Problem Statement

We have a circle of radius $R$ centered at $(X, Y)$. Find the number of grid points (points whose $x$- and $y$-coordinates are both integers) within or on the circle.

Constraints

• $|X| \le 10^5$
• $|Y| \le 10^5$
• $0 \lt R \le 10^5$
• Each of $X$, $Y$, and $R$ has at most four digits after the decimal point.

Input

Input is given from Standard Input in the following format:

X Y R

Output

Print the answer.