<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:

        if len(points) <= 1:
            return len(points)

        points = sorted(points)

        slopeIntercept = {}

        i = 0
        while i < len(points):
            j = i + 1
            while j < len(points):
                currSlope = float('inf')
                if (points[j][0] - points[i][0]) != 0:
                    currSlope = (points[j][1] - points[i][1]) / (points[j][0] - points[i][0])
                
                intercept = points[j][0]
                if currSlope != float('inf'):
                    intercept = points[j][1] - (currSlope * points[j][0])
                
                intercept = round(intercept, 2)
                
                

                if (currSlope, intercept) not in slopeIntercept:
                    slopeIntercept[(currSlope, intercept)] = [(points[i][0], points[i][1]), (points[j][0], points[j][1])]
                else:
                    slopeIntercept[(currSlope, intercept)].append((points[j][0], points[j][1]))
                j += 1
            i += 1
        
        currMax = 0
        for key in slopeIntercept:
            currSet = slopeIntercept[key]
            currSet = set(currSet)
            currMax = max(currMax, len(currSet))

        return currMax


        
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