<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) == 0:
            return 0
        elif len(points) == 1:
            return 1

        n = len(points)
        lines = {}
        line_points = {}

        for i in range(0, n):
            for j in range(i+1, n):
                if points[j][0] != points[i][0]:
                    slope = (points[j][1] - points[i][1])/(points[j][0] - points[i][0])
                    intercept = points[j][1] - slope*points[j][0]
                else:
                    slope = "inf"
                    intercept = points[j][0]

                pair = (slope, intercept)

                if pair not in lines:
                    lines[pair] = 2
                    line_points[pair] = [points[j], points[i]]
                elif points[i] not in line_points[pair] or points[j] not in line_points[pair]:
                    lines[pair] += 1
                    if points[i] not in line_points[pair]:
                        line_points[pair].append(points[i])
                    else:
                        line_points[pair].append(points[j])

                #print(i, j, pair)
        #print(lines, line_points)   

        return max(lines.values())
32100