Coverage

A cellular provider has installed $n$ towers. Each tower covers everything within 1 km of it, and no two towers are closer than 1 km to each other. The coverage region of the network is the set of all points that lie within 1 km of at least one tower.

The provider wants as much of this region as possible to be connected. Connected means that a user at any point of a connected subregion can travel to every other point of that subregion without leaving it. The towers already installed may or may not form a single connected region. The provider has the resources to build one more tower anywhere, including within 1 km of an existing tower.

Given that one more tower is built, what is the largest number of towers, counting the new one, that can lie inside a single connected subregion of the coverage?

The first line contains one integer $n$, the number of towers already installed. ($1 \le n \le 5000$)

Each of the next $n$ lines contains two space-separated real numbers $x_i$ and $y_i$, the position of tower $i$ in km. ($0 \le x_i, y_i \le 10^5$)

The answer is guaranteed to stay the same even if the coverage radius of every tower is increased or decreased by one millimeter.

Print on a single line one integer, the largest number of towers that can lie inside a single connected subregion of the network after one more tower is installed.