<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:
        res = 0
        if len(points) <= 2:
            return len(points)
        xy = defaultdict(list)
        for i in range (len(points)):
            

            for j in range (i+1, len(points)):
            
                if (points[i][0] - points[j][0]) == 0:
                    k = '0.0'
                    b = points[i][0]
                else: 
                    k = (points[i][1] - points[j][1]) / (points[i][0] - points[j][0])
                    b = points[i][1] - k * points[i][0]

                key = str(k)+ str(b)
                if i not in xy[key]:
                    xy[key].append(i)
                if j not in xy[key]:
                    xy[key].append(j)
        
        for key, val in xy.items():
            res = max(len(val), res)
        

        return res

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