<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:
    def outerTrees(self, trees: List[List[int]]) -> List[List[int]]:
        def cross(o, a, b):
            return (a[0] - o[0]) * (b[1] - o[1]) - \
                (a[1] - o[1]) * (b[0] - o[0])
    
        # Remove duplicates and sort the points
        points = sorted(set(map(tuple, trees)))
        
        if len(points) <= 1:
            return points
        
        # Build the lower part of the hull
        lower = []
        for p in points:
            while len(lower) >= 2 and cross(lower[-2], lower[-1], p) < 0:
                lower.pop()
            lower.append(p)
        
        # Build the upper part of the hull
        upper = []
        for p in reversed(points):
            while len(upper) >= 2 and cross(upper[-2], upper[-1], p) < 0:
                upper.pop()
            upper.append(p)
        
        # Concatenate lower and upper to get full hull
        # Remove duplicates by converting to a set
        result = set(lower[:-1] + upper[:-1])
        
        return [list(p) for p in result]
17500