<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:
        # compute slope for each 2 points, keep a [slope, groups]
        nums = len(points)
        if nums < 2:
            return nums
        m = {}
        for i in range(1, nums):
            for j in range(0, i):
                # print(i, j, points[i], points[j])
                if points[i][1] != points[j][1]:
                    slope = float((points[i][0] - points[j][0]) / (
                        points[i][1] - points[j][1])
                    )
                else:
                    slope = float("inf")
                if slope in m:
                    values = m[slope]
                    found = False
                    for value in values:
                        if points[j] in value and points[i] not in value:
                            value.append(points[i])
                            found = True
                            break
                    if not found:
                        values.append([points[i], points[j]])
                else:
                    m[slope] = [[points[j], points[i]]]
        # print(m)
        line = 0
        for v in m.values():
            for a in v:
                line = max(line, len(a))
        return line

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