10098_CircleDrawing

Graphics libraries usually implement drawing of graphics primitives, like lines, polygons and circles. Your task is to write a program that draws circles.

Graphic canvas is represented as an array of X_size by Y_size pixels. Each pixel have a color ranged from 0 to 9. Initially all pixels have color 0. Pixels are thought of as small sqares with the side of length 1. A circle with center (x_c, y_c) and radius R is a set of pixels (x, y) satisfying the inequality (x - x_c)² + (y - y_c)² ≤ R²

To draw a circle, your program should set the color of all pixels in a set defined above to the color of the circle. After drawing N given circles, the program should output the color of all pixels of the canvas.

Input contains numbers X_size  Y_size  N followed by N sets of numbers x_i  y_i  R_i  c_i, describing the coordinates of center, radius and color of i-th circle.

1 ≤ X_size, Y_size ≤ 1000,   1 ≤ N ≤ 10000,   0 ≤ x_i < X_size,   0 ≤ y_i < Y_size,   1 ≤ R_i ≤ 200,   0 ≤ c_i ≤ 9.

Output should contain Y_size lines of X_size characters each, where i-th character of j-th line is a digit corresponding to color of the pixel (i, j).

Sample #1
5 5 1
2 2 1 3

Sample #2
4 3 2
2 2 2 5
0 1 1 9

Sample #1
00000
00300
03330
00300
00000

Sample #2
9050
9955
9555