Your assignment is to implement a simple number guessing game using HTML forms and a Java servlet. The HTML page should introduce the game and provide a form for the user to guess a number on. The servlet should use an HTTP session object to store all session specific data. If the session object is empty, the servlet will need to generate initial values for all session specific data items. Session specific data will include the number to be guessed and the number of guesses so far.

The servlet should return an HTML form indicating whether the guess was high, low, or correct. The form should also indicate how many guesses so far, and allow the user to enter another guess. If a user's guess is closer to the target than the user's previous guess, set the background of the form to red. If a user's guess is farther from the target than the user's previous guess, set the background of the form to blue. This will require additional session specific data to be stored.

When the user has guessed correctly, the servlet should reset all the session specific data, the form should have a background color other than red or blue, and it should invite the user to start playing a new game.