Museum wall construction

Hongjun is extremely rich, and one day he takes an interest in art. He decides to build a museum with his money.

The floor of the museum is flat. For aesthetic reasons he stands $N$ cylindrical pillars on the floor, each perpendicular to it, and every pillar has the same radius $R$. The outer wall is made of glass so thin that its thickness is ignored, and it also stands perpendicular to the floor, so seen from above the wall is a single closed curve.

The wall must enclose every pillar. Hongjun wants the wall that uses the least glass. Compute the length of that wall.

The first line contains two natural numbers $N$ and $R$ separated by a space ($2 \le N \le 1\,000$, $1 \le R \le 100$). $N$ is the number of pillars and $R$ is the radius shared by all of them.

Each of the next $N$ lines contains two integers $x$ and $y$ separated by a space, the coordinates of one pillar center when the floor is viewed as the $xy$ plane ($-10^4 \le x, y \le 10^4$). No two pillars overlap or touch.

Print the minimum length of a wall that encloses every pillar, rounded to six digits after the decimal point, on one line.