<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 {
public:
    int maxPoints(vector<vector<int>>& points) 
    {
        if(points.size()==1) return 1;
        int fin=INT_MIN;
        for(int i=0; i<points.size(); i++)
        {
            unordered_map<float,set<vector<int>>> umap;

            for(int j=0; j<points.size(); j++)
            {
                if(i!=j)
                {
                    float m;
                    if(points[j][0]-points[i][0] == 0) m=INT_MAX;
                    else m = ((float)points[j][1]-(float)points[i][1])/((float)points[j][0]-(float)points[i][0]);
                    // umap[m].insert(points[i]);

                    // cout << m << endl;
                    // cout << points[j][1] <<  " " << points[j][0] << endl;
                    // cout << points[i][1] <<  " " << points[i][0] << endl;

                    // cout << "===" << endl;
                    
                    umap[m].insert(points[j]);
                }
            }
            int ans=INT_MIN;
            for(auto i : umap)
            {
                // cout << i.second;
                int n = i.second.size();
                if(ans < n) ans = n;
            }

            fin = max(fin,ans);
        }

        return fin+1;
        
    }
};
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