import java.util.LinkedList;

interface Shape {
    public String draw();
}

class RectangleTest {
    public static void main(String[] args) {
        Canvas c = new Canvas();

        Point p1 = new Point(new Number(1), new Number(2));
        Point p2 = new Point(new Number(60), new Number(20));
        Rectangle r1 = new Rectangle(p1, p2);
        c.addShape(r1);

        Point p3 = new ColoredPoint(new RationalNumber(1, 2), new RationalNumber(60, 2), Color.purple);
        Point p4 = new ColoredPoint(new RationalNumber(150, 3), new RationalNumber(333, 7), Color.purple);
        Rectangle r2 = new Rectangle(p3, p4);
        c.addShape(r2);

        System.out.println(c.draw());
    }
}

class Canvas implements Shape {
    LinkedList<Shape> shapes = new LinkedList<Shape>();

    public void addShape(Shape sh) {
        shapes.add(sh);
    }

    public String draw() {
        String s = "<svg viewBox=\"0 0 100 100\" xmlns=\"http://www.w3.org/2000/svg\">";
        for (Shape sh : shapes) {
            s += sh.draw();
        }
        s += "</svg>";
        return s;
    }
}

class Rectangle implements Shape {
    protected Point topLeft;
    protected Point bottomRight;

    public Rectangle(Point topLeft, Point bottomRight) {
        this.topLeft = topLeft;
        this.bottomRight = bottomRight;
    }

    public String toString() {
        return "[" + topLeft.toString() + "," + bottomRight.toString() + "]";
    }

    public String draw() {
        String s = "";
        for (Number x = topLeft.x; x.lessThan(bottomRight.x); x = x.plus(Number.One)) {
            for (Number y = topLeft.y; y.lessThan(bottomRight.y); y = y.plus(Number.One)) {
                Point p = topLeft.copyWith(x, y);
                s += p.draw();
            }
        }

        return s;
    }
}

class Point implements Shape {
    protected Number x;
    protected Number y;

    public Point(Number x, Number y) {
        this.x = x;
        this.y = y;
    }

    public String toString() {
        return "(" + x.toString() + "," + y.toString() + ")";
    }

    public String draw() {
        return "<circle cx=\"" + x.toString() + "\" cy=\"" + y.toString() + "\" r=\"0.5\" />";
    }

    public Point copyWith(Number x, Number y) {
        return new Point(x, y);
    }
}

class Number {
    protected double value;
    public static Number One = new Number(1);

    public Number(double value) {
        this.value = value;
    }

    public Number plus(Number other) {
        return new Number(value + other.value);
    }

    public boolean lessThan(Number other) {
        return value < other.value;
    }

    public String toString() {
        return String.valueOf(value);
    }
}

/* Observe that I can EXTEND my program by only APPENDING a new
 * class for RationalNumber, and then modifying just the main
 * method.  I do not need to modify any prior code, including
 * either Point or Rectangle.  They just work!  Asymptotically,
 * instead of having to modify O(m*n) things when adding n new
 * things to a language, I only need to modify O(n).
 */
class RationalNumber extends Number {
    protected double numerator;
    protected double denominator;

    public RationalNumber(double numerator, double denominator) {
        super(numerator / denominator);
        this.numerator = numerator;
        this.denominator = denominator;
    }

    public RationalNumber plus(RationalNumber other) {
        // ensure both numbers have the same denominator
        double num1 = numerator * other.denominator;
        double num2 = other.numerator * denominator;
        double den = denominator * other.denominator;

        return new RationalNumber(num1 + num2, den);
    }

    public String toString() {
        // return String.valueOf(numerator) + "/" + String.valueOf(denominator);
        return String.valueOf(numerator / denominator);
    }
}

enum Color {
    red,
    green,
    blue,
    purple
}

class ColoredPoint extends Point {
    Color c;

    public ColoredPoint(Number x, Number y, Color c) {
        super(x, y);
        this.c = c;
    }

    public String draw() {
        return "<circle cx=\"" + x.toString() + "\" cy=\"" + y.toString() + "\" r=\"0.5\" fill=\"" + c + "\"/>";
    }

    public Point copyWith(Number x, Number y) {
        return new ColoredPoint(x, y, c);
    }
}