<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:

        N = len(points)
        points.sort(key = lambda x : x[0])
        
        grad_ = {}
        di = {}

        max_ = 1

        for i in range(N-1):
            point1 = points[i]
            for j in range(i+1,N):
                
                point2 = points[j]
                if point2[0]-point1[0]==0:
                    grad = float(inf)
                    intercept = point1[0]
                else:
                    grad = (point2[1]-point1[1])/(point2[0]-point1[0])
                    intercept = round(point2[1] - grad*point2[0], 10)
                
                if tuple(point2+[grad,intercept]) not in di.keys():
                    if tuple([grad, intercept]) not in grad_.keys():
                        grad_[tuple([grad, intercept])] = 2
                    else:
                        grad_[tuple([grad, intercept])] += 1
                    if grad_[tuple([grad, intercept])]>max_:
                        max_ = grad_[tuple([grad, intercept])]

                if tuple(point2+[grad, intercept]) not in di.keys():
                    di[tuple(point2+[grad,intercept])] = None
        return(max_)


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