## Problem E. Circle Drawing ≡

 Author: A. Klenin Time limit: 3 sec Input file: input.txt Memory limit: 4 Mb Output file: output.txt

### Statement

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 Xsize by Ysize 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 (xxc)2 + (yyc)2R2

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 Xsize Ysize N followed by N sets of numbers xi yi Ri ci, describing the coordinates of center, radius and color of i-th circle.

### Output file format

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

### Constraints

1 ≤ Xsize, Ysize ≤ 1000, 1 ≤ N ≤ 10000, 0 ≤ xi < Xsize, 0 ≤ yi < Ysize, 1 ≤ Ri ≤ 200, 0 ≤ ci ≤ 9.

### Sample tests

No. Input file (input.txt) Output file (output.txt)
1
5 5 1
2 2 1 3
00000
00300
03330
00300
00000
2
4 3 2
2 2 2 5
0 1 1 9

9050
9955
9555

0.032s 0.008s 15