9710: ABC191 —— D - Circle Lattice Points
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Description
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.
Find the number of grid points (points whose $x$- and $y$-coordinates are both integers) within or on the circle.
Input
Input is given from Standard Input in the following format:
```
$X$ $Y$ $R$
```
```
$X$ $Y$ $R$
```
Output
Print the answer.
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.
- $|Y| \le 10^5$
- $0 \lt R \le 10^5$
- Each of $X$, $Y$, and $R$ has at most four digits after the decimal point.
Sample 1 Input
0.2 0.8 1.1
Sample 1 Output
3
The circle is shown below. The grid points within or on the circle are marked red.
Sample 2 Input
100 100 1
Sample 2 Output
5
X, Y, and R may not have decimal points. Note that we also count the grid points on the circle.
Sample 3 Input
42782.4720 31949.0192 99999.99
Sample 3 Output
31415920098