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
$1 \le n,D,R \le 10^6$
$-10^6 \le x_i,y_i \le 10^6$