import java.awt.*;
import java.awt.image.*;
import javax.imageio.ImageIO;
import java.io.File;
import java.io.IOException;
class Main {
    static final int X = 512, Y = 512;
    static BufferedImage I =
       new BufferedImage(X, Y, BufferedImage.TYPE_BYTE_GRAY);
    static double sx(int i){ return 4*i/(float)X-2;}
    static double sy(int i){ return i/(float)Y;}
    static double sa(double x){return Math.abs(x)*x;}
    static double a(double r, double m) {return r-m/sa(r-(m-1))-(1-m)/sa(r-m);}

    static public void main( String[] args ){
        for (int i = 0; i<X; ++i) for(int j=0; j<Y; ++j)
           I.setRGB(i, j, a(sx(i), sy(j))<0? 0:0xffffff);
        for (int i = 0; i<X; ++i) {
           I.setRGB(i, 0, 0); I.setRGB(i, Y-1, 0);}
        for(int j=0; j<Y; ++j) I.setRGB(X-1, j, 0);
        Frame f = new Frame("Lagrange Points");
        f.add("Center", new MainCanvas());
        f.setSize(new Dimension(X,Y+22));
        f.setVisible(true);
   if(args.length > 0) try {
      File file = new File(args[0]);
      ImageIO.write(I, "png", file );}
   catch (IOException e) {System.err.println("image not saved.");}
}}
class MainCanvas extends Canvas{
    public void paint(Graphics g){g.drawImage(Main.I, 0, 0, Color.red, null);}}