<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) {
        int n=points.size();
        if(n<3) return n;
        unordered_map<string,set<vector<int>>>count;
        for(int i=0; i<n; i++){
            for(int j=i+1; j<n; j++){
                int dx=points[i][0]-points[j][0],  dy=points[i][1]-points[j][1];
                int g = __gcd(dx, dy);
                dx /= g;
                dy /= g;
                if (dy < 0) {
                    dx = -dx;
                    dy = -dy;
                }
                string key=to_string(dx)+"/"+to_string(dy);
                if(dx==0) key+=to_string(points[i][0]);
                if(dy==0) key+=to_string(points[i][1]);
                else key+=to_string(points[i][0])+to_string(points[i][1]);
                count[key].insert({points[i][0],points[i][1]});
                count[key].insert({points[j][0],points[j][1]});
            }
        }
        int ans=2;
        for(auto & pair : count){
            int s=pair.second.size();
            cout<<pair.first<<" "<<s<<endl;
            ans=max(ans,s);
        }
        return ans;
    }
};
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