<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 findVal (pair<int,int> p1 , pair<int,int> p2,  pair<int,int> p3){
        int x1 = p1.first;
        int x2 = p2.first;
        int x3 = p3.first;

        int y1 = p1.second;
        int y2 = p2.second;
        int y3 = p3.second;

        return (y3-y2)*(x2-x1)-(y2-y1)*(x3-x2);
    }
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        sort(trees.begin() , trees.end());

        deque<pair<int,int>> upper , lower;
        vector<vector<int>> result;

        for(auto it:trees){
            int lowSize = lower.size();
            int uppSize = upper.size();
            
            //For lower
            while(lowSize >=2 && findVal(lower[lowSize - 2] , lower[lowSize - 1] , {it[0] , it[1]}) < 0){
                lowSize -- ;
                lower.pop_back();
            }

            //For Upper
            while(uppSize >=2 && findVal(upper[uppSize - 2] , upper[uppSize - 1] , {it[0] , it[1]}) > 0){
                uppSize -- ;
                upper.pop_back();
            }

            upper.push_back({it[0], it[1]});
            lower.push_back({it[0], it[1]}); 
        }


         set<pair<int, int>> st;
        
        for(auto &point : upper) {
            st.insert(point);
        }
        
        for(auto &point : lower) {
            st.insert(point);
        }
        
        for(auto &point : st) {
            result.push_back({point.first, point.second});
        }
        
        return result;
    }
};
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