<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 collections
from typing import *
from fractions import Fraction
from pprint import pp

Point = Tuple #[int, int]
InfSlopeT = float
InfSlope = InfSlopeT(float('inf'))
Line = Tuple[Union[Fraction,InfSlopeT], Fraction] # (m, c) for a line y = mx + c

def line(a: Point, b: Point) -> Line:
    if b[0] == a[0]:
        return (InfSlope, Fraction(a[0]))

    m = Fraction(b[1] - a[1], b[0] - a[0])
    c = Fraction(a[1] * b[0] - a[0] * b[1], b[0] - a[0])
    return (m, c)


def find(points):
    l = len(points)
    groups = collections.defaultdict(set)
    for idx, a in enumerate(points):
        a = tuple(a)
        for offset in range(1, l - idx):
            b = tuple(points[idx + offset])
            lineab = line(a, b)
            groups[lineab].add(idx)
            groups[lineab].add(idx + offset)
    
    #pp(groups)
    if len(points) <= 1:
        return len(points)
    return len(max(groups.items(), key=lambda i: len(i[1]))[1])



class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        return find(points)
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