<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 num(self, points, p1, p2):
        v = [p2[0]-p1[0], p2[1]-p1[1]]
        n = [v[1], -v[0]]
        C = p2[0]*p1[1]-p1[0]*p2[1]
        count = 0
        for p in points:
            sum_v = n[0]*p[0] + n[1]*p[1] + C

            if sum_v == 0:
                count += 1
        return count


    def maxPoints(self, points: List[List[int]]) -> int:
    
        n = len(points)
        if n == 1:
            return 1
        max_num = 0
        d = {}
        for i in range(n):
            for j in range(i+1,n):
                if (i,j) in d or (j,i) in d:
                    continue
                max_num = max(max_num, self.num(points, points[i], points[j]))
                d[(i,j)] = max_num
        return max_num
        
23146