<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:
        combs = list(itertools.combinations(points, 2))
        
        n = 0
        a = 0
        if len(points)==1:
            return 1
        for comb in combs:
            
            if comb[1][0] - comb[0][0] == 0: #vert line
                a =0
                for p in points:
                    if p[0] == comb[0][0]:
                        a+=1
                n = max(n, a)
            else:

                m = (comb[1][1] - comb[0][1]) / (comb[1][0] - comb[0][0])
                b = comb[0][1] - (m * comb[0][0])
                a = 0
                for p in points:
                    # print((m * p[0] + b)-p[1])
                    
                    if abs((m * p[0] + b) - p[1]) < 1e-9:
                        
                        a += 1 
                    
                n = max(n, a)
        return n

                
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