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} ≤ R^{2}

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 file format

Input file 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.

Output file format

Output file 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).