<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 aligned_2(self, x,y, q):
        if x == y :
            return True
        if (x[0]==y[0] ):
            if q == None:
                return True
            else:
                return False
        if (x[1]-y[1])/(x[0]-y[0]) == q:
            return True
        return False

    def maxPoints(self, points: List[List[int]]) -> int:
        if len(points) <= 2:
            return len(points)
        m = 0
        for i in range(1,len(points)):
            if (points[0][0] - points[i][0]) == 0:
                q = None
            else:
                q = (points[0][1] - points[i][1])/(points[0][0] - points[i][0])
            n =2
            for j in range(i+1,len(points)):
                if self.aligned_2(points[0], points[j], q):
                    n+=1
            m = max(m,n)
        return max(m, self.maxPoints(points[1:]))
        
        

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