<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:
        from collections import defaultdict
        dc=defaultdict(list)
        def getslope(p1,p2):
            x1,y1=p1
            x2,y2=p2
            try:
                m=(y2-y1)/(x2-x1)
                c=y1-m*x1
            except:
                m=float('inf')
                c=x1
            return (m,c)
        for i in range(len(points)):
            for j in range(i+1,len(points)):
                m,c=getslope(points[i], points[j])
                points[i], points[j]=tuple(points[i]), tuple(points[j])
                if points[i] not in dc[(m,c)]:
                    dc[(m,c)].append(points[i])    
                if points[j] not in dc[(m,c)]:
                    dc[(m,c)].append(points[j])
        if not dc:
            return 1
        else:
            return max([len(x) for x in dc.values()])


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