<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 get_slope(self, pt1: List[int], pt2: List[int]) -> float:
        x1, y1 = pt1
        x2, y2 = pt2
        if x1 == x2:
            return self.inf
        else:
            return float(y2-y1)/float(x2-x1)
    
    def maxPoints(self, points: List[List[int]]) -> int:
        self.inf = 10**10
        if len(points) == 1:
            return 1
        n = len(points)
        slopes = {}
        for i in range(n):
            for j in range(i+1, n):
                x1, y1 = points[i]
                x2, y2 = points[j]
                s = self.get_slope([x1,y1], [x2,y2])
                if (s,x1,y1) not in slopes:
                    slopes[s,x1,y1] = {(x1,y1), (x2,y2)}
                else:
                    slopes[s,x1,y1].add((x2,y2))
        
        for i in range(n):
            pt = points[i]
            for s,x1,y1 in slopes:
                cur_s = self.get_slope([x1,y1], pt)
                if abs(cur_s-s) <= 1e-25:
                    slopes[s,x1,y1].add((pt[0], pt[1]))
        
        ans = 0
        for val in slopes.values():
            ans = max(ans, len(val))
        
        return ans
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