Hotter Colder

Jack and Jill play a game called Hotter, Colder. Jill has a number between 1 and N, and Jack makes repeated attempts to guess it.

Each of Jack's guesses is a number between 1 and N. In response to each guess, Jill answers hotter, colder or same. For Jack's first guess, Jill answers same. For the remaining guesses Jill answers:

• hotter if this guess is closer to Jill's number than his previous guess
• colder if this guess is farther from Jill's number than his previous guess
• same if this guess is neither closer to nor further from Jill's number than his previous guess.

You are to implement a procedure HC(N) that plays Jack's role. This implementation may repeatedly call Guess(G), with G a number between 1 and N. Guess(G) will return 1 to indicate hotter, -1 to indicate colder or 0 to indicate same. HC(N) must return Jill's number.