<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)==0:
            return 0
        if len(points)==1:
            return 1
        def gcd(a,b):
            while True:
                r = b%a
                if r==0:
                    return a
                else:
                    a,b = r,a

        mp = {}
        n = len(points)
        for i in range(n):
            for j in range(i+1,n):
                x1,y1 = points[i][0],points[i][1]
                x2,y2 = points[j][0],points[j][1]
                a = y1-y2
                b = x2-x1
                c = y1*x2-y2*x1
                # print(a,b,c)
                div = 1
                if a==0 and b==0:
                    c = 1
                elif a==0 and c==0:
                    b = 1
                elif c==0 and b==0:
                    a = 1
                elif b==0:
                    div = gcd(abs(a),abs(c))
                    if a<0:
                        a,b,c = -a,-b,-c
                elif c==0:
                    div = gcd(abs(a),abs(b))
                    if a<0:
                        a,b,c = -a,-b,-c
                elif a==0:
                    div = gcd(abs(b),abs(c))
                    if b<0:
                        a,b,c = -a,-b,-c
                else:
                    div = gcd(abs(a),abs(b))
                    div = gcd(div,abs(c))
                    if a<0:
                        a,b,c = -a,-b,-c
                a,b,c = a//div,b//div,c//div
                pl = (a,b,c)
                if pl in mp:
                    if (x1,y1) not in mp[pl]:
                        mp[pl][(x1,y1)] = 1
                    if (x2,y2) not in mp[pl]:
                        mp[pl][(x2,y2)] = 1
                else:
                    mp[pl] = {}
                    mp[pl][(x1,y1)] = 1
                    mp[pl][(x2,y2)] = 1
        maxlen = 0
        # print(mp)
        for k in mp.keys():
            maxlen = max(maxlen,len(mp[k]))
        return maxlen

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