<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>

import math
class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        
        def norm(loc):
            return (loc[0]**2+loc[1]**2)**0.5

        def get_angle(loc1,loc2):
            del_x = loc1[0] - loc2[0]
            del_y = loc1[1] - loc2[1]
            return math.atan2(del_x,del_y)

        cosine_map = {}
        for i in range(len(points)):
            for j in range(len(points)):
                if i != j:
                    angle = str(get_angle(points[i],points[j]))
                    key = tuple(points[i])
                    if key in cosine_map:
                        # print(key,points[j],angle,cosine_map[key].get(angle,[]))
                        cosine_map[key][angle] = cosine_map[key].get(angle,[]) + [points[j]]
                    else:
                        cosine_map[key] = {angle:[points[j]]}

        # print(cosine_map)
        max_length = 0
        for p1 in cosine_map:
            for p2 in cosine_map[p1]:
                max_length = max(max_length,len(cosine_map[p1][p2]))

        return max_length + 1
    
32409