// Basic Part about the 3n+1 conjecture
//======================================


//(1) Complete the collatz function below. It should
//    recursively calculate the number of steps needed 
//    until the collatz series reaches the number 1.
//    If needed, you can use an auxiliary function that
//    performs the recursion. The function should expect
//    arguments in the range of 1 to 1 Million.

//def collatz(n: Long) : Long = ...


//(2) Complete the collatz_max function below. It should
//    calculate how many steps are needed for each number 
//    from 1 up to a bound and then calculate the maximum number of
//    steps and the corresponding number that needs that many 
//    steps. Again, you should expect bounds in the range of 1
//    up to 1 Million. The first component of the pair is
//    the maximum number of steps and the second is the 
//    corresponding number.

//def collatz_max(bnd: Long) : (Long, Long) = ...