<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
        lines={}
        maxi=0
        for i in range(len(points)):
            for  j in range(i):
                    if points[j][0]==points[i][0]:
                         y_intercept=1e9
                         x_intercept=points[i][0]
                    elif points[j][1]==points[i][1]:
                         y_intercept=points[i][1]
                         x_intercept=1e9
                    else:
                        slope=(points[j][1]-points[i][1])/(points[j][0]-points[i][0])
                        y_intercept=round(points[i][1] - slope*points[i][0],2)
                        x_intercept=round(-y_intercept/slope,2)
                    if str([x_intercept,y_intercept]) in lines:
                         lines[str([x_intercept,y_intercept])]+=1
                         if lines[str([x_intercept,y_intercept])]>maxi:
                               maxi=lines[str([x_intercept,y_intercept])]
                    else:
                         lines.update({str([x_intercept,y_intercept]):1})
        print(lines, maxi)
        det=math.sqrt(1+(8*maxi))
        return max(2,int((1+det)/2))

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