<p>Alice is throwing <code>n</code> darts on a very large wall. You are given an array <code>darts</code> where <code>darts[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the position of the <code>i<sup>th</sup></code> dart that Alice threw on the wall.</p>

<p>Bob knows the positions of the <code>n</code> darts on the wall. He wants to place a dartboard of radius <code>r</code> on the wall so that the maximum number of darts that Alice throws lie&nbsp;on the dartboard.</p>

<p>Given the integer <code>r</code>, return <em>the maximum number of darts that can lie on the dartboard</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_1_1806.png" style="width: 248px; height: 211px;" />
<pre>
<strong>Input:</strong> darts = [[-2,0],[2,0],[0,2],[0,-2]], r = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> Circle dartboard with center in (0,0) and radius = 2 contain all points.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_2_1806.png" style="width: 306px; height: 244px;" />
<pre>
<strong>Input:</strong> darts = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]], r = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> Circle dartboard with center in (0,4) and radius = 5 contain all points except the point (7,8).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= darts.length &lt;= 100</code></li>
	<li><code>darts[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>darts</code>&nbsp;are unique</li>
	<li><code>1 &lt;= r &lt;= 5000</code></li>
</ul>

class Solution {
private:
	vector<vector<double>> dist;
	int n;

	int countPoint(vector<vector<int>>& p, int i, int r)
	{
		vector<pair<double, bool>> events;
		for (int j = 0; j < n; j++)
		{
			if (j != i && dist[i][j] <= 2 * r)
			{
				double A = atan2(p[j][1] - p[i][1], p[j][0] - p[i][0]);
				double B = acos(dist[i][j] / (2.0 * r));
				double alpha = A - B;
				double beta = A + B;
				events.push_back({alpha, false});
				events.push_back({beta, true});
			}
		}
		sort(events.begin(), events.end());
		int cnt = 1;
		int maxi = 1;
		for (int j = 0; j < events.size(); j++)
		{
			if (events[j].second)cnt--;
			else cnt++;
			maxi = max(maxi, cnt);
		}
		return maxi;
	}

public:
	int numPoints(vector<vector<int>>& darts, int r) {
		n = darts.size();
		dist.resize(n, vector<double>(n));
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				dist[i][j] = hypot(darts[i][0] - darts[j][0], darts[i][1] - darts[j][1]);
		int ans = 0;
		for (int i = 0; i < n; i++)
			ans = max(ans, countPoint(darts, i, r));
		return ans;
	}
};
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