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 (xc, yc) and radius R is a set of pixels (x, y) satisfying the inequality (x − xc)² + (y − yc)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 xi yi Ri ci, describing the coordinates of center, radius and color of i-th circle.
1 <= X_size, Y_size <= 1000, 1 <= N <= 10000, 0 <= xi < X_size, 0 <= yi < Y_size, 1 <= Ri <= 212, 0 <= ci <= 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).

5 5 1
2 2 1 3

This problem has huge input and output data,use scanf() and printf() instead of cin and cout to read data to avoid time limit exceed.

Northeastern Europe 2004, Far-Eastern Subregion