// Part 1 about the 3n+1 conceture

//=================================

//(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 auxilary function that

//    performs the recursion. The function should expect

//    arguments in the range of 1 to 1 Million.

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

//(2)  Complete the collatz bound function below. It should

//     calculuate how many steps are needed for each number 

//     from 1 upto a bound and returns the maximum number of

//     steps and the corresponding number that needs that many 

//     steps. You should expect bounds in the range of 1

//     upto 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: Int): (Int, Int) = ...