<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:

        import math

        if len(points) < 2:
            return 1

        def slope(p1, p2):
            if (p2[0] - p1[0]) == 0:
                return "inf"
            return ((p2[1] - p1[1]) / (p2[0] - p1[0]))

        all = {}

        for curr in points:
            for comp in points:
                if comp == curr:
                    continue
                slp = slope(curr, comp)
                if slp == "inf":
                    eq = (curr[0], slope(curr, comp))
                else:
                    eq = (round(curr[1] - slope(curr, comp) * curr[0], 5), slope(curr, comp))
                if eq not in all:
                    all[eq] = [(curr, comp)]
                else:
                    all[eq].append((curr, comp))

        maxiVal = float("-inf")

        for key, val in all.items():
            if len(val) > maxiVal:
                maxiVal = len(val)
        return (int((1 + math.sqrt(1 + 4 * maxiVal)) / 2))


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