Toxic Barrier

Seongjun, king of the Chemical Empire, decided to build his nation's pride — a chemical barrier — to finally be free from the repeated invasions of neighboring countries. The barrier releases a toxin harmful to any creature that comes near, so that no other nation dares to approach.

However, the barrier is difficult to construct, so it must be made as short as possible. It can also harm the king's own people, so it must always stay at a distance of at least $L$ from every building in the country.

Given the coordinates of the country's buildings, find the minimum length of a barrier that encloses all of the buildings at once while keeping a distance of at least $L$ from every building.

The first line contains the number of buildings $N$ and the distance $L$. ($3 \le N \le 1000$, $1 \le L \le 1000$; $N$ and $L$ are integers.)

Each of the next $N$ lines contains the integer coordinates $X_i$ and $Y_i$ of a building. ($-10000 \le X_i, Y_i \le 10000$) All building coordinates are distinct, and each building is small enough to be treated as a single point. The barrier must not cross itself and must not be broken.

Print, on the first line, the minimum length of the barrier that encloses all buildings, rounded to the nearest integer.