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.

Input

Input is given from Standard Input in the following format:
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.

Sample Input 1

0.2 0.8 1.1

Sample Output 1

3

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

Sample Input 2

100 100 1

Sample Output 2

5

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

Sample Input 3

42782.4720 31949.0192 99999.99

Sample Output 3

31415920098

见题面 Input 部分

见题面 Output 部分