D - Circle Lattice Points

Score : $400$ points

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.

0.2 0.8 1.1

3

The circle is shown below. The grid points within or on the circle are marked red.

100 100 1

5

$X$, $Y$, and $R$ may not have decimal points. Note that we also count the grid points on the circle.

42782.4720 31949.0192 99999.99

31415920098