<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:
        # all points in the group have same slope ratio with all others
        m = {}  # slope - [points_set1, points_set2]
        ret = 1
        # ratio_op = lambda x1,x2:(x1[0]-x2[0])/(x1[1]-x2[1])
        def ratio_op(x1,x2):
            if x1[1]==x2[1]:
                return 1<<32
            return (x1[0]-x2[0])/(x1[1]-x2[1])

        for i in range(len(points)-1):
            pt1 = points[i]
            for j in range(i+1,len(points)):
                pt2 = points[j]
                ratio = ratio_op(pt1,pt2)
                m[ratio] = m.get(ratio, [])
                new_set = True
                for set_s in m[ratio]:
                    if tuple(pt1) in set_s or tuple(pt2) in set_s or \
                        any([ratio_op(pt1,p) == ratio for p in set_s]):
                        # add to this set
                        set_s.add(tuple(pt1))
                        set_s.add(tuple(pt2))
                        new_set = False
                        ret = max(ret, len(set_s))
                        break
                if new_set:
                    m[ratio].append(set([tuple(pt1), tuple(pt2)]))
                    ret = max(ret, 2)
        return ret
                
                    
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