<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:
    bool fun(vector<int> a,vector<int> b,vector<int> c)
    {
        if((b[0]-a[0])*(c[1]-b[1])-(b[1]-a[1])*(c[0]-b[0])>=0) return true;
        return false;
    }
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        if(trees.size()<=3) return trees;
        sort(trees.begin(),trees.end());
        vector<vector<int>> a;
        //print(trees);
        for(auto i:trees)
        {
            while(a.size()>1 && !fun(a[a.size()-2],a[a.size()-1],i)) a.pop_back();
            a.push_back(i);
            //print(a);
        }
        if(a.size()==trees.size()) return a;
        for(int j=trees.size()-2;j>=0;j--)
        {
            auto i=trees[j];
            while(a.size()>1 && !fun(a[a.size()-2],a[a.size()-1],i)) a.pop_back();
            a.push_back(i);
        }
        a.pop_back();
        return a;
    }
};
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