Problem I
Guess the Number

I am thinking of a number between $1$ and $1000$, can you guess what number it is? Given a guess, I will tell you whether the guess is too low, too high, or correct. But I will only give you $10$ guesses, so use them wisely!

Interaction

Your program should output guesses for the correct number, in the form of an integer between $1$ and $1000$ on a line on its own. After making each guess, you need to make sure to flush standard out.

After each guess, there will be a response to be read from standard in. This response is a line with one of the following three words:

• “lower” if the number I am thinking of is lower than your guess

• “higher” if the number I am thinking of is higher than your guess

• “correct” if your guess is correct

After having guessed the right answer your program should exit. If you guess incorrectly $10$ times, you won’t get any more chances and your program will be terminated.