<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:
        graph = defaultdict(list)

        for i in range(len(points)-1) :
            for j in range(i+1, len(points)) :
                slope = 10 ** 9

                if (points[j][0] - points[i][0]) != 0 :
                    slope = (points[j][1] - points[i][1]) / (points[j][0] - points[i][0]) 

                graph[(points[i][0], points[i][1])].append((points[j][0], points[j][1],  slope ))
                
        # print(graph)
        def dfsUtil(p, q, dist) :
            # print(p, q, dist)
            max_len = 1
            neighbors = graph[(p, q)]
            # print(neighbors)

            for x, y, distance in neighbors :
                if dist == -sys.maxsize or dist == distance :
                    max_len = max(max_len, 1 + dfsUtil(x, y, distance))

            return max_len 

        
        max_points = 0
        for k in range(len(points)) :
            # print(points[k])
            max_points = max(max_points, dfsUtil(points[k][0], points[k][1], -sys.maxsize))
            # print(points[k], dfsUtil(points[k][0], points[k][1], -sys.maxsize))
        return max_points
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