#1629 Counting Pixels

30  10 s   256 MB  


 Did you know that if you draw a circle that fills the screen on your 1080p high definition display, almost a million pixels are lit? That’s a lot of pixels! But do you know exactly how many pixels are lit? Let’s find out!

Assume that our display is set on a Cartesian grid where every pixel is a perfect unit square. For example, one pixel occupies the area of a square with corners (0,0) and (1,1). A circle can be drawn by specifying its center in grid coordinates and its radius. On our display, a pixel is lit if any part of is covered by the circle being drawn; pixels whose edge or corner are just touched by the circle, however, are not lit.

Your job is to compute the exact number of pixels that are lit when a circle with a given position and radius is drawn.


 The input consists of several test cases, each on a separate line. Each test case consists of three integers, x, y, and r (1 ≤ x,y,r ≤ 106), specifying respectively the center (x,y) and radius of the circle drawn. Input is followed by a single line with x = y = r = 0, which should not be processed.


 For each test case, output on a single line the number of pixels that are lit when the specified circle is drawn. Assume that the entire circle will fit within the area of the display.

Sample Input

Sample Output

1 1 1
5 2 5
0 0 0