<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 get_a_c(self,point1, point2):
        x1,y1 = point1
        x2,y2 = point2

        if x1-x2 == 0:
            return None, x1

        dy = y1-y2 
        dx = x1-x2

        a = (y1-y2) / (x1-x2)
        b = y1 - a * x1

        return a,b
    
    def check_in_line(self,ab, point):
        x,y = point
        a,b = ab
        if a == None:
            if x == b:
                return True
            else:
                return False
        if abs((a*x + b) - y) < 0.00001:
            return True
        else:
            return False

    def maxPoints(self, points: List[List[int]]) -> int:

        tab = [[0] * len(points) for _ in points]
        visited = set()

        max_point = 1

        for i in range(0,len(points)):
            for j in range(i+1, len(points)):
                ab = self.get_a_c(points[i],points[j])
                if ab not in visited:
                    temp_count = 2
                    for k in range(j+1, len(points)):
                        if self.check_in_line(ab, points[k]):
                            temp_count += 1
                    if temp_count > max_point:
                        max_point =  temp_count
                    visited.add(ab)
        
        return max_point
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