Write python code for following:

1) Produce a list that contains the prime numbers below 1000 
   (recall Eratosthenes' sief).

2) Invert a dictionary, assuming the values are unique;
   i.e., create another dictionary whose keys are the values of 
   the first dictionary, and vice versa.
   Try your code on    d = {"1":1, "2":2, "3":3};
   it should produce   d_inv = {1:"1", 2:"2", 3:"3"},  modulo order.
   What if the assumption of unique values is not satisfied?
   Try    d = {"1":1, "2":2, "3":3, "4":3}
   (To get started, initialize   d_inv = dict())

3) Write a python function that applies to trees built from lists with
   numbers in the leafs.
   The function should double the values of the leafs.  
   Example:

       [[[3]],[1,[2]]] ==>  [[[6]],[2,[4]]]

              *
             / \
            /   \
           *     *
          /     / \
         /     /   \
        *     1     *
       /           /
      /           /
     3           2

   The action of the function should be in place, i.e., it should
   modify the incoming list, not create a new one.

   Recommendation: Use recursion, i.e., have the function call itself;
                   it's easy!

   The syntax for defining functions is as follows:

def f(x): 
    <<<do your stuff with x>>>

^^^ blank line for termination ^^^

   [If 3) does not make sense, wait till next class.]