<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:
        if len(points) == 1: return 1
        cnt = Counter()

        def line(p1, p2):
            if p1[0] == p2[0]:
                return inf, p1[0]
            slp =  (p2[1] - p1[1])/(p2[0] - p1[0])
            intercept = (p2[0]*p1[1] - p1[0]*p2[1])/(p2[0] - p1[0])
            return slp, intercept

        # given sum of s, return n such that s == n*(n+1)/2
        def helper(s):
            return int(abs((-1 + math.sqrt(1 + 8*s))//2))

        for i in range(len(points)-1):
            for j in range(i+1, len(points)):
                slp, b = line(points[i], points[j])
                cnt[(slp, b)] += 1

        print(cnt.most_common())
        s = cnt.most_common()[0][1]   
        return helper(s) + 1 
31483