<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 {
    int cross(vector<int>&a,vector<int>&b,vector<int>&c){
        int x1 = b[0]-a[0];
        int y1 = b[1]-a[1];
        int x2 = c[0]-b[0];
        int y2 = c[1]-b[1];
        return (x1*y2-x2*y1);
    }
public:
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        vector<vector<int>>ans;
        int n = trees.size();
        sort(trees.begin(),trees.end(),[&](vector<int>a,vector<int>b){
            if(a[0]==b[0]){
                return a[1]>b[1];
            }
            else{
                return a[0] < b[0];
            }
        });
        for(int i=0; i<n; i++){
            while(ans.size()>=2 && cross(ans[ans.size()-2],ans[ans.size()-1],trees[i])<0){
                ans.pop_back();
            }
            ans.push_back(trees[i]);
        }
        if(ans.size()==n){
            return ans;
        }
        for(int i=n-2; i>=0; i--){
            while(ans.size()>=2 && cross(ans[ans.size()-2],ans[ans.size()-1],trees[i])<0){
                ans.pop_back();
            }
            ans.push_back(trees[i]);
        }
        ans.pop_back();
        return ans;
    }
};
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