Map Labels

One difficult task in modern cartography is placing geographic labels on a map. If every city, town, and village name is written directly on the map, labels may overlap and the map can become unreadable.

You are given the coordinates of points on a Cartesian plane. Each point must receive one rectangular label area. Every rectangle has sides parallel to the coordinate axes, and its width is exactly three times its height.

For each point, exactly one rectangle must be placed with that point as the rectangle's top-left corner. In other words, the label area extends to the right and downward from the point. All label areas must have the same dimensions.

Find the maximum possible height of the rectangles so that, after all points are labeled, no two label areas overlap. Two labels may touch along an edge or at a vertex.

All given coordinates are integers from 0 to 1,000,000, inclusive. Parts of a rectangle may extend outside that coordinate range.

The first line contains an integer N, the number of points on the map. 2 ≤ N ≤ 100,000.

Each of the next N lines contains two integers X and Y, the coordinates of one point. 0 ≤ X, Y ≤ 1,000,000, and no two points have the same coordinates.

Print the height of the rectangle as a real number on the first line. Printing the answer rounded to two decimal places is sufficient.

Your output must have absolute error at most 0.01 from the correct answer.