<p>You are given an array <code>trees</code> where <code>trees[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents the location of a tree in the garden.</p>

<p>Fence the entire garden using the minimum length of rope, as it is expensive. The garden is well-fenced only if <strong>all the trees are enclosed</strong>.</p>

<p>Return <em>the coordinates of trees that are exactly located on the fence perimeter</em>. You may return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/erect2-plane.jpg" style="width: 400px; height: 393px;" />
<pre>
<strong>Input:</strong> trees = [[1,1],[2,2],[2,0],[2,4],[3,3],[4,2]]
<strong>Output:</strong> [[1,1],[2,0],[4,2],[3,3],[2,4]]
<strong>Explanation:</strong> All the trees will be on the perimeter of the fence except the tree at [2, 2], which will be inside the fence.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/24/erect1-plane.jpg" style="width: 400px; height: 393px;" />
<pre>
<strong>Input:</strong> trees = [[1,2],[2,2],[4,2]]
<strong>Output:</strong> [[4,2],[2,2],[1,2]]
<strong>Explanation:</strong> The fence forms a line that passes through all the trees.
</pre>

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

<ul>
	<li><code>1 &lt;= trees.length &lt;= 3000</code></li>
	<li><code>trees[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>
	<li>All the given positions are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    int getAngleRotation(vector<int>v1,vector<int>v2, vector<int>v3)
    {
        return ((v2[0]-v1[0])*(v3[1]-v1[1]))-((v2[1]-v1[1])*(v3[0]-v1[0]));
    }
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        if(trees.size()<=3)
        {
            return trees;
        }
        sort(trees.begin(),trees.end());
        vector<vector<int>>v1,v2;
        v1.push_back(trees[trees.size()-1]);
        v1.push_back(trees[trees.size()-2]);
        for(int i=trees.size()-3;i>=0;i--)
        {
            int vs1=v1.size();
            while(vs1>=2  &&  getAngleRotation(v1[vs1-2],v1[vs1-1],trees[i])<0)
            {
                v1.pop_back();
                vs1--;
            }
            v1.push_back(trees[i]);
        }
        v2.push_back(trees[0]);
        v2.push_back(trees[1]);
        for(int i=2;i<trees.size();i++)
        {
            int vs2=v2.size();
            while(vs2>=2  &&  getAngleRotation(v2[vs2-2],v2[vs2-1],trees[i])<0)
            {
                v2.pop_back();
                vs2--;
            }
            v2.push_back(trees[i]);
        }
        for(int i=0;i<v2.size();i++)
        {
            v1.push_back(v2[i]);
        }
        sort(v1.begin(),v1.end());
        v1.erase(unique(v1.begin(),v1.end()),v1.end());
        return v1;
    }
};
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