SOLVE
LATER
Hackerland has $$n$$ houses in the $$xy$$ plane . You are given $$x$$ and $$y$$ coordinates of all the $$n$$ houses. You plan to drop a bomb on hackerland. The bomb you possess has a destruction radius of $$D$$ . Formally, if you drop the bomb at point $$(a,b)$$, all houses within a distance $$D$$ from this point will be destroyed. You decide to drop the bomb at a point selected uniformly randomly inside a circle of radius $$R$$, centered at $$(0,0)$$. Find the expected value of the number of houses destroyed by the bomb.
Input
The first line contains $$n$$, $$D$$, and $$R$$ respectively.
It is followed by $$n$$ lines.The $$i^{\text{th}}$$ line contains two integers $$x_i$$, and $$y_i$$, representing $$x$$ and $$y$$ coordinates of the $$i^{\text{th}}$$ house.
Output
Output a single line containing the expected value of number of houses destroyed by the bomb to exactly 4 digits after the decimal point. This is equivalent to printf("%.4lf", value)
in C.
Constraints
$$n,D,R,x_i,y_i$$ are integers
$$1 \le n,D,R \le 10^6$$
$$ -10^6 \le x_i,y_i \le 10^6$$
Because $$D = 2$$, and $$R=1$$, no matter where you drop the bomb inside a circle of radius $$R$$ centered at $$(0,0)$$, the point $$(0,0)$$ will always be destroyed. So one house is destroyed no matter where the bomb is dropped. Hence, expected value of number of houses destroyed is $$1$$.