<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) == 1:
            return 1
        d = {}
        for i in range(len(points)):
            l = points[i]
            for j in range(i+1, len(points)):
                r = points[j]
                slope = (r[1] - l[1]) / (r[0] - l[0]) if r[0] != l[0] else float('inf')
                bias = r[1] - slope * r[0] if slope != float('inf') else r[0]
                slope = round(slope, 5) if slope != float('inf') else slope
                bias = round(bias, 5)
                if (slope, bias) not in d:
                    d[(slope, bias)] = 0
                d[(slope, bias)] += 1
        ans = max(d.values()) # kC2 = k * (k-1) // 2
        return math.ceil(math.sqrt(ans * 2))
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