<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();
        map <pair<float, float>, set<pair<int,int>>> m;
        map <int, set<pair<int,int>>> vert;
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                if(j == i) continue;
                int& x1=points[i][0], &y1=points[i][1], 
                &x2=points[j][0], &y2=points[j][1];
                if(y1-y2 == 0) { // a==0
                    m[{0,y1}].insert({x1, y1});
                    m[{0,y2}].insert({x2, y2});
                } else if(x1-x2 == 0) { // x1==x2
                    vert[x1].insert({x1, y1});
                    vert[x2].insert({x2, y2});
                }
                else {
                    float a = float(y1-y2)/(x1-x2);
                    float b = y2 - a*x2;
                    m[{a,b}].insert({x1, y1});
                    m[{a,b}].insert({x2, y2});
                }
            }
        }
        int mx = 1;
        for(auto p: vert) mx = max(mx, (int)p.second.size());
        for(auto p: m) mx = max(mx, (int)(p.second.size()));
        return mx;
    }
};
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