Contest Duration: - (local time) (100 minutes) Back to Home
D - Circle Lattice Points /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

2 次元平面上に中心 (X, Y) 、半径 R の円があります。
この円の内部または周上にある格子点 (x, y 座標がともに整数である点) の個数を求めてください。

### 制約

• |X| \le 10^5
• |Y| \le 10^5
• 0 \lt R \le 10^5
• X, Y, R は高々小数第 4 位まで与えられる

### 入力

X Y R


### 入力例 1

0.2 0.8 1.1


### 出力例 1

3


### 入力例 2

100 100 1


### 出力例 2

5


X, Y, R には小数点が含まれないかもしれません。

### 入力例 3

42782.4720 31949.0192 99999.99


### 出力例 3

31415920098


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


### 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