<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 1
        maxpts = 0
        slopes = [[0 for i in range(len(points))] for j in range(len(points))]
        i = 0
        while i + maxpts <= len(points):
            countSlopes = dict()
            for j in range(i+1, len(points)):
                if points[i][0] == points[j][0]:
                    slopes[i][j] = None
                else:
                    slopes[i][j] = (points[j][1] - points[i][1]) / (points[j][0] - points[i][0])

                if slopes[i][j] == None:
                    if 'UND' not in countSlopes.keys():
                        countSlopes['UND'] = 1
                    else:
                        countSlopes['UND'] += 1
                    if countSlopes['UND'] + 1 > maxpts: maxpts = countSlopes['UND'] + 1
                else:
                    if slopes[i][j] not in countSlopes.keys():
                        countSlopes[slopes[i][j]] = 1
                    else:
                        countSlopes[slopes[i][j]] += 1
                    if countSlopes[slopes[i][j]] + 1 > maxpts: maxpts = countSlopes[slopes[i][j]] + 1
            i += 1



        return maxpts
        
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