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