<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(object):
    def maxPoints(self, points):
        """
        :type points: List[List[int]]
        :rtype: int
        """
        INF = 10**5

        n = len(points)
        pairs = [[0]*n for i in range(n)]
        max_occ = 0
        for i, (x,y) in enumerate(points):
            rep = {}
            for j, (x2, y2) in enumerate(points[i+1:]):
                if x == x2:
                    a = INF
                    b = x
                else:
                    a = (y2-y)/(x2-x)
                    b = y - a*x #y = ax + b, b = y - ax
                pairs[i][j] = (a, b)
                rep[(a, b)] = rep.get((a,b), 0) + 1
                max_occ = max(max_occ, rep[(a,b)])

        # for a in pairs:
        #     for b in a:
        #         print(b, end=", ")
        #     print()
        return max_occ+1

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