append([x1,y1])
                    if [x2,y2] not in cache[key]:
                        cache[key].append([x2,y2])

        max_val = 1
        for key in cache.keys():
            if len(cache[key]) > max_val:
                max_val = len(cache[key])
        return max_val
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