<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>

import math
from fractions import Fraction
class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        num_pts= {}
        for n0 in range(len(points)):
            for n1 in range(n0+1, len(points)):
                if points[n1][0] == points[n0][0]:
                    m = float("inf")
                    b = points[n1][0]
                else:
                    m = Fraction(points[n1][1] - points[n0][1], points[n1][0] - points[n0][0])
                    b = points[n1][1] - m * points[n1][0]
                if (m,b) not in num_pts:
                    num_pts[(m,b)] = 1
                else:
                    num_pts[(m,b)] += 1
        print(num_pts)
        maxval = 0
        for k, v in num_pts.items():
            if v > maxval:
                maxval = v
        return int(math.floor(math.sqrt(maxval * 2))) + 1

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