import java.awt.*;

public class Triangle implements Shape {
    private Point p1;
    private Point p2;
    private Point p3;
    
    public Triangle(Point p1, Point p2, Point p3) {
        if (p1 == null || p2 == null || p3 == null ||
            p1.equals(p2) || p1.equals(p3) || p2.equals(p3)) {
            // colinear points would break this
            throw new IllegalArgumentException();
        }
        
        this.p1 = p1;
        this.p2 = p2;
        this.p3 = p3;
    }
    
    public void draw(Graphics g) {
        this.p1.draw(g);
        this.p2.draw(g);
        this.p3.draw(g);
        g.drawLine(this.p1.getX(), this.p1.getY(),
                   this.p2.getX(), this.p2.getY());
        g.drawLine(this.p2.getX(), this.p2.getY(),
                   this.p3.getX(), this.p3.getY());
        g.drawLine(this.p3.getX(), this.p3.getY(),
                   this.p1.getX(), this.p1.getY());
    }
    
    public double getPerimeter() {
        return p1.distance(p2) + p2.distance(p3) + p3.distance(p1);
    }
    
    public double getArea() {
        // this actually doesn't work for all triangles...
        int maxX = Math.max(this.p1.getX(), Math.max(this.p2.getX(), this.p3.getX()));
        int minX = Math.min(this.p1.getX(), Math.min(this.p2.getX(), this.p3.getX()));
        int maxY = Math.max(this.p1.getY(), Math.max(this.p2.getY(), this.p3.getY()));
        int minY = Math.min(this.p1.getY(), Math.min(this.p2.getY(), this.p3.getY()));
        
        int base = maxX - minX;
        int height = maxY - minY;
        
        return 0.5 * base * height;
    }
    
    public int getMinX() {
        return Math.min(this.p1.getX(), Math.min(this.p2.getX(), this.p3.getX()));
    }
    
    public int getMaxX() {
        return Math.max(this.p1.getX(), Math.max(this.p2.getX(), this.p3.getX()));
    }
    
    public int getMinY() {
        return Math.min(this.p1.getY(), Math.min(this.p2.getY(), this.p3.getY()));
    }
    
    public int getMaxY() {
        return Math.max(this.p1.getY(), Math.max(this.p2.getY(), this.p3.getY()));
    }
    
    public void translate(int dx, int dy) {
        this.p1.translate(dx, dy);
        this.p2.translate(dx, dy);
        this.p3.translate(dx, dy);
    }
    
    public String getType() {
        double d12 = this.p1.distance(this.p2);
        double d13 = this.p1.distance(this.p3);
        double d23 = this.p2.distance(this.p3);
        
        if (d12 == d13 && d13 == d23) {
            return "Equilateral";
        } else if (d12 == d13 || d13 == d23 || d12 == d23) {
            return "Isosceles";
        } else {
            return "Scalene";
        }
    }
}