Erect the Fence

Statement

You are given an array of points, trees, where trees[i] = [xᵢ, yᵢ] represents the location of a tree on a 2D plane. Your goal is to enclose all the trees using the shortest possible length of rope, forming a fence around the garden. A garden is considered well-fenced if every tree lies inside or on the boundary of the fence (i.e., the fence forms the convex hullThis is the smallest convex shape, completely encloses a set of points. of all the points).

Return the coordinates of the trees that lie exactly on the fence perimeter. You can return the answer in any order.

Constraints:

• $1 \leq$ trees.length $\leq 300$

• trees[i].length == $2$

• $0 \leq$ xi, yi $\leq 100$

• All the given positions are unique.

Examples