Circle Drawing

Graphics libraries usually provide functions for drawing primitive shapes such as lines, polygons, and circles. In this problem you will write a program that draws circles.

The canvas is a grid of $X_{size}$ by $Y_{size}$ pixels. Each pixel holds a color from 0 to 9, and initially every pixel has color 0. Each pixel is treated as a small square with side length 1.

A circle with center $(x_c, y_c)$ and radius $R$ is the set of pixels $(x, y)$ that satisfy

$(x - x_c)^2 + (y - y_c)^2 \le R^2$

Drawing a circle means setting the color of every pixel in this set to the circle's color. After drawing the given $N$ circles in order, output the color of every pixel on the canvas.

The input contains the numbers $X_{size}$, $Y_{size}$, $N$, followed by $N$ groups of numbers $x_i$, $y_i$, $R_i$, $c_i$, giving the center coordinates, radius, and color of the $i$-th circle. All numbers are separated by whitespace.

Output $Y_{size}$ lines of $X_{size}$ characters each, where the $i$-th character of the $j$-th line is the digit for the color of pixel $(i, j)$.

• $1 \le X_{size}, Y_{size} \le 1000$
• $1 \le N \le 10000$
• $0 \le x_i < X_{size}$
• $0 \le y_i < Y_{size}$
• $1 \le R_i \le 200$
• $0 \le c_i \le 9$