You are given a 2D integer array trees where trees[i] = [xi, yi] represents the location of the ith tree in the garden.

You are asked to fence the entire garden using the minimum length of rope possible. The garden is well-fenced only if all the trees are enclosed and the rope used forms a perfect circle. A tree is considered enclosed if it is inside or on the border of the circle.

More formally, you must form a circle using the rope with a center (x, y) and radius r where all trees lie inside or on the circle and r is minimum.

Return the center and radius of the circle as a length 3 array [x, y, r]. Answers within 10-5 of the actual answer will be accepted.

 

Example 1:

Input: trees = [[1,1],[2,2],[2,0],[2,4],[3,3],[4,2]]
Output: [2.00000,2.00000,2.00000]
Explanation: The fence will have center = (2, 2) and radius = 2

Example 2:

Input: trees = [[1,2],[2,2],[4,2]]
Output: [2.50000,2.00000,1.50000]
Explanation: The fence will have center = (2.5, 2) and radius = 1.5

 

Constraints:

• 1 <= trees.length <= 3000
• trees[i].length == 2
• 0 <= xi, yi <= 3000