( In JAVA)Define a class named Rectangle. A Rectangle object stores an (x, y) coordinate of its top/left corner, a width, and a height.

Each Rectangle object should have the following public methods:

Rectangle(x, y, width, height) Constructs a new rectangle whose top-left corner is specified by the given coordinates and with the given width and height.

getX() Returns this rectangle's leftmost x-coordinate.

getY() Returns this rectangle's top y-coordinate.

getWidth() Returns this rectangle's width.

getHeight() Returns this rectangle's height.

toString() Returns a String representation of this rectangle, such as "Rectangle[x=1,y=2,width=3,height=4]".

contains(x, y) Returns whether the given Point's coordinates lie inside the bounds of this rectangle.

intersect(rect) Turns this rectangle into the intersection of itself and the given other rectangle rect; that is, the largest rectangular region completely contained within both this rectangle and the given other rectangle. (In the picture at right, the intersection of the two rectagles is the shaded black region.) You may assume that the two rectangles do overlap and therefore have a nonempty intersection.

equals(o) Returns whether the given other object o is a rectangle with the same x/y coordinates, width, and height as this rectangle. You may assume that o refers to a Rectangle object.