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

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 &le; 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.

입력 형식

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.

출력 형식

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).

예제 입력 1

5 5 1
2 2 1 3

예제 출력 1

00000
00300
03330
00300
00000

예제 입력 2

4 3 2
2 2 2 5
0 1 1 9

예제 출력 2

9050
9955
9555