def int_to_roman(input):
   """
   Convert an integer to Roman numerals.

   Examples:
   >>> int_to_roman(0)
   Traceback (most recent call last):
   ValueError: Argument must be between 1 and 3999

   >>> int_to_roman(-1)
   Traceback (most recent call last):
   ValueError: Argument must be between 1 and 3999

   >>> int_to_roman(1.5)
   Traceback (most recent call last):
   TypeError: expected integer, got <type 'float'>

   >>> for i in range(1, 21): print int_to_roman(i)
   ...
   I
   II
   III
   IV
   V
   VI
   VII
   VIII
   IX
   X
   XI
   XII
   XIII
   XIV
   XV
   XVI
   XVII
   XVIII
   XIX
   XX
   >>> print int_to_roman(2000)
   MM
   >>> print int_to_roman(1999)
   MCMXCIX
   """
   if type(input) != type(1):
      raise TypeError, "expected integer, got %s" % type(input)
   if not 0 < input < 4000:
      raise ValueError, "Argument must be between 1 and 3999"   
   ints = (1000, 900,  500, 400, 100,  90, 50,  40, 10,  9,   5,  4,   1)
   nums = ('M',  'CM', 'D', 'CD','C', 'XC','L','XL','X','IX','V','IV','I')
   result = ""
   for i in range(len(ints)):
      count = int(input / ints[i])
      result += nums[i] * count
      input -= ints[i] * count
   return result



def roman_to_int(input):
   """
   Convert a roman numeral to an integer.
   
   >>> r = range(1, 4000)
   >>> nums = [int_to_roman(i) for i in r]
   >>> ints = [roman_to_int(n) for n in nums]
   >>> print r == ints
   1

   >>> roman_to_int('VVVIV')
   Traceback (most recent call last):
    ...
   ValueError: input is not a valid roman numeral: VVVIV
   >>> roman_to_int(1)
   Traceback (most recent call last):
    ...
   TypeError: expected string, got <type 'int'>
   >>> roman_to_int('a')
   Traceback (most recent call last):
    ...
   ValueError: input is not a valid roman numeral: A
   >>> roman_to_int('IL')
   Traceback (most recent call last):
    ...
   ValueError: input is not a valid roman numeral: IL
   """
   if type(input) != type(""):
      raise TypeError, "expected string, got %s" % type(input)
   input = input.upper()
   nums = ['M', 'D', 'C', 'L', 'X', 'V', 'I']
   ints = [1000, 500, 100, 50,  10,  5,   1]
   places = []
   for c in input:
      if not c in nums:
         raise ValueError, "input is not a valid roman numeral: %s" % input
   for i in range(len(input)):
      c = input[i]
      value = ints[nums.index(c)]
      # If the next place holds a larger number, this value is negative.
      try:
         nextvalue = ints[nums.index(input[i +1])]
         if nextvalue > value:
            value *= -1
      except IndexError:
         # there is no next place.
         pass
      places.append(value)
   sum = 0
   for n in places: sum += n
   # Easiest test for validity...
   if int_to_roman(sum) == input:
      return sum
   else:
      raise ValueError, 'input is not a valid roman numeral: %s' % input