Problem 10 : Guess the number

Problem

Ram and Shyam are playing the game of "guessing" a number. In this game, Ram picks up a number randomly k between 1 and n, and tells Shyam the number n. Using the information, Shyam tries to guess the correct number in as less steps as possible. In each step, Shyam comes up with a guess for the number and tells it to Ram. Ram can then respond in three ways: the number is less than k, the number is greater than k, or the number is equal to k. If Shyam guesses the correct answer, the game ends there. Shyam wins the game, if he guesses the correct number in the smallest possible number of steps.

Input and output

The judging for this problem will be done "interactively". Your program will first get as an input the number n. Your program will then have to output your initial guess. Depending upon your guess, your program will get the following possible inputs: greater, if your guess is greater than k, less, if your guess is greater than k, and equal if your guess is correct. On getting e as the input, your program should read for the next value of n. The input will be terminated by the case n=0.

Sample Input and Output

(judge's input are indicated by bold)

10
1
less
2
less
3
less
4
less
5
less
6
equal
0

P.S. : The above input/output corresponds to the case n=10 and k=6. For the above input, the judge will respond with "Wrong answer", since the correct answer has not been guessed within the least possible number of steps.