#!/usr/bin/env python3
# An example of implementing integer factorisation in Python: find all prime numbers that divide a given number

# prime number test
def isPrime(n):
    """Test whether the given number @n@ is a prime number."""
    # +++your code here+++

# build a list of all prime numbers, to be used later 
# use a list comprehension!
primes =  # +++your code here+++

# main fct for first exercise: integer factorisation
def factor(m):
    """For a given integer number @n@, find all prime numbers that divide it."""
    # +++your code here+++
    
# additional function for second exercise: turn a list with repeated entries into a list of pairs of (value, # of occurences)
def cleanup2(xs):
    # +++your code here+++

# Simple provided test() function used in main() to print
# what each function returns vs. what it's supposed to return.
def test(got, expected):
  if got == expected:
    prefix = ' OK '
  else:
    prefix = ' ** '
  print('%s got: %s expected: %s' % (prefix, repr(got), repr(expected)))

if __name__ == '__main__':
  print("Integer factorisation:")
  test(factor(120),[2, 2, 2,3, 5])
  test(cleanup2(factor(120)), [(2, 3), (3, 1), (5, 1)])